0.11/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.15 % Command : run_Leo-III %s %d 0.15/0.36 % Computer : n007.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 960 0.15/0.36 % WCLimit : 120 0.15/0.36 % DateTime : Tue Aug 9 05:11:12 EDT 2022 0.15/0.36 % CPUTime : 0.95/1.04 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 4.71/2.71 % [INFO] Parsing done (1668ms). 4.71/2.74 % [INFO] Running in sequential loop mode. 5.08/3.10 % [INFO] eprover registered as external prover. 5.22/3.11 % [INFO] cvc4 registered as external prover. 5.22/3.12 % [INFO] Scanning for conjecture ... 7.27/4.34 % [INFO] Found a conjecture and 10247 axioms. Running axiom selection ... 11.99/7.75 % [INFO] Axiom selection finished. Selected 7730 axioms (removed 2517 axioms). 16.72/11.00 % [INFO] Problem is higher-order (TPTP THF). 17.23/11.28 % [INFO] Type checking passed. 17.23/11.30 % [CONFIG] Using configuration: timeout(120) with strategy. Searching for refutation ... 176.23/88.50 % External prover 'cvc4' found a proof! 176.23/88.50 % [INFO] Killing All external provers ... 176.23/88.50 % Time passed: 87997ms (effective reasoning time: 85737ms) 176.23/88.50 % Solved by strategy 176.34/88.53 % Axioms used in derivation (7730): fact_4797_dvd__power__le, fact_895_nat__less__add__iff1, fact_9481_or__nat__rec, fact_1127_ring__class_Oring__distribs_I2_J, fact_334_add__less__cancel__right, fact_7105_numeral__power__eq__of__int__cancel__iff, fact_3863_ord__le__eq__trans, fact_5812_dvd__neg__div, fact_4105_order__less__subst1, fact_7262_of__nat__diff, help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T, fact_7020_numeral__le__real__of__nat__iff, fact_859_power__gt1__lemma, fact_6485_abs__not__less__zero, fact_6747_sum__gp__multiplied, fact_785_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, fact_8199_powser__sums__if, fact_2817_mult__le__cancel__right2, fact_7437_ex__le__of__int, fact_1491_mult__eq__0__iff, fact_9456_or__minus__numerals_I4_J, fact_404_add__left__imp__eq, fact_709_diff__strict__right__mono, fact_4722_pinf_I9_J, fact_2246_split__mult__pos__le, fact_902_one__power2, fact_7090_of__int__less__1__iff, fact_1239_less__add__iff1, fact_4102_order__less__subst1, fact_6487_abs__triangle__ineq, fact_2804_VEBT__internal_Omembermima_Osimps_I2_J, fact_1712_diff__numeral__special_I9_J, fact_5520_less__minus__iff, fact_1081_lift__Suc__antimono__le, fact_6403_abs__of__nonpos, fact_8246_cos__30, fact_9497_push__bit__nonnegative__int__iff, fact_9095_gr__one__powr, fact_142_numeral__times__numeral, fact_8376_arccos__minus, fact_5704_neg__numeral__less__numeral, fact_658_one__plus__numeral, fact_7252_int__ops_I7_J, fact_3350_product__nth, fact_7970_fact__Suc, fact_5351_mult__neg__numeral__simps_I1_J, fact_4962_mod2__eq__if, fact_8993_divide__complex__def, fact_25__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062, fact_2665_mult__le__one, fact_2015_mod__Suc__eq, fact_5444_diff__numeral__special_I3_J, fact_7660_summable__divide, fact_205_power__mult, fact_9929_mult__rat, fact_9987_atLeastLessThan__add__Un, fact_9369_and__minus__numerals_I5_J, fact_2158_cong__exp__iff__simps_I6_J, fact_1223_eq__add__iff1, fact_2046_mult__not__zero, fact_3983_order_Oasym, fact_3066_div__mod__decomp__int, fact_7150_neg__numeral__power__eq__of__int__cancel__iff, fact_4477_dvd__add__times__triv__right__iff, fact_3728_max_Ostrict__boundedE, fact_2112_vebt__buildup_Ocases, fact_4094_order__less__irrefl, fact_953_minNullmin, fact_1038_not__less__less__Suc__eq, fact_3034_flip__bit__Suc, fact_16_min__Null__member, fact_7041_of__int__0__less__iff, fact_8667_prod_Odelta, fact_6576_abs__of__neg, fact_6594_abs__diff__less__iff, fact_459_add__mono, fact_5210_uminus__add__conv__diff, fact_624_right__diff__distrib__numeral, fact_3310_pinf_I8_J, fact_1499_mult__cancel__left, fact_8024_fact__le__power, fact_10133_dist__real__def, fact_5691_neg__numeral__le__numeral, fact_5413_diff__numeral__special_I10_J, fact_4491_unit__div__1__unit, fact_1441_VEBT__internal_Onaive__member_Osimps_I3_J, fact_5514_le__imp__neg__le, fact_4170_antisym__conv1, fact_1264_both__member__options__def, fact_7997_fact__ge__1, fact_5526_verit__negate__coefficient_I2_J, fact_6528_abs__real__def, fact_1553_diff__0__right, fact_7887_cos__total, fact_1213_linordered__semidom__class_Oadd__diff__inverse, fact_9055_log__of__power__le, fact_4976_zero__le__even__power, fact_1589_bot__nat__0_Onot__eq__extremum, fact_3967_lt__ex, fact_156_distrib__left__numeral, fact_2948_exp__add__not__zero__imp__right, fact_4324_order__le__less__subst1, fact_6755_gauss__sum__nat, fact_5388_divide__eq__eq__numeral1_I2_J, fact_7305_zero__less__imp__eq__int, fact_2417_divide__nonneg__nonpos, fact_9306_nat__le__eq__zle, fact_5385_eq__divide__eq__numeral1_I2_J, fact_9307_nat__eq__iff, fact_5577_minus__diff__minus, fact_7646_summable__arctan__series, fact_7760_pi__half__gt__zero, fact_9193_real__root__pos__pos, fact_7453_norm__numeral, fact_7213_of__nat__less__0__iff, fact_4365_linorder__le__less__linear, fact_4403_max__absorb2, fact_1115_linorder__neqE__linordered__idom, fact_5065_neg__numeral__eq__iff, fact_2953_power__diff__power__eq, fact_9061_ceiling__log__nat__eq__powr__iff, fact_1960_power__0__left, fact_1151_right__diff__distrib, fact_5066_neg__numeral__eq__iff, fact_2006_mod__diff__eq, fact_227_nat__neq__iff, fact_8135_exp__le__one__iff, fact_1786_zero__less__Suc, fact_2204_zero__le__mult__iff, fact_6889_of__nat__0__eq__iff, fact_5456_dbl__simps_I4_J, fact_4134_order__less__imp__not__eq, fact_9249_nat__0__iff, fact_2345_zero__less__mult__pos2, fact_9479_Suc__0__or__eq, fact_7284_of__int__leD, fact_4498_div__add, fact_3182_int__distrib_I1_J, fact_8981_i__even__power, fact_2670_mult__right__le__one__le, fact_4601_dvd__mult2, fact_7483_norm__mult__ineq, fact_1546_diff__zero, fact_3843_nle__le, fact_4761_dvd__div__mult2__eq, fact_2577_mult__left__less__imp__less, fact_7581_sum_OlessThan__Suc__shift, fact_3687_max_Ocobounded1, fact_5779_square__eq__1__iff, fact_7089_of__int__less__1__iff, fact_1658_diff__gt__0__iff__gt, fact_2431_divide__pos__neg, fact_5020_neg__equal__iff__equal, fact_3455_finite__Diff, fact_515_add__divide__distrib, fact_2397_pos__add__strict, fact_7471_norm__sum, fact_811_Nat_Ole__imp__diff__is__add, fact_343_add__right__cancel, fact_6119_sum_Osame__carrier, fact_4786_le__imp__power__dvd, fact_2830_field__le__mult__one__interval, fact_8244_real__sqrt__ge__abs1, fact_504_add__mono__thms__linordered__field_I5_J, fact_5195_mult__minus1__right, fact_4603_dvd__mult2, fact_3919_order__subst2, fact_5536_neg__numeral__neq__numeral, fact_2612_mult__le__less__imp__less, fact_6418_semiring__norm_I74_J, fact_9701_inverse__complex_Osimps_I2_J, fact_6961_of__nat__power, fact_2441_divide__strict__right__mono, fact_2036_zero__neq__numeral, fact_1845_Suc__pred, fact_1776_mod__mult__self3, fact_2571_mult__le__cancel__left, fact_1731_divide__self__if, fact_1112_power__gt1, fact_5063_neg__less__iff__less, fact_5391_neg__numeral__less__neg__one__iff, fact_4485_dvd__mult__div__cancel, fact_4561_even__power, fact_6743_mask__eq__sum__exp, fact_9293_nat__le__iff, fact_6668_power3__eq__cube, fact_8045_fact__num__eq__if, fact_547_all__nth__imp__all__set, fact_5945_neg__numeral__less__one, fact_7882_sin__gt__zero__02, fact_8085_tan__add, fact_2897_self__le__power, fact_4597_dvd__mult__left, fact_7743_powser__split__head_I1_J, fact_6167_add__divide__eq__if__simps_I3_J, fact_657_one__plus__numeral, fact_463_add__mono__thms__linordered__semiring_I1_J, fact_3308_pinf_I8_J, fact_436_ab__semigroup__add__class_Oadd__ac_I1_J, fact_9672_plus__complex_Osimps_I2_J, fact_8440_pochhammer__eq__0__mono, fact_7962_fact__1, fact_207_left__add__mult__distrib, fact_2185_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq, fact_7134_numeral__power__le__of__nat__cancel__iff, fact_5345_mult__neg__numeral__simps_I2_J, fact_3140_minus__int__code_I1_J, fact_5218_sum_Oempty, fact_729_diff__diff__eq2, fact_4675_div__div__div__same, fact_1823_divide__eq__eq__numeral1_I1_J, fact_6435_sum__zero__power, fact_4681_dvd__power__same, fact_1804_divide__le__0__1__iff, fact_5711_le__minus__one__simps_I2_J, fact_665_numeral__le__one__iff, fact_6421_zero__less__power__abs__iff, fact_3890_dual__order_Oantisym, fact_759_diff__add__inverse2, fact_4322_order__le__less__subst1, fact_8557_gbinomial__factors, fact_7362_sum__gp__offset, fact_9011_complex__inverse, fact_3543_sum_Ofinite__Collect__op, fact_6085_sum_Omono__neutral__right, fact_8052_fact__reduce, fact_6909_of__nat__le__iff, fact_2717_less__divide__eq__1, fact_5712_le__minus__one__simps_I2_J, fact_8977_tan__cot, fact_4986_power__le__zero__eq, fact_8482_gbinomial__ge__n__over__k__pow__k, fact_9340_sgn__power__root, fact_2180_unique__euclidean__semiring__numeral__class_Odiv__less, fact_4179_dense__ge, fact_1837_div__mult__self2, fact_1051_add__Suc__shift, fact_5293_neg__one__eq__numeral__iff, fact_5515_le__imp__neg__le, fact_6472_verit__eq__simplify_I14_J, fact_2655_divide__nonneg__pos, fact_2689_sum__squares__gt__zero__iff, fact_6206_le__minus__divide__eq, fact_3930_order__eq__refl, fact_6876_negative__zle, fact_2695_divide__less__eq, fact_7635_of__int__round__gt, fact_9296_nat__int__add, fact_398_add__right__imp__eq, fact_5548_minus__mult__commute, fact_385_mult_Ocommute, fact_2720_power__le__one, fact_6650_sum_Onat__ivl__Suc_H, fact_2232_mult__right__mono__neg, fact_8083_tan__diff, fact_7830_sin__x__le__x, fact_4968_zero__le__power__eq, fact_8554_binomial__fact, fact_8327_arcsin__ubound, fact_4808_dvd__minus__self, fact_7160_of__int__le__neg__numeral__power__cancel__iff, fact_1141_distrib__right, fact_8770_prod_OatMost__shift, fact_8745_prod__nonneg, fact_9436_atLeast1__atMost__eq__remove0, fact_5277_add__neg__numeral__special_I7_J, fact_6156_eq__divide__eq__numeral_I2_J, fact_9940_mult__rat__cancel, fact_5495_minus__equation__iff, fact_7956_fact__0, fact_2199_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_1440_VEBT__internal_Omembermima_Osimps_I4_J, fact_2102_Zero__neq__Suc, fact_2613_mult__le__less__imp__less, fact_8472_pochhammer__0__left, fact_3274_minf_I4_J, fact_8846_prod_Oin__pairs__0, fact_2810_mult__le__cancel__left2, fact_9093_powr__less__mono2, fact_2285_add__nonneg__eq__0__iff, fact_9256_diff__nat__numeral, fact_7242_zle__int, fact_1219_eq__add__iff2, fact_320_divide__divide__eq__right, fact_1146_combine__common__factor, fact_8243_real__sqrt__ge__abs2, fact_4900_evenE, fact_6683_abs__le__square__iff, fact_684_diff__eq__diff__eq, fact_9133_floor__log__nat__eq__if, fact_2413_zero__le__divide__iff, fact_4097_order__less__irrefl, fact_771_comm__monoid__mult__class_Omult__1, fact_2553_minus__mult__div__eq__mod, fact_2195_not__numeral__le__zero, fact_1758_mod__by__1, fact_1063_lift__Suc__mono__less__iff, fact_2066_mult__right__cancel, fact_2919_vebt__pred_Osimps_I5_J, fact_3054_div__nonneg__neg__le0, fact_2021_le__numeral__extra_I3_J, fact_6369_abs__of__nonneg, fact_2870_power__Suc__less, fact_7902_sin__mono__le__eq, fact_8081_lemma__tan__add1, fact_3644_nth__list__update__eq, fact_1566_div__0, fact_1889_power__decreasing__iff, fact_2060_mult__left__cancel, fact_2157_cong__exp__iff__simps_I6_J, fact_2217_mult__nonneg__nonneg, fact_8708_prod_Ocl__ivl__Suc, fact_2746_add__divide__eq__if__simps_I1_J, fact_4695_subset__divisors__dvd, fact_6173_add__divide__eq__if__simps_I5_J, fact_8484_gbinomial__mult__1_H, fact_3271_minf_I4_J, fact_4191_not__le__imp__less, fact_1565_div__0, fact_6412_semiring__norm_I3_J, fact_2117_not__less0, fact_2624_add__neg__nonpos, fact_6179_power2__eq__iff, fact_2951_exp__not__zero__imp__exp__diff__not__zero, fact_7276_real__of__nat__div, fact_2692_zero__less__two, fact_4571_semiring__parity__class_Oeven__mask__iff, fact_9168_real__root__le__0__iff, fact_2820_mult__less__cancel__left1, fact_4139_order__less__imp__not__eq2, fact_4621_dvdE, fact_7965_fact__Suc__0, fact_8309_arcsin__1, fact_8256_real__sqrt__sum__squares__mult__ge__zero, fact_1006_not__None__eq, fact_7796_cos__pi__half, fact_1174_split__option__all, fact_8180_exp__gt__one, fact_3125_flip__bit__nonnegative__int__iff, fact_531_add__mono__thms__linordered__field_I4_J, fact_3394_finite__nat__set__iff__bounded, fact_8152_real__sqrt__le__mono, fact_452_less__eqE, fact_3005_odd__0__le__power__imp__0__le, fact_7549_round__1, fact_2937_power2__eq__imp__eq, fact_359_semiring__norm_I13_J, fact_477_add__less__imp__less__left, fact_1082_lift__Suc__antimono__le, fact_2637_add__strict__increasing, fact_5325_semiring__norm_I168_J, fact_4189_not__le__imp__less, fact_177_power__add__numeral2, fact_2268_not__one__le__zero, fact_2740_add__frac__num, fact_1366_power__numeral__even, fact_9555_atLeastLessThan__singleton, fact_273_power__even__eq, fact_7233_of__nat__mono, fact_110_numeral__Bit0, fact_4598_dvd__mult__left, fact_8214_sqrt__le__D, fact_4442_dvd__add__triv__left__iff, fact_4186_less__le__not__le, fact_9522_even__not__iff__int, fact_10170_mono__Suc, fact_849_nat__diff__add__eq1, fact_5763_nonzero__minus__divide__divide, fact_4333_order__le__less__subst2, fact_5216_divide__minus1, fact_388_mult_Ocommute, fact_1346_Collect__subset, fact_4056_order__less__asym, fact_6612_cong__exp__iff__simps_I10_J, fact_7243_nonneg__int__cases, fact_5457_dbl__simps_I4_J, fact_7673_summable__zero__power, fact_858_power__gt1__lemma, fact_3990_ord__eq__less__trans, fact_4144_order__less__imp__not__less, fact_9316_nat__div__distrib, fact_5420_minus__1__div__2__eq, fact_9502_push__bit__of__Suc__0, fact_6396_tanh__real__nonneg__iff, fact_5566_add_Oinverse__distrib__swap, fact_7991_fact__not__neg, fact_9450_or__nat__numerals_I1_J, fact_2815_mult__le__cancel__right2, fact_1643_less__add__same__cancel2, fact_8331_fact__code, fact_2294_add__nonneg__nonneg, fact_6871_int__eq__iff__numeral, fact_1620_le__add__same__cancel2, fact_7057_real__of__nat__eq__numeral__power__cancel__iff, fact_875_power__increasing, fact_7342_double__arith__series, fact_5205_diff__minus__eq__add, fact_499_add__mono__thms__linordered__field_I2_J, fact_9119_le__powr__iff, fact_847_less__diff__conv2, fact_748_less__imp__diff__less, fact_456_add__left__mono, fact_5572_minus__diff__commute, fact_6891_of__nat__0__eq__iff, fact_3622_max__0__1_I2_J, fact_4594_dvd__triv__left, fact_3204_atLeastatMost__empty__iff, fact_8364_arccos__le__mono, fact_432_add__mono__thms__linordered__semiring_I4_J, fact_266_power4__eq__xxxx, fact_1424_subset__eq, fact_4129_linorder__less__linear, fact_7130_of__nat__le__numeral__power__cancel__iff, fact_5878_ln__less__zero, fact_6358_semiring__norm_I73_J, fact_1912_not__mod2__eq__Suc__0__eq__0, fact_3242_pinf_I4_J, fact_1471_deg1Leaf, fact_7452_norm__numeral, fact_8593_pochhammer__minus, fact_8204_powser__sums__zero, fact_2462_nonzero__divide__eq__eq, fact_4427_signed__take__bit__Suc, fact_2259_zero__less__numeral, fact_5198_mult__minus1, fact_2434_divide__pos__pos, fact_1445_vebt__pred_Osimps_I7_J, fact_2580_mult__strict__mono, fact_116_divide__numeral__1, fact_2848_mult__imp__le__div__pos, fact_8013_fact__less__mono, fact_1923_unique__euclidean__semiring__numeral__class_Opos__mod__bound, fact_9466_or__not__num__neg_Osimps_I3_J, fact_7323_inverse__of__nat__le, fact_4994_even__mult__exp__div__exp__iff, fact_8158_sums__add, fact_6109_sum_Osame__carrierI, fact_364_power__mult__numeral, fact_380_linordered__field__no__lb, fact_3558_max_Obounded__iff, fact_3090_verit__comp__simplify1_I2_J, fact_4418_even__succ__mod__exp, fact_8419_binomial__Suc__Suc, fact_4027_order_Ostrict__trans, fact_4143_order__less__imp__not__less, fact_7846_abs__sin__le__one, fact_5202_diff__minus__eq__add, fact_6616_power__minus__Bit1, fact_3028_unset__bit__0, fact_1011_mult__Suc__right, fact_2588_mult__right__less__imp__less, fact_8700_prod_OatMost__Suc, fact_2175_nat__mod__eq__lemma, fact_5199_mult__minus1, fact_6480_abs__of__pos, fact_2239_mult__nonpos__nonpos, fact_4342_order__less__le__subst1, fact_7092_of__int__power__le__of__int__cancel__iff, fact_6724_power__mono__even, fact_3586_max_Oabsorb3, fact_233_infinite__descent, fact_2266_not__numeral__less__zero, fact_3806_dbl__simps_I3_J, fact_9344_nat__dvd__iff, fact_8237_geometric__sums, fact_7492_norm__triangle__ineq, fact_5499_equation__minus__iff, fact_6356_tanh__real__le__iff, fact_1142_distrib__right, fact_2836_divide__left__mono, fact_5150_neg__less__eq__nonneg, fact_2941_zero__le__power2, fact_3672_max_OboundedE, fact_3115_set__bit__Suc, fact_4661_dvd__diff, fact_4869_unit__div__mult__swap, fact_6442_Suc__mod__eq__add3__mod__numeral, fact_3869_order__antisym, fact_628_left__diff__distrib__numeral, fact_2733_add__divide__eq__iff, fact_7774_cos__pi__eq__zero, fact_6171_add__divide__eq__if__simps_I5_J, fact_6440_div__Suc__eq__div__add3, fact_3945_ord__eq__le__subst, fact_1337_mult__commute__abs, fact_5278_add__neg__numeral__special_I7_J, fact_3381_old_Oprod_Oinject, fact_7491_norm__triangle__mono, fact_2735_add__num__frac, fact_271_power__even__eq, fact_6848_dbl__inc__simps_I3_J, fact_7101_of__int__eq__numeral__power__cancel__iff, fact_2471_eq__divide__eq, fact_198_power__commuting__commutes, fact_9373_AND__upper1_H, fact_444_add__le__imp__le__left, fact_5481_one__div__2__pow__eq, fact_5463_power__minus1__even, fact_7609_lemma__termdiff1, fact_1927_zero__reorient, fact_3372_mult__less__iff1, fact_6460_abs__mult, fact_7428_complex__mod__minus__le__complex__mod, fact_8685_prod_Odelta_H, fact_7122_of__nat__less__numeral__power__cancel__iff, fact_1611_zero__le__double__add__iff__zero__le__single__add, fact_6607_cong__exp__iff__simps_I13_J, fact_6792_max__Suc__numeral, fact_7787_sin__periodic__pi, fact_844_power__one__over, fact_1303_empty__Diff, fact_6787_pred__numeral__simps_I3_J, fact_1822_eq__divide__eq__numeral1_I1_J, 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fact_9755_drop__bit__Suc__minus__bit0, fact_2172_power__strict__mono, fact_5746_neg__eq__iff__add__eq__0, fact_5998_power__minus__Bit0, fact_5971_minus__divide__eq__eq, fact_352_add__le__cancel__right, fact_1153_left__diff__distrib_H, fact_7357_double__gauss__sum__from__Suc__0, fact_5965_nonzero__neg__divide__eq__eq2, fact_1677_sum__squares__eq__zero__iff, fact_2461_nonzero__divide__eq__eq, fact_8136_one__le__exp__iff, fact_223_power__add, fact_5284_diff__numeral__special_I12_J, fact_6224_power2__eq__1__iff, fact_4100_order__less__subst1, fact_2583_mult__less__cancel__left, fact_5184_verit__minus__simplify_I3_J, fact_7866_cos__monotone__0__pi, fact_1833_div__mult__self4, fact_8215_real__le__rsqrt, fact_8582_gbinomial__reduce__nat, fact_9527_bit__minus__int__iff, fact_1482_mult__zero__left, fact_9684_cmod__le, fact_8254_exp__bound, fact_1019_Suc__1, fact_382_mult_Oleft__commute, fact_8464_gbinomial__of__nat__symmetric, fact_6257_bits__induct, fact_7249_int__plus, 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fact_1722_zero__eq__1__divide__iff, fact_6632_power__numeral__odd, fact_8544_pochhammer__product, fact_267_power4__eq__xxxx, fact_1478_VEBT_Oinject_I2_J, fact_2851_divide__left__mono__neg, fact_8330_fact__code, fact_840_left__right__inverse__power, fact_7470_norm__power, fact_35__092_060open_062is__pred__in__set_A_Iset__vebt_H_Asummary_J_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_Apr_092_060close_062, fact_7239_int__ops_I3_J, fact_7446_norm__mult__numeral1, fact_5738_eq__neg__iff__add__eq__0, fact_967_real__average__minus__second, fact_1616_double__add__le__zero__iff__single__add__le__zero, fact_6374_zero__less__abs__iff, fact_3998_antisym__conv3, fact_5776_numeral__neq__neg__one, fact_5899_neg__numeral__less__zero, fact_4353_order__less__le__subst2, fact_9252_nat__neg__numeral, fact_2522_VEBT__internal_Onaive__member_Osimps_I2_J, fact_9375_AND__upper1, fact_5321_ln__ge__zero__iff, fact_1808_divide__less__0__1__iff, fact_9330_take__bit__int__less__exp, fact_1125_ring__class_Oring__distribs_I2_J, fact_437_ab__semigroup__add__class_Oadd__ac_I1_J, fact_1664_mult__cancel__left1, fact_9131_powr__neg__numeral, fact_2602_mult__le__cancel__left__pos, fact_2839_neg__divide__le__eq, fact_5741_eq__neg__iff__add__eq__0, fact_414_add_Oright__cancel, fact_6659_numeral__Bit1__div__2, fact_9047_le__log__of__power, fact_7524_of__nat__code__if, fact_9377_inc_Osimps_I1_J, fact_720_diff__eq__eq, fact_2050_divisors__zero, fact_656_one__plus__numeral, fact_1811_divide__less__eq__1__neg, fact_615_one__eq__numeral__iff, fact_708_diff__strict__left__mono, fact_3587_max_Oabsorb3, fact_8810_prod_Orelated, fact_2287_add__nonpos__nonpos, fact_7728_summable__norm, fact_8490_pochhammer__rec, fact_8182_sqrt__add__le__add__sqrt, fact_1454_vebt__member_Osimps_I5_J, fact_3149_zmod__le__nonneg__dividend, fact_7005_dbl__inc__simps_I5_J, fact_4883_zdvd__imp__le, fact_3114_set__bit__Suc, fact_1532_add__cancel__right__right, fact_8161_sums__diff, fact_10171_mono__times__nat, fact_7986_fact__ge__zero, 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fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_5283_diff__numeral__special_I12_J, fact_9428_atLeastAtMostSuc__conv, fact_2639_add__strict__increasing, fact_8276_exp__lower__Taylor__quadratic, fact_2484_power__0, fact_616_numeral__eq__one__iff, fact_4848_inf__period_I4_J, fact_8949_choose__row__sum, fact_5157_neg__less__pos, fact_2358_mult__strict__left__mono, fact_3057_neg__imp__zdiv__nonneg__iff, fact_1050_add__Suc, fact_6325_abs__zero, fact_1102_Suc__mult__le__cancel1, fact_2749_add__divide__eq__if__simps_I2_J, fact_41_high__bound__aux, fact_691_diff__left__mono, fact_676_one__reorient, fact_9943_One__rat__def, fact_428_group__cancel_Oadd1, fact_793_le__diff__eq, fact_8022_fact__fact__dvd__fact, fact_4664_dvd__div__eq__iff, fact_1220_eq__add__iff2, fact_6642_abs__add__one__gt__zero, fact_4409_max__absorb1, 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fact_5435_Parity_Oring__1__class_Opower__minus__even, fact_9122_floor__eq2, fact_7227_less__imp__of__nat__less, fact_4414_max__def, fact_2926_le__divide__eq__numeral_I1_J, fact_8434_pochhammer__pos, fact_5792_ab__group__add__class_Oab__diff__conv__add__uminus, fact_591_add__diff__cancel__right_H, fact_4566_power__le__zero__eq__numeral, fact_7215_of__nat__neq__0, fact_4944_power__mono__odd, fact_3682_max_Oorder__iff, fact_7261_nat__leq__as__int, fact_1910_not__mod__2__eq__0__eq__1, fact_541_all__set__conv__all__nth, fact_9163_real__root__le__iff, fact_4265_dual__order_Ostrict__implies__order, fact_3902_antisym, fact_1037_strict__inc__induct, fact_9666_Im__divide__numeral, fact_6327_abs__zero, fact_1950_VEBT__internal_OminNull_Osimps_I1_J, fact_4564_odd__two__times__div__two__succ, fact_9090_powr__less__mono, fact_9407_or__int__unfold, fact_6874_abs__of__nat, fact_134_mult__numeral__left__semiring__numeral, fact_347_add__left__cancel, fact_6895_of__nat__eq__0__iff, fact_6593_abs__diff__less__iff, fact_5209_uminus__add__conv__diff, fact_3326_inf__period_I2_J, fact_4202_order_Ostrict__iff__order, fact_4453_dvd__mult__cancel__left, fact_9818_uminus__int_Oabs__eq, fact_4546_even__diff__nat, fact_3110_verit__sum__simplify, fact_1018_div2__Suc__Suc, fact_44_numeral__less__iff, fact_7958_fact__1, fact_7620_real__sum__nat__ivl__bounded2, fact_5525_minus__less__iff, fact_8117_real__sqrt__eq__1__iff, fact_5629_mod__sum__eq, fact_2369_mult__strict__right__mono, fact_3345_mult__le__cancel__iff1, fact_225_div__times__less__eq__dividend, fact_9674_minus__complex_Osimps_I2_J, fact_4073_ord__eq__less__subst, fact_4863_div__mult__unit2, fact_7705_summable__powser__ignore__initial__segment, fact_6518_abs__le__iff, fact_5794_ab__group__add__class_Oab__diff__conv__add__uminus, fact_4268_dual__order_Ostrict__implies__order, fact_2379_le__iff__diff__le__0, fact_297_add__leD1, fact_3258_minf_I1_J, fact_1615_double__add__le__zero__iff__single__add__le__zero, fact_6704_Suc__div__eq__add3__div, fact_1697_nonzero__mult__divide__mult__cancel__right2, fact_4087_ord__less__eq__subst, fact_6283_exp__mod__exp, fact_5303_left__minus__one__mult__self, fact_4969_zero__le__power__eq, fact_6170_minus__divide__diff__eq__iff, fact_2482_VEBT__internal_OminNull_Oelims_I2_J, fact_6142_ln__eq__minus__one, fact_278_power2__sum, fact_5721_zero__neq__neg__one, fact_5115_of__bool__less__iff, fact_325_times__divide__eq__left, fact_1195_add__le__add__imp__diff__le, fact_7114_of__nat__zero__less__power__iff, fact_7297_of__int__neg__numeral, fact_1376_ex__in__conv, fact_673_less__eq__real__def, fact_2076_comm__monoid__add__class_Oadd__0, fact_83_numeral__le__iff, fact_4676_div__div__div__same, fact_3671_max_OboundedE, fact_8251_sums__if_H, fact_566_mult_Oright__neutral, fact_5777_square__eq__1__iff, fact_3011_VEBT__internal_Oexp__split__high__low_I1_J, fact_9268_take__bit__mult, fact_2485_power__0, fact_740_diff__diff__eq, fact_2101_Zero__not__Suc, fact_8566_gbinomial__negated__upper, fact_8150_norm__exp, fact_4772_div__unit__dvd__iff, fact_7895_cos__plus__cos, fact_5207_uminus__add__conv__diff, fact_4592_dvd__triv__left, fact_5954_not__numeral__less__neg__one, fact_8162_sums__divide, fact_4454_dvd__mult__cancel__left, fact_2226_mult__le__0__iff, fact_8534_Suc__times__gbinomial, fact_1935_vebt__buildup_Osimps_I1_J, fact_6670_power3__eq__cube, fact_4459_dvd__mult__cancel__right, fact_1943_cong__exp__iff__simps_I2_J, fact_8169_real__sqrt__ge__one, fact_7072_of__int__le__numeral__iff, fact_6317_abs__0__eq, fact_2874_power__Suc__le__self, fact_9512_and__not__numerals_I1_J, fact_6738_sum__natinterval__diff, fact_8062_tan__inverse, fact_5344_mult__neg__numeral__simps_I2_J, fact_3553_insert__simp__excp, fact_6264_square__le__1, fact_7118_even__of__nat, fact_2415_divide__nonneg__nonneg, fact_6386_abs__power__minus, fact_4984_even__mask__div__iff_H, fact_7589_sum__lessThan__telescope, fact_9386_mult__inc, fact_4495_unit__div__1__div__1, fact_9030_log__le__cancel__iff, fact_959_maxt__corr__help__empty, fact_6970_of__int__mult, fact_5511_minus__le__iff, fact_538__092_060open_062vebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Apr_092_060close_062, fact_9260_one__less__nat__eq, fact_4824_unity__coeff__ex, fact_4468_unit__prod, fact_8242_sqrt__sum__squares__le__sum__abs, fact_3825_concat__bit__nonnegative__iff, fact_1921_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend, fact_4830_dvd__div__eq__mult, fact_8071_arctan, fact_1914_mod2__gr__0, fact_8051_fact__reduce, fact_6395_tanh__real__nonpos__iff, fact_1609_mult__cancel2, fact_2677_sum__squares__ge__zero, fact_253_mult__2__right, fact_696_diff__right__mono, fact_8559_gbinomial__rec, fact_1078_lift__Suc__mono__le, fact_8415_gbinomial__0_I1_J, fact_3006_odd__0__le__power__imp__0__le, fact_520_add__less__le__mono, fact_6905_of__nat__numeral, fact_8324_sum__atLeastAtMost__code, fact_5975_mult__1s__ring__1_I1_J, fact_6736_sum__natinterval__diff, fact_4599_dvd__mult__left, fact_4455_dvd__mult__cancel__left, fact_1898_power2__less__eq__zero__iff, fact_7269_real__of__nat__div4, fact_8508_pochhammer__of__nat__eq__0__iff, fact_2559_minus__mod__eq__div__mult, fact_6410_semiring__norm_I5_J, fact_5785_group__cancel_Osub2, fact_6228_minus__one__power__iff, fact_1593_le0, fact_206_power__mult, fact_2771_add__divide__eq__if__simps_I4_J, fact_7070_of__int__numeral__le__iff, fact_1459_vebt__pred_Oelims, fact_4800_dvd__power__le, fact_3198_atLeastatMost__empty__iff2, fact_2451_zero__le__power, fact_138_mult__numeral__left__semiring__numeral, fact_4927_power__dvd__imp__le, fact_5058_add_Oinverse__neutral, fact_3991_ord__less__eq__trans, fact_3952_ord__le__eq__subst, fact_7847_abs__cos__le__one, fact_8603_pochhammer__code, fact_2304_add__increasing, fact_411_add_Ocommute, fact_1600_minus__mod__self2, fact_9640_Re__divide__numeral, fact_5460_power__minus1__even, fact_3267_minf_I3_J, fact_5664_zero__less__eq__of__bool, fact_4274_order__le__less, fact_4548_zero__less__power__eq__numeral, fact_8742_atMost__def, fact_2141_power__eq__iff__eq__base, fact_3230_pinf_I2_J, fact_3032_unset__bit__Suc, fact_6355_abs__minus__cancel, fact_251_mult__2__right, fact_7600_geometric__sum, fact_7601_geometric__sum, fact_1942_cong__exp__iff__simps_I2_J, fact_4612_dvd__def, fact_5735_add_Oinverse__unique, fact_9271_take__bit__nat__eq, fact_1876_bits__one__mod__two__eq__one, fact_5352_semiring__norm_I170_J, fact_2354_mult__strict__left__mono__neg, fact_1512_double__zero__sym, fact_146_semiring__norm_I71_J, fact_1875_power__mono__iff, fact_2089_add_Ogroup__left__neutral, fact_1143_combine__common__factor, fact_2773_add__divide__eq__if__simps_I4_J, fact_4522_even__add, fact_5175_ab__left__minus, fact_6017_sum__nonneg__leq__bound, fact_2384_zero__less__one, fact_7657_summable__comparison__test, fact_1197_add__le__add__imp__diff__le, fact_127_field__less__half__sum, fact_3785_nth__list__update, fact_8996_complex__i__not__numeral, fact_7551_sum_OlessThan__Suc, fact_5254_Ball__set__replicate, fact_8485_gbinomial__mult__1, fact_4619_dvdI, fact_7036_of__int__less__0__iff, fact_1797_div__less, fact_8449_zero__less__binomial, fact_2645_frac__le, fact_3137_int__distrib_I3_J, fact_4114_order__less__subst2, fact_370__092_060open_062both__member__options_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ares_092_060close_062, fact_6538_tanh__real__lt__1, fact_4196_order_Oorder__iff__strict, fact_7360_double__gauss__sum__from__Suc__0, fact_3031_unset__bit__Suc, fact_6601_numeral__Bit1, fact_6850_dbl__inc__simps_I3_J, fact_7308_nat__less__real__le, fact_5011_add__scale__eq__noteq, fact_4273_order__le__less, fact_6276_div__pos__neg__trivial, fact_1883_Suc__diff__1, fact_3036_verit__eq__simplify_I8_J, fact_2822_mult__less__cancel__left2, fact_6096_sum_Omono__neutral__left, fact_3849_le__cases3, fact_9520_flip__bit__int__def, fact_9491_XOR__lower, fact_4312_order__le__less__trans, fact_9324_take__bit__nat__eq__self, fact_4187_less__le__not__le, fact_2196_not__numeral__le__zero, fact_9248_nat__1, fact_7909_cos__one__2pi__int, fact_6817_arctan__monotone_H, fact_2864_frac__le__eq, fact_8116_real__sqrt__one, fact_72_numeral__eq__iff, fact_8255_real__sqrt__power__even, fact_5991_uminus__numeral__One, fact_3027_unset__bit__0, fact_322_divide__divide__eq__left, fact_5027_add_Oinverse__inverse, fact_399_add__right__imp__eq, fact_4590_dvd__triv__left, fact_4350_order__less__le__subst1, fact_5891_neg__numeral__le__zero, fact_2448_power__mono, fact_8675_prod_Odelta, fact_1795_diff__is__0__eq_H, fact_3175_split__zmod, fact_3236_pinf_I3_J, fact_2213_mult__nonneg__nonpos, fact_3868_order__antisym, fact_6038_zmod__zminus2__eq__if, fact_351_add__le__cancel__right, fact_7080_of__int__1__le__iff, fact_4460_dvd__mult__cancel__right, fact_1606_mult__is__0, fact_2967_power__minus__mult, fact_9763_fst__divmod__nat, fact_4059_linorder__neq__iff, fact_6750_sum_Oin__pairs, fact_5552_one__neq__neg__one, fact_9489_xor__negative__int__iff, fact_2931_scaling__mono, fact_8551_fact__binomial, fact_1045_not__less__eq__eq, fact_4169_antisym__conv1, fact_4560_even__power, fact_3858_ord__eq__le__trans, fact_5734_add_Oinverse__unique, fact_2283_add__nonneg__eq__0__iff, fact_4444_dvd__add__triv__left__iff, fact_190_power__commutes, fact_5591_mod__minus__right, fact_8176_sums__mult2__iff, fact_5384_eq__divide__eq__numeral1_I2_J, fact_1514_add__cancel__left__left, fact_4554_even__succ__div__two, fact_2152_vebt__pred_Ocases, fact_371__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ares_092_060close_062, fact_3169_zless__imp__add1__zle, fact_5730_ab__group__add__class_Oab__left__minus, fact_9314_nat__diff__distrib, fact_1654_add__less__same__cancel1, fact_7925_sin__monotone__2pi, fact_3971_gt__ex, fact_7827_sin__double, fact_3723_less__max__iff__disj, fact_9562_ex__nat__less__eq, fact_5168_add_Oright__inverse, fact_4463_dvd__times__left__cancel__iff, fact_2247_split__mult__pos__le, fact_9517_xor__int__def, fact_4288_linorder__not__less, fact_4701_not__is__unit__0, fact_9846_pow_Osimps_I3_J, fact_3953_ord__le__eq__subst, fact_484_add__strict__right__mono, fact_6834_dbl__dec__def, fact_1509_add_Oright__neutral, fact_7184_mult__of__nat__commute, fact_9958_rat__number__expand_I5_J, fact_4577_dvd__triv__right, fact_2621_add__neg__nonpos, fact_9843_num__of__nat__One, fact_3957_ord__le__eq__subst, fact_6492_abs__mult__less, fact_1021_Suc__inject, fact_5400_power2__minus, fact_2186_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq, fact_2047_mult__not__zero, fact_2252_mult__mono_H, fact_6846_sum__gp, fact_4751_dvd__div__mult, fact_3100_realpow__pos__nth__unique, fact_8958_pred__numeral__simps_I2_J, fact_1473_deg__1__Leafy, fact_2507_mult__less__mono1, fact_6389_semiring__norm_I14_J, fact_2192_zero__le__numeral, fact_4052_linorder__neqE, fact_4710_minf_I9_J, fact_375_div__mult2__numeral__eq, fact_7575_sum_Onat__diff__reindex, fact_9308_nat__eq__iff2, fact_4584_dvd__mult__right, fact_6837_decr__lemma, fact_7447_norm__mult__numeral1, fact_6618_power__minus__Bit1, fact_4241_dual__order_Ostrict__trans1, fact_6431_sum_Ocl__ivl__Suc, fact_9272_take__bit__nat__less__eq__self, fact_9342_take__bit__int__less__self__iff, fact_3935_linorder__linear, fact_757_diff__cancel2, fact_6433_sum_Ocl__ivl__Suc, fact_7595_one__diff__power__eq, fact_5383_eq__divide__eq__numeral1_I2_J, fact_3119_VEBT__internal_Onaive__member_Opelims_I2_J, fact_7170_of__int__less__neg__numeral__power__cancel__iff, fact_3769_nat__minus__add__max, fact_9355_even__nat__iff, fact_7973_tan__periodic__n, fact_6617_power__minus__Bit1, fact_3227_pinf_I1_J, fact_9349_take__bit__numeral__minus__bit0, fact_5094_minus__add__distrib, fact_4857_unit__eq__div1, fact_9221_mask__nonnegative__int, fact_2481_right__inverse__eq, fact_956_mint__corr__help, fact_7334_linear__plus__1__le__power, fact_4673_dvd__div__eq__cancel, fact_6176_add__divide__eq__if__simps_I6_J, fact_2814_mult__le__cancel__right1, fact_6000_power__minus__Bit0, fact_9383_AND__upper2_H_H, fact_7133_numeral__power__le__of__nat__cancel__iff, fact_6157_eq__divide__eq__numeral_I2_J, fact_7106_of__int__power__less__of__int__cancel__iff, fact_4091_ord__less__eq__subst, fact_4609_dvd__mult, fact_4611_dvd__def, fact_4806_nat__dvd__not__less, fact_179_le__cube, fact_5808_dvd__div__neg, fact_2488_divmod__digit__0_I1_J, fact_7516_norm__triangle__ineq3, fact_3207_decr__mult__lemma, fact_2832_divide__le__eq, fact_2627_add__nonneg__pos, fact_2731_divide__add__eq__iff, fact_3276_minf_I5_J, fact_1671_mult__cancel__right1, help_If_1_1_If_001t__Complex__Ocomplex_T, fact_4147_order__less__imp__not__less, fact_7226_less__imp__of__nat__less, fact_9941_eq__rat_I2_J, fact_1744_power__0__Suc, fact_2702_neg__less__divide__eq, fact_6531_sin__bound__lemma, fact_4366_order__le__imp__less__or__eq, fact_3677_max_OboundedI, fact_9081_powr__numeral, fact_5528_verit__negate__coefficient_I2_J, fact_1171_split__option__ex, fact_6572_abs__if, fact_690_diff__mono, fact_4220_order_Ostrict__iff__not, fact_2794_nat__diff__split, fact_5178_diff__0, fact_1559_diff__self, fact_8015_fact__mod, fact_3575_max__less__iff__conj, fact_7295_of__int__neg__numeral, fact_5104_div__minus__minus, fact_2361_mult__less__cancel__left__disj, fact_5335_diff__numeral__simps_I2_J, fact_692_diff__left__mono, fact_6690_num_Osize_I6_J, fact_92_add__numeral__left, fact_3552_insert__simp__norm, fact_8066_tan__pos__pi2__le, fact_1042_Suc__le__D, fact_7738_sum__less__suminf, fact_5934_neg__numeral__le__neg__one, fact_5959_not__neg__one__less__neg__numeral, fact_4884_mod__greater__zero__iff__not__dvd, fact_2383_not__one__less__zero, fact_6172_add__divide__eq__if__simps_I5_J, fact_7739_pi__less__4, fact_9297_int__minus, fact_161_le__divide__eq__numeral1_I1_J, fact_6550_eq__abs__iff_H, fact_6400_zero__le__divide__abs__iff, fact_9980_String_Ochar__of__ascii__of, fact_9686_Re__exp, fact_1130_ring__class_Oring__distribs_I1_J, fact_6095_sum_Omono__neutral__left, fact_2663_mult__left__le, fact_8751_prod__mono, fact_12__092_060open_0622_A_092_060le_062_Adeg_092_060close_062, fact_4785_div__power, fact_238_le__antisym, fact_1624_le__add__same__cancel1, fact_7798_sin__pi__half, fact_3751_max__add__distrib__right, fact_6491_abs__mult__less, fact_111_numeral__Bit0, fact_1686_nonzero__mult__div__cancel__left, fact_5208_uminus__add__conv__diff, fact_9172_real__root__le__1__iff, fact_4850_inf__period_I4_J, fact_3045_half__nonnegative__int__iff, fact_2311_mult__neg__neg, fact_2009_power__mod, fact_4749_is__unit__mult__iff, fact_112_is__pred__in__set__def, fact_8069_tan__mono__le, fact_6942_of__int__eq__numeral__iff, fact_4587_mult__dvd__mono, fact_9080_floor__divide__eq__div__numeral, fact_5204_diff__minus__eq__add, fact_4507_unit__mult__div__div, fact_7270_int__zle__neg, fact_561__C4_Ohyps_C_I1_J, 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fact_9439_OR__upper, fact_728_diff__diff__eq2, fact_4309_order__le__less__trans, fact_7175_neg__numeral__power__less__of__int__cancel__iff, fact_4078_ord__eq__less__subst, fact_1569_div__0, fact_1777_mod__mult__self3, fact_7365_nat__approx__posE, fact_5056_add_Oinverse__neutral, fact_6950_of__nat__power__eq__of__nat__cancel__iff, fact_6511_abs__leI, fact_4950_even__unset__bit__iff, fact_6309_signed__take__bit__Suc__minus__bit1, fact_3065_split__neg__lemma, fact_8495_pochhammer__Suc, fact_4623_dvdE, fact_7822_cos__diff, fact_2715_divide__less__eq__1, fact_9525_or__not__numerals_I4_J, fact_6521_abs__ge__minus__self, fact_6590_abs__diff__le__iff, fact_2652_divide__le__cancel, fact_9150_cmod__complex__polar, fact_2051_divisors__zero, fact_6587_abs__diff__triangle__ineq, fact_9286_nat__one__as__int, fact_1105_Suc__eq__plus1__left, fact_7893_cos__times__cos, fact_3810_order__refl, fact_4739_dvd__mult__unit__iff_H, fact_2837_divide__left__mono, fact_3324_inf__period_I1_J, fact_8414_gbinomial__0_I1_J, fact_918_nth__equalityI, fact_7282_of__int__leD, fact_3247_pinf_I5_J, fact_5724_add__eq__0__iff, fact_1694_div__mult__mult1__if, fact_9700_csqrt__square, fact_779_mult_Ocomm__neutral, fact_1887_one__div__two__eq__zero, fact_8218_exp__divide__power__eq, fact_6204_of__bool__odd__eq__mod__2, fact_3910_order__subst1, fact_4837_dvd__div__iff__mult, fact_3098_int__power__div__base, fact_8460_gbinomial__Suc__Suc, fact_1096_less__add__Suc1, fact_7526_of__nat__code__if, fact_7320_of__nat__less__two__power, fact_4148_prod__decode__aux_Ocases, fact_4057_order__less__asym, fact_4023_order_Ostrict__trans, fact_582_add__diff__cancel__left, fact_7556_powser__zero, fact_2690_sum__squares__gt__zero__iff, fact_9145_i__complex__of__real, fact_483_add__strict__right__mono, fact_876_power__increasing, fact_4878_is__unit__power__iff, fact_8442_pochhammer__neq__0__mono, fact_366_power__mult__numeral, fact_7289_of__int__lessD, fact_5197_mult__minus1, fact_5328_diff__numeral__simps_I3_J, fact_7358_double__gauss__sum__from__Suc__0, fact_5560_group__cancel_Oneg1, fact_1461_discrete, fact_9167_real__root__lt__0__iff, fact_3791_vebt__insert_Opelims, fact_4227_dual__order_Oorder__iff__strict, fact_6340_abs__1, fact_5084_add__minus__cancel, fact_4497_div__add, fact_1655_add__less__same__cancel1, fact_4903_odd__one, fact_6466_abs__minus__commute, fact_8535_gbinomial__absorption, fact_5580_div__minus__right, fact_66__092_060open_062z_A_092_060noteq_062_Ama_092_060close_062, fact_1920_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend, fact_139_numeral__times__numeral, fact_7955_fact__0, fact_9409_or__negative__int__iff, fact_6979_of__int__power__eq__of__int__cancel__iff, fact_4948_signed__take__bit__int__less__exp, fact_8445_pochhammer__fact, fact_4067_order__less__asym_H, fact_9440_or__int__rec, fact_5586_minus__divide__divide, fact_1672_mult__cancel__right1, fact_6409_semiring__norm_I8_J, fact_806_mult__diff__mult, 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fact_6500_abs__triangle__ineq3, fact_7107_of__int__power__less__of__int__cancel__iff, fact_7443_norm__divide__numeral, fact_9694_complex__eq__0, fact_668_numeral__le__one__iff, help_If_2_1_If_001t__Complex__Ocomplex_T, fact_9124_ln__powr__bound, fact_6943_of__int__eq__numeral__iff, fact_1684_nonzero__mult__div__cancel__right, fact_516_add__divide__distrib, fact_6915_of__nat__mult, fact_6037_zmod__zminus1__eq__if, fact_6634_power__numeral__odd, fact_2209_mult__nonpos__nonneg, fact_4249_dual__order_Ostrict__trans2, fact_9128_minus__log__eq__powr, fact_4773_div__unit__dvd__iff, fact_7816_cos__npi__int, fact_4819_zdvd__period, fact_6218_divide__less__eq__numeral_I2_J, fact_2796_nat__mult__div__cancel1, fact_9944_Fract__of__int__eq, fact_3047_zdiv__mono1, fact_3911_order__subst1, fact_5740_eq__neg__iff__add__eq__0, fact_1241_square__diff__one__factored, fact_5708_not__numeral__less__neg__numeral, fact_377_linordered__field__no__ub, fact_8951_polynomial__product__nat, fact_8123_real__sqrt__ge__0__iff, fact_1647_less__add__same__cancel1, fact_9195_real__root__decreasing, fact_8976_real__inv__sqrt__pow2, fact_3735_max_Ostrict__order__iff, fact_723_eq__diff__eq, fact_6165_add__divide__eq__if__simps_I3_J, fact_812_Nat_Odiff__add__assoc2, fact_1779_mod__mult__self2, fact_4184_less__le__not__le, fact_1023_Suc__lessD, fact_7244_zero__le__imp__eq__int, fact_7032_of__int__0__le__iff, fact_2657_divide__nonpos__neg, fact_5783_group__cancel_Osub2, fact_5909_le__minus__one__simps_I3_J, fact_8273_exp__bound__lemma, fact_2181_unique__euclidean__semiring__numeral__class_Odiv__less, fact_7952_tan__periodic__pi, fact_1749_power__zero__numeral, fact_9057_le__log2__of__power, fact_6623_sum__power__add, fact_1861_le__divide__eq__1__pos, fact_1513_double__zero__sym, fact_4532_zero__le__power__eq__numeral, fact_2382_not__one__less__zero, fact_4075_ord__eq__less__subst, fact_7458_norm__minus__commute, fact_7968_fact__Suc, fact_4028_not__less__iff__gr__or__eq, fact_4348_order__less__le__subst1, fact_6679_sum__Suc__diff, fact_151_distrib__right__numeral, fact_7263_of__nat__diff, fact_3327_inf__period_I2_J, fact_749_eq__diff__iff, fact_8014_Complex__eq__neg__numeral, fact_8417_gbinomial__0_I1_J, fact_1928_zero__reorient, fact_182_mult__le__mono1, fact_1979_mod__mult__mult2, fact_2132_nat__mod__eq__iff, fact_635_Nat_Oadd__diff__assoc, fact_3618_max__0__1_I3_J, fact_1890_power__decreasing__iff, fact_9159_real__root__eq__iff, fact_4334_order__le__less__subst2, fact_5690_neg__numeral__le__numeral, fact_2965_power__minus__mult, fact_3974_dense, fact_150_distrib__right__numeral, fact_6839_nat__ivt__aux, fact_5494_minus__equation__iff, fact_8788_power__sum, fact_4775_dvd__div__unit__iff, fact_2574_mult__le__cancel__right, fact_2623_add__neg__nonpos, fact_685_diff__eq__diff__eq, fact_8638_prod_Oneutral__const, fact_9120_log__le__iff, fact_6988_of__int__power, fact_7499_norm__diff__triangle__less, fact_7051_numeral__power__eq__of__nat__cancel__iff, 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fact_7296_of__int__neg__numeral, fact_1217_square__diff__square__factored, fact_4945_power__mono__odd, fact_4705_minf_I10_J, fact_1528_add__cancel__right__left, fact_6883_of__nat__0, fact_8174_exp__diff, fact_9461_not__bit__Suc__0__Suc, fact_712_add__diff__add, fact_800_less__diff__eq, fact_6238_ln__one__minus__pos__lower__bound, fact_9317_nat__div__distrib_H, fact_2964_power__minus__mult, fact_1932_mod__Suc, fact_1232_ordered__ring__class_Ole__add__iff1, fact_7136_of__int__le__numeral__power__cancel__iff, fact_3946_ord__eq__le__subst, fact_9934_diff__rat, fact_941_mintlistlength, fact_9535_or__not__numerals_I7_J, fact_196_power__mult__distrib, fact_2860_less__divide__eq__numeral_I1_J, fact_5880_ln__ge__zero, fact_5587_minus__divide__divide, fact_8029_Complex__eq__1, fact_7706_pi__ge__zero, fact_4995_even__mult__exp__div__exp__iff, fact_7825_sin__zero__norm__cos__one, fact_514_add__divide__distrib, fact_1798_less__one, fact_1507_add_Oright__neutral, fact_1595_mod__add__self2, fact_6855_of__int__code__if, fact_7785_cos__periodic__pi, fact_6894_of__nat__eq__0__iff, fact_7582_sum_OlessThan__Suc__shift, fact_7835_cos__squared__eq, fact_5774_numeral__neq__neg__one, fact_8154_sums__le, fact_482_add__strict__right__mono, fact_4128_linorder__less__linear, fact_9098_ge__one__powr__ge__zero, fact_4007_dual__order_Oasym, fact_9265_nat__le__numeral__power__cancel__iff, fact_6209_minus__divide__le__eq, fact_5609_sum__product, fact_7614_diff__power__eq__sum, fact_8430_Suc__times__binomial__eq, fact_5237_ln__eq__zero__iff, fact_1192_less__1__mult, fact_9333_take__bit__int__def, fact_7886_cos__monotone__minus__pi__0, fact_6631_numeral__code_I3_J, fact_9483_xor__nat__rec, fact_962_real__arch__pow, fact_8011_fact__less__mono, fact_5957_not__one__less__neg__numeral, fact_9762_drop__bit__of__Suc__0, fact_9530_numeral__or__not__num__eq, fact_5728_ab__group__add__class_Oab__left__minus, fact_7640_suminf__geometric, fact_1116_vebt__pred_Osimps_I4_J, fact_958_mint__corr__help__empty, fact_1827_nonzero__divide__mult__cancel__right, fact_8337_le__arcsin__iff, fact_2414_divide__nonneg__nonneg, fact_4032_not__less__iff__gr__or__eq, fact_6190_div__eq__minus1, fact_7522_ln__series, fact_4099_order__less__subst1, fact_6568_abs__if__raw, fact_2808_mult__le__cancel__left1, fact_4069_order__less__trans, fact_5522_minus__less__iff, fact_7451_norm__le__zero__iff, fact_1009_not__Some__eq, fact_6625_sum_OatLeastAtMost__rev, fact_1077_lift__Suc__mono__le, fact_6694_sum_Oub__add__nat, fact_8539_gbinomial__trinomial__revision, fact_2641_add__strict__increasing2, fact_454_add__left__mono, fact_6160_divide__eq__eq__numeral_I2_J, fact_697_diff__eq__diff__less__eq, fact_666_numeral__le__one__iff, fact_1557_diff__self, fact_9819_one__int__def, fact_1414_double__diff, fact_9508_or__int__def, fact_6344_abs__1, fact_1683_nonzero__mult__div__cancel__right, fact_7161_of__int__le__neg__numeral__power__cancel__iff, fact_5538_neg__numeral__neq__numeral, fact_9552_Sum__Ico__nat, fact_5876_ln__bound, fact_6936_of__int__numeral, fact_3094_verit__comp__simplify1_I1_J, fact_395_ab__semigroup__mult__class_Omult__ac_I1_J, fact_5940_not__one__le__neg__numeral, fact_2238_mult__left__mono, fact_7768_sum__pos__lt__pair, fact_1259_double__not__eq__Suc__double, fact_4817_bezout1__nat, fact_1535_zero__eq__add__iff__both__eq__0, fact_316_times__divide__eq__right, fact_1905_sum__power2__eq__zero__iff, fact_8284_vebt__mint_Opelims, fact_5537_neg__numeral__neq__numeral, fact_1645_less__add__same__cancel2, fact_1598_mod__add__self1, fact_453_add__left__mono, fact_8758_prod__pos, fact_301_add__le__mono1, fact_5698_zero__neq__neg__numeral, fact_2599_mult__le__cancel__left__neg, fact_7081_of__int__1__le__iff, fact_5461_power__minus1__even, fact_713_add__diff__add, fact_4974_zero__le__even__power, fact_4776_dvd__div__unit__iff, fact_479_add__less__imp__less__left, fact_3260_minf_I2_J, fact_2660_divide__nonpos__pos, fact_5573_minus__diff__commute, fact_1961_power__0__left, fact_568_mult__1, fact_354_add__le__cancel__left, fact_2938_power2__eq__imp__eq, fact_7583_sumr__diff__mult__const2, fact_7498_norm__diff__triangle__less, fact_9266_nat__mask__eq, fact_6235_neg__one__power__add__eq__neg__one__power__diff, fact_4534_power__less__zero__eq, fact_1925_zero__reorient, fact_4438_dvd__add__triv__right__iff, fact_1212_linordered__semidom__class_Oadd__diff__inverse, fact_3106_verit__sum__simplify, fact_2014_mod__Suc__Suc__eq, fact_8003_fact__mono, fact_2675_sum__squares__ge__zero, fact_4058_linorder__neq__iff, fact_6523_abs__ge__minus__self, fact_7503_norm__diff__triangle__le, fact_7834_sin__cos__le1, fact_5470_neg__one__odd__power, fact_7894_cos__plus__cos, fact_4922_div2__even__ext__nat, fact_3747_max_Ostrict__coboundedI2, fact_9463_or__not__num__neg_Osimps_I4_J, fact_1226_option_Oexhaust__sel, fact_5427_Power_Oring__1__class_Opower__minus__even, fact_6147_minus__divide__less__eq, fact_1670_mult__cancel__right1, fact_4325_order__le__less__subst1, fact_4048_linorder__neqE, fact_2368_mult__strict__right__mono, fact_3956_ord__le__eq__subst, fact_693_diff__left__mono, fact_8426_zero__less__binomial__iff, fact_6674_sum_OSuc__reindex__ivl, fact_1199_add__le__imp__le__diff, fact_9270_nat__take__bit__eq, fact_2607_mult__right__le__imp__le, fact_8283_vebt__maxt_Opelims, fact_7331_ln__realpow, fact_4961_oddE, fact_6286_crossproduct__eq, fact_8496_pochhammer__Suc, fact_9351_take__bit__eq__mask__iff__exp__dvd, fact_4794_power__le__dvd, fact_9199_odd__real__root__pow, fact_7435_reals__Archimedean2, fact_6869_of__nat__eq__iff, fact_4731_unit__mult__right__cancel, fact_1123_power__odd__eq, fact_9742_max__Suc1, fact_6998_of__nat__of__bool, fact_3948_ord__le__eq__subst, fact_486_add__strict__left__mono, fact_3701_max_Oabsorb__iff1, fact_1721_zero__eq__1__divide__iff, fact_2811_mult__le__cancel__left2, fact_2557_minus__mod__eq__mult__div, fact_9676_times__complex_Osimps_I2_J, fact_5968_nonzero__neg__divide__eq__eq, fact_9329_sgn__power__injE, fact_8040_fact__numeral, fact_7372_lemma__termdiff3, fact_9396_and__nat__numerals_I4_J, fact_6641_abs__add__one__gt__zero, fact_3880_linorder__wlog, fact_8617_pochhammer__times__pochhammer__half, fact_7888_sincos__total__pi__half, fact_6758_Sum__Icc__nat, fact_9931_less__rat, fact_1210_less__add__one, fact_829_numeral__One, fact_6216_pos__minus__divide__le__eq, fact_3676_max_OboundedI, fact_1205_add__mono1, fact_2386_zero__less__one, fact_8258_tan__30, fact_4570_semiring__parity__class_Oeven__mask__iff, fact_7800_cos__periodic, fact_1610_mod__less, fact_4910_bit__eq__rec, fact_8526_binomial__maximum_H, fact_9025_log__less__one__cancel__iff, fact_9040_log__ln, fact_6832_nat__intermed__int__val, fact_2633_add__pos__nonneg, fact_501_add__mono__thms__linordered__field_I5_J, fact_4643_dvd__add__right__iff, fact_5613_sum__distrib__right, fact_6960_of__nat__power, fact_466_add__mono__thms__linordered__semiring_I2_J, fact_7722_summable__geometric, fact_6981_of__int__power__eq__of__int__cancel__iff, fact_3329_imp__le__cong, fact_1989_mod__add__right__eq, fact_9510_flip__bit__nat__def, fact_2736_add__num__frac, fact_2111_nat_Odistinct_I1_J, fact_834_one__le__power, fact_1519_add__cancel__left__right, fact_2241_mult__nonpos__nonpos, fact_2342_zero__less__mult__pos, fact_7616_power__diff__sumr2, fact_2763_divide__diff__eq__iff, fact_9282_nat__mono, fact_8882_less__1__prod, fact_2492_gr0__conv__Suc, fact_8312_arcsin__le__arcsin, fact_5365_semiring__norm_I172_J, fact_1352_lambda__one, fact_8600_gbinomial__absorption_H, fact_6407_zdiv__numeral__Bit1, fact_6290_crossproduct__noteq, fact_3686_max_Ocobounded1, fact_2263_not__numeral__less__zero, fact_2795_nat__one__le__power, fact_768_diff__mult__distrib, fact_2053_no__zero__divisors, fact_3574_max__less__iff__conj, fact_9242_divide__int__def, fact_8095_fact__ge__self, fact_2686_not__sum__squares__lt__zero, fact_8413_binomial__eq__0__iff, fact_3126_set__bit__nonnegative__int__iff, fact_5809_dvd__div__neg, fact_5604_sum__mono, fact_2303_add__increasing, fact_1135_distrib__left, fact_3270_minf_I4_J, fact_1627_add__le__same__cancel2, fact_9470_or__nat__def, fact_346_add__left__cancel, fact_897_power__le__imp__le__exp, fact_802_diff__less__eq, fact_9284_all__nat, fact_5127_of__bool__eq__1__iff, fact_408_add_Oleft__commute, fact_9180_real__root__divide, fact_9951_rat__number__collapse_I5_J, fact_3497_Diff__infinite__finite, fact_6709_abs__sqrt__wlog, fact_6381_abs__neg__one, fact_570_mult__1, fact_585_add__diff__cancel__left_H, fact_6236_neg__one__power__add__eq__neg__one__power__diff, fact_645_one__add__one, fact_8926_prod_Omono__neutral__left, fact_2363_mult__strict__right__mono__neg, fact_1743_power__0__Suc, fact_2511_One__nat__def, fact_6582_abs__triangle__ineq4, fact_1967_zero__power, fact_3241_pinf_I4_J, fact_9065_ceiling__divide__eq__div__numeral, fact_1817_less__divide__eq__1__pos, fact_605_power__one__right, fact_9312_Suc__as__int, fact_5390_neg__numeral__less__neg__one__iff, fact_9174_power2__csqrt, fact_1214_linordered__semidom__class_Oadd__diff__inverse, fact_7469_norm__power, fact_74__092_060open_062x_A_092_060le_062_Ama_092_060close_062, fact_5042_equal__neg__zero, fact_1235_less__add__iff2, fact_5101_minus__diff__eq, fact_3433_old_Oprod_Oexhaust, fact_6901_of__nat__numeral, fact_2442_divide__strict__right__mono, fact_3261_minf_I2_J, fact_2519_vebt__member_Osimps_I3_J, fact_9331_Suc__nat__eq__nat__zadd1, fact_5287_numeral__eq__neg__one__iff, fact_5359_semiring__norm_I171_J, fact_9206_log__base__root, fact_8436_pochhammer__pos, fact_3867_order__antisym, fact_3598_max__0R, fact_1830_nonzero__divide__mult__cancel__left, fact_2994_Suc__n__div__2__gt__zero, fact_6630_numeral__code_I3_J, fact_9501_not__negative__int__iff, fact_7821_cos__one__sin__zero, fact_4747_is__unit__mult__iff, fact_9114_real__of__int__floor__gt__diff__one, fact_4297_order__le__neq__trans, fact_6411_semiring__norm_I4_J, fact_1682_nonzero__mult__div__cancel__right, fact_4068_order__less__trans, fact_4231_dual__order_Oorder__iff__strict, fact_5428_Power_Oring__1__class_Opower__minus__even, fact_3762_nat__mult__max__left, fact_1061_lift__Suc__mono__less__iff, fact_8610_fact__double, fact_6917_of__nat__mult, fact_2319_mult__less__0__iff, fact_7324_real__archimedian__rdiv__eq__0, fact_7500_norm__triangle__le__diff, fact_3987_ord__eq__less__trans, fact_9572_Chebyshev__sum__upper__nat, fact_5784_group__cancel_Osub2, fact_3101_verit__comp__simplify1_I3_J, fact_2265_not__numeral__less__zero, fact_3147_set__bit__greater__eq, fact_3035_flip__bit__Suc, fact_7026_dbl__dec__simps_I1_J, fact_5697_zero__neq__neg__numeral, fact_8087_tan__half, fact_7163_of__int__le__neg__numeral__power__cancel__iff, fact_5380_le__divide__eq__numeral1_I2_J, fact_7632_of__int__round__ge, fact_3277_minf_I5_J, fact_2216_mult__nonneg__nonpos, fact_1306_Diff__empty, fact_2097_power__not__zero, fact_2908_power__diff, fact_4812_less__eq__dvd__minus, fact_3895_dual__order_Otrans, fact_1820_eq__divide__eq__numeral1_I1_J, fact_4938_even__iff__mod__2__eq__zero, fact_3316_minf_I6_J, fact_1623_le__add__same__cancel1, fact_8420_pochhammer__0, fact_5571_minus__diff__commute, fact_9084_square__powr__half, fact_6633_power__numeral__odd, fact_6805_divmod__algorithm__code_I2_J, fact_970_fst, fact_4361_linorder__le__less__linear, fact_7508_norm__diff__ineq, fact_90_numeral__plus__numeral, fact_3963_order__antisym__conv, fact_796_diff__le__eq, fact_9177_real__root__mult, fact_5764_nonzero__minus__divide__right, fact_4600_dvd__mult2, fact_128_bit__concat__def, fact_7606_sum__gp__strict, fact_8985_norm__ii, fact_4655_dvd__add, fact_1462_low__def, fact_39_self__le__ge2__pow, fact_5156_neg__less__pos, fact_5442_power__minus__odd, fact_750_le__diff__iff, fact_4262_order_Ostrict__implies__order, fact_1651_add__less__same__cancel2, fact_4494_unit__div__1__div__1, fact_760_le__numeral__extra_I4_J, fact_6971_of__int__mult, fact_7989_fact__not__neg, fact_7264_of__nat__diff, fact_9560_diff__rat__def, fact_1468_valid__tree__deg__neq__0, fact_7530_round__unique, fact_629_power__inject__exp, fact_8370_cos__arccos__abs, fact_824_one__plus__numeral__commute, fact_1094_less__iff__Suc__add, fact_5057_add_Oinverse__neutral, fact_887_neq__if__length__neq, fact_4448_div__dvd__div, fact_4475_dvd__add__times__triv__left__iff, fact_6978_of__int__diff, fact_8317_fold__atLeastAtMost__nat_Oelims, fact_985_deg__SUcn__Node, fact_3132_mod__neg__neg__trivial, fact_3085_verit__la__disequality, fact_6366_abs__le__self__iff, fact_8773_prod_OatMost__shift, fact_7341_double__arith__series, fact_1233_ordered__ring__class_Ole__add__iff1, fact_2257_mult__mono, fact_5529_verit__negate__coefficient_I2_J, fact_5418_diff__numeral__special_I11_J, fact_7631_of__int__round__le, fact_5780_square__eq__1__iff, fact_1292_DiffI, fact_573_add__diff__cancel, fact_1884_Suc__times__numeral__mod__eq, fact_1085_Suc__le__eq, fact_5507_le__minus__iff, fact_9291_take__bit__decr__eq, fact_4330_order__le__less__subst1, fact_7182_mult__of__nat__commute, fact_6776_dbl__dec__simps_I3_J, fact_6759_odd__mod__4__div__2, fact_4110_order__less__subst2, fact_9173_real__root__ge__1__iff, fact_866_power__less__imp__less__exp, fact_4793_power__le__dvd, help_If_2_1_If_001t__Int__Oint_T, fact_3807_dbl__simps_I3_J, fact_5449_diff__numeral__special_I4_J, fact_8225_real__sqrt__sum__squares__eq__cancel2, fact_1119_invar__vebt_Ointros_I3_J, fact_3933_order__eq__refl, fact_2125_plus__nat_Oadd__0, fact_5347_mult__neg__numeral__simps_I1_J, fact_6133_sum__diff, fact_9680_plus__complex_Ocode, fact_1524_add__cancel__right__left, fact_5407_add__neg__numeral__special_I9_J, fact_2856_convex__bound__le, fact_5354_semiring__norm_I170_J, fact_4279_order__less__le, fact_9071_powr__nonneg__iff, fact_6288_crossproduct__eq, fact_579_add__diff__cancel__left, fact_6987_of__int__power, fact_7017_of__nat__Suc, fact_4096_order__less__irrefl, fact_647_one__add__one, fact_3192_atLeastatMost__subset__iff, fact_996_div__by__1, fact_9744_diff__Suc, fact_9028_zero__less__log__cancel__iff, fact_104_is__num__normalize_I1_J, fact_1204_add__mono1, fact_4602_dvd__mult2, fact_6434_sum__zero__power, fact_1850_div__mult__self1__is__m, fact_9223_sgn__mod, fact_5565_add_Oinverse__distrib__swap, fact_2628_add__nonneg__pos, fact_1629_add__le__same__cancel1, fact_6912_of__nat__add, fact_6621_sum__power__add, fact_3972_gt__ex, fact_7433_real__arch__simple, fact_1789_one__eq__mult__iff, fact_7002_dbl__inc__simps_I4_J, fact_7027_dbl__dec__simps_I1_J, fact_6183_power2__eq__iff, fact_7071_of__int__le__numeral__iff, fact_6348_abs__add__abs, fact_4006_linorder__cases, fact_6851_dbl__inc__simps_I3_J, fact_2033_gr__implies__not__zero, fact_5824_minus__real__def, fact_412_add_Ocommute, fact_7792_sin__cos__squared__add3, fact_6984_of__int__eq__of__int__power__cancel__iff, fact_2330_mult__pos__pos, fact_1261_pred__less__length__list, fact_4827_unity__coeff__ex, fact_5179_diff__0, fact_1628_add__le__same__cancel2, fact_6689_abs__square__eq__1, fact_1015_Suc__numeral, fact_9646_abs__Re__le__cmod, fact_4171_antisym__conv1, fact_791_diff__add, fact_3923_order__subst2, fact_5942_not__one__le__neg__numeral, fact_430_group__cancel_Oadd1, fact_166_divide__less__eq__numeral1_I1_J, fact_5070_mult__minus__left, fact_6391_semiring__norm_I81_J, fact_8271_sin__arctan, fact_7121_of__nat__less__numeral__power__cancel__iff, fact_8629_gbinomial__r__part__sum, fact_5597_sum__mono, fact_773_comm__monoid__mult__class_Omult__1, fact_6997_of__nat__of__bool, fact_6949_of__nat__power__eq__of__nat__cancel__iff, fact_4620_dvdE, fact_8196_exp__of__nat2__mult, fact_8178_sums__mult__iff, fact_4859_unit__eq__div2, fact_1971_mod__mult__right__eq, fact_7086_of__int__1__less__iff, fact_809_add__diff__inverse__nat, fact_9425_pow_Osimps_I1_J, fact_4084_ord__less__eq__subst, fact_5279_add__neg__numeral__special_I7_J, fact_9622_integer__of__num__triv_I1_J, fact_5305_left__minus__one__mult__self, fact_3053_div__positive__int, fact_1234_less__add__iff2, fact_638_power__strict__increasing__iff, fact_2439_zero__less__divide__iff, fact_8970_forall__pos__mono, fact_462_add__mono__thms__linordered__semiring_I1_J, fact_7855_sin__plus__sin, fact_8339_sin__arccos, fact_9528_int__numeral__or__not__num__neg, fact_8571_pochhammer__absorb__comp, fact_6230_minus__one__power__iff, fact_123_both__member__options__ding, fact_2879_power__strict__decreasing, fact_9110_powr__less__iff, fact_8074_Maclaurin__zero, fact_4051_linorder__neqE, fact_7098_of__int__eq__numeral__power__cancel__iff, fact_3167_zdiv__mono2__neg__lemma, fact_5936_not__numeral__le__neg__one, fact_532_add__mono__thms__linordered__field_I4_J, fact_9335_nat__abs__int__diff, fact_2779_one__less__mult, fact_2974_power2__less__imp__less, fact_9285_eq__nat__nat__iff, fact_2906_power__diff, fact_1828_nonzero__divide__mult__cancel__right, fact_9471_or__not__num__neg_Osimps_I2_J, fact_8358_arccos__1, fact_9449_or__nat__numerals_I4_J, fact_2288_add__nonpos__nonpos, fact_6887_of__nat__0__eq__iff, fact_8558_gbinomial__factors, fact_9546_not__int__rec, fact_3564_max_Oabsorb2, fact_1188_option_Oexpand, fact_1501_mult__cancel__right, fact_6069_sum_Omono__neutral__cong__right, fact_1895_power2__eq__iff__nonneg, fact_2212_mult__nonpos__nonneg, fact_4941_odd__iff__mod__2__eq__one, fact_1106_plus__1__eq__Suc, fact_5194_mult__minus1__right, fact_795_diff__le__eq, fact_7191_int__diff__cases, fact_1545_cancel__comm__monoid__add__class_Odiff__cancel, fact_1741_power__0__Suc, fact_1157_right__diff__distrib_H, fact_6543_abs__mult__pos, fact_5110_of__bool__less__eq__iff, fact_4451_signed__take__bit__of__0, fact_3901_antisym, fact_3815_dual__order_Orefl, fact_7917_cos__treble__cos, fact_9269_take__bit__diff, fact_6401_divide__le__0__abs__iff, fact_5517_le__imp__neg__le, fact_3513_finite__image__set, fact_872_power__strict__increasing, fact_8942_sum__choose__lower, fact_64_valid__member__both__member__options, fact_7371_lemma__termdiff3, fact_6681_mod__exhaust__less__4, fact_851_nat__le__add__iff1, fact_7476_nonzero__norm__divide, fact_7185_mult__of__nat__commute, fact_183_mult__le__mono2, fact_9224_less__mask, fact_3918_order__subst1, fact_4704_minf_I10_J, fact_174_power__add__numeral2, fact_3746_max_Ostrict__coboundedI2, fact_4604_dvd__mult2, fact_1906_not__mod__2__eq__1__eq__0, fact_3988_ord__eq__less__trans, fact_9532_and__not__numerals_I7_J, fact_1638_zero__less__double__add__iff__zero__less__single__add, fact_2019_VEBT__internal_Onaive__member_Osimps_I1_J, fact_2803_vebt__insert_Osimps_I3_J, fact_3049_zdiv__eq__0__iff, fact_7211_of__nat__less__0__iff, fact_2062_mult__left__cancel, fact_4364_linorder__le__less__linear, fact_3827_dbl__simps_I5_J, fact_4363_linorder__le__less__linear, fact_7967_fact__Suc__0, fact_5810_dvd__div__neg, fact_6332_abs__numeral, fact_4250_dual__order_Ostrict__trans2, fact_4204_order_Ostrict__iff__order, fact_7067_of__nat__le__of__nat__power__cancel__iff, fact_9434_signed__take__bit__eq__concat__bit, fact_7481_norm__mult__less, fact_7103_numeral__power__eq__of__int__cancel__iff, fact_264_power2__eq__square, fact_3436_finite__Collect__le__nat, fact_137_mult__numeral__left__semiring__numeral, fact_1218_eq__add__iff2, fact_2976_power2__less__imp__less, fact_2388_less__numeral__extra_I1_J, fact_5856_sum_Orelated, fact_5473_neg__one__odd__power, fact_8207_ln__ge__iff, fact_6454_abs__le__D1, fact_2757_power__le__imp__le__base, fact_5523_minus__less__iff, fact_4271_order__le__less, fact_4244_dual__order_Ostrict__trans1, fact_1238_less__add__iff1, fact_7321_of__nat__less__two__power, fact_9148_complex__split__polar, fact_7241_nat__int__comparison_I3_J, fact_141_numeral__times__numeral, fact_2155_divmod__digit__0_I2_J, fact_1165_option_OdiscI, fact_209_mult__numeral__1__right, fact_4263_dual__order_Ostrict__implies__order, fact_5060_neg__less__iff__less, fact_7473_norm__sum, fact_989_nat_Oinject, fact_8514_pochhammer__of__nat__eq__0__lemma_H, fact_8257_arith__geo__mean__sqrt, fact_1644_less__add__same__cancel2, fact_7677_suminf__mult2, fact_803_diff__less__eq, fact_1520_add__cancel__left__right, fact_6473_verit__eq__simplify_I12_J, fact_9287_unset__bit__nat__def, fact_2673_mult__left__le__one__le, fact_6163_minus__divide__add__eq__iff, fact_4654_dvd__add, fact_9288_sgn__root, fact_4965_parity__cases, fact_512_divide__divide__eq__left_H, fact_2149_lambda__zero, fact_4044_dual__order_Ostrict__implies__not__eq, fact_9372_AND__upper2_H, fact_3711_max_OcoboundedI1, fact_8974_exp__plus__inverse__exp, fact_7999_fact__ge__1, fact_8954_choose__linear__sum, fact_7506_norm__triangle__sub, fact_8072_arctan__tan, fact_369_member__inv, fact_6524_abs__less__iff, fact_9632_csqrt_Osimps_I1_J, fact_4890_even__zero, fact_1720_div__self, fact_952_minminNull, fact_7181_mult__of__int__commute, fact_6653_sum_Onat__ivl__Suc_H, fact_4616_dvdI, fact_1110_power__gt1, fact_180_le__square, fact_1041_le__SucI, fact_4971_zero__le__odd__power, fact_7868_sin__zero__iff__int2, fact_2590_mult__strict__mono_H, fact_6227_minus__one__power__iff, fact_7942_sin__zero__iff, fact_7265_of__nat__diff, fact_2818_mult__less__cancel__left1, fact_9939_eq__rat_I1_J, fact_149_distrib__right__numeral, fact_2788_nat__induct__non__zero, fact_290_add__less__mono1, fact_6515_abs__le__D2, fact_9844_num__of__nat__double, fact_4730_unit__mult__right__cancel, fact_7528_divmod__nat__if, fact_4103_order__less__subst1, fact_2071_zero__neq__one, fact_8451_binomial__Suc__Suc__eq__times, fact_1977_mult__mod__right, fact_7149_neg__numeral__power__eq__of__int__cancel__iff, fact_9178_real__root__minus, fact_363_num__double, fact_5282_diff__numeral__special_I12_J, fact_6725_power__mono__even, fact_8975_plus__inverse__ge__2, fact_3131_zle__diff1__eq, fact_6754_mask__eq__sum__exp__nat, fact_5755_less__minus__one__simps_I4_J, fact_4886_mod__eq__dvd__iff__nat, fact_2077_comm__monoid__add__class_Oadd__0, fact_2539_div__mult__mod__eq, fact_8501_pochhammer__eq__0__iff, fact_6701_cong__exp__iff__simps_I7_J, fact_5825_ln__one__minus__pos__upper__bound, fact_3920_order__subst2, fact_3882_linorder__wlog, fact_7750_summable__power__series, fact_8221_real__le__lsqrt, fact_2381_not__one__less__zero, fact_5489_dvd__antisym, fact_5339_mult__neg__numeral__simps_I3_J, fact_2957_nat__induct2, fact_8732_mod__prod__eq, fact_4011_dual__order_Oasym, fact_2934_power2__le__imp__le, fact_2094_power__not__zero, fact_3862_ord__le__eq__trans, fact_6976_of__int__diff, fact_6661_odd__numeral, fact_8248_complex__norm, fact_3999_antisym__conv3, fact_7804_cos__npi2, fact_2407_add__neg__neg, fact_8059_tan__mono__lt__eq, fact_2603_mult__left__le__imp__le, fact_2183_div__positive, fact_9936_Fract__of__nat__eq, fact_1650_add__less__same__cancel2, fact_7537_lessThan__iff, fact_1555_diff__0__right, fact_7268_int__cases4, fact_237_eq__imp__le, fact_8329_arcsin__sin, fact_8151_real__sqrt__less__mono, fact_2585_mult__less__cancel__left, fact_4788_le__imp__power__dvd, fact_5983_mult__1s__ring__1_I2_J, fact_1056_lift__Suc__mono__less, fact_1859_le__divide__eq__1__neg, fact_295_le__add1, fact_106_is__num__normalize_I1_J, fact_1244_invar__vebt_Ointros_I5_J, fact_7448_norm__neg__numeral, fact_6716_abs__square__le__1, fact_1958_mod__le__divisor, fact_6554_abs__eq__iff_H, fact_4573_dvd__field__iff, fact_5408_add__neg__numeral__special_I9_J, fact_1249_vebt__insert_Osimps_I4_J, fact_7023_of__nat__0__less__iff, fact_3982_order_Oasym, fact_2296_add__increasing2, fact_4862_div__mult__unit2, fact_418_add_Oleft__cancel, fact_4332_order__le__less__subst2, fact_1710_mult__divide__mult__cancel__left__if, fact_2706_pos__less__divide__eq, fact_9200_odd__real__root__unique, fact_1070_power__Suc, fact_147_semiring__norm_I68_J, fact_7681_suminf__diff, fact_458_add__mono, fact_8272_exp__bound__lemma, fact_653_power__increasing__iff, fact_2286_add__nonneg__eq__0__iff, fact_1492_mult__eq__0__iff, fact_6591_abs__diff__le__iff, fact_1851_Suc__mod__mult__self1, fact_5072_mult__minus__left, fact_1959_invar__vebt_Ointros_I1_J, fact_8328_arcsin__bounded, fact_2714_divide__strict__left__mono__neg, fact_8771_prod_OatMost__shift, fact_2182_div__positive, fact_5933_neg__numeral__le__neg__one, fact_5028_add_Oinverse__inverse, fact_131_fgh, fact_317_times__divide__eq__right, fact_1319_DiffD1, fact_9072_powr__less__cancel__iff, fact_2845_pos__le__divide__eq, fact_4992_even__mask__div__iff, fact_8821_prod__dvd__prod__subset, fact_2234_mult__right__mono__neg, fact_3250_pinf_I7_J, fact_9305_nat__less__eq__zless, fact_32_abc, fact_7219_of__nat__neq__0, fact_5415_diff__numeral__special_I11_J, fact_5756_numeral__times__minus__swap, fact_2428_divide__neg__neg, fact_4168_antisym__conv1, fact_8438_pochhammer__eq__0__mono, fact_6416_semiring__norm_I16_J, fact_9117_powr__mult__base, fact_5003_signed__take__bit__rec, fact_2535_mod__div__mult__eq, fact_6557_abs__eq__iff_H, help_If_1_1_If_001t__Rat__Orat_T, fact_2291_add__nonneg__nonneg, fact_2703_pos__divide__less__eq, fact_1659_diff__gt__0__iff__gt, fact_7548_round__1, fact_276_power2__sum, fact_4360_order__less__le__subst2, fact_7317_real__of__int__div__aux, fact_56_Collect__mem__eq, fact_621_right__diff__distrib__numeral, fact_7811_sin__2pi__minus, fact_6666_power3__eq__cube, fact_3942_ord__eq__le__subst, fact_8619_gbinomial__partial__row__sum, fact_4036_dual__order_Ostrict__trans, fact_3608_max__number__of_I1_J, fact_3160_plus__int__code_I1_J, fact_5291_neg__one__eq__numeral__iff, fact_6624_sum__power__add, fact_1575_division__ring__divide__zero, fact_307_field__sum__of__halves, fact_3896_dual__order_Otrans, fact_5099_minus__diff__eq, fact_4957_even__flip__bit__iff, fact_30_div__le__mono, fact_7037_of__int__less__0__iff, fact_7009_of__nat__le__0__iff, fact_10135_filterlim__pow__at__bot__even, fact_8470_pochhammer__0__left, fact_1022_Nat_OlessE, fact_3592_max__Suc__Suc, fact_2630_add__nonpos__neg, fact_3109_verit__sum__simplify, fact_2409_divide__le__0__iff, fact_2944_power2__less__0, fact_9304_sgn__real__def, fact_810_less__diff__conv, fact_8000_fact__mono, fact_7468_sum__norm__le, fact_496_add__mono__thms__linordered__field_I1_J, fact_3146_Euclidean__Division_Opos__mod__sign, fact_4954_even__set__bit__iff, fact_2306_add__increasing, fact_9473_bit__nat__iff, fact_7769_machin__Euler, fact_3681_max_Oorder__iff, fact_9412_signed__take__bit__negative__iff, fact_9495_xor__int__rec, fact_2276_zero__less__one__class_Ozero__le__one, fact_8402_pochhammer__double, fact_5083_mult__minus__right, fact_2713_divide__strict__left__mono__neg, fact_2280_add__nonpos__eq__0__iff, fact_2373_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_203_power__mult, fact_564_mult_Oright__neutral, fact_8531_times__binomial__minus1__eq, fact_4874_unit__imp__mod__eq__0, fact_2842_pos__divide__le__eq, fact_594_add__diff__cancel__right_H, fact_5424_minus__1__mod__2__eq, fact_4536_power__less__zero__eq, fact_2366_mult__strict__right__mono, fact_981_le__add__diff__inverse2, fact_6382_abs__neg__one, fact_4639_one__dvd, fact_6870_of__nat__eq__iff, fact_1150_right__diff__distrib, fact_3927_order__subst2, fact_210_mult__numeral__1__right, fact_3087_verit__comp__simplify1_I2_J, fact_6426_power2__abs, fact_2569_mult__le__cancel__left, fact_8325_arcsin__lt__bounded, fact_7966_fact__Suc__0, fact_1868_zero__eq__power2, fact_3619_max__0__1_I3_J, fact_1679_sum__squares__eq__zero__iff, fact_553_in__set__conv__nth, fact_5340_mult__neg__numeral__simps_I3_J, fact_6741_sum__telescope_H_H, fact_5215_divide__minus1, fact_7699_summable__0__powser, fact_7493_norm__triangle__ineq, fact_9378_inc_Osimps_I2_J, fact_4565_odd__two__times__div__two__succ, fact_817_one__le__numeral, fact_911_power2__diff, fact_3020_inrange, fact_7859_cos__diff__cos, fact_6964_of__int__eq__1__iff, fact_4302_order__le__neq__trans, fact_2412_zero__le__divide__iff, fact_2054_no__zero__divisors, 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fact_1578_divide__cancel__right, fact_4935_even__two__times__div__two, fact_4003_linorder__cases, fact_1498_mult__cancel__left, fact_979_le__add__diff__inverse2, fact_144_nat__add__left__cancel__less, fact_2605_mult__left__le__imp__le, fact_9624_integer__of__num__triv_I2_J, fact_5681_split__of__bool, fact_82_member__bound, fact_1892_power__decreasing__iff, fact_5813_dvd__neg__div, fact_2244_mult__left__mono__neg, fact_7111_of__int__less__of__int__power__cancel__iff, fact_357_add__le__cancel__left, fact_5047_neg__equal__0__iff__equal, fact_9507_bit__not__int__iff, fact_4923_even__even__mod__4__iff, fact_534_both__member__options__from__chilf__to__complete__tree, fact_7824_sin__zero__norm__cos__one, fact_9379_inc_Osimps_I3_J, fact_2510_nat__mult__less__cancel1, fact_9751_Suc__0__mod__numeral, fact_1717_div__self, fact_424_group__cancel_Oadd2, fact_6886_of__nat__0, fact_1511_double__zero__sym, fact_1558_diff__self, fact_8140_real__sqrt__pow2, fact_9743_max__Suc2, 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fact_1467_valid__0__not, fact_9116_powr__neg__one, fact_8100_fact__diff__Suc, help_If_2_1_If_001t__Rat__Orat_T, fact_6794_dbl__dec__simps_I2_J, fact_510_divide__divide__times__eq, fact_3179_int__ge__induct, fact_4137_order__less__imp__not__eq, fact_2827_mult__less__cancel__right2, fact_9367_and__minus__numerals_I6_J, fact_7527_of__nat__code__if, fact_2474_divide__eq__eq, fact_762_le__numeral__extra_I4_J, fact_7898_cos__double__less__one, fact_8545_binomial__less__binomial__Suc, fact_6188_uminus__power__if, fact_2909_div__if, fact_6525_abs__less__iff, fact_133_deg__deg__n, fact_8057_tan__monotone, fact_4428_set__decode__Suc, fact_3003_vebt__member_Oelims_I1_J, fact_4613_dvd__def, fact_6913_of__nat__add, fact_8102_sin__tan, fact_263_power2__eq__square, fact_2666_mult__le__one, fact_2530_mult__div__mod__eq, fact_4642_dvd__add__right__iff, fact_8491_pochhammer__rec, fact_4331_order__le__less__subst2, fact_5588_minus__divide__right, fact_2608_mult__right__le__imp__le, fact_4005_linorder__cases, fact_7786_sin__periodic__pi2, fact_5986_divide__eq__minus__1__iff, fact_5446_diff__numeral__special_I3_J, fact_6402_divide__le__0__abs__iff, fact_8695_sum_OatMost__Suc, fact_4627_dvd__productE, fact_4787_le__imp__power__dvd, fact_6153_pos__less__minus__divide__eq, fact_1748_power__zero__numeral, fact_4908_odd__even__add, fact_9142_complex__of__real__add__Complex, fact_1523_add__cancel__left__right, fact_3916_order__subst1, fact_6549_abs__eq__mult, fact_5976_mult__1s__ring__1_I1_J, fact_9058_log2__of__power__less, fact_9104_log__powr, fact_6522_abs__ge__minus__self, fact_7884_cos__is__zero, fact_7212_of__nat__less__0__iff, fact_9341_root__sgn__power, fact_9186_real__root__abs, fact_4424_even__succ__div__exp, fact_3173_q__pos__lemma, fact_5490_signed__take__bit__minus, fact_468_add__mono__thms__linordered__semiring_I2_J, fact_1380_equals0I, fact_8268_exp__ge__one__plus__x__over__n__power__n, fact_7613_diff__power__eq__sum, fact_5445_diff__numeral__special_I3_J, fact_9238_set__encode__def, fact_87_numeral__plus__numeral, fact_5946_neg__numeral__less__one, fact_7602_geometric__sum, fact_71_numeral__eq__iff, fact_5745_neg__eq__iff__add__eq__0, fact_5757_numeral__times__minus__swap, fact_7008_dbl__inc__simps_I5_J, fact_2390_less__numeral__extra_I1_J, fact_9748_prod__decode__aux_Oelims, fact_8195_exp__of__nat2__mult, fact_2913_add__eq__if, fact_2420_divide__nonpos__nonpos, fact_3155_zmod__eq__0__iff, fact_7050_numeral__power__eq__of__nat__cancel__iff, fact_4308_order__neq__le__trans, fact_4530_set__decode__0, fact_7845_cos__ge__minus__one, fact_5452_diff__numeral__special_I4_J, fact_5465_neg__one__even__power, fact_2884_power__decreasing, fact_3926_order__subst2, fact_7842_cos__inj__pi, fact_1591_less__nat__zero__code, fact_998_lessI, fact_202_power__commuting__commutes, fact_7587_sum__lessThan__telescope_H, fact_81_pow__sum, fact_7031_of__int__0__le__iff, fact_1815_less__divide__eq__1__neg, fact_6144_less__minus__divide__eq, fact_208_div__mult2__eq, fact_5674_split__of__bool__asm, fact_160_le__divide__eq__numeral1_I1_J, fact_5147_neg__less__eq__nonneg, fact_845_power__one__over, fact_461_add__mono__thms__linordered__semiring_I1_J, fact_3322_minf_I8_J, fact_5709_not__numeral__less__neg__numeral, fact_9146_complex__of__real__i, fact_7604_round__diff__minimal, fact_8206_lemma__exp__total, fact_8463_gbinomial__of__nat__symmetric, fact_1500_mult__cancel__left, fact_337_inthall, fact_1043_le__Suc__eq, fact_8340_monoseq__def, fact_7849_sin__times__sin, fact_2971_div__exp__mod__exp__eq, fact_2308_add__decreasing, fact_619_numeral__eq__one__iff, fact_7024_of__nat__0__less__iff, fact_4214_order_Ostrict__trans2, fact_2768_diff__frac__eq, fact_1418_subset__iff, fact_9052_log__of__power__less, fact_6774_zdvd1__eq, fact_1114_linorder__neqE__linordered__idom, fact_1488_mult__zero__right, fact_9068_floor__log__nat__eq__powr__iff, fact_2562_minus__div__mult__eq__mod, fact_853_nat__eq__add__iff1, fact_8561_gbinomial__rec, fact_687_diff__commute, fact_6175_add__divide__eq__if__simps_I6_J, fact_6272_minus__power__mult__self, fact_7258_of__nat__max, fact_7318_real__of__nat__div__aux, fact_4195_order_Oorder__iff__strict, fact_8456_gbinomial__pochhammer, fact_2027_less__numeral__extra_I3_J, fact_2792_div__greater__zero__iff, fact_1970_mod__mult__right__eq, fact_4469_unit__prod, fact_5_abh, fact_8494_pochhammer__Suc, fact_6951_of__nat__power__eq__of__nat__cancel__iff, fact_7703_powser__split__head_I3_J, fact_8502_pochhammer__eq__0__iff, fact_524_add__le__less__mono, fact_7667_summable__ignore__initial__segment, fact_9443_take__bit__Suc__from__most, fact_5814_dvd__neg__div, fact_8105_sin__paired, fact_8927_prod_Omono__neutral__left, fact_3917_order__subst1, fact_2683_power__less__imp__less__base, fact_7087_of__int__1__less__iff, fact_8030_tan__def, fact_2995_div__2__gt__zero, fact_2470_eq__divide__eq, fact_5405_add__neg__numeral__special_I9_J, fact_4033_dual__order_Ostrict__trans, fact_2760_div__add__self1, 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fact_1637_zero__less__double__add__iff__zero__less__single__add, fact_5895_not__zero__le__neg__numeral, fact_1521_add__cancel__left__right, fact_6033_real__0__less__add__iff, fact_3947_ord__eq__le__subst, fact_502_add__mono__thms__linordered__field_I5_J, fact_7837_sin__squared__eq, fact_4357_order__less__le__subst2, fact_3768_max__def__raw, fact_3691_max_Ocobounded2, fact_2678_sum__squares__le__zero__iff, fact_9222_not__mask__negative__int, fact_2440_zero__less__divide__iff, fact_8563_gbinomial__index__swap, fact_2037_zero__neq__numeral, fact_6737_sum__natinterval__diff, fact_8253_arsinh__real__aux, fact_2332_mult__pos__neg2, fact_321_divide__divide__eq__left, fact_4126_order__less__imp__triv, fact_3143_zmult__zless__mono2, fact_440_add__le__imp__le__right, fact_4692_zdvd__zdiffD, fact_6667_power3__eq__cube, fact_4796_dvd__power__le, fact_1646_less__add__same__cancel1, fact_683_diff__right__commute, fact_786_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, fact_8959_real__sqrt__inverse, fact_4905_odd__one, fact_5235_ln__less__zero__iff, fact_2405_add__neg__neg, fact_7689_suminf__eq__zero__iff, fact_2376_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_8142_real__sqrt__sum__squares__mult__squared__eq, fact_393_ab__semigroup__mult__class_Omult__ac_I1_J, fact_742_diff__diff__eq, fact_8120_exp__zero, fact_2193_zero__le__numeral, fact_9302_nat__minus__as__int, fact_7367_floor__exists1, fact_7486_norm__add__less, fact_2423_divide__right__mono__neg, fact_1013_diff__Suc__diff__eq2, fact_4672_dvd__div__eq__cancel, fact_906_nat__1__add__1, fact_6722_power__mono__even, fact_2355_mult__strict__left__mono__neg, fact_7793_sin__npi, fact_593_add__diff__cancel__right_H, fact_6339_abs__mult__self__eq, fact_5295_neg__one__eq__numeral__iff, fact_2592_mult__strict__mono_H, fact_2064_mult__right__cancel, fact_852_nat__eq__add__iff2, fact_7279_of__int__nonneg, fact_540__092_060open_062max__in__set_A_Iset__vebt_H_A_ItreeList_A_B_Athe_A_Ivebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_J_Amaxy_092_060close_062, fact_189_power__commutes, fact_2930_half__gt__zero, fact_1619_le__add__same__cancel2, fact_4188_not__le__imp__less, fact_3093_verit__comp__simplify1_I1_J, fact_4164_nless__le, fact_3019_verit__le__mono__div, fact_942_summaxma, fact_6437_power__even__abs__numeral, fact_9565_subset__eq__atLeast0__lessThan__finite, fact_9518_concat__bit__def, fact_9538_and__not__numerals_I6_J, fact_220_power__add, fact_7431_monoseq__realpow, fact_2282_add__nonpos__eq__0__iff, fact_5410_diff__numeral__special_I10_J, fact_229_less__not__refl2, fact_5338_mult__neg__numeral__simps_I3_J, fact_2463_nonzero__divide__eq__eq, fact_9541_push__bit__minus__one, fact_4088_ord__less__eq__subst, fact_3275_minf_I5_J, fact_6849_dbl__inc__simps_I3_J, fact_3159_plus__int__code_I2_J, fact_3652_list__update__swap, fact_6297_power__minus1__odd, fact_4524_even__mod__2__iff, fact_5273_add__neg__numeral__special_I8_J, fact_9318_nat__power__eq, fact_1691_div__mult__mult1, fact_7782_sin__pi__minus, fact_2452_zero__le__power, fact_8779_prod_Ointer__filter, fact_2272_linordered__nonzero__semiring__class_Ozero__le__one, fact_6577_abs__of__neg, fact_9393_and__nat__numerals_I3_J, fact_9338_take__bit__nat__less__self__iff, fact_7759_pi__half__le__two, fact_4224_dense__ge__bounded, fact_7288_of__int__lessD, fact_136_mult__numeral__left__semiring__numeral, fact_5021_neg__equal__iff__equal, fact_3845_nle__le, fact_6158_eq__divide__eq__numeral_I2_J, fact_9656_cmod__plus__Re__le__0__iff, fact_1145_combine__common__factor, fact_7980_fact__2, fact_3861_ord__le__eq__trans, fact_4975_zero__le__even__power, fact_2207_mult__nonneg__nonpos2, fact_7504_norm__triangle__ineq4, fact_3136_int__distrib_I4_J, fact_4335_order__le__less__subst2, fact_2400_add__pos__pos, fact_3022_set__bit__0, fact_9112_real__of__int__floor__add__one__gt, fact_4229_dual__order_Oorder__iff__strict, fact_3105_verit__comp__simplify1_I3_J, fact_4916_dvd__power, fact_2447_power__mono, fact_79__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062, fact_121_valid__insert__both__member__options__add, fact_6423_abs__power2, fact_5718_zero__neq__neg__one, fact_3851_order__class_Oorder__eq__iff, fact_5556_is__num__normalize_I8_J, fact_2984_sum__power2__gt__zero__iff, fact_1904_sum__power2__eq__zero__iff, fact_7741_pi__half__neq__two, fact_474_add__less__imp__less__right, fact_8188_sums__Suc, fact_2220_mult__nonneg__nonneg, fact_1522_add__cancel__left__right, fact_9429_Icc__eq__insert__lb__nat, fact_2680_sum__squares__le__zero__iff, fact_7597_power__diff__1__eq, fact_4449_div__dvd__div, fact_3170_pos__zmult__eq__1__iff, fact_285_less__mono__imp__le__mono, fact_125_div__exp__eq, fact_9339_take__bit__Suc__minus__bit0, fact_431_add__mono__thms__linordered__semiring_I4_J, fact_9566_atLeastLessThanSuc, fact_6260_divide__le__eq__numeral_I2_J, fact_995_div__by__1, fact_1976_mult__mod__right, fact_606_diff__diff__cancel, fact_8063_add__tan__eq, fact_7303_int__le__real__less, fact_7232_of__nat__mono, fact_6527_abs__less__iff, fact_7761_pi__half__ge__zero, fact_2045_mult__not__zero, fact_9524_and__not__numerals_I2_J, fact_6162_minus__divide__add__eq__iff, fact_286_add__lessD1, fact_6968_of__int__1, fact_1666_mult__cancel__left2, fact_2233_mult__right__mono__neg, fact_6314_abs__idempotent, fact_7294_mod__mult2__eq_H, fact_2707_mult__imp__div__pos__less, fact_1098_Suc__diff__Suc, fact_7603_round__diff__minimal, fact_663_numeral__plus__one, fact_2778_diff__Suc__less, fact_7449_norm__neg__numeral, fact_8055_tan__gt__zero, fact_8008_fact__dvd, fact_7510_norm__triangle__ineq2, fact_9077_numeral__powr__numeral__real, fact_5023_neg__equal__iff__equal, fact_6484_abs__not__less__zero, fact_6043_sum__pos2, fact_6304_vebt__buildup_Osimps_I3_J, fact_7228_less__imp__of__nat__less, fact_258_mult__2, fact_5795_ab__group__add__class_Oab__diff__conv__add__uminus, fact_3881_linorder__wlog, fact_1121_power__odd__eq, fact_5349_mult__neg__numeral__simps_I1_J, fact_1211_linordered__semidom__class_Oadd__diff__inverse, fact_2359_mult__strict__left__mono, fact_8410_gchoose__row__sum__weighted, fact_3528_finite__has__maximal, fact_5518_less__minus__iff, fact_4918_dvd__power, fact_76__092_060open_062res_A_060_Ama_092_060close_062, fact_7352_arith__series, fact_4382_bot_Oextremum__uniqueI, fact_8589_pochhammer__minus_H, fact_6604_numeral__Bit1, fact_5545_minus__mult__commute, fact_3934_linorder__linear, fact_2843_pos__divide__le__eq, fact_2406_add__neg__neg, fact_6512_abs__le__D2, fact_7807_sin__cos__squared__add2, fact_9332_nat__less__iff, fact_1208_less__add__one, fact_2949_exp__add__not__zero__imp__left, fact_922_Skolem__list__nth, fact_9343_take__bit__int__greater__eq__self__iff, fact_7580_sum_OlessThan__Suc__shift, fact_2096_power__not__zero, fact_9201_odd__real__root__power__cancel, fact_6910_of__nat__add, fact_6463_abs__one, fact_7840_sin__ge__zero, fact_4480_dvd__add__times__triv__right__iff, fact_2059_mult__left__cancel, fact_9458_or__minus__numerals_I3_J, fact_686_diff__eq__diff__eq, fact_442_add__le__imp__le__right, fact_4318_order__less__le__trans, fact_5956_not__one__less__neg__numeral, fact_9361_take__bit__Suc__minus__bit1, fact_4425_even__succ__div__exp, fact_14_numeral__Bit0__div__2, fact_9975_UNIV__char__of__nat, fact_2187_VEBT__internal_OminNull_Ocases, fact_4317_order__less__le__trans, fact_4082_ord__eq__less__subst, fact_583_add__diff__cancel__left_H, fact_1742_power__0__Suc, fact_9100_powr__mult, fact_1201_add__le__imp__le__diff, fact_814_Nat_Ole__diff__conv2, fact_4702_not__is__unit__0, fact_7926_sin__total, fact_5821_zmult__eq__1__iff, fact_1120_power__odd__eq, fact_4064_order__less__asym_H, fact_192_power__commutes, fact_4031_not__less__iff__gr__or__eq, fact_7097_of__int__le__of__int__power__cancel__iff, fact_8865_prod_OatLeastAtMost__rev, fact_6447_zmod__numeral__Bit1, fact_5519_less__minus__iff, fact_2328_mult__pos__pos, fact_2727_divide__eq__eq__numeral_I1_J, fact_7586_sum__lessThan__telescope_H, fact_704_diff__eq__diff__less, fact_7457_norm__minus__commute, fact_5743_neg__eq__iff__add__eq__0, fact_7073_of__int__le__numeral__iff, fact_4368_order__le__imp__less__or__eq, fact_5214_divide__minus1, fact_6139_sum__diff, fact_2667_mult__le__one, fact_8590_pochhammer__minus, fact_3874_order_Otrans, fact_6609_cong__exp__iff__simps_I12_J, fact_3285_bounded__Max__nat, fact_2254_mult__mono_H, fact_9056_less__log2__of__power, fact_153_distrib__left__numeral, fact_8548_central__binomial__odd, fact_6657_sum_OatLeast__Suc__atMost, fact_3915_order__subst1, fact_2107_old_Onat_Oexhaust, fact_8692_sum_OatMost__Suc, fact_3272_minf_I4_J, fact_7650_summable__cmult__iff, fact_4979_zero__less__power__eq, fact_8019_fact__fact__dvd__fact, fact_8194_exp__minus__inverse, fact_5073_mult__minus__left, fact_1280_empty__iff, fact_5766_nonzero__minus__divide__right, fact_3052_div__int__pos__iff, fact_1693_div__mult__mult2, fact_4555_even__succ__div__two, fact_5955_not__one__less__neg__numeral, fact_8145_exp__times__arg__commute, fact_7795_sin__npi__int, fact_4632_unit__imp__dvd, fact_3844_nle__le, fact_5767_one__neq__neg__numeral, fact_4255_dual__order_Ostrict__iff__not, fact_1494_mult__eq__0__iff, fact_4999_ex__min__if__finite, fact_4111_order__less__subst2, fact_4562_odd__two__times__div__two__nat, fact_1836_div__mult__self2, fact_216_mult__numeral__1, fact_9320_nat__mod__distrib, fact_7773_finite__nat__bounded, fact_4567_power__le__zero__eq__numeral, fact_8175_exp__diff, fact_6745_sum__gp__multiplied, fact_200_power__commuting__commutes, fact_6161_divide__eq__eq__numeral_I2_J, fact_9158_real__root__Suc__0, fact_1168_option_Oexhaust, fact_901_one__power2, fact_6007_sum__nonneg__0, fact_45_numeral__less__iff, fact_6691_power__even__abs, fact_7355_gauss__sum, fact_912_length__induct, fact_3264_minf_I2_J, fact_6124_sum_Osubset__diff, fact_560_VEBT_Oinject_I1_J, fact_1941_unique__euclidean__semiring__numeral__class_Opos__mod__sign, fact_5668_of__bool__less__eq__one, fact_7806_sin__cos__squared__add, fact_130_high__inv, fact_4926_dvd__minus__add, fact_528_add__mono__thms__linordered__field_I3_J, fact_218_mult__numeral__1, fact_3253_pinf_I7_J, fact_5193_mult__minus1__right, fact_4092_ord__less__eq__subst, fact_5396_divide__less__eq__numeral1_I2_J, fact_777_mult_Ocomm__neutral, fact_8114_real__sqrt__less__iff, fact_9226_div__sgn__abs__cancel, fact_1582_divide__cancel__left, fact_1066_power__Suc2, fact_6496_abs__triangle__ineq2__sym, fact_4629_dvd__unit__imp__unit, fact_1480_not__gr__zero, fact_8187_sums__Suc__iff, fact_330_add__less__cancel__left, fact_324_times__divide__eq__left, fact_8953_binomial__r__part__sum, fact_6773_arctan__double, fact_2119_gr__implies__not0, fact_6180_power2__eq__iff, fact_6239_signed__take__bit__int__greater__eq__minus__exp, fact_699_diff__eq__diff__less__eq, fact_2801_divmod__digit__1_I1_J, fact_2065_mult__right__cancel, fact_2892_zero__power2, fact_3846_le__cases3, fact_8783_prod_Ointer__filter, fact_559_real__divide__square__eq, fact_7489_norm__power__ineq, fact_8130_real__sqrt__mult__self, fact_8547_binomial__strict__antimono, fact_181_mult__le__mono, fact_6715_abs__square__le__1, fact_6497_abs__triangle__ineq2__sym, fact_1902_zero__less__power2, fact_7919_unbounded__k__infinite, fact_476_add__less__imp__less__right, fact_349_mi__eq__ma__no__ch, fact_9143_Complex__add__complex__of__real, fact_7858_cos__diff__cos, fact_1572_bits__div__0, fact_5759_numeral__times__minus__swap, fact_9189_real__root__strict__decreasing, fact_299_le__Suc__ex, fact_475_add__less__imp__less__right, fact_9447_xor__Suc__0__eq, fact_1662_mult__cancel__left1, fact_5330_diff__numeral__simps_I3_J, fact_4254_dual__order_Ostrict__iff__not, fact_873_power__strict__increasing, fact_2882_power__strict__decreasing, fact_2548_cancel__div__mod__rules_I2_J, fact_7724_complete__algebra__summable__geometric, fact_2324_mult__pos__neg, fact_124_div__exp__eq, fact_2483_power__0, fact_7143_of__int__less__numeral__power__cancel__iff, fact_4154_leD, fact_8245_ln__sqrt, fact_1860_le__divide__eq__1__neg, fact_6383_abs__power__minus, fact_96_add__numeral__left, fact_7123_numeral__power__less__of__nat__cancel__iff, fact_5232_zero__less__of__bool__iff, fact_3986_ord__eq__less__trans, fact_7429_complex__mod__triangle__ineq2, fact_678_one__reorient, fact_5200_mult__minus1, fact_8577_pochhammer__same, fact_4640_one__dvd, fact_3898_dual__order_Otrans, fact_1571_bits__div__by__0, fact_5939_not__one__le__neg__numeral, fact_2317_mult__less__0__iff, fact_4377_bot_Oextremum__unique, fact_3007_odd__0__le__power__imp__0__le, fact_7280_of__int__nonneg, fact_5416_diff__numeral__special_I11_J, fact_9136_exp__pi__i, fact_2133_vebt__member_Ocases, fact_9257_numeral__power__eq__nat__cancel__iff, fact_7836_cos__squared__eq, fact_26__C33_C, fact_1865_power__strict__decreasing__iff, fact_3218_atLeastAtMost__iff, fact_1353_lambda__one, fact_5374_neg__numeral__less__iff, fact_2422_divide__right__mono__neg, fact_7054_numeral__power__eq__of__nat__cancel__iff, fact_3050_zdiv__mono1__neg, fact_9217_dvd__sgn__mult__iff, fact_5142_neg__le__0__iff__le, fact_3994_ord__less__eq__trans, fact_5464_power__minus1__even, fact_6739_sum__natinterval__diff, fact_2570_mult__le__cancel__left, fact_2877_power__Suc__less__one, fact_9404_and__nat__rec, fact_957_maxt__corr__help, fact_8518_pochhammer__of__nat__eq__0__lemma_H, fact_4789_le__imp__power__dvd, fact_6422_zero__less__power__abs__iff, fact_5949_neg__one__less__numeral, fact_5901_neg__numeral__less__zero, fact_7477_nonzero__norm__divide, fact_3280_minf_I7_J, fact_6824_zdvd__mult__cancel1, fact_8576_pochhammer__same, fact_1699_nonzero__mult__divide__mult__cancel__right, fact_2055_no__zero__divisors, fact_2750_power__inject__base, fact_1100_Suc__mult__less__cancel1, fact_6811_divmod__algorithm__code_I4_J, fact_535_both__member__options__from__complete__tree__to__child, fact_1028_Ex__less__Suc, fact_8573_pochhammer__same, fact_5944_neg__numeral__less__one, fact_5251_signed__take__bit__of__minus__1 176.34/88.54 % No. of inferences in proof: 15464 176.34/88.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 87997 ms resp. 85737 ms w/o parsing 185.24/93.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 185.24/93.62 thf(produc5542196010084753463at_nat_type, type, produc5542196010084753463at_nat: $tType). 185.24/93.62 thf(produc5491161045314408544at_nat_type, type, produc5491161045314408544at_nat: $tType). 185.24/93.62 thf(produc1193250871479095198on_num_type, type, produc1193250871479095198on_num: $tType). 185.24/93.62 thf(produc8306885398267862888on_nat_type, type, produc8306885398267862888on_nat: $tType). 185.24/93.62 thf(produc6121120109295599847at_nat_type, type, produc6121120109295599847at_nat: $tType). 185.24/93.62 thf(produc3368934014287244435at_num_type, type, produc3368934014287244435at_num: $tType). 185.24/93.62 thf(produc4471711990508489141at_nat_type, type, produc4471711990508489141at_nat: $tType). 185.24/93.62 thf(produc7036089656553540234on_num_type, type, produc7036089656553540234on_num: $tType). 185.24/93.62 thf(produc2233624965454879586on_nat_type, type, produc2233624965454879586on_nat: $tType). 185.24/93.62 thf(list_P7413028617227757229T_VEBT_type, type, list_P7413028617227757229T_VEBT: $tType). 185.24/93.62 thf(produc3447558737645232053on_num_type, type, produc3447558737645232053on_num: $tType). 185.24/93.62 thf(produc4953844613479565601on_nat_type, type, produc4953844613479565601on_nat: $tType). 185.24/93.62 thf(produc2963631642982155120at_num_type, type, produc2963631642982155120at_num: $tType). 185.24/93.62 thf(produc7248412053542808358at_nat_type, type, produc7248412053542808358at_nat: $tType). 185.24/93.62 thf(list_P7037539587688870467BT_nat_type, type, list_P7037539587688870467BT_nat: $tType). 185.24/93.62 thf(list_P4547456442757143711BT_int_type, type, list_P4547456442757143711BT_int: $tType). 185.24/93.62 thf(list_P5647936690300460905T_VEBT_type, type, list_P5647936690300460905T_VEBT: $tType). 185.24/93.62 thf(produc8243902056947475879T_VEBT_type, type, produc8243902056947475879T_VEBT: $tType). 185.24/93.62 thf(produc8923325533196201883nteger_type, type, produc8923325533196201883nteger: $tType). 185.24/93.62 thf(list_P3126845725202233233VEBT_o_type, type, list_P3126845725202233233VEBT_o: $tType). 185.24/93.62 thf(list_P7495141550334521929T_VEBT_type, type, list_P7495141550334521929T_VEBT: $tType). 185.24/93.62 thf(list_P8526636022914148096eger_o_type, type, list_P8526636022914148096eger_o: $tType). 185.24/93.62 thf(set_Pr448751882837621926eger_o_type, type, set_Pr448751882837621926eger_o: $tType). 185.24/93.62 thf(option4927543243414619207at_nat_type, type, option4927543243414619207at_nat: $tType). 185.24/93.62 thf(list_P3744719386663036955um_num_type, type, list_P3744719386663036955um_num: $tType). 185.24/93.62 thf(produc9072475918466114483BT_nat_type, type, produc9072475918466114483BT_nat: $tType). 185.24/93.62 thf(produc4894624898956917775BT_int_type, type, produc4894624898956917775BT_int: $tType). 185.24/93.62 thf(set_Pr8218934625190621173um_num_type, type, set_Pr8218934625190621173um_num: $tType). 185.24/93.62 thf(set_Pr6200539531224447659at_num_type, type, set_Pr6200539531224447659at_num: $tType). 185.24/93.62 thf(set_Pr1261947904930325089at_nat_type, type, set_Pr1261947904930325089at_nat: $tType). 185.24/93.62 thf(set_Pr958786334691620121nt_int_type, type, set_Pr958786334691620121nt_int: $tType). 185.24/93.62 thf(list_P7333126701944960589_nat_o_type, type, list_P7333126701944960589_nat_o: $tType). 185.24/93.62 thf(list_P6285523579766656935_o_nat_type, type, list_P6285523579766656935_o_nat: $tType). 185.24/93.62 thf(list_P3795440434834930179_o_int_type, type, list_P3795440434834930179_o_int: $tType). 185.24/93.62 thf(set_list_VEBT_VEBT_type, type, set_list_VEBT_VEBT: $tType). 185.24/93.62 thf(produc334124729049499915VEBT_o_type, type, produc334124729049499915VEBT_o: $tType). 185.24/93.62 thf(produc2504756804600209347T_VEBT_type, type, produc2504756804600209347T_VEBT: $tType). 185.24/93.62 thf(produc6271795597528267376eger_o_type, type, produc6271795597528267376eger_o: $tType). 185.24/93.62 thf(product_prod_num_num_type, type, product_prod_num_num: $tType). 185.24/93.62 thf(product_prod_nat_num_type, type, product_prod_nat_num: $tType). 185.24/93.62 thf(product_prod_nat_nat_type, type, product_prod_nat_nat: $tType). 185.24/93.62 thf(product_prod_int_int_type, type, product_prod_int_int: $tType). 185.24/93.62 thf(list_P4002435161011370285od_o_o_type, type, list_P4002435161011370285od_o_o: $tType). 185.24/93.62 thf(set_list_complex_type, type, set_list_complex: $tType). 185.24/93.62 thf(set_set_complex_type, type, set_set_complex: $tType). 185.24/93.62 thf(list_list_nat_type, type, list_list_nat: $tType). 185.24/93.62 thf(list_VEBT_VEBT_type, type, list_VEBT_VEBT: $tType). 185.24/93.62 thf(set_list_nat_type, type, set_list_nat: $tType). 185.24/93.62 thf(set_list_int_type, type, set_list_int: $tType). 185.24/93.62 thf(product_prod_o_nat_type, type, product_prod_o_nat: $tType). 185.24/93.62 thf(product_prod_o_int_type, type, product_prod_o_int: $tType). 185.24/93.62 thf(list_Code_integer_type, type, list_Code_integer: $tType). 185.24/93.62 thf(set_VEBT_VEBT_type, type, set_VEBT_VEBT: $tType). 185.24/93.62 thf(set_set_nat_type, type, set_set_nat: $tType). 185.24/93.62 thf(set_set_int_type, type, set_set_int: $tType). 185.24/93.62 thf(set_Code_integer_type, type, set_Code_integer: $tType). 185.24/93.62 thf(set_Product_unit_type, type, set_Product_unit: $tType). 185.24/93.62 thf(set_Extended_enat_type, type, set_Extended_enat: $tType). 185.24/93.62 thf(list_complex_type, type, list_complex: $tType). 185.24/93.62 thf(set_list_o_type, type, set_list_o: $tType). 185.24/93.62 thf(product_prod_o_o_type, type, product_prod_o_o: $tType). 185.24/93.62 thf(set_complex_type, type, set_complex: $tType). 185.24/93.62 thf(filter_real_type, type, filter_real: $tType). 185.24/93.62 thf(option_num_type, type, option_num: $tType). 185.24/93.62 thf(option_nat_type, type, option_nat: $tType). 185.24/93.62 thf(filter_nat_type, type, filter_nat: $tType). 185.24/93.62 thf(set_char_type, type, set_char: $tType). 185.24/93.62 thf(list_real_type, type, list_real: $tType). 185.24/93.62 thf(set_real_type, type, set_real: $tType). 185.24/93.62 thf(list_num_type, type, list_num: $tType). 185.24/93.62 thf(list_nat_type, type, list_nat: $tType). 185.24/93.62 thf(list_int_type, type, list_int: $tType). 185.24/93.62 thf(vEBT_VEBT_type, type, vEBT_VEBT: $tType). 185.24/93.62 thf(set_rat_type, type, set_rat: $tType). 185.24/93.62 thf(set_num_type, type, set_num: $tType). 185.24/93.62 thf(set_nat_type, type, set_nat: $tType). 185.24/93.62 thf(set_int_type, type, set_int: $tType). 185.24/93.62 thf(code_integer_type, type, code_integer: $tType). 185.24/93.62 thf(extended_enat_type, type, extended_enat: $tType). 185.24/93.62 thf(list_o_type, type, list_o: $tType). 185.24/93.62 thf(complex_type, type, complex: $tType). 185.24/93.62 thf(set_o_type, type, set_o: $tType). 185.24/93.62 thf(char_type, type, char: $tType). 185.24/93.62 thf(real_type, type, real: $tType). 185.24/93.62 thf(rat_type, type, rat: $tType). 185.24/93.62 thf(num_type, type, num: $tType). 185.24/93.62 thf(nat_type, type, nat: $tType). 185.24/93.62 thf(int_type, type, int: $tType). 185.24/93.62 thf(archim7802044766580827645g_real_type, type, archim7802044766580827645g_real: (real > int)). 185.24/93.62 thf(archim6058952711729229775r_real_type, type, archim6058952711729229775r_real: (real > int)). 185.24/93.62 thf(archim7778729529865785530nd_rat_type, type, archim7778729529865785530nd_rat: (rat > int)). 185.24/93.62 thf(archim8280529875227126926d_real_type, type, archim8280529875227126926d_real: (real > int)). 185.24/93.62 thf(binomial_type, type, binomial: (nat > (nat > nat))). 185.24/93.62 thf(gbinomial_complex_type, type, gbinomial_complex: (complex > (nat > complex))). 185.24/93.62 thf(gbinomial_int_type, type, gbinomial_int: (int > (nat > int))). 185.24/93.62 thf(gbinomial_nat_type, type, gbinomial_nat: (nat > (nat > nat))). 185.24/93.62 thf(gbinomial_rat_type, type, gbinomial_rat: (rat > (nat > rat))). 185.24/93.62 thf(gbinomial_real_type, type, gbinomial_real: (real > (nat > real))). 185.24/93.62 thf(bit_concat_bit_type, type, bit_concat_bit: (nat > (int > (int > int)))). 185.24/93.62 thf(bit_or_not_num_neg_type, type, bit_or_not_num_neg: (num > (num > num))). 185.24/93.62 thf(bit_ri7919022796975470100ot_int_type, type, bit_ri7919022796975470100ot_int: (int > int)). 185.24/93.62 thf(bit_ri631733984087533419it_int_type, type, bit_ri631733984087533419it_int: (nat > (int > int))). 185.24/93.62 thf(bit_se725231765392027082nd_int_type, type, bit_se725231765392027082nd_int: (int > (int > int))). 185.24/93.62 thf(bit_se727722235901077358nd_nat_type, type, bit_se727722235901077358nd_nat: (nat > (nat > nat))). 185.24/93.62 thf(bit_se8568078237143864401it_int_type, type, bit_se8568078237143864401it_int: (nat > (int > int))). 185.24/93.62 thf(bit_se8570568707652914677it_nat_type, type, bit_se8570568707652914677it_nat: (nat > (nat > nat))). 185.24/93.62 thf(bit_se2159334234014336723it_int_type, type, bit_se2159334234014336723it_int: (nat > (int > int))). 185.24/93.62 thf(bit_se2161824704523386999it_nat_type, type, bit_se2161824704523386999it_nat: (nat > (nat > nat))). 185.24/93.62 thf(bit_se2000444600071755411sk_int_type, type, bit_se2000444600071755411sk_int: (nat > int)). 185.24/93.62 thf(bit_se2002935070580805687sk_nat_type, type, bit_se2002935070580805687sk_nat: (nat > nat)). 185.24/93.62 thf(bit_se1409905431419307370or_int_type, type, bit_se1409905431419307370or_int: (int > (int > int))). 185.24/93.62 thf(bit_se1412395901928357646or_nat_type, type, bit_se1412395901928357646or_nat: (nat > (nat > nat))). 185.24/93.62 thf(bit_se545348938243370406it_int_type, type, bit_se545348938243370406it_int: (nat > (int > int))). 185.24/93.62 thf(bit_se547839408752420682it_nat_type, type, bit_se547839408752420682it_nat: (nat > (nat > nat))). 185.24/93.62 thf(bit_se7879613467334960850it_int_type, type, bit_se7879613467334960850it_int: (nat > (int > int))). 185.24/93.62 thf(bit_se7882103937844011126it_nat_type, type, bit_se7882103937844011126it_nat: (nat > (nat > nat))). 185.24/93.62 thf(bit_se2923211474154528505it_int_type, type, bit_se2923211474154528505it_int: (nat > (int > int))). 185.24/93.62 thf(bit_se2925701944663578781it_nat_type, type, bit_se2925701944663578781it_nat: (nat > (nat > nat))). 185.24/93.62 thf(bit_se4203085406695923979it_int_type, type, bit_se4203085406695923979it_int: (nat > (int > int))). 185.24/93.62 thf(bit_se4205575877204974255it_nat_type, type, bit_se4205575877204974255it_nat: (nat > (nat > nat))). 185.24/93.62 thf(bit_se6526347334894502574or_int_type, type, bit_se6526347334894502574or_int: (int > (int > int))). 185.24/93.62 thf(bit_se6528837805403552850or_nat_type, type, bit_se6528837805403552850or_nat: (nat > (nat > nat))). 185.24/93.62 thf(bit_se1146084159140164899it_int_type, type, bit_se1146084159140164899it_int: (int > (nat > $o))). 185.24/93.62 thf(bit_se1148574629649215175it_nat_type, type, bit_se1148574629649215175it_nat: (nat > (nat > $o))). 185.24/93.62 thf(code_integer_of_num_type, type, code_integer_of_num: (num > code_integer)). 185.24/93.62 thf(complex2_type, type, complex2: (real > (real > complex))). 185.24/93.62 thf(im_type, type, im: (complex > real)). 185.24/93.62 thf(re_type, type, re: (complex > real)). 185.24/93.62 thf(csqrt_type, type, csqrt: (complex > complex)). 185.24/93.62 thf(imaginary_unit_type, type, imaginary_unit: complex). 185.24/93.62 thf(divmod_nat_type, type, divmod_nat: (nat > (nat > product_prod_nat_nat))). 185.24/93.62 thf(unique5055182867167087721od_nat_type, type, unique5055182867167087721od_nat: (num > (num > product_prod_nat_nat))). 185.24/93.62 thf(unique5026877609467782581ep_nat_type, type, unique5026877609467782581ep_nat: (num > (product_prod_nat_nat > product_prod_nat_nat))). 185.24/93.62 thf(comm_s2602460028002588243omplex_type, type, comm_s2602460028002588243omplex: (complex > (nat > complex))). 185.24/93.62 thf(comm_s4663373288045622133er_nat_type, type, comm_s4663373288045622133er_nat: (nat > (nat > nat))). 185.24/93.62 thf(comm_s4028243227959126397er_rat_type, type, comm_s4028243227959126397er_rat: (rat > (nat > rat))). 185.24/93.62 thf(comm_s7457072308508201937r_real_type, type, comm_s7457072308508201937r_real: (real > (nat > real))). 185.24/93.62 thf(semiri5044797733671781792omplex_type, type, semiri5044797733671781792omplex: (nat > complex)). 185.24/93.62 thf(semiri1406184849735516958ct_int_type, type, semiri1406184849735516958ct_int: (nat > int)). 185.24/93.62 thf(semiri1408675320244567234ct_nat_type, type, semiri1408675320244567234ct_nat: (nat > nat)). 185.24/93.62 thf(semiri773545260158071498ct_rat_type, type, semiri773545260158071498ct_rat: (nat > rat)). 185.24/93.62 thf(semiri2265585572941072030t_real_type, type, semiri2265585572941072030t_real: (nat > real)). 185.24/93.62 thf(invers8013647133539491842omplex_type, type, invers8013647133539491842omplex: (complex > complex)). 185.24/93.62 thf(inverse_inverse_real_type, type, inverse_inverse_real: (real > real)). 185.24/93.62 thf(at_bot_real_type, type, at_bot_real: filter_real). 185.24/93.62 thf(at_top_real_type, type, at_top_real: filter_real). 185.24/93.62 thf(filterlim_real_real_type, type, filterlim_real_real: ((real > real) > (filter_real > (filter_real > $o)))). 185.24/93.62 thf(finite_card_o_type, type, finite_card_o: (set_o > nat)). 185.24/93.62 thf(finite_card_char_type, type, finite_card_char: (set_char > nat)). 185.24/93.62 thf(finite_finite_nat_type, type, finite_finite_nat: (set_nat > $o)). 185.24/93.62 thf(abs_abs_Code_integer_type, type, abs_abs_Code_integer: (code_integer > code_integer)). 185.24/93.62 thf(abs_abs_int_type, type, abs_abs_int: (int > int)). 185.24/93.62 thf(abs_abs_rat_type, type, abs_abs_rat: (rat > rat)). 185.24/93.62 thf(abs_abs_real_type, type, abs_abs_real: (real > real)). 185.24/93.62 thf(minus_minus_complex_type, type, minus_minus_complex: (complex > (complex > complex))). 185.24/93.62 thf(minus_minus_int_type, type, minus_minus_int: (int > (int > int))). 185.24/93.62 thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))). 185.24/93.62 thf(minus_minus_rat_type, type, minus_minus_rat: (rat > (rat > rat))). 185.24/93.62 thf(minus_minus_real_type, type, minus_minus_real: (real > (real > real))). 185.24/93.62 thf(minus_minus_set_nat_type, type, minus_minus_set_nat: (set_nat > (set_nat > set_nat))). 185.24/93.62 thf(one_one_Code_integer_type, type, one_one_Code_integer: code_integer). 185.24/93.62 thf(one_one_complex_type, type, one_one_complex: complex). 185.24/93.62 thf(one_one_int_type, type, one_one_int: int). 185.24/93.62 thf(one_one_nat_type, type, one_one_nat: nat). 185.24/93.62 thf(one_one_rat_type, type, one_one_rat: rat). 185.24/93.62 thf(one_one_real_type, type, one_one_real: real). 185.24/93.62 thf(plus_plus_complex_type, type, plus_plus_complex: (complex > (complex > complex))). 185.24/93.62 thf(plus_plus_int_type, type, plus_plus_int: (int > (int > int))). 185.24/93.62 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 185.24/93.62 thf(plus_plus_num_type, type, plus_plus_num: (num > (num > num))). 185.24/93.62 thf(plus_plus_rat_type, type, plus_plus_rat: (rat > (rat > rat))). 185.24/93.62 thf(plus_plus_real_type, type, plus_plus_real: (real > (real > real))). 185.24/93.62 thf(sgn_sgn_int_type, type, sgn_sgn_int: (int > int)). 185.24/93.62 thf(sgn_sgn_real_type, type, sgn_sgn_real: (real > real)). 185.24/93.62 thf(times_3573771949741848930nteger_type, type, times_3573771949741848930nteger: (code_integer > (code_integer > code_integer))). 185.24/93.62 thf(times_times_complex_type, type, times_times_complex: (complex > (complex > complex))). 185.24/93.62 thf(times_times_int_type, type, times_times_int: (int > (int > int))). 185.24/93.62 thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))). 185.24/93.62 thf(times_times_num_type, type, times_times_num: (num > (num > num))). 185.24/93.62 thf(times_times_rat_type, type, times_times_rat: (rat > (rat > rat))). 185.24/93.62 thf(times_times_real_type, type, times_times_real: (real > (real > real))). 185.24/93.62 thf(uminus1351360451143612070nteger_type, type, uminus1351360451143612070nteger: (code_integer > code_integer)). 185.24/93.62 thf(uminus1482373934393186551omplex_type, type, uminus1482373934393186551omplex: (complex > complex)). 185.24/93.62 thf(uminus_uminus_int_type, type, uminus_uminus_int: (int > int)). 185.24/93.62 thf(uminus_uminus_rat_type, type, uminus_uminus_rat: (rat > rat)). 185.24/93.62 thf(uminus_uminus_real_type, type, uminus_uminus_real: (real > real)). 185.24/93.62 thf(zero_zero_complex_type, type, zero_zero_complex: complex). 185.24/93.62 thf(zero_zero_int_type, type, zero_zero_int: int). 185.24/93.62 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 185.24/93.62 thf(zero_zero_rat_type, type, zero_zero_rat: rat). 185.24/93.62 thf(zero_zero_real_type, type, zero_zero_real: real). 185.24/93.62 thf(groups2073611262835488442omplex_type, type, groups2073611262835488442omplex: ((nat > complex) > (set_nat > complex))). 185.24/93.62 thf(groups3539618377306564664at_int_type, type, groups3539618377306564664at_int: ((nat > int) > (set_nat > int))). 185.24/93.62 thf(groups3542108847815614940at_nat_type, type, groups3542108847815614940at_nat: ((nat > nat) > (set_nat > nat))). 185.24/93.62 thf(groups2906978787729119204at_rat_type, type, groups2906978787729119204at_rat: ((nat > rat) > (set_nat > rat))). 185.24/93.62 thf(groups6591440286371151544t_real_type, type, groups6591440286371151544t_real: ((nat > real) > (set_nat > real))). 185.24/93.62 thf(groups6464643781859351333omplex_type, type, groups6464643781859351333omplex: ((nat > complex) > (set_nat > complex))). 185.24/93.62 thf(groups705719431365010083at_int_type, type, groups705719431365010083at_int: ((nat > int) > (set_nat > int))). 185.24/93.62 thf(groups708209901874060359at_nat_type, type, groups708209901874060359at_nat: ((nat > nat) > (set_nat > nat))). 185.24/93.62 thf(groups73079841787564623at_rat_type, type, groups73079841787564623at_rat: ((nat > rat) > (set_nat > rat))). 185.24/93.62 thf(groups129246275422532515t_real_type, type, groups129246275422532515t_real: ((nat > real) > (set_nat > real))). 185.24/93.62 thf(if_complex_type, type, if_complex: ($o > (complex > (complex > complex)))). 185.24/93.62 thf(if_int_type, type, if_int: ($o > (int > (int > int)))). 185.24/93.62 thf(if_nat_type, type, if_nat: ($o > (nat > (nat > nat)))). 185.24/93.62 thf(if_option_nat_type, type, if_option_nat: ($o > (option_nat > (option_nat > option_nat)))). 185.24/93.62 thf(if_Pro6206227464963214023at_nat_type, type, if_Pro6206227464963214023at_nat: ($o > (product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)))). 185.24/93.62 thf(if_rat_type, type, if_rat: ($o > (rat > (rat > rat)))). 185.24/93.62 thf(if_real_type, type, if_real: ($o > (real > (real > real)))). 185.24/93.62 thf(if_VEBT_VEBT_type, type, if_VEBT_VEBT: ($o > (vEBT_VEBT > (vEBT_VEBT > vEBT_VEBT)))). 185.24/93.62 thf(abs_Integ_type, type, abs_Integ: (product_prod_nat_nat > int)). 185.24/93.62 thf(nat2_type, type, nat2: (int > nat)). 185.24/93.62 thf(ring_18347121197199848620nteger_type, type, ring_18347121197199848620nteger: (int > code_integer)). 185.24/93.62 thf(ring_17405671764205052669omplex_type, type, ring_17405671764205052669omplex: (int > complex)). 185.24/93.62 thf(ring_1_of_int_int_type, type, ring_1_of_int_int: (int > int)). 185.24/93.62 thf(ring_1_of_int_rat_type, type, ring_1_of_int_rat: (int > rat)). 185.24/93.62 thf(ring_1_of_int_real_type, type, ring_1_of_int_real: (int > real)). 185.24/93.62 thf(sup_sup_set_nat_type, type, sup_sup_set_nat: (set_nat > (set_nat > set_nat))). 185.24/93.62 thf(set_VEBT_VEBT2_type, type, set_VEBT_VEBT2: (list_VEBT_VEBT > set_VEBT_VEBT)). 185.24/93.62 thf(list_u1324408373059187874T_VEBT_type, type, list_u1324408373059187874T_VEBT: (list_VEBT_VEBT > (nat > (vEBT_VEBT > list_VEBT_VEBT)))). 185.24/93.62 thf(nth_Pr4953567300277697838T_VEBT_type, type, nth_Pr4953567300277697838T_VEBT: (list_P7413028617227757229T_VEBT > (nat > produc8243902056947475879T_VEBT))). 185.24/93.62 thf(nth_VEBT_VEBT_type, type, nth_VEBT_VEBT: (list_VEBT_VEBT > (nat > vEBT_VEBT))). 185.24/93.62 thf(produc4743750530478302277T_VEBT_type, type, produc4743750530478302277T_VEBT: (list_VEBT_VEBT > (list_VEBT_VEBT > list_P7413028617227757229T_VEBT))). 185.24/93.62 thf(replicate_VEBT_VEBT_type, type, replicate_VEBT_VEBT: (nat > (vEBT_VEBT > list_VEBT_VEBT))). 185.24/93.62 thf(suc_type, type, suc: (nat > nat)). 185.24/93.62 thf(compow_nat_nat_type, type, compow_nat_nat: (nat > ((nat > nat) > (nat > nat)))). 185.24/93.62 thf(case_nat_nat_type, type, case_nat_nat: (nat > ((nat > nat) > (nat > nat)))). 185.24/93.62 thf(semiri8010041392384452111omplex_type, type, semiri8010041392384452111omplex: (nat > complex)). 185.24/93.62 thf(semiri1314217659103216013at_int_type, type, semiri1314217659103216013at_int: (nat > int)). 185.24/93.62 thf(semiri1316708129612266289at_nat_type, type, semiri1316708129612266289at_nat: (nat > nat)). 185.24/93.62 thf(semiri681578069525770553at_rat_type, type, semiri681578069525770553at_rat: (nat > rat)). 185.24/93.62 thf(semiri5074537144036343181t_real_type, type, semiri5074537144036343181t_real: (nat > real)). 185.24/93.62 thf(semiri8422978514062236437ux_nat_type, type, semiri8422978514062236437ux_nat: ((nat > nat) > (nat > (nat > nat)))). 185.24/93.62 thf(size_s6755466524823107622T_VEBT_type, type, size_s6755466524823107622T_VEBT: (list_VEBT_VEBT > nat)). 185.24/93.62 thf(size_size_num_type, type, size_size_num: (num > nat)). 185.24/93.62 thf(size_size_option_nat_type, type, size_size_option_nat: (option_nat > nat)). 185.24/93.62 thf(size_s170228958280169651at_nat_type, type, size_s170228958280169651at_nat: (option4927543243414619207at_nat > nat)). 185.24/93.62 thf(nat_prod_decode_aux_type, type, nat_prod_decode_aux: (nat > (nat > product_prod_nat_nat))). 185.24/93.62 thf(nat_set_decode_type, type, nat_set_decode: (nat > set_nat)). 185.24/93.62 thf(nat_set_encode_type, type, nat_set_encode: (set_nat > nat)). 185.24/93.62 thf(nat_triangle_type, type, nat_triangle: (nat > nat)). 185.24/93.62 thf(root_type, type, root: (nat > (real > real))). 185.24/93.62 thf(sqrt_type, type, sqrt: (real > real)). 185.24/93.62 thf(bitM_type, type, bitM: (num > num)). 185.24/93.62 thf(inc_type, type, inc: (num > num)). 185.24/93.62 thf(neg_nu7009210354673126013omplex_type, type, neg_nu7009210354673126013omplex: (complex > complex)). 185.24/93.62 thf(neg_numeral_dbl_int_type, type, neg_numeral_dbl_int: (int > int)). 185.24/93.62 thf(neg_numeral_dbl_rat_type, type, neg_numeral_dbl_rat: (rat > rat)). 185.24/93.62 thf(neg_numeral_dbl_real_type, type, neg_numeral_dbl_real: (real > real)). 185.24/93.62 thf(neg_nu6511756317524482435omplex_type, type, neg_nu6511756317524482435omplex: (complex > complex)). 185.24/93.62 thf(neg_nu3811975205180677377ec_int_type, type, neg_nu3811975205180677377ec_int: (int > int)). 185.24/93.62 thf(neg_nu3179335615603231917ec_rat_type, type, neg_nu3179335615603231917ec_rat: (rat > rat)). 185.24/93.62 thf(neg_nu6075765906172075777c_real_type, type, neg_nu6075765906172075777c_real: (real > real)). 185.24/93.62 thf(neg_nu8557863876264182079omplex_type, type, neg_nu8557863876264182079omplex: (complex > complex)). 185.24/93.62 thf(neg_nu5851722552734809277nc_int_type, type, neg_nu5851722552734809277nc_int: (int > int)). 185.24/93.62 thf(neg_nu5219082963157363817nc_rat_type, type, neg_nu5219082963157363817nc_rat: (rat > rat)). 185.24/93.62 thf(neg_nu8295874005876285629c_real_type, type, neg_nu8295874005876285629c_real: (real > real)). 185.24/93.62 thf(bit0_type, type, bit0: (num > num)). 185.24/93.62 thf(bit1_type, type, bit1: (num > num)). 185.24/93.62 thf(one_type, type, one: num). 185.24/93.62 thf(size_num_type, type, size_num: (num > nat)). 185.24/93.62 thf(num_of_nat_type, type, num_of_nat: (nat > num)). 185.24/93.62 thf(numera6620942414471956472nteger_type, type, numera6620942414471956472nteger: (num > code_integer)). 185.24/93.62 thf(numera6690914467698888265omplex_type, type, numera6690914467698888265omplex: (num > complex)). 185.24/93.62 thf(numeral_numeral_int_type, type, numeral_numeral_int: (num > int)). 185.24/93.62 thf(numeral_numeral_nat_type, type, numeral_numeral_nat: (num > nat)). 185.24/93.62 thf(numeral_numeral_rat_type, type, numeral_numeral_rat: (num > rat)). 185.24/93.62 thf(numeral_numeral_real_type, type, numeral_numeral_real: (num > real)). 185.24/93.62 thf(pow_type, type, pow: (num > (num > num))). 185.24/93.62 thf(pred_numeral_type, type, pred_numeral: (num > nat)). 185.24/93.62 thf(sqr_type, type, sqr: (num > num)). 185.24/93.62 thf(none_nat_type, type, none_nat: option_nat). 185.24/93.62 thf(none_P5556105721700978146at_nat_type, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat). 185.24/93.62 thf(some_nat_type, type, some_nat: (nat > option_nat)). 185.24/93.62 thf(some_P7363390416028606310at_nat_type, type, some_P7363390416028606310at_nat: (product_prod_nat_nat > option4927543243414619207at_nat)). 185.24/93.62 thf(size_option_nat_type, type, size_option_nat: ((nat > nat) > (option_nat > nat))). 185.24/93.62 thf(size_o8335143837870341156at_nat_type, type, size_o8335143837870341156at_nat: ((product_prod_nat_nat > nat) > (option4927543243414619207at_nat > nat))). 185.24/93.62 thf(the_nat_type, type, the_nat: (option_nat > nat)). 185.24/93.62 thf(bot_bot_set_nat_type, type, bot_bot_set_nat: set_nat). 185.24/93.62 thf(ord_le6747313008572928689nteger_type, type, ord_le6747313008572928689nteger: (code_integer > (code_integer > $o))). 185.24/93.62 thf(ord_less_int_type, type, ord_less_int: (int > (int > $o))). 185.24/93.62 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 185.24/93.62 thf(ord_less_num_type, type, ord_less_num: (num > (num > $o))). 185.24/93.62 thf(ord_less_rat_type, type, ord_less_rat: (rat > (rat > $o))). 185.24/93.62 thf(ord_less_real_type, type, ord_less_real: (real > (real > $o))). 185.24/93.62 thf(ord_le3102999989581377725nteger_type, type, ord_le3102999989581377725nteger: (code_integer > (code_integer > $o))). 185.24/93.62 thf(ord_less_eq_int_type, type, ord_less_eq_int: (int > (int > $o))). 185.24/93.62 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 185.24/93.62 thf(ord_less_eq_num_type, type, ord_less_eq_num: (num > (num > $o))). 185.24/93.62 thf(ord_less_eq_rat_type, type, ord_less_eq_rat: (rat > (rat > $o))). 185.24/93.62 thf(ord_less_eq_real_type, type, ord_less_eq_real: (real > (real > $o))). 185.24/93.62 thf(ord_less_eq_set_nat_type, type, ord_less_eq_set_nat: (set_nat > (set_nat > $o))). 185.24/93.62 thf(ord_max_int_type, type, ord_max_int: (int > (int > int))). 185.24/93.62 thf(ord_max_nat_type, type, ord_max_nat: (nat > (nat > nat))). 185.24/93.62 thf(order_mono_nat_nat_type, type, order_mono_nat_nat: ((nat > nat) > $o)). 185.24/93.62 thf(top_top_set_o_type, type, top_top_set_o: set_o). 185.24/93.62 thf(top_top_set_char_type, type, top_top_set_char: set_char). 185.24/93.62 thf(power_8256067586552552935nteger_type, type, power_8256067586552552935nteger: (code_integer > (nat > code_integer))). 185.24/93.62 thf(power_power_complex_type, type, power_power_complex: (complex > (nat > complex))). 185.24/93.62 thf(power_power_int_type, type, power_power_int: (int > (nat > int))). 185.24/93.62 thf(power_power_nat_type, type, power_power_nat: (nat > (nat > nat))). 185.24/93.62 thf(power_power_rat_type, type, power_power_rat: (rat > (nat > rat))). 185.24/93.62 thf(power_power_real_type, type, power_power_real: (real > (nat > real))). 185.24/93.62 thf(product_Pair_nat_nat_type, type, product_Pair_nat_nat: (nat > (nat > product_prod_nat_nat))). 185.24/93.62 thf(produc738532404422230701BT_nat_type, type, produc738532404422230701BT_nat: (vEBT_VEBT > (nat > produc9072475918466114483BT_nat))). 185.24/93.62 thf(produc537772716801021591T_VEBT_type, type, produc537772716801021591T_VEBT: (vEBT_VEBT > (vEBT_VEBT > produc8243902056947475879T_VEBT))). 185.24/93.62 thf(produc1917071388513777916omplex_type, type, produc1917071388513777916omplex: ((nat > (nat > complex)) > (product_prod_nat_nat > complex))). 185.24/93.62 thf(produc6840382203811409530at_int_type, type, produc6840382203811409530at_int: ((nat > (nat > int)) > (product_prod_nat_nat > int))). 185.24/93.62 thf(produc6842872674320459806at_nat_type, type, produc6842872674320459806at_nat: ((nat > (nat > nat)) > (product_prod_nat_nat > nat))). 185.24/93.62 thf(produc2626176000494625587at_nat_type, type, produc2626176000494625587at_nat: ((nat > (nat > product_prod_nat_nat)) > (product_prod_nat_nat > product_prod_nat_nat))). 185.24/93.62 thf(produc6207742614233964070at_rat_type, type, produc6207742614233964070at_rat: ((nat > (nat > rat)) > (product_prod_nat_nat > rat))). 185.24/93.62 thf(produc1703576794950452218t_real_type, type, produc1703576794950452218t_real: ((nat > (nat > real)) > (product_prod_nat_nat > real))). 185.24/93.62 thf(product_fst_nat_nat_type, type, product_fst_nat_nat: (product_prod_nat_nat > nat)). 185.24/93.62 thf(product_snd_nat_nat_type, type, product_snd_nat_nat: (product_prod_nat_nat > nat)). 185.24/93.62 thf(fract_type, type, fract: (int > (int > rat))). 185.24/93.62 thf(real_V975177566351809787t_real_type, type, real_V975177566351809787t_real: (real > (real > real))). 185.24/93.62 thf(real_V1022390504157884413omplex_type, type, real_V1022390504157884413omplex: (complex > real)). 185.24/93.62 thf(real_V7735802525324610683m_real_type, type, real_V7735802525324610683m_real: (real > real)). 185.24/93.62 thf(real_V4546457046886955230omplex_type, type, real_V4546457046886955230omplex: (real > complex)). 185.24/93.62 thf(divide1717551699836669952omplex_type, type, divide1717551699836669952omplex: (complex > (complex > complex))). 185.24/93.62 thf(divide_divide_int_type, type, divide_divide_int: (int > (int > int))). 185.24/93.62 thf(divide_divide_nat_type, type, divide_divide_nat: (nat > (nat > nat))). 185.24/93.62 thf(divide_divide_rat_type, type, divide_divide_rat: (rat > (rat > rat))). 185.24/93.62 thf(divide_divide_real_type, type, divide_divide_real: (real > (real > real))). 185.24/93.62 thf(dvd_dvd_Code_integer_type, type, dvd_dvd_Code_integer: (code_integer > (code_integer > $o))). 185.24/93.62 thf(dvd_dvd_complex_type, type, dvd_dvd_complex: (complex > (complex > $o))). 185.24/93.62 thf(dvd_dvd_int_type, type, dvd_dvd_int: (int > (int > $o))). 185.24/93.62 thf(dvd_dvd_nat_type, type, dvd_dvd_nat: (nat > (nat > $o))). 185.24/93.62 thf(dvd_dvd_rat_type, type, dvd_dvd_rat: (rat > (rat > $o))). 185.24/93.62 thf(dvd_dvd_real_type, type, dvd_dvd_real: (real > (real > $o))). 185.24/93.62 thf(modulo_modulo_int_type, type, modulo_modulo_int: (int > (int > int))). 185.24/93.62 thf(modulo_modulo_nat_type, type, modulo_modulo_nat: (nat > (nat > nat))). 185.24/93.62 thf(zero_n2684676970156552555ol_int_type, type, zero_n2684676970156552555ol_int: ($o > int)). 185.24/93.62 thf(zero_n2687167440665602831ol_nat_type, type, zero_n2687167440665602831ol_nat: ($o > nat)). 185.24/93.62 thf(suminf_complex_type, type, suminf_complex: ((nat > complex) > complex)). 185.24/93.62 thf(suminf_real_type, type, suminf_real: ((nat > real) > real)). 185.24/93.62 thf(summable_real_type, type, summable_real: ((nat > real) > $o)). 185.24/93.62 thf(sums_complex_type, type, sums_complex: ((nat > complex) > (complex > $o))). 185.24/93.62 thf(sums_nat_type, type, sums_nat: ((nat > nat) > (nat > $o))). 185.24/93.62 thf(sums_real_type, type, sums_real: ((nat > real) > (real > $o))). 185.24/93.62 thf(collect_nat_type, type, collect_nat: ((nat > $o) > set_nat)). 185.24/93.62 thf(image_nat_char_type, type, image_nat_char: ((nat > char) > (set_nat > set_char))). 185.24/93.62 thf(image_char_nat_type, type, image_char_nat: ((char > nat) > (set_char > set_nat))). 185.24/93.62 thf(insert_nat_type, type, insert_nat: (nat > (set_nat > set_nat))). 185.24/93.62 thf(set_fo1517530859248394432omplex_type, type, set_fo1517530859248394432omplex: ((nat > (complex > complex)) > (nat > (nat > (complex > complex))))). 185.24/93.62 thf(set_fo2584398358068434914at_nat_type, type, set_fo2584398358068434914at_nat: ((nat > (nat > nat)) > (nat > (nat > (nat > nat))))). 185.24/93.62 thf(set_fo1949268297981939178at_rat_type, type, set_fo1949268297981939178at_rat: ((nat > (rat > rat)) > (nat > (nat > (rat > rat))))). 185.24/93.62 thf(set_fo3111899725591712190t_real_type, type, set_fo3111899725591712190t_real: ((nat > (real > real)) > (nat > (nat > (real > real))))). 185.24/93.62 thf(set_or1269000886237332187st_nat_type, type, set_or1269000886237332187st_nat: (nat > (nat > set_nat))). 185.24/93.62 thf(set_or4665077453230672383an_nat_type, type, set_or4665077453230672383an_nat: (nat > (nat > set_nat))). 185.24/93.62 thf(set_ord_atMost_nat_type, type, set_ord_atMost_nat: (nat > set_nat)). 185.24/93.62 thf(set_ord_lessThan_nat_type, type, set_ord_lessThan_nat: (nat > set_nat)). 185.24/93.62 thf(ascii_of_type, type, ascii_of: (char > char)). 185.24/93.62 thf(comm_s629917340098488124ar_nat_type, type, comm_s629917340098488124ar_nat: (char > nat)). 185.24/93.62 thf(unique3096191561947761185of_nat_type, type, unique3096191561947761185of_nat: (nat > char)). 185.24/93.62 thf(topolo6980174941875973593q_real_type, type, topolo6980174941875973593q_real: ((nat > real) > $o)). 185.24/93.62 thf(arccos_type, type, arccos: (real > real)). 185.24/93.62 thf(arcsin_type, type, arcsin: (real > real)). 185.24/93.62 thf(arctan_type, type, arctan: (real > real)). 185.24/93.62 thf(cos_complex_type, type, cos_complex: (complex > complex)). 185.24/93.62 thf(cos_real_type, type, cos_real: (real > real)). 185.24/93.62 thf(cos_coeff_type, type, cos_coeff: (nat > real)). 185.24/93.62 thf(exp_complex_type, type, exp_complex: (complex > complex)). 185.24/93.62 thf(exp_real_type, type, exp_real: (real > real)). 185.24/93.62 thf(ln_ln_real_type, type, ln_ln_real: (real > real)). 185.24/93.62 thf(log_type, type, log: (real > (real > real))). 185.24/93.62 thf(pi_type, type, pi: real). 185.24/93.62 thf(powr_real_type, type, powr_real: (real > (real > real))). 185.24/93.62 thf(sin_complex_type, type, sin_complex: (complex > complex)). 185.24/93.62 thf(sin_real_type, type, sin_real: (real > real)). 185.24/93.62 thf(sin_coeff_type, type, sin_coeff: (nat > real)). 185.24/93.62 thf(tan_complex_type, type, tan_complex: (complex > complex)). 185.24/93.62 thf(tan_real_type, type, tan_real: (real > real)). 185.24/93.62 thf(tanh_complex_type, type, tanh_complex: (complex > complex)). 185.24/93.62 thf(tanh_real_type, type, tanh_real: (real > real)). 185.24/93.62 thf(vEBT_Leaf_type, type, vEBT_Leaf: ($o > ($o > vEBT_VEBT))). 185.24/93.62 thf(vEBT_Node_type, type, vEBT_Node: (option4927543243414619207at_nat > (nat > (list_VEBT_VEBT > (vEBT_VEBT > vEBT_VEBT))))). 185.24/93.62 thf(vEBT_V8194947554948674370ptions_type, type, vEBT_V8194947554948674370ptions: (vEBT_VEBT > (nat > $o))). 185.24/93.62 thf(vEBT_VEBT_high_type, type, vEBT_VEBT_high: (nat > (nat > nat))). 185.24/93.62 thf(vEBT_V5917875025757280293ildren_type, type, vEBT_V5917875025757280293ildren: (nat > (list_VEBT_VEBT > (nat > $o)))). 185.24/93.62 thf(vEBT_VEBT_low_type, type, vEBT_VEBT_low: (nat > (nat > nat))). 185.24/93.62 thf(vEBT_VEBT_membermima_type, type, vEBT_VEBT_membermima: (vEBT_VEBT > (nat > $o))). 185.24/93.62 thf(vEBT_V4351362008482014158ma_rel_type, type, vEBT_V4351362008482014158ma_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 185.24/93.62 thf(vEBT_V5719532721284313246member_type, type, vEBT_V5719532721284313246member: (vEBT_VEBT > (nat > $o))). 185.24/93.62 thf(vEBT_V5765760719290551771er_rel_type, type, vEBT_V5765760719290551771er_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 185.24/93.62 thf(vEBT_invar_vebt_type, type, vEBT_invar_vebt: (vEBT_VEBT > (nat > $o))). 185.24/93.62 thf(vEBT_set_vebt_type, type, vEBT_set_vebt: (vEBT_VEBT > set_nat)). 185.24/93.62 thf(vEBT_vebt_buildup_type, type, vEBT_vebt_buildup: (nat > vEBT_VEBT)). 185.24/93.62 thf(vEBT_vebt_insert_type, type, vEBT_vebt_insert: (vEBT_VEBT > (nat > vEBT_VEBT))). 185.24/93.62 thf(vEBT_vebt_insert_rel_type, type, vEBT_vebt_insert_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 185.24/93.62 thf(vEBT_VEBT_bit_concat_type, type, vEBT_VEBT_bit_concat: (nat > (nat > (nat > nat)))). 185.24/93.62 thf(vEBT_VEBT_minNull_type, type, vEBT_VEBT_minNull: (vEBT_VEBT > $o)). 185.24/93.62 thf(vEBT_VEBT_set_vebt_type, type, vEBT_VEBT_set_vebt: (vEBT_VEBT > set_nat)). 185.24/93.62 thf(vEBT_vebt_member_type, type, vEBT_vebt_member: (vEBT_VEBT > (nat > $o))). 185.24/93.62 thf(vEBT_vebt_member_rel_type, type, vEBT_vebt_member_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 185.24/93.62 thf(vEBT_VEBT_add_type, type, vEBT_VEBT_add: (option_nat > (option_nat > option_nat))). 185.24/93.62 thf(vEBT_VEBT_greater_type, type, vEBT_VEBT_greater: (option_nat > (option_nat > $o))). 185.24/93.62 thf(vEBT_VEBT_less_type, type, vEBT_VEBT_less: (option_nat > (option_nat > $o))). 185.24/93.62 thf(vEBT_VEBT_lesseq_type, type, vEBT_VEBT_lesseq: (option_nat > (option_nat > $o))). 185.24/93.62 thf(vEBT_VEBT_max_in_set_type, type, vEBT_VEBT_max_in_set: (set_nat > (nat > $o))). 185.24/93.62 thf(vEBT_VEBT_min_in_set_type, type, vEBT_VEBT_min_in_set: (set_nat > (nat > $o))). 185.24/93.62 thf(vEBT_VEBT_mul_type, type, vEBT_VEBT_mul: (option_nat > (option_nat > option_nat))). 185.24/93.62 thf(vEBT_vebt_maxt_type, type, vEBT_vebt_maxt: (vEBT_VEBT > option_nat)). 185.24/93.62 thf(vEBT_vebt_maxt_rel_type, type, vEBT_vebt_maxt_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 185.24/93.62 thf(vEBT_vebt_mint_type, type, vEBT_vebt_mint: (vEBT_VEBT > option_nat)). 185.24/93.62 thf(vEBT_vebt_mint_rel_type, type, vEBT_vebt_mint_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 185.24/93.62 thf(vEBT_is_pred_in_set_type, type, vEBT_is_pred_in_set: (set_nat > (nat > (nat > $o)))). 185.24/93.62 thf(vEBT_vebt_pred_type, type, vEBT_vebt_pred: (vEBT_VEBT > (nat > option_nat))). 185.24/93.62 thf(vEBT_vebt_pred_rel_type, type, vEBT_vebt_pred_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 185.24/93.62 thf(accp_P2887432264394892906BT_nat_type, type, accp_P2887432264394892906BT_nat: ((produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o)) > (produc9072475918466114483BT_nat > $o))). 185.24/93.62 thf(accp_VEBT_VEBT_type, type, accp_VEBT_VEBT: ((vEBT_VEBT > (vEBT_VEBT > $o)) > (vEBT_VEBT > $o))). 185.24/93.62 thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))). 185.24/93.62 thf(member_VEBT_VEBT_type, type, member_VEBT_VEBT: (vEBT_VEBT > (set_VEBT_VEBT > $o))). 185.24/93.62 thf(deg_type, type, deg: nat). 185.24/93.62 thf(m_type, type, m: nat). 185.24/93.62 thf(ma_type, type, ma: nat). 185.24/93.62 thf(maxy_type, type, maxy: nat). 185.24/93.62 thf(mi_type, type, mi: nat). 185.24/93.62 thf(na_type, type, na: nat). 185.24/93.62 thf(pr_type, type, pr: nat). 185.24/93.62 thf(res_type, type, res: nat). 185.24/93.62 thf(summary_type, type, summary: vEBT_VEBT). 185.24/93.62 thf(treeList_type, type, treeList: list_VEBT_VEBT). 185.24/93.62 thf(xa_type, type, xa: nat). 185.24/93.62 thf(za_type, type, za: nat). 185.24/93.62 thf(3161,axiom,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) != zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7216_of__nat__neq__0)). 185.24/93.62 thf(18180,plain,((! [A:nat]: ~ ((semiri1314217659103216013at_int @ (suc @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3161])). 185.24/93.62 thf(7095,axiom,((! [A:nat,B:num]: ((divide_divide_nat @ (suc @ (suc @ (suc @ A))) @ (numeral_numeral_nat @ B)) = (divide_divide_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6441_Suc__div__eq__add3__div__numeral)). 185.24/93.62 thf(31885,plain,((! [A:nat,B:num]: ((divide_divide_nat @ (suc @ (suc @ (suc @ A))) @ (numeral_numeral_nat @ B)) = (divide_divide_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ (numeral_numeral_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7095])). 185.24/93.62 thf(5474,axiom,((! [A:rat]: ((times_times_rat @ A @ one_one_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_mult_Oright__neutral)). 185.24/93.62 thf(25953,plain,((! [A:rat]: ((times_times_rat @ A @ one_one_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5474])). 185.24/93.62 thf(6368,axiom,((! [A:nat,B:code_integer]: (((power_8256067586552552935nteger @ (abs_abs_Code_integer @ B) @ A) = (power_8256067586552552935nteger @ B @ A)) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6691_power__even__abs)). 185.24/93.62 thf(29176,plain,((! [A:nat,B:code_integer]: (((power_8256067586552552935nteger @ (abs_abs_Code_integer @ B) @ A) = (power_8256067586552552935nteger @ B @ A)) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6368])). 185.24/93.62 thf(1939,axiom,((! [A:num,B:num,C:(num > real),D:real]: ((ord_less_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)) <= (ord_less_eq_real @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4353_order__less__le__subst2)). 185.24/93.62 thf(14221,plain,((! [A:num,B:num,C:(num > real),D:real]: ((ord_less_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)) | ~ (ord_less_eq_real @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1939])). 185.24/93.62 thf(2559,axiom,((! [A:real,B:real,C:real,D:real]: ((((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ C @ (minus_minus_real @ B @ A)) @ D)) @ B)) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2931_scaling__mono)). 185.24/93.62 thf(16216,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ C @ (minus_minus_real @ B @ A)) @ D)) @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2559])). 185.24/93.62 thf(4845,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (minus_minus_int @ B @ C)) = (ord_less_eq_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_794_le__diff__eq)). 185.24/93.62 thf(23563,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (minus_minus_int @ B @ C)) = (ord_less_eq_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4845])). 185.24/93.62 thf(4900,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6495_abs__triangle__ineq2__sym)). 185.24/93.62 thf(23764,plain,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4900])). 185.24/93.62 thf(2458,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2238_mult__left__mono)). 185.24/93.62 thf(15874,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2458])). 185.24/93.62 thf(7209,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2084_add_Ocomm__neutral)). 185.24/93.62 thf(32287,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7209])). 185.24/93.62 thf(3795,axiom,((! [A:real,B:real,C:real]: ((((powr_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ (powr_real @ A @ C) @ (powr_real @ B @ C))) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9099_powr__divide)). 185.24/93.62 thf(20194,plain,((! [A:real,B:real,C:real]: (((powr_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ (powr_real @ A @ C) @ (powr_real @ B @ C))) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3795])). 185.24/93.62 thf(658,axiom,((! [A:nat,B:nat,C:(nat > real)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_real @ (groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & (((groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_real) <= (ord_less_nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8705_prod_Ocl__ivl__Suc)). 185.24/93.62 thf(9929,plain,((! [A:nat,B:nat,C:(nat > real)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_real @ (groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & (((groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_real) | ~ (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[658])). 185.24/93.62 thf(1569,axiom,((! [A:rat,B:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ B)) @ (plus_plus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6582_abs__triangle__ineq4)). 185.24/93.62 thf(12928,plain,((! [A:rat,B:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ B)) @ (plus_plus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569])). 185.24/93.62 thf(1767,axiom,((! [A:num]: ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ one)) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1946_cong__exp__iff__simps_I1_J)). 185.24/93.62 thf(13650,plain,((! [A:num]: ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ one)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767])). 185.24/93.62 thf(5053,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2130_nat__mult__eq__cancel__disj)). 185.24/93.62 thf(24338,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5053])). 185.24/93.62 thf(4258,axiom,((! [A:nat,B:int]: ((times_times_int @ (semiri1314217659103216013at_int @ A) @ B) = (times_times_int @ B @ (semiri1314217659103216013at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7182_mult__of__nat__commute)). 185.24/93.62 thf(21624,plain,((! [A:nat,B:int]: ((times_times_int @ (semiri1314217659103216013at_int @ A) @ B) = (times_times_int @ B @ (semiri1314217659103216013at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4258])). 185.24/93.62 thf(5737,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3972_gt__ex)). 185.24/93.62 thf(26820,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5737])). 185.24/93.62 thf(4295,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ B @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3985_order_Oasym)). 185.24/93.62 thf(21729,plain,((! [A:int,B:int]: (~ (ord_less_int @ B @ A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4295])). 185.24/93.62 thf(2437,axiom,((! [A:real,B:real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5555_is__num__normalize_I8_J)). 185.24/93.62 thf(15806,plain,((! [A:real,B:real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2437])). 185.24/93.62 thf(5589,axiom,((! [A:nat]: ((^ [B:nat]: (times_times_nat @ B @ A)) = (times_times_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1336_mult__commute__abs)). 185.24/93.62 thf(26329,plain,((! [A:nat]: ((^ [B:nat]: (times_times_nat @ B @ A)) = (times_times_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5589])). 185.24/93.62 thf(5899,axiom,((! [A:nat,B:int]: (((B = one_one_int) | (ord_less_nat @ zero_zero_nat @ A)) => (dvd_dvd_int @ B @ (power_power_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4920_dvd__power)). 185.24/93.62 thf(27536,plain,((! [A:nat,B:int]: (((B = one_one_int) | (ord_less_nat @ zero_zero_nat @ A)) => (dvd_dvd_int @ B @ (power_power_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5899])). 185.24/93.62 thf(3815,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3970_gt__ex)). 185.24/93.62 thf(20256,plain,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3815])). 185.24/93.62 thf(2724,axiom,((! [A:real,B:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1650_add__less__same__cancel2)). 185.24/93.62 thf(16794,plain,((! [A:real,B:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2724])). 185.24/93.62 thf(2140,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ A @ B)) = (((ord_less_eq_real @ A @ B) & (ord_less_real @ B @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ B) & (ord_less_eq_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2854_le__divide__eq__1)). 185.24/93.62 thf(14852,plain,((! [A:real,B:real]: ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ A @ B)) = (((ord_less_eq_real @ A @ B) & (ord_less_real @ B @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ B) & (ord_less_eq_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2140])). 185.24/93.62 thf(3540,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) <= (! [C:rat]: (((ord_less_rat @ C @ one_one_rat) => (ord_less_eq_rat @ (times_times_rat @ C @ A) @ B)) <= (ord_less_rat @ zero_zero_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2831_field__le__mult__one__interval)). 185.24/93.62 thf(19370,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) | ~ (! [C:rat]: (((ord_less_rat @ C @ one_one_rat) => (ord_less_eq_rat @ (times_times_rat @ C @ A) @ B)) | ~ (ord_less_rat @ zero_zero_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3540])). 185.24/93.62 thf(5613,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => (((modulo_modulo_nat @ C @ B) = A) <= (dvd_dvd_nat @ B @ (minus_minus_nat @ C @ A)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4928_mod__nat__eqI)). 185.24/93.62 thf(26413,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => (((modulo_modulo_nat @ C @ B) = A) | ~ (dvd_dvd_nat @ B @ (minus_minus_nat @ C @ A)))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5613])). 185.24/93.62 thf(6365,axiom,((! [A:nat]: ((semiri773545260158071498ct_rat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (times_times_rat @ (times_times_rat @ (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (comm_s4028243227959126397er_rat @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one))) @ A)) @ (semiri773545260158071498ct_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8609_fact__double)). 185.24/93.62 thf(29163,plain,((! [A:nat]: ((semiri773545260158071498ct_rat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (times_times_rat @ (times_times_rat @ (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (comm_s4028243227959126397er_rat @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one))) @ A)) @ (semiri773545260158071498ct_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6365])). 185.24/93.62 thf(6708,axiom,(((plus_plus_rat @ (uminus_uminus_rat @ one_one_rat) @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5408_add__neg__numeral__special_I9_J)). 185.24/93.62 thf(30353,plain,(((plus_plus_rat @ (uminus_uminus_rat @ one_one_rat) @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6708])). 185.24/93.62 thf(368,axiom,((! [A:real,B:real,C:real]: ((((ord_less_real @ C @ (log @ A @ B)) = (ord_less_real @ (powr_real @ A @ C) @ B)) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9107_less__log__iff)). 185.24/93.62 thf(8960,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ C @ (log @ A @ B)) = (ord_less_real @ (powr_real @ A @ C) @ B)) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])). 185.24/93.62 thf(497,axiom,((! [A:real]: (((cos_real @ (arccos @ A)) = A) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8370_cos__arccos__abs)). 185.24/93.62 thf(9405,plain,((! [A:real]: (((cos_real @ (arccos @ A)) = A) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[497])). 185.24/93.62 thf(5428,axiom,((! [A:num]: (one != (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6473_verit__eq__simplify_I12_J)). 185.24/93.62 thf(25680,plain,((! [A:num]: ~ (one = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5428])). 185.24/93.62 thf(3193,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ B) @ A) = (modulo_modulo_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1598_mod__add__self1)). 185.24/93.62 thf(18279,plain,((! [A:int,B:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ B) @ A) = (modulo_modulo_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3193])). 185.24/93.62 thf(5563,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((suc @ (minus_minus_nat @ A @ one_one_nat)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1883_Suc__diff__1)). 185.24/93.62 thf(26250,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((suc @ (minus_minus_nat @ A @ one_one_nat)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5563])). 185.24/93.62 thf(2510,axiom,((! [A:complex]: (((sin_complex @ A) = zero_zero_complex) => ((real_V1022390504157884413omplex @ (cos_complex @ A)) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7825_sin__zero__norm__cos__one)). 185.24/93.62 thf(16054,plain,((! [A:complex]: (((sin_complex @ A) = zero_zero_complex) => ((real_V1022390504157884413omplex @ (cos_complex @ A)) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2510])). 185.24/93.62 thf(2949,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((((ord_less_rat @ (divide_divide_rat @ A @ D) @ (divide_divide_rat @ B @ C)) <= (ord_less_eq_rat @ C @ D)) <= (ord_less_rat @ zero_zero_rat @ C)) <= (ord_less_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2648_frac__less)). 185.24/93.62 thf(17507,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (divide_divide_rat @ A @ D) @ (divide_divide_rat @ B @ C)) | ~ (ord_less_eq_rat @ C @ D) | ~ (ord_less_rat @ zero_zero_rat @ C) | ~ (ord_less_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2949])). 185.24/93.62 thf(3029,axiom,((! [A:num]: (imaginary_unit != (numera6690914467698888265omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8996_complex__i__not__numeral)). 185.24/93.62 thf(17759,plain,((! [A:num]: ~ (imaginary_unit = (numera6690914467698888265omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3029])). 185.24/93.62 thf(3896,axiom,((! [A:int,B:int]: ((minus_minus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) = (times_times_int @ (plus_plus_int @ A @ B) @ (minus_minus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1217_square__diff__square__factored)). 185.24/93.62 thf(20503,plain,((! [A:int,B:int]: ((minus_minus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) = (times_times_int @ (plus_plus_int @ A @ B) @ (minus_minus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3896])). 185.24/93.62 thf(2948,axiom,((! [A:int,B:int]: (((dvd_dvd_int @ A @ one_one_int) <= (dvd_dvd_int @ B @ one_one_int)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4631_dvd__unit__imp__unit)). 185.24/93.62 thf(17505,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) | ~ (dvd_dvd_int @ B @ one_one_int) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2948])). 185.24/93.62 thf(5516,axiom,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ A @ one_one_int) => (ord_less_int @ (power_power_int @ A @ (suc @ B)) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2878_power__Suc__less__one)). 185.24/93.62 thf(26098,plain,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ A @ one_one_int) => (ord_less_int @ (power_power_int @ A @ (suc @ B)) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5516])). 185.24/93.62 thf(1101,axiom,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) => ((uminus1482373934393186551omplex @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5735_add_Oinverse__unique)). 185.24/93.62 thf(11472,plain,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) => ((uminus1482373934393186551omplex @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101])). 185.24/93.62 thf(1884,axiom,((ord_less_eq_rat @ one_one_rat @ one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_761_le__numeral__extra_I4_J)). 185.24/93.62 thf(14038,plain,((ord_less_eq_rat @ one_one_rat @ one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1884])). 185.24/93.62 thf(6562,axiom,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2269_not__one__le__zero)). 185.24/93.62 thf(29879,plain,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6562])). 185.24/93.62 thf(4959,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (modulo_modulo_nat @ A @ B) @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2535_mod__div__mult__eq)). 185.24/93.62 thf(23969,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (modulo_modulo_nat @ A @ B) @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4959])). 185.24/93.62 thf(4932,axiom,((! [A:$o,B:$o]: ((((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ zero_zero_nat)) <= (A)) & ((((B) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ one_one_nat))) & (((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = none_nat) <= (~ (B)))) <= (~ (A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2188_vebt__mint_Osimps_I1_J)). 185.24/93.62 thf(23872,plain,((! [A:$o,B:$o]: ((((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ zero_zero_nat)) | ~ (A)) & ((((B) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ one_one_nat))) & (((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = none_nat) | (B))) | (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4932])). 185.24/93.62 thf(2388,axiom,((! [A:rat,B:rat]: ((dvd_dvd_rat @ A @ B) => (~ (! [C:rat]: (B != (times_times_rat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4622_dvdE)). 185.24/93.62 thf(15628,plain,((! [A:rat,B:rat]: ((dvd_dvd_rat @ A @ B) => (~ (! [C:rat]: ~ (B = (times_times_rat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2388])). 185.24/93.62 thf(3637,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ C @ A)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1839_div__mult__self1)). 185.24/93.62 thf(19672,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ C @ A)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3637])). 185.24/93.62 thf(1856,axiom,((! [A:num]: (ord_less_rat @ (uminus_uminus_rat @ one_one_rat) @ (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5949_neg__one__less__numeral)). 185.24/93.62 thf(13955,plain,((! [A:num]: (ord_less_rat @ (uminus_uminus_rat @ one_one_rat) @ (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1856])). 185.24/93.62 thf(5572,axiom,((! [A:code_integer]: ((abs_abs_Code_integer @ (abs_abs_Code_integer @ A)) = (abs_abs_Code_integer @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6315_abs__idempotent)). 185.24/93.62 thf(26279,plain,((! [A:code_integer]: ((abs_abs_Code_integer @ (abs_abs_Code_integer @ A)) = (abs_abs_Code_integer @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5572])). 185.24/93.62 thf(5031,axiom,((! [A:num,B:num]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (uminus_uminus_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5340_mult__neg__numeral__simps_I3_J)). 185.24/93.62 thf(24195,plain,((! [A:num,B:num]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (uminus_uminus_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5031])). 185.24/93.62 thf(3041,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_ab__semigroup__add__class_Oadd__ac_I1_J)). 185.24/93.62 thf(17803,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3041])). 185.24/93.62 thf(785,axiom,((! [A:real,B:nat,C:(nat > real)]: (((summable_real @ C) <= (! [D:nat]: ((ord_less_eq_nat @ B @ D) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (C @ (suc @ D))) @ (times_times_real @ A @ (real_V7735802525324610683m_real @ (C @ D))))))) <= (ord_less_real @ A @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7752_summable__ratio__test)). 185.24/93.62 thf(10410,plain,((! [A:real,B:nat,C:(nat > real)]: ((summable_real @ (C)) | ~ (! [D:nat]: ((ord_less_eq_nat @ B @ D) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (C @ (suc @ D))) @ (times_times_real @ A @ (real_V7735802525324610683m_real @ (C @ D)))))) | ~ (ord_less_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[785])). 185.24/93.62 thf(3217,axiom,((imaginary_unit != one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8995_complex__i__not__one)). 185.24/93.62 thf(18360,plain,((~ (imaginary_unit = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3217])). 185.24/93.62 thf(3593,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1138_distrib__left)). 185.24/93.62 thf(19540,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3593])). 185.24/93.62 thf(2804,axiom,((! [A:int]: (((abs_abs_int @ A) = (uminus_uminus_int @ A)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6406_abs__of__nonpos)). 185.24/93.62 thf(17043,plain,((! [A:int]: (((abs_abs_int @ A) = (uminus_uminus_int @ A)) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2804])). 185.24/93.62 thf(1631,axiom,((ord_less_eq_real @ one_one_real @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_760_le__numeral__extra_I4_J)). 185.24/93.62 thf(13162,plain,((ord_less_eq_real @ one_one_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631])). 185.24/93.62 thf(4832,axiom,((! [A:real]: (((suminf_real @ (power_power_real @ A)) = (divide_divide_real @ one_one_real @ (minus_minus_real @ one_one_real @ A))) <= (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7640_suminf__geometric)). 185.24/93.62 thf(23519,plain,((! [A:real]: (((suminf_real @ (power_power_real @ A)) = (divide_divide_real @ one_one_real @ (minus_minus_real @ one_one_real @ A))) | ~ (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4832])). 185.24/93.62 thf(206,axiom,((! [A:rat,B:nat]: ((gbinomial_rat @ A @ (suc @ B)) = (plus_plus_rat @ (gbinomial_rat @ (minus_minus_rat @ A @ one_one_rat) @ (suc @ B)) @ (gbinomial_rat @ (minus_minus_rat @ A @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8477_gbinomial__addition__formula)). 185.24/93.62 thf(8398,plain,((! [A:rat,B:nat]: ((gbinomial_rat @ A @ (suc @ B)) = (plus_plus_rat @ (gbinomial_rat @ (minus_minus_rat @ A @ one_one_rat) @ (suc @ B)) @ (gbinomial_rat @ (minus_minus_rat @ A @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 185.24/93.62 thf(3821,axiom,(((neg_nu8557863876264182079omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7002_dbl__inc__simps_I4_J)). 185.24/93.62 thf(20273,plain,(((neg_nu8557863876264182079omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3821])). 185.24/93.62 thf(7659,axiom,((! [A:num]: ((bit0 @ A) != one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_semiring__norm_I85_J)). 185.24/93.62 thf(33732,plain,((! [A:num]: ~ ((bit0 @ A) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7659])). 185.24/93.62 thf(2675,axiom,((! [A:nat]: (((semiri5074537144036343181t_real @ A) = one_one_real) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6930_of__nat__eq__1__iff)). 185.24/93.62 thf(16598,plain,((! [A:nat]: (((semiri5074537144036343181t_real @ A) = one_one_real) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2675])). 185.24/93.62 thf(1296,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((divide_divide_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (divide_divide_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1693_div__mult__mult2)). 185.24/93.62 thf(12055,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (divide_divide_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296])). 185.24/93.62 thf(3872,axiom,((! [A:rat,B:rat,C:(rat > num),D:num]: (((ord_less_num @ (C @ B) @ D) => ((ord_less_num @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4115_order__less__subst2)). 185.24/93.62 thf(20432,plain,((! [A:rat,B:rat,C:(rat > num),D:num]: (((ord_less_num @ (C @ B) @ D) => ((ord_less_num @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3872])). 185.24/93.62 thf(730,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((sin_real @ (arcsin @ A)) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8308_sin__arcsin)). 185.24/93.62 thf(10166,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((sin_real @ (arcsin @ A)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[730])). 185.24/93.62 thf(1497,axiom,((! [A:num]: ((numeral_numeral_int @ (bit1 @ A)) = (plus_plus_int @ (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6631_numeral__code_I3_J)). 185.24/93.62 thf(12710,plain,((! [A:num]: ((numeral_numeral_int @ (bit1 @ A)) = (plus_plus_int @ (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497])). 185.24/93.62 thf(4422,axiom,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ A @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (plus_plus_rat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_725_add__diff__eq)). 185.24/93.62 thf(22153,plain,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ A @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (plus_plus_rat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4422])). 185.24/93.62 thf(6680,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1093_less__imp__Suc__add)). 185.24/93.62 thf(30266,plain,((! [A:nat,B:nat]: (? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6680])). 185.24/93.62 thf(1463,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2405_add__neg__neg)). 185.24/93.62 thf(12607,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463])). 185.24/93.62 thf(1093,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) => (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4382_bot_Oextremum__uniqueI)). 185.24/93.62 thf(11445,plain,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) => (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093])). 185.24/93.62 thf(6538,axiom,((! [A:rat,B:nat]: (((power_power_rat @ A @ B) = zero_zero_rat) = ((ord_less_nat @ zero_zero_nat @ B) & (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1840_power__eq__0__iff)). 185.24/93.62 thf(29802,plain,((! [A:rat,B:nat]: (((power_power_rat @ A @ B) = zero_zero_rat) = ((ord_less_nat @ zero_zero_nat @ B) & (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6538])). 185.24/93.62 thf(2768,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (times_times_rat @ B @ A) @ B) <= (ord_less_eq_rat @ zero_zero_rat @ B)) <= (ord_less_eq_rat @ A @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2662_mult__left__le)). 185.24/93.62 thf(16928,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (times_times_rat @ B @ A) @ B) | ~ (ord_less_eq_rat @ zero_zero_rat @ B) | ~ (ord_less_eq_rat @ A @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2768])). 185.24/93.62 thf(2273,axiom,((! [A:nat,B:nat,C:int]: ((plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ B) @ C)) = (plus_plus_int @ (semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7250_zadd__int__left)). 185.24/93.62 thf(15278,plain,((! [A:nat,B:nat,C:int]: ((plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ B) @ C)) = (plus_plus_int @ (semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2273])). 185.24/93.62 thf(649,axiom,((! [A:rat,B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (times_times_rat @ (gbinomial_rat @ A @ C) @ (minus_minus_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))) @ (semiri681578069525770553at_rat @ C)))) @ (set_ord_atMost_nat @ B)) = (times_times_rat @ (divide_divide_rat @ (plus_plus_rat @ (semiri681578069525770553at_rat @ B) @ one_one_rat) @ (numeral_numeral_rat @ (bit0 @ one))) @ (gbinomial_rat @ A @ (plus_plus_nat @ B @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8619_gbinomial__partial__row__sum)). 185.24/93.62 thf(9886,plain,((! [A:rat,B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (times_times_rat @ (gbinomial_rat @ A @ C) @ (minus_minus_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))) @ (semiri681578069525770553at_rat @ C)))) @ (set_ord_atMost_nat @ B)) = (times_times_rat @ (divide_divide_rat @ (plus_plus_rat @ (semiri681578069525770553at_rat @ B) @ one_one_rat) @ (numeral_numeral_rat @ (bit0 @ one))) @ (gbinomial_rat @ A @ (plus_plus_nat @ B @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[649])). 185.24/93.62 thf(6457,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_left__add__twice)). 185.24/93.62 thf(29505,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6457])). 185.24/93.62 thf(7727,axiom,((vEBT_V5917875025757280293ildren = (^ [A:nat,B:list_VEBT_VEBT,C:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ B @ (vEBT_VEBT_high @ C @ A)) @ (vEBT_VEBT_low @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_in__children__def)). 185.24/93.62 thf(33917,plain,(((vEBT_V5917875025757280293ildren) = (^ [A:nat,B:list_VEBT_VEBT,C:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ B @ (vEBT_VEBT_high @ C @ A)) @ (vEBT_VEBT_low @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7727])). 185.24/93.62 thf(6627,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_nat__less__induct)). 185.24/93.62 thf(30093,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6627])). 185.24/93.62 thf(4438,axiom,((! [A:produc9072475918466114483BT_nat]: (((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))) => (((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))))) <= (! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E))))) <= (! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2133_vebt__member_Ocases)). 185.24/93.62 thf(22210,plain,((! [A:produc9072475918466114483BT_nat]: (((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))) => (((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))))) | ~ (! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E))))) | ~ (! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4438])). 185.24/93.62 thf(2901,axiom,((~ (ord_less_int @ one_one_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2383_not__one__less__zero)). 185.24/93.62 thf(17358,plain,((~ (ord_less_int @ one_one_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2901])). 185.24/93.62 thf(6547,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ B) @ (times_times_nat @ A @ (power_power_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_864_power__less__power__Suc)). 185.24/93.62 thf(29830,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ B) @ (times_times_nat @ A @ (power_power_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6547])). 185.24/93.62 thf(892,axiom,((! [A:(nat > real),B:set_nat]: (ord_less_eq_real @ (abs_abs_real @ (groups6591440286371151544t_real @ A @ B)) @ (groups6591440286371151544t_real @ (^ [C:nat]: (abs_abs_real @ (A @ C))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6398_sum__abs)). 185.24/93.62 thf(10785,plain,((! [A:(nat > real),B:set_nat]: (ord_less_eq_real @ (abs_abs_real @ (groups6591440286371151544t_real @ (A) @ B)) @ (groups6591440286371151544t_real @ (^ [C:nat]: (abs_abs_real @ (A @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[892])). 185.24/93.62 thf(6494,axiom,((! [A:num,B:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (modulo_modulo_nat @ (numeral_numeral_nat @ one) @ (numeral_numeral_nat @ (bit0 @ B)))) = ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6698_cong__exp__iff__simps_I11_J)). 185.24/93.62 thf(29644,plain,((! [A:num,B:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (modulo_modulo_nat @ (numeral_numeral_nat @ one) @ (numeral_numeral_nat @ (bit0 @ B)))) = ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6494])). 185.24/93.62 thf(404,axiom,((! [A:int]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ zero_zero_int) = (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7035_of__int__le__0__iff)). 185.24/93.62 thf(9077,plain,((! [A:int]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ zero_zero_int) = (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])). 185.24/93.62 thf(4857,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => ((minus_minus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (times_times_complex @ B @ A) @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2765_diff__divide__eq__iff)). 185.24/93.62 thf(23595,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => ((minus_minus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (times_times_complex @ B @ A) @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4857])). 185.24/93.62 thf(6300,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ (divide_divide_nat @ B @ A)) = B) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4485_dvd__mult__div__cancel)). 185.24/93.62 thf(28926,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ (divide_divide_nat @ B @ A)) = B) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6300])). 185.24/93.62 thf(1449,axiom,((! [A:complex,B:nat]: ((exp_complex @ (times_times_complex @ A @ (semiri8010041392384452111omplex @ B))) = (power_power_complex @ (exp_complex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8195_exp__of__nat2__mult)). 185.24/93.62 thf(12564,plain,((! [A:complex,B:nat]: ((exp_complex @ (times_times_complex @ A @ (semiri8010041392384452111omplex @ B))) = (power_power_complex @ (exp_complex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449])). 185.24/93.62 thf(3667,axiom,((! [A:nat]: ((fract @ (semiri1314217659103216013at_int @ A) @ one_one_int) = (semiri681578069525770553at_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9936_Fract__of__nat__eq)). 185.24/93.62 thf(19772,plain,((! [A:nat]: ((fract @ (semiri1314217659103216013at_int @ A) @ one_one_int) = (semiri681578069525770553at_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3667])). 185.24/93.62 thf(3089,axiom,((! [A:rat,B:rat,C:rat]: (((A != zero_zero_rat) => ((divide_divide_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (divide_divide_rat @ B @ C))) & (((divide_divide_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = zero_zero_rat) <= (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1710_mult__divide__mult__cancel__left__if)). 185.24/93.62 thf(17950,plain,((! [A:rat,B:rat,C:rat]: (((~ (A = zero_zero_rat)) => ((divide_divide_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (divide_divide_rat @ B @ C))) & (((divide_divide_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = zero_zero_rat) | ~ (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3089])). 185.24/93.62 thf(2814,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = ((B = zero_zero_real) | (dvd_dvd_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4459_dvd__mult__cancel__right)). 185.24/93.62 thf(17072,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = ((B = zero_zero_real) | (dvd_dvd_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2814])). 185.24/93.62 thf(3652,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_add__left__cancel)). 185.24/93.62 thf(19726,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3652])). 185.24/93.62 thf(7234,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (suc @ B)) = (case_nat_nat @ zero_zero_nat @ (^ [C:nat]: (C)) @ (minus_minus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9744_diff__Suc)). 185.24/93.62 thf(32383,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (suc @ B)) = (case_nat_nat @ zero_zero_nat @ (^ [C:nat]: (C)) @ (minus_minus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7234])). 185.24/93.62 thf(131,axiom,((! [A:(nat > complex),B:(nat > real)]: (((summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C)))) <= (summable_real @ B)) <= (? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (A @ D)) @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7707_summable__norm__comparison__test)). 185.24/93.62 thf(8154,plain,((! [A:(nat > complex),B:(nat > real)]: ((summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C)))) | ~ (summable_real @ (B)) | ~ (? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (A @ D)) @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 185.24/93.62 thf(3098,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ A)) = (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4439_dvd__add__triv__right__iff)). 185.24/93.62 thf(17986,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ A)) = (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3098])). 185.24/93.62 thf(5364,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ (binomial @ A @ B)) = (times_times_nat @ A @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8453_binomial__absorb__comp)). 185.24/93.62 thf(25489,plain,((! [A:nat,B:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ (binomial @ A @ B)) = (times_times_nat @ A @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5364])). 185.24/93.62 thf(4288,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))) @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7516_norm__triangle__ineq3)). 185.24/93.62 thf(21710,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))) @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4288])). 185.24/93.62 thf(1017,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ B @ A) @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2766_diff__divide__eq__iff)). 185.24/93.62 thf(11211,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ B @ A) @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017])). 185.24/93.62 thf(1694,axiom,((! [A:nat]: ((semiri8010041392384452111omplex @ (suc @ A)) = (plus_plus_complex @ one_one_complex @ (semiri8010041392384452111omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7013_of__nat__Suc)). 185.24/93.62 thf(13402,plain,((! [A:nat]: ((semiri8010041392384452111omplex @ (suc @ A)) = (plus_plus_complex @ one_one_complex @ (semiri8010041392384452111omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694])). 185.24/93.62 thf(2183,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_3966_order__antisym__conv)). 185.24/93.62 thf(15009,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)],[2183])). 185.24/93.62 thf(2686,axiom,((! [A:int]: ((ord_less_real @ zero_zero_real @ (ring_1_of_int_real @ A)) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7039_of__int__0__less__iff)). 185.24/93.62 thf(16676,plain,((! [A:int]: ((ord_less_real @ zero_zero_real @ (ring_1_of_int_real @ A)) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2686])). 185.24/93.62 thf(2059,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ zero_zero_rat @ A)) <= (ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2344_zero__less__mult__pos2)). 185.24/93.62 thf(14606,plain,((! [A:rat,B:rat]: (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ zero_zero_rat @ A)) | ~ (ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2059])). 185.24/93.62 thf(5012,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1004_diff__Suc__Suc)). 185.24/93.62 thf(24141,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5012])). 185.24/93.62 thf(1073,axiom,((! [A:rat,B:num,C:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) @ C) = (ord_less_rat @ (times_times_rat @ C @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5396_divide__less__eq__numeral1_I2_J)). 185.24/93.62 thf(11372,plain,((! [A:rat,B:num,C:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) @ C) = (ord_less_rat @ (times_times_rat @ C @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073])). 185.24/93.62 thf(3138,axiom,(((cos_real @ zero_zero_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7781_cos__zero)). 185.24/93.62 thf(18107,plain,(((cos_real @ zero_zero_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3138])). 185.24/93.62 thf(6664,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) <= (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_power__less__imp__less__exp)). 185.24/93.62 thf(30213,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) | ~ (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6664])). 185.24/93.62 thf(577,axiom,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_Code_integer) = (ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ A) @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6718_abs__square__less__1)). 185.24/93.62 thf(9648,plain,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_Code_integer) = (ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ A) @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[577])). 185.24/93.62 thf(2779,axiom,((! [A:real,B:real]: ((abs_abs_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6350_abs__divide)). 185.24/93.62 thf(16962,plain,((! [A:real,B:real]: ((abs_abs_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2779])). 185.24/93.62 thf(5649,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ (power_power_rat @ A @ B) @ zero_zero_rat) = ((ord_less_rat @ A @ zero_zero_rat) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4535_power__less__zero__eq)). 185.24/93.62 thf(26530,plain,((! [A:rat,B:nat]: ((ord_less_rat @ (power_power_rat @ A @ B) @ zero_zero_rat) = ((ord_less_rat @ A @ zero_zero_rat) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5649])). 185.24/93.62 thf(7688,axiom,((! [A:complex,B:complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_complex @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = (uminus1482373934393186551omplex @ B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6181_power2__eq__iff)). 185.24/93.62 thf(33807,plain,((! [A:complex,B:complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_complex @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = (uminus1482373934393186551omplex @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7688])). 185.24/93.62 thf(5677,axiom,((! [A:real,B:real,C:num]: (((divide_divide_real @ A @ B) = (uminus_uminus_real @ (numeral_numeral_real @ C))) = (((B != zero_zero_real) => (A = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B))) & (((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real) <= (B = zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6159_divide__eq__eq__numeral_I2_J)). 185.24/93.62 thf(26625,plain,((! [A:real,B:real,C:num]: (((divide_divide_real @ A @ B) = (uminus_uminus_real @ (numeral_numeral_real @ C))) = (((~ (B = zero_zero_real)) => (A = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B))) & (((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real) | ~ (B = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5677])). 185.24/93.62 thf(7636,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2994_Suc__n__div__2__gt__zero)). 185.24/93.62 thf(33675,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7636])). 185.24/93.62 thf(2568,axiom,((! [A:nat,B:nat]: (((ord_max_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3593_max__nat_Oeq__neutr__iff)). 185.24/93.62 thf(16243,plain,((! [A:nat,B:nat]: (((ord_max_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2568])). 185.24/93.62 thf(7589,axiom,((! [A:nat]: (((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1868_zero__eq__power2)). 185.24/93.62 thf(33537,plain,((! [A:nat]: (((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7589])). 185.24/93.62 thf(7367,axiom,((! [A:real,B:num]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ (power_power_real @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1364_power__numeral__even)). 185.24/93.62 thf(32819,plain,((! [A:real,B:num]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ (power_power_real @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7367])). 185.24/93.62 thf(6332,axiom,((! [A:int]: ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_mult__2)). 185.24/93.62 thf(29039,plain,((! [A:int]: ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = (plus_plus_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6332])). 185.24/93.62 thf(1765,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((B = (uminus_uminus_real @ (divide_divide_real @ C @ A))) = ((times_times_real @ B @ A) = (uminus_uminus_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5963_nonzero__neg__divide__eq__eq2)). 185.24/93.62 thf(13643,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((B = (uminus_uminus_real @ (divide_divide_real @ C @ A))) = ((times_times_real @ B @ A) = (uminus_uminus_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765])). 185.24/93.62 thf(1451,axiom,((! [A:nat,B:int]: ((bit_se8570568707652914677it_nat @ A @ (nat2 @ B)) = (nat2 @ (bit_se8568078237143864401it_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9764_drop__bit__nat__eq)). 185.24/93.62 thf(12570,plain,((! [A:nat,B:int]: ((bit_se8570568707652914677it_nat @ A @ (nat2 @ B)) = (nat2 @ (bit_se8568078237143864401it_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451])). 185.24/93.62 thf(4198,axiom,((! [A:real,B:real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5588_minus__divide__right)). 185.24/93.62 thf(21439,plain,((! [A:real,B:real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ A @ (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4198])). 185.24/93.62 thf(7616,axiom,(((size_s6755466524823107622T_VEBT @ treeList) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73__C4_Ohyps_C_I4_J)). 185.24/93.62 thf(33616,plain,(((size_s6755466524823107622T_VEBT @ treeList) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7616])). 185.24/93.62 thf(7274,axiom,((! [A:nat]: ((power_power_rat @ one_one_rat @ A) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_power__one)). 185.24/93.62 thf(32507,plain,((! [A:nat]: ((power_power_rat @ one_one_rat @ A) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7274])). 185.24/93.62 thf(2376,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((B != zero_zero_rat) => (((divide_divide_rat @ C @ A) = (divide_divide_rat @ D @ B)) = ((times_times_rat @ C @ B) = (times_times_rat @ D @ A)))) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2478_frac__eq__eq)). 185.24/93.62 thf(15596,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((~ (B = zero_zero_rat)) => (((divide_divide_rat @ C @ A) = (divide_divide_rat @ D @ B)) = ((times_times_rat @ C @ B) = (times_times_rat @ D @ A)))) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2376])). 185.24/93.62 thf(835,axiom,((! [A:int]: ((sin_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ (ring_1_of_int_real @ A))) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7812_sin__int__2pin)). 185.24/93.62 thf(10577,plain,((! [A:int]: ((sin_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ (ring_1_of_int_real @ A))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[835])). 185.24/93.62 thf(3458,axiom,((! [A:real]: ? [B:int]: (ord_less_eq_real @ A @ (ring_1_of_int_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7436_ex__le__of__int)). 185.24/93.62 thf(19101,plain,((! [A:real]: ? [B:int]: (ord_less_eq_real @ A @ (ring_1_of_int_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3458])). 185.24/93.62 thf(435,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (ord_max_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3687_max_Ocobounded1)). 185.24/93.62 thf(9180,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (ord_max_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[435])). 185.24/93.62 thf(2047,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ B) = ((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) & (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6519_abs__le__iff)). 185.24/93.62 thf(14574,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ B) = ((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) & (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047])). 185.24/93.62 thf(2266,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2929_half__gt__zero)). 185.24/93.62 thf(15257,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2266])). 185.24/93.62 thf(2281,axiom,((! [A:rat]: ((minus_minus_rat @ (times_times_rat @ A @ A) @ one_one_rat) = (times_times_rat @ (plus_plus_rat @ A @ one_one_rat) @ (minus_minus_rat @ A @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1242_square__diff__one__factored)). 185.24/93.62 thf(15303,plain,((! [A:rat]: ((minus_minus_rat @ (times_times_rat @ A @ A) @ one_one_rat) = (times_times_rat @ (plus_plus_rat @ A @ one_one_rat) @ (minus_minus_rat @ A @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2281])). 185.24/93.62 thf(2154,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((ord_less_eq_int @ B @ (modulo_modulo_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) => ((minus_minus_int @ (modulo_modulo_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ B) = (modulo_modulo_int @ A @ B))) <= (ord_less_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2528_divmod__digit__1_I2_J)). 185.24/93.62 thf(14912,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((ord_less_eq_int @ B @ (modulo_modulo_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) => ((minus_minus_int @ (modulo_modulo_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ B) = (modulo_modulo_int @ A @ B))) | ~ (ord_less_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2154])). 185.24/93.62 thf(2677,axiom,((! [A:num,B:nat,C:int]: ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ B) @ (ring_18347121197199848620nteger @ C)) = (ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7165_neg__numeral__power__le__of__int__cancel__iff)). 185.24/93.62 thf(16604,plain,((! [A:num,B:nat,C:int]: ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ B) @ (ring_18347121197199848620nteger @ C)) = (ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2677])). 185.24/93.62 thf(5500,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_group__cancel_Oadd2)). 185.24/93.62 thf(26048,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5500])). 185.24/93.62 thf(7600,axiom,((bit_se1148574629649215175it_nat = (^ [A:nat,B:nat]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9476_bit__nat__def)). 185.24/93.62 thf(33575,plain,(((bit_se1148574629649215175it_nat) = (^ [A:nat,B:nat]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7600])). 185.24/93.62 thf(1995,axiom,((! [A:nat]: (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3436_finite__Collect__le__nat)). 185.24/93.62 thf(14404,plain,((! [A:nat]: (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1995])). 185.24/93.62 thf(58,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)) = (groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7643_sum__bounds__lt__plus1)). 185.24/93.62 thf(7922,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)) = (groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 185.24/93.62 thf(744,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (powr_real @ (ln_ln_real @ A) @ B) @ (times_times_real @ (powr_real @ B @ B) @ A))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9125_ln__powr__bound2)). 185.24/93.62 thf(10213,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (powr_real @ (ln_ln_real @ A) @ B) @ (times_times_real @ (powr_real @ B @ B) @ A))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[744])). 185.24/93.62 thf(6107,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ (root @ A @ B) @ zero_zero_real) = (ord_less_eq_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9168_real__root__le__0__iff)). 185.24/93.62 thf(28241,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ (root @ A @ B) @ zero_zero_real) = (ord_less_eq_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6107])). 185.24/93.62 thf(2950,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ one_one_rat @ A) => (ord_less_rat @ one_one_rat @ (power_power_rat @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1110_power__gt1)). 185.24/93.62 thf(17510,plain,((! [A:rat,B:nat]: ((ord_less_rat @ one_one_rat @ A) => (ord_less_rat @ one_one_rat @ (power_power_rat @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2950])). 185.24/93.62 thf(5040,axiom,((ord_less_nat @ res @ xa)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__092_060open_062res_A_060_Ax_092_060close_062)). 185.24/93.62 thf(24301,plain,((ord_less_nat @ res @ xa)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5040])). 185.24/93.62 thf(6669,axiom,((! [A:code_integer,B:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (power_8256067586552552935nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4559_even__power)). 185.24/93.62 thf(30234,plain,((! [A:code_integer,B:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (power_8256067586552552935nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6669])). 185.24/93.62 thf(5385,axiom,((! [A:num,B:num,C:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5358_semiring__norm_I171_J)). 185.24/93.62 thf(25552,plain,((! [A:num,B:num,C:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5385])). 185.24/93.62 thf(2335,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) <= (ord_less_eq_real @ (abs_abs_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6512_abs__le__D2)). 185.24/93.62 thf(15472,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2335])). 185.24/93.62 thf(5941,axiom,((! [A:real,B:num]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_real @ (times_times_real @ A @ (power_power_real @ A @ (numeral_numeral_nat @ B))) @ (power_power_real @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6633_power__numeral__odd)). 185.24/93.62 thf(27664,plain,((! [A:real,B:num]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_real @ (times_times_real @ A @ (power_power_real @ A @ (numeral_numeral_nat @ B))) @ (power_power_real @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5941])). 185.24/93.62 thf(4053,axiom,((! [A:int,B:int,C:nat]: (((ring_1_of_int_rat @ A) = (power_power_rat @ (ring_1_of_int_rat @ B) @ C)) = (A = (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6979_of__int__power__eq__of__int__cancel__iff)). 185.24/93.62 thf(20993,plain,((! [A:int,B:int,C:nat]: (((ring_1_of_int_rat @ A) = (power_power_rat @ (ring_1_of_int_rat @ B) @ C)) = (A = (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4053])). 185.24/93.62 thf(1311,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ (abs_abs_real @ B))) = ((ord_less_eq_real @ zero_zero_real @ A) | (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6399_zero__le__divide__abs__iff)). 185.24/93.62 thf(12109,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ (abs_abs_real @ B))) = ((ord_less_eq_real @ zero_zero_real @ A) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311])). 185.24/93.62 thf(6769,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ A @ C) <= (ord_less_num @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3252_pinf_I7_J)). 185.24/93.62 thf(30638,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ A @ C) | ~ (ord_less_num @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6769])). 185.24/93.62 thf(3831,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real)) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2418_divide__nonpos__nonneg)). 185.24/93.62 thf(20300,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real)) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3831])). 185.24/93.62 thf(4168,axiom,((dvd_dvd_complex = (^ [A:complex,B:complex]: ((A = zero_zero_complex) => (B = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4572_dvd__field__iff)). 185.24/93.62 thf(21348,plain,(((dvd_dvd_complex) = (^ [A:complex,B:complex]: ((A = zero_zero_complex) => (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4168])). 185.24/93.62 thf(2885,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ B @ A)) = (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3058_pos__imp__zdiv__nonneg__iff)). 185.24/93.62 thf(17307,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ B @ A)) = (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2885])). 185.24/93.62 thf(6909,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ one_one_nat @ (power_power_nat @ A @ B))) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2900_one__less__power)). 185.24/93.62 thf(31160,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ one_one_nat @ (power_power_nat @ A @ B))) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6909])). 185.24/93.62 thf(1053,axiom,((! [A:int,B:nat]: (((ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => ((bit_se2923211474154528505it_int @ B @ A) = A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9348_take__bit__int__eq__self)). 185.24/93.62 thf(11313,plain,((! [A:int,B:nat]: (((ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => ((bit_se2923211474154528505it_int @ B @ A) = A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053])). 185.24/93.62 thf(523,axiom,(((cos_real @ pi) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7783_cos__pi)). 185.24/93.62 thf(9485,plain,(((cos_real @ pi) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[523])). 185.24/93.62 thf(6936,axiom,((! [A:num]: (one_one_real != (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5767_one__neq__neg__numeral)). 185.24/93.62 thf(31256,plain,((! [A:num]: ~ (one_one_real = (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6936])). 185.24/93.62 thf(4650,axiom,((! [A:real,B:real,C:real]: ((((times_times_real @ B @ A) = C) => (B = (divide_divide_real @ C @ A))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2465_eq__divide__imp)). 185.24/93.62 thf(22893,plain,((! [A:real,B:real,C:real]: ((((times_times_real @ B @ A) = C) => (B = (divide_divide_real @ C @ A))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4650])). 185.24/93.62 thf(7154,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_999_Suc__mono)). 185.24/93.62 thf(32098,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7154])). 185.24/93.62 thf(6202,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ B @ (bit0 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9457_or__minus__numerals_I8_J)). 185.24/93.62 thf(28610,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ B @ (bit0 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6202])). 185.24/93.62 thf(1003,axiom,((! [A:set_nat,B:(nat > (nat > $o))]: ((finite_finite_nat @ A) => ((((! [C:nat]: ((member_nat @ C @ A) => (? [D:nat]: ((member_nat @ D @ A) & (B @ C @ D))))) => (A = bot_bot_set_nat)) <= (! [C:nat,D:nat,E:nat]: ((B @ C @ D) => ((B @ C @ E) <= (B @ D @ E))))) <= (! [C:nat]: ~ (B @ C @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7906_finite__transitivity__chain)). 185.24/93.62 thf(11164,plain,((! [A:set_nat,B:(nat > (nat > $o))]: ((finite_finite_nat @ A) => (((! [C:nat]: ((member_nat @ C @ A) => (? [D:nat]: ((member_nat @ D @ A) & (B @ C @ D))))) => (A = bot_bot_set_nat)) | ~ (! [C:nat,D:nat,E:nat]: ((B @ C @ D) => ((B @ C @ E) | ~ (B @ D @ E)))) | ~ (! [C:nat]: ~ (B @ C @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003])). 185.24/93.62 thf(5348,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((((C) <= (? [D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E)))) => (((~ (! [D:nat,E:list_VEBT_VEBT]: ((C = (~ (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))))) <= (? [F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ D) @ E @ F)))))) <= (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT]: ((C = (~ ((B = E) | ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one))))))) | (B = D)))) <= (? [H:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H)))))) <= (! [D:nat,E:nat]: ((? [F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G))) => (C = (~ ((B = E) | (B = D)))))))) <= ((? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E))) => (C))) <= ((vEBT_VEBT_membermima @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3013_VEBT__internal_Omembermima_Oelims_I1_J)). 185.24/93.62 thf(25398,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: ((((C) | ~ (? [D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E)))) => (~ (! [D:nat,E:list_VEBT_VEBT]: ((C = (~ (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))))) | ~ (? [F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ D) @ E @ F))))) | ~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT]: ((C = (~ ((B = E) | ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one))))))) | (B = D)))) | ~ (? [H:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H))))) | ~ (! [D:nat,E:nat]: ((? [F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G))) => (C = (~ ((B = E) | (B = D)))))))) | ~ ((? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E))) => (C)) | ~ ((vEBT_VEBT_membermima @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5348])). 185.24/93.62 thf(2364,axiom,((suc = (^ [A:nat]: (nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9312_Suc__as__int)). 185.24/93.62 thf(15558,plain,(((suc) = (^ [A:nat]: (nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2364])). 185.24/93.62 thf(3246,axiom,((finite_finite_nat = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3396_finite__nat__set__iff__bounded__le)). 185.24/93.62 thf(18442,plain,(((finite_finite_nat) = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3246])). 185.24/93.62 thf(2621,axiom,((! [A:complex,B:complex,C:complex]: (((A != zero_zero_complex) => ((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (times_times_complex @ B @ A) @ C) @ A))) & (((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = B) <= (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2744_add__divide__eq__if__simps_I1_J)). 185.24/93.62 thf(16427,plain,((! [A:complex,B:complex,C:complex]: (((~ (A = zero_zero_complex)) => ((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (times_times_complex @ B @ A) @ C) @ A))) & (((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = B) | ~ (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2621])). 185.24/93.62 thf(3621,axiom,((ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5712_le__minus__one__simps_I2_J)). 185.24/93.62 thf(19623,plain,((ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3621])). 185.24/93.62 thf(7373,axiom,((! [A:num,B:nat,C:int]: (((power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B) = (ring_1_of_int_real @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7147_neg__numeral__power__eq__of__int__cancel__iff)). 185.24/93.62 thf(32839,plain,((! [A:num,B:nat,C:int]: (((power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B) = (ring_1_of_int_real @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7373])). 185.24/93.62 thf(2913,axiom,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5944_neg__numeral__less__one)). 185.24/93.62 thf(17394,plain,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2913])). 185.24/93.62 thf(7464,axiom,((! [A:(product_prod_nat_nat > $o),B:product_prod_nat_nat]: ((! [C:nat,D:nat]: (A @ (product_Pair_nat_nat @ C @ D))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3423_prod__cases)). 185.24/93.62 thf(33159,plain,((! [A:(product_prod_nat_nat > $o),B:product_prod_nat_nat]: ((! [C:nat,D:nat]: (A @ (product_Pair_nat_nat @ C @ D))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7464])). 185.24/93.62 thf(811,axiom,((! [A:(nat > real)]: ((topolo6980174941875973593q_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_8352_monoI1)). 185.24/93.62 thf(10495,plain,((! [A:(nat > real)]: ((topolo6980174941875973593q_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)],[811])). 185.24/93.62 thf(172,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (((log @ A @ A) = one_one_real) <= (A != one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9023_log__eq__one)). 185.24/93.62 thf(8283,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (((log @ A @ A) = one_one_real) | (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 185.24/93.62 thf(6443,axiom,((! [A:complex,B:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ B)) = (uminus1482373934393186551omplex @ (times_times_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5081_mult__minus__right)). 185.24/93.62 thf(29462,plain,((! [A:complex,B:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ B)) = (uminus1482373934393186551omplex @ (times_times_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6443])). 185.24/93.62 thf(3392,axiom,((! [A:num,B:num,C:rat]: ((plus_plus_rat @ (numeral_numeral_rat @ A) @ (plus_plus_rat @ (numeral_numeral_rat @ B) @ C)) = (plus_plus_rat @ (numeral_numeral_rat @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add__numeral__left)). 185.24/93.62 thf(18906,plain,((! [A:num,B:num,C:rat]: ((plus_plus_rat @ (numeral_numeral_rat @ A) @ (plus_plus_rat @ (numeral_numeral_rat @ B) @ C)) = (plus_plus_rat @ (numeral_numeral_rat @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3392])). 185.24/93.62 thf(2357,axiom,((! [A:nat,B:int]: (((bit_ri631733984087533419it_int @ A @ B) = B) = ((ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ B) & (ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6274_signed__take__bit__int__eq__self__iff)). 185.24/93.62 thf(15537,plain,((! [A:nat,B:int]: (((bit_ri631733984087533419it_int @ A @ B) = B) = ((ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ B) & (ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2357])). 185.24/93.62 thf(7238,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: ((((vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ B @ C @ F) @ A) <= (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) <= (ord_less_eq_nat @ one_one_nat @ B)) <= (ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_both__member__options__from__chilf__to__complete__tree)). 185.24/93.62 thf(32395,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: ((vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ B @ C @ F) @ A) | ~ (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_eq_nat @ one_one_nat @ B) | ~ (ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7238])). 185.24/93.62 thf(1134,axiom,((! [A:real,B:real]: (((abs_abs_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (abs_abs_real @ B) @ (abs_abs_real @ A))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6506_nonzero__abs__divide)). 185.24/93.62 thf(11581,plain,((! [A:real,B:real]: (((abs_abs_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (abs_abs_real @ B) @ (abs_abs_real @ A))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134])). 185.24/93.62 thf(6134,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) <= (ord_less_eq_nat @ B @ zero_zero_nat)) <= (ord_less_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2623_add__neg__nonpos)). 185.24/93.62 thf(28324,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_eq_nat @ B @ zero_zero_nat) | ~ (ord_less_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6134])). 185.24/93.62 thf(2603,axiom,((! [A:int,B:num,C:nat]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7160_of__int__le__neg__numeral__power__cancel__iff)). 185.24/93.62 thf(16372,plain,((! [A:int,B:num,C:nat]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2603])). 185.24/93.62 thf(2512,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (((ord_less_real @ C @ A) & (ord_less_real @ B @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2370_mult__less__cancel__right__disj)). 185.24/93.62 thf(16060,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (((ord_less_real @ C @ A) & (ord_less_real @ B @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2512])). 185.24/93.62 thf(3679,axiom,((! [A:nat]: ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (plus_plus_rat @ (semiri681578069525770553at_rat @ A) @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7358_double__gauss__sum__from__Suc__0)). 185.24/93.62 thf(19804,plain,((! [A:nat]: ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ (semiri681578069525770553at_rat) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (plus_plus_rat @ (semiri681578069525770553at_rat @ A) @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3679])). 185.24/93.62 thf(588,axiom,((! [A:int]: ((sin_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7795_sin__npi__int)). 185.24/93.62 thf(9685,plain,((! [A:int]: ((sin_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[588])). 185.24/93.62 thf(4414,axiom,((! [A:rat]: (ord_less_rat @ (minus_minus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7635_of__int__round__gt)). 185.24/93.62 thf(22133,plain,((! [A:rat]: (ord_less_rat @ (minus_minus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4414])). 185.24/93.62 thf(2369,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => (? [C:nat]: (ord_less_rat @ B @ (times_times_rat @ (semiri681578069525770553at_rat @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7374_ex__less__of__nat__mult)). 185.24/93.62 thf(15573,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => (? [C:nat]: (ord_less_rat @ B @ (times_times_rat @ (semiri681578069525770553at_rat @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2369])). 185.24/93.62 thf(6068,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ one_one_nat) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4564_odd__two__times__div__two__succ)). 185.24/93.62 thf(28097,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ one_one_nat) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6068])). 185.24/93.62 thf(6065,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_num @ A @ B) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4300_order__le__neq__trans)). 185.24/93.62 thf(28088,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_num @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6065])). 185.24/93.62 thf(5465,axiom,((! [A:rat,B:rat]: ((A = (times_times_rat @ B @ A)) = ((B = one_one_rat) | (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1671_mult__cancel__right1)). 185.24/93.62 thf(25837,plain,((! [A:rat,B:rat]: ((A = (times_times_rat @ B @ A)) = ((B = one_one_rat) | (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5465])). 185.24/93.62 thf(5125,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_one__reorient)). 185.24/93.62 thf(24600,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5125])). 185.24/93.62 thf(2844,axiom,((! [A:rat]: ? [B:rat]: (ord_less_rat @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_linordered__field__no__lb)). 185.24/93.62 thf(17175,plain,((! [A:rat]: ? [B:rat]: (ord_less_rat @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2844])). 185.24/93.62 thf(5155,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((times_times_nat @ (binomial @ C @ B) @ (binomial @ B @ A)) = (times_times_nat @ (binomial @ C @ A) @ (binomial @ (minus_minus_nat @ C @ A) @ (minus_minus_nat @ B @ A))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8452_choose__mult)). 185.24/93.62 thf(24733,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((times_times_nat @ (binomial @ C @ B) @ (binomial @ B @ A)) = (times_times_nat @ (binomial @ C @ A) @ (binomial @ (minus_minus_nat @ C @ A) @ (minus_minus_nat @ B @ A))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5155])). 185.24/93.62 thf(332,axiom,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((finite_finite_nat @ A) => (((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = zero_zero_rat))) => ((groups2906978787729119204at_rat @ C @ B) = (groups2906978787729119204at_rat @ C @ A))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6095_sum_Omono__neutral__left)). 185.24/93.62 thf(8843,plain,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((finite_finite_nat @ A) => (((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = zero_zero_rat))) => ((groups2906978787729119204at_rat @ (C) @ B) = (groups2906978787729119204at_rat @ (C) @ A))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 185.24/93.62 thf(6228,axiom,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1549_diff__zero)). 185.24/93.62 thf(28686,plain,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6228])). 185.24/93.62 thf(4060,axiom,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8593_pochhammer__minus)). 185.24/93.62 thf(21012,plain,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4060])). 185.24/93.62 thf(92,axiom,((! [A:rat,B:nat]: ((((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)) = (semiri681578069525770553at_rat @ B)) <= (A = one_one_rat)) & ((A != one_one_rat) => ((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)) = (divide_divide_rat @ (minus_minus_rat @ one_one_rat @ (power_power_rat @ A @ B)) @ (minus_minus_rat @ one_one_rat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7606_sum__gp__strict)). 185.24/93.62 thf(8030,plain,((! [A:rat,B:nat]: ((((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)) = (semiri681578069525770553at_rat @ B)) | ~ (A = one_one_rat)) & ((~ (A = one_one_rat)) => ((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)) = (divide_divide_rat @ (minus_minus_rat @ one_one_rat @ (power_power_rat @ A @ B)) @ (minus_minus_rat @ one_one_rat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 185.24/93.62 thf(3468,axiom,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ A @ (divide_divide_rat @ B @ C)) = (divide_divide_rat @ (times_times_rat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_divide__divide__eq__right)). 185.24/93.62 thf(19148,plain,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ A @ (divide_divide_rat @ B @ C)) = (divide_divide_rat @ (times_times_rat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3468])). 185.24/93.62 thf(3594,axiom,((! [A:int,B:int]: ((divide_divide_int @ (modulo_modulo_int @ A @ B) @ B) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1767_mod__div__trivial)). 185.24/93.62 thf(19543,plain,((! [A:int,B:int]: ((divide_divide_int @ (modulo_modulo_int @ A @ B) @ B) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3594])). 185.24/93.62 thf(5743,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B) <= (ord_less_eq_real @ (abs_abs_real @ A) @ (sqrt @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8230_sqrt__ge__absD)). 185.24/93.62 thf(26842,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ (sqrt @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5743])). 185.24/93.62 thf(704,axiom,((! [A:int,B:code_integer]: (((ord_le6747313008572928689nteger @ one_one_Code_integer @ B) | (A = zero_zero_int)) <= (ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ (ring_18347121197199848620nteger @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7288_of__int__lessD)). 185.24/93.62 thf(10081,plain,((! [A:int,B:code_integer]: ((ord_le6747313008572928689nteger @ one_one_Code_integer @ B) | (A = zero_zero_int) | ~ (ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ (ring_18347121197199848620nteger @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[704])). 185.24/93.62 thf(6520,axiom,((! [A:num,B:num]: (((numeral_numeral_real @ A) = (numeral_numeral_real @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_numeral__eq__iff)). 185.24/93.62 thf(29736,plain,((! [A:num,B:num]: (((numeral_numeral_real @ A) = (numeral_numeral_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6520])). 185.24/93.62 thf(2492,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ (times_times_rat @ A @ B) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2321_mult__neg__pos)). 185.24/93.62 thf(15995,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ (times_times_rat @ A @ B) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2492])). 185.24/93.62 thf(1571,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) => (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_add__less__imp__less__left)). 185.24/93.62 thf(12934,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) => (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571])). 185.24/93.62 thf(6965,axiom,(((modulo_modulo_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5424_minus__1__mod__2__eq)). 185.24/93.62 thf(31391,plain,(((modulo_modulo_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6965])). 185.24/93.62 thf(3532,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (ord_less_eq_rat @ (times_times_rat @ C @ A) @ (uminus_uminus_rat @ B))) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6213_neg__minus__divide__le__eq)). 185.24/93.62 thf(19350,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (ord_less_eq_rat @ (times_times_rat @ C @ A) @ (uminus_uminus_rat @ B))) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3532])). 185.24/93.62 thf(1394,axiom,((! [A:real,B:real]: ((dvd_dvd_real @ A @ B) => ((divide_divide_real @ (uminus_uminus_real @ B) @ A) = (uminus_uminus_real @ (divide_divide_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5812_dvd__neg__div)). 185.24/93.62 thf(12383,plain,((! [A:real,B:real]: ((dvd_dvd_real @ A @ B) => ((divide_divide_real @ (uminus_uminus_real @ B) @ A) = (uminus_uminus_real @ (divide_divide_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394])). 185.24/93.62 thf(3464,axiom,((! [A:nat,B:vEBT_VEBT]: (((vEBT_vebt_buildup @ A) = B) => (((A = zero_zero_nat) => (B != (vEBT_Leaf @ ($false) @ ($false)))) => (((B != (vEBT_Leaf @ ($false) @ ($false))) <= (A = (suc @ zero_zero_nat))) => (~ (! [C:nat]: ((A = (suc @ (suc @ C))) => (~ (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C)))) => (B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C))) => (B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5001_vebt__buildup_Oelims)). 185.24/93.62 thf(19117,plain,((! [A:nat,B:vEBT_VEBT]: (((vEBT_vebt_buildup @ A) = B) => (((A = zero_zero_nat) => (~ (B = (vEBT_Leaf @ ($false) @ ($false))))) => ((~ (B = (vEBT_Leaf @ ($false) @ ($false))) | ~ (A = (suc @ zero_zero_nat))) => (~ (! [C:nat]: ((A = (suc @ (suc @ C))) => (~ (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C)))) => (B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C))) => (B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3464])). 185.24/93.62 thf(3900,axiom,((! [A:real,B:real,C:real]: ((A = C) <= ((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_add__right__imp__eq)). 185.24/93.62 thf(20516,plain,((! [A:real,B:real,C:real]: ((A = C) | ~ ((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3900])). 185.24/93.62 thf(4942,axiom,((! [A:num,B:nat,C:nat]: (((power_power_int @ (numeral_numeral_int @ A) @ B) = (semiri1314217659103216013at_int @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7051_numeral__power__eq__of__nat__cancel__iff)). 185.24/93.62 thf(23914,plain,((! [A:num,B:nat,C:nat]: (((power_power_int @ (numeral_numeral_int @ A) @ B) = (semiri1314217659103216013at_int @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4942])). 185.24/93.62 thf(5001,axiom,((! [A:nat]: ((power_power_real @ (uminus_uminus_real @ one_one_real) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6293_power__minus1__odd)). 185.24/93.62 thf(24108,plain,((! [A:nat]: ((power_power_real @ (uminus_uminus_real @ one_one_real) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5001])). 185.24/93.62 thf(5288,axiom,((ord_less_num = (^ [A:num,B:num]: (~ (ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4254_dual__order_Ostrict__iff__not)). 185.24/93.62 thf(25214,plain,(((ord_less_num) = (^ [A:num,B:num]: (~ (ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5288])). 185.24/93.62 thf(3112,axiom,((! [A:num,B:nat,C:int]: ((ord_le6747313008572928689nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ B) @ (ring_18347121197199848620nteger @ C)) = (ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7175_neg__numeral__power__less__of__int__cancel__iff)). 185.24/93.62 thf(18033,plain,((! [A:num,B:nat,C:int]: ((ord_le6747313008572928689nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ B) @ (ring_18347121197199848620nteger @ C)) = (ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3112])). 185.24/93.62 thf(5003,axiom,((! [A:int,B:int]: ((times_times_int @ (uminus_uminus_int @ A) @ B) = (times_times_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5546_minus__mult__commute)). 185.24/93.62 thf(24114,plain,((! [A:int,B:int]: ((times_times_int @ (uminus_uminus_int @ A) @ B) = (times_times_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5003])). 185.24/93.62 thf(642,axiom,((bit_se4205575877204974255it_nat = (^ [A:nat,B:nat]: (nat2 @ (bit_se4203085406695923979it_int @ A @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9287_unset__bit__nat__def)). 185.24/93.62 thf(9864,plain,(((bit_se4205575877204974255it_nat) = (^ [A:nat,B:nat]: (nat2 @ (bit_se4203085406695923979it_int @ A @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[642])). 185.24/93.62 thf(7071,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3932_order__eq__refl)). 185.24/93.62 thf(31808,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7071])). 185.24/93.62 thf(2092,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = zero_zero_real) = (B = (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5723_add__eq__0__iff)). 185.24/93.62 thf(14709,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = zero_zero_real) = (B = (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2092])). 185.24/93.62 thf(6561,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) <= (ord_less_eq_nat @ zero_zero_nat @ A)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2253_mult__mono_H)). 185.24/93.62 thf(29876,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6561])). 185.24/93.62 thf(1695,axiom,((! [A:(rat > $o),B:(rat > $o),C:(rat > $o),D:(rat > $o)]: (((? [E:rat]: ! [F:rat]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) <= (ord_less_rat @ E @ F))) <= (? [E:rat]: ! [F:rat]: (((C @ F) = (D @ F)) <= (ord_less_rat @ E @ F)))) <= (? [E:rat]: ! [F:rat]: (((A @ F) = (B @ F)) <= (ord_less_rat @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3226_pinf_I1_J)). 185.24/93.62 thf(13405,plain,((! [A:(rat > $o),B:(rat > $o),C:(rat > $o),D:(rat > $o)]: (? [E:rat]: ! [F:rat]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) | ~ (ord_less_rat @ E @ F)) | ~ (? [E:rat]: ! [F:rat]: (((C @ F) = (D @ F)) | ~ (ord_less_rat @ E @ F))) | ~ (? [E:rat]: ! [F:rat]: (((A @ F) = (B @ F)) | ~ (ord_less_rat @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695])). 185.24/93.62 thf(773,axiom,((! [A:real,B:nat]: (((A != one_one_real) => ((log @ A @ (power_power_real @ A @ B)) = (semiri5074537144036343181t_real @ B))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9035_log__pow__cancel)). 185.24/93.62 thf(10363,plain,((! [A:real,B:nat]: (((~ (A = one_one_real)) => ((log @ A @ (power_power_real @ A @ B)) = (semiri5074537144036343181t_real @ B))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[773])). 185.24/93.62 thf(654,axiom,((! [A:(nat > nat),B:(nat > nat),C:set_nat]: ((groups708209901874060359at_nat @ (^ [D:nat]: (times_times_nat @ (A @ D) @ (B @ D))) @ C) = (times_times_nat @ (groups708209901874060359at_nat @ A @ C) @ (groups708209901874060359at_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8725_prod_Odistrib)). 185.24/93.62 thf(9907,plain,((! [A:(nat > nat),B:(nat > nat),C:set_nat]: ((groups708209901874060359at_nat @ (^ [D:nat]: (times_times_nat @ (A @ D) @ (B @ D))) @ C) = (times_times_nat @ (groups708209901874060359at_nat @ (A) @ C) @ (groups708209901874060359at_nat @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[654])). 185.24/93.62 thf(2531,axiom,((! [A:int,B:int]: ((A != B) => ((ord_less_int @ B @ A) <= (~ (ord_less_int @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4052_linorder__neqE)). 185.24/93.62 thf(16124,plain,((! [A:int,B:int]: ((~ (A = B)) => ((ord_less_int @ B @ A) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2531])). 185.24/93.62 thf(5069,axiom,((zero_zero_rat != (uminus_uminus_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5721_zero__neq__neg__one)). 185.24/93.62 thf(24400,plain,((~ (zero_zero_rat = (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5069])). 185.24/93.62 thf(5573,axiom,((! [A:num]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ one_one_int)) = (A != one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5390_neg__numeral__less__neg__one__iff)). 185.24/93.62 thf(26282,plain,((! [A:num]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ one_one_int)) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5573])). 185.24/93.62 thf(277,axiom,((! [A:real]: (((ord_less_eq_real @ zero_zero_real @ (tan_real @ A)) <= (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8066_tan__pos__pi2__le)). 185.24/93.62 thf(8639,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (tan_real @ A)) | ~ (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 185.24/93.62 thf(2947,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ A @ C) <= (ord_less_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4309_order__le__less__trans)). 185.24/93.62 thf(17502,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ A @ C) | ~ (ord_less_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2947])). 185.24/93.62 thf(2133,axiom,((! [A:num,B:code_integer]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (times_3573771949741848930nteger @ B @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5760_numeral__times__minus__swap)). 185.24/93.62 thf(14833,plain,((! [A:num,B:code_integer]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (times_3573771949741848930nteger @ B @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2133])). 185.24/93.62 thf(5734,axiom,((! [A:nat,B:int,C:int]: (((ord_less_eq_int @ (abs_abs_int @ B) @ (abs_abs_int @ C)) => (ord_less_eq_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A))) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6725_power__mono__even)). 185.24/93.62 thf(26810,plain,((! [A:nat,B:int,C:int]: (((ord_less_eq_int @ (abs_abs_int @ B) @ (abs_abs_int @ C)) => (ord_less_eq_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A))) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5734])). 185.24/93.62 thf(2725,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_eq_real @ B @ C)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3340_mult__le__cancel__iff2)). 185.24/93.62 thf(16797,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_eq_real @ B @ C)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2725])). 185.24/93.62 thf(2448,axiom,((! [A:complex,B:complex]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7517_norm__triangle__ineq3)). 185.24/93.62 thf(15838,plain,((! [A:complex,B:complex]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2448])). 185.24/93.62 thf(2317,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((C != A) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3239_pinf_I3_J)). 185.24/93.62 thf(15413,plain,((! [A:int]: ? [B:int]: ! [C:int]: (~ (C = A) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2317])). 185.24/93.62 thf(1081,axiom,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ A @ (plus_plus_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_add_Oassoc)). 185.24/93.62 thf(11394,plain,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ A @ (plus_plus_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081])). 185.24/93.62 thf(4160,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ (divide_divide_rat @ A @ C) @ (divide_divide_rat @ B @ C)) <= (ord_less_eq_rat @ zero_zero_rat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2411_divide__right__mono)). 185.24/93.62 thf(21326,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ (divide_divide_rat @ A @ C) @ (divide_divide_rat @ B @ C)) | ~ (ord_less_eq_rat @ zero_zero_rat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4160])). 185.24/93.62 thf(5894,axiom,((! [A:real,B:real]: ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6458_abs__mult)). 185.24/93.62 thf(27519,plain,((! [A:real,B:real]: ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5894])). 185.24/93.62 thf(6146,axiom,((! [A:complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1552_diff__0__right)). 185.24/93.62 thf(28373,plain,((! [A:complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6146])). 185.24/93.62 thf(344,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (bit_ri7919022796975470100ot_int @ (bit_se725231765392027082nd_int @ (minus_minus_int @ (numeral_numeral_int @ A) @ one_one_int) @ (minus_minus_int @ (numeral_numeral_int @ B) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9504_or__minus__minus__numerals)). 185.24/93.62 thf(8887,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (bit_ri7919022796975470100ot_int @ (bit_se725231765392027082nd_int @ (minus_minus_int @ (numeral_numeral_int @ A) @ one_one_int) @ (minus_minus_int @ (numeral_numeral_int @ B) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])). 185.24/93.62 thf(1981,axiom,((! [A:real,B:nat]: ((real_V7735802525324610683m_real @ (power_power_real @ A @ B)) = (power_power_real @ (real_V7735802525324610683m_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7469_norm__power)). 185.24/93.62 thf(14358,plain,((! [A:real,B:nat]: ((real_V7735802525324610683m_real @ (power_power_real @ A @ B)) = (power_power_real @ (real_V7735802525324610683m_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1981])). 185.24/93.62 thf(6159,axiom,((! [A:nat]: (((A != zero_zero_nat) => ((power_power_real @ zero_zero_real @ A) = zero_zero_real)) & ((A = zero_zero_nat) => ((power_power_real @ zero_zero_real @ A) = one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1962_power__0__left)). 185.24/93.62 thf(28455,plain,((! [A:nat]: (((~ (A = zero_zero_nat)) => ((power_power_real @ zero_zero_real @ A) = zero_zero_real)) & ((A = zero_zero_nat) => ((power_power_real @ zero_zero_real @ A) = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6159])). 185.24/93.62 thf(4099,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((nat2 @ (modulo_modulo_int @ A @ B)) = (modulo_modulo_nat @ (nat2 @ A) @ (nat2 @ B))) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9320_nat__mod__distrib)). 185.24/93.62 thf(21136,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((nat2 @ (modulo_modulo_int @ A @ B)) = (modulo_modulo_nat @ (nat2 @ A) @ (nat2 @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4099])). 185.24/93.62 thf(5866,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2215_mult__nonneg__nonpos)). 185.24/93.62 thf(27418,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5866])). 185.24/93.62 thf(7112,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ A)) @ (suc @ (suc @ D)) @ E @ F) @ B) = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_option_nat @ (((vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_nat) & (vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ C @ B) @ (some_nat @ C) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)) <= (~ (ord_less_nat @ A @ B))) & ((ord_less_nat @ A @ B) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ A)) @ (suc @ (suc @ D)) @ E @ F) @ B) = (some_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1445_vebt__pred_Osimps_I7_J)). 185.24/93.62 thf(31934,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ A)) @ (suc @ (suc @ D)) @ E @ F) @ B) = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_option_nat @ (~ ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) & (vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ C @ B) @ (some_nat @ C) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)) | (ord_less_nat @ A @ B)) & ((ord_less_nat @ A @ B) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ A)) @ (suc @ (suc @ D)) @ E @ F) @ B) = (some_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7112])). 185.24/93.62 thf(305,axiom,((! [A:real]: ((divide_divide_real @ one_one_real @ (tan_real @ A)) = (tan_real @ (minus_minus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8062_tan__inverse)). 185.24/93.62 thf(8755,plain,((! [A:real]: ((divide_divide_real @ one_one_real @ (tan_real @ A)) = (tan_real @ (minus_minus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 185.24/93.62 thf(1119,axiom,((neg_nu8557863876264182079omplex = (^ [A:complex]: (plus_plus_complex @ (plus_plus_complex @ A @ A) @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7312_dbl__inc__def)). 185.24/93.62 thf(11527,plain,(((neg_nu8557863876264182079omplex) = (^ [A:complex]: (plus_plus_complex @ (plus_plus_complex @ A @ A) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119])). 185.24/93.62 thf(3964,axiom,((! [A:int]: ((bit_se2159334234014336723it_int @ zero_zero_nat @ A) = (plus_plus_int @ (zero_n2684676970156552555ol_int @ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5005_flip__bit__0)). 185.24/93.62 thf(20726,plain,((! [A:int]: ((bit_se2159334234014336723it_int @ zero_zero_nat @ A) = (plus_plus_int @ (zero_n2684676970156552555ol_int @ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3964])). 185.24/93.62 thf(1493,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((times_times_complex @ (divide1717551699836669952omplex @ A @ B) @ (divide1717551699836669952omplex @ C @ D)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_times__divide__times__eq)). 185.24/93.62 thf(12699,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((times_times_complex @ (divide1717551699836669952omplex @ A @ B) @ (divide1717551699836669952omplex @ C @ D)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493])). 185.24/93.62 thf(3241,axiom,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5924_neg__numeral__le__one)). 185.24/93.62 thf(18429,plain,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3241])). 185.24/93.62 thf(894,axiom,((! [A:nat,B:nat]: ((times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ (gbinomial_complex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ A)) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (gbinomial_complex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ one_one_complex) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8562_gbinomial__index__swap)). 185.24/93.62 thf(10790,plain,((! [A:nat,B:nat]: ((times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ (gbinomial_complex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ A)) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (gbinomial_complex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ one_one_complex) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[894])). 185.24/93.62 thf(5259,axiom,((! [A:complex]: (((uminus1482373934393186551omplex @ A) = zero_zero_complex) = (A = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5047_neg__equal__0__iff__equal)). 185.24/93.62 thf(25082,plain,((! [A:complex]: (((uminus1482373934393186551omplex @ A) = zero_zero_complex) = (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5259])). 185.24/93.62 thf(5080,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1522_add__cancel__left__right)). 185.24/93.62 thf(24432,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5080])). 185.24/93.62 thf(52,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)) = (groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7642_sum__bounds__lt__plus1)). 185.24/93.62 thf(7903,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)) = (groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 185.24/93.62 thf(3658,axiom,((! [A:real,B:real]: ((one_one_real = (divide_divide_real @ A @ B)) = ((B != zero_zero_real) & (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1725_eq__divide__eq__1)). 185.24/93.62 thf(19743,plain,((! [A:real,B:real]: ((one_one_real = (divide_divide_real @ A @ B)) = (~ (B = zero_zero_real) & (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3658])). 185.24/93.62 thf(1417,axiom,((! [A:num,B:(rat > num),C:rat,D:rat]: ((A = (B @ C)) => ((ord_less_rat @ C @ D) => ((ord_less_num @ A @ (B @ D)) <= (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_num @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4080_ord__eq__less__subst)). 185.24/93.62 thf(12462,plain,((! [A:num,B:(rat > num),C:rat,D:rat]: ((A = (B @ C)) => ((ord_less_rat @ C @ D) => ((ord_less_num @ A @ (B @ D)) | ~ (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_num @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417])). 185.24/93.62 thf(6061,axiom,((! [A:complex,B:num]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_complex @ (times_times_complex @ A @ (power_power_complex @ A @ (numeral_numeral_nat @ B))) @ (power_power_complex @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6632_power__numeral__odd)). 185.24/93.62 thf(28077,plain,((! [A:complex,B:num]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_complex @ (times_times_complex @ A @ (power_power_complex @ A @ (numeral_numeral_nat @ B))) @ (power_power_complex @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6061])). 185.24/93.62 thf(2306,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => ((ord_less_eq_int @ D @ zero_zero_int) => (((divide_divide_int @ A @ B) = C) <= (ord_less_int @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3068_int__div__neg__eq)). 185.24/93.62 thf(15380,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => ((ord_less_eq_int @ D @ zero_zero_int) => (((divide_divide_int @ A @ B) = C) | ~ (ord_less_int @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2306])). 185.24/93.62 thf(7456,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = ((E = A) | (E = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2918_VEBT__internal_Omembermima_Osimps_I3_J)). 185.24/93.62 thf(33113,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = ((E = A) | (E = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7456])). 185.24/93.62 thf(5956,axiom,((! [A:num,B:num]: ((uminus_uminus_real @ (numeral_numeral_real @ A)) != (numeral_numeral_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5535_neg__numeral__neq__numeral)). 185.24/93.62 thf(27708,plain,((! [A:num,B:num]: ~ ((uminus_uminus_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5956])). 185.24/93.62 thf(145,axiom,((! [A:num]: ((im @ (numera6690914467698888265omplex @ A)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9662_complex__Im__numeral)). 185.24/93.62 thf(8200,plain,((! [A:num]: ((im @ (numera6690914467698888265omplex @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 185.24/93.62 thf(1506,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((B = (ord_max_nat @ B @ A)) & (B != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3734_max_Ostrict__order__iff)). 185.24/93.62 thf(12738,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((B = (ord_max_nat @ B @ A)) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506])). 185.24/93.62 thf(6331,axiom,((! [A:num]: ((inc @ (bit0 @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9378_inc_Osimps_I2_J)). 185.24/93.62 thf(29036,plain,((! [A:num]: ((inc @ (bit0 @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6331])). 185.24/93.62 thf(7034,axiom,((! [A:code_integer]: (((power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_Code_integer) = ((abs_abs_Code_integer @ A) = one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6686_abs__square__eq__1)). 185.24/93.62 thf(31693,plain,((! [A:code_integer]: (((power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_Code_integer) = ((abs_abs_Code_integer @ A) = one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7034])). 185.24/93.62 thf(507,axiom,((! [A:real,B:nat,C:set_nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (power_power_real @ A @ (plus_plus_nat @ B @ D))) @ C) = (times_times_real @ (power_power_real @ A @ B) @ (groups6591440286371151544t_real @ (power_power_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6624_sum__power__add)). 185.24/93.62 thf(9437,plain,((! [A:real,B:nat,C:set_nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (power_power_real @ A @ (plus_plus_nat @ B @ D))) @ C) = (times_times_real @ (power_power_real @ A @ B) @ (groups6591440286371151544t_real @ (power_power_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])). 185.24/93.62 thf(391,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_eq_real @ (arcsin @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((sin_real @ (arcsin @ A)) = A) & (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A))) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8334_arcsin)). 185.24/93.62 thf(9032,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_eq_real @ (arcsin @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((sin_real @ (arcsin @ A)) = A) & (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A))) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[391])). 185.24/93.62 thf(3418,axiom,((! [A:num,B:nat,C:int]: ((ord_less_rat @ (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7174_neg__numeral__power__less__of__int__cancel__iff)). 185.24/93.62 thf(18985,plain,((! [A:num,B:nat,C:int]: ((ord_less_rat @ (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3418])). 185.24/93.62 thf(1444,axiom,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ A @ (plus_plus_rat @ B @ C)) = (minus_minus_rat @ (minus_minus_rat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_734_diff__add__eq__diff__diff__swap)). 185.24/93.62 thf(12549,plain,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ A @ (plus_plus_rat @ B @ C)) = (minus_minus_rat @ (minus_minus_rat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444])). 185.24/93.62 thf(3689,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((((ord_less_eq_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ D @ B)) = (ord_less_eq_rat @ (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ D @ A)) @ (times_times_rat @ A @ B)) @ zero_zero_rat)) <= (B != zero_zero_rat)) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2864_frac__le__eq)). 185.24/93.62 thf(19841,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ D @ B)) = (ord_less_eq_rat @ (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ D @ A)) @ (times_times_rat @ A @ B)) @ zero_zero_rat)) | (B = zero_zero_rat) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3689])). 185.24/93.62 thf(4521,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (semiri5074537144036343181t_real @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7060_of__nat__power__le__of__nat__cancel__iff)). 185.24/93.62 thf(22485,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (semiri5074537144036343181t_real @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4521])). 185.24/93.62 thf(6539,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1602_add__is__0)). 185.24/93.62 thf(29805,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6539])). 185.24/93.62 thf(6516,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4294_order__less__imp__le)). 185.24/93.62 thf(29723,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6516])). 185.24/93.62 thf(1428,axiom,((! [A:real]: ((ord_less_real @ one_one_real @ (sqrt @ A)) = (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8126_real__sqrt__gt__1__iff)). 185.24/93.62 thf(12500,plain,((! [A:real]: ((ord_less_real @ one_one_real @ (sqrt @ A)) = (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428])). 185.24/93.62 thf(854,axiom,((bit_se1409905431419307370or_int = (^ [A:int,B:int]: (bit_ri7919022796975470100ot_int @ (bit_se725231765392027082nd_int @ (bit_ri7919022796975470100ot_int @ A) @ (bit_ri7919022796975470100ot_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9508_or__int__def)). 185.24/93.62 thf(10658,plain,(((bit_se1409905431419307370or_int) = (^ [A:int,B:int]: (bit_ri7919022796975470100ot_int @ (bit_se725231765392027082nd_int @ (bit_ri7919022796975470100ot_int @ A) @ (bit_ri7919022796975470100ot_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[854])). 185.24/93.62 thf(6802,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: ((((((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ E)) @ B @ C @ F) @ D) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ (ord_max_nat @ A @ E))) @ B @ (list_u1324408373059187874T_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ F))) <= (D != E)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) <= (ord_less_nat @ D @ A)) <= (ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3553_insert__simp__excp)). 185.47/93.63 thf(30743,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: (((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ E)) @ B @ C @ F) @ D) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ (ord_max_nat @ A @ E))) @ B @ (list_u1324408373059187874T_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ F))) | (D = E) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | ~ (ord_less_nat @ D @ A) | ~ (ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6802])). 185.47/93.63 thf(954,axiom,((ord_less_real @ (uminus_uminus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) @ pi)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7762_m2pi__less__pi)). 185.47/93.63 thf(11008,plain,((ord_less_real @ (uminus_uminus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) @ pi)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[954])). 185.47/93.63 thf(2993,axiom,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ B) = B) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1516_add__cancel__left__left)). 185.47/93.63 thf(17656,plain,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ B) = B) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2993])). 185.47/93.63 thf(2301,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ (times_times_int @ A @ (divide_divide_int @ B @ A)) @ (modulo_modulo_int @ B @ A)) @ C) = (plus_plus_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2548_cancel__div__mod__rules_I2_J)). 185.47/93.63 thf(15361,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ (times_times_int @ A @ (divide_divide_int @ B @ A)) @ (modulo_modulo_int @ B @ A)) @ C) = (plus_plus_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2301])). 185.47/93.63 thf(4696,axiom,((! [A:rat,B:(real > rat),C:real,D:real]: ((A = (B @ C)) => (((! [E:real,F:real]: ((ord_less_rat @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F))) => (ord_less_rat @ A @ (B @ D))) <= (ord_less_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4074_ord__eq__less__subst)). 185.47/93.63 thf(23056,plain,((! [A:rat,B:(real > rat),C:real,D:real]: ((A = (B @ C)) => (((! [E:real,F:real]: ((ord_less_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))) => (ord_less_rat @ A @ (B @ D))) | ~ (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4696])). 185.47/93.63 thf(5299,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) => ((ord_less_nat @ B @ C) <= (ord_less_eq_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2577_mult__left__less__imp__less)). 185.47/93.63 thf(25246,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) => ((ord_less_nat @ B @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5299])). 185.47/93.63 thf(4596,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT]: (((size_s6755466524823107622T_VEBT @ A) = B) => ((A = (replicate_VEBT_VEBT @ B @ C)) <= (! [D:vEBT_VEBT]: ((D = C) <= (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5803_replicate__eqI)). 185.47/93.63 thf(22717,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT]: (((size_s6755466524823107622T_VEBT @ A) = B) => ((A = (replicate_VEBT_VEBT @ B @ C)) | ~ (! [D:vEBT_VEBT]: ((D = C) | ~ (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4596])). 185.47/93.63 thf(335,axiom,((! [A:set_nat,B:nat,C:(nat > rat)]: ((finite_finite_nat @ A) => (((~ (member_nat @ B @ A)) => ((groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (D = B) @ (C @ D) @ one_one_rat)) @ A) = one_one_rat)) & (((groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (D = B) @ (C @ D) @ one_one_rat)) @ A) = (C @ B)) <= (member_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8675_prod_Odelta)). 185.47/93.63 thf(8855,plain,((! [A:set_nat,B:nat,C:(nat > rat)]: ((finite_finite_nat @ A) => (((~ (member_nat @ B @ A)) => ((groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (D = B) @ (C @ D) @ one_one_rat)) @ A) = one_one_rat)) & (((groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (D = B) @ (C @ D) @ one_one_rat)) @ A) = (C @ B)) | ~ (member_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 185.47/93.63 thf(7239,axiom,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_mult_Oright__neutral)). 185.47/93.63 thf(32398,plain,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7239])). 185.47/93.63 thf(2187,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ one_one_real @ one_one_real)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_854_gt__half__sum)). 185.47/93.63 thf(15019,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ one_one_real @ one_one_real)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2187])). 185.47/93.63 thf(2342,axiom,((! [A:real]: (((cos_real @ A) = zero_zero_real) = (? [B:int]: (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) & (A = (times_times_real @ (ring_1_of_int_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7940_cos__zero__iff__int)). 185.47/93.63 thf(15490,plain,((! [A:real]: (((cos_real @ A) = zero_zero_real) = (? [B:int]: (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) & (A = (times_times_real @ (ring_1_of_int_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2342])). 185.47/93.63 thf(1021,axiom,((((=) @ rat) = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ B @ A) & (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3905_Orderings_Oorder__eq__iff)). 185.47/93.63 thf(11224,plain,((((=) @ rat) = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ B @ A) & (ord_less_eq_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021])). 185.47/93.63 thf(5436,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) = (ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6685_abs__le__square__iff)). 185.47/93.63 thf(25737,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) = (ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5436])). 185.47/93.63 thf(1051,axiom,((! [A:num]: ~ (ord_less_rat @ (numeral_numeral_rat @ A) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2264_not__numeral__less__zero)). 185.47/93.63 thf(11308,plain,((! [A:num]: ~ (ord_less_rat @ (numeral_numeral_rat @ A) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051])). 185.47/93.63 thf(1453,axiom,((! [A:real,B:real,C:real,D:real]: ((A = B) => ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ C) @ B)) @ D) <= (ord_less_eq_real @ (abs_abs_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6531_sin__bound__lemma)). 185.47/93.63 thf(12575,plain,((! [A:real,B:real,C:real,D:real]: ((A = B) => ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ C) @ B)) @ D) | ~ (ord_less_eq_real @ (abs_abs_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1453])). 185.47/93.63 thf(387,axiom,((! [A:rat,B:nat]: ((gbinomial_rat @ (plus_plus_rat @ A @ one_one_rat) @ (suc @ B)) = (times_times_rat @ (gbinomial_rat @ A @ B) @ (divide_divide_rat @ (plus_plus_rat @ A @ one_one_rat) @ (semiri681578069525770553at_rat @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8561_gbinomial__rec)). 185.47/93.63 thf(9020,plain,((! [A:rat,B:nat]: ((gbinomial_rat @ (plus_plus_rat @ A @ one_one_rat) @ (suc @ B)) = (times_times_rat @ (gbinomial_rat @ A @ B) @ (divide_divide_rat @ (plus_plus_rat @ A @ one_one_rat) @ (semiri681578069525770553at_rat @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])). 185.47/93.63 thf(4448,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (((powr_real @ A @ B) = one_one_real) = (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9073_powr__eq__one__iff)). 185.47/93.63 thf(22242,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (((powr_real @ A @ B) = one_one_real) = (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4448])). 185.47/93.63 thf(5355,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3321_minf_I8_J)). 185.47/93.63 thf(25462,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5355])). 185.47/93.63 thf(1575,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ (divide_divide_rat @ C @ B)) = (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ C @ A)) & (B != zero_zero_rat) & ((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2438_divide__less__cancel)). 185.47/93.63 thf(12949,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ (divide_divide_rat @ C @ B)) = (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ C @ A)) & ~ (B = zero_zero_rat) & ((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575])). 185.47/93.63 thf(6307,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (times_times_nat @ B @ C)) = (power_power_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_power__mult)). 185.47/93.63 thf(28949,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (times_times_nat @ B @ C)) = (power_power_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6307])). 185.47/93.63 thf(4170,axiom,((ord_less_rat @ (uminus_uminus_rat @ one_one_rat) @ zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5917_less__minus__one__simps_I1_J)). 185.47/93.63 thf(21353,plain,((ord_less_rat @ (uminus_uminus_rat @ one_one_rat) @ zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4170])). 185.47/93.63 thf(1066,axiom,((! [A:nat]: (((semiri681578069525770553at_rat @ A) = one_one_rat) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6932_of__nat__eq__1__iff)). 185.47/93.63 thf(11350,plain,((! [A:nat]: (((semiri681578069525770553at_rat @ A) = one_one_rat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066])). 185.47/93.63 thf(569,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((gbinomial_rat @ (semiri681578069525770553at_rat @ B) @ A) = (gbinomial_rat @ (semiri681578069525770553at_rat @ B) @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8464_gbinomial__of__nat__symmetric)). 185.47/93.63 thf(9621,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((gbinomial_rat @ (semiri681578069525770553at_rat @ B) @ A) = (gbinomial_rat @ (semiri681578069525770553at_rat @ B) @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[569])). 185.47/93.63 thf(6919,axiom,((! [A:nat,B:list_VEBT_VEBT,C:list_VEBT_VEBT]: (((nth_Pr4953567300277697838T_VEBT @ (produc4743750530478302277T_VEBT @ B @ C) @ A) = (produc537772716801021591T_VEBT @ (nth_VEBT_VEBT @ B @ (divide_divide_nat @ A @ (size_s6755466524823107622T_VEBT @ C))) @ (nth_VEBT_VEBT @ C @ (modulo_modulo_nat @ A @ (size_s6755466524823107622T_VEBT @ C))))) <= (ord_less_nat @ A @ (times_times_nat @ (size_s6755466524823107622T_VEBT @ B) @ (size_s6755466524823107622T_VEBT @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3350_product__nth)). 185.47/93.63 thf(31192,plain,((! [A:nat,B:list_VEBT_VEBT,C:list_VEBT_VEBT]: (((nth_Pr4953567300277697838T_VEBT @ (produc4743750530478302277T_VEBT @ B @ C) @ A) = (produc537772716801021591T_VEBT @ (nth_VEBT_VEBT @ B @ (divide_divide_nat @ A @ (size_s6755466524823107622T_VEBT @ C))) @ (nth_VEBT_VEBT @ C @ (modulo_modulo_nat @ A @ (size_s6755466524823107622T_VEBT @ C))))) | ~ (ord_less_nat @ A @ (times_times_nat @ (size_s6755466524823107622T_VEBT @ B) @ (size_s6755466524823107622T_VEBT @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6919])). 185.47/93.63 thf(5360,axiom,((! [A:num,B:nat,C:nat]: (((power_power_real @ (numeral_numeral_real @ A) @ B) = (semiri5074537144036343181t_real @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7052_numeral__power__eq__of__nat__cancel__iff)). 185.47/93.63 thf(25476,plain,((! [A:num,B:nat,C:nat]: (((power_power_real @ (numeral_numeral_real @ A) @ B) = (semiri5074537144036343181t_real @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5360])). 185.47/93.63 thf(5092,axiom,((! [A:nat,B:nat,C:nat]: ((? [D:nat,E:nat]: ((A = (times_times_nat @ D @ E)) & (dvd_dvd_nat @ D @ B) & (dvd_dvd_nat @ E @ C))) <= (dvd_dvd_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4625_division__decomp)). 185.47/93.63 thf(24464,plain,((! [A:nat,B:nat,C:nat]: (? [D:nat,E:nat]: ((A = (times_times_nat @ D @ E)) & (dvd_dvd_nat @ D @ B) & (dvd_dvd_nat @ E @ C)) | ~ (dvd_dvd_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5092])). 185.47/93.63 thf(7483,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ (suc @ C)) @ D @ E) @ F) = (if_VEBT_VEBT @ (~ ((F = B) | (F = A)) & (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (ord_less_nat @ F @ A) @ F @ A) @ (ord_max_nat @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ B))) @ (suc @ (suc @ C)) @ (list_u1324408373059187874T_VEBT @ D @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ E @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ E)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ (suc @ C)) @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3789_vebt__insert_Osimps_I5_J)). 185.47/93.63 thf(33219,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ (suc @ C)) @ D @ E) @ F) = (if_VEBT_VEBT @ (~ ((F = B) | (F = A)) & (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (ord_less_nat @ F @ A) @ F @ A) @ (ord_max_nat @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ B))) @ (suc @ (suc @ C)) @ (list_u1324408373059187874T_VEBT @ D @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ E @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ F @ A) @ A @ F) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ E)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ (suc @ C)) @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7483])). 185.47/93.63 thf(224,axiom,((filterlim_real_real @ sqrt @ at_top_real @ at_top_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10124_sqrt__at__top)). 185.47/93.63 thf(8450,plain,((filterlim_real_real @ (sqrt) @ at_top_real @ at_top_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 185.47/93.63 thf(725,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (ring_1_of_int_int @ A)) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7041_of__int__0__less__iff)). 185.47/93.63 thf(10149,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ (ring_1_of_int_int @ A)) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[725])). 185.47/93.63 thf(3107,axiom,((! [A:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one))) = (uminus1351360451143612070nteger @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5984_mult__1s__ring__1_I2_J)). 185.47/93.63 thf(18018,plain,((! [A:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one))) = (uminus1351360451143612070nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3107])). 185.47/93.63 thf(7174,axiom,((one_one_nat = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2511_One__nat__def)). 185.47/93.63 thf(32170,plain,((one_one_nat = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7174])). 185.47/93.63 thf(3153,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (uminus_uminus_rat @ A) @ B) = (ord_less_rat @ (uminus_uminus_rat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5524_minus__less__iff)). 185.47/93.63 thf(18152,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (uminus_uminus_rat @ A) @ B) = (ord_less_rat @ (uminus_uminus_rat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3153])). 185.47/93.63 thf(7101,axiom,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1490_mult__zero__right)). 185.47/93.63 thf(31904,plain,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7101])). 185.47/93.63 thf(620,axiom,((! [A:int,B:num,C:nat]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7163_of__int__le__neg__numeral__power__cancel__iff)). 185.47/93.63 thf(9791,plain,((! [A:int,B:num,C:nat]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[620])). 185.47/93.63 thf(3312,axiom,((! [A:nat,B:vEBT_VEBT,C:(vEBT_VEBT > $o)]: ((! [D:vEBT_VEBT]: ((C @ D) <= (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ A @ B))))) = ((A = zero_zero_nat) | (C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5254_Ball__set__replicate)). 185.47/93.63 thf(18646,plain,((! [A:nat,B:vEBT_VEBT,C:(vEBT_VEBT > $o)]: ((! [D:vEBT_VEBT]: ((C @ D) | ~ (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ A @ B))))) = ((A = zero_zero_nat) | (C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3312])). 185.47/93.63 thf(64,axiom,((! [A:nat,B:nat]: ((member_nat @ A @ (set_ord_lessThan_nat @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7537_lessThan__iff)). 185.47/93.63 thf(7940,plain,((! [A:nat,B:nat]: ((member_nat @ A @ (set_ord_lessThan_nat @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 185.47/93.63 thf(1461,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ A @ C) <= (ord_less_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4027_order_Ostrict__trans)). 185.47/93.63 thf(12602,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ A @ C) | ~ (ord_less_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1461])). 185.47/93.63 thf(2697,axiom,((! [A:int]: (((divide_divide_int @ one_one_int @ (divide_divide_int @ one_one_int @ A)) = A) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4495_unit__div__1__div__1)). 185.47/93.63 thf(16708,plain,((! [A:int]: (((divide_divide_int @ one_one_int @ (divide_divide_int @ one_one_int @ A)) = A) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2697])). 185.47/93.63 thf(6302,axiom,((! [A:num,B:num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (numeral_numeral_real @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5347_mult__neg__numeral__simps_I1_J)). 185.47/93.63 thf(28932,plain,((! [A:num,B:num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (numeral_numeral_real @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6302])). 185.47/93.63 thf(5305,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1460_discrete)). 185.47/93.63 thf(25260,plain,(((ord_less_nat) = (^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5305])). 185.47/93.63 thf(1032,axiom,((! [A:rat]: ((times_times_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ A)) = (times_times_rat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6338_abs__mult__self__eq)). 185.47/93.63 thf(11256,plain,((! [A:rat]: ((times_times_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ A)) = (times_times_rat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032])). 185.47/93.63 thf(6040,axiom,((! [A:real]: ((times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ one))) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5980_mult__1s__ring__1_I2_J)). 185.47/93.63 thf(28013,plain,((! [A:real]: ((times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ one))) = (uminus_uminus_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6040])). 185.47/93.63 thf(1382,axiom,((! [A:nat,B:nat,C:int]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4789_le__imp__power__dvd)). 185.47/93.63 thf(12334,plain,((! [A:nat,B:nat,C:int]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382])). 185.47/93.63 thf(1319,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4634_unit__imp__dvd)). 185.47/93.63 thf(12129,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319])). 185.47/93.63 thf(1610,axiom,((! [A:nat,B:nat,C:rat]: (((~ (ord_less_nat @ A @ B)) => (((C != one_one_rat) => ((groups2906978787729119204at_rat @ (power_power_rat @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (divide_divide_rat @ (minus_minus_rat @ (power_power_rat @ C @ B) @ (power_power_rat @ C @ (suc @ A))) @ (minus_minus_rat @ one_one_rat @ C)))) & (((groups2906978787729119204at_rat @ (power_power_rat @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (semiri681578069525770553at_rat @ (minus_minus_nat @ (plus_plus_nat @ A @ one_one_nat) @ B))) <= (C = one_one_rat)))) & ((ord_less_nat @ A @ B) => ((groups2906978787729119204at_rat @ (power_power_rat @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6846_sum__gp)). 185.47/93.63 thf(13073,plain,((! [A:nat,B:nat,C:rat]: (((~ (ord_less_nat @ A @ B)) => (((~ (C = one_one_rat)) => ((groups2906978787729119204at_rat @ (power_power_rat @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (divide_divide_rat @ (minus_minus_rat @ (power_power_rat @ C @ B) @ (power_power_rat @ C @ (suc @ A))) @ (minus_minus_rat @ one_one_rat @ C)))) & (((groups2906978787729119204at_rat @ (power_power_rat @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (semiri681578069525770553at_rat @ (minus_minus_nat @ (plus_plus_nat @ A @ one_one_nat) @ B))) | ~ (C = one_one_rat)))) & ((ord_less_nat @ A @ B) => ((groups2906978787729119204at_rat @ (power_power_rat @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610])). 185.47/93.63 thf(2014,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => ((divide_divide_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (divide_divide_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1707_nonzero__mult__divide__mult__cancel__left)). 185.47/93.63 thf(14468,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => ((divide_divide_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (divide_divide_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2014])). 185.47/93.63 thf(3377,axiom,((! [A:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ zero_zero_int) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5164_neg__less__0__iff__less)). 185.47/93.63 thf(18851,plain,((! [A:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ zero_zero_int) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3377])). 185.47/93.63 thf(5552,axiom,((! [A:num]: ((semiri1316708129612266289at_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6904_of__nat__numeral)). 185.47/93.63 thf(26218,plain,((! [A:num]: ((semiri1316708129612266289at_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5552])). 185.47/93.63 thf(3988,axiom,((! [A:rat]: (((plus_plus_rat @ A @ A) = zero_zero_rat) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3025_double__eq__0__iff)). 185.47/93.63 thf(20798,plain,((! [A:rat]: (((plus_plus_rat @ A @ A) = zero_zero_rat) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3988])). 185.47/93.63 thf(95,axiom,((! [A:nat,B:(nat > real),C:real,D:nat]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (groups6591440286371151544t_real @ B @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ C))) <= (! [E:nat]: ((ord_less_nat @ E @ A) => (ord_less_eq_real @ (B @ E) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7623_real__sum__nat__ivl__bounded2)). 185.47/93.63 thf(8044,plain,((! [A:nat,B:(nat > real),C:real,D:nat]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (groups6591440286371151544t_real @ (B) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ C))) | ~ (! [E:nat]: ((ord_less_nat @ E @ A) => (ord_less_eq_real @ (B @ E) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 185.47/93.63 thf(6052,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => ((ord_less_eq_nat @ B @ C) <= (ord_less_nat @ one_one_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4927_power__dvd__imp__le)). 185.47/93.63 thf(28045,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => ((ord_less_eq_nat @ B @ C) | ~ (ord_less_nat @ one_one_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6052])). 185.47/93.63 thf(7263,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ (modulo_modulo_nat @ A @ B) @ C) @ B) = (modulo_modulo_nat @ (plus_plus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1991_mod__add__left__eq)). 185.47/93.63 thf(32475,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ (modulo_modulo_nat @ A @ B) @ C) @ B) = (modulo_modulo_nat @ (plus_plus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7263])). 185.47/93.63 thf(217,axiom,((divide1717551699836669952omplex = (^ [A:complex,B:complex]: (times_times_complex @ A @ (invers8013647133539491842omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8993_divide__complex__def)). 185.47/93.63 thf(8434,plain,(((divide1717551699836669952omplex) = (^ [A:complex,B:complex]: (times_times_complex @ A @ (invers8013647133539491842omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 185.47/93.63 thf(6768,axiom,((! [A:product_prod_nat_nat]: ? [B:nat,C:nat]: (A = (product_Pair_nat_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3428_surj__pair)). 185.47/93.63 thf(30635,plain,((! [A:product_prod_nat_nat]: ? [B:nat,C:nat]: (A = (product_Pair_nat_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6768])). 185.47/93.63 thf(3901,axiom,((! [A:real]: ((! [B:real]: ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (abs_abs_real @ A) @ B))) => (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6540_dense__eq0__I)). 185.47/93.63 thf(20520,plain,((! [A:real]: ((! [B:real]: ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (abs_abs_real @ A) @ B))) => (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3901])). 185.47/93.63 thf(7388,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2211_mult__nonpos__nonneg)). 185.47/93.63 thf(32886,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7388])). 185.47/93.63 thf(4601,axiom,((ord_less_eq_real @ (exp_real @ one_one_real) @ (numeral_numeral_real @ (bit1 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8216_exp__le)). 185.47/93.63 thf(22738,plain,((ord_less_eq_real @ (exp_real @ one_one_real) @ (numeral_numeral_real @ (bit1 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4601])). 185.47/93.63 thf(1618,axiom,((! [A:num]: ((numeral_numeral_int @ (bit0 @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_numeral__Bit0)). 185.47/93.63 thf(13110,plain,((! [A:num]: ((numeral_numeral_int @ (bit0 @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618])). 185.47/93.63 thf(3466,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (dvd_dvd_nat @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4887_finite__divisors__nat)). 185.47/93.63 thf(19142,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (dvd_dvd_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3466])). 185.47/93.63 thf(6810,axiom,((! [A:real]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) = (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6715_abs__square__le__1)). 185.47/93.63 thf(30775,plain,((! [A:real]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) = (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6810])). 185.47/93.63 thf(4271,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (minus_minus_int @ A @ B)) = (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1635_diff__ge__0__iff__ge)). 185.47/93.63 thf(21662,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (minus_minus_int @ A @ B)) = (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4271])). 185.47/93.63 thf(430,axiom,((! [A:nat,B:int]: (ord_less_eq_int @ (bit_se4203085406695923979it_int @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3148_unset__bit__less__eq)). 185.47/93.63 thf(9163,plain,((! [A:nat,B:int]: (ord_less_eq_int @ (bit_se4203085406695923979it_int @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])). 185.47/93.63 thf(5747,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((? [C:nat]: ((ord_less_nat @ (power_power_nat @ A @ C) @ B) & (ord_less_eq_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_916_ex__power__ivl2)). 185.47/93.63 thf(26852,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (? [C:nat]: ((ord_less_nat @ (power_power_nat @ A @ C) @ B) & (ord_less_eq_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat)))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5747])). 185.47/93.63 thf(5017,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((ord_less_eq_real @ one_one_real @ C) => (ord_less_eq_real @ (root @ B @ C) @ (root @ A @ C))) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9195_real__root__decreasing)). 185.47/93.63 thf(24156,plain,((! [A:nat,B:nat,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((ord_less_eq_real @ one_one_real @ C) => (ord_less_eq_real @ (root @ B @ C) @ (root @ A @ C))) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5017])). 185.47/93.63 thf(3684,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_eq_int @ (times_times_int @ B @ A) @ zero_zero_int)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2208_mult__nonneg__nonpos2)). 185.47/93.63 thf(19819,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_eq_int @ (times_times_int @ B @ A) @ zero_zero_int)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3684])). 185.47/93.63 thf(3417,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((divide_divide_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ A) = (plus_plus_int @ B @ (divide_divide_int @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1833_div__mult__self4)). 185.47/93.63 thf(18981,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ A) = (plus_plus_int @ B @ (divide_divide_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3417])). 185.47/93.63 thf(4922,axiom,((! [A:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ one) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_mult__numeral__1)). 185.47/93.63 thf(23846,plain,((! [A:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4922])). 185.47/93.63 thf(6864,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((A != B) => ((the_nat @ (vEBT_vebt_maxt @ E)) = (vEBT_VEBT_high @ B @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))))) <= (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_942_summaxma)). 185.47/93.63 thf(31004,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((~ (A = B)) => ((the_nat @ (vEBT_vebt_maxt @ E)) = (vEBT_VEBT_high @ B @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))))) | ~ (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6864])). 185.47/93.63 thf(7618,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ (suc @ C)) @ D @ E) @ F) = (((F != B) => (((~ (ord_less_nat @ F @ A)) => (((((ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) <= (~ (ord_less_nat @ B @ F))) & ~ (ord_less_nat @ B @ F))) & ~ (ord_less_nat @ F @ A))) <= (F != A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1454_vebt__member_Osimps_I5_J)). 185.47/93.63 thf(33619,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ (suc @ C)) @ D @ E) @ F) = (((~ (F = B)) => (((~ (ord_less_nat @ F @ A)) => (((((ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) | (ord_less_nat @ B @ F)) & ~ (ord_less_nat @ B @ F))) & ~ (ord_less_nat @ F @ A))) | (F = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7618])). 185.47/93.63 thf(4476,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((B = C) => (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3864_ord__le__eq__trans)). 185.47/93.63 thf(22333,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((B = C) => (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4476])). 185.47/93.63 thf(5647,axiom,((! [A:nat,B:num,C:nat]: (((semiri8010041392384452111omplex @ A) = (power_power_complex @ (numera6690914467698888265omplex @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7055_real__of__nat__eq__numeral__power__cancel__iff)). 185.47/93.63 thf(26525,plain,((! [A:nat,B:num,C:nat]: (((semiri8010041392384452111omplex @ A) = (power_power_complex @ (numera6690914467698888265omplex @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5647])). 185.47/93.63 thf(2622,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ one_one_int) = ((dvd_dvd_int @ B @ one_one_int) & (dvd_dvd_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4749_is__unit__mult__iff)). 185.47/93.63 thf(16434,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ one_one_int) = ((dvd_dvd_int @ B @ one_one_int) & (dvd_dvd_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2622])). 185.47/93.63 thf(7531,axiom,((! [A:num]: (((numeral_numeral_nat @ A) = one_one_nat) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_numeral__eq__one__iff)). 185.47/93.63 thf(33384,plain,((! [A:num]: (((numeral_numeral_nat @ A) = one_one_nat) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7531])). 185.47/93.63 thf(6170,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_784_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right)). 185.47/93.63 thf(28494,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6170])). 185.47/93.63 thf(5328,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ B @ (suc @ (plus_plus_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2913_add__eq__if)). 185.47/93.63 thf(25343,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ B @ (suc @ (plus_plus_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5328])). 185.47/93.63 thf(4747,axiom,((! [A:real,B:real,C:real]: (((dvd_dvd_real @ A @ (plus_plus_real @ C @ B)) = (dvd_dvd_real @ A @ C)) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4647_dvd__add__left__iff)). 185.47/93.63 thf(23219,plain,((! [A:real,B:real,C:real]: (((dvd_dvd_real @ A @ (plus_plus_real @ C @ B)) = (dvd_dvd_real @ A @ C)) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4747])). 185.47/93.63 thf(7136,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4603_dvd__mult2)). 185.47/93.63 thf(32026,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7136])). 185.47/93.63 thf(5443,axiom,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_num @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3993_ord__less__eq__trans)). 185.47/93.63 thf(25769,plain,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_num @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5443])). 185.47/93.63 thf(2108,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ A @ B) => ((divide_divide_int @ A @ B) = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3038_div__pos__pos__trivial)). 185.47/93.63 thf(14750,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ A @ B) => ((divide_divide_int @ A @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2108])). 185.47/93.63 thf(4687,axiom,((! [A:int,B:nat,C:nat]: (((ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (ord_less_nat @ B @ C)) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_power__strict__increasing__iff)). 185.47/93.63 thf(23021,plain,((! [A:int,B:nat,C:nat]: (((ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (ord_less_nat @ B @ C)) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4687])). 185.47/93.63 thf(3501,axiom,((! [A:code_integer]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ (abs_abs_Code_integer @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6521_abs__ge__minus__self)). 185.47/93.63 thf(19259,plain,((! [A:code_integer]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ (abs_abs_Code_integer @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3501])). 185.47/93.63 thf(7000,axiom,((! [A:real]: ((root @ zero_zero_nat @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9160_root__0)). 185.47/93.63 thf(31553,plain,((! [A:real]: ((root @ zero_zero_nat @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7000])). 185.47/93.63 thf(6899,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1001_Suc__le__mono)). 185.47/93.63 thf(31128,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6899])). 185.47/93.63 thf(3552,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = one_one_nat)) & ((A != zero_zero_nat) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8472_pochhammer__0__left)). 185.47/93.63 thf(19406,plain,((! [A:nat]: (((A = zero_zero_nat) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = one_one_nat)) & ((~ (A = zero_zero_nat)) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3552])). 185.47/93.63 thf(3816,axiom,(((neg_nu8295874005876285629c_real @ zero_zero_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6992_dbl__inc__simps_I2_J)). 185.47/93.63 thf(20258,plain,(((neg_nu8295874005876285629c_real @ zero_zero_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3816])). 185.47/93.63 thf(2548,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ B @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4011_dual__order_Oasym)). 185.47/93.63 thf(16184,plain,((! [A:int,B:int]: (~ (ord_less_int @ B @ A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2548])). 185.47/93.63 thf(3993,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ (abs_abs_rat @ B))) = ((B = zero_zero_rat) | (ord_less_eq_rat @ zero_zero_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6400_zero__le__divide__abs__iff)). 185.47/93.63 thf(20813,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ (abs_abs_rat @ B))) = ((B = zero_zero_rat) | (ord_less_eq_rat @ zero_zero_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3993])). 185.47/93.63 thf(2859,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_eq_real @ (times_times_real @ C @ A) @ B)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2838_neg__divide__le__eq)). 185.47/93.63 thf(17221,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_eq_real @ (times_times_real @ C @ A) @ B)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2859])). 185.47/93.63 thf(823,axiom,((! [A:num,B:num]: ~ (ord_le6747313008572928689nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5709_not__numeral__less__neg__numeral)). 185.47/93.63 thf(10542,plain,((! [A:num,B:num]: ~ (ord_le6747313008572928689nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[823])). 185.47/93.63 thf(70,axiom,((! [A:set_nat]: ((? [B:nat]: (ord_less_eq_set_nat @ A @ (set_ord_lessThan_nat @ B))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7773_finite__nat__bounded)). 185.47/93.63 thf(7958,plain,((! [A:set_nat]: (? [B:nat]: (ord_less_eq_set_nat @ A @ (set_ord_lessThan_nat @ B)) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 185.47/93.63 thf(2714,axiom,((~ (ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5907_le__minus__one__simps_I3_J)). 185.47/93.63 thf(16765,plain,((~ (ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2714])). 185.47/93.63 thf(3165,axiom,((! [A:real,B:real]: ((plus_plus_real @ (cos_real @ A) @ (cos_real @ B)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (cos_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))) @ (cos_real @ (divide_divide_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7895_cos__plus__cos)). 185.47/93.63 thf(18193,plain,((! [A:real,B:real]: ((plus_plus_real @ (cos_real @ A) @ (cos_real @ B)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (cos_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))) @ (cos_real @ (divide_divide_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3165])). 185.47/93.63 thf(5023,axiom,((times_times_real = (^ [A:real,B:real]: (times_times_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_mult_Ocommute)). 185.47/93.63 thf(24173,plain,(((times_times_real) = (^ [A:real,B:real]: (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5023])). 185.47/93.63 thf(2735,axiom,((! [A:num,B:real]: ((real_V7735802525324610683m_real @ (times_times_real @ (numeral_numeral_real @ A) @ B)) = (times_times_real @ (numeral_numeral_real @ A) @ (real_V7735802525324610683m_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7446_norm__mult__numeral1)). 185.47/93.63 thf(16830,plain,((! [A:num,B:real]: ((real_V7735802525324610683m_real @ (times_times_real @ (numeral_numeral_real @ A) @ B)) = (times_times_real @ (numeral_numeral_real @ A) @ (real_V7735802525324610683m_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2735])). 185.47/93.63 thf(6605,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (dvd_dvd_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ D))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4797_dvd__power__le)). 185.47/93.63 thf(30021,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (dvd_dvd_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ D))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6605])). 185.47/93.63 thf(6078,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ (divide_divide_nat @ B @ A) @ C) = (divide_divide_nat @ (times_times_nat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4751_dvd__div__mult)). 185.47/93.63 thf(28129,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ (divide_divide_nat @ B @ A) @ C) = (divide_divide_nat @ (times_times_nat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6078])). 185.47/93.63 thf(299,axiom,((! [A:real]: ? [B:real]: ((ord_less_eq_real @ B @ pi) & ((cos_real @ B) = (cos_real @ A)) & ((sin_real @ B) = (sin_real @ A)) & (ord_less_real @ (uminus_uminus_real @ pi) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7829_sincos__principal__value)). 185.47/93.63 thf(8709,plain,((! [A:real]: ? [B:real]: ((ord_less_eq_real @ B @ pi) & ((cos_real @ B) = (cos_real @ A)) & ((sin_real @ B) = (sin_real @ A)) & (ord_less_real @ (uminus_uminus_real @ pi) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 185.47/93.63 thf(1371,axiom,((! [A:int,B:int]: ~ (ord_less_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2687_not__sum__squares__lt__zero)). 185.47/93.63 thf(12299,plain,((! [A:int,B:int]: ~ (ord_less_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371])). 185.47/93.63 thf(3776,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_eq_real @ C @ D) => (ord_less_real @ (divide_divide_real @ A @ D) @ (divide_divide_real @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2647_frac__less)). 185.47/93.63 thf(20136,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_eq_real @ C @ D) => (ord_less_real @ (divide_divide_real @ A @ D) @ (divide_divide_real @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3776])). 185.47/93.63 thf(4190,axiom,((! [A:rat,B:rat,C:(rat > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3921_order__subst2)). 185.47/93.63 thf(21418,plain,((! [A:rat,B:rat,C:(rat > nat),D:nat]: (((ord_less_eq_nat @ (C @ B) @ D) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4190])). 185.47/93.63 thf(490,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (arctan @ A) @ (arctan @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6818_arctan__le__iff)). 185.47/93.63 thf(9383,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (arctan @ A) @ (arctan @ B)) = (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[490])). 185.47/93.63 thf(4244,axiom,((! [A:num]: ((neg_nu8557863876264182079omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu6511756317524482435omplex @ (numera6690914467698888265omplex @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6864_dbl__inc__simps_I1_J)). 185.47/93.63 thf(21585,plain,((! [A:num]: ((neg_nu8557863876264182079omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu6511756317524482435omplex @ (numera6690914467698888265omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4244])). 185.47/93.63 thf(2285,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4788_le__imp__power__dvd)). 185.47/93.63 thf(15314,plain,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2285])). 185.47/93.63 thf(6761,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4289_linorder__not__less)). 185.47/93.63 thf(30603,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6761])). 185.47/93.63 thf(7409,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_add__mult__distrib2)). 185.47/93.63 thf(32972,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7409])). 185.47/93.63 thf(5426,axiom,((! [A:num]: ~ (ord_less_num @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3093_verit__comp__simplify1_I1_J)). 185.47/93.63 thf(25673,plain,((! [A:num]: ~ (ord_less_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5426])). 185.47/93.63 thf(1039,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1424_subset__eq)). 185.47/93.63 thf(11277,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ A) => (member_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039])). 185.47/93.63 thf(7215,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit1 @ A) @ (bit1 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6358_semiring__norm_I73_J)). 185.47/93.63 thf(32310,plain,((! [A:num,B:num]: ((ord_less_eq_num @ (bit1 @ A) @ (bit1 @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7215])). 185.47/93.63 thf(7279,axiom,((! [A:nat,B:num,C:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7121_of__nat__less__numeral__power__cancel__iff)). 185.47/93.63 thf(32522,plain,((! [A:nat,B:num,C:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7279])). 185.47/93.63 thf(2988,axiom,((! [A:nat]: ((groups3542108847815614940at_nat @ (binomial @ A) @ (set_ord_atMost_nat @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8949_choose__row__sum)). 185.47/93.63 thf(17641,plain,((! [A:nat]: ((groups3542108847815614940at_nat @ (binomial @ A) @ (set_ord_atMost_nat @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2988])). 185.47/93.63 thf(7710,axiom,(((modulo_modulo_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1879_one__mod__two__eq__one)). 185.47/93.63 thf(33870,plain,(((modulo_modulo_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7710])). 185.47/93.63 thf(3860,axiom,((! [A:num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_816_one__le__numeral)). 185.47/93.63 thf(20400,plain,((! [A:num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3860])). 185.47/93.63 thf(7168,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)) | ((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2496_one__is__add)). 185.47/93.63 thf(32150,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)) | ((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7168])). 185.47/93.63 thf(5371,axiom,((! [A:num]: ((plus_plus_num @ one @ (bit0 @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6412_semiring__norm_I3_J)). 185.47/93.63 thf(25508,plain,((! [A:num]: ((plus_plus_num @ one @ (bit0 @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5371])). 185.47/93.63 thf(3414,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ C @ B)) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4605_dvd__mult)). 185.47/93.63 thf(18972,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ C @ B)) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3414])). 185.47/93.63 thf(613,axiom,((! [A:set_nat]: ((minus_minus_set_nat @ A @ bot_bot_set_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1306_Diff__empty)). 185.47/93.63 thf(9769,plain,((! [A:set_nat]: ((minus_minus_set_nat @ A @ bot_bot_set_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[613])). 185.47/93.63 thf(6991,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (times_times_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) = ((ord_less_nat @ C @ B) | ((ord_less_eq_nat @ B @ C) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ C @ B))))) | ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4994_even__mult__exp__div__exp__iff)). 185.47/93.63 thf(31517,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (times_times_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) = ((ord_less_nat @ C @ B) | ((ord_less_eq_nat @ B @ C) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ C @ B))))) | ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6991])). 185.47/93.63 thf(6734,axiom,((! [A:int,B:nat]: ((A != zero_zero_int) => ((power_power_int @ A @ B) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2097_power__not__zero)). 185.47/93.63 thf(30459,plain,((! [A:int,B:nat]: ((~ (A = zero_zero_int)) => (~ ((power_power_int @ A @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6734])). 185.47/93.63 thf(6697,axiom,((! [A:nat]: (((power_power_real @ zero_zero_real @ A) = zero_zero_real) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1967_zero__power)). 185.47/93.63 thf(30318,plain,((! [A:nat]: (((power_power_real @ zero_zero_real @ A) = zero_zero_real) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6697])). 185.47/93.63 thf(6503,axiom,((! [A:nat]: ((zero_zero_nat = (semiri1316708129612266289at_nat @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6890_of__nat__0__eq__iff)). 185.47/93.63 thf(29677,plain,((! [A:nat]: ((zero_zero_nat = (semiri1316708129612266289at_nat @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6503])). 185.47/93.63 thf(1309,axiom,((! [A:(real > (real > $o)),B:real,C:real]: (((! [D:real]: (A @ D @ D)) => ((A @ B @ C) <= (! [D:real,E:real]: ((A @ D @ E) <= (A @ E @ D))))) <= (! [D:real,E:real]: ((A @ D @ E) <= (ord_less_real @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4018_linorder__less__wlog)). 185.47/93.63 thf(12089,plain,((! [A:(real > (real > $o)),B:real,C:real]: (((! [D:real]: (A @ D @ D)) => ((A @ B @ C) | ~ (! [D:real,E:real]: ((A @ D @ E) | ~ (A @ E @ D))))) | ~ (! [D:real,E:real]: ((A @ D @ E) | ~ (ord_less_real @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309])). 185.47/93.63 thf(3569,axiom,((! [A:int]: ((~ (! [B:nat]: ((~ (ord_less_nat @ zero_zero_nat @ B)) <= (A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ B)))))) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7327_neg__int__cases)). 185.47/93.63 thf(19462,plain,((! [A:int]: (~ (! [B:nat]: (~ (ord_less_nat @ zero_zero_nat @ B) | ~ (A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ B))))) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3569])). 185.47/93.63 thf(4493,axiom,((! [A:complex]: ((comm_s2602460028002588243omplex @ A @ zero_zero_nat) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8420_pochhammer__0)). 185.47/93.63 thf(22384,plain,((! [A:complex]: ((comm_s2602460028002588243omplex @ A @ zero_zero_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4493])). 185.47/93.63 thf(7665,axiom,(((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) = (some_nat @ pr))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538__092_060open_062vebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Apr_092_060close_062)). 185.47/93.63 thf(33751,plain,(((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) = (some_nat @ pr))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7665])). 185.47/93.63 thf(4039,axiom,((one_one_nat = (nat2 @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9286_nat__one__as__int)). 185.47/93.63 thf(20954,plain,((one_one_nat = (nat2 @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4039])). 185.47/93.63 thf(764,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ (times_times_int @ (sgn_sgn_int @ A) @ (abs_abs_int @ B)) @ (times_times_int @ (sgn_sgn_int @ A) @ (abs_abs_int @ C))) = (divide_divide_int @ (abs_abs_int @ B) @ (abs_abs_int @ C))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9226_div__sgn__abs__cancel)). 185.47/93.63 thf(10331,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (times_times_int @ (sgn_sgn_int @ A) @ (abs_abs_int @ B)) @ (times_times_int @ (sgn_sgn_int @ A) @ (abs_abs_int @ C))) = (divide_divide_int @ (abs_abs_int @ B) @ (abs_abs_int @ C))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[764])). 185.47/93.63 thf(4919,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ (divide_divide_nat @ C @ A))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4781_div__plus__div__distrib__dvd__left)). 185.47/93.63 thf(23825,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ (divide_divide_nat @ C @ A))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4919])). 185.47/93.63 thf(4868,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => (! [D:rat,E:rat]: ((~ (dvd_dvd_rat @ A @ (plus_plus_rat @ D @ C))) = (~ (dvd_dvd_rat @ A @ (plus_plus_rat @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)) @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4849_inf__period_I4_J)). 185.47/93.63 thf(23633,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => (! [D:rat,E:rat]: ((~ (dvd_dvd_rat @ A @ (plus_plus_rat @ D @ C))) = (~ (dvd_dvd_rat @ A @ (plus_plus_rat @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4868])). 185.47/93.63 thf(2441,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((nat2 @ (minus_minus_int @ A @ B)) = (minus_minus_nat @ (nat2 @ A) @ (nat2 @ B))) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9313_nat__diff__distrib_H)). 185.47/93.63 thf(15816,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((nat2 @ (minus_minus_int @ A @ B)) = (minus_minus_nat @ (nat2 @ A) @ (nat2 @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2441])). 185.47/93.63 thf(5192,axiom,(((csqrt @ one_one_complex) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9157_csqrt__1)). 185.47/93.63 thf(24850,plain,(((csqrt @ one_one_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5192])). 185.47/93.63 thf(7587,axiom,((! [A:num]: (ord_less_num @ one @ (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_semiring__norm_I76_J)). 185.47/93.63 thf(33532,plain,((! [A:num]: (ord_less_num @ one @ (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7587])). 185.47/93.63 thf(4000,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((? [C:rat]: ((ord_less_rat @ zero_zero_rat @ C) & (ord_less_rat @ C @ B) & (ord_less_rat @ C @ A))) <= (ord_less_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2026_field__lbound__gt__zero)). 185.47/93.63 thf(20835,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => (? [C:rat]: ((ord_less_rat @ zero_zero_rat @ C) & (ord_less_rat @ C @ B) & (ord_less_rat @ C @ A)) | ~ (ord_less_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4000])). 185.47/93.63 thf(291,axiom,((! [A:(nat > real)]: ((! [B:nat]: (ord_less_eq_real @ (A @ B) @ (A @ (suc @ B)))) => (topolo6980174941875973593q_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8393_mono__SucI1)). 185.47/93.63 thf(8682,plain,((! [A:(nat > real)]: ((! [B:nat]: (ord_less_eq_real @ (A @ B) @ (A @ (suc @ B)))) => (topolo6980174941875973593q_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 185.47/93.63 thf(1067,axiom,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (comm_s2602460028002588243omplex @ A @ B)) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ (divide1717551699836669952omplex @ one_one_complex @ (numera6690914467698888265omplex @ (bit0 @ one)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8400_pochhammer__double)). 185.47/93.63 thf(11353,plain,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (comm_s2602460028002588243omplex @ A @ B)) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ (divide1717551699836669952omplex @ one_one_complex @ (numera6690914467698888265omplex @ (bit0 @ one)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067])). 185.47/93.63 thf(3561,axiom,((! [A:rat,B:num,C:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) @ C) = (ord_less_eq_rat @ (times_times_rat @ C @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5382_divide__le__eq__numeral1_I2_J)). 185.47/93.63 thf(19438,plain,((! [A:rat,B:num,C:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) @ C) = (ord_less_eq_rat @ (times_times_rat @ C @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3561])). 185.47/93.63 thf(6885,axiom,((! [A:real]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1897_power2__less__eq__zero__iff)). 185.47/93.63 thf(31084,plain,((! [A:real]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6885])). 185.47/93.63 thf(2162,axiom,((! [A:real,B:real,C:real]: ((((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => (ord_less_eq_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B))) <= (ord_less_eq_real @ C @ zero_zero_real)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2850_divide__left__mono__neg)). 185.47/93.63 thf(14937,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => (ord_less_eq_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B))) | ~ (ord_less_eq_real @ C @ zero_zero_real) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2162])). 185.47/93.63 thf(1734,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4281_linorder__not__le)). 185.47/93.63 thf(13548,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734])). 185.47/93.63 thf(2410,axiom,((! [A:rat,B:rat]: (((abs_abs_rat @ (times_times_rat @ A @ B)) = (times_times_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))) <= (((ord_less_eq_rat @ A @ zero_zero_rat) | (ord_less_eq_rat @ zero_zero_rat @ A)) & ((ord_less_eq_rat @ zero_zero_rat @ B) | (ord_less_eq_rat @ B @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6548_abs__eq__mult)). 185.47/93.63 thf(15703,plain,((! [A:rat,B:rat]: (((abs_abs_rat @ (times_times_rat @ A @ B)) = (times_times_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))) | ~ (((ord_less_eq_rat @ A @ zero_zero_rat) | (ord_less_eq_rat @ zero_zero_rat @ A)) & ((ord_less_eq_rat @ zero_zero_rat @ B) | (ord_less_eq_rat @ B @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2410])). 185.47/93.63 thf(6038,axiom,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ B @ C)) = (divide_divide_nat @ (divide_divide_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_div__mult2__eq)). 185.47/93.63 thf(28008,plain,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ B @ C)) = (divide_divide_nat @ (divide_divide_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6038])). 185.47/93.63 thf(2540,axiom,((! [A:rat,B:rat,C:rat]: (((B = (divide_divide_rat @ C @ A)) = ((times_times_rat @ B @ A) = C)) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2460_nonzero__eq__divide__eq)). 185.47/93.63 thf(16156,plain,((! [A:rat,B:rat,C:rat]: (((B = (divide_divide_rat @ C @ A)) = ((times_times_rat @ B @ A) = C)) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2540])). 185.47/93.63 thf(1600,axiom,((! [A:rat,B:(rat > rat),C:rat,D:rat]: ((((! [E:rat,F:rat]: ((ord_less_rat @ (B @ E) @ (B @ F)) <= (ord_less_rat @ E @ F))) => (ord_less_rat @ A @ (B @ D))) <= (ord_less_rat @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4079_ord__eq__less__subst)). 185.47/93.63 thf(13035,plain,((! [A:rat,B:(rat > rat),C:rat,D:rat]: (((! [E:rat,F:rat]: ((ord_less_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_rat @ E @ F))) => (ord_less_rat @ A @ (B @ D))) | ~ (ord_less_rat @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600])). 185.47/93.63 thf(3237,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (((ord_less_eq_rat @ A @ zero_zero_rat) => (ord_less_rat @ C @ B)) & ((ord_less_rat @ B @ C) <= (ord_less_eq_rat @ zero_zero_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2584_mult__less__cancel__left)). 185.47/93.63 thf(18416,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (((ord_less_eq_rat @ A @ zero_zero_rat) => (ord_less_rat @ C @ B)) & ((ord_less_rat @ B @ C) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3237])). 185.47/93.63 thf(697,axiom,((gbinomial_rat = (^ [A:rat,B:nat]: (if_rat @ (B = zero_zero_nat) @ one_one_rat @ (divide_divide_rat @ (set_fo1949268297981939178at_rat @ (^ [C:nat]: (times_times_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_rat) @ (semiri773545260158071498ct_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8612_gbinomial__code)). 185.47/93.63 thf(10061,plain,(((gbinomial_rat) = (^ [A:rat,B:nat]: (if_rat @ (B = zero_zero_nat) @ one_one_rat @ (divide_divide_rat @ (set_fo1949268297981939178at_rat @ (^ [C:nat]: (times_times_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_rat) @ (semiri773545260158071498ct_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[697])). 185.47/93.63 thf(6552,axiom,((! [A:nat]: ((the_nat @ (some_nat @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1186_option_Osel)). 185.47/93.63 thf(29844,plain,((! [A:nat]: ((the_nat @ (some_nat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6552])). 185.47/93.63 thf(3721,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3861_ord__le__eq__trans)). 185.47/93.63 thf(19951,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3721])). 185.47/93.63 thf(1405,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((C = D) & (ord_less_rat @ A @ B)) => (ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_add__mono__thms__linordered__field_I1_J)). 185.47/93.63 thf(12415,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((C = D) & (ord_less_rat @ A @ B)) => (ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405])). 185.47/93.63 thf(5562,axiom,((! [A:nat]: ((times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A)) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5298_minus__one__mult__self)). 185.47/93.63 thf(26247,plain,((! [A:nat]: ((times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A)) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5562])). 185.47/93.63 thf(295,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (log @ A @ B) @ one_one_real) = (ord_less_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9025_log__less__one__cancel__iff)). 185.47/93.63 thf(8695,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (log @ A @ B) @ one_one_real) = (ord_less_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 185.47/93.63 thf(3314,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (minus_minus_int @ A @ B) @ C) = (ord_less_int @ A @ (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_803_diff__less__eq)). 185.47/93.63 thf(18652,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (minus_minus_int @ A @ B) @ C) = (ord_less_int @ A @ (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3314])). 185.47/93.63 thf(4795,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ B)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1830_nonzero__divide__mult__cancel__left)). 185.47/93.63 thf(23406,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ (times_times_real @ A @ B)) = (divide_divide_real @ one_one_real @ B)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4795])). 185.47/93.63 thf(7152,axiom,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_mult__1)). 185.47/93.63 thf(32091,plain,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7152])). 185.47/93.63 thf(2772,axiom,((! [A:code_integer,B:code_integer,C:nat]: ((dvd_dvd_Code_integer @ A @ B) => (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4677_dvd__power__same)). 185.47/93.63 thf(16940,plain,((! [A:code_integer,B:code_integer,C:nat]: ((dvd_dvd_Code_integer @ A @ B) => (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2772])). 185.47/93.63 thf(5287,axiom,((! [A:num,B:num]: (((ord_less_eq_num @ B @ A) = (B = A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3964_order__antisym__conv)). 185.47/93.63 thf(25211,plain,((! [A:num,B:num]: (((ord_less_eq_num @ B @ A) = (B = A)) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5287])). 185.47/93.63 thf(4785,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B))) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2239_mult__nonpos__nonpos)). 185.47/93.63 thf(23374,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B))) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4785])). 185.47/93.63 thf(4358,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ one_one_int)) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4542_even__plus__one__iff)). 185.47/93.63 thf(21961,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ one_one_int)) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4358])). 185.47/93.63 thf(5974,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_real @ C @ one_one_real) => (ord_less_eq_real @ (power_power_real @ C @ B) @ (power_power_real @ C @ A))) <= (ord_less_eq_real @ zero_zero_real @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2883_power__decreasing)). 185.47/93.63 thf(27811,plain,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_real @ C @ one_one_real) => (ord_less_eq_real @ (power_power_real @ C @ B) @ (power_power_real @ C @ A))) | ~ (ord_less_eq_real @ zero_zero_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5974])). 185.47/93.63 thf(1518,axiom,((! [A:num,B:nat,C:int]: ((ord_less_rat @ (power_power_rat @ (numeral_numeral_rat @ A) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7145_numeral__power__less__of__int__cancel__iff)). 185.47/93.63 thf(12774,plain,((! [A:num,B:nat,C:int]: ((ord_less_rat @ (power_power_rat @ (numeral_numeral_rat @ A) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518])). 185.47/93.63 thf(1783,axiom,((! [A:nat,B:num]: (((suc @ A) = (numeral_numeral_nat @ B)) = (A = (pred_numeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6782_Suc__eq__numeral)). 185.47/93.63 thf(13707,plain,((! [A:nat,B:num]: (((suc @ A) = (numeral_numeral_nat @ B)) = (A = (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783])). 185.47/93.63 thf(6673,axiom,((! [A:nat,B:nat,C:nat]: ((groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ A @ (times_times_nat @ (semiri1316708129612266289at_nat @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C)) = (divide_divide_nat @ (times_times_nat @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ C) @ one_one_nat) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (times_times_nat @ (semiri1316708129612266289at_nat @ C) @ B))) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7353_arith__series)). 185.47/93.63 thf(30245,plain,((! [A:nat,B:nat,C:nat]: ((groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ A @ (times_times_nat @ (semiri1316708129612266289at_nat @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C)) = (divide_divide_nat @ (times_times_nat @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ C) @ one_one_nat) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (times_times_nat @ (semiri1316708129612266289at_nat @ C) @ B))) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6673])). 185.47/93.63 thf(3862,axiom,((! [A:num,B:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5692_neg__numeral__le__numeral)). 185.47/93.63 thf(20405,plain,((! [A:num,B:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3862])). 185.47/93.63 thf(6322,axiom,((! [A:num]: ((power_power_real @ zero_zero_real @ (numeral_numeral_nat @ A)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1748_power__zero__numeral)). 185.47/93.63 thf(29007,plain,((! [A:num]: ((power_power_real @ zero_zero_real @ (numeral_numeral_nat @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6322])). 185.47/93.63 thf(906,axiom,((! [A:int,B:int]: (((A = zero_zero_int) | (ord_less_int @ one_one_int @ B)) <= (ord_less_int @ (abs_abs_int @ (ring_1_of_int_int @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7291_of__int__lessD)). 185.47/93.63 thf(10837,plain,((! [A:int,B:int]: ((A = zero_zero_int) | (ord_less_int @ one_one_int @ B) | ~ (ord_less_int @ (abs_abs_int @ (ring_1_of_int_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[906])). 185.47/93.63 thf(2823,axiom,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ C) <= (ord_less_eq_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7495_norm__triangle__le)). 185.47/93.63 thf(17104,plain,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ C) | ~ (ord_less_eq_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2823])). 185.47/93.63 thf(168,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => (((ord_less_eq_int @ (groups3539618377306564664at_int @ C @ B) @ (groups3539618377306564664at_int @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => (ord_less_eq_int @ zero_zero_int @ (C @ D))))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6200_sum__mono2)). 185.47/93.63 thf(8271,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => ((ord_less_eq_int @ (groups3539618377306564664at_int @ (C) @ B) @ (groups3539618377306564664at_int @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => (ord_less_eq_int @ zero_zero_int @ (C @ D)))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 185.47/93.63 thf(4780,axiom,((! [A:nat,B:nat]: ((semiri8010041392384452111omplex @ (divide_divide_nat @ A @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (semiri8010041392384452111omplex @ A) @ (semiri8010041392384452111omplex @ (modulo_modulo_nat @ A @ B))) @ (semiri8010041392384452111omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7300_field__char__0__class_Oof__nat__div)). 185.47/93.63 thf(23359,plain,((! [A:nat,B:nat]: ((semiri8010041392384452111omplex @ (divide_divide_nat @ A @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (semiri8010041392384452111omplex @ A) @ (semiri8010041392384452111omplex @ (modulo_modulo_nat @ A @ B))) @ (semiri8010041392384452111omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4780])). 185.47/93.63 thf(3343,axiom,((! [A:rat,B:rat,C:rat]: (((((~ (ord_less_eq_rat @ C @ B)) <= (ord_less_eq_rat @ A @ C)) => (((~ ((ord_less_eq_rat @ C @ A) => (~ (ord_less_eq_rat @ A @ B)))) <= ((ord_less_eq_rat @ B @ C) => (~ (ord_less_eq_rat @ C @ A)))) <= ((ord_less_eq_rat @ C @ B) => (~ (ord_less_eq_rat @ B @ A))))) <= ((ord_less_eq_rat @ B @ A) => (~ (ord_less_eq_rat @ A @ C)))) <= ((~ (ord_less_eq_rat @ B @ C)) <= (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3846_le__cases3)). 185.47/93.63 thf(18741,plain,((! [A:rat,B:rat,C:rat]: (((~ (ord_less_eq_rat @ C @ B) | ~ (ord_less_eq_rat @ A @ C)) => (~ ((ord_less_eq_rat @ C @ A) => (~ (ord_less_eq_rat @ A @ B))) | ~ ((ord_less_eq_rat @ B @ C) => (~ (ord_less_eq_rat @ C @ A))) | ~ ((ord_less_eq_rat @ C @ B) => (~ (ord_less_eq_rat @ B @ A))))) | ~ ((ord_less_eq_rat @ B @ A) => (~ (ord_less_eq_rat @ A @ C))) | ~ (~ (ord_less_eq_rat @ B @ C) | ~ (ord_less_eq_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3343])). 185.47/93.63 thf(685,axiom,((! [A:nat,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (gbinomial_real @ (semiri5074537144036343181t_real @ C) @ A)) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (gbinomial_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ B) @ one_one_real) @ (plus_plus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8597_gbinomial__sum__up__index)). 185.47/93.63 thf(10017,plain,((! [A:nat,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (gbinomial_real @ (semiri5074537144036343181t_real @ C) @ A)) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (gbinomial_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ B) @ one_one_real) @ (plus_plus_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[685])). 185.47/93.63 thf(2945,axiom,((! [A:int,B:int]: (((ord_less_eq_rat @ one_one_rat @ (fract @ B @ A)) = (ord_less_eq_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9956_one__le__Fract__iff)). 185.47/93.63 thf(17495,plain,((! [A:int,B:int]: (((ord_less_eq_rat @ one_one_rat @ (fract @ B @ A)) = (ord_less_eq_int @ A @ B)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2945])). 185.47/93.63 thf(6875,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3936_linorder__linear)). 185.47/93.63 thf(31052,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6875])). 185.47/93.63 thf(136,axiom,((! [A:real]: ((sin_real @ (plus_plus_real @ pi @ A)) = (uminus_uminus_real @ (sin_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7786_sin__periodic__pi2)). 185.47/93.63 thf(8169,plain,((! [A:real]: ((sin_real @ (plus_plus_real @ pi @ A)) = (uminus_uminus_real @ (sin_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 185.47/93.63 thf(6644,axiom,((! [A:nat]: ((semiri1316708129612266289at_nat @ (suc @ A)) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7218_of__nat__neq__0)). 185.47/93.63 thf(30145,plain,((! [A:nat]: ~ ((semiri1316708129612266289at_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6644])). 185.47/93.63 thf(4792,axiom,((! [A:rat,B:rat]: ((one_one_rat = (divide_divide_rat @ A @ B)) = ((B = A) & (B != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1726_eq__divide__eq__1)). 185.47/93.63 thf(23396,plain,((! [A:rat,B:rat]: ((one_one_rat = (divide_divide_rat @ A @ B)) = ((B = A) & ~ (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4792])). 185.47/93.63 thf(3435,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9387_even__and__iff__int)). 185.47/93.63 thf(19037,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3435])). 185.47/93.63 thf(4122,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4143_order__less__imp__not__less)). 185.47/93.63 thf(21207,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4122])). 185.47/93.63 thf(6295,axiom,((ord_less_eq_num = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4230_dual__order_Oorder__iff__strict)). 185.47/93.63 thf(28911,plain,(((ord_less_eq_num) = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6295])). 185.47/93.63 thf(438,axiom,((! [A:nat,B:nat,C:(nat > rat)]: ((((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = zero_zero_rat) <= (~ (ord_less_eq_nat @ A @ B))) & ((ord_less_eq_nat @ A @ B) => ((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_rat @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6737_sum__natinterval__diff)). 185.47/93.63 thf(9191,plain,((! [A:nat,B:nat,C:(nat > rat)]: ((((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = zero_zero_rat) | (ord_less_eq_nat @ A @ B)) & ((ord_less_eq_nat @ A @ B) => ((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_rat @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])). 185.47/93.63 thf(6050,axiom,((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2693_zero__less__two)). 185.47/93.63 thf(28042,plain,((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6050])). 185.47/93.63 thf(6383,axiom,(((^ [A:complex]: (A)) = (times_times_complex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1352_lambda__one)). 185.47/93.63 thf(29223,plain,(((^ [A:complex]: (A)) = (times_times_complex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6383])). 185.47/93.63 thf(4654,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = zero_zero_int) => ((uminus_uminus_int @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5734_add_Oinverse__unique)). 185.47/93.63 thf(22910,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = zero_zero_int) => ((uminus_uminus_int @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4654])). 185.47/93.63 thf(5501,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9448_or__nat__numerals_I2_J)). 185.47/93.63 thf(26053,plain,((! [A:num]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5501])). 185.47/93.63 thf(7626,axiom,(((power_power_complex @ one_one_complex @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_905_one__power2)). 185.47/93.63 thf(33648,plain,(((power_power_complex @ one_one_complex @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7626])). 185.47/93.63 thf(6090,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_add__le__imp__le__right)). 185.47/93.63 thf(28173,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6090])). 185.47/93.63 thf(7218,axiom,((! [A:num,B:num,C:num]: (((B = C) => (ord_less_eq_num @ A @ C)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3862_ord__le__eq__trans)). 185.47/93.63 thf(32319,plain,((! [A:num,B:num,C:num]: (((B = C) => (ord_less_eq_num @ A @ C)) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7218])). 185.47/93.63 thf(1945,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((plus_plus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (divide_divide_real @ (plus_plus_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6162_minus__divide__add__eq__iff)). 185.47/93.63 thf(14241,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((plus_plus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (divide_divide_real @ (plus_plus_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945])). 185.47/93.63 thf(2805,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_diff__strict__right__mono)). 185.47/93.63 thf(17046,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2805])). 185.47/93.63 thf(6887,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2509_nat__mult__eq__cancel1)). 185.47/93.63 thf(31089,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6887])). 185.47/93.63 thf(1558,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ one_one_real @ (exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8180_exp__gt__one)). 185.47/93.63 thf(12896,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ one_one_real @ (exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558])). 185.47/93.63 thf(6762,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9449_or__nat__numerals_I4_J)). 185.47/93.63 thf(30606,plain,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6762])). 185.47/93.63 thf(1652,axiom,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (times_times_real @ A @ B)) = (times_times_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7460_norm__mult)). 185.47/93.63 thf(13227,plain,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (times_times_real @ A @ B)) = (times_times_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652])). 185.47/93.63 thf(6056,axiom,((! [A:int,B:int]: ((abs_abs_int @ (minus_minus_int @ A @ B)) = (abs_abs_int @ (minus_minus_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6468_abs__minus__commute)). 185.47/93.63 thf(28057,plain,((! [A:int,B:int]: ((abs_abs_int @ (minus_minus_int @ A @ B)) = (abs_abs_int @ (minus_minus_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6056])). 185.47/93.63 thf(5101,axiom,((! [A:int]: ((abs_abs_int @ (abs_abs_int @ A)) = (abs_abs_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6314_abs__idempotent)). 185.47/93.63 thf(24491,plain,((! [A:int]: ((abs_abs_int @ (abs_abs_int @ A)) = (abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5101])). 185.47/93.63 thf(2289,axiom,((! [A:nat,B:int]: ((ord_less_int @ (bit_se2923211474154528505it_int @ A @ B) @ B) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9342_take__bit__int__less__self__iff)). 185.47/93.63 thf(15325,plain,((! [A:nat,B:int]: ((ord_less_int @ (bit_se2923211474154528505it_int @ A @ B) @ B) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2289])). 185.47/93.63 thf(5085,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3253_pinf_I7_J)). 185.47/93.63 thf(24445,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5085])). 185.47/93.63 thf(1523,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => (ord_less_int @ (abs_abs_int @ (modulo_modulo_int @ B @ A)) @ (abs_abs_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6822_abs__mod__less)). 185.47/93.63 thf(12789,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => (ord_less_int @ (abs_abs_int @ (modulo_modulo_int @ B @ A)) @ (abs_abs_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523])). 185.47/93.63 thf(3045,axiom,((! [A:nat]: (((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ (^ [B:nat]: (if_complex @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri8010041392384452111omplex @ (binomial @ A @ B)) @ zero_zero_complex)) @ (set_ord_atMost_nat @ A))) = (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8625_choose__odd__sum)). 185.47/93.63 thf(17815,plain,((! [A:nat]: (((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ (^ [B:nat]: (if_complex @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri8010041392384452111omplex @ (binomial @ A @ B)) @ zero_zero_complex)) @ (set_ord_atMost_nat @ A))) = (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3045])). 185.47/93.63 thf(362,axiom,((! [A:real,B:(nat > real)]: (((A != zero_zero_real) => (summable_real @ B)) <= (summable_real @ (^ [C:nat]: (times_times_real @ A @ (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7672_summable__mult__D)). 185.47/93.63 thf(8943,plain,((! [A:real,B:(nat > real)]: (((~ (A = zero_zero_real)) => (summable_real @ (B))) | ~ (summable_real @ (^ [C:nat]: (times_times_real @ A @ (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])). 185.47/93.63 thf(554,axiom,((! [A:real]: (((ord_less_eq_real @ A @ pi) => (ord_less_eq_real @ zero_zero_real @ (sin_real @ A))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7840_sin__ge__zero)). 185.47/93.63 thf(9572,plain,((! [A:real]: (((ord_less_eq_real @ A @ pi) => (ord_less_eq_real @ zero_zero_real @ (sin_real @ A))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[554])). 185.47/93.63 thf(3118,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ (divide_divide_int @ A @ B) @ zero_zero_int) <= (ord_less_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3055_div__nonpos__pos__le0)). 185.47/93.63 thf(18050,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (divide_divide_int @ A @ B) @ zero_zero_int) | ~ (ord_less_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3118])). 185.47/93.63 thf(7300,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ C @ (divide_divide_nat @ B @ A)) = (divide_divide_nat @ (times_times_nat @ C @ B) @ A)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4754_div__mult__swap)). 185.47/93.63 thf(32599,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ C @ (divide_divide_nat @ B @ A)) = (divide_divide_nat @ (times_times_nat @ C @ B) @ A)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7300])). 185.47/93.63 thf(5103,axiom,((! [A:nat,B:nat,C:(nat > num),D:num]: ((((ord_less_eq_num @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_num @ (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_3957_ord__le__eq__subst)). 185.47/93.63 thf(24497,plain,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_num @ (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)],[5103])). 185.47/93.63 thf(1843,axiom,((! [A:int]: ((ord_less_real @ (ring_1_of_int_real @ A) @ one_one_real) = (ord_less_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7089_of__int__less__1__iff)). 185.47/93.63 thf(13918,plain,((! [A:int]: ((ord_less_real @ (ring_1_of_int_real @ A) @ one_one_real) = (ord_less_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1843])). 185.47/93.63 thf(3014,axiom,((! [A:rat,B:rat]: (((B = A) <= (ord_less_eq_rat @ B @ A)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3890_dual__order_Oantisym)). 185.47/93.63 thf(17715,plain,((! [A:rat,B:rat]: ((B = A) | ~ (ord_less_eq_rat @ B @ A) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3014])). 185.47/93.63 thf(4022,axiom,((! [A:num,B:num,C:num]: ((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) != (modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ C)) @ (numeral_numeral_int @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6613_cong__exp__iff__simps_I10_J)). 185.47/93.63 thf(20909,plain,((! [A:num,B:num,C:num]: ~ ((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ C)) @ (numeral_numeral_int @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4022])). 185.47/93.63 thf(2955,axiom,((ord_less_eq_rat @ zero_zero_rat @ one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2276_zero__less__one__class_Ozero__le__one)). 185.47/93.63 thf(17524,plain,((ord_less_eq_rat @ zero_zero_rat @ one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2955])). 185.47/93.63 thf(17,axiom,((! [A:complex,B:nat]: ((A != one_one_complex) => ((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (power_power_complex @ A @ B) @ one_one_complex) @ (minus_minus_complex @ A @ one_one_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7600_geometric__sum)). 185.47/93.63 thf(7781,plain,((! [A:complex,B:nat]: ((~ (A = one_one_complex)) => ((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (power_power_complex @ A @ B) @ one_one_complex) @ (minus_minus_complex @ A @ one_one_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 185.47/93.63 thf(7610,axiom,((! [A:num,B:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ one)) = (modulo_modulo_nat @ (numeral_numeral_nat @ B) @ (numeral_numeral_nat @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2068_cong__exp__iff__simps_I4_J)). 185.47/93.63 thf(33601,plain,((! [A:num,B:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ one)) = (modulo_modulo_nat @ (numeral_numeral_nat @ B) @ (numeral_numeral_nat @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7610])). 185.47/93.63 thf(6181,axiom,((! [A:rat,B:nat]: ((ord_less_eq_rat @ one_one_rat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_rat @ A @ (power_power_rat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2895_self__le__power)). 185.47/93.63 thf(28531,plain,((! [A:rat,B:nat]: ((ord_less_eq_rat @ one_one_rat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_rat @ A @ (power_power_rat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6181])). 185.47/93.63 thf(357,axiom,((! [A:real]: ((gbinomial_real @ A @ zero_zero_nat) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8415_gbinomial__0_I1_J)). 185.47/93.63 thf(8928,plain,((! [A:real]: ((gbinomial_real @ A @ zero_zero_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])). 185.47/93.63 thf(3488,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_5514_le__imp__neg__le)). 185.47/93.63 thf(19213,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)],[3488])). 185.47/93.63 thf(5137,axiom,((! [A:nat,B:nat]: ? [C:nat]: ! [D:nat]: ((ord_less_nat @ D @ C) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B)) = (dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4711_minf_I9_J)). 185.47/93.63 thf(24666,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5137])). 185.47/93.63 thf(6241,axiom,((! [A:nat,B:real]: ((times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5301_left__minus__one__mult__self)). 185.47/93.63 thf(28734,plain,((! [A:nat,B:real]: ((times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6241])). 185.47/93.63 thf(2295,axiom,((ord_less_int = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4280_order__less__le)). 185.47/93.63 thf(15346,plain,(((ord_less_int) = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2295])). 185.47/93.63 thf(5026,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1494_mult__eq__0__iff)). 185.47/93.63 thf(24181,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5026])). 185.47/93.63 thf(692,axiom,((! [A:nat,B:nat,C:(nat > real)]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_real @ (groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_real @ (C @ A) @ (groups6591440286371151544t_real @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6677_sum_OSuc__reindex__ivl)). 185.47/93.63 thf(10039,plain,((! [A:nat,B:nat,C:(nat > real)]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_real @ (groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_real @ (C @ A) @ (groups6591440286371151544t_real @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[692])). 185.47/93.63 thf(7704,axiom,((! [A:complex]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_complex @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_power2__eq__square)). 185.47/93.63 thf(33854,plain,((! [A:complex]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_complex @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7704])). 185.47/93.63 thf(376,axiom,((! [A:num]: ~ (ord_le6747313008572928689nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5954_not__numeral__less__neg__one)). 185.47/93.63 thf(8988,plain,((! [A:num]: ~ (ord_le6747313008572928689nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[376])). 185.47/93.63 thf(1185,axiom,((minus_minus_int = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5788_diff__conv__add__uminus)). 185.47/93.63 thf(11724,plain,(((minus_minus_int) = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185])). 185.47/93.63 thf(5366,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = ((dvd_dvd_nat @ A @ one_one_nat) | (ord_less_eq_nat @ B @ C))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4913_dvd__power__iff)). 185.47/93.63 thf(25494,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = ((dvd_dvd_nat @ A @ one_one_nat) | (ord_less_eq_nat @ B @ C))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5366])). 185.47/93.63 thf(6439,axiom,((! [A:(nat > $o),B:nat]: (((~ (A @ zero_zero_nat)) => (? [C:nat]: ((ord_less_eq_nat @ C @ B) & (A @ C) & ! [D:nat]: ((~ (A @ D)) <= (ord_less_nat @ D @ C))))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2498_ex__least__nat__le)). 185.47/93.63 thf(29441,plain,((! [A:(nat > $o),B:nat]: (((~ (A @ zero_zero_nat)) => (? [C:nat]: ((ord_less_eq_nat @ C @ B) & (A @ C) & ! [D:nat]: (~ (A @ D) | ~ (ord_less_nat @ D @ C))))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6439])). 185.47/93.63 thf(2628,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ? [C:nat]: (B = (plus_plus_int @ A @ (semiri1314217659103216013at_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7253_zle__iff__zadd)). 185.47/93.63 thf(16449,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ? [C:nat]: (B = (plus_plus_int @ A @ (semiri1314217659103216013at_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2628])). 185.47/93.63 thf(1899,axiom,((! [A:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (uminus_uminus_rat @ A)) = (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5137_neg__0__le__iff__le)). 185.47/93.63 thf(14078,plain,((! [A:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (uminus_uminus_rat @ A)) = (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1899])). 185.47/93.63 thf(5907,axiom,((! [A:num]: ((plus_plus_complex @ (numera6690914467698888265omplex @ A) @ one_one_complex) = (numera6690914467698888265omplex @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_numeral__plus__one)). 185.47/93.64 thf(27561,plain,((! [A:num]: ((plus_plus_complex @ (numera6690914467698888265omplex @ A) @ one_one_complex) = (numera6690914467698888265omplex @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5907])). 185.47/93.64 thf(4319,axiom,((! [A:rat,B:(nat > rat),C:nat,D:nat]: ((((ord_less_eq_rat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_rat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))) <= (ord_less_eq_nat @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3946_ord__eq__le__subst)). 185.47/93.64 thf(21834,plain,((! [A:rat,B:(nat > rat),C:nat,D:nat]: ((ord_less_eq_rat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_less_eq_nat @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4319])). 185.47/93.64 thf(3801,axiom,((! [A:set_nat]: ((finite_finite_nat @ A) => ((A != bot_bot_set_nat) => (? [B:nat]: ((member_nat @ B @ A) & ! [C:nat]: ((member_nat @ C @ A) => ((B = C) <= (ord_less_eq_nat @ B @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3528_finite__has__maximal)). 185.47/93.64 thf(20213,plain,((! [A:set_nat]: ((finite_finite_nat @ A) => ((~ (A = bot_bot_set_nat)) => (? [B:nat]: ((member_nat @ B @ A) & ! [C:nat]: ((member_nat @ C @ A) => ((B = C) | ~ (ord_less_eq_nat @ B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3801])). 185.47/93.64 thf(2371,axiom,((! [A:real,B:real]: ((real_V1022390504157884413omplex @ (complex2 @ A @ B)) = (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8248_complex__norm)). 185.47/93.64 thf(15579,plain,((! [A:real,B:real]: ((real_V1022390504157884413omplex @ (complex2 @ A @ B)) = (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2371])). 185.47/93.64 thf(629,axiom,((! [A:set_nat,B:(nat > rat),C:rat,D:nat]: ((finite_finite_nat @ A) => ((! [E:nat]: ((ord_less_eq_rat @ zero_zero_rat @ (B @ E)) <= (member_nat @ E @ A))) => (((groups2906978787729119204at_rat @ B @ A) = C) => ((ord_less_eq_rat @ (B @ D) @ C) <= (member_nat @ D @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6017_sum__nonneg__leq__bound)). 185.47/93.64 thf(9818,plain,((! [A:set_nat,B:(nat > rat),C:rat,D:nat]: ((finite_finite_nat @ A) => ((! [E:nat]: ((ord_less_eq_rat @ zero_zero_rat @ (B @ E)) | ~ (member_nat @ E @ A))) => (((groups2906978787729119204at_rat @ (B) @ A) = C) => ((ord_less_eq_rat @ (B @ D) @ C) | ~ (member_nat @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[629])). 185.47/93.64 thf(5354,axiom,(((ord_less_nat @ za @ xa) & (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ za))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Az_A_092_060and_062_Az_A_060_Ax_092_060close_062)). 185.47/93.64 thf(25459,plain,(((ord_less_nat @ za @ xa) & (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ za))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5354])). 185.47/93.64 thf(2563,axiom,((! [A:int,B:int]: ((ord_less_int @ B @ A) <= (~ (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4192_not__le__imp__less)). 185.47/93.64 thf(16229,plain,((! [A:int,B:int]: ((ord_less_int @ B @ A) | (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2563])). 185.47/93.64 thf(6277,axiom,((! [A:int]: ((minus_minus_int @ zero_zero_int @ A) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5823_minus__int__code_I2_J)). 185.47/93.64 thf(28858,plain,((! [A:int]: ((minus_minus_int @ zero_zero_int @ A) = (uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6277])). 185.47/93.64 thf(1282,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = (uminus_uminus_real @ one_one_real)) = ((B != zero_zero_real) & (A = (uminus_uminus_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5985_divide__eq__minus__1__iff)). 185.47/93.64 thf(12013,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = (uminus_uminus_real @ one_one_real)) = (~ (B = zero_zero_real) & (A = (uminus_uminus_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282])). 185.47/93.64 thf(5870,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => ((minus_minus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ B) @ (times_times_complex @ C @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6169_minus__divide__diff__eq__iff)). 185.47/93.64 thf(27429,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => ((minus_minus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ B) @ (times_times_complex @ C @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5870])). 185.47/93.64 thf(1997,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2217_mult__nonneg__nonneg)). 185.47/93.64 thf(14409,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1997])). 185.47/93.64 thf(6831,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1796_diff__is__0__eq)). 185.47/93.64 thf(30841,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6831])). 185.47/93.64 thf(5425,axiom,((! [A:real,B:real,C:real,D:real]: ((power_power_real @ (sqrt @ (times_times_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (plus_plus_real @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (plus_plus_real @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8142_real__sqrt__sum__squares__mult__squared__eq)). 185.47/93.64 thf(25670,plain,((! [A:real,B:real,C:real,D:real]: ((power_power_real @ (sqrt @ (times_times_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (plus_plus_real @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (plus_plus_real @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5425])). 185.47/93.64 thf(3300,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1533_add__cancel__right__right)). 185.47/93.64 thf(18603,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3300])). 185.47/93.64 thf(4529,axiom,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_group__cancel_Oadd1)). 185.47/93.64 thf(22508,plain,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4529])). 185.47/93.64 thf(2259,axiom,((! [A:int,B:int,C:int,D:int]: (((A = B) & (ord_less_eq_int @ C @ D)) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_add__mono__thms__linordered__semiring_I2_J)). 185.47/93.64 thf(15239,plain,((! [A:int,B:int,C:int,D:int]: (((A = B) & (ord_less_eq_int @ C @ D)) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2259])). 185.47/93.64 thf(3364,axiom,((! [A:int,B:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))) = ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) != (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4520_odd__add)). 185.47/93.64 thf(18810,plain,((! [A:int,B:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))) = (~ ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3364])). 185.47/93.64 thf(2623,axiom,((! [A:nat,B:nat]: (dvd_dvd_real @ (times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B)) @ (semiri2265585572941072030t_real @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8021_fact__fact__dvd__fact)). 185.47/93.64 thf(16437,plain,((! [A:nat,B:nat]: (dvd_dvd_real @ (times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B)) @ (semiri2265585572941072030t_real @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2623])). 185.47/93.64 thf(4613,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ (abs_abs_real @ B)) @ zero_zero_real) = ((ord_less_eq_real @ A @ zero_zero_real) | (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6401_divide__le__0__abs__iff)). 185.47/93.64 thf(22770,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ (abs_abs_real @ B)) @ zero_zero_real) = ((ord_less_eq_real @ A @ zero_zero_real) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4613])). 185.47/93.64 thf(6604,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ B) @ B) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1751_mod__mult__self2__is__0)). 185.47/93.64 thf(30018,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ B) @ B) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6604])). 185.47/93.64 thf(3886,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_eq_nat @ C @ A) => (B @ C))) = (! [C:nat]: ((member_nat @ C @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3078_all__nat__less)). 185.47/93.64 thf(20477,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_eq_nat @ C @ A) => (B @ C))) = (! [C:nat]: ((member_nat @ C @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3886])). 185.47/93.64 thf(976,axiom,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_820_not__numeral__less__one)). 185.47/93.64 thf(11080,plain,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[976])). 185.47/93.64 thf(6237,axiom,((! [A:complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1541_cancel__comm__monoid__add__class_Odiff__cancel)). 185.47/93.64 thf(28718,plain,((! [A:complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6237])). 185.47/93.64 thf(3833,axiom,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ A) = (semiri5074537144036343181t_real @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6868_of__nat__eq__iff)). 185.47/93.64 thf(20305,plain,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ A) = (semiri5074537144036343181t_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3833])). 185.47/93.64 thf(5812,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_813_Nat_Odiff__add__assoc)). 185.47/93.64 thf(27138,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5812])). 185.47/93.64 thf(5042,axiom,((! [A:nat]: ((zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6203_of__bool__odd__eq__mod__2)). 185.47/93.64 thf(24305,plain,((! [A:nat]: ((zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5042])). 185.47/93.64 thf(5211,axiom,((! [A:complex]: ((zero_zero_complex = A) = (A = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1925_zero__reorient)). 185.47/93.64 thf(24907,plain,((! [A:complex]: ((zero_zero_complex = A) = (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5211])). 185.47/93.64 thf(1582,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ B)) = ((dvd_dvd_complex @ A @ C) | (B = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4458_dvd__mult__cancel__right)). 185.47/93.64 thf(12971,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ B)) = ((dvd_dvd_complex @ A @ C) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582])). 185.47/93.64 thf(5694,axiom,((! [A:int,B:nat]: ((power_power_int @ (uminus_uminus_int @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_int @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5427_Power_Oring__1__class_Opower__minus__even)). 185.47/93.64 thf(26679,plain,((! [A:int,B:nat]: ((power_power_int @ (uminus_uminus_int @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_int @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5694])). 185.47/93.64 thf(2996,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9058_log2__of__power__less)). 185.47/93.64 thf(17665,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2996])). 185.47/93.64 thf(1627,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (minus_minus_int @ (modulo_modulo_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ (minus_minus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2002_mod__diff__left__eq)). 185.47/93.64 thf(13152,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (minus_minus_int @ (modulo_modulo_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ (minus_minus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627])). 185.47/93.64 thf(3796,axiom,((! [A:int,B:num]: (((ring_1_of_int_real @ A) = (numeral_numeral_real @ B)) = (A = (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6941_of__int__eq__numeral__iff)). 185.47/93.64 thf(20198,plain,((! [A:int,B:num]: (((ring_1_of_int_real @ A) = (numeral_numeral_real @ B)) = (A = (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3796])). 185.47/93.64 thf(6514,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1002_add__Suc__right)). 185.47/93.64 thf(29717,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6514])). 185.47/93.64 thf(5888,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2397_pos__add__strict)). 185.47/93.64 thf(27492,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5888])). 185.47/93.64 thf(4379,axiom,((~ (ord_less_eq_rat @ one_one_rat @ (uminus_uminus_rat @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5716_le__minus__one__simps_I4_J)). 185.47/93.64 thf(22030,plain,((~ (ord_less_eq_rat @ one_one_rat @ (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4379])). 185.47/93.64 thf(2105,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (((plus_plus_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real)))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2283_add__nonneg__eq__0__iff)). 185.47/93.64 thf(14741,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (((plus_plus_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real)))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2105])). 185.47/93.64 thf(7008,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((power_power_rat @ zero_zero_rat @ A) = one_one_rat)) & ((A != zero_zero_nat) => ((power_power_rat @ zero_zero_rat @ A) = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1960_power__0__left)). 185.47/93.64 thf(31578,plain,((! [A:nat]: (((A = zero_zero_nat) => ((power_power_rat @ zero_zero_rat @ A) = one_one_rat)) & ((~ (A = zero_zero_nat)) => ((power_power_rat @ zero_zero_rat @ A) = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7008])). 185.47/93.64 thf(2552,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ B @ A) @ zero_zero_real) <= (ord_less_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2332_mult__pos__neg2)). 185.47/93.64 thf(16196,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ B @ A) @ zero_zero_real) | ~ (ord_less_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2552])). 185.47/93.64 thf(3953,axiom,((neg_nu5851722552734809277nc_int = (^ [A:int]: (plus_plus_int @ (plus_plus_int @ A @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7315_dbl__inc__def)). 185.47/93.64 thf(20694,plain,(((neg_nu5851722552734809277nc_int) = (^ [A:int]: (plus_plus_int @ (plus_plus_int @ A @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3953])). 185.47/93.64 thf(6692,axiom,((! [A:nat,B:nat,C:nat]: ((((modulo_modulo_nat @ B @ C) = (modulo_modulo_nat @ A @ C)) = (dvd_dvd_nat @ C @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4886_mod__eq__dvd__iff__nat)). 185.47/93.64 thf(30301,plain,((! [A:nat,B:nat,C:nat]: ((((modulo_modulo_nat @ B @ C) = (modulo_modulo_nat @ A @ C)) = (dvd_dvd_nat @ C @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6692])). 185.47/93.64 thf(3162,axiom,((! [A:real,B:real]: (((ord_less_real @ B @ A) <= (~ (ord_less_real @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1113_linorder__neqE__linordered__idom)). 185.47/93.64 thf(18184,plain,((! [A:real,B:real]: ((ord_less_real @ B @ A) | (ord_less_real @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3162])). 185.47/93.64 thf(6685,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1590_neq0__conv)). 185.47/93.64 thf(30283,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6685])). 185.47/93.64 thf(6654,axiom,((! [A:nat,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_real @ (uminus_uminus_real @ B) @ A) = (power_power_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5434_Parity_Oring__1__class_Opower__minus__even)). 185.47/93.64 thf(30181,plain,((! [A:nat,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_real @ (uminus_uminus_real @ B) @ A) = (power_power_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6654])). 185.47/93.64 thf(5204,axiom,((! [A:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ one))) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6659_numeral__Bit1__div__2)). 185.47/93.64 thf(24885,plain,((! [A:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ one))) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5204])). 185.47/93.64 thf(7305,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (power_power_nat @ A @ B)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2790_power__gt__expt)). 185.47/93.64 thf(32614,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (power_power_nat @ A @ B)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7305])). 185.47/93.64 thf(2063,axiom,((! [A:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2194_not__numeral__le__zero)). 185.47/93.64 thf(14617,plain,((! [A:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063])). 185.47/93.64 thf(4336,axiom,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (uminus_uminus_real @ (numeral_numeral_real @ C))) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ C))) <= (~ (ord_less_real @ B @ zero_zero_real))) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B) @ A)))) & ((ord_less_eq_real @ A @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B)) <= (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6260_divide__le__eq__numeral_I2_J)). 185.47/93.64 thf(21889,plain,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (uminus_uminus_real @ (numeral_numeral_real @ C))) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ C))) | (ord_less_real @ B @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B) @ A)))) & ((ord_less_eq_real @ A @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B)) | ~ (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4336])). 185.47/93.64 thf(5285,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((((times_times_nat @ (divide_divide_nat @ B @ A) @ (divide_divide_nat @ D @ C)) = (divide_divide_nat @ (times_times_nat @ B @ D) @ (times_times_nat @ A @ C))) <= (dvd_dvd_nat @ C @ D)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4766_div__mult__div__if__dvd)). 185.47/93.64 thf(25204,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((times_times_nat @ (divide_divide_nat @ B @ A) @ (divide_divide_nat @ D @ C)) = (divide_divide_nat @ (times_times_nat @ B @ D) @ (times_times_nat @ A @ C))) | ~ (dvd_dvd_nat @ C @ D) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5285])). 185.47/93.64 thf(6031,axiom,((! [A:product_prod_nat_nat]: ((size_s170228958280169651at_nat @ (some_P7363390416028606310at_nat @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2499_option_Osize_I4_J)). 185.47/93.64 thf(27986,plain,((! [A:product_prod_nat_nat]: ((size_s170228958280169651at_nat @ (some_P7363390416028606310at_nat @ A)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6031])). 185.47/93.64 thf(889,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => (((log @ A @ (powr_real @ A @ B)) = B) <= (A != one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9078_log__powr__cancel)). 185.47/93.64 thf(10775,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => (((log @ A @ (powr_real @ A @ B)) = B) | (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[889])). 185.47/93.64 thf(5376,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1535_zero__eq__add__iff__both__eq__0)). 185.47/93.64 thf(25527,plain,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5376])). 185.47/93.64 thf(6121,axiom,((! [A:nat]: ((A = (suc @ (minus_minus_nat @ A @ one_one_nat))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2910_Suc__pred_H)). 185.47/93.64 thf(28288,plain,((! [A:nat]: ((A = (suc @ (minus_minus_nat @ A @ one_one_nat))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6121])). 185.47/93.64 thf(140,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((? [C:real]: ((ord_less_real @ zero_zero_real @ C) & (ord_less_real @ C @ B) & ((sin_real @ B) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (sin_coeff @ D) @ (power_power_real @ B @ D))) @ (set_ord_lessThan_nat @ A)) @ (times_times_real @ (divide_divide_real @ (sin_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ A)) @ pi))) @ (semiri2265585572941072030t_real @ A)) @ (power_power_real @ B @ A)))))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8090_Maclaurin__sin__expansion3)). 185.47/93.64 thf(8182,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & (ord_less_real @ C @ B) & ((sin_real @ B) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (sin_coeff @ D) @ (power_power_real @ B @ D))) @ (set_ord_lessThan_nat @ A)) @ (times_times_real @ (divide_divide_real @ (sin_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ A)) @ pi))) @ (semiri2265585572941072030t_real @ A)) @ (power_power_real @ B @ A))))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 185.47/93.64 thf(113,axiom,((times_times_complex = (^ [A:complex,B:complex]: (complex2 @ (minus_minus_real @ (times_times_real @ (re @ A) @ (re @ B)) @ (times_times_real @ (im @ A) @ (im @ B))) @ (plus_plus_real @ (times_times_real @ (re @ A) @ (im @ B)) @ (times_times_real @ (im @ A) @ (re @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9689_times__complex_Ocode)). 185.47/93.64 thf(8101,plain,(((times_times_complex) = (^ [A:complex,B:complex]: (complex2 @ (minus_minus_real @ (times_times_real @ (re @ A) @ (re @ B)) @ (times_times_real @ (im @ A) @ (im @ B))) @ (plus_plus_real @ (times_times_real @ (re @ A) @ (im @ B)) @ (times_times_real @ (im @ A) @ (re @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 185.47/93.64 thf(4895,axiom,((! [A:set_nat,B:nat]: ((finite_finite_nat @ A) => ((~ (member_nat @ B @ A)) => ((nat_set_encode @ (insert_nat @ B @ A)) = (plus_plus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (nat_set_encode @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9419_set__encode__insert)). 185.47/93.64 thf(23745,plain,((! [A:set_nat,B:nat]: ((finite_finite_nat @ A) => ((~ (member_nat @ B @ A)) => ((nat_set_encode @ (insert_nat @ B @ A)) = (plus_plus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (nat_set_encode @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4895])). 185.47/93.64 thf(1100,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4039_order_Ostrict__implies__not__eq)). 185.47/93.64 thf(11468,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100])). 185.47/93.64 thf(3779,axiom,((! [A:rat]: ((ord_less_rat @ (divide_divide_rat @ one_one_rat @ A) @ zero_zero_rat) = (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1809_divide__less__0__1__iff)). 185.47/93.64 thf(20145,plain,((! [A:rat]: ((ord_less_rat @ (divide_divide_rat @ one_one_rat @ A) @ zero_zero_rat) = (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3779])). 185.47/93.64 thf(4500,axiom,((! [A:real,B:real]: (((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2404_add__neg__neg)). 185.47/93.64 thf(22402,plain,((! [A:real,B:real]: (((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4500])). 185.47/93.64 thf(5484,axiom,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ C @ B)) = ((B = zero_zero_int) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1505_mult__cancel__right)). 185.47/93.64 thf(25997,plain,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ C @ B)) = ((B = zero_zero_int) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5484])). 185.47/93.64 thf(940,axiom,((! [A:num,B:int]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_eq_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7070_of__int__numeral__le__iff)). 185.47/93.64 thf(10959,plain,((! [A:num,B:int]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_eq_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[940])). 185.47/93.64 thf(5687,axiom,((! [A:complex]: ((times_times_complex @ A @ (numera6690914467698888265omplex @ (bit0 @ one))) = (plus_plus_complex @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_mult__2__right)). 185.47/93.64 thf(26657,plain,((! [A:complex]: ((times_times_complex @ A @ (numera6690914467698888265omplex @ (bit0 @ one))) = (plus_plus_complex @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5687])). 185.47/93.64 thf(1257,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ one_one_rat) = (((ord_less_rat @ A @ B) & (ord_less_rat @ zero_zero_rat @ B)) | ((ord_less_rat @ B @ zero_zero_rat) & (ord_less_rat @ B @ A)) | (B = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2716_divide__less__eq__1)). 185.47/93.64 thf(11945,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ one_one_rat) = (((ord_less_rat @ A @ B) & (ord_less_rat @ zero_zero_rat @ B)) | ((ord_less_rat @ B @ zero_zero_rat) & (ord_less_rat @ B @ A)) | (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257])). 185.47/93.64 thf(7632,axiom,((! [A:$o]: ((divide_divide_nat @ (zero_n2687167440665602831ol_nat @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5431_of__bool__half__eq__0)). 185.47/93.64 thf(33663,plain,((! [A:$o]: ((divide_divide_nat @ (zero_n2687167440665602831ol_nat @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7632])). 185.47/93.64 thf(4580,axiom,((! [A:int,B:int]: (A = (plus_plus_int @ (times_times_int @ (divide_divide_int @ A @ B) @ B) @ (modulo_modulo_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3066_div__mod__decomp__int)). 185.47/93.64 thf(22671,plain,((! [A:int,B:int]: (A = (plus_plus_int @ (times_times_int @ (divide_divide_int @ A @ B) @ B) @ (modulo_modulo_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4580])). 185.47/93.64 thf(1573,axiom,((! [A:int]: (ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ (abs_abs_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6642_abs__add__one__gt__zero)). 185.47/93.64 thf(12939,plain,((! [A:int]: (ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ (abs_abs_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573])). 185.47/93.64 thf(1952,axiom,((! [A:int]: ((zero_zero_int = (plus_plus_int @ A @ A)) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1513_double__zero__sym)). 185.47/93.64 thf(14264,plain,((! [A:int]: ((zero_zero_int = (plus_plus_int @ A @ A)) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1952])). 185.47/93.64 thf(7325,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (binomial @ B @ A) @ (power_power_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8433_binomial__le__pow)). 185.47/93.64 thf(32683,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (binomial @ B @ A) @ (power_power_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7325])). 185.47/93.64 thf(986,axiom,((! [A:nat,B:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7226_less__imp__of__nat__less)). 185.47/93.64 thf(11112,plain,((! [A:nat,B:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[986])). 185.47/93.64 thf(514,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat)]: (((ord_less_eq_set_nat @ A @ B) => ((groups3542108847815614940at_nat @ C @ (minus_minus_set_nat @ B @ A)) = (minus_minus_nat @ (groups3542108847815614940at_nat @ C @ B) @ (groups3542108847815614940at_nat @ C @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6645_sum__diff__nat)). 185.47/93.64 thf(9460,plain,((! [A:set_nat,B:set_nat,C:(nat > nat)]: (((ord_less_eq_set_nat @ A @ B) => ((groups3542108847815614940at_nat @ (C) @ (minus_minus_set_nat @ B @ A)) = (minus_minus_nat @ (groups3542108847815614940at_nat @ (C) @ B) @ (groups3542108847815614940at_nat @ (C) @ A)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[514])). 185.47/93.64 thf(792,axiom,((! [A:rat,B:nat,C:set_nat]: ((groups2906978787729119204at_rat @ (^ [D:nat]: (power_power_rat @ A @ (plus_plus_nat @ B @ D))) @ C) = (times_times_rat @ (power_power_rat @ A @ B) @ (groups2906978787729119204at_rat @ (power_power_rat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6622_sum__power__add)). 185.47/93.64 thf(10433,plain,((! [A:rat,B:nat,C:set_nat]: ((groups2906978787729119204at_rat @ (^ [D:nat]: (power_power_rat @ A @ (plus_plus_nat @ B @ D))) @ C) = (times_times_rat @ (power_power_rat @ A @ B) @ (groups2906978787729119204at_rat @ (power_power_rat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[792])). 185.47/93.64 thf(538,axiom,((! [A:real]: ((ord_less_eq_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6140_ln__add__one__self__le__self)). 185.47/93.64 thf(9526,plain,((! [A:real]: ((ord_less_eq_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[538])). 185.47/93.64 thf(7268,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ C) => ((divide_divide_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ (divide_divide_nat @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4497_div__add)). 185.47/93.64 thf(32490,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ C) => ((divide_divide_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ (divide_divide_nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7268])). 185.47/93.64 thf(2841,axiom,((! [A:rat,B:rat]: (ord_less_eq_rat @ (times_times_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ B) @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_sum__squares__bound)). 185.47/93.64 thf(17164,plain,((! [A:rat,B:rat]: (ord_less_eq_rat @ (times_times_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ B) @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2841])). 185.47/93.64 thf(5442,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1155_left__diff__distrib_H)). 185.47/93.64 thf(25766,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5442])). 185.47/93.64 thf(5524,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = (~ (ord_less_eq_num @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4163_nless__le)). 185.47/93.64 thf(26124,plain,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = (~ (ord_less_eq_num @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5524])). 185.47/93.64 thf(5967,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (A = B))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1896_power2__eq__iff__nonneg)). 185.47/93.64 thf(27789,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (A = B))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5967])). 185.47/93.64 thf(5196,axiom,((! [A:num]: ((divide_divide_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)) = (product_fst_nat_nat @ (unique5055182867167087721od_nat @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9760_Suc__0__div__numeral)). 185.47/93.64 thf(24861,plain,((! [A:num]: ((divide_divide_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)) = (product_fst_nat_nat @ (unique5055182867167087721od_nat @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5196])). 185.47/93.64 thf(5947,axiom,((! [A:int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_int) = ((A = (uminus_uminus_int @ one_one_int)) | (A = one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6223_power2__eq__1__iff)). 185.47/93.64 thf(27683,plain,((! [A:int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_int) = ((A = (uminus_uminus_int @ one_one_int)) | (A = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5947])). 185.47/93.64 thf(973,axiom,((! [A:int,B:nat]: ((dvd_dvd_nat @ (nat2 @ A) @ B) = (((ord_less_eq_int @ zero_zero_int @ A) => (dvd_dvd_int @ A @ (semiri1314217659103216013at_int @ B))) & ((B = zero_zero_nat) <= (~ (ord_less_eq_int @ zero_zero_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9344_nat__dvd__iff)). 185.47/93.64 thf(11072,plain,((! [A:int,B:nat]: ((dvd_dvd_nat @ (nat2 @ A) @ B) = (((ord_less_eq_int @ zero_zero_int @ A) => (dvd_dvd_int @ A @ (semiri1314217659103216013at_int @ B))) & ((B = zero_zero_nat) | (ord_less_eq_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[973])). 185.47/93.64 thf(1545,axiom,((! [A:num,B:num]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_numeral__le__iff)). 185.47/93.64 thf(12852,plain,((! [A:num,B:num]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1545])). 185.47/93.64 thf(420,axiom,((! [A:complex,B:complex]: ((im @ (times_times_complex @ A @ B)) = (plus_plus_real @ (times_times_real @ (re @ A) @ (im @ B)) @ (times_times_real @ (im @ A) @ (re @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9676_times__complex_Osimps_I2_J)). 185.47/93.64 thf(9127,plain,((! [A:complex,B:complex]: ((im @ (times_times_complex @ A @ B)) = (plus_plus_real @ (times_times_real @ (re @ A) @ (im @ B)) @ (times_times_real @ (im @ A) @ (re @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[420])). 185.47/93.64 thf(5234,axiom,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_num @ C @ A) => (ord_less_num @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4242_dual__order_Ostrict__trans1)). 185.47/93.64 thf(24990,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_num @ C @ A) => (ord_less_num @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5234])). 185.47/93.64 thf(3700,axiom,((! [A:(rat > $o),B:rat]: ((? [C:rat]: (A @ (times_times_rat @ B @ C))) = (? [C:rat]: ((A @ C) & (dvd_dvd_rat @ B @ (plus_plus_rat @ C @ zero_zero_rat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4826_unity__coeff__ex)). 185.47/93.64 thf(19873,plain,((! [A:(rat > $o),B:rat]: ((? [C:rat]: (A @ (times_times_rat @ B @ C))) = (? [C:rat]: ((A @ C) & (dvd_dvd_rat @ B @ (plus_plus_rat @ C @ zero_zero_rat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3700])). 185.47/93.64 thf(3353,axiom,((! [A:rat,B:nat,C:nat]: ((ord_less_rat @ one_one_rat @ A) => ((ord_less_eq_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) => (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_898_power__le__imp__le__exp)). 185.47/93.64 thf(18781,plain,((! [A:rat,B:nat,C:nat]: ((ord_less_rat @ one_one_rat @ A) => ((ord_less_eq_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) => (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3353])). 185.47/93.64 thf(6321,axiom,((! [A:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5199_mult__minus1)). 185.47/93.64 thf(29004,plain,((! [A:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6321])). 185.47/93.64 thf(672,axiom,((! [A:(nat > complex),B:set_nat]: (((groups6464643781859351333omplex @ A @ B) != one_one_complex) => (~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = one_one_complex))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8712_prod_Onot__neutral__contains__not__neutral)). 185.47/93.64 thf(9978,plain,((! [A:(nat > complex),B:set_nat]: ((~ ((groups6464643781859351333omplex @ (A) @ B) = one_one_complex)) => (~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = one_one_complex))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[672])). 185.47/93.64 thf(3062,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4372_bot_Oextremum)). 185.47/93.64 thf(17871,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3062])). 185.47/93.64 thf(5720,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ A @ (suc @ (suc @ (suc @ B)))) = (divide_divide_nat @ A @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6440_div__Suc__eq__div__add3)). 185.47/93.64 thf(26770,plain,((! [A:nat,B:nat]: ((divide_divide_nat @ A @ (suc @ (suc @ (suc @ B)))) = (divide_divide_nat @ A @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5720])). 185.47/93.64 thf(5335,axiom,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = B) = ((uminus1482373934393186551omplex @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5493_minus__equation__iff)). 185.47/93.64 thf(25363,plain,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = B) = ((uminus1482373934393186551omplex @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5335])). 185.47/93.64 thf(6427,axiom,(((uminus1482373934393186551omplex @ zero_zero_complex) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5057_add_Oinverse__neutral)). 185.47/93.64 thf(29403,plain,(((uminus1482373934393186551omplex @ zero_zero_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6427])). 185.47/93.64 thf(4968,axiom,((! [A:nat,B:rat]: ((times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5304_left__minus__one__mult__self)). 185.47/93.64 thf(23992,plain,((! [A:nat,B:rat]: ((times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4968])). 185.47/93.64 thf(2616,axiom,((one_one_complex = (complex2 @ one_one_real @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8028_one__complex_Ocode)). 185.47/93.64 thf(16413,plain,((one_one_complex = (complex2 @ one_one_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2616])). 185.47/93.64 thf(452,axiom,((! [A:num,B:num]: (((~ (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B)))) => ((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ A)))) & ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) => ((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5311_max__number__of_I4_J)). 185.47/93.64 thf(9233,plain,((! [A:num,B:num]: (((~ (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B)))) => ((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ A)))) & ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) => ((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[452])). 185.47/93.64 thf(5302,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (times_times_complex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5076_minus__mult__minus)). 185.47/93.64 thf(25253,plain,((! [A:complex,B:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (times_times_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5302])). 185.47/93.64 thf(4734,axiom,((! [A:real,B:real]: (((complex2 @ A @ B) = one_one_complex) = ((B = zero_zero_real) & (A = one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8029_Complex__eq__1)). 185.47/93.64 thf(23179,plain,((! [A:real,B:real]: (((complex2 @ A @ B) = one_one_complex) = ((B = zero_zero_real) & (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4734])). 185.47/93.64 thf(130,axiom,((! [A:rat,B:rat,C:nat]: ((A != zero_zero_rat) => ((minus_minus_rat @ (divide_divide_rat @ (minus_minus_rat @ (power_power_rat @ (plus_plus_rat @ B @ A) @ C) @ (power_power_rat @ B @ C)) @ A) @ (times_times_rat @ (semiri681578069525770553at_rat @ C) @ (power_power_rat @ B @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))) = (times_times_rat @ A @ (groups2906978787729119204at_rat @ (^ [D:nat]: (groups2906978787729119204at_rat @ (^ [E:nat]: (times_times_rat @ (power_power_rat @ (plus_plus_rat @ B @ A) @ E) @ (power_power_rat @ B @ (minus_minus_nat @ (minus_minus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ E)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat)) @ D)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7533_lemma__termdiff2)). 185.47/93.64 thf(8150,plain,((! [A:rat,B:rat,C:nat]: ((~ (A = zero_zero_rat)) => ((minus_minus_rat @ (divide_divide_rat @ (minus_minus_rat @ (power_power_rat @ (plus_plus_rat @ B @ A) @ C) @ (power_power_rat @ B @ C)) @ A) @ (times_times_rat @ (semiri681578069525770553at_rat @ C) @ (power_power_rat @ B @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))) = (times_times_rat @ A @ (groups2906978787729119204at_rat @ (^ [D:nat]: (groups2906978787729119204at_rat @ (^ [E:nat]: (times_times_rat @ (power_power_rat @ (plus_plus_rat @ B @ A) @ E) @ (power_power_rat @ B @ (minus_minus_nat @ (minus_minus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ E)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat)) @ D)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 185.47/93.64 thf(2647,axiom,((! [A:int]: ((minus_minus_int @ (times_times_int @ A @ A) @ one_one_int) = (times_times_int @ (plus_plus_int @ A @ one_one_int) @ (minus_minus_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1243_square__diff__one__factored)). 185.47/93.64 thf(16513,plain,((! [A:int]: ((minus_minus_int @ (times_times_int @ A @ A) @ one_one_int) = (times_times_int @ (plus_plus_int @ A @ one_one_int) @ (minus_minus_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2647])). 185.47/93.64 thf(3770,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (abs_abs_rat @ A) @ B) = ((ord_less_rat @ A @ B) & (ord_less_rat @ (uminus_uminus_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6526_abs__less__iff)). 185.47/93.64 thf(20117,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (abs_abs_rat @ A) @ B) = ((ord_less_rat @ A @ B) & (ord_less_rat @ (uminus_uminus_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3770])). 185.47/93.64 thf(3261,axiom,((ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5913_le__minus__one__simps_I1_J)). 185.47/93.64 thf(18482,plain,((ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3261])). 185.47/93.64 thf(1877,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => ((((modulo_modulo_int @ A @ B) = D) <= (ord_less_int @ B @ D)) <= (ord_less_eq_int @ D @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3172_int__mod__neg__eq)). 185.47/93.64 thf(14014,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => (((modulo_modulo_int @ A @ B) = D) | ~ (ord_less_int @ B @ D) | ~ (ord_less_eq_int @ D @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877])). 185.47/93.64 thf(7284,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (modulo_modulo_nat @ A @ B)) @ B) = (modulo_modulo_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2015_mod__Suc__eq)). 185.47/93.64 thf(32539,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (modulo_modulo_nat @ A @ B)) @ B) = (modulo_modulo_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7284])). 185.47/93.64 thf(5777,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (sqrt @ B)) <= (ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8215_real__le__rsqrt)). 185.47/93.64 thf(26950,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (sqrt @ B)) | ~ (ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5777])). 185.47/93.64 thf(3171,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) & (ord_less_real @ A @ B)) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_add__mono__thms__linordered__field_I3_J)). 185.47/93.64 thf(18210,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) & (ord_less_real @ A @ B)) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3171])). 185.47/93.64 thf(1757,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ A @ (uminus1482373934393186551omplex @ B)) = (plus_plus_complex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5204_diff__minus__eq__add)). 185.47/93.64 thf(13623,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ A @ (uminus1482373934393186551omplex @ B)) = (plus_plus_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757])). 185.47/93.64 thf(4878,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ B @ (bit_se1409905431419307370or_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9422_or__greater__eq)). 185.47/93.64 thf(23665,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ B @ (bit_se1409905431419307370or_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4878])). 185.47/93.64 thf(7106,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2796_nat__mult__div__cancel1)). 185.47/93.64 thf(31917,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7106])). 185.47/93.64 thf(5844,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((product_Pair_nat_nat @ A @ B) = (product_Pair_nat_nat @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3386_prod_Oinject)). 185.47/93.64 thf(27346,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((product_Pair_nat_nat @ A @ B) = (product_Pair_nat_nat @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5844])). 185.47/93.64 thf(4633,axiom,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (times_times_real @ A @ B)) @ (times_times_real @ C @ D)) @ (plus_plus_real @ (times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_real @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_L2__set__mult__ineq__lemma)). 185.47/93.64 thf(22843,plain,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (times_times_real @ A @ B)) @ (times_times_real @ C @ D)) @ (plus_plus_real @ (times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_real @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4633])). 185.47/93.64 thf(3650,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C) => (dvd_dvd_Code_integer @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4580_dvd__mult__right)). 185.47/93.64 thf(19722,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C) => (dvd_dvd_Code_integer @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3650])). 185.47/93.64 thf(1914,axiom,((! [A:nat,B:int]: ((ord_less_int @ (bit_se545348938243370406it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9498_push__bit__negative__int__iff)). 185.47/93.64 thf(14124,plain,((! [A:nat,B:int]: ((ord_less_int @ (bit_se545348938243370406it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1914])). 185.47/93.64 thf(3319,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ (divide_divide_real @ A @ B)) = (((ord_less_real @ A @ B) & (ord_less_real @ B @ zero_zero_real)) | ((ord_less_real @ B @ A) & (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2717_less__divide__eq__1)). 185.47/93.64 thf(18667,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ (divide_divide_real @ A @ B)) = (((ord_less_real @ A @ B) & (ord_less_real @ B @ zero_zero_real)) | ((ord_less_real @ B @ A) & (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3319])). 185.47/93.64 thf(6836,axiom,((! [A:real,B:real,C:real]: (((times_times_real @ A @ B) = (times_times_real @ A @ C)) = ((A = zero_zero_real) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1497_mult__cancel__left)). 185.47/93.64 thf(30856,plain,((! [A:real,B:real,C:real]: (((times_times_real @ A @ B) = (times_times_real @ A @ C)) = ((A = zero_zero_real) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6836])). 185.47/93.64 thf(4196,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6581_abs__triangle__ineq4)). 185.47/93.64 thf(21435,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4196])). 185.47/93.64 thf(888,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (minus_minus_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)) @ (divide_divide_real @ (minus_minus_real @ A @ B) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6202_ln__diff__le)). 185.47/93.64 thf(10772,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (minus_minus_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)) @ (divide_divide_real @ (minus_minus_real @ A @ B) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[888])). 185.47/93.64 thf(4592,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_eq_real @ C @ A) <= (ord_less_real @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3313_minf_I6_J)). 185.47/93.64 thf(22706,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_eq_real @ C @ A) | ~ (ord_less_real @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4592])). 185.47/93.64 thf(4439,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) = (ord_less_eq_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4287_linorder__not__less)). 185.47/93.64 thf(22214,plain,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) = (ord_less_eq_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4439])). 185.47/93.64 thf(2268,axiom,((! [A:real,B:real]: ((minus_minus_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ A) = (divide_divide_real @ (minus_minus_real @ B @ A) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_real__average__minus__first)). 185.47/93.64 thf(15263,plain,((! [A:real,B:real]: ((minus_minus_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ A) = (divide_divide_real @ (minus_minus_real @ B @ A) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2268])). 185.47/93.64 thf(5513,axiom,((! [A:nat,B:num,C:nat]: (((semiri5074537144036343181t_real @ A) = (power_power_real @ (numeral_numeral_real @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7057_real__of__nat__eq__numeral__power__cancel__iff)). 185.47/93.64 thf(26089,plain,((! [A:nat,B:num,C:nat]: (((semiri5074537144036343181t_real @ A) = (power_power_real @ (numeral_numeral_real @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5513])). 185.47/93.64 thf(5082,axiom,((! [A:num]: ~ (ord_less_num @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4014_dual__order_Oirrefl)). 185.47/93.64 thf(24437,plain,((! [A:num]: ~ (ord_less_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5082])). 185.47/93.64 thf(708,axiom,((ord_less_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7739_pi__less__4)). 185.47/93.64 thf(10093,plain,((ord_less_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[708])). 185.47/93.64 thf(2030,axiom,((! [A:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4502_signed__take__bit__numeral__of__1)). 185.47/93.64 thf(14519,plain,((! [A:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2030])). 185.47/93.64 thf(6242,axiom,((! [A:num]: ((numeral_numeral_real @ A) != (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5772_numeral__neq__neg__one)). 185.47/93.64 thf(28737,plain,((! [A:num]: ~ ((numeral_numeral_real @ A) = (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6242])). 185.47/93.64 thf(919,axiom,((! [A:set_nat,B:(nat > int)]: ((! [C:nat]: ((ord_less_int @ zero_zero_int @ (B @ C)) <= (member_nat @ C @ A))) => (ord_less_int @ zero_zero_int @ (groups705719431365010083at_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8758_prod__pos)). 185.47/93.64 thf(10881,plain,((! [A:set_nat,B:(nat > int)]: ((! [C:nat]: ((ord_less_int @ zero_zero_int @ (B @ C)) | ~ (member_nat @ C @ A))) => (ord_less_int @ zero_zero_int @ (groups705719431365010083at_int @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[919])). 185.47/93.64 thf(6995,axiom,((! [A:nat,B:nat]: (ord_less_nat @ (minus_minus_nat @ A @ B) @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_diff__less__Suc)). 185.47/93.64 thf(31536,plain,((! [A:nat,B:nat]: (ord_less_nat @ (minus_minus_nat @ A @ B) @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6995])). 185.47/93.64 thf(2235,axiom,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: ((? [E:real]: ! [F:real]: ((ord_less_real @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) <= (ord_less_real @ E @ F))) => (? [E:real]: ! [F:real]: ((ord_less_real @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3230_pinf_I2_J)). 185.47/93.64 thf(15158,plain,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: ((? [E:real]: ! [F:real]: ((ord_less_real @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) | ~ (ord_less_real @ E @ F))) => (? [E:real]: ! [F:real]: ((ord_less_real @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2235])). 185.47/93.64 thf(6432,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ (modulo_modulo_nat @ A @ B) @ B) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1766_mod__div__trivial)). 185.47/93.64 thf(29420,plain,((! [A:nat,B:nat]: ((divide_divide_nat @ (modulo_modulo_nat @ A @ B) @ B) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6432])). 185.47/93.64 thf(4396,axiom,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5900_neg__numeral__less__zero)). 185.47/93.64 thf(22083,plain,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4396])). 185.47/93.64 thf(5653,axiom,((! [A:(product_prod_nat_nat > nat),B:product_prod_nat_nat]: ((size_o8335143837870341156at_nat @ A @ (some_P7363390416028606310at_nat @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4420_option_Osize__gen_I2_J)). 185.47/93.64 thf(26542,plain,((! [A:(product_prod_nat_nat > nat),B:product_prod_nat_nat]: ((size_o8335143837870341156at_nat @ (A) @ (some_P7363390416028606310at_nat @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5653])). 185.47/93.64 thf(6663,axiom,((! [A:num,B:num]: ((bit1 @ A) != (bit0 @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6328_semiring__norm_I89_J)). 185.47/93.64 thf(30209,plain,((! [A:num,B:num]: ~ ((bit1 @ A) = (bit0 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6663])). 185.47/93.64 thf(397,axiom,((! [A:(real > $o),B:real]: (((! [C:nat]: (A @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ (suc @ C))))) => ((A @ B) <= (ord_less_real @ zero_zero_real @ B))) <= (! [C:real,D:real]: ((ord_less_real @ C @ D) => ((A @ D) <= (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8969_forall__pos__mono__1)). 185.47/93.64 thf(9052,plain,((! [A:(real > $o),B:real]: (((! [C:nat]: (A @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ (suc @ C))))) => ((A @ B) | ~ (ord_less_real @ zero_zero_real @ B))) | ~ (! [C:real,D:real]: ((ord_less_real @ C @ D) => ((A @ D) | ~ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[397])). 185.47/93.64 thf(1750,axiom,((! [A:$o,B:$o]: ~ (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1470_Leaf__0__not)). 185.47/93.64 thf(13596,plain,((! [A:$o,B:$o]: ~ (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750])). 185.47/93.64 thf(1318,axiom,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ A @ (times_times_complex @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_divide__divide__eq__left_H)). 185.47/93.64 thf(12126,plain,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ A @ (times_times_complex @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318])). 185.47/93.64 thf(2975,axiom,((! [A:nat]: ~ (ord_less_real @ (semiri5074537144036343181t_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7212_of__nat__less__0__iff)). 185.47/93.64 thf(17594,plain,((! [A:nat]: ~ (ord_less_real @ (semiri5074537144036343181t_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2975])). 185.47/93.64 thf(7398,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = A) = ((A = zero_zero_int) | (B = one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1668_mult__cancel__left2)). 185.47/93.64 thf(32913,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = A) = ((A = zero_zero_int) | (B = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7398])). 185.47/93.64 thf(43,axiom,((set_ord_lessThan_nat = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7562_lessThan__def)). 185.47/93.64 thf(7873,plain,(((set_ord_lessThan_nat) = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 185.47/93.64 thf(5308,axiom,((! [A:int]: ((minus_minus_int @ zero_zero_int @ A) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5178_diff__0)). 185.47/93.64 thf(25268,plain,((! [A:int]: ((minus_minus_int @ zero_zero_int @ A) = (uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5308])). 185.47/93.64 thf(957,axiom,((! [A:real]: ? [B:real]: ((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((tan_real @ B) = A) & ! [C:real]: ((C = B) <= ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ C) & ((tan_real @ C) = A) & (ord_less_real @ C @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) & (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8056_tan__total)). 185.47/93.64 thf(11014,plain,((! [A:real]: ? [B:real]: ((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((tan_real @ B) = A) & ! [C:real]: ((C = B) | ~ ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ C) & ((tan_real @ C) = A) & (ord_less_real @ C @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) & (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[957])). 185.47/93.64 thf(2389,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ B @ A)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1941_unique__euclidean__semiring__numeral__class_Opos__mod__sign)). 185.47/93.64 thf(15632,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ B @ A)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2389])). 185.47/93.64 thf(29,axiom,((! [A:nat,B:(nat > rat),C:rat,D:nat]: (((ord_less_eq_rat @ (groups2906978787729119204at_rat @ B @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_rat @ (semiri681578069525770553at_rat @ A) @ C)) <= (ord_less_eq_rat @ zero_zero_rat @ C)) <= (! [E:nat]: ((ord_less_nat @ E @ A) => (ord_less_eq_rat @ (B @ E) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7620_real__sum__nat__ivl__bounded2)). 185.47/93.64 thf(7824,plain,((! [A:nat,B:(nat > rat),C:rat,D:nat]: ((ord_less_eq_rat @ (groups2906978787729119204at_rat @ (B) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_rat @ (semiri681578069525770553at_rat @ A) @ C)) | ~ (ord_less_eq_rat @ zero_zero_rat @ C) | ~ (! [E:nat]: ((ord_less_nat @ E @ A) => (ord_less_eq_rat @ (B @ E) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 185.47/93.64 thf(341,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ A) => ((! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))) => ((ord_less_real @ zero_zero_real @ (suminf_real @ A)) <= (ord_less_real @ zero_zero_real @ (A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7713_suminf__pos2)). 185.47/93.64 thf(8879,plain,((! [A:(nat > real),B:nat]: ((summable_real @ (A)) => ((! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))) => ((ord_less_real @ zero_zero_real @ (suminf_real @ (A))) | ~ (ord_less_real @ zero_zero_real @ (A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 185.47/93.64 thf(3369,axiom,((! [A:nat,B:int]: ((bit_se2923211474154528505it_int @ (suc @ A) @ B) = (plus_plus_int @ (times_times_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (zero_n2684676970156552555ol_int @ (bit_se1146084159140164899it_int @ B @ A))) @ (bit_se2923211474154528505it_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9443_take__bit__Suc__from__most)). 185.47/93.64 thf(18824,plain,((! [A:nat,B:int]: ((bit_se2923211474154528505it_int @ (suc @ A) @ B) = (plus_plus_int @ (times_times_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (zero_n2684676970156552555ol_int @ (bit_se1146084159140164899it_int @ B @ A))) @ (bit_se2923211474154528505it_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3369])). 185.47/93.64 thf(2377,axiom,((! [A:nat,B:int]: (((semiri1314217659103216013at_int @ A) = B) = ((ord_less_eq_int @ zero_zero_int @ B) & (A = (nat2 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9294_int__eq__iff)). 185.47/93.64 thf(15600,plain,((! [A:nat,B:int]: (((semiri1314217659103216013at_int @ A) = B) = ((ord_less_eq_int @ zero_zero_int @ B) & (A = (nat2 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2377])). 185.47/93.64 thf(5347,axiom,((! [A:(nat > real),B:real]: ((sums_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ zero_zero_real @ C))) @ B) = ((A @ zero_zero_nat) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8138_powser__sums__zero__iff)). 185.47/93.64 thf(25395,plain,((! [A:(nat > real),B:real]: ((sums_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ zero_zero_real @ C))) @ B) = ((A @ zero_zero_nat) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5347])). 185.47/93.64 thf(5454,axiom,((! [A:int,B:nat]: ((ord_less_int @ (power_power_int @ A @ B) @ zero_zero_int) = ((ord_less_int @ A @ zero_zero_int) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4536_power__less__zero__eq)). 185.47/93.64 thf(25805,plain,((! [A:int,B:nat]: ((ord_less_int @ (power_power_int @ A @ B) @ zero_zero_int) = ((ord_less_int @ A @ zero_zero_int) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5454])). 185.47/93.64 thf(7114,axiom,((! [A:num]: (ord_less_eq_num @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3815_dual__order_Orefl)). 185.47/93.64 thf(31945,plain,((! [A:num]: (ord_less_eq_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7114])). 185.47/93.64 thf(99,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ A) => ((! [C:nat]: ((ord_less_real @ zero_zero_real @ (A @ C)) <= (ord_less_eq_nat @ B @ C))) => (ord_less_real @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B)) @ (suminf_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7738_sum__less__suminf)). 185.47/93.64 thf(8057,plain,((! [A:(nat > real),B:nat]: ((summable_real @ (A)) => ((! [C:nat]: ((ord_less_real @ zero_zero_real @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C))) => (ord_less_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B)) @ (suminf_real @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 185.47/93.64 thf(2099,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ A @ C) <= (ord_less_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3251_pinf_I7_J)). 185.47/93.64 thf(14726,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ A @ C) | ~ (ord_less_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2099])). 185.47/93.64 thf(461,axiom,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((sin_real @ A) = (divide_divide_real @ (tan_real @ A) @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ (tan_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8102_sin__tan)). 185.47/93.64 thf(9261,plain,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((sin_real @ A) = (divide_divide_real @ (tan_real @ A) @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ (tan_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[461])). 185.47/93.64 thf(3037,axiom,((modulo_modulo_nat = (^ [A:nat,B:nat]: (if_nat @ (ord_less_nat @ A @ B) @ A @ (modulo_modulo_nat @ (minus_minus_nat @ A @ B) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2178_mod__if)). 185.47/93.64 thf(17791,plain,(((modulo_modulo_nat) = (^ [A:nat,B:nat]: (if_nat @ (ord_less_nat @ A @ B) @ A @ (modulo_modulo_nat @ (minus_minus_nat @ A @ B) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3037])). 185.47/93.64 thf(504,axiom,((! [A:int]: ((bit_se4203085406695923979it_int @ zero_zero_nat @ A) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3027_unset__bit__0)). 185.47/93.64 thf(9428,plain,((! [A:int]: ((bit_se4203085406695923979it_int @ zero_zero_nat @ A) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[504])). 185.47/93.64 thf(2816,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5160_neg__0__less__iff__less)). 185.47/93.64 thf(17079,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2816])). 185.47/93.64 thf(286,axiom,((complex2 = (^ [A:real,B:real]: (plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9147_Complex__eq)). 185.47/93.64 thf(8667,plain,(((complex2) = (^ [A:real,B:real]: (plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 185.47/93.64 thf(7732,axiom,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = B) | (A = (uminus_uminus_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6179_power2__eq__iff)). 185.47/93.64 thf(33929,plain,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = B) | (A = (uminus_uminus_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7732])). 185.47/93.64 thf(4110,axiom,((! [A:rat,B:nat]: ((gbinomial_rat @ (uminus_uminus_rat @ A) @ B) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (gbinomial_rat @ (minus_minus_rat @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8581_gbinomial__minus)). 185.47/93.64 thf(21171,plain,((! [A:rat,B:nat]: ((gbinomial_rat @ (uminus_uminus_rat @ A) @ B) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (gbinomial_rat @ (minus_minus_rat @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4110])). 185.47/93.64 thf(238,axiom,((! [A:real,B:real]: (((A != one_one_real) => ((ord_less_real @ zero_zero_real @ B) => ((log @ A @ (inverse_inverse_real @ B)) = (uminus_uminus_real @ (log @ A @ B))))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9050_log__inverse)). 185.47/93.64 thf(8490,plain,((! [A:real,B:real]: (((~ (A = one_one_real)) => ((ord_less_real @ zero_zero_real @ B) => ((log @ A @ (inverse_inverse_real @ B)) = (uminus_uminus_real @ (log @ A @ B))))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 185.47/93.64 thf(248,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9529_int__numeral__not__or__num__neg)). 185.47/93.64 thf(8519,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 185.47/93.64 thf(1248,axiom,((! [A:real,B:(rat > real),C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D)))) <= (ord_less_real @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4341_order__less__le__subst1)). 185.47/93.64 thf(11917,plain,((! [A:real,B:(rat > real),C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D)))) | ~ (ord_less_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248])). 185.47/93.64 thf(2856,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ B @ (divide_divide_rat @ C @ A)) = (ord_less_rat @ C @ (times_times_rat @ B @ A))) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2702_neg__less__divide__eq)). 185.47/93.64 thf(17211,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ B @ (divide_divide_rat @ C @ A)) = (ord_less_rat @ C @ (times_times_rat @ B @ A))) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2856])). 185.47/93.64 thf(3541,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ (times_times_complex @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_times__divide__eq__left)). 185.47/93.64 thf(19374,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ (times_times_complex @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3541])). 185.47/93.64 thf(3397,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => ((dvd_dvd_rat @ A @ (plus_plus_rat @ C @ B)) = (dvd_dvd_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4648_dvd__add__left__iff)). 185.47/93.64 thf(18921,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => ((dvd_dvd_rat @ A @ (plus_plus_rat @ C @ B)) = (dvd_dvd_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3397])). 185.47/93.64 thf(7438,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (sqrt @ A) @ B) <= (ord_less_eq_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8221_real__le__lsqrt)). 185.47/93.64 thf(33062,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (sqrt @ A) @ B) | ~ (ord_less_eq_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7438])). 185.47/93.64 thf(5384,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((dvd_dvd_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)) = (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4513_pow__divides__pow__iff)). 185.47/93.64 thf(25548,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((dvd_dvd_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)) = (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5384])). 185.47/93.64 thf(2756,axiom,((! [A:real]: (((sin_real @ A) = zero_zero_real) = (? [B:nat]: ((A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ? [B:nat]: ((A = (uminus_uminus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7942_sin__zero__iff)). 185.47/93.64 thf(16894,plain,((! [A:real]: (((sin_real @ A) = zero_zero_real) = (? [B:nat]: ((A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ? [B:nat]: ((A = (uminus_uminus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2756])). 185.47/93.64 thf(1263,axiom,((! [A:int,B:int,C:int]: ((((divide_divide_int @ B @ A) = C) = (B = (times_times_int @ C @ A))) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4857_unit__eq__div1)). 185.47/93.64 thf(11962,plain,((! [A:int,B:int,C:int]: ((((divide_divide_int @ B @ A) = C) = (B = (times_times_int @ C @ A))) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263])). 185.47/93.64 thf(1043,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ (times_times_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ C)) @ (times_times_rat @ B @ D)) <= (ord_less_rat @ (abs_abs_rat @ C) @ D)) <= (ord_less_rat @ (abs_abs_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6492_abs__mult__less)). 185.47/93.64 thf(11288,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ (times_times_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ C)) @ (times_times_rat @ B @ D)) | ~ (ord_less_rat @ (abs_abs_rat @ C) @ D) | ~ (ord_less_rat @ (abs_abs_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043])). 185.47/93.64 thf(7304,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ (times_times_nat @ B @ A) @ B) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2663_mult__left__le)). 185.47/93.64 thf(32611,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7304])). 185.47/93.64 thf(2471,axiom,((! [A:int,B:nat,C:int,D:nat]: ((dvd_dvd_int @ (power_power_int @ A @ B) @ C) => ((dvd_dvd_int @ (power_power_int @ A @ D) @ C) <= (ord_less_eq_nat @ D @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4794_power__le__dvd)). 185.47/93.64 thf(15916,plain,((! [A:int,B:nat,C:int,D:nat]: ((dvd_dvd_int @ (power_power_int @ A @ B) @ C) => ((dvd_dvd_int @ (power_power_int @ A @ D) @ C) | ~ (ord_less_eq_nat @ D @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2471])). 185.47/93.64 thf(5820,axiom,((! [A:num,B:complex]: ((real_V1022390504157884413omplex @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ B)) = (times_times_real @ (numeral_numeral_real @ A) @ (real_V1022390504157884413omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7447_norm__mult__numeral1)). 185.47/93.64 thf(27259,plain,((! [A:num,B:complex]: ((real_V1022390504157884413omplex @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ B)) = (times_times_real @ (numeral_numeral_real @ A) @ (real_V1022390504157884413omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5820])). 185.47/93.64 thf(974,axiom,((! [A:nat,B:list_VEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => (member_VEBT_VEBT @ (nth_VEBT_VEBT @ B @ A) @ (set_VEBT_VEBT2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_932_nth__mem)). 185.47/93.64 thf(11075,plain,((! [A:nat,B:list_VEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => (member_VEBT_VEBT @ (nth_VEBT_VEBT @ B @ A) @ (set_VEBT_VEBT2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[974])). 185.47/93.64 thf(2732,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ B) = (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1626_add__le__same__cancel2)). 185.47/93.64 thf(16817,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ B) = (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2732])). 185.47/93.64 thf(6937,axiom,((! [A:num,B:num]: ((minus_minus_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (numeral_numeral_int @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5333_diff__numeral__simps_I2_J)). 185.47/93.64 thf(31260,plain,((! [A:num,B:num]: ((minus_minus_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (numeral_numeral_int @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6937])). 185.47/93.64 thf(176,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ (ord_max_int @ A @ B) @ C) = (ord_max_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3758_max__diff__distrib__left)). 185.47/93.64 thf(8298,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ (ord_max_int @ A @ B) @ C) = (ord_max_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 185.47/93.64 thf(4308,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((C = D) & (ord_less_eq_rat @ A @ B)) => (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_add__mono__thms__linordered__semiring_I3_J)). 185.47/93.64 thf(21766,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((C = D) & (ord_less_eq_rat @ A @ B)) => (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4308])). 185.47/93.64 thf(67,axiom,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ A @ (set_ord_atMost_nat @ B)) = (times_times_nat @ (A @ zero_zero_nat) @ (groups708209901874060359at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8772_prod_OatMost__shift)). 185.47/93.64 thf(7949,plain,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (A) @ (set_ord_atMost_nat @ B)) = (times_times_nat @ (A @ zero_zero_nat) @ (groups708209901874060359at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 185.47/93.64 thf(4259,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = (divide_divide_real @ C @ B)) = ((A = C) | (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1578_divide__cancel__right)). 185.47/93.64 thf(21627,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = (divide_divide_real @ C @ B)) = ((A = C) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4259])). 185.47/93.64 thf(7261,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_add__less__cancel__right)). 185.47/93.64 thf(32469,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7261])). 185.47/93.64 thf(5047,axiom,((! [A:nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4445_dvd__1__left)). 185.47/93.64 thf(24323,plain,((! [A:nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5047])). 185.47/93.64 thf(527,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (arccos @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8379_arccos__le__pi2)). 185.47/93.64 thf(9494,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (arccos @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[527])). 185.47/93.64 thf(1567,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ A @ B)) = ((B = zero_zero_int) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ zero_zero_int @ B)) | ((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ B @ zero_zero_int)) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3052_div__int__pos__iff)). 185.47/93.64 thf(12921,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ A @ B)) = ((B = zero_zero_int) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ zero_zero_int @ B)) | ((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ B @ zero_zero_int)) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567])). 185.47/93.64 thf(3571,axiom,((! [A:nat,B:nat,C:rat]: ((ord_less_nat @ A @ B) => ((ord_less_rat @ one_one_rat @ C) => (ord_less_rat @ (power_power_rat @ C @ A) @ (power_power_rat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_power__strict__increasing)). 185.47/93.64 thf(19468,plain,((! [A:nat,B:nat,C:rat]: ((ord_less_nat @ A @ B) => ((ord_less_rat @ one_one_rat @ C) => (ord_less_rat @ (power_power_rat @ C @ A) @ (power_power_rat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3571])). 185.47/93.64 thf(3277,axiom,((! [A:num,B:nat,C:int]: ((ord_less_real @ (power_power_real @ (numeral_numeral_real @ A) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7144_numeral__power__less__of__int__cancel__iff)). 185.47/93.64 thf(18536,plain,((! [A:num,B:nat,C:int]: ((ord_less_real @ (power_power_real @ (numeral_numeral_real @ A) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3277])). 185.47/93.64 thf(5932,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (power_power_nat @ A @ (suc @ B)) @ one_one_nat) <= (ord_less_nat @ A @ one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2877_power__Suc__less__one)). 185.47/93.64 thf(27637,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (power_power_nat @ A @ (suc @ B)) @ one_one_nat) | ~ (ord_less_nat @ A @ one_one_nat) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5932])). 185.47/93.64 thf(4203,axiom,((! [A:(nat > real),B:real,C:real]: ((sums_real @ (^ [D:nat]: (times_times_real @ C @ (A @ D))) @ (times_times_real @ C @ B)) <= (sums_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8157_sums__mult)). 185.47/93.64 thf(21454,plain,((! [A:(nat > real),B:real,C:real]: ((sums_real @ (^ [D:nat]: (times_times_real @ C @ (A @ D))) @ (times_times_real @ C @ B)) | ~ (sums_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4203])). 185.47/93.64 thf(743,axiom,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((log @ (root @ A @ B) @ C) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (log @ B @ C))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9206_log__base__root)). 185.47/93.64 thf(10209,plain,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((log @ (root @ A @ B) @ C) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (log @ B @ C))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[743])). 185.47/93.64 thf(2672,axiom,((! [A:real,B:nat]: ((exp_real @ (times_times_real @ A @ (semiri5074537144036343181t_real @ B))) = (power_power_real @ (exp_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8196_exp__of__nat2__mult)). 185.47/93.64 thf(16587,plain,((! [A:real,B:nat]: ((exp_real @ (times_times_real @ A @ (semiri5074537144036343181t_real @ B))) = (power_power_real @ (exp_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2672])). 185.47/93.64 thf(6822,axiom,(((('!') @ option_nat) = (^ [A:(option_nat > $o)]: ((A @ none_nat) & ! [B:nat]: (A @ (some_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1174_split__option__all)). 185.47/93.64 thf(30814,plain,(((('!') @ option_nat) = (^ [A:(option_nat > $o)]: ((A @ none_nat) & ! [B:nat]: (A @ (some_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6822])). 185.47/93.64 thf(2191,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B))) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2312_mult__neg__neg)). 185.47/93.64 thf(15034,plain,((! [A:rat,B:rat]: (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B))) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2191])). 185.47/93.64 thf(4933,axiom,((! [A:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_numeral__le__one__iff)). 185.47/93.64 thf(23885,plain,((! [A:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (ord_less_eq_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4933])). 185.47/93.64 thf(380,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_eq_real @ zero_zero_real @ (log @ A @ B)) = (ord_less_eq_real @ one_one_real @ B)) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9034_zero__le__log__cancel__iff)). 185.47/93.64 thf(9000,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_eq_real @ zero_zero_real @ (log @ A @ B)) = (ord_less_eq_real @ one_one_real @ B)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])). 185.47/93.64 thf(2727,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ (times_times_int @ B @ C)) @ B) = (modulo_modulo_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1780_mod__mult__self2)). 185.47/93.64 thf(16804,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ (times_times_int @ B @ C)) @ B) = (modulo_modulo_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2727])). 185.47/93.64 thf(447,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((arccos @ (uminus_uminus_real @ A)) = (minus_minus_real @ pi @ (arccos @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8378_arccos__minus__abs)). 185.47/93.64 thf(9218,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((arccos @ (uminus_uminus_real @ A)) = (minus_minus_real @ pi @ (arccos @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[447])). 185.47/93.64 thf(4370,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ A @ (bitM @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9458_or__minus__numerals_I3_J)). 185.47/93.64 thf(21999,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ A @ (bitM @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4370])). 185.47/93.64 thf(7443,axiom,((! [A:num]: ~ (ord_less_num @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4095_order__less__irrefl)). 185.47/93.64 thf(33077,plain,((! [A:num]: ~ (ord_less_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7443])). 185.47/93.64 thf(6492,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_nat__add__left__cancel__le)). 185.47/93.64 thf(29640,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6492])). 185.47/93.64 thf(6633,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ (modulo_modulo_nat @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2538_div__mult__mod__eq)). 185.47/93.64 thf(30112,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ (modulo_modulo_nat @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6633])). 185.47/93.64 thf(6852,axiom,((! [A:int,B:int]: ((abs_abs_int @ (times_times_int @ A @ B)) = (times_times_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6460_abs__mult)). 185.47/93.64 thf(30940,plain,((! [A:int,B:int]: ((abs_abs_int @ (times_times_int @ A @ B)) = (times_times_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6852])). 185.47/93.64 thf(4105,axiom,((! [A:rat,B:rat,C:num]: ((ord_less_eq_rat @ A @ (divide_divide_rat @ B @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)))) = (ord_less_eq_rat @ B @ (times_times_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5380_le__divide__eq__numeral1_I2_J)). 185.47/93.64 thf(21156,plain,((! [A:rat,B:rat,C:num]: ((ord_less_eq_rat @ A @ (divide_divide_rat @ B @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)))) = (ord_less_eq_rat @ B @ (times_times_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4105])). 185.47/93.64 thf(1001,axiom,((! [A:nat]: (ord_less_eq_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1314217659103216013at_int @ (power_power_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8024_fact__le__power)). 185.47/93.64 thf(11160,plain,((! [A:nat]: (ord_less_eq_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1314217659103216013at_int @ (power_power_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001])). 185.47/93.64 thf(883,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ B) @ C) => ((ord_less_nat @ C @ (power_power_nat @ A @ (plus_plus_nat @ B @ one_one_nat))) => (((archim6058952711729229775r_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ C))) = (semiri1314217659103216013at_int @ B)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9133_floor__log__nat__eq__if)). 185.47/93.64 thf(10747,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ B) @ C) => ((ord_less_nat @ C @ (power_power_nat @ A @ (plus_plus_nat @ B @ one_one_nat))) => (((archim6058952711729229775r_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ C))) = (semiri1314217659103216013at_int @ B)) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[883])). 185.47/93.64 thf(6154,axiom,((! [A:int,B:int]: ((minus_minus_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ (uminus_uminus_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5571_minus__diff__commute)). 185.47/93.64 thf(28398,plain,((! [A:int,B:int]: ((minus_minus_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ (uminus_uminus_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6154])). 185.47/93.64 thf(1026,axiom,((! [A:rat]: ((plus_plus_rat @ zero_zero_rat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2088_add_Ogroup__left__neutral)). 185.47/93.64 thf(11239,plain,((! [A:rat]: ((plus_plus_rat @ zero_zero_rat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026])). 185.47/93.64 thf(7537,axiom,(((power_power_real @ one_one_real @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_903_one__power2)). 185.47/93.64 thf(33399,plain,(((power_power_real @ one_one_real @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7537])). 185.47/93.64 thf(1619,axiom,((! [A:real]: ((((sin_real @ (arccos @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8339_sin__arccos)). 185.47/93.64 thf(13113,plain,((! [A:real]: (((sin_real @ (arccos @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) | ~ (ord_less_eq_real @ A @ one_one_real) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619])). 185.47/93.64 thf(4155,axiom,((! [A:num,B:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5706_not__numeral__less__neg__numeral)). 185.47/93.64 thf(21311,plain,((! [A:num,B:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4155])). 185.47/93.64 thf(1400,axiom,((! [A:real,B:real]: ((A != B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4133_order__less__imp__not__eq)). 185.47/93.64 thf(12398,plain,((! [A:real,B:real]: (~ (A = B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400])). 185.47/93.64 thf(3472,axiom,((~ (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5920_less__minus__one__simps_I3_J)). 185.47/93.64 thf(19159,plain,((~ (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3472])). 185.47/93.64 thf(6529,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (modulo_modulo_nat @ A @ B) @ (times_times_nat @ B @ (divide_divide_nat @ A @ B))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2532_mod__mult__div__eq)). 185.47/93.64 thf(29773,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (modulo_modulo_nat @ A @ B) @ (times_times_nat @ B @ (divide_divide_nat @ A @ B))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6529])). 185.47/93.64 thf(7692,axiom,((! [A:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_rat) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1867_zero__eq__power2)). 185.47/93.64 thf(33818,plain,((! [A:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_rat) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7692])). 185.47/93.64 thf(6412,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6462_abs__one)). 185.47/93.64 thf(29346,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6412])). 185.47/93.64 thf(6114,axiom,((! [A:(nat > complex)]: (sums_complex @ (^ [B:nat]: (times_times_complex @ (A @ B) @ (power_power_complex @ zero_zero_complex @ B))) @ (A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8203_powser__sums__zero)). 185.47/93.64 thf(28263,plain,((! [A:(nat > complex)]: (sums_complex @ (^ [B:nat]: (times_times_complex @ (A @ B) @ (power_power_complex @ zero_zero_complex @ B))) @ (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6114])). 185.47/93.64 thf(2867,axiom,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ one_one_nat) = (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1471_deg1Leaf)). 185.47/93.64 thf(17246,plain,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ one_one_nat) = (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2867])). 185.47/93.64 thf(5032,axiom,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_996_div__by__1)). 185.47/93.64 thf(24198,plain,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5032])). 185.47/93.64 thf(2017,axiom,((! [A:nat]: (ord_less_eq_real @ zero_zero_real @ (semiri2265585572941072030t_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7986_fact__ge__zero)). 185.47/93.64 thf(14478,plain,((! [A:nat]: (ord_less_eq_real @ zero_zero_real @ (semiri2265585572941072030t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2017])). 185.47/93.64 thf(4157,axiom,((! [A:real,B:real]: ((times_times_real @ (exp_real @ A) @ (exp_real @ B)) = (exp_real @ (plus_plus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8171_mult__exp__exp)). 185.47/93.64 thf(21316,plain,((! [A:real,B:real]: ((times_times_real @ (exp_real @ A) @ (exp_real @ B)) = (exp_real @ (plus_plus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4157])). 185.47/93.64 thf(532,axiom,((bot_bot_set_nat = (collect_nat @ (^ [A:nat]: (($false)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1340_empty__def)). 185.47/93.64 thf(9509,plain,((bot_bot_set_nat = (collect_nat @ (^ [A:nat]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[532])). 185.47/93.64 thf(6975,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_mint @ A) = B) => ((((? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) => (B != none_nat)) => (~ (! [C:nat]: ((? [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))) => (B != (some_nat @ C)))))) <= (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((~ (C)) => (((B = none_nat) <= (~ (D))) & ((B = (some_nat @ one_one_nat)) <= (D)))) & ((B = (some_nat @ zero_zero_nat)) <= (C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2887_vebt__mint_Oelims)). 185.47/93.64 thf(31449,plain,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_mint @ A) = B) => ((((? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) => (~ (B = none_nat))) => (~ (! [C:nat]: ((? [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))) => (~ (B = (some_nat @ C))))))) | ~ (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((~ (C)) => (((B = none_nat) | (D)) & ((B = (some_nat @ one_one_nat)) | ~ (D)))) & ((B = (some_nat @ zero_zero_nat)) | ~ (C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6975])). 185.47/93.64 thf(4918,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT]: (((list_u1324408373059187874T_VEBT @ A @ B @ C) = A) <= (ord_less_eq_nat @ (size_s6755466524823107622T_VEBT @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3640_list__update__beyond)). 185.47/93.64 thf(23821,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT]: (((list_u1324408373059187874T_VEBT @ A @ B @ C) = A) | ~ (ord_less_eq_nat @ (size_s6755466524823107622T_VEBT @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4918])). 185.47/93.64 thf(7329,axiom,((! [A:nat]: (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ A)))) => ((vEBT_vebt_buildup @ (suc @ (suc @ A))) = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (suc @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ A))) => ((vEBT_vebt_buildup @ (suc @ (suc @ A))) = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6304_vebt__buildup_Osimps_I3_J)). 185.47/93.64 thf(32700,plain,((! [A:nat]: (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ A)))) => ((vEBT_vebt_buildup @ (suc @ (suc @ A))) = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (suc @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ A))) => ((vEBT_vebt_buildup @ (suc @ (suc @ A))) = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7329])). 185.47/93.64 thf(3871,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((A = B) & (ord_less_eq_rat @ C @ D)) => (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_add__mono__thms__linordered__semiring_I2_J)). 185.47/93.64 thf(20428,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((A = B) & (ord_less_eq_rat @ C @ D)) => (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3871])). 185.47/93.64 thf(1659,axiom,((! [A:(nat > rat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_rat @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_rat @ (A @ C) @ (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1080_lift__Suc__antimono__le)). 185.47/93.64 thf(13298,plain,((! [A:(nat > rat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_rat @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_rat @ (A @ C) @ (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659])). 185.47/93.64 thf(1764,axiom,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5095_minus__add__distrib)). 185.47/93.64 thf(13640,plain,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764])). 185.47/93.64 thf(3147,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((modulo_modulo_int @ B @ A) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4874_unit__imp__mod__eq__0)). 185.47/93.64 thf(18133,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((modulo_modulo_int @ B @ A) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3147])). 185.47/93.64 thf(7150,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((suc @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1845_Suc__pred)). 185.47/93.64 thf(32086,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((suc @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7150])). 185.47/93.64 thf(5010,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_power__increasing__iff)). 185.47/93.64 thf(24134,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5010])). 185.47/93.64 thf(624,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ln_ln_real @ (times_times_real @ A @ B)) = (plus_plus_real @ (ln_ln_real @ A) @ (ln_ln_real @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6141_ln__mult)). 185.47/93.64 thf(9801,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ln_ln_real @ (times_times_real @ A @ B)) = (plus_plus_real @ (ln_ln_real @ A) @ (ln_ln_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[624])). 185.47/93.64 thf(330,axiom,((bit_concat_bit = (^ [A:nat,B:int,C:int]: (bit_se1409905431419307370or_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se545348938243370406it_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9518_concat__bit__def)). 185.47/93.64 thf(8838,plain,(((bit_concat_bit) = (^ [A:nat,B:int,C:int]: (bit_se1409905431419307370or_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se545348938243370406it_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 185.47/93.64 thf(4148,axiom,((semiri2265585572941072030t_real = (^ [A:nat]: (if_real @ (A = zero_zero_nat) @ one_one_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8048_fact__num__eq__if)). 185.47/93.64 thf(21285,plain,(((semiri2265585572941072030t_real) = (^ [A:nat]: (if_real @ (A = zero_zero_nat) @ one_one_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4148])). 185.47/93.64 thf(5776,axiom,((! [A:num,B:num,C:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5360_semiring__norm_I171_J)). 185.47/93.64 thf(26947,plain,((! [A:num,B:num,C:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5776])). 185.47/93.64 thf(5892,axiom,((! [A:real,B:real,C:real]: ((((minus_minus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (divide_divide_real @ (minus_minus_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)) @ A)) <= (A != zero_zero_real)) & (((minus_minus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (uminus_uminus_real @ C)) <= (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6174_add__divide__eq__if__simps_I6_J)). 185.47/93.64 thf(27505,plain,((! [A:real,B:real,C:real]: ((((minus_minus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (divide_divide_real @ (minus_minus_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)) @ A)) | (A = zero_zero_real)) & (((minus_minus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (uminus_uminus_real @ C)) | ~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5892])). 185.47/93.64 thf(2381,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4632_unit__imp__dvd)). 185.47/93.64 thf(15611,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2381])). 185.47/93.64 thf(3579,axiom,((! [A:complex,B:complex,C:complex]: ((((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A)) <= (A != zero_zero_complex)) & ((A = zero_zero_complex) => ((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2747_add__divide__eq__if__simps_I2_J)). 185.47/93.64 thf(19490,plain,((! [A:complex,B:complex,C:complex]: ((((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A)) | (A = zero_zero_complex)) & ((A = zero_zero_complex) => ((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3579])). 185.47/93.64 thf(5258,axiom,((! [A:option4927543243414619207at_nat]: ((A != none_P5556105721700978146at_nat) => (~ (! [B:product_prod_nat_nat]: (A != (some_P7363390416028606310at_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1167_option_Oexhaust)). 185.47/93.64 thf(25078,plain,((! [A:option4927543243414619207at_nat]: ((~ (A = none_P5556105721700978146at_nat)) => (~ (! [B:product_prod_nat_nat]: ~ (A = (some_P7363390416028606310at_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5258])). 185.47/93.64 thf(2086,axiom,((! [A:rat,B:rat]: ((A = (plus_plus_rat @ B @ A)) = (B = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1526_add__cancel__right__left)). 185.47/93.64 thf(14689,plain,((! [A:rat,B:rat]: ((A = (plus_plus_rat @ B @ A)) = (B = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2086])). 185.47/93.64 thf(2307,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1132_comm__semiring__class_Odistrib)). 185.47/93.64 thf(15384,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2307])). 185.47/93.64 thf(2780,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_5510_minus__le__iff)). 185.47/93.64 thf(16965,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)],[2780])). 185.47/93.64 thf(1880,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => (((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) = C) = ((uminus1482373934393186551omplex @ B) = (times_times_complex @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5967_nonzero__neg__divide__eq__eq)). 185.47/93.64 thf(14025,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => (((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) = C) = ((uminus1482373934393186551omplex @ B) = (times_times_complex @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880])). 185.47/93.64 thf(6948,axiom,((unique5055182867167087721od_nat = (^ [A:num,B:num]: (product_Pair_nat_nat @ (divide_divide_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) @ (modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6831_divmod_H__nat__def)). 185.47/93.64 thf(31298,plain,(((unique5055182867167087721od_nat) = (^ [A:num,B:num]: (product_Pair_nat_nat @ (divide_divide_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) @ (modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6948])). 185.47/93.64 thf(4913,axiom,((! [A:nat]: ((power_power_real @ (uminus_uminus_real @ one_one_real) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5460_power__minus1__even)). 185.47/93.64 thf(23800,plain,((! [A:nat]: ((power_power_real @ (uminus_uminus_real @ one_one_real) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4913])). 185.47/93.64 thf(786,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (? [B:real]: (((tan_real @ B) = A) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & (ord_less_eq_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8065_tan__total__pos)). 185.47/93.64 thf(10414,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (? [B:real]: (((tan_real @ B) = A) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & (ord_less_eq_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[786])). 185.47/93.64 thf(7402,axiom,((! [A:(nat > num),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_num @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_num @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1081_lift__Suc__antimono__le)). 185.47/93.64 thf(32930,plain,((! [A:(nat > num),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_num @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_num @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7402])). 185.47/93.64 thf(7080,axiom,((! [A:nat,B:nat]: (((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4509_unit__div__mult__self)). 185.47/93.64 thf(31835,plain,((! [A:nat,B:nat]: (((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7080])). 185.47/93.64 thf(3974,axiom,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ A @ B) = (plus_plus_rat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_add_Oright__cancel)). 185.47/93.64 thf(20761,plain,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ A @ B) = (plus_plus_rat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3974])). 185.47/93.64 thf(6274,axiom,(((minus_minus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5415_diff__numeral__special_I11_J)). 185.47/93.64 thf(28850,plain,(((minus_minus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6274])). 185.47/93.64 thf(4051,axiom,((! [A:int,B:nat,C:int]: ((ord_less_real @ (power_power_real @ (ring_1_of_int_real @ A) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7109_of__int__less__of__int__power__cancel__iff)). 185.47/93.64 thf(20986,plain,((! [A:int,B:nat,C:int]: ((ord_less_real @ (power_power_real @ (ring_1_of_int_real @ A) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_int @ (power_power_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4051])). 185.47/93.64 thf(6553,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_VEBT_max_in_set @ (vEBT_VEBT_set_vebt @ A) @ C) <= ((vEBT_vebt_maxt @ A) = (some_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_945_maxt__corr)). 185.47/93.64 thf(29847,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_VEBT_max_in_set @ (vEBT_VEBT_set_vebt @ A) @ C) | ~ ((vEBT_vebt_maxt @ A) = (some_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6553])). 185.47/93.64 thf(4467,axiom,((! [A:nat,B:nat,C:int]: (((ord_less_int @ zero_zero_int @ (bit_se2923211474154528505it_int @ B @ C)) <= (bit_se1146084159140164899it_int @ C @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9432_bit__imp__take__bit__positive)). 185.47/93.64 thf(22300,plain,((! [A:nat,B:nat,C:int]: ((ord_less_int @ zero_zero_int @ (bit_se2923211474154528505it_int @ B @ C)) | ~ (bit_se1146084159140164899it_int @ C @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4467])). 185.47/93.64 thf(2247,axiom,((! [A:complex,B:complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ (real_V1022390504157884413omplex @ A)) @ (real_V1022390504157884413omplex @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7429_complex__mod__triangle__ineq2)). 185.47/93.64 thf(15207,plain,((! [A:complex,B:complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ (real_V1022390504157884413omplex @ A)) @ (real_V1022390504157884413omplex @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2247])). 185.47/93.64 thf(4086,axiom,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (plus_plus_rat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_731_diff__add__eq)). 185.47/93.64 thf(21096,plain,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (plus_plus_rat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4086])). 185.47/93.64 thf(6626,axiom,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = (uminus1482373934393186551omplex @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5022_neg__equal__iff__equal)). 185.47/93.64 thf(30090,plain,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = (uminus1482373934393186551omplex @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6626])). 185.47/93.64 thf(1195,axiom,((! [A:rat]: ? [B:rat]: (ord_less_rat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3971_gt__ex)). 185.47/93.64 thf(11756,plain,((! [A:rat]: ? [B:rat]: (ord_less_rat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195])). 185.47/93.64 thf(880,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_eq_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ B) => (((ord_less_eq_real @ (arcsin @ A) @ B) = (ord_less_eq_real @ A @ (sin_real @ B))) <= (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8336_arcsin__le__iff)). 185.47/93.64 thf(10737,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_eq_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ B) => (((ord_less_eq_real @ (arcsin @ A) @ B) = (ord_less_eq_real @ A @ (sin_real @ B))) | ~ (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[880])). 185.47/93.64 thf(1127,axiom,((! [A:$o]: ((divide_divide_int @ (zero_n2684676970156552555ol_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5432_of__bool__half__eq__0)). 185.47/93.64 thf(11549,plain,((! [A:$o]: ((divide_divide_int @ (zero_n2684676970156552555ol_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127])). 185.47/93.64 thf(2911,axiom,((abs_abs_real = (^ [A:real]: (if_real @ (ord_less_real @ A @ zero_zero_real) @ (uminus_uminus_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6572_abs__if)). 185.47/93.64 thf(17390,plain,(((abs_abs_real) = (^ [A:real]: (if_real @ (ord_less_real @ A @ zero_zero_real) @ (uminus_uminus_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2911])). 185.47/93.64 thf(3359,axiom,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5930_neg__one__le__numeral)). 185.47/93.64 thf(18800,plain,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3359])). 185.47/93.64 thf(6681,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((((dvd_dvd_nat @ D @ (minus_minus_nat @ B @ A)) = (dvd_dvd_nat @ D @ (plus_plus_nat @ B @ (minus_minus_nat @ (times_times_nat @ C @ D) @ A)))) <= (ord_less_eq_nat @ A @ (times_times_nat @ C @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4926_dvd__minus__add)). 185.47/93.64 thf(30269,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((dvd_dvd_nat @ D @ (minus_minus_nat @ B @ A)) = (dvd_dvd_nat @ D @ (plus_plus_nat @ B @ (minus_minus_nat @ (times_times_nat @ C @ D) @ A)))) | ~ (ord_less_eq_nat @ A @ (times_times_nat @ C @ D)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6681])). 185.47/93.64 thf(6265,axiom,((! [A:nat,B:rat,C:rat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((ord_less_eq_rat @ B @ C) => (ord_less_eq_rat @ (power_power_rat @ B @ A) @ (power_power_rat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4944_power__mono__odd)). 185.47/93.64 thf(28811,plain,((! [A:nat,B:rat,C:rat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((ord_less_eq_rat @ B @ C) => (ord_less_eq_rat @ (power_power_rat @ B @ A) @ (power_power_rat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6265])). 185.47/93.64 thf(5662,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4158_leI)). 185.47/93.64 thf(26581,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5662])). 185.47/93.64 thf(2871,axiom,((! [A:int,B:int]: (((divide_divide_int @ A @ B) = zero_zero_int) = (((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_int @ A @ B)) | ((ord_less_int @ B @ A) & (ord_less_eq_int @ A @ zero_zero_int)) | (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3049_zdiv__eq__0__iff)). 185.47/93.64 thf(17258,plain,((! [A:int,B:int]: (((divide_divide_int @ A @ B) = zero_zero_int) = (((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_int @ A @ B)) | ((ord_less_int @ B @ A) & (ord_less_eq_int @ A @ zero_zero_int)) | (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2871])). 185.47/93.64 thf(7429,axiom,(((neg_nu5851722552734809277nc_int @ one_one_int) = (numeral_numeral_int @ (bit1 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6851_dbl__inc__simps_I3_J)). 185.47/93.64 thf(33036,plain,(((neg_nu5851722552734809277nc_int @ one_one_int) = (numeral_numeral_int @ (bit1 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7429])). 185.47/93.64 thf(2880,axiom,((! [A:nat,B:nat,C:(nat > rat),D:rat]: (((ord_less_eq_rat @ (C @ B) @ D) => ((ord_less_rat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_rat @ (C @ E) @ (C @ F)) <= (ord_less_nat @ E @ F))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4359_order__less__le__subst2)). 185.47/93.64 thf(17285,plain,((! [A:nat,B:nat,C:(nat > rat),D:rat]: (((ord_less_eq_rat @ (C @ B) @ D) => ((ord_less_rat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_nat @ E @ F))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2880])). 185.47/93.64 thf(1216,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((nat2 @ (divide_divide_int @ B @ A)) = (divide_divide_nat @ (nat2 @ B) @ (nat2 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9317_nat__div__distrib_H)). 185.47/93.64 thf(11816,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((nat2 @ (divide_divide_int @ B @ A)) = (divide_divide_nat @ (nat2 @ B) @ (nat2 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216])). 185.47/93.64 thf(7549,axiom,((! [A:nat]: ((plus_plus_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1016_add__2__eq__Suc_H)). 185.47/93.64 thf(33431,plain,((! [A:nat]: ((plus_plus_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7549])). 185.47/93.64 thf(2159,axiom,((! [A:real]: ((power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_real @ one_one_real @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7838_sin__squared__eq)). 185.47/93.64 thf(14927,plain,((! [A:real]: ((power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_real @ one_one_real @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2159])). 185.47/93.64 thf(4313,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ C) <= (ord_less_int @ zero_zero_int @ A)) <= (ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2606_mult__left__le__imp__le)). 185.47/93.64 thf(21781,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ B @ C) | ~ (ord_less_int @ zero_zero_int @ A) | ~ (ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4313])). 185.47/93.64 thf(2350,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ (plus_plus_int @ C @ (times_times_int @ (plus_plus_int @ (abs_abs_int @ (minus_minus_int @ C @ B)) @ one_one_int) @ A))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6838_incr__lemma)). 185.47/93.64 thf(15514,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ (plus_plus_int @ C @ (times_times_int @ (plus_plus_int @ (abs_abs_int @ (minus_minus_int @ C @ B)) @ one_one_int) @ A))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2350])). 185.47/93.64 thf(304,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ B)))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9540_or__not__numerals_I6_J)). 185.47/93.64 thf(8752,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ B)))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 185.47/93.64 thf(5393,axiom,((! [A:num,B:num]: ((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit0 @ B)) = (produc2626176000494625587at_nat @ (^ [C:nat,D:nat]: (product_Pair_nat_nat @ C @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) @ one_one_nat))) @ (unique5055182867167087721od_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6860_divmod__algorithm__code_I6_J)). 185.47/93.64 thf(25576,plain,((! [A:num,B:num]: ((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit0 @ B)) = (produc2626176000494625587at_nat @ (^ [C:nat,D:nat]: (product_Pair_nat_nat @ C @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) @ one_one_nat))) @ (unique5055182867167087721od_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5393])). 185.47/93.64 thf(5695,axiom,((! [A:nat,B:num,C:nat]: (((semiri1316708129612266289at_nat @ A) = (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7058_real__of__nat__eq__numeral__power__cancel__iff)). 185.47/93.64 thf(26682,plain,((! [A:nat,B:num,C:nat]: (((semiri1316708129612266289at_nat @ A) = (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5695])). 185.47/93.64 thf(7712,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_numeral__Bit0)). 185.47/93.64 thf(33875,plain,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7712])). 185.47/93.64 thf(543,axiom,(((tan_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit1 @ one)))) = (sqrt @ (numeral_numeral_real @ (bit1 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8233_tan__60)). 185.47/93.64 thf(9540,plain,(((tan_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit1 @ one)))) = (sqrt @ (numeral_numeral_real @ (bit1 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[543])). 185.47/93.64 thf(7227,axiom,((bit_se1412395901928357646or_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9481_or__nat__rec)). 185.47/93.64 thf(32363,plain,(((bit_se1412395901928357646or_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7227])). 185.47/93.64 thf(4229,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ (bit_se725231765392027082nd_int @ A @ C) @ B) <= (ord_less_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9382_AND__upper1_H_H)). 185.47/93.64 thf(21534,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ (bit_se725231765392027082nd_int @ A @ C) @ B) | ~ (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4229])). 185.47/93.64 thf(6588,axiom,(((semiri5044797733671781792omplex @ (suc @ zero_zero_nat)) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7963_fact__Suc__0)). 185.47/93.64 thf(29971,plain,(((semiri5044797733671781792omplex @ (suc @ zero_zero_nat)) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6588])). 185.47/93.64 thf(7340,axiom,((! [A:num,B:nat,C:int]: (((power_power_complex @ (numera6690914467698888265omplex @ A) @ B) = (ring_17405671764205052669omplex @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7102_numeral__power__eq__of__int__cancel__iff)). 185.47/93.64 thf(32738,plain,((! [A:num,B:nat,C:int]: (((power_power_complex @ (numera6690914467698888265omplex @ A) @ B) = (ring_17405671764205052669omplex @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7340])). 185.47/93.64 thf(521,axiom,((bit_se7879613467334960850it_int = (^ [A:nat,B:int]: (bit_se1409905431419307370or_int @ B @ (bit_se545348938243370406it_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9519_set__bit__int__def)). 185.47/93.64 thf(9481,plain,(((bit_se7879613467334960850it_int) = (^ [A:nat,B:int]: (bit_se1409905431419307370or_int @ B @ (bit_se545348938243370406it_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[521])). 185.47/93.64 thf(6087,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_mult_Oleft__commute)). 185.47/93.64 thf(28164,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6087])). 185.47/93.64 thf(615,axiom,((! [A:real,B:nat]: ? [C:real]: ((sin_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (sin_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (sin_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8093_Maclaurin__sin__expansion)). 185.47/93.64 thf(9774,plain,((! [A:real,B:nat]: ? [C:real]: ((sin_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (sin_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (sin_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[615])). 185.47/93.64 thf(1598,axiom,((! [A:rat,B:rat]: ((dvd_dvd_rat @ A @ B) => (((divide_divide_rat @ B @ A) = zero_zero_rat) = (B = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4726_dvd__div__eq__0__iff)). 185.47/93.64 thf(13029,plain,((! [A:rat,B:rat]: ((dvd_dvd_rat @ A @ B) => (((divide_divide_rat @ B @ A) = zero_zero_rat) = (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598])). 185.47/93.64 thf(6803,axiom,((ord_less_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_4255_dual__order_Ostrict__iff__not)). 185.47/93.64 thf(30747,plain,(((ord_less_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)],[6803])). 185.47/93.64 thf(914,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (ln_ln_real @ (minus_minus_real @ one_one_real @ A)) @ (uminus_uminus_real @ A)) <= (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5825_ln__one__minus__pos__upper__bound)). 185.47/93.64 thf(10859,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (ln_ln_real @ (minus_minus_real @ one_one_real @ A)) @ (uminus_uminus_real @ A)) | ~ (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[914])). 185.47/93.64 thf(5847,axiom,((! [A:real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6317_abs__0__eq)). 185.47/93.64 thf(27355,plain,((! [A:real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5847])). 185.47/93.64 thf(3081,axiom,((! [A:nat]: (((semiri8010041392384452111omplex @ A) = one_one_complex) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6928_of__nat__eq__1__iff)). 185.47/93.64 thf(17924,plain,((! [A:nat]: (((semiri8010041392384452111omplex @ A) = one_one_complex) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3081])). 185.47/93.64 thf(1170,axiom,((! [A:nat,B:int]: ((bit_se4203085406695923979it_int @ (suc @ A) @ B) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se4203085406695923979it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3031_unset__bit__Suc)). 185.47/93.64 thf(11684,plain,((! [A:nat,B:int]: ((bit_se4203085406695923979it_int @ (suc @ A) @ B) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se4203085406695923979it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170])). 185.47/93.64 thf(1286,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ A @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_field__less__half__sum)). 185.47/93.64 thf(12026,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ A @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286])). 185.47/93.64 thf(3031,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B)) = (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ C @ A)) & ((ord_less_eq_rat @ A @ C) <= (ord_less_rat @ zero_zero_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2573_mult__le__cancel__right)). 185.47/93.64 thf(17766,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B)) = (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ C @ A)) & ((ord_less_eq_rat @ A @ C) | ~ (ord_less_rat @ zero_zero_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3031])). 185.47/93.64 thf(2892,axiom,((! [A:real,B:(num > real),C:num,D:num]: (((ord_less_num @ C @ D) => ((ord_less_real @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))))) <= (ord_less_real @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4100_order__less__subst1)). 185.47/93.64 thf(17330,plain,((! [A:real,B:(num > real),C:num,D:num]: (((ord_less_num @ C @ D) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))))) | ~ (ord_less_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2892])). 185.47/93.64 thf(7130,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_vebt_member @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1466_vebt__member_Osimps_I2_J)). 185.47/93.64 thf(31994,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_vebt_member @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7130])). 185.47/93.64 thf(4722,axiom,((! [A:set_nat,B:(nat > nat)]: ((finite_finite_nat @ A) => (((groups3542108847815614940at_nat @ B @ A) = one_one_nat) = (? [C:nat]: ((member_nat @ C @ A) & ((B @ C) = one_one_nat) & ! [D:nat]: ((member_nat @ D @ A) => ((C != D) => ((B @ D) = zero_zero_nat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6599_sum__eq__1__iff)). 185.47/93.64 thf(23144,plain,((! [A:set_nat,B:(nat > nat)]: ((finite_finite_nat @ A) => (((groups3542108847815614940at_nat @ (B) @ A) = one_one_nat) = (? [C:nat]: ((member_nat @ C @ A) & ((B @ C) = one_one_nat) & ! [D:nat]: ((member_nat @ D @ A) => ((~ (C = D)) => ((B @ D) = zero_zero_nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4722])). 185.47/93.64 thf(2403,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ C @ D) => ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)) <= (ord_less_eq_rat @ zero_zero_rat @ C)))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2591_mult__strict__mono_H)). 185.47/93.64 thf(15683,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ C @ D) => ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)) | ~ (ord_less_eq_rat @ zero_zero_rat @ C)))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2403])). 185.47/93.64 thf(6889,axiom,((! [A:nat]: (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer))) & (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = one_one_Code_integer) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6231_minus__one__power__iff)). 185.47/93.64 thf(31096,plain,((! [A:nat]: (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer))) & (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = one_one_Code_integer) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6889])). 185.47/93.64 thf(352,axiom,((! [A:complex]: ((im @ (invers8013647133539491842omplex @ A)) = (divide_divide_real @ (uminus_uminus_real @ (im @ A)) @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9701_inverse__complex_Osimps_I2_J)). 185.47/93.64 thf(8911,plain,((! [A:complex]: ((im @ (invers8013647133539491842omplex @ A)) = (divide_divide_real @ (uminus_uminus_real @ (im @ A)) @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 185.47/93.64 thf(4426,axiom,((! [A:num]: ~ (ord_less_rat @ (uminus_uminus_rat @ one_one_rat) @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5961_not__neg__one__less__neg__numeral)). 185.47/93.64 thf(22165,plain,((! [A:num]: ~ (ord_less_rat @ (uminus_uminus_rat @ one_one_rat) @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4426])). 185.47/93.64 thf(2839,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (ord_max_nat @ A @ B) @ C) = ((ord_less_nat @ A @ C) & (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3574_max__less__iff__conj)). 185.47/93.64 thf(17158,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (ord_max_nat @ A @ B) @ C) = ((ord_less_nat @ A @ C) & (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2839])). 185.47/93.64 thf(4955,axiom,((! [A:real]: ((times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ A)) = (times_times_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6337_abs__mult__self__eq)). 185.47/93.64 thf(23956,plain,((! [A:real]: ((times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ A)) = (times_times_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4955])). 185.47/93.64 thf(6788,axiom,((! [A:(list_VEBT_VEBT > $o),B:list_VEBT_VEBT]: ((! [C:list_VEBT_VEBT]: ((! [D:list_VEBT_VEBT]: ((A @ D) <= (ord_less_nat @ (size_s6755466524823107622T_VEBT @ D) @ (size_s6755466524823107622T_VEBT @ C)))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_912_length__induct)). 185.47/93.64 thf(30694,plain,((! [A:(list_VEBT_VEBT > $o),B:list_VEBT_VEBT]: ((! [C:list_VEBT_VEBT]: ((! [D:list_VEBT_VEBT]: ((A @ D) | ~ (ord_less_nat @ (size_s6755466524823107622T_VEBT @ D) @ (size_s6755466524823107622T_VEBT @ C)))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6788])). 185.47/93.64 thf(4417,axiom,((! [A:num,B:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_numeral__plus__numeral)). 185.47/93.64 thf(22140,plain,((! [A:num,B:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4417])). 185.47/93.64 thf(5405,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_786_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2)). 185.47/93.64 thf(25611,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5405])). 185.47/93.64 thf(2204,axiom,((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5710_le__minus__one__simps_I2_J)). 185.47/93.64 thf(15072,plain,((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2204])). 185.47/93.64 thf(3240,axiom,((! [A:nat,B:(rat > nat),C:rat,D:rat]: ((((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))) <= (ord_less_eq_rat @ C @ D)) <= (ord_less_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4344_order__less__le__subst1)). 185.47/93.64 thf(18425,plain,((! [A:nat,B:(rat > nat),C:rat,D:rat]: (((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_nat @ A @ (B @ D))) | ~ (ord_less_eq_rat @ C @ D) | ~ (ord_less_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3240])). 185.47/93.64 thf(2683,axiom,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5556_is__num__normalize_I8_J)). 185.47/93.64 thf(16668,plain,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2683])). 185.47/93.64 thf(7578,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ (binomial @ C @ B) @ (binomial @ C @ A)) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8528_binomial__antimono)). 185.47/93.64 thf(33511,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (binomial @ C @ B) @ (binomial @ C @ A)) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7578])). 185.47/93.64 thf(3317,axiom,((! [A:int,B:nat,C:nat]: ((divide_divide_int @ A @ (times_times_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C))) = (divide_divide_int @ (divide_divide_int @ A @ (semiri1314217659103216013at_int @ B)) @ (semiri1314217659103216013at_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7220_div__mult2__eq_H)). 185.47/93.64 thf(18661,plain,((! [A:int,B:nat,C:nat]: ((divide_divide_int @ A @ (times_times_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C))) = (divide_divide_int @ (divide_divide_int @ A @ (semiri1314217659103216013at_int @ B)) @ (semiri1314217659103216013at_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3317])). 185.47/93.64 thf(3859,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (plus_plus_real @ B @ (times_times_real @ C @ A)) @ A)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2739_add__frac__num)). 185.47/93.64 thf(20396,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (plus_plus_real @ B @ (times_times_real @ C @ A)) @ A)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3859])). 185.47/93.64 thf(6060,axiom,((! [A:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real) = ((A = one_one_real) | (A = (uminus_uminus_real @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6222_power2__eq__1__iff)). 185.47/93.64 thf(28074,plain,((! [A:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real) = ((A = one_one_real) | (A = (uminus_uminus_real @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6060])). 185.47/93.64 thf(5718,axiom,((! [A:nat,B:code_integer]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (power_8256067586552552935nteger @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5438_Parity_Oring__1__class_Opower__minus__even)). 185.47/93.64 thf(26763,plain,((! [A:nat,B:code_integer]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (power_8256067586552552935nteger @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5718])). 185.47/93.64 thf(1781,axiom,((! [A:nat,B:rat]: (((gbinomial_rat @ B @ A) = (times_times_rat @ (divide_divide_rat @ B @ (semiri681578069525770553at_rat @ A)) @ (gbinomial_rat @ (minus_minus_rat @ B @ one_one_rat) @ (minus_minus_nat @ A @ one_one_nat)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8600_gbinomial__absorption_H)). 185.47/93.64 thf(13700,plain,((! [A:nat,B:rat]: (((gbinomial_rat @ B @ A) = (times_times_rat @ (divide_divide_rat @ B @ (semiri681578069525770553at_rat @ A)) @ (gbinomial_rat @ (minus_minus_rat @ B @ one_one_rat) @ (minus_minus_nat @ A @ one_one_nat)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781])). 185.47/93.64 thf(5854,axiom,(((numeral_numeral_real @ one) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_830_numeral__One)). 185.47/93.64 thf(27378,plain,(((numeral_numeral_real @ one) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5854])). 185.47/93.64 thf(4491,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (sqrt @ A)) <= (ord_less_eq_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8169_real__sqrt__ge__one)). 185.47/93.64 thf(22379,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (sqrt @ A)) | ~ (ord_less_eq_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4491])). 185.47/93.64 thf(4208,axiom,((ord_max_nat = (^ [A:nat,B:nat]: (if_nat @ (ord_less_eq_nat @ A @ B) @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3767_max__def__raw)). 185.47/93.64 thf(21467,plain,(((ord_max_nat) = (^ [A:nat,B:nat]: (if_nat @ (ord_less_eq_nat @ A @ B) @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4208])). 185.47/93.64 thf(5655,axiom,((! [A:nat,B:nat,C:nat]: (((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))) & ((A = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1802_nat__mult__div__cancel__disj)). 185.47/93.64 thf(26547,plain,((! [A:nat,B:nat,C:nat]: (((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))) & ((A = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5655])). 185.47/93.64 thf(748,axiom,((! [A:(real > $o),B:real]: ((! [C:real,D:real]: ((ord_less_real @ C @ D) => ((A @ D) <= (A @ C)))) => (((ord_less_real @ zero_zero_real @ B) => (A @ B)) <= (! [C:nat]: ((C != zero_zero_nat) => (A @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8970_forall__pos__mono)). 185.47/93.64 thf(10230,plain,((! [A:(real > $o),B:real]: ((! [C:real,D:real]: ((ord_less_real @ C @ D) => ((A @ D) | ~ (A @ C)))) => (((ord_less_real @ zero_zero_real @ B) => (A @ B)) | ~ (! [C:nat]: ((~ (C = zero_zero_nat)) => (A @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[748])). 185.47/93.64 thf(790,axiom,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ B)))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9539_and__not__numerals_I9_J)). 185.47/93.64 thf(10427,plain,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ B)))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[790])). 185.47/93.64 thf(4953,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A)) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6603_numeral__Bit1)). 185.47/93.64 thf(23949,plain,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A)) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4953])). 185.47/93.64 thf(4659,axiom,((! [A:num]: ((neg_nu7009210354673126013omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3827_dbl__simps_I5_J)). 185.47/93.64 thf(22925,plain,((! [A:num]: ((neg_nu7009210354673126013omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4659])). 185.47/93.64 thf(4442,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => ((plus_plus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (plus_plus_rat @ B @ (times_times_rat @ C @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2740_add__frac__num)). 185.47/93.64 thf(22223,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => ((plus_plus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (plus_plus_rat @ B @ (times_times_rat @ C @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4442])). 185.47/93.64 thf(6463,axiom,((! [A:int,B:num]: ((power_power_int @ (uminus_uminus_int @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5999_power__minus__Bit0)). 185.47/93.64 thf(29532,plain,((! [A:int,B:num]: ((power_power_int @ (uminus_uminus_int @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6463])). 185.47/93.64 thf(5782,axiom,((! [A:rat,B:nat]: ((power_power_rat @ A @ (suc @ B)) = (times_times_rat @ A @ (power_power_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1071_power__Suc)). 185.47/93.64 thf(26964,plain,((! [A:rat,B:nat]: ((power_power_rat @ A @ (suc @ B)) = (times_times_rat @ A @ (power_power_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5782])). 185.47/93.64 thf(3824,axiom,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ (plus_plus_int @ B @ one_one_int)) = (plus_plus_int @ one_one_int @ (bit_se2923211474154528505it_int @ A @ B))) <= ((bit_se2923211474154528505it_int @ A @ B) != (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9350_take__bit__incr__eq)). 185.47/93.64 thf(20280,plain,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ (plus_plus_int @ B @ one_one_int)) = (plus_plus_int @ one_one_int @ (bit_se2923211474154528505it_int @ A @ B))) | ((bit_se2923211474154528505it_int @ A @ B) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3824])). 185.47/93.64 thf(6002,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = A) = ((A = zero_zero_complex) | (B = one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1665_mult__cancel__left2)). 185.47/93.64 thf(27906,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = A) = ((A = zero_zero_complex) | (B = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6002])). 185.47/93.64 thf(5911,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ A)) = zero_zero_nat) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8017_fact__mod)). 185.47/93.64 thf(27573,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ A)) = zero_zero_nat) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5911])). 185.47/93.64 thf(4449,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((~ (ord_less_real @ A @ B)) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4172_antisym__conv2)). 185.47/93.64 thf(22246,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((~ (ord_less_real @ A @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4449])). 185.47/93.64 thf(2443,axiom,((! [A:int,B:int]: ? [C:int]: ! [D:int]: ((ord_less_int @ D @ C) => ((dvd_dvd_int @ A @ (plus_plus_int @ D @ B)) = (dvd_dvd_int @ A @ (plus_plus_int @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4712_minf_I9_J)). 185.47/93.64 thf(15823,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2443])). 185.47/93.64 thf(7514,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) => (ord_less_nat @ (binomial @ C @ A) @ (binomial @ C @ B))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8546_binomial__strict__mono)). 185.47/93.64 thf(33326,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) => (ord_less_nat @ (binomial @ C @ A) @ (binomial @ C @ B))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7514])). 185.47/93.64 thf(1758,axiom,((! [A:nat,B:nat]: ((ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6907_of__nat__le__iff)). 185.47/93.64 thf(13626,plain,((! [A:nat,B:nat]: ((ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758])). 185.47/93.64 thf(1090,axiom,((! [A:rat]: ((ord_less_rat @ (uminus_uminus_rat @ A) @ A) = (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5157_neg__less__pos)). 185.47/93.64 thf(11436,plain,((! [A:rat]: ((ord_less_rat @ (uminus_uminus_rat @ A) @ A) = (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090])). 185.47/93.64 thf(6166,axiom,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = ((A = zero_zero_complex) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1496_mult__cancel__left)). 185.47/93.64 thf(28482,plain,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = ((A = zero_zero_complex) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6166])). 185.47/93.64 thf(2944,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5589_minus__divide__right)). 185.47/93.64 thf(17492,plain,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2944])). 185.47/93.64 thf(400,axiom,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((log @ C @ (root @ A @ B)) = (divide_divide_real @ (log @ C @ B) @ (semiri5074537144036343181t_real @ A))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9205_log__root)). 185.47/93.64 thf(9064,plain,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((log @ C @ (root @ A @ B)) = (divide_divide_real @ (log @ C @ B) @ (semiri5074537144036343181t_real @ A))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[400])). 185.47/93.64 thf(7054,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_add__diff__cancel__left)). 185.47/93.64 thf(31761,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7054])). 185.47/93.64 thf(2749,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_ri631733984087533419it_int @ A @ B)) = (~ (bit_se1146084159140164899it_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9411_signed__take__bit__nonnegative__iff)). 185.47/93.64 thf(16868,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_ri631733984087533419it_int @ A @ B)) = (~ (bit_se1146084159140164899it_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2749])). 185.47/93.64 thf(7221,axiom,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => ((C @ B) <= (! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) <= (C @ D))))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_dec__induct)). 185.47/93.64 thf(32331,plain,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => ((C @ B) | ~ (! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) | ~ (C @ D))))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7221])). 185.47/93.64 thf(7292,axiom,((! [A:$o,B:$o]: (((A) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ one_one_nat))) & ((~ (A)) => (((B) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ zero_zero_nat))) & (((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = none_nat) <= (~ (B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2189_vebt__maxt_Osimps_I1_J)). 185.47/93.64 thf(32565,plain,((! [A:$o,B:$o]: (((A) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ one_one_nat))) & ((~ (A)) => (((B) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ zero_zero_nat))) & (((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = none_nat) | (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7292])). 185.47/93.64 thf(2453,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ B) <= (dvd_dvd_int @ A @ C)) <= (dvd_dvd_int @ A @ (minus_minus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4692_zdvd__zdiffD)). 185.47/93.64 thf(15863,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) | ~ (dvd_dvd_int @ A @ C) | ~ (dvd_dvd_int @ A @ (minus_minus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2453])). 185.47/93.64 thf(7506,axiom,((! [A:rat,B:nat]: ((power_power_rat @ (uminus_uminus_rat @ A) @ B) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (power_power_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5996_power__minus)). 185.47/93.64 thf(33305,plain,((! [A:rat,B:nat]: ((power_power_rat @ (uminus_uminus_rat @ A) @ B) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (power_power_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7506])). 185.47/93.64 thf(6730,axiom,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: ((A != B) <= ((size_s6755466524823107622T_VEBT @ A) != (size_s6755466524823107622T_VEBT @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_887_neq__if__length__neq)). 185.47/93.64 thf(30446,plain,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: (~ (A = B) | ((size_s6755466524823107622T_VEBT @ A) = (size_s6755466524823107622T_VEBT @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6730])). 185.47/93.64 thf(7725,axiom,(((size_s6755466524823107622T_VEBT @ treeList) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36__092_060open_062length_AtreeList_A_061_A2_A_094_An_092_060close_062)). 185.47/93.64 thf(33912,plain,(((size_s6755466524823107622T_VEBT @ treeList) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7725])). 185.47/93.64 thf(5800,axiom,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3157_times__int__code_I1_J)). 185.47/93.64 thf(27098,plain,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5800])). 185.47/93.64 thf(5025,axiom,((! [A:int,B:num]: ((ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ zero_zero_int) = ((ord_less_int @ A @ zero_zero_int) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4539_power__less__zero__eq__numeral)). 185.47/93.64 thf(24178,plain,((! [A:int,B:num]: ((ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ zero_zero_int) = ((ord_less_int @ A @ zero_zero_int) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5025])). 185.47/93.64 thf(7560,axiom,((! [A:complex]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5399_power2__minus)). 185.47/93.64 thf(33463,plain,((! [A:complex]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7560])). 185.47/93.64 thf(1222,axiom,((! [A:int,B:int,C:int]: ((A = (plus_plus_int @ B @ C)) => ((uminus_uminus_int @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5561_group__cancel_Oneg1)). 185.47/93.64 thf(11834,plain,((! [A:int,B:int,C:int]: ((A = (plus_plus_int @ B @ C)) => ((uminus_uminus_int @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222])). 185.47/93.64 thf(3942,axiom,((! [A:(nat > complex),B:complex,C:complex]: ((sums_complex @ A @ B) => (sums_complex @ (^ [D:nat]: (divide1717551699836669952omplex @ (A @ D) @ C)) @ (divide1717551699836669952omplex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8162_sums__divide)). 185.47/93.64 thf(20662,plain,((! [A:(nat > complex),B:complex,C:complex]: ((sums_complex @ (A) @ B) => (sums_complex @ (^ [D:nat]: (divide1717551699836669952omplex @ (A @ D) @ C)) @ (divide1717551699836669952omplex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3942])). 185.47/93.64 thf(637,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ (ord_max_int @ A @ C) @ (ord_max_int @ B @ D)) <= (ord_less_eq_int @ C @ D)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3657_max_Omono)). 185.47/93.64 thf(9845,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ (ord_max_int @ A @ C) @ (ord_max_int @ B @ D)) | ~ (ord_less_eq_int @ C @ D) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[637])). 185.47/93.64 thf(2291,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ C @ zero_zero_rat) => ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) => (ord_less_eq_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ C @ B)))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2851_divide__left__mono__neg)). 185.47/93.64 thf(15335,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ C @ zero_zero_rat) => ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) => (ord_less_eq_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ C @ B)))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2291])). 185.47/93.64 thf(184,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (((cos_real @ (arccos @ A)) = A) & (ord_less_eq_real @ (arccos @ A) @ pi) & (ord_less_eq_real @ zero_zero_real @ (arccos @ A)))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8377_arccos)). 185.47/93.64 thf(8325,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (((cos_real @ (arccos @ A)) = A) & (ord_less_eq_real @ (arccos @ A) @ pi) & (ord_less_eq_real @ zero_zero_real @ (arccos @ A)))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 185.47/93.64 thf(1323,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ (modulo_modulo_int @ B @ C)) @ C) = (modulo_modulo_int @ (plus_plus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1989_mod__add__right__eq)). 185.47/93.64 thf(12141,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ (modulo_modulo_int @ B @ C)) @ C) = (modulo_modulo_int @ (plus_plus_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323])). 185.47/93.64 thf(2582,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)) <= (ord_less_rat @ C @ D)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_add__le__less__mono)). 185.47/93.64 thf(16304,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)) | ~ (ord_less_rat @ C @ D) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2582])). 185.47/93.64 thf(2742,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ A @ B) = (ord_less_rat @ C @ D)) <= ((minus_minus_rat @ A @ B) = (minus_minus_rat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_704_diff__eq__diff__less)). 185.47/93.64 thf(16849,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ A @ B) = (ord_less_rat @ C @ D)) | ~ ((minus_minus_rat @ A @ B) = (minus_minus_rat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2742])). 185.47/93.64 thf(5880,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_less__irrefl__nat)). 185.47/93.64 thf(27460,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5880])). 185.47/93.64 thf(1126,axiom,((! [A:int,B:int]: ((((modulo_modulo_int @ A @ B) = zero_zero_int) => ((modulo_modulo_int @ (uminus_uminus_int @ A) @ B) = zero_zero_int)) & (((modulo_modulo_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ B @ (modulo_modulo_int @ A @ B))) <= ((modulo_modulo_int @ A @ B) != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6037_zmod__zminus1__eq__if)). 185.47/93.64 thf(11542,plain,((! [A:int,B:int]: ((((modulo_modulo_int @ A @ B) = zero_zero_int) => ((modulo_modulo_int @ (uminus_uminus_int @ A) @ B) = zero_zero_int)) & (((modulo_modulo_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ B @ (modulo_modulo_int @ A @ B))) | ((modulo_modulo_int @ A @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126])). 185.47/93.64 thf(4779,axiom,((! [A:int]: (((plus_plus_int @ A @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = zero_zero_int) <= ((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2515_bits__stable__imp__add__self)). 185.47/93.64 thf(23356,plain,((! [A:int]: (((plus_plus_int @ A @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = zero_zero_int) | ~ ((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4779])). 185.47/93.64 thf(605,axiom,((! [A:int,B:num]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (numeral_numeral_int @ B)) = (ord_less_eq_int @ A @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7073_of__int__le__numeral__iff)). 185.47/93.64 thf(9746,plain,((! [A:int,B:num]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (numeral_numeral_int @ B)) = (ord_less_eq_int @ A @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[605])). 185.47/93.64 thf(6100,axiom,((! [A:rat,B:rat]: ((A = (uminus_uminus_rat @ B)) = (B = (uminus_uminus_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5499_equation__minus__iff)). 185.47/93.64 thf(28201,plain,((! [A:rat,B:rat]: ((A = (uminus_uminus_rat @ B)) = (B = (uminus_uminus_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6100])). 185.47/93.64 thf(1862,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2624_add__neg__nonpos)). 185.47/93.64 thf(13970,plain,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1862])). 185.47/93.64 thf(1637,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ B @ A)) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1528_add__cancel__right__left)). 185.47/93.64 thf(13179,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ B @ A)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637])). 185.47/93.64 thf(3012,axiom,((plus_plus_real = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_add_Ocommute)). 185.47/93.64 thf(17710,plain,(((plus_plus_real) = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3012])). 185.47/93.64 thf(7643,axiom,((ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28__C4_Ohyps_C_I10_J)). 185.47/93.64 thf(33690,plain,((ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7643])). 185.47/93.64 thf(3973,axiom,((! [A:real,B:real]: ((? [C:real]: ((ord_less_eq_real @ C @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) & (A = (cos_real @ C)) & (B = (sin_real @ C)) & (ord_less_eq_real @ zero_zero_real @ C))) <= ((plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7889_sincos__total__2pi__le)). 185.47/93.64 thf(20752,plain,((! [A:real,B:real]: (? [C:real]: ((ord_less_eq_real @ C @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) & (A = (cos_real @ C)) & (B = (sin_real @ C)) & (ord_less_eq_real @ zero_zero_real @ C)) | ~ ((plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3973])). 185.47/93.64 thf(806,axiom,((! [A:(nat > int),B:nat,C:nat,D:nat]: ((groups705719431365010083at_int @ A @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ C) @ (plus_plus_nat @ D @ C))) = (groups705719431365010083at_int @ (^ [E:nat]: (A @ (plus_plus_nat @ E @ C))) @ (set_or1269000886237332187st_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8792_prod_Oshift__bounds__cl__nat__ivl)). 185.47/93.64 thf(10474,plain,((! [A:(nat > int),B:nat,C:nat,D:nat]: ((groups705719431365010083at_int @ (A) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ C) @ (plus_plus_nat @ D @ C))) = (groups705719431365010083at_int @ (^ [E:nat]: (A @ (plus_plus_nat @ E @ C))) @ (set_or1269000886237332187st_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[806])). 185.47/93.64 thf(4191,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((plus_plus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ D)) = (plus_plus_rat @ (times_times_rat @ A @ D) @ (times_times_rat @ C @ B))) = ((A = C) | (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6286_crossproduct__eq)). 185.47/93.64 thf(21422,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((plus_plus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ D)) = (plus_plus_rat @ (times_times_rat @ A @ D) @ (times_times_rat @ C @ B))) = ((A = C) | (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4191])). 185.47/93.64 thf(1842,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_795_diff__le__eq)). 185.47/93.64 thf(13915,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_eq_real @ A @ (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842])). 185.47/93.64 thf(4905,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ (comm_s4028243227959126397er_rat @ A @ B)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8435_pochhammer__pos)). 185.47/93.64 thf(23777,plain,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ (comm_s4028243227959126397er_rat @ A @ B)) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4905])). 185.47/93.64 thf(3372,axiom,((! [A:int,B:int]: (((((modulo_modulo_int @ B @ A) != zero_zero_int) => ((divide_divide_int @ (uminus_uminus_int @ B) @ A) = (minus_minus_int @ (uminus_uminus_int @ (divide_divide_int @ B @ A)) @ one_one_int))) & (((modulo_modulo_int @ B @ A) = zero_zero_int) => ((divide_divide_int @ (uminus_uminus_int @ B) @ A) = (uminus_uminus_int @ (divide_divide_int @ B @ A))))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6254_zdiv__zminus1__eq__if)). 185.47/93.64 thf(18834,plain,((! [A:int,B:int]: ((((~ ((modulo_modulo_int @ B @ A) = zero_zero_int)) => ((divide_divide_int @ (uminus_uminus_int @ B) @ A) = (minus_minus_int @ (uminus_uminus_int @ (divide_divide_int @ B @ A)) @ one_one_int))) & (((modulo_modulo_int @ B @ A) = zero_zero_int) => ((divide_divide_int @ (uminus_uminus_int @ B) @ A) = (uminus_uminus_int @ (divide_divide_int @ B @ A))))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3372])). 185.47/93.64 thf(6015,axiom,((! [A:int,B:int]: ((((A = B) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)) <= ((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2940_power2__eq__imp__eq)). 185.47/93.64 thf(27942,plain,((! [A:int,B:int]: ((A = B) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ ((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6015])). 185.47/93.64 thf(2476,axiom,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) = ((plus_plus_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5743_neg__eq__iff__add__eq__0)). 185.47/93.64 thf(15931,plain,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) = ((plus_plus_real @ A @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2476])). 185.47/93.64 thf(3057,axiom,((semiri1406184849735516958ct_int = (^ [A:nat]: (semiri1314217659103216013at_int @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8330_fact__code)). 185.47/93.64 thf(17856,plain,(((semiri1406184849735516958ct_int) = (^ [A:nat]: (semiri1314217659103216013at_int @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3057])). 185.47/93.64 thf(4943,axiom,((! [A:nat,B:int]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_int @ (uminus_uminus_int @ B) @ A) = (power_power_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5435_Parity_Oring__1__class_Opower__minus__even)). 185.47/93.64 thf(23917,plain,((! [A:nat,B:int]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_int @ (uminus_uminus_int @ B) @ A) = (power_power_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4943])). 185.47/93.64 thf(6932,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((A = B) | (A = C)) => (((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_insert__simp__mima)). 185.47/93.64 thf(31239,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((A = B) | (A = C)) => (((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F)) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6932])). 185.47/93.64 thf(5161,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_diff__right__commute)). 185.47/93.64 thf(24755,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5161])). 185.47/93.64 thf(6079,axiom,((! [A:nat]: ((power_power_real @ one_one_real @ A) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_power__one)). 185.47/93.64 thf(28133,plain,((! [A:nat]: ((power_power_real @ one_one_real @ A) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6079])). 185.47/93.64 thf(5102,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_ab__semigroup__mult__class_Omult__ac_I1_J)). 185.47/93.64 thf(24494,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5102])). 185.47/93.64 thf(2430,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (exp_complex @ A) @ (exp_complex @ B)) = (exp_complex @ (plus_plus_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8170_mult__exp__exp)). 185.47/93.64 thf(15776,plain,((! [A:complex,B:complex]: ((times_times_complex @ (exp_complex @ A) @ (exp_complex @ B)) = (exp_complex @ (plus_plus_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2430])). 185.47/93.64 thf(7547,axiom,((nat_triangle = (^ [A:nat]: (divide_divide_nat @ (times_times_nat @ A @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4416_triangle__def)). 185.47/93.64 thf(33426,plain,(((nat_triangle) = (^ [A:nat]: (divide_divide_nat @ (times_times_nat @ A @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7547])). 185.47/93.64 thf(1145,axiom,((! [A:real,B:real]: ((A = (uminus_uminus_real @ B)) = ((plus_plus_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5738_eq__neg__iff__add__eq__0)). 185.47/93.64 thf(11613,plain,((! [A:real,B:real]: ((A = (uminus_uminus_real @ B)) = ((plus_plus_real @ A @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145])). 185.47/93.64 thf(1871,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ B) => (ord_less_eq_int @ (uminus_uminus_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6515_abs__le__D2)). 185.47/93.64 thf(13997,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ B) => (ord_less_eq_int @ (uminus_uminus_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1871])). 185.47/93.64 thf(4686,axiom,((vEBT_VEBT_min_in_set = (^ [A:set_nat,B:nat]: ((member_nat @ B @ A) & ! [C:nat]: ((ord_less_eq_nat @ B @ C) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_min__in__set__def)). 185.47/93.64 thf(23019,plain,(((vEBT_VEBT_min_in_set) = (^ [A:set_nat,B:nat]: ((member_nat @ B @ A) & ! [C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4686])). 185.47/93.64 thf(3205,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ (times_times_int @ A @ B) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4470_unit__prod)). 185.47/93.64 thf(18321,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ (times_times_int @ A @ B) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3205])). 185.47/93.64 thf(824,axiom,(((zero_n2684676970156552555ol_int @ ($true)) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5122_of__bool__eq_I2_J)). 185.47/93.64 thf(10545,plain,(((zero_n2684676970156552555ol_int @ ($true)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[824])). 185.47/93.64 thf(3427,axiom,((! [A:int,B:int,C:nat,D:nat]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ D)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4799_dvd__power__le)). 185.47/93.64 thf(19012,plain,((! [A:int,B:int,C:nat,D:nat]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ D)) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3427])). 185.47/93.64 thf(3,axiom,((! [A:nat,B:(nat > int),C:int,D:nat]: (((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ (groups3539618377306564664at_int @ B @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ C))) <= (! [E:nat]: ((ord_less_eq_int @ (B @ E) @ C) <= (ord_less_nat @ E @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7621_real__sum__nat__ivl__bounded2)). 185.47/93.64 thf(7734,plain,((! [A:nat,B:(nat > int),C:int,D:nat]: (((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ (groups3539618377306564664at_int @ (B) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ C))) | ~ (! [E:nat]: ((ord_less_eq_int @ (B @ E) @ C) | ~ (ord_less_nat @ E @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 185.47/93.64 thf(7091,axiom,(((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ one_one_real)) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5281_diff__numeral__special_I12_J)). 185.47/93.64 thf(31872,plain,(((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ one_one_real)) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7091])). 185.47/93.64 thf(7594,axiom,((! [A:real]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_power2__eq__square)). 185.47/93.64 thf(33558,plain,((! [A:real]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7594])). 185.47/93.64 thf(2926,axiom,((! [A:nat,B:complex]: ((exp_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ A) @ B)) = (power_power_complex @ (exp_complex @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8197_exp__of__nat__mult)). 185.47/93.64 thf(17433,plain,((! [A:nat,B:complex]: ((exp_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ A) @ B)) = (power_power_complex @ (exp_complex @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2926])). 185.47/93.64 thf(4808,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ B @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4147_order__less__imp__not__less)). 185.47/93.64 thf(23443,plain,((! [A:int,B:int]: (~ (ord_less_int @ B @ A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4808])). 185.47/93.64 thf(7016,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ B))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2257_mult__mono)). 185.47/93.64 thf(31610,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7016])). 185.47/93.64 thf(1611,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ C)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_add__strict__right__mono)). 185.47/93.64 thf(13083,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ C)) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611])). 185.47/93.64 thf(3654,axiom,((bit_ri7919022796975470100ot_int = (^ [A:int]: (plus_plus_int @ (zero_n2684676970156552555ol_int @ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri7919022796975470100ot_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9546_not__int__rec)). 185.47/93.64 thf(19732,plain,(((bit_ri7919022796975470100ot_int) = (^ [A:int]: (plus_plus_int @ (zero_n2684676970156552555ol_int @ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri7919022796975470100ot_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3654])). 185.47/93.64 thf(912,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (ord_max_int @ A @ C) @ B) <= (ord_less_eq_int @ C @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3677_max_OboundedI)). 185.47/93.64 thf(10854,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (ord_max_int @ A @ C) @ B) | ~ (ord_less_eq_int @ C @ B) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[912])). 185.47/93.64 thf(6025,axiom,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1604_diff__self__eq__0)). 185.47/93.64 thf(27968,plain,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6025])). 185.47/93.64 thf(703,axiom,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ B) = (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5525_minus__less__iff)). 185.47/93.64 thf(10078,plain,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ B) = (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[703])). 185.47/93.64 thf(7282,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4288_linorder__not__less)). 185.47/93.64 thf(32533,plain,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7282])). 185.47/93.64 thf(5242,axiom,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (suc @ zero_zero_nat)) => (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4989_even__mod__4__div__2)). 185.47/93.64 thf(25018,plain,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (suc @ zero_zero_nat)) => (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5242])). 185.47/93.64 thf(6437,axiom,((! [A:real]: ((times_times_real @ A @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5192_mult__minus1__right)). 185.47/93.64 thf(29433,plain,((! [A:real]: ((times_times_real @ A @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6437])). 185.47/93.64 thf(3398,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (ord_max_nat @ B @ C)) = ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3696_le__max__iff__disj)). 185.47/93.64 thf(18925,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (ord_max_nat @ B @ C)) = ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3398])). 185.47/93.64 thf(6285,axiom,((! [A:complex,B:num]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6000_power__minus__Bit0)). 185.47/93.64 thf(28879,plain,((! [A:complex,B:num]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6285])). 185.47/93.64 thf(6379,axiom,((! [A:real,B:real]: ((minus_minus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5575_minus__diff__minus)). 185.47/93.64 thf(29210,plain,((! [A:real,B:real]: ((minus_minus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6379])). 185.47/93.64 thf(3339,axiom,((! [A:num,B:num,C:real]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5322_semiring__norm_I168_J)). 185.47/93.64 thf(18728,plain,((! [A:num,B:num,C:real]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3339])). 185.47/93.64 thf(3447,axiom,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((B @ D) != one_one_rat))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((C @ D) != one_one_rat))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((times_times_rat @ (B @ D) @ (C @ D)) != one_one_rat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3541_prod_Ofinite__Collect__op)). 185.47/93.64 thf(19069,plain,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((B @ D) = one_one_rat))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((C @ D) = one_one_rat))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((times_times_rat @ (B @ D) @ (C @ D)) = one_one_rat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3447])). 185.47/93.64 thf(6879,axiom,((! [A:nat,B:nat]: (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) != zero_zero_int) => ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2948_exp__add__not__zero__imp__right)). 185.47/93.64 thf(31065,plain,((! [A:nat,B:nat]: ((~ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) = zero_zero_int)) => (~ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6879])). 185.47/93.64 thf(6344,axiom,(((cos_real @ (numeral_numeral_real @ (bit0 @ one))) != zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7864_cos__two__neq__zero)). 185.47/93.64 thf(29091,plain,((~ ((cos_real @ (numeral_numeral_real @ (bit0 @ one))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6344])). 185.47/93.64 thf(1136,axiom,((! [A:real,B:real]: ((((divide_divide_real @ B @ A) = one_one_real) = (B = A)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2480_right__inverse__eq)). 185.47/93.64 thf(11588,plain,((! [A:real,B:real]: ((((divide_divide_real @ B @ A) = one_one_real) = (B = A)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136])). 185.47/93.64 thf(6616,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (plus_plus_nat @ (modulo_modulo_nat @ B @ A) @ A)) | ((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (modulo_modulo_nat @ B @ A)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2524_mod__double__modulus)). 185.47/93.64 thf(30058,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (plus_plus_nat @ (modulo_modulo_nat @ B @ A) @ A)) | ((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (modulo_modulo_nat @ B @ A)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6616])). 185.47/93.64 thf(337,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (((sin_real @ (arcsin @ A)) = A) & (ord_less_eq_real @ (arcsin @ A) @ pi) & (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A)))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8335_arcsin__pi)). 185.47/93.64 thf(8866,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (((sin_real @ (arcsin @ A)) = A) & (ord_less_eq_real @ (arcsin @ A) @ pi) & (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A)))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 185.47/93.64 thf(1994,axiom,((! [A:nat,B:(rat > nat),C:rat,D:rat]: (((ord_less_rat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) <= (! [E:rat,F:rat]: ((ord_less_nat @ (B @ E) @ (B @ F)) <= (ord_less_rat @ E @ F))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4081_ord__eq__less__subst)). 185.47/93.64 thf(14396,plain,((! [A:nat,B:(rat > nat),C:rat,D:rat]: (((ord_less_rat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:rat,F:rat]: ((ord_less_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_rat @ E @ F))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1994])). 185.47/93.64 thf(5684,axiom,((! [A:nat]: ((power_power_complex @ imaginary_unit @ (times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8981_i__even__power)). 185.47/93.64 thf(26648,plain,((! [A:nat]: ((power_power_complex @ imaginary_unit @ (times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5684])). 185.47/93.64 thf(164,axiom,((! [A:real,B:real]: (((ord_less_real @ A @ B) => ((ord_less_eq_real @ B @ one_one_real) => (ord_less_real @ (arcsin @ A) @ (arcsin @ B)))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8315_arcsin__less__arcsin)). 185.47/93.64 thf(8256,plain,((! [A:real,B:real]: (((ord_less_real @ A @ B) => ((ord_less_eq_real @ B @ one_one_real) => (ord_less_real @ (arcsin @ A) @ (arcsin @ B)))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 185.47/93.64 thf(2120,axiom,((! [A:int,B:int]: ((((divide_divide_int @ B @ A) = (plus_plus_int @ (divide_divide_int @ (minus_minus_int @ B @ A) @ A) @ one_one_int)) <= (ord_less_eq_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3046_div__pos__geq)). 185.47/93.64 thf(14790,plain,((! [A:int,B:int]: (((divide_divide_int @ B @ A) = (plus_plus_int @ (divide_divide_int @ (minus_minus_int @ B @ A) @ A) @ one_one_int)) | ~ (ord_less_eq_int @ A @ B) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2120])). 185.47/93.64 thf(959,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBT]: ((if_VEBT_VEBT @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T)). 185.47/93.64 thf(11024,plain,((! [A:vEBT_VEBT,B:vEBT_VEBT]: ((if_VEBT_VEBT @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[959])). 185.47/93.64 thf(1442,axiom,((! [A:num]: ~ (ord_less_eq_rat @ (numeral_numeral_rat @ A) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2195_not__numeral__le__zero)). 185.47/93.64 thf(12543,plain,((! [A:num]: ~ (ord_less_eq_rat @ (numeral_numeral_rat @ A) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442])). 185.47/93.64 thf(2586,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (? [B:nat]: ((ord_less_nat @ zero_zero_nat @ B) & (A = (semiri1314217659103216013at_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7305_zero__less__imp__eq__int)). 185.47/93.64 thf(16319,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (? [B:nat]: ((ord_less_nat @ zero_zero_nat @ B) & (A = (semiri1314217659103216013at_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2586])). 185.47/93.64 thf(1742,axiom,((! [A:num,B:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (divide_divide_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6407_zdiv__numeral__Bit1)). 185.47/93.64 thf(13571,plain,((! [A:num,B:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (divide_divide_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742])). 185.47/93.64 thf(6469,axiom,((ord_less_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_4186_less__le__not__le)). 185.47/93.64 thf(29557,plain,(((ord_less_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)],[6469])). 185.47/93.64 thf(6512,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_add__mult__distrib)). 185.47/93.64 thf(29708,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6512])). 185.47/93.64 thf(5717,axiom,((! [A:rat,B:nat]: ((ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ B)) = (((ord_less_eq_rat @ zero_zero_rat @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4969_zero__le__power__eq)). 185.47/93.64 thf(26760,plain,((! [A:rat,B:nat]: ((ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ B)) = (((ord_less_eq_rat @ zero_zero_rat @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5717])). 185.47/93.64 thf(1387,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (((ord_less_eq_real @ (divide_divide_real @ C @ B) @ (divide_divide_real @ C @ A)) <= (ord_less_real @ zero_zero_real @ (times_times_real @ B @ A))) <= (ord_less_eq_real @ zero_zero_real @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2836_divide__left__mono)). 185.47/93.64 thf(12356,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (divide_divide_real @ C @ B) @ (divide_divide_real @ C @ A)) | ~ (ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)) | ~ (ord_less_eq_real @ zero_zero_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387])). 185.47/93.64 thf(5198,axiom,((! [A:int]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ one)) @ A) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5976_mult__1s__ring__1_I1_J)). 185.47/93.64 thf(24867,plain,((! [A:int]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ one)) @ A) = (uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5198])). 185.47/93.64 thf(4034,axiom,((! [A:real]: (ord_less_eq_real @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A)) @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7630_of__int__round__le)). 185.47/93.64 thf(20941,plain,((! [A:real]: (ord_less_eq_real @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A)) @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4034])). 185.47/93.64 thf(6686,axiom,((! [A:real,B:num,C:num]: ((power_power_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (power_power_real @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_power__mult__numeral)). 185.47/93.64 thf(30286,plain,((! [A:real,B:num,C:num]: ((power_power_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (power_power_real @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6686])). 185.47/93.64 thf(1396,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ C) => (ord_less_int @ A @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4072_order__less__trans)). 185.47/93.64 thf(12388,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ C) => (ord_less_int @ A @ C)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396])). 185.47/93.64 thf(3184,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) => (ord_less_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C))) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_702_diff__strict__mono)). 185.47/93.64 thf(18252,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) => (ord_less_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C))) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3184])). 185.47/93.64 thf(2635,axiom,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide_divide_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7463_norm__divide)). 185.47/93.64 thf(16469,plain,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide_divide_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2635])). 185.47/93.64 thf(4238,axiom,((! [A:real,B:(nat > real),C:real]: ((A != zero_zero_real) => ((sums_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ (times_times_real @ A @ C)) = (sums_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8179_sums__mult__iff)). 185.47/93.64 thf(21560,plain,((! [A:real,B:(nat > real),C:real]: ((~ (A = zero_zero_real)) => ((sums_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ (times_times_real @ A @ C)) = (sums_real @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4238])). 185.47/93.64 thf(2611,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ B @ C) @ (divide_divide_rat @ A @ C)) <= (ord_less_eq_rat @ C @ zero_zero_rat)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2423_divide__right__mono__neg)). 185.47/93.64 thf(16398,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ B @ C) @ (divide_divide_rat @ A @ C)) | ~ (ord_less_eq_rat @ C @ zero_zero_rat) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2611])). 185.47/93.64 thf(6497,axiom,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1485_mult__zero__left)). 185.47/93.64 thf(29653,plain,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6497])). 185.47/93.64 thf(5551,axiom,((! [A:rat,B:num]: ((ord_less_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ zero_zero_rat) = ((ord_less_rat @ A @ zero_zero_rat) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4538_power__less__zero__eq__numeral)). 185.47/93.64 thf(26215,plain,((! [A:rat,B:num]: ((ord_less_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ zero_zero_rat) = ((ord_less_rat @ A @ zero_zero_rat) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5551])). 185.47/93.64 thf(4851,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ (bit_se725231765392027082nd_int @ C @ A) @ B) <= (ord_less_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9383_AND__upper2_H_H)). 185.47/93.64 thf(23578,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ (bit_se725231765392027082nd_int @ C @ A) @ B) | ~ (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4851])). 185.47/93.64 thf(2095,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7494_norm__triangle__le)). 185.47/93.64 thf(14716,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2095])). 185.47/93.64 thf(7094,axiom,((! [A:real]: ((minus_minus_real @ A @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1557_diff__self)). 185.47/93.64 thf(31882,plain,((! [A:real]: ((minus_minus_real @ A @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7094])). 185.47/93.64 thf(5318,axiom,((! [A:num,B:num,C:int]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (times_times_int @ (numeral_numeral_int @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5363_semiring__norm_I172_J)). 185.47/93.64 thf(25300,plain,((! [A:num,B:num,C:int]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (times_times_int @ (numeral_numeral_int @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5318])). 185.47/93.64 thf(6343,axiom,((! [A:option_nat,B:nat]: ((A != none_nat) <= (A = (some_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1165_option_OdiscI)). 185.47/93.64 thf(29086,plain,((! [A:option_nat,B:nat]: (~ (A = none_nat) | ~ (A = (some_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6343])). 185.47/93.64 thf(39,axiom,((! [A:real,B:nat]: ((((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)) = (divide_divide_real @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ B)) @ (minus_minus_real @ one_one_real @ A))) <= (A != one_one_real)) & (((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)) = (semiri5074537144036343181t_real @ B)) <= (A = one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7607_sum__gp__strict)). 185.47/93.64 thf(7856,plain,((! [A:real,B:nat]: ((((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)) = (divide_divide_real @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ B)) @ (minus_minus_real @ one_one_real @ A))) | (A = one_one_real)) & (((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)) = (semiri5074537144036343181t_real @ B)) | ~ (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 185.47/93.64 thf(2557,axiom,((ring_1_of_int_int = (^ [A:int]: (if_int @ (A = zero_zero_int) @ zero_zero_int @ (if_int @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_int @ (ring_1_of_int_int @ (uminus_uminus_int @ A))) @ (if_int @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (ring_1_of_int_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (ring_1_of_int_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6855_of__int__code__if)). 185.47/93.64 thf(16211,plain,(((ring_1_of_int_int) = (^ [A:int]: (if_int @ (A = zero_zero_int) @ zero_zero_int @ (if_int @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_int @ (ring_1_of_int_int @ (uminus_uminus_int @ A))) @ (if_int @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (ring_1_of_int_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (ring_1_of_int_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2557])). 185.47/93.64 thf(3864,axiom,(((neg_numeral_dbl_rat @ zero_zero_rat) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3823_dbl__simps_I2_J)). 185.47/93.64 thf(20409,plain,(((neg_numeral_dbl_rat @ zero_zero_rat) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3864])). 185.47/93.64 thf(7102,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_mult_Ocommute)). 185.47/93.64 thf(31907,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7102])). 185.47/93.64 thf(290,axiom,((! [A:set_nat,B:set_nat,C:(nat > real)]: (((ord_less_eq_set_nat @ B @ A) => ((groups6591440286371151544t_real @ C @ (minus_minus_set_nat @ A @ B)) = (minus_minus_real @ (groups6591440286371151544t_real @ C @ A) @ (groups6591440286371151544t_real @ C @ B)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6139_sum__diff)). 185.47/93.64 thf(8678,plain,((! [A:set_nat,B:set_nat,C:(nat > real)]: (((ord_less_eq_set_nat @ B @ A) => ((groups6591440286371151544t_real @ (C) @ (minus_minus_set_nat @ A @ B)) = (minus_minus_real @ (groups6591440286371151544t_real @ (C) @ A) @ (groups6591440286371151544t_real @ (C) @ B)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 185.47/93.64 thf(6953,axiom,((! [A:num,B:num,C:(num > nat),D:nat]: (((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4339_order__le__less__subst2)). 185.47/93.64 thf(31312,plain,((! [A:num,B:num,C:(num > nat),D:nat]: (((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6953])). 185.47/93.64 thf(426,axiom,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups6591440286371151544t_real @ (^ [D:nat]: (plus_plus_real @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6752_sum_Oin__pairs)). 185.47/93.64 thf(9148,plain,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups6591440286371151544t_real @ (^ [D:nat]: (plus_plus_real @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[426])). 185.47/93.64 thf(185,axiom,((! [A:real,B:(nat > real)]: (((summable_real @ B) => (? [C:nat]: ! [D:nat]: ((ord_less_real @ (real_V7735802525324610683m_real @ (suminf_real @ (^ [E:nat]: (B @ (plus_plus_nat @ E @ D))))) @ A) <= (ord_less_eq_nat @ C @ D)))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7748_suminf__exist__split)). 185.47/93.64 thf(8330,plain,((! [A:real,B:(nat > real)]: (((summable_real @ (B)) => (? [C:nat]: ! [D:nat]: ((ord_less_real @ (real_V7735802525324610683m_real @ (suminf_real @ (^ [E:nat]: (B @ (plus_plus_nat @ E @ D))))) @ A) | ~ (ord_less_eq_nat @ C @ D)))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 185.47/93.64 thf(5055,axiom,((! [A:nat,B:nat]: (((power_power_int @ (uminus_uminus_int @ one_one_int) @ (plus_plus_nat @ B @ A)) = (power_power_int @ (uminus_uminus_int @ one_one_int) @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6233_neg__one__power__add__eq__neg__one__power__diff)). 185.47/93.64 thf(24355,plain,((! [A:nat,B:nat]: (((power_power_int @ (uminus_uminus_int @ one_one_int) @ (plus_plus_nat @ B @ A)) = (power_power_int @ (uminus_uminus_int @ one_one_int) @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5055])). 185.47/93.64 thf(3545,axiom,((! [A:nat,B:nat]: ((semiri681578069525770553at_rat @ (power_power_nat @ A @ B)) = (power_power_rat @ (semiri681578069525770553at_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6961_of__nat__power)). 185.47/93.64 thf(19387,plain,((! [A:nat,B:nat]: ((semiri681578069525770553at_rat @ (power_power_nat @ A @ B)) = (power_power_rat @ (semiri681578069525770553at_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3545])). 185.47/93.64 thf(5253,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9416_or__minus__numerals_I6_J)). 185.47/93.64 thf(25050,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5253])). 185.47/93.64 thf(7440,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1648_less__add__same__cancel1)). 185.47/93.64 thf(33068,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7440])). 185.47/93.64 thf(6174,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat) = ((dvd_dvd_nat @ B @ one_one_nat) & (dvd_dvd_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4748_is__unit__mult__iff)). 185.47/93.64 thf(28509,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat) = ((dvd_dvd_nat @ B @ one_one_nat) & (dvd_dvd_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6174])). 185.47/93.64 thf(829,axiom,(((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ one_one_int)) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9512_and__not__numerals_I1_J)). 185.47/93.64 thf(10559,plain,(((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ one_one_int)) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[829])). 185.47/93.64 thf(7289,axiom,((! [A:int,B:int]: ((plus_plus_int @ A @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_left__add__twice)). 185.47/93.64 thf(32554,plain,((! [A:int,B:int]: ((plus_plus_int @ A @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7289])). 185.47/93.64 thf(3126,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (modulo_modulo_int @ B @ C)) <= (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4683_dvd__mod)). 185.47/93.64 thf(18072,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (modulo_modulo_int @ B @ C)) | ~ (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3126])). 185.47/93.64 thf(7032,axiom,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & (dvd_dvd_nat @ C @ B) & (((minus_minus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ B @ E)) = C) | ((minus_minus_nat @ (times_times_nat @ B @ D) @ (times_times_nat @ A @ E)) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4817_bezout1__nat)). 185.47/93.64 thf(31684,plain,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & (dvd_dvd_nat @ C @ B) & (((minus_minus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ B @ E)) = C) | ((minus_minus_nat @ (times_times_nat @ B @ D) @ (times_times_nat @ A @ E)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7032])). 185.47/93.64 thf(6375,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_eq_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1619_le__add__same__cancel2)). 185.47/93.64 thf(29199,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_eq_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6375])). 185.47/93.64 thf(5461,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9393_and__nat__numerals_I3_J)). 185.47/93.64 thf(25824,plain,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5461])). 185.47/93.64 thf(6712,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_vebt_maxt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = (some_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1246_vebt__maxt_Osimps_I3_J)). 185.47/93.64 thf(30365,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_vebt_maxt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = (some_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6712])). 185.47/93.64 thf(296,axiom,((! [A:complex,B:nat]: (((re @ (power_power_complex @ A @ B)) = (power_power_real @ (re @ A) @ B)) <= ((im @ A) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9664_Re__power__real)). 185.47/93.64 thf(8699,plain,((! [A:complex,B:nat]: (((re @ (power_power_complex @ A @ B)) = (power_power_real @ (re @ A) @ B)) | ~ ((im @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 185.47/93.64 thf(3521,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C)) = (ord_less_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_add__less__cancel__left)). 185.47/93.64 thf(19318,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C)) = (ord_less_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3521])). 185.47/93.64 thf(2072,axiom,((! [A:real,B:real,C:(real > rat),D:rat]: ((((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_rat @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))) => (ord_less_rat @ (C @ A) @ D))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4084_ord__less__eq__subst)). 185.47/93.64 thf(14644,plain,((! [A:real,B:real,C:(real > rat),D:rat]: ((((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))) => (ord_less_rat @ (C @ A) @ D))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2072])). 185.47/93.64 thf(3007,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2633_add__pos__nonneg)). 185.47/93.64 thf(17697,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3007])). 185.47/93.64 thf(3018,axiom,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ one_one_int @ (semiri1314217659103216013at_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7014_of__nat__Suc)). 185.47/93.64 thf(17727,plain,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ one_one_int @ (semiri1314217659103216013at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3018])). 185.47/93.64 thf(820,axiom,((! [A:(nat > real),B:real,C:real]: (((summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ C @ D)))) <= (ord_less_real @ (real_V7735802525324610683m_real @ C) @ (real_V7735802525324610683m_real @ B))) <= (summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7734_powser__inside)). 185.47/93.64 thf(10530,plain,((! [A:(nat > real),B:real,C:real]: ((summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ C @ D)))) | ~ (ord_less_real @ (real_V7735802525324610683m_real @ C) @ (real_V7735802525324610683m_real @ B)) | ~ (summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[820])). 185.47/93.64 thf(7257,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2116_not__gr0)). 185.47/93.64 thf(32456,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7257])). 185.47/93.64 thf(5142,axiom,((! [A:real]: (sums_real @ (^ [B:nat]: (times_times_real @ (divide_divide_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (semiri2265585572941072030t_real @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat))) @ (power_power_real @ A @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))) @ (sin_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8105_sin__paired)). 185.47/93.64 thf(24683,plain,((! [A:real]: (sums_real @ (^ [B:nat]: (times_times_real @ (divide_divide_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (semiri2265585572941072030t_real @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat))) @ (power_power_real @ A @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))) @ (sin_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5142])). 185.47/93.64 thf(6645,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_3285_bounded__Max__nat)). 185.47/93.64 thf(30149,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)],[6645])). 185.47/93.64 thf(1104,axiom,((! [A:nat,B:nat]: ~ (vEBT_V5719532721284313246member @ (vEBT_vebt_buildup @ A) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_buildup__nothing__in__leaf)). 185.47/93.64 thf(11481,plain,((! [A:nat,B:nat]: ~ (vEBT_V5719532721284313246member @ (vEBT_vebt_buildup @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104])). 185.47/93.64 thf(6137,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3094_verit__comp__simplify1_I1_J)). 185.47/93.64 thf(28345,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6137])). 185.47/93.64 thf(5953,axiom,(((^ [A:real]: (zero_zero_real)) = (times_times_real @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2147_lambda__zero)). 185.47/93.64 thf(27700,plain,(((^ [A:real]: (zero_zero_real)) = (times_times_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5953])). 185.47/93.64 thf(4690,axiom,((! [A:nat]: ((ord_less_int @ zero_zero_int @ (semiri1314217659103216013at_int @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7021_of__nat__0__less__iff)). 185.47/93.64 thf(23030,plain,((! [A:nat]: ((ord_less_int @ zero_zero_int @ (semiri1314217659103216013at_int @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4690])). 185.47/93.64 thf(3486,axiom,((! [A:rat,B:rat]: (ord_less_eq_rat @ (minus_minus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B)) @ (abs_abs_rat @ (minus_minus_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6496_abs__triangle__ineq2__sym)). 185.47/93.64 thf(19209,plain,((! [A:rat,B:rat]: (ord_less_eq_rat @ (minus_minus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B)) @ (abs_abs_rat @ (minus_minus_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3486])). 185.47/93.64 thf(2596,axiom,((! [A:nat,B:nat,C:nat]: (((semiri5074537144036343181t_real @ A) = (power_power_real @ (semiri5074537144036343181t_real @ B) @ C)) = (A = (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6949_of__nat__power__eq__of__nat__cancel__iff)). 185.47/93.64 thf(16351,plain,((! [A:nat,B:nat,C:nat]: (((semiri5074537144036343181t_real @ A) = (power_power_real @ (semiri5074537144036343181t_real @ B) @ C)) = (A = (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2596])). 185.47/93.64 thf(3158,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_real @ A @ (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_diff__less__eq)). 185.47/93.64 thf(18171,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (minus_minus_real @ A @ B) @ C) = (ord_less_real @ A @ (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3158])). 185.47/93.64 thf(6474,axiom,((! [A:num]: ((size_num @ (bit1 @ A)) = (plus_plus_nat @ (size_num @ A) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9212_num_Osize__gen_I3_J)). 185.47/93.64 thf(29572,plain,((! [A:num]: ((size_num @ (bit1 @ A)) = (plus_plus_nat @ (size_num @ A) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6474])). 185.47/93.64 thf(1380,axiom,((! [A:real]: ((ord_less_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A) => ((ord_less_real @ (sin_real @ A) @ zero_zero_real) <= (ord_less_real @ A @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7923_sin__less__zero)). 185.47/93.64 thf(12324,plain,((! [A:real]: ((ord_less_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A) => ((ord_less_real @ (sin_real @ A) @ zero_zero_real) | ~ (ord_less_real @ A @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380])). 185.47/93.64 thf(6235,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) => ((ord_less_eq_nat @ A @ C) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2609_mult__right__le__imp__le)). 185.47/93.64 thf(28714,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6235])). 185.47/93.64 thf(2144,axiom,((! [A:real,B:real,C:real]: ((divide_divide_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_745_diff__divide__distrib)). 185.47/93.64 thf(14871,plain,((! [A:real,B:real,C:real]: ((divide_divide_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2144])). 185.47/93.64 thf(1221,axiom,((! [A:complex,B:complex,C:nat]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ one_one_real) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C))) @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)))) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7521_norm__power__diff)). 185.47/93.64 thf(11831,plain,((! [A:complex,B:complex,C:nat]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ one_one_real) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C))) @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)))) | ~ (ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221])). 185.47/93.64 thf(5559,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_rat @ (times_times_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ B @ A))) @ (semiri773545260158071498ct_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8033_choose__dvd)). 185.47/93.64 thf(26240,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_rat @ (times_times_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ B @ A))) @ (semiri773545260158071498ct_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5559])). 185.47/93.64 thf(2938,axiom,((! [A:real,B:real]: ((exp_real @ (minus_minus_real @ A @ B)) = (divide_divide_real @ (exp_real @ A) @ (exp_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8175_exp__diff)). 185.47/93.64 thf(17475,plain,((! [A:real,B:real]: ((exp_real @ (minus_minus_real @ A @ B)) = (divide_divide_real @ (exp_real @ A) @ (exp_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2938])). 185.47/93.64 thf(2109,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_int @ A @ B)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4958_even__diff__iff)). 185.47/93.64 thf(14754,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_int @ A @ B)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2109])). 185.47/93.64 thf(1946,axiom,((! [A:rat,B:int]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A)))) @ (abs_abs_rat @ (minus_minus_rat @ A @ (ring_1_of_int_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7604_round__diff__minimal)). 185.47/93.64 thf(14245,plain,((! [A:rat,B:int]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A)))) @ (abs_abs_rat @ (minus_minus_rat @ A @ (ring_1_of_int_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1946])). 185.47/93.64 thf(57,axiom,((! [A:rat,B:nat]: ((A != one_one_rat) => ((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)) = (divide_divide_rat @ (minus_minus_rat @ (power_power_rat @ A @ B) @ one_one_rat) @ (minus_minus_rat @ A @ one_one_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7601_geometric__sum)). 185.47/93.64 thf(7918,plain,((! [A:rat,B:nat]: ((~ (A = one_one_rat)) => ((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)) = (divide_divide_rat @ (minus_minus_rat @ (power_power_rat @ A @ B) @ one_one_rat) @ (minus_minus_rat @ A @ one_one_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 185.47/93.64 thf(4346,axiom,((! [A:nat,B:nat]: (((ord_max_nat @ A @ B) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4402_max__absorb2)). 185.47/93.64 thf(21921,plain,((! [A:nat,B:nat]: (((ord_max_nat @ A @ B) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4346])). 185.47/93.64 thf(6184,axiom,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3852_order__class_Oorder__eq__iff)). 185.47/93.64 thf(28541,plain,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6184])). 185.47/93.64 thf(6796,axiom,(((neg_numeral_dbl_rat @ one_one_rat) = (numeral_numeral_rat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3806_dbl__simps_I3_J)). 185.47/93.64 thf(30722,plain,(((neg_numeral_dbl_rat @ one_one_rat) = (numeral_numeral_rat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6796])). 185.47/93.64 thf(4303,axiom,((! [A:int,B:nat]: (((nat2 @ A) = B) = (((A = (semiri1314217659103216013at_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)) & ((~ (ord_less_eq_int @ zero_zero_int @ A)) => (B = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9307_nat__eq__iff)). 185.47/93.64 thf(21752,plain,((! [A:int,B:nat]: (((nat2 @ A) = B) = (((A = (semiri1314217659103216013at_int @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ A)) & ((~ (ord_less_eq_int @ zero_zero_int @ A)) => (B = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4303])). 185.47/93.64 thf(3789,axiom,((! [A:int,B:int]: ((A = B) | (ord_less_int @ B @ A) | (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4132_linorder__less__linear)). 185.47/93.64 thf(20177,plain,((! [A:int,B:int]: ((A = B) | (ord_less_int @ B @ A) | (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3789])). 185.47/93.64 thf(5494,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (suc @ (suc @ A))) @ B) = (modulo_modulo_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6705_Suc__mod__eq__add3__mod)). 185.47/93.64 thf(26029,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (suc @ (suc @ A))) @ B) = (modulo_modulo_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5494])). 185.47/93.64 thf(3069,axiom,((! [A:real,B:real,C:real,D:real]: ((A != zero_zero_real) => ((B != zero_zero_real) => ((plus_plus_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ D @ B)) = (divide_divide_real @ (plus_plus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A)) @ (times_times_real @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2742_add__frac__eq)). 185.47/93.64 thf(17888,plain,((! [A:real,B:real,C:real,D:real]: ((~ (A = zero_zero_real)) => ((~ (B = zero_zero_real)) => ((plus_plus_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ D @ B)) = (divide_divide_real @ (plus_plus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A)) @ (times_times_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3069])). 185.47/93.64 thf(1676,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) <= (ord_less_nat @ C @ D)) <= (ord_less_real @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4101_order__less__subst1)). 185.47/93.64 thf(13346,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: (((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) | ~ (ord_less_nat @ C @ D) | ~ (ord_less_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676])). 185.47/93.64 thf(1298,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ one_one_rat @ (divide_divide_rat @ A @ B)) = (((ord_less_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ A @ B)) | ((ord_less_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2855_le__divide__eq__1)). 185.47/93.64 thf(12062,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ one_one_rat @ (divide_divide_rat @ A @ B)) = (((ord_less_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ A @ B)) | ((ord_less_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298])). 185.47/93.64 thf(5220,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) <= (ord_less_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8097_fact__less__mono__nat)). 185.47/93.64 thf(24934,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) | ~ (ord_less_nat @ A @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5220])). 185.47/93.64 thf(1030,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (minus_minus_nat @ A @ B) @ B) = (ord_max_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3769_nat__minus__add__max)). 185.47/93.64 thf(11250,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (minus_minus_nat @ A @ B) @ B) = (ord_max_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030])). 185.47/93.64 thf(813,axiom,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit1 @ one))))) = (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7899_sin__30)). 185.47/93.64 thf(10501,plain,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit1 @ one))))) = (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[813])). 185.47/93.64 thf(5843,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (~ (ord_less_num @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3282_minf_I7_J)). 185.47/93.64 thf(27344,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (~ (ord_less_num @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5843])). 185.47/93.64 thf(3294,axiom,((semiri5074537144036343181t_real = (^ [A:nat]: (if_real @ (A = zero_zero_nat) @ zero_zero_real @ (produc1703576794950452218t_real @ (^ [B:nat,C:nat]: (if_real @ (C = zero_zero_nat) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B)) @ (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B)) @ one_one_real))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7525_of__nat__code__if)). 185.47/93.64 thf(18585,plain,(((semiri5074537144036343181t_real) = (^ [A:nat]: (if_real @ (A = zero_zero_nat) @ zero_zero_real @ (produc1703576794950452218t_real @ (^ [B:nat,C:nat]: (if_real @ (C = zero_zero_nat) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B)) @ (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B)) @ one_one_real))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3294])). 185.47/93.64 thf(5330,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1092_le__imp__less__Suc)). 185.47/93.64 thf(25348,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5330])). 185.47/93.64 thf(7120,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_left__diff__distrib_H)). 185.47/93.64 thf(31960,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7120])). 185.47/93.64 thf(4836,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ B @ (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = (ord_less_rat @ (times_times_rat @ B @ A) @ (uminus_uminus_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6153_pos__less__minus__divide__eq)). 185.47/93.64 thf(23532,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ B @ (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = (ord_less_rat @ (times_times_rat @ B @ A) @ (uminus_uminus_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4836])). 185.47/93.64 thf(2379,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1520_add__cancel__left__right)). 185.47/93.64 thf(15605,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2379])). 185.47/93.64 thf(6564,axiom,((! [A:num,B:num,C:rat]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (times_times_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5365_semiring__norm_I172_J)). 185.47/93.64 thf(29884,plain,((! [A:num,B:num,C:rat]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (times_times_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6564])). 185.47/93.64 thf(7334,axiom,((! [A:real]: ((minus_minus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1553_diff__0__right)). 185.47/93.64 thf(32719,plain,((! [A:real]: ((minus_minus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7334])). 185.47/93.64 thf(4324,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (times_times_rat @ A @ B) @ zero_zero_rat) <= (ord_less_rat @ B @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2325_mult__pos__neg)). 185.47/93.64 thf(21856,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (times_times_rat @ A @ B) @ zero_zero_rat) | ~ (ord_less_rat @ B @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4324])). 185.47/93.64 thf(846,axiom,((! [A:int]: ~ (! [B:nat,C:int]: (A != (times_times_int @ (sgn_sgn_int @ C) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9220_int__sgnE)). 185.47/93.64 thf(10633,plain,((! [A:int]: ~ (! [B:nat,C:int]: ~ (A = (times_times_int @ (sgn_sgn_int @ C) @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[846])). 185.47/93.64 thf(2529,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_set_nat @ (set_or1269000886237332187st_nat @ A @ B) @ (set_or1269000886237332187st_nat @ C @ D)) = (((ord_less_eq_nat @ C @ A) & (ord_less_eq_nat @ B @ D)) | ~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3192_atLeastatMost__subset__iff)). 185.47/93.64 thf(16118,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_set_nat @ (set_or1269000886237332187st_nat @ A @ B) @ (set_or1269000886237332187st_nat @ C @ D)) = (((ord_less_eq_nat @ C @ A) & (ord_less_eq_nat @ B @ D)) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2529])). 185.47/93.64 thf(4285,axiom,((! [A:rat,B:rat,C:nat]: ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ (^ [D:nat]: (plus_plus_rat @ A @ (times_times_rat @ (semiri681578069525770553at_rat @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_rat @ (plus_plus_rat @ (semiri681578069525770553at_rat @ C) @ one_one_rat) @ (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ (times_times_rat @ (semiri681578069525770553at_rat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7341_double__arith__series)). 185.47/93.64 thf(21701,plain,((! [A:rat,B:rat,C:nat]: ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ (^ [D:nat]: (plus_plus_rat @ A @ (times_times_rat @ (semiri681578069525770553at_rat @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_rat @ (plus_plus_rat @ (semiri681578069525770553at_rat @ C) @ one_one_rat) @ (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ (times_times_rat @ (semiri681578069525770553at_rat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4285])). 185.47/93.64 thf(5507,axiom,((bit_se727722235901077358nd_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9404_and__nat__rec)). 185.47/93.64 thf(26072,plain,(((bit_se727722235901077358nd_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5507])). 185.47/93.64 thf(2546,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) <= (ord_less_int @ B @ zero_zero_int)) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2313_mult__neg__neg)). 185.47/93.64 thf(16179,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) | ~ (ord_less_int @ B @ zero_zero_int) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2546])). 185.47/93.64 thf(5731,axiom,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_right__diff__distrib__numeral)). 185.47/93.64 thf(26802,plain,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5731])). 185.47/93.64 thf(7042,axiom,((deg = (plus_plus_nat @ na @ m))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65__C4_Ohyps_C_I6_J)). 185.47/93.64 thf(31716,plain,((deg = (plus_plus_nat @ na @ m))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7042])). 185.47/93.64 thf(6306,axiom,((! [A:nat,B:nat,C:nat]: (((((divide_divide_nat @ B @ A) = C) = (B = (times_times_nat @ C @ A))) <= (dvd_dvd_nat @ A @ B)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4830_dvd__div__eq__mult)). 185.47/93.64 thf(28945,plain,((! [A:nat,B:nat,C:nat]: ((((divide_divide_nat @ B @ A) = C) = (B = (times_times_nat @ C @ A))) | ~ (dvd_dvd_nat @ A @ B) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6306])). 185.47/93.64 thf(4095,axiom,((! [A:num]: ((semiri1314217659103216013at_int @ (numeral_numeral_nat @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7239_int__ops_I3_J)). 185.47/93.64 thf(21124,plain,((! [A:num]: ((semiri1314217659103216013at_int @ (numeral_numeral_nat @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4095])). 185.47/93.64 thf(80,axiom,((finite_finite_nat = (^ [A:set_nat]: ? [B:nat]: (ord_less_eq_set_nat @ A @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7772_finite__nat__iff__bounded)). 185.47/93.64 thf(7993,plain,(((finite_finite_nat) = (^ [A:set_nat]: ? [B:nat]: (ord_less_eq_set_nat @ A @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 185.47/93.64 thf(2934,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (powr_real @ B @ A) @ (powr_real @ C @ A)) <= (ord_less_eq_real @ B @ C))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9087_powr__mono2)). 185.47/93.64 thf(17463,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (powr_real @ B @ A) @ (powr_real @ C @ A)) | ~ (ord_less_eq_real @ B @ C))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2934])). 185.47/93.64 thf(7465,axiom,((! [A:rat,B:rat,C:nat]: (((times_times_rat @ (power_power_rat @ A @ C) @ B) = (times_times_rat @ B @ (power_power_rat @ A @ C))) <= ((times_times_rat @ A @ B) = (times_times_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_power__commuting__commutes)). 185.47/93.64 thf(33162,plain,((! [A:rat,B:rat,C:nat]: (((times_times_rat @ (power_power_rat @ A @ C) @ B) = (times_times_rat @ B @ (power_power_rat @ A @ C))) | ~ ((times_times_rat @ A @ B) = (times_times_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7465])). 185.47/93.64 thf(7255,axiom,((! [A:int,B:nat,C:nat]: ((A != zero_zero_int) => (((ord_less_eq_nat @ B @ C) => ((divide_divide_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B)) = (power_power_int @ A @ (minus_minus_nat @ C @ B)))) & ((~ (ord_less_eq_nat @ B @ C)) => ((divide_divide_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B)) = (divide_divide_int @ one_one_int @ (power_power_int @ A @ (minus_minus_nat @ B @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2954_power__diff__power__eq)). 185.47/93.64 thf(32447,plain,((! [A:int,B:nat,C:nat]: ((~ (A = zero_zero_int)) => (((ord_less_eq_nat @ B @ C) => ((divide_divide_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B)) = (power_power_int @ A @ (minus_minus_nat @ C @ B)))) & ((~ (ord_less_eq_nat @ B @ C)) => ((divide_divide_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B)) = (divide_divide_int @ one_one_int @ (power_power_int @ A @ (minus_minus_nat @ B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7255])). 185.47/93.64 thf(266,axiom,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((! [D:nat]: (((C @ D) = zero_zero_complex) <= (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups2073611262835488442omplex @ C @ A) = (groups2073611262835488442omplex @ C @ B))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6084_sum_Omono__neutral__right)). 185.47/93.64 thf(8603,plain,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((! [D:nat]: (((C @ D) = zero_zero_complex) | ~ (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups2073611262835488442omplex @ (C) @ A) = (groups2073611262835488442omplex @ (C) @ B))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 185.47/93.64 thf(5400,axiom,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = ((B = C) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1500_mult__cancel__left)). 185.47/93.64 thf(25595,plain,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = ((B = C) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5400])). 185.47/93.64 thf(5928,axiom,((! [A:num,B:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ B)) = (times_times_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5756_numeral__times__minus__swap)). 185.47/93.64 thf(27624,plain,((! [A:num,B:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ B)) = (times_times_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5928])). 185.47/93.64 thf(1824,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((? [B:nat]: ((A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) <= ((sin_real @ A) = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7941_sin__zero__lemma)). 185.47/93.64 thf(13841,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (? [B:nat]: ((A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ ((sin_real @ A) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1824])). 185.47/93.64 thf(2439,axiom,((! [A:(nat > $o),B:nat]: (finite_finite_nat @ (collect_nat @ (^ [C:nat]: ((A @ C) & (ord_less_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3401_finite__M__bounded__by__nat)). 185.47/93.64 thf(15812,plain,((! [A:(nat > $o),B:nat]: (finite_finite_nat @ (collect_nat @ (^ [C:nat]: ((A @ C) & (ord_less_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2439])). 185.47/93.64 thf(6177,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2161824704523386999it_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) != (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4957_even__flip__bit__iff)). 185.47/93.64 thf(28518,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2161824704523386999it_nat @ A @ B)) = (~ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) = (A = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6177])). 185.47/93.64 thf(667,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((gbinomial_real @ B @ A) = (plus_plus_real @ (gbinomial_real @ (minus_minus_real @ B @ one_one_real) @ (minus_minus_nat @ A @ one_one_nat)) @ (gbinomial_real @ (minus_minus_real @ B @ one_one_real) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8583_gbinomial__reduce__nat)). 185.47/93.64 thf(9960,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((gbinomial_real @ B @ A) = (plus_plus_real @ (gbinomial_real @ (minus_minus_real @ B @ one_one_real) @ (minus_minus_nat @ A @ one_one_nat)) @ (gbinomial_real @ (minus_minus_real @ B @ one_one_real) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[667])). 185.47/93.64 thf(6196,axiom,((! [A:num]: ((abs_abs_Code_integer @ (numera6620942414471956472nteger @ A)) = (numera6620942414471956472nteger @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6332_abs__numeral)). 185.47/93.64 thf(28595,plain,((! [A:num]: ((abs_abs_Code_integer @ (numera6620942414471956472nteger @ A)) = (numera6620942414471956472nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6196])). 185.47/93.64 thf(4893,axiom,((semiri773545260158071498ct_rat = (^ [A:nat]: (semiri681578069525770553at_rat @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8331_fact__code)). 185.47/93.64 thf(23739,plain,(((semiri773545260158071498ct_rat) = (^ [A:nat]: (semiri681578069525770553at_rat @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4893])). 185.47/93.64 thf(4101,axiom,((! [A:rat,B:nat,C:nat]: (((ord_less_eq_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) = (ord_less_eq_nat @ B @ C)) <= (ord_less_rat @ one_one_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_power__increasing__iff)). 185.47/93.64 thf(21143,plain,((! [A:rat,B:nat,C:nat]: (((ord_less_eq_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) = (ord_less_eq_nat @ B @ C)) | ~ (ord_less_rat @ one_one_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4101])). 185.47/93.64 thf(6230,axiom,((! [A:nat,B:real,C:real]: ((((root @ A @ C) = B) <= ((power_power_real @ B @ A) = C)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9200_odd__real__root__unique)). 185.47/93.64 thf(28691,plain,((! [A:nat,B:real,C:real]: (((root @ A @ C) = B) | ~ ((power_power_real @ B @ A) = C) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6230])). 185.47/93.64 thf(5446,axiom,((! [A:nat]: ((times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A)) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5299_minus__one__mult__self)). 185.47/93.64 thf(25781,plain,((! [A:nat]: ((times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A)) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5446])). 185.47/93.64 thf(2079,axiom,((! [A:int]: ((? [B:nat]: (A = (semiri1314217659103216013at_int @ B))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7244_zero__le__imp__eq__int)). 185.47/93.64 thf(14669,plain,((! [A:int]: (? [B:nat]: (A = (semiri1314217659103216013at_int @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2079])). 185.47/93.64 thf(5897,axiom,((! [A:num,B:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ B)) = (times_times_int @ B @ (uminus_uminus_int @ (numeral_numeral_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5757_numeral__times__minus__swap)). 185.47/93.64 thf(27528,plain,((! [A:num,B:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ B)) = (times_times_int @ B @ (uminus_uminus_int @ (numeral_numeral_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5897])). 185.47/93.64 thf(6707,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_old_Onat_Oinject)). 185.47/93.64 thf(30350,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6707])). 185.47/93.64 thf(139,axiom,((! [A:real,B:real]: (((powr_real @ (inverse_inverse_real @ A) @ B) = (inverse_inverse_real @ (powr_real @ A @ B))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9101_inverse__powr)). 185.47/93.64 thf(8178,plain,((! [A:real,B:real]: (((powr_real @ (inverse_inverse_real @ A) @ B) = (inverse_inverse_real @ (powr_real @ A @ B))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 185.47/93.64 thf(4503,axiom,((! [A:complex,B:nat,C:nat]: (((comm_s2602460028002588243omplex @ A @ B) = zero_zero_complex) => ((ord_less_eq_nat @ B @ C) => ((comm_s2602460028002588243omplex @ A @ C) = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8438_pochhammer__eq__0__mono)). 185.47/93.64 thf(22412,plain,((! [A:complex,B:nat,C:nat]: (((comm_s2602460028002588243omplex @ A @ B) = zero_zero_complex) => ((ord_less_eq_nat @ B @ C) => ((comm_s2602460028002588243omplex @ A @ C) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4503])). 185.47/93.64 thf(3077,axiom,((! [A:rat,B:rat]: ((A != B) = ((ord_less_rat @ B @ A) | (ord_less_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4059_linorder__neq__iff)). 185.47/93.64 thf(17911,plain,((! [A:rat,B:rat]: ((~ (A = B)) = ((ord_less_rat @ B @ A) | (ord_less_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3077])). 185.47/93.64 thf(3278,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ C)) = (((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_eq_real @ A @ zero_zero_real) <= (~ (ord_less_real @ C @ zero_zero_real))) & ((ord_less_real @ C @ zero_zero_real) => (ord_less_eq_real @ B @ (times_times_real @ A @ C))))) & ((ord_less_eq_real @ (times_times_real @ A @ C) @ B) <= (ord_less_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2834_le__divide__eq)). 185.47/93.64 thf(18539,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ C)) = (((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_eq_real @ A @ zero_zero_real) | (ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ C @ zero_zero_real) => (ord_less_eq_real @ B @ (times_times_real @ A @ C))))) & ((ord_less_eq_real @ (times_times_real @ A @ C) @ B) | ~ (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3278])). 185.47/93.64 thf(6034,axiom,((! [A:rat,B:rat]: (((times_times_rat @ A @ B) = A) = ((A = zero_zero_rat) | (B = one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1667_mult__cancel__left2)). 185.47/93.64 thf(27996,plain,((! [A:rat,B:rat]: (((times_times_rat @ A @ B) = A) = ((A = zero_zero_rat) | (B = one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6034])). 185.47/93.64 thf(5030,axiom,((! [A:num,B:num,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5357_semiring__norm_I171_J)). 185.47/93.64 thf(24192,plain,((! [A:num,B:num,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5030])). 185.47/93.64 thf(7088,axiom,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_762_le__numeral__extra_I4_J)). 185.47/93.64 thf(31864,plain,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7088])). 185.47/93.64 thf(7630,axiom,(((code_integer_of_num @ (bit0 @ one)) = (numera6620942414471956472nteger @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9624_integer__of__num__triv_I2_J)). 185.47/93.64 thf(33659,plain,(((code_integer_of_num @ (bit0 @ one)) = (numera6620942414471956472nteger @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7630])). 185.47/93.64 thf(4806,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => (((divide_divide_int @ B @ A) = (minus_minus_int @ (uminus_uminus_int @ (divide_divide_int @ (abs_abs_int @ B) @ (abs_abs_int @ A))) @ (zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ A @ B))))) <= ((sgn_sgn_int @ B) != (sgn_sgn_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9237_div__noneq__sgn__abs)). 185.47/93.64 thf(23436,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => (((divide_divide_int @ B @ A) = (minus_minus_int @ (uminus_uminus_int @ (divide_divide_int @ (abs_abs_int @ B) @ (abs_abs_int @ A))) @ (zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ A @ B))))) | ((sgn_sgn_int @ B) = (sgn_sgn_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4806])). 185.47/93.64 thf(510,axiom,((! [A:real,B:real]: (((((tan_real @ A) = B) => ((arctan @ B) = A)) <= (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8073_arctan__unique)). 185.47/93.64 thf(9447,plain,((! [A:real,B:real]: ((((tan_real @ A) = B) => ((arctan @ B) = A)) | ~ (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[510])). 185.47/93.64 thf(2815,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ B @ (divide_divide_rat @ C @ A)) = (ord_less_rat @ (times_times_rat @ B @ A) @ C)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2706_pos__less__divide__eq)). 185.47/93.64 thf(17075,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ B @ (divide_divide_rat @ C @ A)) = (ord_less_rat @ (times_times_rat @ B @ A) @ C)) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2815])). 185.47/93.64 thf(3943,axiom,((! [A:real,B:real]: ((B != A) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4138_order__less__imp__not__eq2)). 185.47/93.64 thf(20665,plain,((! [A:real,B:real]: (~ (B = A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3943])). 185.47/93.64 thf(7039,axiom,((! [A:complex]: (((csqrt @ A) = one_one_complex) = (A = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9156_csqrt__eq__1)). 185.47/93.64 thf(31706,plain,((! [A:complex]: (((csqrt @ A) = one_one_complex) = (A = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7039])). 185.47/93.64 thf(842,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => (((log @ B @ C) = (divide_divide_real @ (log @ A @ C) @ (log @ A @ B))) <= (A != one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9041_log__base__change)). 185.47/93.64 thf(10619,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => (((log @ B @ C) = (divide_divide_real @ (log @ A @ C) @ (log @ A @ B))) | (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[842])). 185.47/93.64 thf(2153,axiom,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (times_times_nat @ A @ B)) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6915_of__nat__mult)). 185.47/93.64 thf(14909,plain,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (times_times_nat @ A @ B)) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2153])). 185.47/93.64 thf(5216,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_less__not__refl)). 185.47/93.64 thf(24922,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5216])). 185.47/93.64 thf(1664,axiom,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ A @ B) @ C) @ (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (ord_less_eq_rat @ C @ (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1229_ordered__ring__class_Ole__add__iff2)). 185.47/93.64 thf(13313,plain,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ A @ B) @ C) @ (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (ord_less_eq_rat @ C @ (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664])). 185.47/93.64 thf(939,axiom,((! [A:real,B:nat]: ? [C:real]: ((ord_less_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A)) & ((cos_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (cos_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (cos_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7948_Maclaurin__cos__expansion)). 185.47/93.64 thf(10955,plain,((! [A:real,B:nat]: ? [C:real]: ((ord_less_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A)) & ((cos_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (cos_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (cos_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[939])). 185.47/93.64 thf(2590,axiom,((! [A:real]: ? [B:nat]: (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7432_real__arch__simple)). 185.47/93.64 thf(16332,plain,((! [A:real]: ? [B:nat]: (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2590])). 185.47/93.64 thf(5938,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (times_times_rat @ B @ C)) = (times_times_rat @ B @ (times_times_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_mult_Oleft__commute)). 185.47/93.64 thf(27655,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (times_times_rat @ B @ C)) = (times_times_rat @ B @ (times_times_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5938])). 185.47/93.64 thf(5286,axiom,((! [A:int,B:int]: (((uminus_uminus_int @ A) = B) = ((uminus_uminus_int @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5492_minus__equation__iff)). 185.47/93.64 thf(25208,plain,((! [A:int,B:int]: (((uminus_uminus_int @ A) = B) = ((uminus_uminus_int @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5286])). 185.47/93.64 thf(5949,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ one_one_nat) => ((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ C @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1865_power__strict__decreasing__iff)). 185.47/93.64 thf(27687,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ one_one_nat) => ((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ C @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5949])). 185.47/93.64 thf(5762,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1088_Suc__le__lessD)). 185.47/93.64 thf(26897,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5762])). 185.47/93.64 thf(675,axiom,((! [A:real]: (ord_less_real @ A @ (plus_plus_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9112_real__of__int__floor__add__one__gt)). 185.47/93.64 thf(9989,plain,((! [A:real]: (ord_less_real @ A @ (plus_plus_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[675])). 185.47/93.64 thf(3794,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo2584398358068434914at_nat @ (^ [D:nat]: (plus_plus_nat @ (A @ D))) @ B @ C @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8323_sum__atLeastAtMost__code)). 185.47/93.64 thf(20191,plain,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo2584398358068434914at_nat @ (^ [D:nat]: (plus_plus_nat @ (A @ D))) @ B @ C @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3794])). 185.47/93.64 thf(7455,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ (power_power_real @ A @ B) @ zero_zero_real) = ((((ord_less_eq_real @ A @ zero_zero_real) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ((A = zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4986_power__le__zero__eq)). 185.47/93.64 thf(33110,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ (power_power_real @ A @ B) @ zero_zero_real) = ((((ord_less_eq_real @ A @ zero_zero_real) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ((A = zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7455])). 185.47/93.64 thf(3760,axiom,((! [A:complex]: ((power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_complex @ one_one_complex @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7835_cos__squared__eq)). 185.47/93.64 thf(20070,plain,((! [A:complex]: ((power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_complex @ one_one_complex @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3760])). 185.47/93.64 thf(4062,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = C) = (((A = (times_times_complex @ C @ B)) <= (B != zero_zero_complex)) & ((C = zero_zero_complex) <= (B = zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2473_divide__eq__eq)). 185.47/93.64 thf(21017,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = C) = (((A = (times_times_complex @ C @ B)) | (B = zero_zero_complex)) & ((C = zero_zero_complex) | ~ (B = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4062])). 185.47/93.64 thf(932,axiom,((minus_minus_complex = (^ [A:complex,B:complex]: (complex2 @ (minus_minus_real @ (re @ A) @ (re @ B)) @ (minus_minus_real @ (im @ A) @ (im @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9682_minus__complex_Ocode)). 185.47/93.64 thf(10935,plain,(((minus_minus_complex) = (^ [A:complex,B:complex]: (complex2 @ (minus_minus_real @ (re @ A) @ (re @ B)) @ (minus_minus_real @ (im @ A) @ (im @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[932])). 185.47/93.64 thf(7269,axiom,((ord_less_num = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & ~ (ord_less_eq_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4220_order_Ostrict__iff__not)). 185.47/93.64 thf(32494,plain,(((ord_less_num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & ~ (ord_less_eq_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7269])). 185.47/93.64 thf(2473,axiom,((! [A:nat,B:nat]: ((bot_bot_set_nat = (set_or1269000886237332187st_nat @ A @ B)) = (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3198_atLeastatMost__empty__iff2)). 185.47/93.64 thf(15922,plain,((! [A:nat,B:nat]: ((bot_bot_set_nat = (set_or1269000886237332187st_nat @ A @ B)) = (~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2473])). 185.47/93.64 thf(3346,axiom,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (abs_abs_rat @ A)) = (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6373_zero__less__abs__iff)). 185.47/93.64 thf(18760,plain,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (abs_abs_rat @ A)) = (~ (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3346])). 185.47/93.64 thf(2843,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => (~ ((! [C:int]: (B != (times_times_int @ A @ C))) <= (A != zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4822_unit__dvdE)). 185.47/93.64 thf(17168,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => (~ (! [C:int]: ~ (B = (times_times_int @ A @ C)) | (A = zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2843])). 185.47/93.64 thf(6071,axiom,((! [A:num,B:num,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (times_times_nat @ (numeral_numeral_nat @ B) @ C)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_mult__numeral__left__semiring__numeral)). 185.47/93.64 thf(28106,plain,((! [A:num,B:num,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (times_times_nat @ (numeral_numeral_nat @ B) @ C)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6071])). 185.47/93.64 thf(2298,axiom,((semiri1314217659103216013at_int = (^ [A:nat]: (abs_Integ @ (product_Pair_nat_nat @ A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9817_int__def)). 185.47/93.64 thf(15353,plain,(((semiri1314217659103216013at_int) = (^ [A:nat]: (abs_Integ @ (product_Pair_nat_nat @ A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2298])). 185.47/93.64 thf(241,axiom,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit1 @ one)))) = (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7904_cos__60)). 185.47/93.64 thf(8500,plain,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit1 @ one)))) = (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 185.47/93.64 thf(6942,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((A = B) = (C = D)) <= ((minus_minus_rat @ A @ B) = (minus_minus_rat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_diff__eq__diff__eq)). 185.47/93.64 thf(31276,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((A = B) = (C = D)) | ~ ((minus_minus_rat @ A @ B) = (minus_minus_rat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6942])). 185.47/93.64 thf(4341,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ (divide_divide_rat @ B @ A) @ C) = (ord_less_rat @ (times_times_rat @ C @ A) @ B)) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2700_neg__divide__less__eq)). 185.47/93.64 thf(21903,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ (divide_divide_rat @ B @ A) @ C) = (ord_less_rat @ (times_times_rat @ C @ A) @ B)) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4341])). 185.47/93.64 thf(1420,axiom,((! [A:real]: (ord_less_eq_real @ (sin_real @ A) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7831_sin__le__one)). 185.47/93.64 thf(12475,plain,((! [A:real]: (ord_less_eq_real @ (sin_real @ A) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1420])). 185.47/93.64 thf(3120,axiom,((finite_finite_nat = (^ [A:set_nat]: ? [B:nat]: (ord_less_eq_set_nat @ A @ (set_ord_atMost_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8793_finite__nat__iff__bounded__le)). 185.47/93.64 thf(18056,plain,(((finite_finite_nat) = (^ [A:set_nat]: ? [B:nat]: (ord_less_eq_set_nat @ A @ (set_ord_atMost_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3120])). 185.47/93.64 thf(761,axiom,((! [A:(complex > (complex > $o)),B:set_nat,C:(nat > complex),D:(nat > complex)]: ((((finite_finite_nat @ B) => ((A @ (groups6464643781859351333omplex @ C @ B) @ (groups6464643781859351333omplex @ D @ B)) <= (! [E:nat]: ((A @ (C @ E) @ (D @ E)) <= (member_nat @ E @ B))))) <= (! [E:complex,F:complex,G:complex,H:complex]: ((A @ (times_times_complex @ E @ F) @ (times_times_complex @ G @ H)) <= ((A @ E @ G) & (A @ F @ H))))) <= (A @ one_one_complex @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8804_prod_Orelated)). 185.47/93.64 thf(10305,plain,((! [A:(complex > (complex > $o)),B:set_nat,C:(nat > complex),D:(nat > complex)]: (((finite_finite_nat @ B) => ((A @ (groups6464643781859351333omplex @ (C) @ B) @ (groups6464643781859351333omplex @ (D) @ B)) | ~ (! [E:nat]: ((A @ (C @ E) @ (D @ E)) | ~ (member_nat @ E @ B))))) | ~ (! [E:complex,F:complex,G:complex,H:complex]: ((A @ (times_times_complex @ E @ F) @ (times_times_complex @ G @ H)) | ~ ((A @ E @ G) & (A @ F @ H)))) | ~ (A @ one_one_complex @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[761])). 185.47/93.64 thf(1268,axiom,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ A @ B) @ C) @ (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ A @ D) @ B) @ C) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1232_ordered__ring__class_Ole__add__iff1)). 185.47/93.64 thf(11976,plain,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ A @ B) @ C) @ (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ A @ D) @ B) @ C) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268])). 185.47/93.64 thf(6733,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_mult_Oassoc)). 185.47/93.64 thf(30456,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6733])). 185.47/93.64 thf(4483,axiom,((unique5026877609467782581ep_nat = (^ [A:num]: (produc2626176000494625587at_nat @ (^ [B:nat,C:nat]: (if_Pro6206227464963214023at_nat @ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ C) @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat) @ (minus_minus_nat @ C @ (numeral_numeral_nat @ A))) @ (product_Pair_nat_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7349_divmod__step__def)). 185.47/93.64 thf(22353,plain,(((unique5026877609467782581ep_nat) = (^ [A:num]: (produc2626176000494625587at_nat @ (^ [B:nat,C:nat]: (if_Pro6206227464963214023at_nat @ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ C) @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat) @ (minus_minus_nat @ C @ (numeral_numeral_nat @ A))) @ (product_Pair_nat_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4483])). 185.47/93.64 thf(1680,axiom,((! [A:complex]: (((sin_complex @ A) = zero_zero_complex) <= ((cos_complex @ A) = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7820_cos__one__sin__zero)). 185.47/93.64 thf(13360,plain,((! [A:complex]: (((sin_complex @ A) = zero_zero_complex) | ~ ((cos_complex @ A) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680])). 185.47/93.64 thf(412,axiom,((! [A:set_nat,B:(nat > real),C:(nat > $o)]: (((groups129246275422532515t_real @ B @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & (C @ D))))) = (groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (C @ D) @ (B @ D) @ one_one_real)) @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8779_prod_Ointer__filter)). 185.47/93.64 thf(9099,plain,((! [A:set_nat,B:(nat > real),C:(nat > $o)]: (((groups129246275422532515t_real @ (B) @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & (C @ D))))) = (groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (C @ D) @ (B @ D) @ one_one_real)) @ A)) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])). 185.47/93.64 thf(1791,axiom,(((abs_abs_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = one_one_Code_integer)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6382_abs__neg__one)). 185.47/93.64 thf(13732,plain,(((abs_abs_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1791])). 185.47/93.64 thf(1723,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_max_nat @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3568_max_Oabsorb1)). 185.47/93.64 thf(13511,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_max_nat @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723])). 185.47/93.64 thf(3401,axiom,((! [A:nat,B:nat,C:(nat > nat)]: (((groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_nat @ (C @ A) @ (groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6656_sum_OatLeast__Suc__atMost)). 185.47/93.64 thf(18933,plain,((! [A:nat,B:nat,C:(nat > nat)]: (((groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_nat @ (C @ A) @ (groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3401])). 185.47/93.64 thf(5440,axiom,((! [A:nat,B:real]: (((ord_less_real @ one_one_real @ (root @ A @ B)) = (ord_less_real @ one_one_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9171_real__root__gt__1__iff)). 185.47/93.64 thf(25760,plain,((! [A:nat,B:real]: (((ord_less_real @ one_one_real @ (root @ A @ B)) = (ord_less_real @ one_one_real @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5440])). 185.47/93.64 thf(4116,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se545348938243370406it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9497_push__bit__nonnegative__int__iff)). 185.47/93.64 thf(21188,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se545348938243370406it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4116])). 185.47/93.64 thf(239,axiom,((! [A:set_nat,B:(nat > complex)]: (((groups6464643781859351333omplex @ B @ A) = one_one_complex) <= (~ (finite_finite_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8651_prod_Oinfinite)). 185.47/93.64 thf(8494,plain,((! [A:set_nat,B:(nat > complex)]: (((groups6464643781859351333omplex @ (B) @ A) = one_one_complex) | (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 185.47/93.64 thf(4548,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ A @ B) => (ord_less_rat @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4305_order__neq__le__trans)). 185.47/93.64 thf(22569,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ A @ B) => (ord_less_rat @ A @ B)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4548])). 185.47/93.64 thf(1085,axiom,((! [A:num]: ((abs_abs_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6334_abs__numeral)). 185.47/93.64 thf(11421,plain,((! [A:num]: ((abs_abs_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085])). 185.47/93.64 thf(839,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (numeral_numeral_int @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9523_and__not__numerals_I4_J)). 185.47/93.64 thf(10587,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (numeral_numeral_int @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[839])). 185.47/93.64 thf(6340,axiom,((! [A:rat,B:rat]: ((A = (times_times_rat @ A @ B)) = ((B = one_one_rat) | (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1663_mult__cancel__left1)). 185.47/93.64 thf(29063,plain,((! [A:rat,B:rat]: ((A = (times_times_rat @ A @ B)) = ((B = one_one_rat) | (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6340])). 185.47/93.64 thf(6273,axiom,((! [A:real,B:real,C:num]: ((times_times_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ C)) = (minus_minus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_left__diff__distrib__numeral)). 185.47/93.64 thf(28847,plain,((! [A:real,B:real,C:num]: ((times_times_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ C)) = (minus_minus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6273])). 185.47/93.64 thf(7598,axiom,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3036_verit__eq__simplify_I8_J)). 185.47/93.64 thf(33568,plain,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7598])). 185.47/93.64 thf(1813,axiom,((! [A:int,B:int,C:int]: ((divide_divide_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ (divide_divide_int @ B @ C)) @ (divide_divide_int @ (times_times_int @ A @ (modulo_modulo_int @ B @ C)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2551_div__mult1__eq)). 185.47/93.64 thf(13803,plain,((! [A:int,B:int,C:int]: ((divide_divide_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ (divide_divide_int @ B @ C)) @ (divide_divide_int @ (times_times_int @ A @ (modulo_modulo_int @ B @ C)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1813])). 185.47/93.64 thf(2308,axiom,((! [A:nat]: ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ semiri1314217659103216013at_int @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7357_double__gauss__sum__from__Suc__0)). 185.47/93.64 thf(15387,plain,((! [A:nat]: ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ (semiri1314217659103216013at_int) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2308])). 185.47/93.64 thf(6309,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ C @ B))) = ((A = C) | (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6287_crossproduct__eq)). 185.47/93.64 thf(28954,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ C @ B))) = ((A = C) | (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6309])). 185.47/93.64 thf(1014,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ (uminus_uminus_real @ B)) = zero_zero_real) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5112_real__add__minus__iff)). 185.47/93.64 thf(11203,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ (uminus_uminus_real @ B)) = zero_zero_real) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014])). 185.47/93.64 thf(1737,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ B @ C) => (ord_less_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4314_order__le__less__trans)). 185.47/93.64 thf(13558,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ B @ C) => (ord_less_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737])). 185.47/93.64 thf(4674,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (ord_less_real @ A @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4205_order_Ostrict__trans1)). 185.47/93.64 thf(22974,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (ord_less_real @ A @ C)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4674])). 185.47/93.64 thf(5862,axiom,((! [A:nat,B:int,C:int]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => ((((power_power_int @ B @ A) = (power_power_int @ C @ A)) = (B = C)) <= (ord_less_eq_int @ zero_zero_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2141_power__eq__iff__eq__base)). 185.47/93.64 thf(27407,plain,((! [A:nat,B:int,C:int]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => ((((power_power_int @ B @ A) = (power_power_int @ C @ A)) = (B = C)) | ~ (ord_less_eq_int @ zero_zero_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5862])). 185.47/93.64 thf(4839,axiom,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ C @ B) => (((ord_less_eq_rat @ zero_zero_rat @ E) => ((ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ D @ A) @ (times_times_rat @ E @ C)) @ B) <= ((plus_plus_rat @ D @ E) = one_one_rat))) <= (ord_less_eq_rat @ zero_zero_rat @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2857_convex__bound__le)). 185.47/93.64 thf(23542,plain,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ C @ B) => (((ord_less_eq_rat @ zero_zero_rat @ E) => ((ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ D @ A) @ (times_times_rat @ E @ C)) @ B) | ~ ((plus_plus_rat @ D @ E) = one_one_rat))) | ~ (ord_less_eq_rat @ zero_zero_rat @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4839])). 185.47/93.64 thf(1209,axiom,((! [A:real]: (((sin_real @ A) = zero_zero_real) => ((abs_abs_real @ (cos_real @ A)) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7826_sin__zero__abs__cos__one)). 185.47/93.64 thf(11798,plain,((! [A:real]: (((sin_real @ A) = zero_zero_real) => ((abs_abs_real @ (cos_real @ A)) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209])). 185.47/93.64 thf(4088,axiom,((! [A:int,B:int]: ((A != B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3980_less__imp__neq)). 185.47/93.64 thf(21101,plain,((! [A:int,B:int]: (~ (A = B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4088])). 185.47/93.64 thf(562,axiom,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((ord_less_eq_set_nat @ A @ B) => (((groups2906978787729119204at_rat @ C @ B) = (plus_plus_rat @ (groups2906978787729119204at_rat @ C @ (minus_minus_set_nat @ B @ A)) @ (groups2906978787729119204at_rat @ C @ A))) <= (finite_finite_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6124_sum_Osubset__diff)). 185.47/93.64 thf(9597,plain,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((ord_less_eq_set_nat @ A @ B) => (((groups2906978787729119204at_rat @ (C) @ B) = (plus_plus_rat @ (groups2906978787729119204at_rat @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups2906978787729119204at_rat @ (C) @ A))) | ~ (finite_finite_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[562])). 185.47/93.64 thf(7277,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_div__le__mono)). 185.47/93.64 thf(32516,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7277])). 185.47/93.64 thf(6250,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (power_power_nat @ A @ B)) = (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6960_of__nat__power)). 185.47/93.64 thf(28758,plain,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (power_power_nat @ A @ B)) = (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6250])). 185.47/93.64 thf(6591,axiom,((! [A:num]: ((~ (ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ A)))) = (A != one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5378_not__neg__one__le__neg__numeral__iff)). 185.47/93.64 thf(29978,plain,((! [A:num]: ((~ (ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ A)))) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6591])). 185.47/93.64 thf(5849,axiom,((! [A:real]: (((sqrt @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8113_real__sqrt__eq__zero__cancel__iff)). 185.47/93.64 thf(27362,plain,((! [A:real]: (((sqrt @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5849])). 185.47/93.64 thf(6489,axiom,(((numera6690914467698888265omplex @ one) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_829_numeral__One)). 185.47/93.64 thf(29631,plain,(((numera6690914467698888265omplex @ one) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6489])). 185.47/93.64 thf(6630,axiom,((! [A:complex,B:complex,C:nat]: (((times_times_complex @ A @ B) = one_one_complex) => ((times_times_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C)) = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_838_left__right__inverse__power)). 185.47/93.64 thf(30102,plain,((! [A:complex,B:complex,C:nat]: (((times_times_complex @ A @ B) = one_one_complex) => ((times_times_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C)) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6630])). 185.47/93.64 thf(2689,axiom,((! [A:num,B:nat]: ((ord_less_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (ord_less_nat @ (pred_numeral @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6786_less__numeral__Suc)). 185.47/93.64 thf(16684,plain,((! [A:num,B:nat]: ((ord_less_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (ord_less_nat @ (pred_numeral @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2689])). 185.47/93.64 thf(7705,axiom,((((vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) = (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_aaa)). 185.47/93.64 thf(33857,plain,((((vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) = (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7705])). 185.47/93.64 thf(5827,axiom,(((('?') @ option_nat) = (^ [A:(option_nat > $o)]: (? [B:nat]: (A @ (some_nat @ B)) | (A @ none_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1171_split__option__ex)). 185.47/93.64 thf(27280,plain,(((('?') @ option_nat) = (^ [A:(option_nat > $o)]: (? [B:nat]: (A @ (some_nat @ B)) | (A @ none_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5827])). 185.47/93.64 thf(154,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ (sgn_sgn_int @ A) @ B) @ C) = ((dvd_dvd_int @ B @ C) & ((A = zero_zero_int) => (C = zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9215_sgn__mult__dvd__iff)). 185.47/93.64 thf(8225,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ (sgn_sgn_int @ A) @ B) @ C) = ((dvd_dvd_int @ B @ C) & ((A = zero_zero_int) => (C = zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 185.47/93.64 thf(3529,axiom,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = (ord_less_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4285_linorder__not__le)). 185.47/93.64 thf(19342,plain,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = (ord_less_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3529])). 185.47/93.64 thf(7237,axiom,((! [A:real,B:nat]: ((power_power_real @ (uminus_uminus_real @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5426_Power_Oring__1__class_Opower__minus__even)). 185.47/93.64 thf(32392,plain,((! [A:real,B:nat]: ((power_power_real @ (uminus_uminus_real @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7237])). 185.47/93.64 thf(7603,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ (power_power_nat @ A @ B)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_self__le__ge2__pow)). 185.47/93.64 thf(33580,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ (power_power_nat @ A @ B)) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7603])). 185.47/93.64 thf(4070,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ A @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_int @ (groups3539618377306564664at_int @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8693_sum_OatMost__Suc)). 185.47/93.64 thf(21043,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_int @ (groups3539618377306564664at_int @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4070])). 185.47/93.64 thf(4262,axiom,((! [A:num]: ((neg_nu8295874005876285629c_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (neg_nu6075765906172075777c_real @ (numeral_numeral_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6862_dbl__inc__simps_I1_J)). 185.47/93.64 thf(21637,plain,((! [A:num]: ((neg_nu8295874005876285629c_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (neg_nu6075765906172075777c_real @ (numeral_numeral_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4262])). 185.47/93.64 thf(5691,axiom,((! [A:nat,B:real]: (((abs_abs_real @ (root @ A @ (power_power_real @ B @ A))) = (abs_abs_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9191_root__abs__power)). 185.47/93.64 thf(26669,plain,((! [A:nat,B:real]: (((abs_abs_real @ (root @ A @ (power_power_real @ B @ A))) = (abs_abs_real @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5691])). 185.47/93.64 thf(3048,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ one_one_int) @ B) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3180_add1__zle__eq)). 185.47/93.64 thf(17824,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ one_one_int) @ B) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3048])). 185.47/93.64 thf(2096,axiom,((! [A:num,B:num]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5341_mult__neg__numeral__simps_I3_J)). 185.47/93.64 thf(14718,plain,((! [A:num,B:num]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2096])). 185.47/93.64 thf(5733,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (~ (? [D:nat]: (~ (A @ D) & (B = (plus_plus_nat @ C @ D))) | ((ord_less_nat @ B @ C) & ~ (A @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2793_nat__diff__split__asm)). 185.47/93.64 thf(26807,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (~ (? [D:nat]: (~ (A @ D) & (B = (plus_plus_nat @ C @ D))) | ((ord_less_nat @ B @ C) & ~ (A @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5733])). 185.47/93.64 thf(7128,axiom,((! [A:int]: ((ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_int) = (ord_less_int @ (abs_abs_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6721_abs__square__less__1)). 185.47/93.64 thf(31988,plain,((! [A:int]: ((ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_int) = (ord_less_int @ (abs_abs_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7128])). 185.47/93.64 thf(7262,axiom,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1544_cancel__comm__monoid__add__class_Odiff__cancel)). 185.47/93.64 thf(32472,plain,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7262])). 185.47/93.64 thf(515,axiom,((! [A:num,B:nat,C:int]: ((ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7146_numeral__power__less__of__int__cancel__iff)). 185.47/93.64 thf(9464,plain,((! [A:num,B:nat,C:int]: ((ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])). 185.47/93.64 thf(4362,axiom,((! [A:int,B:num,C:nat]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (ord_less_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7168_of__int__less__neg__numeral__power__cancel__iff)). 185.47/93.64 thf(21975,plain,((! [A:int,B:num,C:nat]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (ord_less_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4362])). 185.47/93.64 thf(771,axiom,((! [A:real,B:real,C:real]: (((((plus_plus_real @ C @ (log @ A @ B)) = (log @ A @ (times_times_real @ (powr_real @ A @ C) @ B))) <= (ord_less_real @ zero_zero_real @ B)) <= (A != one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9126_add__log__eq__powr)). 185.47/93.64 thf(10356,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ C @ (log @ A @ B)) = (log @ A @ (times_times_real @ (powr_real @ A @ C) @ B))) | ~ (ord_less_real @ zero_zero_real @ B) | (A = one_one_real) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[771])). 185.47/93.64 thf(3918,axiom,((! [A:real,B:real]: ((A != zero_zero_real) => ((divide_divide_real @ (times_times_real @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1681_nonzero__mult__div__cancel__right)). 185.47/93.64 thf(20583,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real)) => ((divide_divide_real @ (times_times_real @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3918])). 185.47/93.64 thf(3811,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (minus_minus_int @ A @ B) @ C) = (ord_less_eq_int @ A @ (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_797_diff__le__eq)). 185.47/93.64 thf(20245,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (minus_minus_int @ A @ B) @ C) = (ord_less_eq_int @ A @ (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3811])). 185.47/93.64 thf(6738,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2513_diff__add__0)). 185.47/93.64 thf(30474,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6738])). 185.47/93.64 thf(194,axiom,((! [A:(nat > real),B:nat,C:real]: ((summable_real @ (^ [D:nat]: (times_times_real @ (A @ (plus_plus_nat @ D @ B)) @ (power_power_real @ C @ D)))) = (summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7705_summable__powser__ignore__initial__segment)). 185.47/93.64 thf(8357,plain,((! [A:(nat > real),B:nat,C:real]: ((summable_real @ (^ [D:nat]: (times_times_real @ (A @ (plus_plus_nat @ D @ B)) @ (power_power_real @ C @ D)))) = (summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 185.47/93.64 thf(6958,axiom,((! [A:int]: ((abs_abs_int @ (uminus_uminus_int @ A)) = (abs_abs_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6353_abs__minus__cancel)). 185.47/93.64 thf(31372,plain,((! [A:int]: ((abs_abs_int @ (uminus_uminus_int @ A)) = (abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6958])). 185.47/93.64 thf(5488,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ A) = (ord_less_eq_nat @ B @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1631_add__le__same__cancel1)). 185.47/93.64 thf(26008,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ A) = (ord_less_eq_nat @ B @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5488])). 185.47/93.64 thf(5045,axiom,((! [A:num]: (one_one_complex != (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5769_one__neq__neg__numeral)). 185.47/93.64 thf(24316,plain,((! [A:num]: ~ (one_one_complex = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5045])). 185.47/93.64 thf(7011,axiom,((! [A:(rat > $o),B:rat,C:(rat > $o)]: (((! [D:rat,E:rat]: (((A @ D) & (C @ D)) = ((A @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))) & (C @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)))))) <= (! [D:rat,E:rat]: ((C @ D) = (C @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)))))) <= (! [D:rat,E:rat]: ((A @ D) = (A @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3324_inf__period_I1_J)). 185.47/93.64 thf(31593,plain,((! [A:(rat > $o),B:rat,C:(rat > $o)]: (! [D:rat,E:rat]: (((A @ D) & (C @ D)) = ((A @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))) & (C @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))))) | ~ (! [D:rat,E:rat]: ((C @ D) = (C @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))))) | ~ (! [D:rat,E:rat]: ((A @ D) = (A @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7011])). 185.47/93.64 thf(1088,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B))) <= (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2415_divide__nonneg__nonneg)). 185.47/93.64 thf(11431,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B))) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088])). 185.47/93.64 thf(3154,axiom,((! [A:rat,B:rat,C:(rat > num),D:num]: ((((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3949_ord__le__eq__subst)). 185.47/93.64 thf(18155,plain,((! [A:rat,B:rat,C:(rat > num),D:num]: ((((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3154])). 185.47/93.64 thf(3854,axiom,((! [A:rat,B:rat,C:(rat > real),D:real]: ((ord_less_rat @ A @ B) => (((C @ B) = D) => ((ord_less_real @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_real @ (C @ E) @ (C @ F)) <= (ord_less_rat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4088_ord__less__eq__subst)). 185.47/93.64 thf(20377,plain,((! [A:rat,B:rat,C:(rat > real),D:real]: ((ord_less_rat @ A @ B) => (((C @ B) = D) => ((ord_less_real @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_real @ (C @ E) @ (C @ F)) | ~ (ord_less_rat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3854])). 185.47/93.64 thf(280,axiom,((! [A:nat,B:real,C:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ B @ C)) => (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_real @ (log @ B @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ C))) <= (ord_less_real @ one_one_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9052_log__of__power__less)). 185.47/93.64 thf(8647,plain,((! [A:nat,B:real,C:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ B @ C)) => (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_real @ (log @ B @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ C))) | ~ (ord_less_real @ one_one_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[280])). 185.47/93.64 thf(1293,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ B) = (minus_minus_complex @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5209_uminus__add__conv__diff)). 185.47/93.64 thf(12046,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ B) = (minus_minus_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293])). 185.47/93.64 thf(6444,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ (times_times_nat @ A @ (suc @ B))) => ((divide_divide_nat @ C @ A) = B)) <= (ord_less_eq_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1117_div__nat__eqI)). 185.47/93.64 thf(29465,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ (times_times_nat @ A @ (suc @ B))) => ((divide_divide_nat @ C @ A) = B)) | ~ (ord_less_eq_nat @ (times_times_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6444])). 185.47/93.64 thf(1048,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3181_int__distrib_I2_J)). 185.47/93.64 thf(11299,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048])). 185.47/93.64 thf(3742,axiom,((! [A:rat,B:rat]: (((divide_divide_rat @ (abs_abs_rat @ B) @ A) = (abs_abs_rat @ (divide_divide_rat @ B @ A))) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6563_abs__div__pos)). 185.47/93.64 thf(20017,plain,((! [A:rat,B:rat]: (((divide_divide_rat @ (abs_abs_rat @ B) @ A) = (abs_abs_rat @ (divide_divide_rat @ B @ A))) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3742])). 185.47/93.64 thf(7308,axiom,((! [A:nat,B:real]: (((root @ A @ (power_power_real @ B @ A)) = B) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9201_odd__real__root__power__cancel)). 185.47/93.64 thf(32623,plain,((! [A:nat,B:real]: (((root @ A @ (power_power_real @ B @ A)) = B) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7308])). 185.47/93.64 thf(1755,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6499_abs__triangle__ineq3)). 185.47/93.64 thf(13619,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755])). 185.47/93.64 thf(4715,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((times_times_complex @ (semiri5044797733671781792omplex @ A) @ (semiri8010041392384452111omplex @ (binomial @ B @ A))) = (divide1717551699836669952omplex @ (semiri5044797733671781792omplex @ B) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8550_fact__binomial)). 185.47/93.64 thf(23123,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((times_times_complex @ (semiri5044797733671781792omplex @ A) @ (semiri8010041392384452111omplex @ (binomial @ B @ A))) = (divide1717551699836669952omplex @ (semiri5044797733671781792omplex @ B) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4715])). 185.47/93.64 thf(1931,axiom,((! [A:nat,B:nat,C:(nat > int)]: (((groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_int @ (C @ A) @ (groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6655_sum_OatLeast__Suc__atMost)). 185.47/93.64 thf(14173,plain,((! [A:nat,B:nat,C:(nat > int)]: (((groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_int @ (C @ A) @ (groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1931])). 185.47/93.64 thf(3244,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri8010041392384452111omplex @ (binomial @ B @ A)) = (divide1717551699836669952omplex @ (semiri5044797733671781792omplex @ B) @ (times_times_complex @ (semiri5044797733671781792omplex @ A) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ B @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8553_binomial__fact)). 185.47/93.64 thf(18436,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri8010041392384452111omplex @ (binomial @ B @ A)) = (divide1717551699836669952omplex @ (semiri5044797733671781792omplex @ B) @ (times_times_complex @ (semiri5044797733671781792omplex @ A) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3244])). 185.47/93.64 thf(6155,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_vebt_member @ A @ B) = C) => ((accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ A @ B)) => (((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B))) <= (~ (C))))) => ((! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F) @ B))) <= (~ (C))))) => ((! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F) @ B))) <= (~ (C))))) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B))) <= (C = ((B != D) => ((B != E) => (~ (ord_less_nat @ B @ D) & ((~ (ord_less_nat @ B @ D)) => (~ (ord_less_nat @ E @ B) & ((((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G))) <= (~ (ord_less_nat @ E @ B)))))))))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))))))) <= (! [D:$o,E:$o]: (((C = (((B = zero_zero_nat) => (D)) & (((B = one_one_nat) & ((E) <= (B = one_one_nat))) <= (B != zero_zero_nat)))) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)))) <= (A = (vEBT_Leaf @ D @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3116_vebt__member_Opelims_I1_J)). 185.47/93.64 thf(28401,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_vebt_member @ A @ B) = C) => ((accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ A @ B)) => (((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B)) | (C)))) => ((! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F) @ B)) | (C)))) => ((! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F) @ B)) | (C)))) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B)) | ~ (C = ((~ (B = D)) => ((~ (B = E)) => (~ (ord_less_nat @ B @ D) & ((~ (ord_less_nat @ B @ D)) => (~ (ord_less_nat @ E @ B) & ((((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G))) | (ord_less_nat @ E @ B)))))))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))))))) | ~ (! [D:$o,E:$o]: (((C = (((B = zero_zero_nat) => (D)) & (((B = one_one_nat) & ((E) | ~ (B = one_one_nat))) | (B = zero_zero_nat)))) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)))) | ~ (A = (vEBT_Leaf @ D @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6155])). 185.47/93.64 thf(4975,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ (divide_divide_nat @ A @ B) @ one_one_nat) <= (dvd_dvd_nat @ B @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4488_unit__div)). 185.47/93.64 thf(24013,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ (divide_divide_nat @ A @ B) @ one_one_nat) | ~ (dvd_dvd_nat @ B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4975])). 185.47/93.64 thf(7696,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_mult__2)). 185.47/93.64 thf(33832,plain,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7696])). 185.47/93.64 thf(3050,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) = (((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ A @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ zero_zero_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2204_zero__le__mult__iff)). 185.47/93.64 thf(17830,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) = (((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ A @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3050])). 185.47/93.64 thf(7171,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4249_dual__order_Ostrict__trans2)). 185.47/93.64 thf(32161,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7171])). 185.47/93.64 thf(3706,axiom,((! [A:int,B:int,C:int]: ((((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = zero_zero_int) <= (A = zero_zero_int)) & ((A != zero_zero_int) => ((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (divide_divide_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1695_div__mult__mult1__if)). 185.47/93.64 thf(19895,plain,((! [A:int,B:int,C:int]: ((((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = zero_zero_int) | ~ (A = zero_zero_int)) & ((~ (A = zero_zero_int)) => ((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (divide_divide_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3706])). 185.47/93.64 thf(3878,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) <= (! [C:rat]: ((ord_less_eq_rat @ A @ (plus_plus_rat @ B @ C)) <= (ord_less_rat @ zero_zero_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2620_field__le__epsilon)). 185.47/93.64 thf(20450,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) | ~ (! [C:rat]: ((ord_less_eq_rat @ A @ (plus_plus_rat @ B @ C)) | ~ (ord_less_rat @ zero_zero_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3878])). 185.47/93.64 thf(6459,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_812_Nat_Odiff__add__assoc2)). 185.47/93.64 thf(29512,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6459])). 185.47/93.64 thf(2515,axiom,((! [A:real,B:real,C:real,D:real]: ((minus_minus_complex @ (complex2 @ A @ B) @ (complex2 @ C @ D)) = (complex2 @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7983_complex__diff)). 185.47/93.64 thf(16067,plain,((! [A:real,B:real,C:real,D:real]: ((minus_minus_complex @ (complex2 @ A @ B) @ (complex2 @ C @ D)) = (complex2 @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2515])). 185.47/93.64 thf(4304,axiom,((! [A:num,B:num]: ((plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5188_add__neg__numeral__simps_I3_J)). 185.47/93.64 thf(21755,plain,((! [A:num,B:num]: ((plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4304])). 185.47/93.64 thf(4014,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ (uminus_uminus_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6035_real__0__le__add__iff)). 185.47/93.64 thf(20881,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ (uminus_uminus_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4014])). 185.47/93.64 thf(6106,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((sqrt @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8241_sqrt__even__pow2)). 185.47/93.64 thf(28238,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((sqrt @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6106])). 185.47/93.64 thf(4581,axiom,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ A) @ (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6520_abs__ge__minus__self)). 185.47/93.64 thf(22674,plain,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ A) @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4581])). 185.47/93.64 thf(1264,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ (abs_abs_int @ A) @ B) <= (ord_less_eq_int @ (uminus_uminus_int @ A) @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6511_abs__leI)). 185.47/93.64 thf(11966,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ B) | ~ (ord_less_eq_int @ (uminus_uminus_int @ A) @ B) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264])). 185.47/93.64 thf(5324,axiom,((! [A:real]: ((minus_minus_real @ zero_zero_real @ A) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5182_verit__minus__simplify_I3_J)). 185.47/93.64 thf(25324,plain,((! [A:real]: ((minus_minus_real @ zero_zero_real @ A) = (uminus_uminus_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5324])). 185.47/93.64 thf(5093,axiom,((! [A:real]: ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7911_cos__double__cos)). 185.47/93.64 thf(24469,plain,((! [A:real]: ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5093])). 185.47/93.64 thf(4332,axiom,((! [A:real]: (((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ zero_zero_real @ (cos_real @ A))) <= (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7927_cos__gt__zero__pi)). 185.47/93.64 thf(21880,plain,((! [A:real]: (((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ zero_zero_real @ (cos_real @ A))) | ~ (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4332])). 185.47/93.64 thf(6422,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) => ((B = A) <= (ord_less_eq_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3891_dual__order_Oantisym)). 185.47/93.64 thf(29388,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) => ((B = A) | ~ (ord_less_eq_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6422])). 185.47/93.64 thf(6406,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_not__add__less2)). 185.47/93.64 thf(29330,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6406])). 185.47/93.64 thf(4538,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (divide_divide_rat @ B @ C)) = (divide_divide_rat @ (times_times_rat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_times__divide__eq__right)). 185.47/93.64 thf(22536,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (divide_divide_rat @ B @ C)) = (divide_divide_rat @ (times_times_rat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4538])). 185.47/93.64 thf(1885,axiom,((! [A:nat,B:nat]: (((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ B) = zero_zero_complex) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8504_pochhammer__of__nat__eq__0__iff)). 185.47/93.64 thf(14039,plain,((! [A:nat,B:nat]: (((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ B) = zero_zero_complex) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885])). 185.47/93.64 thf(4171,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3045_half__nonnegative__int__iff)). 185.47/93.64 thf(21354,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4171])). 185.47/93.64 thf(6897,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ C @ D) => (dvd_dvd_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4588_mult__dvd__mono)). 185.47/93.64 thf(31124,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ C @ D) => (dvd_dvd_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6897])). 185.47/93.64 thf(2895,axiom,((! [A:int,B:int]: ((abs_abs_int @ (plus_plus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))) = (plus_plus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6348_abs__add__abs)). 185.47/93.64 thf(17339,plain,((! [A:int,B:int]: ((abs_abs_int @ (plus_plus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))) = (plus_plus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2895])). 185.47/93.64 thf(365,axiom,((! [A:num]: ((ord_max_int @ (numeral_numeral_int @ A) @ zero_zero_int) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3614_max__0__1_I4_J)). 185.47/93.64 thf(8951,plain,((! [A:num]: ((ord_max_int @ (numeral_numeral_int @ A) @ zero_zero_int) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])). 185.47/93.64 thf(6337,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1593_le0)). 185.47/93.64 thf(29055,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6337])). 185.47/93.64 thf(6243,axiom,(((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1886_bits__1__div__2)). 185.47/93.64 thf(28741,plain,(((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6243])). 185.47/93.64 thf(5411,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_ab__semigroup__mult__class_Omult__ac_I1_J)). 185.47/93.64 thf(25630,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5411])). 185.47/93.64 thf(315,axiom,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => (((~ (member_nat @ B @ A)) => ((groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (D = B) @ (C @ D) @ one_one_real)) @ A) = one_one_real)) & ((member_nat @ B @ A) => ((groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (D = B) @ (C @ D) @ one_one_real)) @ A) = (C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8671_prod_Odelta)). 185.47/93.64 thf(8785,plain,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => (((~ (member_nat @ B @ A)) => ((groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (D = B) @ (C @ D) @ one_one_real)) @ A) = one_one_real)) & ((member_nat @ B @ A) => ((groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (D = B) @ (C @ D) @ one_one_real)) @ A) = (C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 185.47/93.64 thf(4936,axiom,((! [A:vEBT_VEBT,B:nat]: ((((vEBT_vebt_maxt @ A) = none_nat) => ((vEBT_VEBT_set_vebt @ A) = bot_bot_set_nat)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_959_maxt__corr__help__empty)). 185.47/93.64 thf(23896,plain,((! [A:vEBT_VEBT,B:nat]: ((((vEBT_vebt_maxt @ A) = none_nat) => ((vEBT_VEBT_set_vebt @ A) = bot_bot_set_nat)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4936])). 185.47/93.64 thf(1919,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2235_mult__left__mono)). 185.47/93.64 thf(14141,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919])). 185.47/93.64 thf(7129,axiom,((! [A:rat]: ((zero_zero_rat = (uminus_uminus_rat @ A)) = (zero_zero_rat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5053_neg__0__equal__iff__equal)). 185.47/93.64 thf(31991,plain,((! [A:rat]: ((zero_zero_rat = (uminus_uminus_rat @ A)) = (zero_zero_rat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7129])). 185.47/93.64 thf(7003,axiom,((! [A:int,B:num,C:num,D:int]: ((times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ (times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_power__add__numeral2)). 185.47/93.64 thf(31561,plain,((! [A:int,B:num,C:num,D:int]: ((times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ (times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7003])). 185.47/93.64 thf(4215,axiom,((! [A:nat,B:nat]: (((semiri681578069525770553at_rat @ A) = (semiri681578069525770553at_rat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6870_of__nat__eq__iff)). 185.47/93.64 thf(21494,plain,((! [A:nat,B:nat]: (((semiri681578069525770553at_rat @ A) = (semiri681578069525770553at_rat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4215])). 185.47/93.64 thf(1818,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((fract @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (fract @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9940_mult__rat__cancel)). 185.47/93.64 thf(13820,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((fract @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (fract @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818])). 185.47/93.64 thf(1097,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_int @ B @ A) => ((modulo_modulo_int @ A @ B) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3132_mod__neg__neg__trivial)). 185.47/93.64 thf(11458,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_int @ B @ A) => ((modulo_modulo_int @ A @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097])). 185.47/93.64 thf(483,axiom,((! [A:(nat > real),B:real]: (((! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))) => (((ord_less_real @ B @ one_one_real) => (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))) <= (ord_less_eq_real @ zero_zero_real @ B))) <= (! [C:nat]: (ord_less_eq_real @ (A @ C) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7750_summable__power__series)). 185.47/93.64 thf(9360,plain,((! [A:(nat > real),B:real]: (((! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))) => (((ord_less_real @ B @ one_one_real) => (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))) | ~ (ord_less_eq_real @ zero_zero_real @ B))) | ~ (! [C:nat]: (ord_less_eq_real @ (A @ C) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[483])). 185.47/93.64 thf(2940,axiom,((! [A:num,B:num]: ((ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (ord_less_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5373_neg__numeral__less__iff)). 185.47/93.64 thf(17481,plain,((! [A:num,B:num]: ((ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (ord_less_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2940])). 185.47/93.64 thf(5884,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ A) <= (A = (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4618_dvdI)). 185.47/93.64 thf(27477,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ A) | ~ (A = (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5884])). 185.47/93.64 thf(6821,axiom,((! [A:int]: ((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ A) => ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_int) <= (ord_less_eq_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6267_square__le__1)). 185.47/93.64 thf(30812,plain,((! [A:int]: ((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ A) => ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_int) | ~ (ord_less_eq_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6821])). 185.47/93.64 thf(355,axiom,((! [A:(nat > int),B:set_nat,C:nat]: ((power_power_int @ (groups705719431365010083at_int @ A @ B) @ C) = (groups705719431365010083at_int @ (^ [D:nat]: (power_power_int @ (A @ D) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8729_prod__power__distrib)). 185.47/93.64 thf(8919,plain,((! [A:(nat > int),B:set_nat,C:nat]: ((power_power_int @ (groups705719431365010083at_int @ (A) @ B) @ C) = (groups705719431365010083at_int @ (^ [D:nat]: (power_power_int @ (A @ D) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[355])). 185.47/93.64 thf(1094,axiom,((! [A:rat,B:rat]: ((A != zero_zero_rat) => ((divide_divide_rat @ A @ (times_times_rat @ B @ A)) = (divide_divide_rat @ one_one_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1828_nonzero__divide__mult__cancel__right)). 185.47/93.64 thf(11448,plain,((! [A:rat,B:rat]: ((~ (A = zero_zero_rat)) => ((divide_divide_rat @ A @ (times_times_rat @ B @ A)) = (divide_divide_rat @ one_one_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094])). 185.47/93.64 thf(6293,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) => (ord_less_nat @ C @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_less__add__eq__less)). 185.47/93.64 thf(28904,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) => (ord_less_nat @ C @ D)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6293])). 185.47/93.64 thf(2460,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = zero_zero_int) = (B = (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5724_add__eq__0__iff)). 185.47/93.64 thf(15881,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = zero_zero_int) = (B = (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2460])). 185.47/93.64 thf(5612,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) != zero_zero_int) => ((B != zero_zero_int) & (A != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2047_mult__not__zero)). 185.47/93.64 thf(26406,plain,((! [A:int,B:int]: ((~ ((times_times_int @ A @ B) = zero_zero_int)) => (~ (B = zero_zero_int) & ~ (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5612])). 185.47/93.64 thf(2875,axiom,((! [A:rat]: ((ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_rat) = (ord_less_eq_rat @ (abs_abs_rat @ A) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6716_abs__square__le__1)). 185.47/93.64 thf(17270,plain,((! [A:rat]: ((ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_rat) = (ord_less_eq_rat @ (abs_abs_rat @ A) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2875])). 185.47/93.64 thf(1006,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((B = (times_times_real @ C @ A)) => ((divide_divide_real @ B @ A) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2468_divide__eq__imp)). 185.47/93.64 thf(11178,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((B = (times_times_real @ C @ A)) => ((divide_divide_real @ B @ A) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006])). 185.47/93.64 thf(2284,axiom,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ (plus_plus_nat @ A @ C) @ A)) @ (set_ord_atMost_nat @ B)) = (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ one_one_nat) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8943_choose__rising__sum_I2_J)). 185.47/93.64 thf(15311,plain,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ (plus_plus_nat @ A @ C) @ A)) @ (set_ord_atMost_nat @ B)) = (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ one_one_nat) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2284])). 185.47/93.64 thf(4186,axiom,((! [A:rat]: ~ (ord_less_rat @ (times_times_rat @ A @ A) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2315_not__square__less__zero)). 185.47/93.64 thf(21407,plain,((! [A:rat]: ~ (ord_less_rat @ (times_times_rat @ A @ A) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4186])). 185.47/93.64 thf(249,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (numeral_numeral_int @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9532_and__not__numerals_I7_J)). 185.47/93.64 thf(8522,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (numeral_numeral_int @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 185.47/93.64 thf(1589,axiom,((! [A:nat,B:nat,C:(nat > int)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_int @ (C @ (suc @ B)) @ (groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6651_sum_Onat__ivl__Suc_H)). 185.47/93.64 thf(12993,plain,((! [A:nat,B:nat,C:(nat > int)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_int @ (C @ (suc @ B)) @ (groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589])). 185.47/93.64 thf(2980,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7240_nat__int__comparison_I2_J)). 185.47/93.64 thf(17613,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2980])). 185.47/93.64 thf(6007,axiom,((! [A:nat,B:nat]: ? [C:nat]: ! [D:nat]: ((ord_less_nat @ D @ C) => ((~ (dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B))) = (~ (dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4706_minf_I10_J)). 185.47/93.64 thf(27920,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6007])). 185.47/93.64 thf(4637,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2980_sum__power2__le__zero__iff)). 185.47/93.64 thf(22859,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4637])). 185.47/93.64 thf(1299,axiom,((! [A:nat,B:nat]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7225_of__nat__less__imp__less)). 185.47/93.64 thf(12065,plain,((! [A:nat,B:nat]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B)) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299])). 185.47/93.64 thf(1013,axiom,((! [A:real]: ((plus_plus_real @ A @ (uminus_uminus_real @ A)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5167_add_Oright__inverse)). 185.47/93.64 thf(11200,plain,((! [A:real]: ((plus_plus_real @ A @ (uminus_uminus_real @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013])). 185.47/93.64 thf(5075,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ (suc @ B)) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2170_mod__Suc__le__divisor)). 185.47/93.64 thf(24418,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ (suc @ B)) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5075])). 185.47/93.64 thf(5523,axiom,((! [A:int,B:num]: ((power_power_int @ (uminus_uminus_int @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus_uminus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6616_power__minus__Bit1)). 185.47/93.64 thf(26121,plain,((! [A:int,B:num]: ((power_power_int @ (uminus_uminus_int @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus_uminus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5523])). 185.47/93.64 thf(6063,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2326_mult__pos__neg)). 185.47/93.64 thf(28082,plain,((! [A:nat,B:nat]: (((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6063])). 185.47/93.64 thf(6395,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) => ((dvd_dvd_nat @ B @ C) <= (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4881_dvd__mult__cancel)). 185.47/93.64 thf(29264,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) => ((dvd_dvd_nat @ B @ C) | ~ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6395])). 185.47/93.64 thf(1560,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1253_subset__empty)). 185.47/93.64 thf(12901,plain,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560])). 185.47/93.64 thf(4573,axiom,((! [A:rat]: ((ord_less_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_rat) = (ord_less_rat @ (abs_abs_rat @ A) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6720_abs__square__less__1)). 185.47/93.64 thf(22653,plain,((! [A:rat]: ((ord_less_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_rat) = (ord_less_rat @ (abs_abs_rat @ A) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4573])). 185.47/93.64 thf(7037,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = A) = ((divide_divide_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1916_mod__eq__self__iff__div__eq__0)). 185.47/93.64 thf(31701,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = A) = ((divide_divide_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7037])). 185.47/93.64 thf(4444,axiom,((! [A:rat]: ((divide_divide_rat @ zero_zero_rat @ A) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1567_div__0)). 185.47/93.64 thf(22229,plain,((! [A:rat]: ((divide_divide_rat @ zero_zero_rat @ A) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4444])). 185.47/93.64 thf(5141,axiom,((! [A:nat,B:num,C:num]: ((times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ B)) @ (power_power_nat @ A @ (numeral_numeral_nat @ C))) = (power_power_nat @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_power__add__numeral)). 185.47/93.64 thf(24680,plain,((! [A:nat,B:num,C:num]: ((times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ B)) @ (power_power_nat @ A @ (numeral_numeral_nat @ C))) = (power_power_nat @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5141])). 185.47/93.64 thf(6152,axiom,((! [A:num]: (zero_zero_rat != (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5700_zero__neq__neg__numeral)). 185.47/93.64 thf(28391,plain,((! [A:num]: ~ (zero_zero_rat = (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6152])). 185.47/93.64 thf(102,axiom,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_int @ (groups705719431365010083at_int @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8699_prod_OlessThan__Suc)). 185.47/93.64 thf(8069,plain,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_int @ (groups705719431365010083at_int @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 185.47/93.64 thf(5113,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ C) @ D @ E) @ F) = ((F = A) | ((ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) & ((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)))) | (F = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1440_VEBT__internal_Omembermima_Osimps_I4_J)). 185.47/93.64 thf(24558,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ C) @ D @ E) @ F) = ((F = A) | ((ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) & ((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)))) | (F = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5113])). 185.47/93.64 thf(6310,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ A @ B)) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4443_dvd__add__triv__left__iff)). 185.47/93.64 thf(28957,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ A @ B)) = (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6310])). 185.47/93.64 thf(1214,axiom,((! [A:int,B:int]: (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ A @ B)) @ (plus_plus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6583_abs__triangle__ineq4)). 185.47/93.64 thf(11812,plain,((! [A:int,B:int]: (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ A @ B)) @ (plus_plus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214])). 185.47/93.64 thf(2231,axiom,((! [A:real,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) <= (ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_897_power__le__imp__le__exp)). 185.47/93.64 thf(15146,plain,((! [A:real,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2231])). 185.47/93.64 thf(1881,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((~ (ord_less_eq_real @ A @ C)) <= (ord_less_real @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3318_minf_I8_J)). 185.47/93.64 thf(14029,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (ord_less_eq_real @ A @ C) | ~ (ord_less_real @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1881])). 185.47/93.64 thf(3111,axiom,((! [A:nat,B:int]: ((A = (nat2 @ B)) = (((B = (semiri1314217659103216013at_int @ A)) <= (ord_less_eq_int @ zero_zero_int @ B)) & ((A = zero_zero_nat) <= (~ (ord_less_eq_int @ zero_zero_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9308_nat__eq__iff2)). 185.47/93.64 thf(18030,plain,((! [A:nat,B:int]: ((A = (nat2 @ B)) = (((B = (semiri1314217659103216013at_int @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ B)) & ((A = zero_zero_nat) | (ord_less_eq_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3111])). 185.47/93.64 thf(3444,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ A) @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8244_real__sqrt__ge__abs1)). 185.47/93.64 thf(19063,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ A) @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3444])). 185.47/93.64 thf(2567,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3777_set__update__memI)). 185.47/93.64 thf(16240,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2567])). 185.47/93.64 thf(1457,axiom,((! [A:int,B:int]: (((times_times_int @ (divide_divide_int @ B @ A) @ A) = B) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4510_unit__div__mult__self)). 185.47/93.64 thf(12589,plain,((! [A:int,B:int]: (((times_times_int @ (divide_divide_int @ B @ A) @ A) = B) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457])). 185.47/93.64 thf(6779,axiom,(((uminus_uminus_real @ (numeral_numeral_real @ one)) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5988_uminus__numeral__One)). 185.47/93.64 thf(30667,plain,(((uminus_uminus_real @ (numeral_numeral_real @ one)) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6779])). 185.47/93.64 thf(4463,axiom,((! [A:num,B:num,C:(num > rat),D:rat]: ((ord_less_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_rat @ (C @ E) @ (C @ F)) <= (ord_less_num @ E @ F))) => (ord_less_rat @ (C @ A) @ D)) <= (ord_less_eq_rat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4358_order__less__le__subst2)). 185.47/93.64 thf(22287,plain,((! [A:num,B:num,C:(num > rat),D:rat]: ((ord_less_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_num @ E @ F))) => (ord_less_rat @ (C @ A) @ D)) | ~ (ord_less_eq_rat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4463])). 185.47/93.64 thf(1634,axiom,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ C)))) = (ord_less_eq_real @ B @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5379_le__divide__eq__numeral1_I2_J)). 185.47/93.64 thf(13170,plain,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ C)))) = (ord_less_eq_real @ B @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634])). 185.47/93.64 thf(5296,axiom,((! [A:nat]: ((member_nat @ zero_zero_nat @ (nat_set_decode @ A)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4530_set__decode__0)). 185.47/93.64 thf(25236,plain,((! [A:nat]: ((member_nat @ zero_zero_nat @ (nat_set_decode @ A)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5296])). 185.47/93.64 thf(3692,axiom,((! [A:rat]: ? [B:int]: (ord_less_rat @ (ring_1_of_int_rat @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7439_ex__of__int__less)). 185.47/93.64 thf(19851,plain,((! [A:rat]: ? [B:int]: (ord_less_rat @ (ring_1_of_int_rat @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3692])). 185.47/93.64 thf(6286,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_nat @ (binomial @ C @ B) @ (binomial @ C @ A)) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ C @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8547_binomial__strict__antimono)). 185.47/93.64 thf(28882,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (binomial @ C @ B) @ (binomial @ C @ A)) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ C @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6286])). 185.47/93.64 thf(5918,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_785_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2)). 185.47/93.64 thf(27593,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5918])). 185.47/93.64 thf(5637,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (times_times_rat @ A @ B) @ C) = (times_times_rat @ A @ (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_mult_Oassoc)). 185.47/93.64 thf(26489,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (times_times_rat @ A @ B) @ C) = (times_times_rat @ A @ (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5637])). 185.47/93.64 thf(625,axiom,((! [A:nat,B:nat]: ((if_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Nat__Onat_T)). 185.47/93.64 thf(9805,plain,((! [A:nat,B:nat]: ((if_nat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[625])). 185.47/93.64 thf(3163,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (times_times_rat @ C @ A) @ (times_times_rat @ C @ B)) <= (ord_less_rat @ zero_zero_rat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2357_mult__strict__left__mono)). 185.47/93.64 thf(18187,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (times_times_rat @ C @ A) @ (times_times_rat @ C @ B)) | ~ (ord_less_rat @ zero_zero_rat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3163])). 185.47/93.64 thf(5874,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2402_add__pos__pos)). 185.47/93.64 thf(27442,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5874])). 185.47/93.64 thf(583,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3564_max_Oabsorb2)). 185.47/93.64 thf(9668,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[583])). 185.47/93.64 thf(6809,axiom,((! [A:$o,B:$o]: ((ord_less_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B)) = ((B) & ~ (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5115_of__bool__less__iff)). 185.47/93.64 thf(30766,plain,((! [A:$o,B:$o]: ((ord_less_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B)) = ((B) & ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6809])). 185.47/93.64 thf(1534,axiom,((dvd_dvd_real = (^ [A:real,B:real]: ((B = zero_zero_real) <= (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4573_dvd__field__iff)). 185.47/93.64 thf(12819,plain,(((dvd_dvd_real) = (^ [A:real,B:real]: ((B = zero_zero_real) | ~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534])). 185.47/93.64 thf(4966,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8529_binomial__le__pow2)). 185.47/93.64 thf(23988,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4966])). 185.47/93.64 thf(2489,axiom,((! [A:(int > (int > $o)),B:int,C:int]: (((! [D:int]: (A @ D @ D)) => ((A @ B @ C) <= (! [D:int,E:int]: ((A @ E @ D) => (A @ D @ E))))) <= (! [D:int,E:int]: ((ord_less_int @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4022_linorder__less__wlog)). 185.47/93.64 thf(15971,plain,((! [A:(int > (int > $o)),B:int,C:int]: (((! [D:int]: (A @ D @ D)) => ((A @ B @ C) | ~ (! [D:int,E:int]: ((A @ E @ D) => (A @ D @ E))))) | ~ (! [D:int,E:int]: ((ord_less_int @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2489])). 185.47/93.64 thf(451,axiom,((! [A:real]: (((ord_less_real @ (ln_ln_real @ A) @ zero_zero_real) = (ord_less_real @ A @ one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5235_ln__less__zero__iff)). 185.47/93.64 thf(9230,plain,((! [A:real]: (((ord_less_real @ (ln_ln_real @ A) @ zero_zero_real) = (ord_less_real @ A @ one_one_real)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[451])). 185.47/93.64 thf(7069,axiom,((! [A:int]: (((uminus_uminus_int @ A) = zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5046_neg__equal__0__iff__equal)). 185.47/93.64 thf(31802,plain,((! [A:int]: (((uminus_uminus_int @ A) = zero_zero_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7069])). 185.47/93.64 thf(7122,axiom,((mi != ma)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67__092_060open_062mi_A_092_060noteq_062_Ama_092_060close_062)). 185.47/93.64 thf(31966,plain,((~ (mi = ma))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7122])). 185.47/93.64 thf(966,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ (sgn_sgn_int @ B) @ C)) = ((B = zero_zero_int) | (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9217_dvd__sgn__mult__iff)). 185.47/93.64 thf(11051,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ (sgn_sgn_int @ B) @ C)) = ((B = zero_zero_int) | (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[966])). 185.47/93.64 thf(2263,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ A @ C) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3250_pinf_I7_J)). 185.47/93.64 thf(15250,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ A @ C) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2263])). 185.47/93.64 thf(3777,axiom,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ B) => ((member_nat @ C @ A) => (member_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1431_subsetD)). 185.47/93.64 thf(20139,plain,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ B) => ((member_nat @ C @ A) => (member_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3777])). 185.47/93.64 thf(3479,axiom,((! [A:real,B:num]: (((powr_real @ A @ (numeral_numeral_real @ B)) = (power_power_real @ A @ (numeral_numeral_nat @ B))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9081_powr__numeral)). 185.47/93.64 thf(19184,plain,((! [A:real,B:num]: (((powr_real @ A @ (numeral_numeral_real @ B)) = (power_power_real @ A @ (numeral_numeral_nat @ B))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3479])). 185.47/93.64 thf(6587,axiom,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: (((? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F))))) <= (? [E:num]: ! [F:num]: (((C @ F) = (D @ F)) <= (ord_less_num @ E @ F)))) <= (? [E:num]: ! [F:num]: (((A @ F) = (B @ F)) <= (ord_less_num @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3227_pinf_I1_J)). 185.47/93.64 thf(29961,plain,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F)))) | ~ (? [E:num]: ! [F:num]: (((C @ F) = (D @ F)) | ~ (ord_less_num @ E @ F))) | ~ (? [E:num]: ! [F:num]: (((A @ F) = (B @ F)) | ~ (ord_less_num @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6587])). 185.47/93.64 thf(5262,axiom,((! [A:option_nat,B:option_nat]: ((((A != none_nat) => (((the_nat @ A) = (the_nat @ B)) <= (B != none_nat))) => (A = B)) <= ((A = none_nat) = (B = none_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1188_option_Oexpand)). 185.47/93.64 thf(25090,plain,((! [A:option_nat,B:option_nat]: ((((~ (A = none_nat)) => (((the_nat @ A) = (the_nat @ B)) | (B = none_nat))) => (A = B)) | ~ ((A = none_nat) = (B = none_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5262])). 185.47/93.64 thf(1597,axiom,((! [A:real,B:nat,C:nat]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_eq_nat @ C @ B)) <= (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1889_power__decreasing__iff)). 185.47/93.64 thf(13025,plain,((! [A:real,B:nat,C:nat]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_eq_nat @ C @ B)) | ~ (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597])). 185.47/93.64 thf(6043,axiom,(((semiri1408675320244567234ct_nat @ one_one_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7962_fact__1)). 185.47/93.64 thf(28022,plain,(((semiri1408675320244567234ct_nat @ one_one_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6043])). 185.47/93.64 thf(5064,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4940_odd__iff__mod__2__eq__one)). 185.47/93.64 thf(24386,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5064])). 185.47/93.64 thf(1608,axiom,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: ((member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ B @ C))) = ((A = C) & (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5262_in__set__replicate)). 185.47/93.64 thf(13067,plain,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: ((member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ B @ C))) = ((A = C) & ~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608])). 185.47/93.64 thf(1752,axiom,((! [A:nat]: (bot_bot_set_nat != (set_ord_atMost_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8723_not__empty__eq__Iic__eq__empty)). 185.47/93.64 thf(13608,plain,((! [A:nat]: ~ (bot_bot_set_nat = (set_ord_atMost_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752])). 185.47/93.64 thf(3648,axiom,((! [A:(rat > $o),B:(rat > $o),C:(rat > $o),D:(rat > $o)]: ((? [E:rat]: ! [F:rat]: (((A @ F) = (B @ F)) <= (ord_less_rat @ E @ F))) => ((? [E:rat]: ! [F:rat]: (((C @ F) = (D @ F)) <= (ord_less_rat @ E @ F))) => (? [E:rat]: ! [F:rat]: ((ord_less_rat @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3231_pinf_I2_J)). 185.47/93.64 thf(19710,plain,((! [A:(rat > $o),B:(rat > $o),C:(rat > $o),D:(rat > $o)]: ((? [E:rat]: ! [F:rat]: (((A @ F) = (B @ F)) | ~ (ord_less_rat @ E @ F))) => ((? [E:rat]: ! [F:rat]: (((C @ F) = (D @ F)) | ~ (ord_less_rat @ E @ F))) => (? [E:rat]: ! [F:rat]: ((ord_less_rat @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3648])). 185.47/93.64 thf(6389,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ (abs_abs_Code_integer @ B)) = (ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_8256067586552552935nteger @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6682_abs__le__square__iff)). 185.47/93.64 thf(29243,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ (abs_abs_Code_integer @ B)) = (ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_8256067586552552935nteger @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6389])). 185.47/93.64 thf(4841,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((A = B) | (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4193_order_Oorder__iff__strict)). 185.47/93.64 thf(23551,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((A = B) | (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4841])). 185.47/93.64 thf(3389,axiom,(((neg_nu7009210354673126013omplex @ zero_zero_complex) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3821_dbl__simps_I2_J)). 185.47/93.64 thf(18898,plain,(((neg_nu7009210354673126013omplex @ zero_zero_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3389])). 185.47/93.64 thf(6523,axiom,((! [A:rat]: ((times_times_rat @ A @ one_one_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_777_mult_Ocomm__neutral)). 185.47/93.64 thf(29744,plain,((! [A:rat]: ((times_times_rat @ A @ one_one_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6523])). 185.47/93.64 thf(5873,axiom,((! [A:option_nat]: ((A != none_nat) => ((some_nat @ (the_nat @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_972_option_Ocollapse)). 185.47/93.64 thf(27439,plain,((! [A:option_nat]: ((~ (A = none_nat)) => ((some_nat @ (the_nat @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5873])). 185.47/93.64 thf(4630,axiom,((! [A:rat,B:rat]: ((A != zero_zero_rat) => (((divide_divide_rat @ B @ A) = one_one_rat) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2481_right__inverse__eq)). 185.47/93.64 thf(22834,plain,((! [A:rat,B:rat]: ((~ (A = zero_zero_rat)) => (((divide_divide_rat @ B @ A) = one_one_rat) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4630])). 185.47/93.64 thf(4789,axiom,((~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5910_le__minus__one__simps_I3_J)). 185.47/93.64 thf(23387,plain,((~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4789])). 185.47/93.64 thf(2556,axiom,((! [A:nat]: ((nat2 @ (bit_se2000444600071755411sk_int @ A)) = (bit_se2002935070580805687sk_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9266_nat__mask__eq)). 185.47/93.64 thf(16208,plain,((! [A:nat]: ((nat2 @ (bit_se2000444600071755411sk_int @ A)) = (bit_se2002935070580805687sk_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2556])). 185.47/93.64 thf(4368,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_nat @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4354_order__less__le__subst2)). 185.47/93.64 thf(21992,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_nat @ A @ B) => ((ord_less_eq_real @ (C @ B) @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4368])). 185.47/93.64 thf(1941,axiom,((! [A:real]: (((sin_real @ A) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))) <= (ord_less_eq_real @ zero_zero_real @ (sin_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8277_sin__cos__sqrt)). 185.47/93.64 thf(14228,plain,((! [A:real]: (((sin_real @ A) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))) | ~ (ord_less_eq_real @ zero_zero_real @ (sin_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1941])). 185.47/93.64 thf(4896,axiom,((! [A:int,B:int]: (((ord_less_eq_rat @ (fract @ B @ A) @ one_one_rat) = (ord_less_eq_int @ B @ A)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9955_Fract__le__one__iff)). 185.47/93.64 thf(23749,plain,((! [A:int,B:int]: (((ord_less_eq_rat @ (fract @ B @ A) @ one_one_rat) = (ord_less_eq_int @ B @ A)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4896])). 185.47/93.64 thf(1498,axiom,((! [A:nat,B:nat]: ((modulo_modulo_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (times_times_int @ (zero_n2684676970156552555ol_int @ (ord_less_nat @ A @ B)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6283_exp__mod__exp)). 185.47/93.64 thf(12713,plain,((! [A:nat,B:nat]: ((modulo_modulo_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (times_times_int @ (zero_n2684676970156552555ol_int @ (ord_less_nat @ A @ B)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498])). 185.47/93.64 thf(4999,axiom,((! [A:nat,B:nat]: ((B != zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2119_gr__implies__not0)). 185.47/93.64 thf(24100,plain,((! [A:nat,B:nat]: (~ (B = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4999])). 185.47/93.64 thf(804,axiom,((! [A:real]: ((times_times_complex @ (real_V4546457046886955230omplex @ A) @ imaginary_unit) = (complex2 @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9146_complex__of__real__i)). 185.47/93.64 thf(10469,plain,((! [A:real]: ((times_times_complex @ (real_V4546457046886955230omplex @ A) @ imaginary_unit) = (complex2 @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[804])). 185.47/93.64 thf(3284,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (minus_minus_int @ (modulo_modulo_int @ A @ B) @ (modulo_modulo_int @ C @ B)) @ B) = (modulo_modulo_int @ (minus_minus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2006_mod__diff__eq)). 185.47/93.64 thf(18556,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (minus_minus_int @ (modulo_modulo_int @ A @ B) @ (modulo_modulo_int @ C @ B)) @ B) = (modulo_modulo_int @ (minus_minus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3284])). 185.47/93.64 thf(6253,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (power_power_nat @ A @ B)) <= (ord_less_eq_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2795_nat__one__le__power)). 185.47/93.64 thf(28773,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (power_power_nat @ A @ B)) | ~ (ord_less_eq_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6253])). 185.47/93.64 thf(3137,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ (divide_divide_real @ B @ C))) = (((((~ (ord_less_real @ C @ zero_zero_real)) => (ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_real @ C @ zero_zero_real) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C)))) <= (~ (ord_less_real @ zero_zero_real @ C))) & ((ord_less_eq_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B)) <= (ord_less_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6206_le__minus__divide__eq)). 185.47/93.64 thf(18104,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ (divide_divide_real @ B @ C))) = (((((~ (ord_less_real @ C @ zero_zero_real)) => (ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_real @ C @ zero_zero_real) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C)))) | (ord_less_real @ zero_zero_real @ C)) & ((ord_less_eq_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B)) | ~ (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3137])). 185.47/93.64 thf(4142,axiom,((! [A:num]: (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4846_even__numeral)). 185.47/93.64 thf(21268,plain,((! [A:num]: (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4142])). 185.47/93.64 thf(4962,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((product_Pair_nat_nat @ A @ B) = (product_Pair_nat_nat @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3381_old_Oprod_Oinject)). 185.47/93.64 thf(23977,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((product_Pair_nat_nat @ A @ B) = (product_Pair_nat_nat @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4962])). 185.47/93.64 thf(5310,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ ((ord_less_eq_nat @ B @ A) & ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) != zero_zero_nat))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6301_exp__div__exp__eq)). 185.47/93.64 thf(25275,plain,((! [A:nat,B:nat]: ((divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ ((ord_less_eq_nat @ B @ A) & ~ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = zero_zero_nat))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5310])). 185.47/93.64 thf(3524,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (comm_s4663373288045622133er_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8467_pochhammer__nonneg)). 185.47/93.64 thf(19327,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (comm_s4663373288045622133er_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3524])). 185.47/93.64 thf(2132,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1646_less__add__same__cancel1)). 185.47/93.64 thf(14830,plain,((! [A:real,B:real]: ((ord_less_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2132])). 185.47/93.64 thf(2765,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((powr_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (powr_real @ A @ C) @ (powr_real @ B @ C))) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9100_powr__mult)). 185.47/93.64 thf(16919,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((powr_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (powr_real @ A @ C) @ (powr_real @ B @ C))) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2765])). 185.47/93.64 thf(5690,axiom,((! [A:num,B:num]: ((minus_minus_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (numeral_numeral_rat @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5335_diff__numeral__simps_I2_J)). 185.47/93.64 thf(26666,plain,((! [A:num,B:num]: ((minus_minus_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (numeral_numeral_rat @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5690])). 185.47/93.64 thf(7495,axiom,((! [A:real,B:nat]: ((abs_abs_real @ (power_power_real @ (uminus_uminus_real @ A) @ B)) = (abs_abs_real @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6383_abs__power__minus)). 185.47/93.64 thf(33270,plain,((! [A:real,B:nat]: ((abs_abs_real @ (power_power_real @ (uminus_uminus_real @ A) @ B)) = (abs_abs_real @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7495])). 185.47/93.64 thf(7259,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1690_div__mult__mult1)). 185.47/93.64 thf(32462,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7259])). 185.47/93.64 thf(852,axiom,((ord_less_real @ zero_zero_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7760_pi__half__gt__zero)). 185.47/93.64 thf(10655,plain,((ord_less_real @ zero_zero_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[852])). 185.47/93.64 thf(7572,axiom,((! [A:num]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6661_odd__numeral)). 185.47/93.64 thf(33495,plain,((! [A:num]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7572])). 185.47/93.64 thf(310,axiom,(((tan_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8061_tan__minus__45)). 185.47/93.64 thf(8770,plain,(((tan_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 185.47/93.64 thf(333,axiom,((! [A:real,B:real,C:real]: ((plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ (complex2 @ B @ C)) = (complex2 @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9142_complex__of__real__add__Complex)). 185.47/93.64 thf(8849,plain,((! [A:real,B:real,C:real]: ((plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ (complex2 @ B @ C)) = (complex2 @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 185.47/93.64 thf(502,axiom,((! [A:nat,B:nat]: (((gbinomial_real @ (semiri5074537144036343181t_real @ B) @ A) = (gbinomial_real @ (semiri5074537144036343181t_real @ B) @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8463_gbinomial__of__nat__symmetric)). 185.47/93.64 thf(9420,plain,((! [A:nat,B:nat]: (((gbinomial_real @ (semiri5074537144036343181t_real @ B) @ A) = (gbinomial_real @ (semiri5074537144036343181t_real @ B) @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])). 185.47/93.64 thf(5406,axiom,(((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5407_add__neg__numeral__special_I9_J)). 185.47/93.64 thf(25615,plain,(((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5406])). 185.47/93.64 thf(2958,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C) => (ord_less_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7484_norm__triangle__lt)). 185.47/93.64 thf(17530,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C) => (ord_less_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2958])). 185.47/93.64 thf(4828,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((C != A) <= (ord_less_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3241_pinf_I4_J)). 185.47/93.64 thf(23507,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: (~ (C = A) | ~ (ord_less_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4828])). 185.47/93.64 thf(6764,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((root @ A @ B) = zero_zero_real) = (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9161_real__root__eq__0__iff)). 185.47/93.64 thf(30611,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((root @ A @ B) = zero_zero_real) = (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6764])). 185.47/93.64 thf(5972,axiom,((! [A:num]: ((archim7778729529865785530nd_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7555_round__neg__numeral)). 185.47/93.64 thf(27804,plain,((! [A:num]: ((archim7778729529865785530nd_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5972])). 185.47/93.64 thf(4668,axiom,((! [A:int]: (ord_less_eq_int @ (uminus_uminus_int @ A) @ (abs_abs_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6523_abs__ge__minus__self)). 185.47/93.64 thf(22951,plain,((! [A:int]: (ord_less_eq_int @ (uminus_uminus_int @ A) @ (abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4668])). 185.47/93.64 thf(1272,axiom,((! [A:complex]: ((plus_plus_complex @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7806_sin__cos__squared__add)). 185.47/93.64 thf(11986,plain,((! [A:complex]: ((plus_plus_complex @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272])). 185.47/93.64 thf(1782,axiom,((! [A:real,B:real]: ((A != B) => ((ord_less_real @ A @ B) <= (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4303_order__neq__le__trans)). 185.47/93.64 thf(13704,plain,((! [A:real,B:real]: ((~ (A = B)) => ((ord_less_real @ A @ B) | ~ (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1782])). 185.47/93.64 thf(3876,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3177_le__imp__0__less)). 185.47/93.64 thf(20445,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3876])). 185.47/93.64 thf(2020,axiom,((! [A:nat]: ((set_or4665077453230672383an_nat @ A @ (suc @ A)) = (insert_nat @ A @ bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9555_atLeastLessThan__singleton)). 185.47/93.64 thf(14487,plain,((! [A:nat]: ((set_or4665077453230672383an_nat @ A @ (suc @ A)) = (insert_nat @ A @ bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020])). 185.47/93.64 thf(6882,axiom,((! [A:num,B:num]: ((plus_plus_num @ A @ (inc @ B)) = (inc @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9371_add__inc)). 185.47/93.64 thf(31075,plain,((! [A:num,B:num]: ((plus_plus_num @ A @ (inc @ B)) = (inc @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6882])). 185.47/93.64 thf(6186,axiom,((dvd_dvd_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4613_dvd__def)). 185.47/93.64 thf(28546,plain,(((dvd_dvd_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6186])). 185.47/93.64 thf(6267,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2115_gr0I)). 185.47/93.64 thf(28817,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6267])). 185.47/93.64 thf(3440,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ (plus_plus_rat @ A @ one_one_rat) @ (plus_plus_rat @ B @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1204_add__mono1)). 185.47/93.64 thf(19052,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ (plus_plus_rat @ A @ one_one_rat) @ (plus_plus_rat @ B @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3440])). 185.47/93.64 thf(7381,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1532_add__cancel__right__right)). 185.47/93.64 thf(32863,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7381])). 185.47/93.64 thf(7193,axiom,((! [A:num,B:num]: (((numeral_numeral_rat @ A) = (numeral_numeral_rat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_numeral__eq__iff)). 185.47/93.64 thf(32229,plain,((! [A:num,B:num]: (((numeral_numeral_rat @ A) = (numeral_numeral_rat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7193])). 185.47/93.64 thf(7018,axiom,((! [A:rat]: (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2942_zero__le__power2)). 185.47/93.64 thf(31616,plain,((! [A:rat]: (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7018])). 185.47/93.64 thf(7281,axiom,((! [A:num,B:num,C:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) != (modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ C)) @ (numeral_numeral_nat @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6612_cong__exp__iff__simps_I10_J)). 185.47/93.64 thf(32529,plain,((! [A:num,B:num,C:num]: ~ ((modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ C)) @ (numeral_numeral_nat @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7281])). 185.47/93.64 thf(1007,axiom,((minus_minus_rat = (^ [A:rat,B:rat]: (plus_plus_rat @ A @ (uminus_uminus_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9560_diff__rat__def)). 185.47/93.64 thf(11183,plain,(((minus_minus_rat) = (^ [A:rat,B:rat]: (plus_plus_rat @ A @ (uminus_uminus_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007])). 185.47/93.64 thf(3006,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)) => (ord_less_real @ (divide_divide_real @ C @ B) @ (divide_divide_real @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2711_divide__strict__left__mono)). 185.47/93.64 thf(17694,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)) => (ord_less_real @ (divide_divide_real @ C @ B) @ (divide_divide_real @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3006])). 185.47/93.64 thf(7605,axiom,((! [A:complex,B:nat]: ((power_power_complex @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_complex @ (power_power_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_power__even__eq)). 185.47/93.64 thf(33586,plain,((! [A:complex,B:nat]: ((power_power_complex @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_complex @ (power_power_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7605])). 185.47/93.64 thf(5657,axiom,((! [A:nat,B:(nat > int),C:int]: ((! [D:nat]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (B @ (plus_plus_nat @ D @ one_one_nat)) @ (B @ D))) @ one_one_int) <= (ord_less_nat @ D @ A))) => (((ord_less_eq_int @ C @ (B @ A)) => (? [D:nat]: ((ord_less_eq_nat @ D @ A) & ((B @ D) = C)))) <= (ord_less_eq_int @ (B @ zero_zero_nat) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6840_nat0__intermed__int__val)). 185.47/93.64 thf(26557,plain,((! [A:nat,B:(nat > int),C:int]: ((! [D:nat]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (B @ (plus_plus_nat @ D @ one_one_nat)) @ (B @ D))) @ one_one_int) | ~ (ord_less_nat @ D @ A))) => (((ord_less_eq_int @ C @ (B @ A)) => (? [D:nat]: ((ord_less_eq_nat @ D @ A) & ((B @ D) = C)))) | ~ (ord_less_eq_int @ (B @ zero_zero_nat) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5657])). 185.47/93.64 thf(98,axiom,((! [A:(nat > real),B:nat,C:real]: ((sums_real @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ B))) @ (minus_minus_real @ C @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B)))) = (sums_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8210_sums__iff__shift_H)). 185.47/93.64 thf(8054,plain,((! [A:(nat > real),B:nat,C:real]: ((sums_real @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ B))) @ (minus_minus_real @ C @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B)))) = (sums_real @ (A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[98])). 185.47/93.64 thf(1024,axiom,((! [A:rat,B:nat,C:nat]: ((ord_less_rat @ one_one_rat @ A) => ((ord_less_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_power__strict__increasing__iff)). 185.47/93.64 thf(11232,plain,((! [A:rat,B:nat,C:nat]: ((ord_less_rat @ one_one_rat @ A) => ((ord_less_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024])). 185.47/93.64 thf(4664,axiom,((! [A:rat,B:rat,C:nat]: ((power_power_rat @ (divide_divide_rat @ A @ B) @ C) = (divide_divide_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_power__divide)). 185.47/93.64 thf(22938,plain,((! [A:rat,B:rat,C:nat]: ((power_power_rat @ (divide_divide_rat @ A @ B) @ C) = (divide_divide_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4664])). 185.47/93.64 thf(5784,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = B) = ((A = one_one_real) | (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1674_mult__cancel__right2)). 185.47/93.64 thf(26970,plain,((! [A:real,B:real]: (((times_times_real @ A @ B) = B) = ((A = one_one_real) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5784])). 185.47/93.64 thf(5808,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (((A @ zero_zero_nat) & (C = zero_zero_nat)) | ? [D:nat]: ((A @ D) & (ord_less_nat @ B @ (times_times_nat @ C @ (suc @ D))) & (ord_less_eq_nat @ (times_times_nat @ C @ D) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2969_split__div_H)). 185.47/93.64 thf(27124,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (((A @ zero_zero_nat) & (C = zero_zero_nat)) | ? [D:nat]: ((A @ D) & (ord_less_nat @ B @ (times_times_nat @ C @ (suc @ D))) & (ord_less_eq_nat @ (times_times_nat @ C @ D) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5808])). 185.47/93.64 thf(3610,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ C @ D) => (((ord_less_eq_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D))) <= (ord_less_eq_rat @ zero_zero_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2252_mult__mono_H)). 185.47/93.64 thf(19589,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ C @ D) => (((ord_less_eq_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D))) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3610])). 185.47/93.64 thf(3287,axiom,((! [A:nat]: ((ord_less_real @ zero_zero_real @ (sin_real @ (divide_divide_real @ pi @ (semiri5074537144036343181t_real @ A)))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7934_sin__pi__divide__n__gt__0)). 185.47/93.64 thf(18565,plain,((! [A:nat]: ((ord_less_real @ zero_zero_real @ (sin_real @ (divide_divide_real @ pi @ (semiri5074537144036343181t_real @ A)))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3287])). 185.47/93.64 thf(3599,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (minus_minus_rat @ A @ B)) = (ord_less_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1659_diff__gt__0__iff__gt)). 185.47/93.64 thf(19557,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (minus_minus_rat @ A @ B)) = (ord_less_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3599])). 185.47/93.64 thf(4049,axiom,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ one_one_real) => ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (arctan @ A)) = (arctan @ (divide_divide_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6773_arctan__double)). 185.47/93.64 thf(20981,plain,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ one_one_real) => ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (arctan @ A)) = (arctan @ (divide_divide_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4049])). 185.47/93.64 thf(7515,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C)) <= (! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1077_lift__Suc__mono__le)). 185.47/93.64 thf(33329,plain,((! [A:(nat > nat),B:nat,C:nat]: ((ord_less_eq_nat @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C) | ~ (! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7515])). 185.47/93.64 thf(4788,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((nat2 @ (times_times_int @ A @ B)) = (times_times_nat @ (nat2 @ (uminus_uminus_int @ A)) @ (nat2 @ (uminus_uminus_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9334_nat__mult__distrib__neg)). 185.47/93.64 thf(23383,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((nat2 @ (times_times_int @ A @ B)) = (times_times_nat @ (nat2 @ (uminus_uminus_int @ A)) @ (nat2 @ (uminus_uminus_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4788])). 185.47/93.64 thf(3723,axiom,((! [A:int]: ((ord_less_real @ (ring_1_of_int_real @ A) @ zero_zero_real) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7036_of__int__less__0__iff)). 185.47/93.64 thf(19959,plain,((! [A:int]: ((ord_less_real @ (ring_1_of_int_real @ A) @ zero_zero_real) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3723])). 185.47/93.64 thf(3961,axiom,((! [A:nat]: (ord_less_eq_rat @ zero_zero_rat @ (semiri681578069525770553at_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7208_of__nat__0__le__iff)). 185.47/93.64 thf(20719,plain,((! [A:nat]: (ord_less_eq_rat @ zero_zero_rat @ (semiri681578069525770553at_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3961])). 185.47/93.64 thf(6429,axiom,((! [A:rat,B:nat]: ((ord_less_eq_rat @ zero_zero_rat @ A) <= (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3006_odd__0__le__power__imp__0__le)). 185.47/93.64 thf(29410,plain,((! [A:rat,B:nat]: ((ord_less_eq_rat @ zero_zero_rat @ A) | ~ (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6429])). 185.47/93.64 thf(1270,axiom,(((exp_real @ zero_zero_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8120_exp__zero)). 185.47/93.64 thf(11981,plain,(((exp_real @ zero_zero_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270])). 185.47/93.64 thf(2282,axiom,((neg_nu6511756317524482435omplex = (^ [A:complex]: (minus_minus_complex @ (plus_plus_complex @ A @ A) @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6833_dbl__dec__def)). 185.47/93.64 thf(15306,plain,(((neg_nu6511756317524482435omplex) = (^ [A:complex]: (minus_minus_complex @ (plus_plus_complex @ A @ A) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2282])). 185.47/93.64 thf(2893,axiom,((! [A:int,B:num]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_eq_int @ A @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7071_of__int__le__numeral__iff)). 185.47/93.64 thf(17334,plain,((! [A:int,B:num]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_eq_int @ A @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2893])). 185.47/93.64 thf(2657,axiom,((! [A:rat]: ~ (ord_less_rat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3092_verit__comp__simplify1_I1_J)). 185.47/93.64 thf(16540,plain,((! [A:rat]: ~ (ord_less_rat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2657])). 185.47/93.64 thf(4530,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ B) = ((ord_le3102999989581377725nteger @ A @ B) & (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6517_abs__le__iff)). 185.47/93.64 thf(22513,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ B) = ((ord_le3102999989581377725nteger @ A @ B) & (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4530])). 185.47/93.64 thf(7063,axiom,((! [A:rat,B:num]: ((power_power_rat @ (uminus_uminus_rat @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6001_power__minus__Bit0)). 185.47/93.64 thf(31785,plain,((! [A:rat,B:num]: ((power_power_rat @ (uminus_uminus_rat @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7063])). 185.47/93.64 thf(1834,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = ((plus_plus_real @ A @ C) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_721_eq__diff__eq)). 185.47/93.64 thf(13878,plain,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = ((plus_plus_real @ A @ C) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1834])). 185.47/93.64 thf(1987,axiom,((! [A:rat]: (dvd_dvd_rat @ one_one_rat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4638_one__dvd)). 185.47/93.64 thf(14376,plain,((! [A:rat]: (dvd_dvd_rat @ one_one_rat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1987])). 185.47/93.64 thf(3164,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) = ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ (uminus_uminus_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6516_abs__le__iff)). 185.47/93.64 thf(18190,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) = ((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ (uminus_uminus_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3164])). 185.47/93.64 thf(566,axiom,((! [A:(nat > complex)]: ((groups2073611262835488442omplex @ A @ bot_bot_set_nat) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5217_sum_Oempty)). 185.47/93.64 thf(9612,plain,((! [A:(nat > complex)]: ((groups2073611262835488442omplex @ (A) @ bot_bot_set_nat) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[566])). 185.47/93.64 thf(1710,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5528_verit__negate__coefficient_I2_J)). 185.47/93.64 thf(13456,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710])). 185.47/93.64 thf(2061,axiom,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C)) = (minus_minus_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_add__diff__cancel__left)). 185.47/93.64 thf(14611,plain,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C)) = (minus_minus_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2061])). 185.47/93.64 thf(349,axiom,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ A @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups129246275422532515t_real @ (^ [C:nat]: (times_times_real @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) @ (set_ord_atMost_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8843_prod_Oin__pairs__0)). 185.47/93.64 thf(8902,plain,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ (A) @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups129246275422532515t_real @ (^ [C:nat]: (times_times_real @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) @ (set_ord_atMost_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 185.47/93.64 thf(4952,axiom,((! [A:num,B:int]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) => ((power_power_int @ (abs_abs_int @ B) @ (numeral_numeral_nat @ A)) = (power_power_int @ B @ (numeral_numeral_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6439_power__even__abs__numeral)). 185.47/93.64 thf(23945,plain,((! [A:num,B:int]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) => ((power_power_int @ (abs_abs_int @ B) @ (numeral_numeral_nat @ A)) = (power_power_int @ B @ (numeral_numeral_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4952])). 185.47/93.64 thf(2068,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ B @ A) <= (~ (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4189_not__le__imp__less)). 185.47/93.64 thf(14633,plain,((! [A:rat,B:rat]: ((ord_less_rat @ B @ A) | (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068])). 185.47/93.64 thf(4898,axiom,((! [A:rat,B:rat,C:(rat > rat),D:rat]: ((((ord_less_eq_rat @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F))))) <= (ord_less_eq_rat @ (C @ B) @ D)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3919_order__subst2)). 185.47/93.64 thf(23756,plain,((! [A:rat,B:rat,C:(rat > rat),D:rat]: ((ord_less_eq_rat @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F)))) | ~ (ord_less_eq_rat @ (C @ B) @ D) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4898])). 185.47/93.64 thf(3121,axiom,((abs_abs_int = (^ [A:int]: (if_int @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6569_abs__if__raw)). 185.47/93.64 thf(18058,plain,(((abs_abs_int) = (^ [A:int]: (if_int @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3121])). 185.47/93.64 thf(4214,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ A @ B) <= (A != B)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4299_order__le__neq__trans)). 185.47/93.64 thf(21491,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) | (A = B) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4214])). 185.47/93.64 thf(7273,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ A @ (times_times_nat @ B @ C))) @ C) = (modulo_modulo_nat @ (suc @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1851_Suc__mod__mult__self1)). 185.47/93.64 thf(32504,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ A @ (times_times_nat @ B @ C))) @ C) = (modulo_modulo_nat @ (suc @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7273])). 185.47/93.64 thf(1369,axiom,((! [A:real,B:real,C:real,D:real]: ((A != zero_zero_real) => (((minus_minus_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ D @ B)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A)) @ (times_times_real @ A @ B))) <= (B != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2769_diff__frac__eq)). 185.47/93.64 thf(12291,plain,((! [A:real,B:real,C:real,D:real]: ((~ (A = zero_zero_real)) => (((minus_minus_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ D @ B)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A)) @ (times_times_real @ A @ B))) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369])). 185.47/93.64 thf(4987,axiom,((! [A:vEBT_VEBT,B:nat]: ((((~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT]: ((? [F:vEBT_VEBT]: (A = (vEBT_Node @ C @ (suc @ D) @ E @ F))) => ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))))))))) <= (! [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ C @ zero_zero_nat @ D @ E)))) <= (! [C:$o,D:$o]: ((((B = zero_zero_nat) => (C)) & (((B = one_one_nat) & ((D) <= (B = one_one_nat))) <= (B != zero_zero_nat))) <= (A = (vEBT_Leaf @ C @ D))))) <= (~ (vEBT_V5719532721284313246member @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3002_VEBT__internal_Onaive__member_Oelims_I3_J)). 185.47/93.64 thf(24045,plain,((! [A:vEBT_VEBT,B:nat]: (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT]: ((? [F:vEBT_VEBT]: (A = (vEBT_Node @ C @ (suc @ D) @ E @ F))) => ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))))))) | ~ (! [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ C @ zero_zero_nat @ D @ E))) | ~ (! [C:$o,D:$o]: ((((B = zero_zero_nat) => (C)) & (((B = one_one_nat) & ((D) | ~ (B = one_one_nat))) | (B = zero_zero_nat))) | ~ (A = (vEBT_Leaf @ C @ D)))) | (vEBT_V5719532721284313246member @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4987])). 185.47/93.64 thf(1253,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ (divide_divide_int @ A @ B) @ (divide_divide_int @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3051_zdiv__mono2__neg)). 185.47/93.64 thf(11934,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ (divide_divide_int @ A @ B) @ (divide_divide_int @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253])). 185.47/93.64 thf(1579,axiom,((! [A:num,B:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (numeral_numeral_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5691_neg__numeral__le__numeral)). 185.47/93.64 thf(12961,plain,((! [A:num,B:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (numeral_numeral_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579])). 185.47/93.64 thf(680,axiom,((! [A:nat,B:nat]: ((if_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Nat__Onat_T)). 185.47/93.64 thf(10003,plain,((! [A:nat,B:nat]: ((if_nat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[680])). 185.47/93.64 thf(1246,axiom,((! [A:real,B:nat,C:real,D:nat]: (((dvd_dvd_real @ (power_power_real @ A @ D) @ C) <= (ord_less_eq_nat @ D @ B)) <= (dvd_dvd_real @ (power_power_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4793_power__le__dvd)). 185.47/93.64 thf(11911,plain,((! [A:real,B:nat,C:real,D:nat]: ((dvd_dvd_real @ (power_power_real @ A @ D) @ C) | ~ (ord_less_eq_nat @ D @ B) | ~ (dvd_dvd_real @ (power_power_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246])). 185.47/93.64 thf(4945,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (semiri1316708129612266289at_nat @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7044_of__nat__power__less__of__nat__cancel__iff)). 185.47/93.64 thf(23924,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (semiri1316708129612266289at_nat @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4945])). 185.47/93.64 thf(2010,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ A @ B) => (((ord_less_eq_real @ zero_zero_real @ D) => ((((plus_plus_real @ D @ E) = one_one_real) => (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ D @ A) @ (times_times_real @ E @ C)) @ B)) <= (ord_less_eq_real @ zero_zero_real @ E))) <= (ord_less_eq_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2856_convex__bound__le)). 185.47/93.64 thf(14455,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ A @ B) => (((ord_less_eq_real @ zero_zero_real @ D) => ((((plus_plus_real @ D @ E) = one_one_real) => (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ D @ A) @ (times_times_real @ E @ C)) @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ E))) | ~ (ord_less_eq_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2010])). 185.47/93.64 thf(4903,axiom,((! [A:nat]: ((ord_max_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3598_max__0R)). 185.47/93.64 thf(23771,plain,((! [A:nat]: ((ord_max_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4903])). 185.47/93.64 thf(3293,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = ((plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) = E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1221_eq__add__iff1)). 185.47/93.64 thf(18582,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = ((plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3293])). 185.47/93.64 thf(1042,axiom,((! [A:num,B:num]: ((ord_less_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_numeral__less__iff)). 185.47/93.64 thf(11285,plain,((! [A:num,B:num]: ((ord_less_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042])). 185.47/93.64 thf(5803,axiom,((! [A:int,B:num]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_int @ (times_times_int @ A @ (power_power_int @ A @ (numeral_numeral_nat @ B))) @ (power_power_int @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6636_power__numeral__odd)). 185.47/93.64 thf(27107,plain,((! [A:int,B:num]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_int @ (times_times_int @ A @ (power_power_int @ A @ (numeral_numeral_nat @ B))) @ (power_power_int @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5803])). 185.47/93.64 thf(3850,axiom,((! [A:rat,B:rat,C:rat]: (((uminus_uminus_rat @ (divide_divide_rat @ A @ B)) = C) = (((B != zero_zero_rat) => ((uminus_uminus_rat @ A) = (times_times_rat @ C @ B))) & ((B = zero_zero_rat) => (C = zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5971_minus__divide__eq__eq)). 185.47/93.64 thf(20364,plain,((! [A:rat,B:rat,C:rat]: (((uminus_uminus_rat @ (divide_divide_rat @ A @ B)) = C) = (((~ (B = zero_zero_rat)) => ((uminus_uminus_rat @ A) = (times_times_rat @ C @ B))) & ((B = zero_zero_rat) => (C = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3850])). 185.47/93.64 thf(2717,axiom,((! [A:real,B:nat,C:nat]: ((ord_less_real @ one_one_real @ A) => (((power_power_real @ A @ B) = (power_power_real @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_power__inject__exp)). 185.47/93.64 thf(16772,plain,((! [A:real,B:nat,C:nat]: ((ord_less_real @ one_one_real @ A) => (((power_power_real @ A @ B) = (power_power_real @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2717])). 185.47/93.64 thf(816,axiom,((! [A:(nat > real)]: (((ord_less_eq_real @ zero_zero_real @ (suminf_real @ A)) <= (! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B)))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7686_suminf__nonneg)). 185.47/93.64 thf(10516,plain,((! [A:(nat > real)]: ((ord_less_eq_real @ zero_zero_real @ (suminf_real @ (A))) | ~ (! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[816])). 185.47/93.64 thf(6771,axiom,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3043_zmod__numeral__Bit0)). 185.47/93.64 thf(30643,plain,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6771])). 185.47/93.64 thf(1055,axiom,((! [A:int,B:int]: ((minus_minus_int @ A @ (uminus_uminus_int @ B)) = (plus_plus_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5203_diff__minus__eq__add)). 185.47/93.64 thf(11321,plain,((! [A:int,B:int]: ((minus_minus_int @ A @ (uminus_uminus_int @ B)) = (plus_plus_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055])). 185.47/93.64 thf(3197,axiom,((! [A:int,B:nat,C:nat]: ((modulo_modulo_int @ A @ (times_times_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C))) = (plus_plus_int @ (times_times_int @ (semiri1314217659103216013at_int @ B) @ (modulo_modulo_int @ (divide_divide_int @ A @ (semiri1314217659103216013at_int @ B)) @ (semiri1314217659103216013at_int @ C))) @ (modulo_modulo_int @ A @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7293_mod__mult2__eq_H)). 185.47/93.64 thf(18292,plain,((! [A:int,B:nat,C:nat]: ((modulo_modulo_int @ A @ (times_times_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C))) = (plus_plus_int @ (times_times_int @ (semiri1314217659103216013at_int @ B) @ (modulo_modulo_int @ (divide_divide_int @ A @ (semiri1314217659103216013at_int @ B)) @ (semiri1314217659103216013at_int @ C))) @ (modulo_modulo_int @ A @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3197])). 185.47/93.64 thf(1114,axiom,((! [A:int]: ((plus_plus_int @ A @ (uminus_uminus_int @ A)) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5168_add_Oright__inverse)). 185.47/93.64 thf(11512,plain,((! [A:int]: ((plus_plus_int @ A @ (uminus_uminus_int @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114])). 185.47/93.64 thf(325,axiom,((! [A:real]: (((nat2 @ (archim6058952711729229775r_real @ A)) = zero_zero_nat) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9319_nat__floor__neg)). 185.47/93.64 thf(8819,plain,((! [A:real]: (((nat2 @ (archim6058952711729229775r_real @ A)) = zero_zero_nat) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 185.47/93.64 thf(5050,axiom,(((('?') @ option4927543243414619207at_nat) = (^ [A:(option4927543243414619207at_nat > $o)]: (? [B:product_prod_nat_nat]: (A @ (some_P7363390416028606310at_nat @ B)) | (A @ none_P5556105721700978146at_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1170_split__option__ex)). 185.47/93.64 thf(24330,plain,(((('?') @ option4927543243414619207at_nat) = (^ [A:(option4927543243414619207at_nat > $o)]: (? [B:product_prod_nat_nat]: (A @ (some_P7363390416028606310at_nat @ B)) | (A @ none_P5556105721700978146at_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5050])). 185.47/93.64 thf(2421,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_add_Oright__cancel)). 185.47/93.64 thf(15742,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2421])). 185.47/93.64 thf(1123,axiom,((! [A:complex]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (exp_complex @ A)) @ (numeral_numeral_real @ (bit0 @ one))) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8250_exp__bound__half)). 185.47/93.64 thf(11538,plain,((! [A:complex]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (exp_complex @ A)) @ (numeral_numeral_real @ (bit0 @ one))) | ~ (ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123])). 185.47/93.64 thf(1378,axiom,((! [A:num]: ~ (ord_less_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5955_not__one__less__neg__numeral)). 185.47/93.64 thf(12319,plain,((! [A:num]: ~ (ord_less_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378])). 185.47/93.64 thf(2806,axiom,((! [A:nat]: (ord_less_rat @ zero_zero_rat @ (semiri773545260158071498ct_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7992_fact__gt__zero)). 185.47/93.64 thf(17049,plain,((! [A:nat]: (ord_less_rat @ zero_zero_rat @ (semiri773545260158071498ct_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2806])). 185.47/93.64 thf(3615,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6751_sum_Oin__pairs)). 185.47/93.64 thf(19604,plain,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3615])). 185.47/93.64 thf(1230,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((A = zero_zero_real) <= (! [C:nat]: ((ord_less_eq_real @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ A) @ B) <= (ord_less_nat @ zero_zero_nat @ C))))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7324_real__archimedian__rdiv__eq__0)). 185.47/93.64 thf(11859,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((A = zero_zero_real) | ~ (! [C:nat]: ((ord_less_eq_real @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ A) @ B) | ~ (ord_less_nat @ zero_zero_nat @ C))))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230])). 185.47/93.64 thf(5588,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ (power_power_int @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1068_power__Suc2)). 185.47/93.64 thf(26326,plain,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ (power_power_int @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5588])). 185.47/93.64 thf(1907,axiom,((! [A:nat,B:nat,C:complex]: ((dvd_dvd_complex @ (power_power_complex @ C @ A) @ (power_power_complex @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4790_le__imp__power__dvd)). 185.47/93.64 thf(14103,plain,((! [A:nat,B:nat,C:complex]: ((dvd_dvd_complex @ (power_power_complex @ C @ A) @ (power_power_complex @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1907])). 185.47/93.64 thf(3125,axiom,((! [A:num]: ~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5898_not__zero__le__neg__numeral)). 185.47/93.64 thf(18069,plain,((! [A:num]: ~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3125])). 185.47/93.64 thf(2966,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ one @ (bitM @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9444_or__minus__numerals_I5_J)). 185.47/93.64 thf(17562,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ one @ (bitM @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2966])). 185.47/93.64 thf(3553,axiom,((! [A:complex]: (((real_V1022390504157884413omplex @ A) = one_one_real) => (~ (! [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ B @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => (A != (complex2 @ (cos_real @ B) @ (sin_real @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7951_complex__unimodular__polar)). 185.47/93.64 thf(19414,plain,((! [A:complex]: (((real_V1022390504157884413omplex @ A) = one_one_real) => (~ (! [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ B @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => (~ (A = (complex2 @ (cos_real @ B) @ (sin_real @ B))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3553])). 185.47/93.64 thf(3656,axiom,((! [A:real,B:real,C:real]: (((minus_minus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (minus_minus_real @ B @ (times_times_real @ C @ A)) @ A)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2763_divide__diff__eq__iff)). 185.47/93.64 thf(19736,plain,((! [A:real,B:real,C:real]: (((minus_minus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (minus_minus_real @ B @ (times_times_real @ C @ A)) @ A)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3656])). 185.47/93.64 thf(4741,axiom,((! [A:num]: ((numeral_numeral_int @ (bit1 @ A)) = (plus_plus_int @ (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6604_numeral__Bit1)). 185.47/93.64 thf(23204,plain,((! [A:num]: ((numeral_numeral_int @ (bit1 @ A)) = (plus_plus_int @ (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4741])). 185.47/93.64 thf(2935,axiom,((! [A:int,B:int]: ((ord_less_int @ (modulo_modulo_int @ B @ A) @ A) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3153_Euclidean__Division_Opos__mod__bound)). 185.47/93.64 thf(17466,plain,((! [A:int,B:int]: ((ord_less_int @ (modulo_modulo_int @ B @ A) @ A) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2935])). 185.47/93.64 thf(5729,axiom,((! [A:nat]: ((power_power_complex @ zero_zero_complex @ (suc @ A)) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1745_power__0__Suc)). 185.47/93.64 thf(26795,plain,((! [A:nat]: ((power_power_complex @ zero_zero_complex @ (suc @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5729])). 185.47/93.64 thf(6832,axiom,((! [A:num,B:num]: ((ord_less_num @ (bit1 @ A) @ (bit0 @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6391_semiring__norm_I81_J)). 185.47/93.64 thf(30844,plain,((! [A:num,B:num]: ((ord_less_num @ (bit1 @ A) @ (bit0 @ B)) = (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6832])). 185.47/93.64 thf(6014,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ (A @ B) @ C) @ (A @ (plus_plus_nat @ B @ C))) <= (! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) <= (ord_less_nat @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_mono__nat__linear__lb)). 185.47/93.64 thf(27938,plain,((! [A:(nat > nat),B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ (A @ B) @ C) @ (A @ (plus_plus_nat @ B @ C))) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) | ~ (ord_less_nat @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6014])). 185.47/93.64 thf(7593,axiom,((! [A:(nat > $o),B:nat]: (((! [C:nat,D:$o]: ((((divide_divide_nat @ (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ D) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (numeral_numeral_nat @ (bit0 @ one))) = C) => (A @ (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ D) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) <= (A @ C))) => (A @ B)) <= (! [C:nat]: (((divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) = C) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6257_bits__induct)). 185.47/93.64 thf(33549,plain,((! [A:(nat > $o),B:nat]: (((! [C:nat,D:$o]: ((((divide_divide_nat @ (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ D) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (numeral_numeral_nat @ (bit0 @ one))) = C) => (A @ (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ D) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) | ~ (A @ C))) => (A @ B)) | ~ (! [C:nat]: (((divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) = C) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7593])). 185.47/93.64 thf(4649,axiom,((~ (ord_less_rat @ zero_zero_rat @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2028_less__numeral__extra_I3_J)). 185.47/93.64 thf(22891,plain,((~ (ord_less_rat @ zero_zero_rat @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4649])). 185.47/93.64 thf(7670,axiom,((ord_less_nat @ za @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24__092_060open_062z_A_060_A2_A_094_Adeg_092_060close_062)). 185.47/93.64 thf(33761,plain,((ord_less_nat @ za @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7670])). 185.47/93.64 thf(3419,axiom,((! [A:int,B:int]: ((minus_minus_int @ A @ (times_times_int @ B @ (divide_divide_int @ A @ B))) = (modulo_modulo_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2554_minus__mult__div__eq__mod)). 185.47/93.64 thf(18988,plain,((! [A:int,B:int]: ((minus_minus_int @ A @ (times_times_int @ B @ (divide_divide_int @ A @ B))) = (modulo_modulo_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3419])). 185.47/93.64 thf(6225,axiom,((zero_zero_complex != (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5720_zero__neq__neg__one)). 185.47/93.64 thf(28677,plain,((~ (zero_zero_complex = (uminus1482373934393186551omplex @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6225])). 185.47/93.64 thf(1909,axiom,((~ (ord_less_real @ one_one_real @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2380_not__one__less__zero)). 185.47/93.64 thf(14109,plain,((~ (ord_less_real @ one_one_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1909])). 185.47/93.64 thf(1973,axiom,((! [A:real,B:real,C:real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_divide__divide__eq__left)). 185.47/93.64 thf(14334,plain,((! [A:real,B:real,C:real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1973])). 185.47/93.64 thf(4495,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2410_divide__right__mono)). 185.47/93.64 thf(22389,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4495])). 185.47/93.64 thf(1362,axiom,((! [A:rat]: ((~ (! [B:rat]: ((ord_less_rat @ zero_zero_rat @ B) => (! [C:rat]: ((A != (plus_plus_rat @ B @ C)) <= (ord_less_rat @ zero_zero_rat @ C)))))) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9548_obtain__pos__sum)). 185.47/93.64 thf(12269,plain,((! [A:rat]: (~ (! [B:rat]: ((ord_less_rat @ zero_zero_rat @ B) => (! [C:rat]: (~ (A = (plus_plus_rat @ B @ C)) | ~ (ord_less_rat @ zero_zero_rat @ C))))) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362])). 185.47/93.64 thf(3698,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4057_order__less__asym)). 185.47/93.64 thf(19868,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3698])). 185.47/93.64 thf(4522,axiom,((! [A:(nat > int),B:nat,C:nat]: (((ord_less_int @ (A @ B) @ (A @ C)) <= (ord_less_nat @ B @ C)) <= (! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_lift__Suc__mono__less)). 185.47/93.64 thf(22488,plain,((! [A:(nat > int),B:nat,C:nat]: ((ord_less_int @ (A @ B) @ (A @ C)) | ~ (ord_less_nat @ B @ C) | ~ (! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4522])). 185.47/93.64 thf(6386,axiom,((! [A:nat,B:real]: (((ord_less_real @ (root @ A @ B) @ one_one_real) = (ord_less_real @ B @ one_one_real)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9170_real__root__lt__1__iff)). 185.47/93.64 thf(29231,plain,((! [A:nat,B:real]: (((ord_less_real @ (root @ A @ B) @ one_one_real) = (ord_less_real @ B @ one_one_real)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6386])). 185.47/93.64 thf(5128,axiom,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_mult_Oright__neutral)). 185.47/93.64 thf(24609,plain,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5128])). 185.47/93.64 thf(1075,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3817_dual__order_Orefl)). 185.47/93.64 thf(11378,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075])). 185.47/93.64 thf(3745,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2331_mult__pos__pos)). 185.47/93.64 thf(20027,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) | ~ (ord_less_int @ zero_zero_int @ B) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3745])). 185.47/93.64 thf(6698,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2508_mult__less__mono2)). 185.47/93.64 thf(30321,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6698])). 185.47/93.64 thf(265,axiom,((! [A:int,B:int,C:int]: ((~ ((ord_less_int @ A @ C) => (~ (ord_less_int @ B @ C)))) <= (ord_less_int @ (ord_max_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3729_max_Ostrict__boundedE)). 185.47/93.64 thf(8600,plain,((! [A:int,B:int,C:int]: (~ ((ord_less_int @ A @ C) => (~ (ord_less_int @ B @ C))) | ~ (ord_less_int @ (ord_max_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[265])). 185.47/93.64 thf(4914,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1683_nonzero__mult__div__cancel__right)). 185.47/93.64 thf(23803,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4914])). 185.47/93.64 thf(7035,axiom,((! [A:nat,B:nat,C:rat]: (((ord_less_rat @ zero_zero_rat @ C) => ((ord_less_rat @ (power_power_rat @ C @ B) @ (power_power_rat @ C @ A)) <= (ord_less_rat @ C @ one_one_rat))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2880_power__strict__decreasing)). 185.47/93.64 thf(31696,plain,((! [A:nat,B:nat,C:rat]: (((ord_less_rat @ zero_zero_rat @ C) => ((ord_less_rat @ (power_power_rat @ C @ B) @ (power_power_rat @ C @ A)) | ~ (ord_less_rat @ C @ one_one_rat))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7035])). 185.47/93.64 thf(5877,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = (times_times_nat @ (modulo_modulo_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1979_mod__mult__mult2)). 185.47/93.64 thf(27451,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = (times_times_nat @ (modulo_modulo_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5877])). 185.47/93.64 thf(157,axiom,((! [A:int,B:nat]: (ord_less_eq_int @ A @ (bit_se7879613467334960850it_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3147_set__bit__greater__eq)). 185.47/93.64 thf(8235,plain,((! [A:int,B:nat]: (ord_less_eq_int @ A @ (bit_se7879613467334960850it_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 185.47/93.64 thf(3375,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1250_empty__subsetI)). 185.47/93.64 thf(18846,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3375])). 185.47/93.64 thf(4566,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_add__strict__right__mono)). 185.47/93.64 thf(22627,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4566])). 185.47/93.64 thf(6054,axiom,((! [A:nat,B:nat,C:int]: ((ord_less_nat @ A @ B) => ((ord_less_int @ zero_zero_int @ C) => ((ord_less_int @ C @ one_one_int) => (ord_less_int @ (power_power_int @ C @ B) @ (power_power_int @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2882_power__strict__decreasing)). 185.47/93.64 thf(28050,plain,((! [A:nat,B:nat,C:int]: ((ord_less_nat @ A @ B) => ((ord_less_int @ zero_zero_int @ C) => ((ord_less_int @ C @ one_one_int) => (ord_less_int @ (power_power_int @ C @ B) @ (power_power_int @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6054])). 185.47/93.64 thf(3188,axiom,((! [A:int,B:int,C:nat]: ((dvd_dvd_int @ A @ B) => (dvd_dvd_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4680_dvd__power__same)). 185.47/93.64 thf(18264,plain,((! [A:int,B:int,C:nat]: ((dvd_dvd_int @ A @ B) => (dvd_dvd_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3188])). 185.47/93.64 thf(2818,axiom,((! [A:nat,B:nat]: (((~ (ord_less_eq_nat @ A @ B)) => ((nat2 @ (abs_abs_int @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))) = (minus_minus_nat @ A @ B))) & ((ord_less_eq_nat @ A @ B) => ((nat2 @ (abs_abs_int @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))) = (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9335_nat__abs__int__diff)). 185.47/93.64 thf(17085,plain,((! [A:nat,B:nat]: (((~ (ord_less_eq_nat @ A @ B)) => ((nat2 @ (abs_abs_int @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))) = (minus_minus_nat @ A @ B))) & ((ord_less_eq_nat @ A @ B) => ((nat2 @ (abs_abs_int @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))) = (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2818])). 185.47/93.64 thf(1349,axiom,((! [A:real]: (((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A)) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) <= (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6306_abs__ln__one__plus__x__minus__x__bound__nonpos)). 185.47/93.64 thf(12229,plain,((! [A:real]: (((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A)) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349])). 185.47/93.64 thf(3798,axiom,((! [A:int,B:int,C:nat]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (ring_1_of_int_rat @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7107_of__int__power__less__of__int__cancel__iff)). 185.47/93.64 thf(20203,plain,((! [A:int,B:int,C:nat]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (ring_1_of_int_rat @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3798])). 185.47/93.64 thf(7621,axiom,(((image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char) = (set_or4665077453230672383an_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ one)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9978_range__nat__of__char)). 185.47/93.64 thf(33627,plain,(((image_char_nat @ (comm_s629917340098488124ar_nat) @ top_top_set_char) = (set_or4665077453230672383an_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ one)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7621])). 185.47/93.64 thf(2044,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((ord_less_int @ A @ B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_add__mono__thms__linordered__field_I1_J)). 185.47/93.64 thf(14564,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ ((ord_less_int @ A @ B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2044])). 185.47/93.64 thf(5900,axiom,((! [A:real,B:real]: ((uminus_uminus_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5099_minus__diff__eq)). 185.47/93.64 thf(27541,plain,((! [A:real,B:real]: ((uminus_uminus_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5900])). 185.47/93.64 thf(2578,axiom,(((archim7778729529865785530nd_rat @ one_one_rat) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7549_round__1)). 185.47/93.64 thf(16272,plain,(((archim7778729529865785530nd_rat @ one_one_rat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2578])). 185.47/93.64 thf(943,axiom,((! [A:real]: (((sin_real @ A) = zero_zero_real) = (? [B:int]: (A = (times_times_real @ (ring_1_of_int_real @ B) @ pi)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7868_sin__zero__iff__int2)). 185.47/93.64 thf(10967,plain,((! [A:real]: (((sin_real @ A) = zero_zero_real) = (? [B:int]: (A = (times_times_real @ (ring_1_of_int_real @ B) @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[943])). 185.47/93.64 thf(4377,axiom,((! [A:nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_nat @ (C @ (suc @ B)) @ (groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6652_sum_Onat__ivl__Suc_H)). 185.47/93.64 thf(22023,plain,((! [A:nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_nat @ (C @ (suc @ B)) @ (groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4377])). 185.47/93.64 thf(1190,axiom,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_bits__div__by__1)). 185.47/93.64 thf(11741,plain,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190])). 185.47/93.64 thf(7511,axiom,(((power_power_complex @ imaginary_unit @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8992_power2__i)). 185.47/93.64 thf(33319,plain,(((power_power_complex @ imaginary_unit @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7511])). 185.47/93.64 thf(3969,axiom,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = B) = ((ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) & (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9347_take__bit__int__eq__self__iff)). 185.47/93.64 thf(20740,plain,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = B) = ((ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) & (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3969])). 185.47/93.64 thf(1334,axiom,((! [A:num,B:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_numeral__le__iff)). 185.47/93.64 thf(12180,plain,((! [A:num,B:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334])). 185.47/93.64 thf(3716,axiom,((! [A:nat]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ semiri8010041392384452111omplex @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7356_double__gauss__sum__from__Suc__0)). 185.47/93.64 thf(19937,plain,((! [A:nat]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ (semiri8010041392384452111omplex) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3716])). 185.47/93.64 thf(7104,axiom,((! [A:nat,B:nat]: (((semiri1316708129612266289at_nat @ A) = (semiri1316708129612266289at_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6869_of__nat__eq__iff)). 185.47/93.64 thf(31911,plain,((! [A:nat,B:nat]: (((semiri1316708129612266289at_nat @ A) = (semiri1316708129612266289at_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7104])). 185.47/93.64 thf(6890,axiom,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: (((some_P7363390416028606310at_nat @ A) = (some_P7363390416028606310at_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_option_Oinject)). 185.47/93.64 thf(31103,plain,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: (((some_P7363390416028606310at_nat @ A) = (some_P7363390416028606310at_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6890])). 185.47/93.64 thf(3893,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7248_int__ops_I5_J)). 185.47/93.64 thf(20494,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3893])). 185.47/93.64 thf(5542,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_int @ A @ (power_power_int @ (power_power_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_power__odd__eq)). 185.47/93.64 thf(26190,plain,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_int @ A @ (power_power_int @ (power_power_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5542])). 185.47/93.64 thf(6349,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7987_fact__ge__zero)). 185.47/93.64 thf(29112,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6349])). 185.47/93.64 thf(2561,axiom,((! [A:num]: ((neg_nu8295874005876285629c_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7006_dbl__inc__simps_I5_J)). 185.47/93.64 thf(16223,plain,((! [A:num]: ((neg_nu8295874005876285629c_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2561])). 185.47/93.64 thf(201,axiom,((! [A:rat]: ((gbinomial_rat @ A @ zero_zero_nat) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8416_gbinomial__0_I1_J)). 185.47/93.64 thf(8384,plain,((! [A:rat]: ((gbinomial_rat @ A @ zero_zero_nat) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 185.47/93.64 thf(6533,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_add__leD1)). 185.47/93.64 thf(29788,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6533])). 185.47/93.64 thf(2659,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ C @ B)) = ((A = C) | (B = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1577_divide__cancel__right)). 185.47/93.64 thf(16545,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ C @ B)) = ((A = C) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2659])). 185.47/93.64 thf(7343,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9451_or__nat__numerals_I3_J)). 185.47/93.64 thf(32747,plain,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7343])). 185.47/93.64 thf(453,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (arcsin @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8327_arcsin__ubound)). 185.47/93.64 thf(9240,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (arcsin @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[453])). 185.47/93.64 thf(6799,axiom,((! [A:nat,B:nat]: ((times_times_nat @ A @ (suc @ B)) = (plus_plus_nat @ A @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1011_mult__Suc__right)). 185.47/93.64 thf(30734,plain,((! [A:nat,B:nat]: ((times_times_nat @ A @ (suc @ B)) = (plus_plus_nat @ A @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6799])). 185.47/93.64 thf(1219,axiom,(((nat_set_decode @ zero_zero_nat) = bot_bot_set_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4504_set__decode__zero)). 185.47/93.64 thf(11827,plain,(((nat_set_decode @ zero_zero_nat) = bot_bot_set_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219])). 185.47/93.64 thf(5034,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (~ (! [B:nat]: (A != (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4960_oddE)). 185.47/93.64 thf(24205,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (~ (! [B:nat]: ~ (A = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5034])). 185.47/93.64 thf(2137,axiom,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (B @ C)))) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1346_Collect__subset)). 185.47/93.64 thf(14844,plain,((! [A:set_nat,B:(nat > $o)]: (ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (B @ C)))) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2137])). 185.47/93.64 thf(6247,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4056_order__less__asym)). 185.47/93.64 thf(28751,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6247])). 185.47/93.64 thf(275,axiom,((! [A:nat,B:nat,C:(nat > real)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_real @ (C @ (suc @ B)) @ (groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6653_sum_Onat__ivl__Suc_H)). 185.47/93.64 thf(8632,plain,((! [A:nat,B:nat,C:(nat > real)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_real @ (C @ (suc @ B)) @ (groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 185.47/93.64 thf(297,axiom,((! [A:option_nat,B:option_nat]: ((if_option_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T)). 185.47/93.64 thf(8703,plain,((! [A:option_nat,B:option_nat]: ((if_option_nat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 185.47/93.64 thf(7431,axiom,((! [A:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) = (plus_plus_complex @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_mult__2)). 185.47/93.64 thf(33041,plain,((! [A:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) = (plus_plus_complex @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7431])). 185.47/93.64 thf(6596,axiom,((! [A:num]: ((minus_minus_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (nat2 @ (minus_minus_int @ (numeral_numeral_int @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9261_nat__numeral__diff__1)). 185.47/93.64 thf(29993,plain,((! [A:num]: ((minus_minus_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (nat2 @ (minus_minus_int @ (numeral_numeral_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6596])). 185.47/93.64 thf(1227,axiom,((! [A:nat,B:num]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_nat @ A @ (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7018_real__of__nat__less__numeral__iff)). 185.47/93.64 thf(11849,plain,((! [A:nat,B:num]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_nat @ A @ (numeral_numeral_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227])). 185.47/93.64 thf(670,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ zero_zero_real @ (arccos @ A))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8365_arccos__lbound)). 185.47/93.64 thf(9973,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ zero_zero_real @ (arccos @ A))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[670])). 185.47/93.64 thf(6500,axiom,((! [A:nat,B:list_VEBT_VEBT,C:nat,D:vEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ D) @ C) = D) <= (A = C)) & (((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ D) @ C) = (nth_VEBT_VEBT @ B @ C)) <= (A != C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3785_nth__list__update)). 185.47/93.64 thf(29663,plain,((! [A:nat,B:list_VEBT_VEBT,C:nat,D:vEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ D) @ C) = D) | ~ (A = C)) & (((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ D) @ C) = (nth_VEBT_VEBT @ B @ C)) | (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6500])). 185.47/93.64 thf(7220,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ (minus_minus_nat @ A @ B) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2131_mod__geq)). 185.47/93.64 thf(32328,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ (minus_minus_nat @ A @ B) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7220])). 185.47/93.64 thf(2166,axiom,((! [A:nat,B:nat]: ((dvd_dvd_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8005_fact__dvd)). 185.47/93.64 thf(14949,plain,((! [A:nat,B:nat]: ((dvd_dvd_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2166])). 185.47/93.64 thf(3996,axiom,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o),C:nat]: (((B @ (nth_VEBT_VEBT @ A @ C)) <= (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A))) <= (! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)) => (B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_inthall)). 185.47/93.64 thf(20822,plain,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o),C:nat]: ((B @ (nth_VEBT_VEBT @ A @ C)) | ~ (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)) | ~ (! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)) => (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3996])). 185.47/93.64 thf(857,axiom,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ B) => (summable_real @ (^ [C:nat]: (minus_minus_real @ (A @ C) @ (B @ C))))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7661_summable__diff)). 185.47/93.64 thf(10665,plain,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ (B)) => (summable_real @ (^ [C:nat]: (minus_minus_real @ (A @ C) @ (B @ C))))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[857])). 185.47/93.64 thf(7674,axiom,((! [A:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (suc @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1017_add__2__eq__Suc)). 185.47/93.64 thf(33771,plain,((! [A:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (suc @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7674])). 185.47/93.64 thf(5238,axiom,((! [A:num]: (zero_zero_complex != (numera6690914467698888265omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2035_zero__neq__numeral)). 185.47/93.64 thf(25003,plain,((! [A:num]: ~ (zero_zero_complex = (numera6690914467698888265omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5238])). 185.47/93.64 thf(6687,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7995_fact__gt__zero)). 185.47/93.64 thf(30289,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6687])). 185.47/93.64 thf(936,axiom,((! [A:real]: ((ord_less_eq_real @ (arctan @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6783_arctan__le__zero__iff)). 185.47/93.64 thf(10945,plain,((! [A:real]: ((ord_less_eq_real @ (arctan @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[936])). 185.47/93.64 thf(1722,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((plus_plus_rat @ A @ D) = (plus_plus_rat @ B @ (plus_plus_rat @ C @ D))) <= (A = (plus_plus_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_group__cancel_Oadd1)). 185.47/93.64 thf(13506,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((plus_plus_rat @ A @ D) = (plus_plus_rat @ B @ (plus_plus_rat @ C @ D))) | ~ (A = (plus_plus_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722])). 185.47/93.64 thf(6777,axiom,(((sqrt @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8112_real__sqrt__zero)). 185.47/93.64 thf(30662,plain,(((sqrt @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6777])). 185.47/93.64 thf(5680,axiom,((! [A:nat,B:nat,C:int]: ((((ord_less_eq_int @ C @ one_one_int) => (ord_less_eq_int @ (power_power_int @ C @ B) @ (power_power_int @ C @ A))) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2886_power__decreasing)). 185.47/93.64 thf(26634,plain,((! [A:nat,B:nat,C:int]: (((ord_less_eq_int @ C @ one_one_int) => (ord_less_eq_int @ (power_power_int @ C @ B) @ (power_power_int @ C @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5680])). 185.47/93.64 thf(2978,axiom,((! [A:real,B:real,C:real]: (((A = zero_zero_real) => ((plus_plus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = C)) & (((plus_plus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (divide_divide_real @ (plus_plus_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)) @ A)) <= (A != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6165_add__divide__eq__if__simps_I3_J)). 185.47/93.64 thf(17603,plain,((! [A:real,B:real,C:real]: (((A = zero_zero_real) => ((plus_plus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = C)) & (((plus_plus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (divide_divide_real @ (plus_plus_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)) @ A)) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2978])). 185.47/93.64 thf(1682,axiom,((! [A:num]: ((neg_numeral_dbl_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3830_dbl__simps_I5_J)). 185.47/93.64 thf(13365,plain,((! [A:num]: ((neg_numeral_dbl_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682])). 185.47/93.64 thf(4697,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ (times_times_rat @ A @ B) @ zero_zero_rat)) <= (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2210_mult__nonpos__nonneg)). 185.47/93.64 thf(23064,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ (times_times_rat @ A @ B) @ zero_zero_rat)) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4697])). 185.47/93.64 thf(2444,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= ((ord_less_real @ C @ D) & (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_add__mono__thms__linordered__field_I2_J)). 185.47/93.64 thf(15824,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ ((ord_less_real @ C @ D) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2444])). 185.47/93.64 thf(3722,axiom,((! [A:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5730_ab__group__add__class_Oab__left__minus)). 185.47/93.64 thf(19956,plain,((! [A:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3722])). 185.47/93.64 thf(5114,axiom,((! [A:num]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5451_diff__numeral__special_I4_J)). 185.47/93.64 thf(24561,plain,((! [A:num]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5114])). 185.47/93.64 thf(6353,axiom,((! [A:int,B:num,C:nat]: (((ring_18347121197199848620nteger @ A) = (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7156_of__int__eq__neg__numeral__power__cancel__iff)). 185.47/93.64 thf(29123,plain,((! [A:int,B:num,C:nat]: (((ring_18347121197199848620nteger @ A) = (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6353])). 185.47/93.64 thf(2584,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) => (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_add__less__imp__less__left)). 185.47/93.64 thf(16315,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) => (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2584])). 185.47/93.64 thf(5534,axiom,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1798_less__one)). 185.47/93.64 thf(26160,plain,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5534])). 185.47/93.64 thf(1869,axiom,(((plus_plus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ one_one_complex)) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5278_add__neg__numeral__special_I7_J)). 185.47/93.64 thf(13992,plain,(((plus_plus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ one_one_complex)) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1869])). 185.47/93.64 thf(2292,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (times_times_int @ (modulo_modulo_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1980_mod__mult__mult2)). 185.47/93.64 thf(15338,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (times_times_int @ (modulo_modulo_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2292])). 185.47/93.64 thf(7425,axiom,(((neg_nu3811975205180677377ec_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6762_dbl__dec__simps_I4_J)). 185.47/93.64 thf(33026,plain,(((neg_nu3811975205180677377ec_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7425])). 185.47/93.64 thf(3067,axiom,((! [A:real]: ((sums_real @ (^ [B:nat]: (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (power_power_real @ A @ B))) @ (divide_divide_real @ one_one_real @ (power_power_real @ (minus_minus_real @ one_one_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8281_geometric__deriv__sums)). 185.47/93.64 thf(17884,plain,((! [A:real]: ((sums_real @ (^ [B:nat]: (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (power_power_real @ A @ B))) @ (divide_divide_real @ one_one_real @ (power_power_real @ (minus_minus_real @ one_one_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3067])). 185.47/93.64 thf(3799,axiom,((! [A:real,B:real]: ((A != zero_zero_real) => ((real_V7735802525324610683m_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (real_V7735802525324610683m_real @ B) @ (real_V7735802525324610683m_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7476_nonzero__norm__divide)). 185.47/93.64 thf(20206,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real)) => ((real_V7735802525324610683m_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (real_V7735802525324610683m_real @ B) @ (real_V7735802525324610683m_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3799])). 185.47/93.64 thf(5152,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4065_order__less__asym_H)). 185.47/93.64 thf(24723,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5152])). 185.47/93.64 thf(6607,axiom,((! [A:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one)) @ A) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5977_mult__1s__ring__1_I1_J)). 185.47/93.64 thf(30026,plain,((! [A:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one)) @ A) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6607])). 185.47/93.64 thf(6417,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((A != zero_zero_nat) => (((plus_plus_nat @ B @ (times_times_nat @ A @ D)) != (plus_plus_nat @ C @ (times_times_nat @ A @ E))) <= ((B = C) & (D != E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5013_add__scale__eq__noteq)). 185.47/93.64 thf(29360,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((~ (A = zero_zero_nat)) => (~ ((plus_plus_nat @ B @ (times_times_nat @ A @ D)) = (plus_plus_nat @ C @ (times_times_nat @ A @ E))) | ~ ((B = C) & ~ (D = E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6417])). 185.47/93.64 thf(1967,axiom,((! [A:real]: (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8253_arsinh__real__aux)). 185.47/93.64 thf(14316,plain,((! [A:real]: (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1967])). 185.47/93.64 thf(4477,axiom,(((size_size_num @ one) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2099_num_Osize_I4_J)). 185.47/93.64 thf(22338,plain,(((size_size_num @ one) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4477])). 185.47/93.64 thf(1479,axiom,((! [A:nat]: ((one_one_complex = (semiri8010041392384452111omplex @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6923_of__nat__1__eq__iff)). 185.47/93.64 thf(12657,plain,((! [A:nat]: ((one_one_complex = (semiri8010041392384452111omplex @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479])). 185.47/93.64 thf(2205,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D))))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2616_mult__less__le__imp__less)). 185.47/93.64 thf(15073,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D))))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2205])). 185.47/93.64 thf(4350,axiom,((! [A:(rat > (rat > $o)),B:rat,C:rat]: (((A @ B @ C) <= (! [D:rat,E:rat]: ((A @ D @ E) <= (A @ E @ D)))) <= (! [D:rat,E:rat]: ((ord_less_eq_rat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3880_linorder__wlog)). 185.47/93.64 thf(21931,plain,((! [A:(rat > (rat > $o)),B:rat,C:rat]: ((A @ B @ C) | ~ (! [D:rat,E:rat]: ((A @ D @ E) | ~ (A @ E @ D))) | ~ (! [D:rat,E:rat]: ((ord_less_eq_rat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4350])). 185.47/93.64 thf(6649,axiom,((! [A:int,B:int,C:num]: ((times_times_int @ (minus_minus_int @ A @ B) @ (numeral_numeral_int @ C)) = (minus_minus_int @ (times_times_int @ A @ (numeral_numeral_int @ C)) @ (times_times_int @ B @ (numeral_numeral_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_left__diff__distrib__numeral)). 185.47/93.64 thf(30166,plain,((! [A:int,B:int,C:num]: ((times_times_int @ (minus_minus_int @ A @ B) @ (numeral_numeral_int @ C)) = (minus_minus_int @ (times_times_int @ A @ (numeral_numeral_int @ C)) @ (times_times_int @ B @ (numeral_numeral_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6649])). 185.47/93.64 thf(7291,axiom,((! [A:nat,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_real @ (abs_abs_real @ B) @ A) = (power_power_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6692_power__even__abs)). 185.47/93.64 thf(32561,plain,((! [A:nat,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_real @ (abs_abs_real @ B) @ A) = (power_power_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7291])). 185.47/93.64 thf(1677,axiom,((! [A:int,B:int]: (((divide_divide_int @ (times_times_int @ B @ A) @ A) = B) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1684_nonzero__mult__div__cancel__right)). 185.47/93.64 thf(13350,plain,((! [A:int,B:int]: (((divide_divide_int @ (times_times_int @ B @ A) @ A) = B) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677])). 185.47/93.64 thf(4818,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_rat @ (semiri681578069525770553at_rat @ A) @ B) = (semiri681578069525770553at_rat @ C)) = ((power_power_nat @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6956_of__nat__eq__of__nat__power__cancel__iff)). 185.47/93.64 thf(23475,plain,((! [A:nat,B:nat,C:nat]: (((power_power_rat @ (semiri681578069525770553at_rat @ A) @ B) = (semiri681578069525770553at_rat @ C)) = ((power_power_nat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4818])). 185.47/93.64 thf(4481,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) <= (ord_less_real @ zero_zero_real @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2366_mult__strict__right__mono)). 185.47/93.64 thf(22348,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) | ~ (ord_less_real @ zero_zero_real @ C) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4481])). 185.47/93.64 thf(4421,axiom,((! [A:int,B:nat,C:int]: (((power_power_real @ (ring_1_of_int_real @ A) @ B) = (ring_1_of_int_real @ C)) = ((power_power_int @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6984_of__int__eq__of__int__power__cancel__iff)). 185.47/93.64 thf(22150,plain,((! [A:int,B:nat,C:int]: (((power_power_real @ (ring_1_of_int_real @ A) @ B) = (ring_1_of_int_real @ C)) = ((power_power_int @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4421])). 185.47/93.64 thf(5794,axiom,((! [A:real,B:real]: (((B = zero_zero_real) | (A = zero_zero_real)) <= ((times_times_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2049_divisors__zero)). 185.47/93.64 thf(27002,plain,((! [A:real,B:real]: ((B = zero_zero_real) | (A = zero_zero_real) | ~ ((times_times_real @ A @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5794])). 185.47/93.64 thf(1262,axiom,((! [A:num]: ((neg_nu3811975205180677377ec_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (neg_nu5851722552734809277nc_int @ (numeral_numeral_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7026_dbl__dec__simps_I1_J)). 185.47/93.64 thf(11959,plain,((! [A:num]: ((neg_nu3811975205180677377ec_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (neg_nu5851722552734809277nc_int @ (numeral_numeral_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262])). 185.47/93.64 thf(4600,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (ord_max_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3746_max_Ostrict__coboundedI2)). 185.47/93.64 thf(22735,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (ord_max_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4600])). 185.47/93.64 thf(3921,axiom,((! [A:int,B:int]: (((times_times_int @ B @ (divide_divide_int @ one_one_int @ A)) = (divide_divide_int @ B @ A)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4507_unit__mult__div__div)). 185.47/93.64 thf(20592,plain,((! [A:int,B:int]: (((times_times_int @ B @ (divide_divide_int @ one_one_int @ A)) = (divide_divide_int @ B @ A)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3921])). 185.47/93.64 thf(7001,axiom,((! [A:nat,B:num]: ((bit_se8568078237143864401it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (bit_se8568078237143864401it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ (inc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9757_drop__bit__Suc__minus__bit1)). 185.47/93.64 thf(31556,plain,((! [A:nat,B:num]: ((bit_se8568078237143864401it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (bit_se8568078237143864401it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ (inc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7001])). 185.47/93.64 thf(1084,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_V5719532721284313246member @ (vEBT_Leaf @ A @ B) @ C) = ((((C = one_one_nat) & ((C = one_one_nat) => (B))) <= (C != zero_zero_nat)) & ((C = zero_zero_nat) => (A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2019_VEBT__internal_Onaive__member_Osimps_I1_J)). 185.47/93.64 thf(11404,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_V5719532721284313246member @ (vEBT_Leaf @ A @ B) @ C) = ((((C = one_one_nat) & ((C = one_one_nat) => (B))) | (C = zero_zero_nat)) & ((C = zero_zero_nat) => (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084])). 185.47/93.64 thf(3946,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ A @ B) => ((ord_less_rat @ zero_zero_rat @ C) => ((ord_less_rat @ C @ D) => (ord_less_rat @ (divide_divide_rat @ A @ D) @ (divide_divide_rat @ B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2650_frac__less2)). 185.47/93.64 thf(20675,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ A @ B) => ((ord_less_rat @ zero_zero_rat @ C) => ((ord_less_rat @ C @ D) => (ord_less_rat @ (divide_divide_rat @ A @ D) @ (divide_divide_rat @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3946])). 185.47/93.64 thf(192,axiom,((! [A:real]: (((ord_less_eq_real @ (ln_ln_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5320_ln__le__zero__iff)). 185.47/93.64 thf(8352,plain,((! [A:real]: (((ord_less_eq_real @ (ln_ln_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ one_one_real)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 185.47/93.64 thf(5719,axiom,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6895_of__nat__eq__0__iff)). 185.47/93.64 thf(26767,plain,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5719])). 185.47/93.64 thf(519,axiom,((! [A:real,B:real,C:real]: (((A != one_one_real) => (((minus_minus_real @ C @ (log @ A @ B)) = (log @ A @ (divide_divide_real @ (powr_real @ A @ C) @ B))) <= (ord_less_real @ zero_zero_real @ B))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9128_minus__log__eq__powr)). 185.47/93.64 thf(9475,plain,((! [A:real,B:real,C:real]: (((~ (A = one_one_real)) => (((minus_minus_real @ C @ (log @ A @ B)) = (log @ A @ (divide_divide_real @ (powr_real @ A @ C) @ B))) | ~ (ord_less_real @ zero_zero_real @ B))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])). 185.47/93.64 thf(4245,axiom,((! [A:nat,B:nat]: (ord_less_eq_real @ (minus_minus_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B))) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7330_real__of__nat__div3)). 185.47/93.64 thf(21588,plain,((! [A:nat,B:nat]: (ord_less_eq_real @ (minus_minus_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B))) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4245])). 185.47/93.64 thf(6837,axiom,((! [A:nat]: ((groups3542108847815614940at_nat @ (binomial @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)) @ (set_ord_atMost_nat @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8953_binomial__r__part__sum)). 185.47/93.64 thf(30859,plain,((! [A:nat]: ((groups3542108847815614940at_nat @ (binomial @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)) @ (set_ord_atMost_nat @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6837])). 185.47/93.64 thf(4591,axiom,((! [A:real,B:real,C:real,D:real]: (((C != D) & (A != B)) = ((plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) != (plus_plus_real @ (times_times_real @ A @ D) @ (times_times_real @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6289_crossproduct__noteq)). 185.47/93.64 thf(22703,plain,((! [A:real,B:real,C:real,D:real]: ((~ (C = D) & ~ (A = B)) = (~ ((plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) = (plus_plus_real @ (times_times_real @ A @ D) @ (times_times_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4591])). 185.47/93.64 thf(3334,axiom,((! [A:nat,B:nat]: (((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ (minus_minus_nat @ B @ C) @ (minus_minus_nat @ A @ C))) @ (set_ord_atMost_nat @ A)) = (binomial @ (suc @ B) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8946_sum__choose__diagonal)). 185.47/93.64 thf(18713,plain,((! [A:nat,B:nat]: (((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ (minus_minus_nat @ B @ C) @ (minus_minus_nat @ A @ C))) @ (set_ord_atMost_nat @ A)) = (binomial @ (suc @ B) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3334])). 185.47/93.64 thf(995,axiom,((! [A:real,B:real,C:(real > num),D:num]: ((((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))) => (ord_less_num @ (C @ A) @ D)) <= (ord_less_num @ (C @ B) @ D)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4110_order__less__subst2)). 185.47/93.64 thf(11139,plain,((! [A:real,B:real,C:(real > num),D:num]: (((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))) => (ord_less_num @ (C @ A) @ D)) | ~ (ord_less_num @ (C @ B) @ D) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[995])). 185.47/93.64 thf(7110,axiom,((! [A:nat]: ((power_power_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1742_power__0__Suc)). 185.47/93.64 thf(31928,plain,((! [A:nat]: ((power_power_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7110])). 185.47/93.64 thf(1434,axiom,((! [A:int,B:nat]: (((ord_less_eq_nat @ B @ (nat2 @ A)) = (ord_less_eq_int @ (semiri1314217659103216013at_int @ B) @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9309_le__nat__iff)). 185.47/93.64 thf(12517,plain,((! [A:int,B:nat]: (((ord_less_eq_nat @ B @ (nat2 @ A)) = (ord_less_eq_int @ (semiri1314217659103216013at_int @ B) @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434])). 185.47/93.64 thf(4036,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) & (ord_less_real @ A @ B)) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_add__mono__thms__linordered__field_I5_J)). 185.47/93.64 thf(20946,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) & (ord_less_real @ A @ B)) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4036])). 185.47/93.64 thf(3960,axiom,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6277_add__0__iff)). 185.47/93.64 thf(20716,plain,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3960])). 185.47/93.64 thf(6419,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ C) => ((divide_divide_nat @ (divide_divide_nat @ C @ A) @ (divide_divide_nat @ B @ A)) = (divide_divide_nat @ C @ B))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4675_div__div__div__same)). 185.47/93.64 thf(29378,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ C) => ((divide_divide_nat @ (divide_divide_nat @ C @ A) @ (divide_divide_nat @ B @ A)) = (divide_divide_nat @ C @ B))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6419])). 185.47/93.64 thf(6617,axiom,((! [A:real,B:real]: (((complex2 @ A @ B) = (uminus1482373934393186551omplex @ one_one_complex)) = ((B = zero_zero_real) & (A = (uminus_uminus_real @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8042_Complex__eq__neg__1)). 185.47/93.64 thf(30062,plain,((! [A:real,B:real]: (((complex2 @ A @ B) = (uminus1482373934393186551omplex @ one_one_complex)) = ((B = zero_zero_real) & (A = (uminus_uminus_real @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6617])). 185.47/93.64 thf(3979,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (plus_plus_real @ (plus_plus_real @ one_one_real @ A) @ (divide_divide_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))) @ (exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8276_exp__lower__Taylor__quadratic)). 185.47/93.64 thf(20777,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (plus_plus_real @ (plus_plus_real @ one_one_real @ A) @ (divide_divide_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))) @ (exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3979])). 185.47/93.64 thf(5506,axiom,((! [A:num,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) => ((power_power_real @ (abs_abs_real @ B) @ (numeral_numeral_nat @ A)) = (power_power_real @ B @ (numeral_numeral_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6438_power__even__abs__numeral)). 185.47/93.64 thf(26068,plain,((! [A:num,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) => ((power_power_real @ (abs_abs_real @ B) @ (numeral_numeral_nat @ A)) = (power_power_real @ B @ (numeral_numeral_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5506])). 185.47/93.64 thf(1889,axiom,((! [A:real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1808_divide__less__0__1__iff)). 185.47/93.64 thf(14051,plain,((! [A:real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1889])). 185.47/93.64 thf(2974,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (ord_less_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_add__less__cancel__right)). 185.47/93.64 thf(17591,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (ord_less_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2974])). 185.47/93.64 thf(1,conjecture,((vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 185.47/93.64 thf(2,negated_conjecture,((~ (vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(neg_conjecture,[status(cth)],[1])). 185.47/93.64 thf(7733,plain,((~ (vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 185.47/93.64 thf(557,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat)]: ((ord_less_eq_set_nat @ A @ B) => (((groups708209901874060359at_nat @ C @ B) = (times_times_nat @ (groups708209901874060359at_nat @ C @ (minus_minus_set_nat @ B @ A)) @ (groups708209901874060359at_nat @ C @ A))) <= (finite_finite_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8900_prod_Osubset__diff)). 185.47/93.64 thf(9580,plain,((! [A:set_nat,B:set_nat,C:(nat > nat)]: ((ord_less_eq_set_nat @ A @ B) => (((groups708209901874060359at_nat @ (C) @ B) = (times_times_nat @ (groups708209901874060359at_nat @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups708209901874060359at_nat @ (C) @ A))) | ~ (finite_finite_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[557])). 185.47/93.64 thf(1621,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) = ((vEBT_VEBT_add @ (some_nat @ A) @ (some_nat @ B)) = (some_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_983_add__shift)). 185.47/93.64 thf(13134,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) = ((vEBT_VEBT_add @ (some_nat @ A) @ (some_nat @ B)) = (some_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621])). 185.47/93.64 thf(2483,axiom,((! [A:rat]: (ord_less_eq_rat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3814_dual__order_Orefl)). 185.47/93.64 thf(15954,plain,((! [A:rat]: (ord_less_eq_rat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2483])). 185.47/93.64 thf(4136,axiom,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (divide_divide_rat @ A @ B)) = (divide_divide_rat @ (uminus_uminus_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5584_minus__divide__left)). 185.47/93.64 thf(21249,plain,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (divide_divide_rat @ A @ B)) = (divide_divide_rat @ (uminus_uminus_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4136])). 185.47/93.64 thf(2645,axiom,((abs_abs_real = (^ [A:real]: (if_real @ (ord_less_real @ A @ zero_zero_real) @ (uminus_uminus_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6528_abs__real__def)). 185.47/93.64 thf(16508,plain,(((abs_abs_real) = (^ [A:real]: (if_real @ (ord_less_real @ A @ zero_zero_real) @ (uminus_uminus_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2645])). 185.47/93.64 thf(5386,axiom,((! [A:num,B:nat,C:int]: (((power_power_rat @ (numeral_numeral_rat @ A) @ B) = (ring_1_of_int_rat @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7104_numeral__power__eq__of__int__cancel__iff)). 185.47/93.64 thf(25555,plain,((! [A:num,B:nat,C:int]: (((power_power_rat @ (numeral_numeral_rat @ A) @ B) = (ring_1_of_int_rat @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5386])). 185.47/93.64 thf(819,axiom,((! [A:int]: ((divide_divide_int @ (bit_ri7919022796975470100ot_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = (bit_ri7919022796975470100ot_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9521_not__int__div__2)). 185.47/93.64 thf(10527,plain,((! [A:int]: ((divide_divide_int @ (bit_ri7919022796975470100ot_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = (bit_ri7919022796975470100ot_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[819])). 185.47/93.64 thf(7059,axiom,((! [A:num,B:num,C:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) != (modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ C)) @ (numeral_numeral_nat @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6609_cong__exp__iff__simps_I12_J)). 185.47/93.64 thf(31773,plain,((! [A:num,B:num,C:num]: ~ ((modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ C)) @ (numeral_numeral_nat @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7059])). 185.47/93.64 thf(3445,axiom,((bit_ri631733984087533419it_int = (^ [A:nat,B:int]: (if_int @ (A = zero_zero_nat) @ (uminus_uminus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri631733984087533419it_int @ (minus_minus_nat @ A @ one_one_nat) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5003_signed__take__bit__rec)). 185.47/93.64 thf(19065,plain,(((bit_ri631733984087533419it_int) = (^ [A:nat,B:int]: (if_int @ (A = zero_zero_nat) @ (uminus_uminus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri631733984087533419it_int @ (minus_minus_nat @ A @ one_one_nat) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3445])). 185.47/93.64 thf(6255,axiom,((! [A:int]: ((times_times_int @ (abs_abs_int @ A) @ (abs_abs_int @ A)) = (times_times_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6339_abs__mult__self__eq)). 185.47/93.64 thf(28779,plain,((! [A:int]: ((times_times_int @ (abs_abs_int @ A) @ (abs_abs_int @ A)) = (times_times_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6255])). 185.47/93.64 thf(4339,axiom,((! [A:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (plus_plus_rat @ A @ A)) = (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1612_zero__le__double__add__iff__zero__le__single__add)). 185.47/93.64 thf(21897,plain,((! [A:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (plus_plus_rat @ A @ A)) = (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4339])). 185.47/93.64 thf(7124,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat,G:nat]: ((((~ (ord_less_nat @ B @ A)) => ((B != A) => (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ E)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ G @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ D @ (the_nat @ (vEBT_vebt_mint @ E)))))) @ (suc @ (divide_divide_nat @ G @ (numeral_numeral_nat @ (bit0 @ one))))) @ (size_s6755466524823107622T_VEBT @ D)))) <= (F = (suc @ (suc @ G)))) <= (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_966_nested__mint)). 185.47/93.64 thf(31971,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat,G:nat]: (((~ (ord_less_nat @ B @ A)) => ((~ (B = A)) => (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ E)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ G @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ D @ (the_nat @ (vEBT_vebt_mint @ E)))))) @ (suc @ (divide_divide_nat @ G @ (numeral_numeral_nat @ (bit0 @ one))))) @ (size_s6755466524823107622T_VEBT @ D)))) | ~ (F = (suc @ (suc @ G))) | ~ (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7124])). 185.47/93.64 thf(7424,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (((C != zero_zero_nat) => (! [D:nat,E:nat]: ((ord_less_nat @ E @ C) => ((A @ D) <= (B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)))))) & ((A @ zero_zero_nat) <= (C = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2914_split__div)). 185.47/93.64 thf(33023,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (((~ (C = zero_zero_nat)) => (! [D:nat,E:nat]: ((ord_less_nat @ E @ C) => ((A @ D) | ~ (B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)))))) & ((A @ zero_zero_nat) | ~ (C = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7424])). 185.47/93.64 thf(2997,axiom,((! [A:nat,B:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6897_of__nat__less__iff)). 185.47/93.64 thf(17667,plain,((! [A:nat,B:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2997])). 185.47/93.64 thf(496,axiom,((! [A:real,B:real]: (((((ord_less_eq_real @ B @ pi) => ((ord_less_eq_real @ (cos_real @ A) @ (cos_real @ B)) = (ord_less_eq_real @ B @ A))) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ A @ pi)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7843_cos__mono__le__eq)). 185.47/93.64 thf(9401,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ pi) => ((ord_less_eq_real @ (cos_real @ A) @ (cos_real @ B)) = (ord_less_eq_real @ B @ A))) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ A @ pi) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[496])). 185.47/93.64 thf(3970,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ B @ (times_3573771949741848930nteger @ C @ A)) = (dvd_dvd_Code_integer @ B @ C)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4744_dvd__mult__unit__iff)). 185.47/93.64 thf(20743,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ B @ (times_3573771949741848930nteger @ C @ A)) = (dvd_dvd_Code_integer @ B @ C)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3970])). 185.47/93.64 thf(6757,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3994_ord__less__eq__trans)). 185.47/93.64 thf(30590,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6757])). 185.47/93.64 thf(7208,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ C @ B)) <= (ord_less_nat @ A @ one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1891_power__decreasing__iff)). 185.47/93.64 thf(32283,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ C @ B)) | ~ (ord_less_nat @ A @ one_one_nat) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7208])). 185.47/93.64 thf(1954,axiom,((minus_minus_real = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5792_ab__group__add__class_Oab__diff__conv__add__uminus)). 185.47/93.64 thf(14270,plain,(((minus_minus_real) = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1954])). 185.47/93.64 thf(3705,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ C @ B) @ (times_times_real @ C @ A)) <= (ord_less_eq_real @ C @ zero_zero_real)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2242_mult__left__mono__neg)). 185.47/93.64 thf(19892,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ C @ B) @ (times_times_real @ C @ A)) | ~ (ord_less_eq_real @ C @ zero_zero_real) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3705])). 185.47/93.64 thf(3485,axiom,((! [A:num]: ((numeral_numeral_real @ (bit1 @ A)) = (plus_plus_real @ (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A)) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6628_numeral__code_I3_J)). 185.47/93.64 thf(19206,plain,((! [A:num]: ((numeral_numeral_real @ (bit1 @ A)) = (plus_plus_real @ (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A)) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3485])). 185.47/93.64 thf(6830,axiom,((! [A:num,B:num,C:real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5352_semiring__norm_I170_J)). 185.47/93.64 thf(30838,plain,((! [A:num,B:num,C:real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6830])). 185.47/93.64 thf(3350,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((ring_1_of_int_real @ (divide_divide_int @ B @ A)) = (divide_divide_real @ (ring_1_of_int_real @ B) @ (ring_1_of_int_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7277_real__of__int__div)). 185.47/93.64 thf(18773,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((ring_1_of_int_real @ (divide_divide_int @ B @ A)) = (divide_divide_real @ (ring_1_of_int_real @ B) @ (ring_1_of_int_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3350])). 185.47/93.64 thf(2803,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_add__less__le__mono)). 185.47/93.64 thf(17040,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2803])). 185.47/93.64 thf(116,axiom,((! [A:set_nat,B:(nat > int)]: ((ord_less_eq_int @ zero_zero_int @ (groups705719431365010083at_int @ B @ A)) <= (! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_int @ zero_zero_int @ (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8745_prod__nonneg)). 185.47/93.64 thf(8109,plain,((! [A:set_nat,B:(nat > int)]: ((ord_less_eq_int @ zero_zero_int @ (groups705719431365010083at_int @ (B) @ A)) | ~ (! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_int @ zero_zero_int @ (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 185.47/93.64 thf(7697,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_left__add__twice)). 185.47/93.64 thf(33835,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7697])). 185.47/93.64 thf(2215,axiom,((! [A:int,B:int]: ((((modulo_modulo_int @ B @ A) = (modulo_modulo_int @ (minus_minus_int @ B @ A) @ A)) <= (ord_less_eq_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3135_mod__pos__geq)). 185.47/93.64 thf(15105,plain,((! [A:int,B:int]: (((modulo_modulo_int @ B @ A) = (modulo_modulo_int @ (minus_minus_int @ B @ A) @ A)) | ~ (ord_less_eq_int @ A @ B) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2215])). 185.47/93.64 thf(6478,axiom,((! [A:option4927543243414619207at_nat]: ((A != none_P5556105721700978146at_nat) = (? [B:product_prod_nat_nat]: (A = (some_P7363390416028606310at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1005_not__None__eq)). 185.47/93.64 thf(29585,plain,((! [A:option4927543243414619207at_nat]: ((~ (A = none_P5556105721700978146at_nat)) = (? [B:product_prod_nat_nat]: (A = (some_P7363390416028606310at_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6478])). 185.47/93.64 thf(3787,axiom,((! [A:nat,B:nat,C:nat]: ((~ ((ord_less_nat @ A @ C) => (~ (ord_less_nat @ B @ C)))) <= (ord_less_nat @ (ord_max_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3728_max_Ostrict__boundedE)). 185.47/93.64 thf(20171,plain,((! [A:nat,B:nat,C:nat]: (~ ((ord_less_nat @ A @ C) => (~ (ord_less_nat @ B @ C))) | ~ (ord_less_nat @ (ord_max_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3787])). 185.47/93.64 thf(7522,axiom,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) != one_one_nat) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1906_not__mod__2__eq__1__eq__0)). 185.47/93.64 thf(33353,plain,((! [A:nat]: ((~ ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7522])). 185.47/93.64 thf(798,axiom,((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5751_less__minus__one__simps_I2_J)). 185.47/93.64 thf(10454,plain,((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[798])). 185.47/93.64 thf(1883,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((comm_s7457072308508201937r_real @ C @ B) = (times_times_real @ (comm_s7457072308508201937r_real @ C @ A) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ C @ (semiri5074537144036343181t_real @ A)) @ (minus_minus_nat @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8542_pochhammer__product)). 185.47/93.64 thf(14034,plain,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((comm_s7457072308508201937r_real @ C @ B) = (times_times_real @ (comm_s7457072308508201937r_real @ C @ A) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ C @ (semiri5074537144036343181t_real @ A)) @ (minus_minus_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1883])). 185.47/93.64 thf(2085,axiom,((! [A:nat]: ((groups3539618377306564664at_int @ semiri1314217659103216013at_int @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) = (divide_divide_int @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7354_gauss__sum)). 185.47/93.64 thf(14686,plain,((! [A:nat]: ((groups3539618377306564664at_int @ (semiri1314217659103216013at_int) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) = (divide_divide_int @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2085])). 185.47/93.64 thf(1802,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => ((dvd_dvd_rat @ A @ (minus_minus_rat @ B @ C)) <= (dvd_dvd_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4660_dvd__diff)). 185.47/93.64 thf(13771,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => ((dvd_dvd_rat @ A @ (minus_minus_rat @ B @ C)) | ~ (dvd_dvd_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1802])). 185.47/93.64 thf(2173,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5096_minus__add__distrib)). 185.47/93.64 thf(14981,plain,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2173])). 185.47/93.64 thf(4520,axiom,((! [A:complex,B:complex]: ((((cos_complex @ B) != zero_zero_complex) => (((cos_complex @ (minus_minus_complex @ A @ B)) != zero_zero_complex) => ((tan_complex @ (minus_minus_complex @ A @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (tan_complex @ A) @ (tan_complex @ B)) @ (plus_plus_complex @ one_one_complex @ (times_times_complex @ (tan_complex @ A) @ (tan_complex @ B))))))) <= ((cos_complex @ A) != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8082_tan__diff)). 185.47/93.64 thf(22481,plain,((! [A:complex,B:complex]: (((~ ((cos_complex @ B) = zero_zero_complex)) => ((~ ((cos_complex @ (minus_minus_complex @ A @ B)) = zero_zero_complex)) => ((tan_complex @ (minus_minus_complex @ A @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (tan_complex @ A) @ (tan_complex @ B)) @ (plus_plus_complex @ one_one_complex @ (times_times_complex @ (tan_complex @ A) @ (tan_complex @ B))))))) | ((cos_complex @ A) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4520])). 185.47/93.64 thf(2035,axiom,((! [A:complex,B:complex,C:real,D:nat]: ((((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ (power_power_complex @ (plus_plus_complex @ B @ A) @ D) @ (power_power_complex @ B @ D)) @ A) @ (times_times_complex @ (semiri8010041392384452111omplex @ D) @ (power_power_complex @ B @ (minus_minus_nat @ D @ (suc @ zero_zero_nat)))))) @ (times_times_real @ (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ D) @ (semiri5074537144036343181t_real @ (minus_minus_nat @ D @ (suc @ zero_zero_nat)))) @ (power_power_real @ C @ (minus_minus_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (real_V1022390504157884413omplex @ A))) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ B @ A)) @ C)) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7372_lemma__termdiff3)). 185.47/93.64 thf(14533,plain,((! [A:complex,B:complex,C:real,D:nat]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ (power_power_complex @ (plus_plus_complex @ B @ A) @ D) @ (power_power_complex @ B @ D)) @ A) @ (times_times_complex @ (semiri8010041392384452111omplex @ D) @ (power_power_complex @ B @ (minus_minus_nat @ D @ (suc @ zero_zero_nat)))))) @ (times_times_real @ (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ D) @ (semiri5074537144036343181t_real @ (minus_minus_nat @ D @ (suc @ zero_zero_nat)))) @ (power_power_real @ C @ (minus_minus_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (real_V1022390504157884413omplex @ A))) | ~ (ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ B @ A)) @ C) | ~ (ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ C) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2035])). 185.47/93.64 thf(468,axiom,((! [A:int,B:nat]: ((ring_1_of_int_int @ (power_power_int @ A @ B)) = (power_power_int @ (ring_1_of_int_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6989_of__int__power)). 185.47/93.64 thf(9304,plain,((! [A:int,B:nat]: ((ring_1_of_int_int @ (power_power_int @ A @ B)) = (power_power_int @ (ring_1_of_int_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])). 185.47/93.64 thf(6009,axiom,((! [A:nat]: ((A = zero_zero_nat) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2123_bot__nat__0_Oextremum__uniqueI)). 185.47/93.64 thf(27923,plain,((! [A:nat]: ((A = zero_zero_nat) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6009])). 185.47/93.64 thf(6361,axiom,((! [A:real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5041_equal__neg__zero)). 185.47/93.64 thf(29150,plain,((! [A:real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6361])). 185.47/93.64 thf(5264,axiom,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1568_div__0)). 185.47/93.64 thf(25102,plain,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5264])). 185.47/93.64 thf(7611,axiom,(((vEBT_VEBT_high @ res @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) = pr)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062high_Ares_A_Ideg_Adiv_A2_J_A_061_Apr_092_060close_062)). 185.47/93.64 thf(33604,plain,(((vEBT_VEBT_high @ res @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) = pr)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7611])). 185.47/93.64 thf(4923,axiom,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_num @ A @ C) <= (ord_less_eq_num @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4214_order_Ostrict__trans2)). 185.47/93.64 thf(23849,plain,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_num @ A @ C) | ~ (ord_less_eq_num @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4923])). 185.47/93.64 thf(6482,axiom,((! [A:num,B:(nat > num),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3947_ord__eq__le__subst)). 185.47/93.64 thf(29595,plain,((! [A:num,B:(nat > num),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6482])). 185.47/93.64 thf(2605,axiom,((! [A:complex,B:nat]: ((gbinomial_complex @ (uminus1482373934393186551omplex @ A) @ B) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (gbinomial_complex @ (minus_minus_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8579_gbinomial__minus)). 185.47/93.64 thf(16379,plain,((! [A:complex,B:nat]: ((gbinomial_complex @ (uminus1482373934393186551omplex @ A) @ B) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (gbinomial_complex @ (minus_minus_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2605])). 185.47/93.64 thf(7660,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4524_even__mod__2__iff)). 185.47/93.64 thf(33736,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7660])). 185.47/93.64 thf(5223,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_3863_ord__le__eq__trans)). 185.47/93.64 thf(24943,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)],[5223])). 185.47/93.64 thf(7385,axiom,((! [A:rat,B:rat]: ((power_power_rat @ (plus_plus_rat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_power2__sum)). 185.47/93.64 thf(32876,plain,((! [A:rat,B:rat]: ((power_power_rat @ (plus_plus_rat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7385])). 185.47/93.64 thf(2572,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4361_linorder__le__less__linear)). 185.47/93.64 thf(16255,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2572])). 185.47/93.64 thf(3036,axiom,((! [A:complex,B:complex,C:complex]: ((((minus_minus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = B) <= (A = zero_zero_complex)) & (((minus_minus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (times_times_complex @ B @ A) @ C) @ A)) <= (A != zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2771_add__divide__eq__if__simps_I4_J)). 185.47/93.64 thf(17783,plain,((! [A:complex,B:complex,C:complex]: ((((minus_minus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = B) | ~ (A = zero_zero_complex)) & (((minus_minus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (times_times_complex @ B @ A) @ C) @ A)) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3036])). 185.47/93.64 thf(1642,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (uminus_uminus_real @ (times_times_real @ A @ A)) @ (times_times_real @ B @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5820_real__minus__mult__self__le)). 185.47/93.64 thf(13195,plain,((! [A:real,B:real]: (ord_less_eq_real @ (uminus_uminus_real @ (times_times_real @ A @ A)) @ (times_times_real @ B @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642])). 185.47/93.64 thf(2428,axiom,((! [A:nat]: (((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ (^ [B:nat]: (if_int @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri1314217659103216013at_int @ (binomial @ A @ B)) @ zero_zero_int)) @ (set_ord_atMost_nat @ A))) = (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8622_choose__even__sum)). 185.47/93.64 thf(15763,plain,((! [A:nat]: (((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ (^ [B:nat]: (if_int @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri1314217659103216013at_int @ (binomial @ A @ B)) @ zero_zero_int)) @ (set_ord_atMost_nat @ A))) = (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2428])). 185.47/93.64 thf(142,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (((ord_less_eq_real @ (log @ A @ B) @ (log @ A @ C)) = (ord_less_eq_real @ B @ C)) <= (ord_less_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9030_log__le__cancel__iff)). 185.47/93.64 thf(8190,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (((ord_less_eq_real @ (log @ A @ B) @ (log @ A @ C)) = (ord_less_eq_real @ B @ C)) | ~ (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 185.47/93.64 thf(5329,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = (uminus1482373934393186551omplex @ one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5472_neg__one__odd__power)). 185.47/93.64 thf(25345,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = (uminus1482373934393186551omplex @ one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5329])). 185.47/93.64 thf(6556,axiom,((! [A:real,B:real]: (((((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (A = B)) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1893_power2__eq__iff__nonneg)). 185.47/93.64 thf(29856,plain,((! [A:real,B:real]: ((((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (A = B)) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6556])). 185.47/93.64 thf(787,axiom,((! [A:(nat > real),B:(nat > real)]: ((((minus_minus_real @ (suminf_real @ A) @ (suminf_real @ B)) = (suminf_real @ (^ [C:nat]: (minus_minus_real @ (A @ C) @ (B @ C))))) <= (summable_real @ B)) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7681_suminf__diff)). 185.47/93.64 thf(10419,plain,((! [A:(nat > real),B:(nat > real)]: (((minus_minus_real @ (suminf_real @ (A)) @ (suminf_real @ (B))) = (suminf_real @ (^ [C:nat]: (minus_minus_real @ (A @ C) @ (B @ C))))) | ~ (summable_real @ (B)) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[787])). 185.47/93.64 thf(2345,axiom,((! [A:complex,B:complex,C:complex]: ((((A = C) <= (dvd_dvd_complex @ B @ C)) <= (dvd_dvd_complex @ B @ A)) <= ((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4669_dvd__div__eq__cancel)). 185.47/93.64 thf(15500,plain,((! [A:complex,B:complex,C:complex]: ((A = C) | ~ (dvd_dvd_complex @ B @ C) | ~ (dvd_dvd_complex @ B @ A) | ~ ((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2345])). 185.47/93.64 thf(6727,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_eq__imp__le)). 185.47/93.64 thf(30436,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6727])). 185.47/93.64 thf(4504,axiom,((! [A:nat]: ((sin_real @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ pi) @ (numeral_numeral_real @ (bit0 @ one)))) = (power_power_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7771_sin__cos__npi)). 185.47/93.64 thf(22416,plain,((! [A:nat]: ((sin_real @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ pi) @ (numeral_numeral_real @ (bit0 @ one)))) = (power_power_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4504])). 185.47/93.64 thf(413,axiom,((! [A:nat,B:rat]: (((gbinomial_rat @ B @ A) = (plus_plus_rat @ (gbinomial_rat @ (minus_minus_rat @ B @ one_one_rat) @ (minus_minus_nat @ A @ one_one_nat)) @ (gbinomial_rat @ (minus_minus_rat @ B @ one_one_rat) @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8584_gbinomial__reduce__nat)). 185.47/93.64 thf(9103,plain,((! [A:nat,B:rat]: (((gbinomial_rat @ B @ A) = (plus_plus_rat @ (gbinomial_rat @ (minus_minus_rat @ B @ one_one_rat) @ (minus_minus_nat @ A @ one_one_nat)) @ (gbinomial_rat @ (minus_minus_rat @ B @ one_one_rat) @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])). 185.47/93.64 thf(7580,axiom,((vEBT_invar_vebt @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ na)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33__092_060open_062invar__vebt_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_An_092_060close_062)). 185.47/93.64 thf(33517,plain,((vEBT_invar_vebt @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7580])). 185.47/93.64 thf(848,axiom,((! [A:complex,B:nat]: (((im @ (power_power_complex @ A @ B)) = zero_zero_real) <= ((im @ A) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9661_Im__power__real)). 185.47/93.64 thf(10641,plain,((! [A:complex,B:nat]: (((im @ (power_power_complex @ A @ B)) = zero_zero_real) | ~ ((im @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[848])). 185.47/93.64 thf(7641,axiom,((ord_less_eq_nat @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ pr)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__092_060open_062high_Az_A_Ideg_Adiv_A2_J_A_092_060le_062_Apr_092_060close_062)). 185.47/93.64 thf(33687,plain,((ord_less_eq_nat @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ pr)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7641])). 185.47/93.64 thf(1568,axiom,((! [A:real,B:real]: ((B != A) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4043_dual__order_Ostrict__implies__not__eq)). 185.47/93.64 thf(12924,plain,((! [A:real,B:real]: (~ (B = A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568])). 185.47/93.64 thf(7021,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_add__left__cancel)). 185.47/93.64 thf(31624,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7021])). 185.47/93.64 thf(2312,axiom,((! [A:rat,B:rat]: (((divide_divide_rat @ (uminus_uminus_rat @ B) @ A) = (uminus_uminus_rat @ (divide_divide_rat @ B @ A))) <= (dvd_dvd_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5815_dvd__neg__div)). 185.47/93.64 thf(15398,plain,((! [A:rat,B:rat]: (((divide_divide_rat @ (uminus_uminus_rat @ B) @ A) = (uminus_uminus_rat @ (divide_divide_rat @ B @ A))) | ~ (dvd_dvd_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2312])). 185.47/93.64 thf(5571,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ C)) @ A @ E @ F) @ B) = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_option_nat @ ((vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_nat)) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ D @ B) @ (some_nat @ D) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1307_pred__lesseq__max)). 185.47/93.64 thf(26275,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ C)) @ A @ E @ F) @ B) = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_option_nat @ ((vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))) & ~ ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat)) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ D @ B) @ (some_nat @ D) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5571])). 185.47/93.64 thf(2436,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_real @ (times_times_real @ C @ A) @ B)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2699_neg__divide__less__eq)). 185.47/93.64 thf(15802,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_real @ (times_times_real @ C @ A) @ B)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2436])). 185.47/93.64 thf(5660,axiom,((! [A:nat]: ((suc @ (bit_se2002935070580805687sk_nat @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9229_Suc__mask__eq__exp)). 185.47/93.64 thf(26571,plain,((! [A:nat]: ((suc @ (bit_se2002935070580805687sk_nat @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5660])). 185.47/93.64 thf(5665,axiom,((! [A:nat,B:nat]: (((binomial @ A @ (suc @ B)) = (plus_plus_nat @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ (suc @ B)) @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8549_binomial__addition__formula)). 185.47/93.64 thf(26589,plain,((! [A:nat,B:nat]: (((binomial @ A @ (suc @ B)) = (plus_plus_nat @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ (suc @ B)) @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5665])). 185.47/93.64 thf(1366,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (times_times_real @ B @ A) @ B) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ A @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2661_mult__left__le)). 185.47/93.64 thf(12281,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ B @ A) @ B) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366])). 185.47/93.64 thf(477,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => ((arcsin @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (arcsin @ A)))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8311_arcsin__minus)). 185.47/93.64 thf(9336,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => ((arcsin @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (arcsin @ A)))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])). 185.47/93.64 thf(4510,axiom,((! [A:$o]: ((ord_less_int @ zero_zero_int @ (zero_n2684676970156552555ol_int @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5233_zero__less__of__bool__iff)). 185.47/93.64 thf(22442,plain,((! [A:$o]: ((ord_less_int @ zero_zero_int @ (zero_n2684676970156552555ol_int @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4510])). 185.47/93.64 thf(3743,axiom,((! [A:nat]: ((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ A) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ (semiri2265585572941072030t_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8577_pochhammer__same)). 185.47/93.64 thf(20021,plain,((! [A:nat]: ((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ A) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ (semiri2265585572941072030t_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3743])). 185.47/93.64 thf(7436,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: (((ord_less_nat @ D @ A) => ((((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ B @ C @ F) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ (ord_max_nat @ A @ E))) @ B @ (list_u1324408373059187874T_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ F))) <= (A != E)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) <= (ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3552_insert__simp__norm)). 185.47/93.64 thf(33055,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: (((ord_less_nat @ D @ A) => (((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ B @ C @ F) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ (ord_max_nat @ A @ E))) @ B @ (list_u1324408373059187874T_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ F))) | (A = E) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7436])). 185.47/93.64 thf(6270,axiom,((! [A:vEBT_VEBT,B:nat]: (((~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT]: ((~ (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)))) <= (? [F:vEBT_VEBT]: (A = (vEBT_Node @ C @ (suc @ D) @ E @ F)))))) <= (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((((D) <= (B = one_one_nat)) & (B = one_one_nat)) <= (B != zero_zero_nat)) & ((C) <= (B = zero_zero_nat))))))) <= (vEBT_V5719532721284313246member @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3001_VEBT__internal_Onaive__member_Oelims_I2_J)). 185.47/93.64 thf(28826,plain,((! [A:vEBT_VEBT,B:nat]: (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT]: (~ (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))) | ~ (? [F:vEBT_VEBT]: (A = (vEBT_Node @ C @ (suc @ D) @ E @ F))))) | ~ (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((((D) | ~ (B = one_one_nat)) & (B = one_one_nat)) | (B = zero_zero_nat)) & ((C) | ~ (B = zero_zero_nat)))))) | ~ (vEBT_V5719532721284313246member @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6270])). 185.47/93.64 thf(49,axiom,((! [A:complex,B:nat]: ((minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ B)) = (times_times_complex @ (minus_minus_complex @ one_one_complex @ A) @ (groups2073611262835488442omplex @ (^ [C:nat]: (power_power_complex @ A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7625_one__diff__power__eq_H)). 185.47/93.64 thf(7894,plain,((! [A:complex,B:nat]: ((minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ B)) = (times_times_complex @ (minus_minus_complex @ one_one_complex @ A) @ (groups2073611262835488442omplex @ (^ [C:nat]: (power_power_complex @ A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 185.47/93.64 thf(3750,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ B @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))))) => ((ord_less_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ B) <= (ord_less_real @ (abs_abs_real @ C) @ (divide_divide_real @ B @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8266_real__sqrt__sum__squares__less)). 185.47/93.64 thf(20042,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ B @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))))) => ((ord_less_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ B) | ~ (ord_less_real @ (abs_abs_real @ C) @ (divide_divide_real @ B @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3750])). 185.47/93.64 thf(536,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((~ (member_nat @ A @ C)) <= (member_nat @ A @ (minus_minus_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1323_DiffD2)). 185.47/93.64 thf(9520,plain,((! [A:nat,B:set_nat,C:set_nat]: (~ (member_nat @ A @ C) | ~ (member_nat @ A @ (minus_minus_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[536])). 185.47/93.64 thf(3853,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (powr_real @ A @ B) @ (powr_real @ A @ C)) = (ord_less_eq_real @ B @ C)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9076_powr__le__cancel__iff)). 185.47/93.64 thf(20373,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (powr_real @ A @ B) @ (powr_real @ A @ C)) = (ord_less_eq_real @ B @ C)) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3853])). 185.47/93.64 thf(1389,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => (((C @ F) & (A @ F)) = ((B @ F) & (D @ F))))) <= (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((C @ F) = (D @ F))))) <= (? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) <= (ord_less_int @ F @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3259_minf_I1_J)). 185.47/93.64 thf(12362,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => (((C @ F) & (A @ F)) = ((B @ F) & (D @ F)))) | ~ (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((C @ F) = (D @ F)))) | ~ (? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) | ~ (ord_less_int @ F @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389])). 185.47/93.64 thf(3778,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (minus_minus_rat @ A @ B)) = (ord_less_eq_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1634_diff__ge__0__iff__ge)). 185.47/93.64 thf(20142,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (minus_minus_rat @ A @ B)) = (ord_less_eq_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3778])). 185.47/93.64 thf(7583,axiom,((! [A:int]: ((power_power_int @ (uminus_uminus_int @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5398_power2__minus)). 185.47/93.64 thf(33522,plain,((! [A:int]: ((power_power_int @ (uminus_uminus_int @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7583])). 185.47/93.64 thf(3843,axiom,((! [A:int,B:int]: (((ord_less_int @ B @ A) => ((divide_divide_int @ A @ B) = zero_zero_int)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3037_div__neg__neg__trivial)). 185.47/93.64 thf(20344,plain,((! [A:int,B:int]: (((ord_less_int @ B @ A) => ((divide_divide_int @ A @ B) = zero_zero_int)) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3843])). 185.47/93.64 thf(7315,axiom,((semiri1316708129612266289at_nat = (^ [A:nat]: (if_nat @ (A = zero_zero_nat) @ zero_zero_nat @ (produc6842872674320459806at_nat @ (^ [B:nat,C:nat]: (if_nat @ (C = zero_zero_nat) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (semiri1316708129612266289at_nat @ B)) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (semiri1316708129612266289at_nat @ B)) @ one_one_nat))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7526_of__nat__code__if)). 185.47/93.64 thf(32655,plain,(((semiri1316708129612266289at_nat) = (^ [A:nat]: (if_nat @ (A = zero_zero_nat) @ zero_zero_nat @ (produc6842872674320459806at_nat @ (^ [B:nat,C:nat]: (if_nat @ (C = zero_zero_nat) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (semiri1316708129612266289at_nat @ B)) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (semiri1316708129612266289at_nat @ B)) @ one_one_nat))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7315])). 185.47/93.64 thf(4971,axiom,((! [A:num]: ((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1747_power__zero__numeral)). 185.47/93.64 thf(24000,plain,((! [A:num]: ((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4971])). 185.47/93.64 thf(1891,axiom,((! [A:nat]: ((semiri8010041392384452111omplex @ (suc @ A)) != zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7215_of__nat__neq__0)). 185.47/93.64 thf(14056,plain,((! [A:nat]: ~ ((semiri8010041392384452111omplex @ (suc @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1891])). 185.47/93.64 thf(1748,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (times_times_rat @ A @ B)) = (((ord_less_eq_rat @ one_one_rat @ B) <= (ord_less_rat @ zero_zero_rat @ A)) & ((ord_less_eq_rat @ B @ one_one_rat) <= (ord_less_rat @ A @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2807_mult__le__cancel__left1)). 185.47/93.64 thf(13590,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (times_times_rat @ A @ B)) = (((ord_less_eq_rat @ one_one_rat @ B) | ~ (ord_less_rat @ zero_zero_rat @ A)) & ((ord_less_eq_rat @ B @ one_one_rat) | ~ (ord_less_rat @ A @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748])). 185.47/93.64 thf(3127,axiom,((! [A:nat,B:nat]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6900_of__nat__less__iff)). 185.47/93.64 thf(18075,plain,((! [A:nat,B:nat]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3127])). 185.47/93.64 thf(6639,axiom,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = zero_zero_nat) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit1 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit0 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6681_mod__exhaust__less__4)). 185.47/93.64 thf(30130,plain,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = zero_zero_nat) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit1 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit0 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6639])). 185.47/93.64 thf(7720,axiom,((! [A:code_integer]: ((abs_abs_Code_integer @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6423_abs__power2)). 185.47/93.64 thf(33898,plain,((! [A:code_integer]: ((abs_abs_Code_integer @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7720])). 185.47/93.64 thf(843,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_eq_real @ zero_zero_real @ (arccos @ A)) & (ord_less_eq_real @ (arccos @ A) @ pi)) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8373_arccos__bounded)). 185.47/93.64 thf(10623,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_eq_real @ zero_zero_real @ (arccos @ A)) & (ord_less_eq_real @ (arccos @ A) @ pi)) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[843])). 185.47/93.64 thf(5116,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_851_nat__le__add__iff1)). 185.47/93.64 thf(24568,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5116])). 185.47/93.64 thf(6532,axiom,((! [A:nat,B:nat]: ((A = B) <= ((suc @ A) = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1021_Suc__inject)). 185.47/93.64 thf(29784,plain,((! [A:nat,B:nat]: ((A = B) | ~ ((suc @ A) = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6532])). 185.47/93.64 thf(3429,axiom,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ (minus_minus_int @ (uminus_uminus_int @ A) @ one_one_int) @ B) = (~ (bit_se1146084159140164899it_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9426_bit__not__int__iff_H)). 185.47/93.64 thf(19020,plain,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ (minus_minus_int @ (uminus_uminus_int @ A) @ one_one_int) @ B) = (~ (bit_se1146084159140164899it_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3429])). 185.47/93.64 thf(4412,axiom,((bit_ri631733984087533419it_int = (^ [A:nat,B:int]: (minus_minus_int @ (bit_se2923211474154528505it_int @ (suc @ A) @ B) @ (times_times_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ A)) @ (zero_n2684676970156552555ol_int @ (bit_se1146084159140164899it_int @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9406_signed__take__bit__eq__take__bit__minus)). 185.47/93.64 thf(22127,plain,(((bit_ri631733984087533419it_int) = (^ [A:nat,B:int]: (minus_minus_int @ (bit_se2923211474154528505it_int @ (suc @ A) @ B) @ (times_times_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ A)) @ (zero_n2684676970156552555ol_int @ (bit_se1146084159140164899it_int @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4412])). 185.47/93.64 thf(212,axiom,((! [A:rat,B:nat]: ((gbinomial_rat @ (plus_plus_rat @ A @ one_one_rat) @ (suc @ B)) = (times_times_rat @ (divide_divide_rat @ (plus_plus_rat @ A @ one_one_rat) @ (semiri681578069525770553at_rat @ (suc @ B))) @ (gbinomial_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8558_gbinomial__factors)). 185.47/93.64 thf(8416,plain,((! [A:rat,B:nat]: ((gbinomial_rat @ (plus_plus_rat @ A @ one_one_rat) @ (suc @ B)) = (times_times_rat @ (divide_divide_rat @ (plus_plus_rat @ A @ one_one_rat) @ (semiri681578069525770553at_rat @ (suc @ B))) @ (gbinomial_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 185.47/93.64 thf(4798,axiom,((! [A:int,B:int]: ~ (ord_less_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2989_not__sum__power2__lt__zero)). 185.47/93.64 thf(23415,plain,((! [A:int,B:int]: ~ (ord_less_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4798])). 185.47/93.64 thf(5136,axiom,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_num @ A @ C) <= (ord_less_num @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4312_order__le__less__trans)). 185.47/93.64 thf(24663,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_num @ A @ C) | ~ (ord_less_num @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5136])). 185.47/93.64 thf(1414,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4047_dual__order_Ostrict__implies__not__eq)). 185.47/93.64 thf(12453,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414])). 185.47/93.64 thf(632,axiom,((! [A:int,B:num,C:nat]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (numeral_numeral_int @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7143_of__int__less__numeral__power__cancel__iff)). 185.47/93.64 thf(9832,plain,((! [A:int,B:num,C:nat]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (numeral_numeral_int @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[632])). 185.47/93.64 thf(3191,axiom,((! [A:num,B:num]: ((bit_or_not_num_neg @ (bit1 @ A) @ (bit0 @ B)) = (bitM @ (bit_or_not_num_neg @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9472_or__not__num__neg_Osimps_I8_J)). 185.47/93.64 thf(18273,plain,((! [A:num,B:num]: ((bit_or_not_num_neg @ (bit1 @ A) @ (bit0 @ B)) = (bitM @ (bit_or_not_num_neg @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3191])). 185.47/93.64 thf(1045,axiom,((! [A:rat,B:rat]: (dvd_dvd_rat @ A @ (times_times_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4577_dvd__triv__right)). 185.47/93.64 thf(11293,plain,((! [A:rat,B:rat]: (dvd_dvd_rat @ A @ (times_times_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045])). 185.47/93.64 thf(6595,axiom,((! [A:complex,B:num,C:num,D:complex]: ((times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ B)) @ (times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_power__add__numeral2)). 185.47/93.64 thf(29990,plain,((! [A:complex,B:num,C:num,D:complex]: ((times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ B)) @ (times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6595])). 185.47/93.64 thf(74,axiom,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (^ [C:nat]: (A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (groups708209901874060359at_nat @ A @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8857_prod_Onat__diff__reindex)). 185.47/93.64 thf(7969,plain,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (^ [C:nat]: (A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (groups708209901874060359at_nat @ (A) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 185.47/93.64 thf(2985,axiom,((ord_less_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5915_less__minus__one__simps_I1_J)). 185.47/93.64 thf(17633,plain,((ord_less_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2985])). 185.47/93.64 thf(7552,axiom,(((power_power_rat @ one_one_rat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_901_one__power2)). 185.47/93.64 thf(33440,plain,(((power_power_rat @ one_one_rat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7552])). 185.47/93.64 thf(4328,axiom,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_997_div__by__1)). 185.47/93.64 thf(21867,plain,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4328])). 185.47/93.64 thf(4450,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4262_order_Ostrict__implies__order)). 185.47/93.64 thf(22249,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4450])). 185.47/93.64 thf(1688,axiom,((! [A:rat,B:rat]: ? [C:rat]: ! [D:rat]: (((dvd_dvd_rat @ A @ (plus_plus_rat @ D @ B)) = (dvd_dvd_rat @ A @ (plus_plus_rat @ D @ B))) <= (ord_less_rat @ D @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4710_minf_I9_J)). 185.47/93.64 thf(13382,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1688])). 185.47/93.64 thf(3130,axiom,((! [A:int]: (((semiri1314217659103216013at_int @ (nat2 @ A)) = A) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9295_nat__0__le)). 185.47/93.64 thf(18084,plain,((! [A:int]: (((semiri1314217659103216013at_int @ (nat2 @ A)) = A) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3130])). 185.47/93.64 thf(2507,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((divide_divide_int @ B @ (uminus_uminus_int @ A)) = (uminus_uminus_int @ (divide_divide_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5808_dvd__div__neg)). 185.47/93.64 thf(16045,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((divide_divide_int @ B @ (uminus_uminus_int @ A)) = (uminus_uminus_int @ (divide_divide_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2507])). 185.47/93.64 thf(844,axiom,((! [A:int]: ((cos_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ (ring_1_of_int_real @ A))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7813_cos__int__2pin)). 185.47/93.64 thf(10626,plain,((! [A:int]: ((cos_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ (ring_1_of_int_real @ A))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[844])). 185.47/93.64 thf(402,axiom,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => (finite_finite_nat @ (minus_minus_set_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3455_finite__Diff)). 185.47/93.64 thf(9071,plain,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => (finite_finite_nat @ (minus_minus_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])). 185.47/93.64 thf(4472,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (ord_max_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3711_max_OcoboundedI1)). 185.47/93.64 thf(22316,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (ord_max_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4472])). 185.47/93.64 thf(1766,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_max_nat @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4408_max__absorb1)). 185.47/93.64 thf(13647,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_max_nat @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766])). 185.47/93.64 thf(6287,axiom,((! [A:nat]: ((size_size_option_nat @ (some_nat @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2500_option_Osize_I4_J)). 185.47/93.64 thf(28885,plain,((! [A:nat]: ((size_size_option_nat @ (some_nat @ A)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6287])). 185.47/93.64 thf(6985,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_nat @ (vEBT_VEBT_high @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) <= (ord_less_nat @ zero_zero_nat @ C)) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3011_VEBT__internal_Oexp__split__high__low_I1_J)). 185.47/93.64 thf(31500,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (vEBT_VEBT_high @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) | ~ (ord_less_nat @ zero_zero_nat @ C) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6985])). 185.47/93.64 thf(5232,axiom,((! [A:nat,B:nat,C:nat]: (((((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_782_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add)). 185.47/93.64 thf(24982,plain,((! [A:nat,B:nat,C:nat]: ((((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5232])). 185.47/93.64 thf(5976,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_add__less__le__mono)). 185.47/93.64 thf(27817,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5976])). 185.47/93.64 thf(6974,axiom,((! [A:nat,B:nat]: ((binomial @ (suc @ A) @ (suc @ B)) = (divide_divide_nat @ (times_times_nat @ (suc @ A) @ (binomial @ A @ B)) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8451_binomial__Suc__Suc__eq__times)). 185.47/93.64 thf(31446,plain,((! [A:nat,B:nat]: ((binomial @ (suc @ A) @ (suc @ B)) = (divide_divide_nat @ (times_times_nat @ (suc @ A) @ (binomial @ A @ B)) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6974])). 185.47/93.64 thf(5773,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1213_linordered__semidom__class_Oadd__diff__inverse)). 185.47/93.64 thf(26938,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5773])). 185.47/93.64 thf(3065,axiom,(((neg_nu6075765906172075777c_real @ zero_zero_real) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6794_dbl__dec__simps_I2_J)). 185.47/93.64 thf(17879,plain,(((neg_nu6075765906172075777c_real @ zero_zero_real) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3065])). 185.47/93.64 thf(27,axiom,((! [A:nat]: ((groups6591440286371151544t_real @ (^ [B:nat]: (times_times_real @ (cos_coeff @ B) @ (power_power_real @ zero_zero_real @ B))) @ (set_ord_lessThan_nat @ (suc @ A))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7645_sumr__cos__zero__one)). 185.47/93.64 thf(7818,plain,((! [A:nat]: ((groups6591440286371151544t_real @ (^ [B:nat]: (times_times_real @ (cos_coeff @ B) @ (power_power_real @ zero_zero_real @ B))) @ (set_ord_lessThan_nat @ (suc @ A))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 185.47/93.64 thf(5313,axiom,((! [A:num,B:num,C:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ C)) = (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5354_semiring__norm_I170_J)). 185.47/93.64 thf(25285,plain,((! [A:num,B:num,C:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ C)) = (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5313])). 185.47/93.64 thf(3577,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ C) <= (ord_less_eq_real @ B @ (times_times_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2846_mult__imp__div__pos__le)). 185.47/93.64 thf(19485,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ C) | ~ (ord_less_eq_real @ B @ (times_times_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3577])). 185.47/93.64 thf(359,axiom,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_nat @ (A @ zero_zero_nat) @ (groups708209901874060359at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8736_prod_OatMost__Suc__shift)). 185.47/93.64 thf(8934,plain,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_nat @ (A @ zero_zero_nat) @ (groups708209901874060359at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[359])). 185.47/93.64 thf(4406,axiom,((vEBT_VEBT_set_vebt = (^ [A:vEBT_VEBT]: (collect_nat @ (vEBT_vebt_member @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1263_set__vebt_H__def)). 185.47/93.64 thf(22112,plain,(((vEBT_VEBT_set_vebt) = (^ [A:vEBT_VEBT]: (collect_nat @ (vEBT_vebt_member @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4406])). 185.47/93.64 thf(3213,axiom,((! [A:rat,B:rat]: ((((ord_less_eq_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ zero_zero_rat @ A)) | ((ord_less_eq_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ A @ zero_zero_rat))) => (ord_less_eq_rat @ (times_times_rat @ A @ B) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2222_split__mult__neg__le)). 185.47/93.64 thf(18348,plain,((! [A:rat,B:rat]: ((((ord_less_eq_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ zero_zero_rat @ A)) | ((ord_less_eq_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ A @ zero_zero_rat))) => (ord_less_eq_rat @ (times_times_rat @ A @ B) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3213])). 185.47/93.64 thf(1458,axiom,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ A @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2435_divide__less__0__iff)). 185.47/93.64 thf(12593,plain,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ A @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458])). 185.47/93.64 thf(2051,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_add__diff__cancel)). 185.47/93.64 thf(14584,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2051])). 185.47/93.64 thf(759,axiom,((! [A:vEBT_VEBT,B:$o]: (((((B) <= (? [C:$o]: (A = (vEBT_Leaf @ ($true) @ C)))) => (((~ ((? [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F))) => (B))) <= ((~ (B)) <= (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))))) <= ((? [C:$o]: (A = (vEBT_Leaf @ C @ ($true)))) => (B)))) <= ((A = (vEBT_Leaf @ ($false) @ ($false))) => (~ (B)))) <= ((vEBT_VEBT_minNull @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2565_VEBT__internal_OminNull_Oelims_I1_J)). 185.47/93.64 thf(10271,plain,((! [A:vEBT_VEBT,B:$o]: ((((B) | ~ (? [C:$o]: (A = (vEBT_Leaf @ ($true) @ C)))) => (~ ((? [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F))) => (B)) | ~ (~ (B) | ~ (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) | ~ ((? [C:$o]: (A = (vEBT_Leaf @ C @ ($true)))) => (B)))) | ~ ((A = (vEBT_Leaf @ ($false) @ ($false))) => (~ (B))) | ~ ((vEBT_VEBT_minNull @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[759])). 185.47/93.64 thf(5273,axiom,((! [A:rat]: ((times_times_rat @ one_one_rat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_mult__1)). 185.47/93.64 thf(25153,plain,((! [A:rat]: ((times_times_rat @ one_one_rat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5273])). 185.47/93.64 thf(7012,axiom,((! [A:nat]: ((groups3542108847815614940at_nat @ (^ [B:nat]: (times_times_nat @ B @ (binomial @ A @ B))) @ (set_ord_atMost_nat @ A)) = (times_times_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8954_choose__linear__sum)). 185.47/93.64 thf(31597,plain,((! [A:nat]: ((groups3542108847815614940at_nat @ (^ [B:nat]: (times_times_nat @ B @ (binomial @ A @ B))) @ (set_ord_atMost_nat @ A)) = (times_times_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7012])). 185.47/93.64 thf(4064,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (semiri5074537144036343181t_real @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7043_of__nat__power__less__of__nat__cancel__iff)). 185.47/93.64 thf(21024,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (semiri5074537144036343181t_real @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4064])). 185.47/93.64 thf(1658,axiom,((! [A:int,B:int]: (((ord_less_int @ B @ A) <= (~ (ord_less_int @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1115_linorder__neqE__linordered__idom)). 185.47/93.64 thf(13295,plain,((! [A:int,B:int]: ((ord_less_int @ B @ A) | (ord_less_int @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658])). 185.47/93.64 thf(6086,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => (((! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)) <= (! [D:nat]: ((B = (suc @ D)) => (C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1037_strict__inc__induct)). 185.47/93.64 thf(28153,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => (((! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)) | ~ (! [D:nat]: ((B = (suc @ D)) => (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6086])). 185.47/93.64 thf(4276,axiom,(((neg_nu8295874005876285629c_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7000_dbl__inc__simps_I4_J)). 185.47/93.64 thf(21677,plain,(((neg_nu8295874005876285629c_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4276])). 185.47/93.64 thf(3945,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_rat @ A @ C) <= (ord_less_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4311_order__le__less__trans)). 185.47/93.64 thf(20672,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_rat @ A @ C) | ~ (ord_less_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3945])). 185.47/93.64 thf(546,axiom,((! [A:set_nat,B:(nat > rat)]: ((ord_less_eq_rat @ (groups73079841787564623at_rat @ B @ A) @ one_one_rat) <= (! [C:nat]: ((member_nat @ C @ A) => ((ord_less_eq_rat @ (B @ C) @ one_one_rat) & (ord_less_eq_rat @ zero_zero_rat @ (B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8798_prod__le__1)). 185.47/93.64 thf(9548,plain,((! [A:set_nat,B:(nat > rat)]: ((ord_less_eq_rat @ (groups73079841787564623at_rat @ (B) @ A) @ one_one_rat) | ~ (! [C:nat]: ((member_nat @ C @ A) => ((ord_less_eq_rat @ (B @ C) @ one_one_rat) & (ord_less_eq_rat @ zero_zero_rat @ (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[546])). 185.47/93.64 thf(3484,axiom,((! [A:real,B:real,C:real]: (((! [D:real]: (((ord_less_eq_real @ C @ D) <= (ord_less_real @ D @ B)) <= (ord_less_real @ A @ D))) => (ord_less_eq_real @ C @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4223_dense__ge__bounded)). 185.47/93.64 thf(19201,plain,((! [A:real,B:real,C:real]: (((! [D:real]: ((ord_less_eq_real @ C @ D) | ~ (ord_less_real @ D @ B) | ~ (ord_less_real @ A @ D))) => (ord_less_eq_real @ C @ A)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3484])). 185.47/93.64 thf(2633,axiom,((! [A:num]: (one_one_Code_integer != (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5771_one__neq__neg__numeral)). 185.47/93.64 thf(16463,plain,((! [A:num]: ~ (one_one_Code_integer = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2633])). 185.47/93.64 thf(549,axiom,((! [A:real]: (ord_less_eq_real @ (minus_minus_real @ A @ one_one_real) @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9115_real__of__int__floor__ge__diff__one)). 185.47/93.64 thf(9557,plain,((! [A:real]: (ord_less_eq_real @ (minus_minus_real @ A @ one_one_real) @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[549])). 185.47/93.64 thf(4935,axiom,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3925_order__subst2)). 185.47/93.64 thf(23892,plain,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4935])). 185.47/93.64 thf(928,axiom,((! [A:nat,B:nat,C:(nat > complex)]: (((ord_less_eq_nat @ A @ B) => ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_complex @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat))))) & ((~ (ord_less_eq_nat @ A @ B)) => ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6736_sum__natinterval__diff)). 185.47/93.64 thf(10918,plain,((! [A:nat,B:nat,C:(nat > complex)]: (((ord_less_eq_nat @ A @ B) => ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_complex @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat))))) & ((~ (ord_less_eq_nat @ A @ B)) => ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[928])). 185.47/93.64 thf(2327,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => ((divide_divide_int @ (times_times_int @ A @ B) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1689_nonzero__mult__div__cancel__left)). 185.47/93.64 thf(15445,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (times_times_int @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2327])). 185.47/93.64 thf(2479,axiom,((? [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) & ! [B:real]: (((ord_less_eq_real @ zero_zero_real @ B) & ((cos_real @ B) = zero_zero_real) & (ord_less_eq_real @ B @ (numeral_numeral_real @ (bit0 @ one)))) => (B = A)) & ((cos_real @ A) = zero_zero_real) & (ord_less_eq_real @ A @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7884_cos__is__zero)). 185.47/93.64 thf(15939,plain,((? [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) & ! [B:real]: (((ord_less_eq_real @ zero_zero_real @ B) & ((cos_real @ B) = zero_zero_real) & (ord_less_eq_real @ B @ (numeral_numeral_real @ (bit0 @ one)))) => (B = A)) & ((cos_real @ A) = zero_zero_real) & (ord_less_eq_real @ A @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2479])). 185.47/93.64 thf(7157,axiom,((! [A:num,B:num]: ((minus_minus_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (numera6690914467698888265omplex @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5334_diff__numeral__simps_I2_J)). 185.47/93.64 thf(32110,plain,((! [A:num,B:num]: ((minus_minus_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (numera6690914467698888265omplex @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7157])). 185.47/93.64 thf(4588,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (ord_less_eq_real @ (abs_abs_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6453_abs__le__D1)). 185.47/93.64 thf(22695,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4588])). 185.47/93.64 thf(7401,axiom,((! [A:nat]: ((((num_of_nat @ (suc @ A)) = (inc @ (num_of_nat @ A))) <= (ord_less_nat @ zero_zero_nat @ A)) & (((num_of_nat @ (suc @ A)) = one) <= (~ (ord_less_nat @ zero_zero_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9839_num__of__nat_Osimps_I2_J)). 185.47/93.64 thf(32923,plain,((! [A:nat]: ((((num_of_nat @ (suc @ A)) = (inc @ (num_of_nat @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)) & (((num_of_nat @ (suc @ A)) = one) | (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7401])). 185.47/93.64 thf(4261,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => ((B = one_one_nat) => (? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1473_deg__1__Leafy)). 185.47/93.64 thf(21633,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => ((B = one_one_nat) => (? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4261])). 185.47/93.64 thf(1953,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (bit_se725231765392027082nd_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9376_AND__lower)). 185.47/93.64 thf(14267,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (bit_se725231765392027082nd_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1953])). 185.47/93.64 thf(2386,axiom,(((semiri8010041392384452111omplex @ one_one_nat) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6918_of__nat__1)). 185.47/93.64 thf(15623,plain,(((semiri8010041392384452111omplex @ one_one_nat) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2386])). 185.47/93.64 thf(5381,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ B @ A)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ B)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2779_one__less__mult)). 185.47/93.64 thf(25540,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ B @ A)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ B) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5381])). 185.47/93.64 thf(6933,axiom,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (C)) @ (set_or4665077453230672383an_nat @ A @ B)) = (divide_divide_nat @ (minus_minus_nat @ (times_times_nat @ B @ (minus_minus_nat @ B @ one_one_nat)) @ (times_times_nat @ A @ (minus_minus_nat @ A @ one_one_nat))) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9552_Sum__Ico__nat)). 185.47/93.64 thf(31247,plain,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (C)) @ (set_or4665077453230672383an_nat @ A @ B)) = (divide_divide_nat @ (minus_minus_nat @ (times_times_nat @ B @ (minus_minus_nat @ B @ one_one_nat)) @ (times_times_nat @ A @ (minus_minus_nat @ A @ one_one_nat))) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6933])). 185.47/93.64 thf(4058,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ B @ zero_zero_rat) | (ord_less_rat @ A @ zero_zero_rat)) <= (ord_less_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2393_add__less__zeroD)). 185.47/93.64 thf(21007,plain,((! [A:rat,B:rat]: ((ord_less_rat @ B @ zero_zero_rat) | (ord_less_rat @ A @ zero_zero_rat) | ~ (ord_less_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4058])). 185.47/93.64 thf(7463,axiom,((! [A:num]: (one_one_int != (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5768_one__neq__neg__numeral)). 185.47/93.64 thf(33155,plain,((! [A:num]: ~ (one_one_int = (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7463])). 185.47/93.64 thf(7044,axiom,((! [A:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5194_mult__minus1__right)). 185.47/93.64 thf(31721,plain,((! [A:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7044])). 185.47/93.64 thf(1464,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2328_mult__pos__pos)). 185.47/93.64 thf(12610,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464])). 185.47/93.64 thf(3613,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ C) => ((divide_divide_int @ C @ (divide_divide_int @ B @ A)) = (times_times_int @ (divide_divide_int @ C @ B) @ A))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4758_div__div__eq__right)). 185.47/93.64 thf(19598,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ C) => ((divide_divide_int @ C @ (divide_divide_int @ B @ A)) = (times_times_int @ (divide_divide_int @ C @ B) @ A))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3613])). 185.47/93.64 thf(2322,axiom,((! [A:real,B:real]: (((divide_divide_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (divide_divide_real @ B @ A)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5761_nonzero__minus__divide__divide)). 185.47/93.64 thf(15430,plain,((! [A:real,B:real]: (((divide_divide_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (divide_divide_real @ B @ A)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2322])). 185.47/93.64 thf(627,axiom,((! [A:nat]: ((set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A) = (minus_minus_set_nat @ (set_ord_atMost_nat @ A) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9436_atLeast1__atMost__eq__remove0)). 185.47/93.64 thf(9811,plain,((! [A:nat]: ((set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A) = (minus_minus_set_nat @ (set_ord_atMost_nat @ A) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[627])). 185.47/93.64 thf(3950,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7508_norm__diff__ineq)). 185.47/93.64 thf(20687,plain,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3950])). 185.47/93.64 thf(35,axiom,((! [A:real,B:nat]: ((minus_minus_real @ (power_power_real @ A @ B) @ one_one_real) = (times_times_real @ (minus_minus_real @ A @ one_one_real) @ (groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7599_power__diff__1__eq)). 185.47/93.64 thf(7845,plain,((! [A:real,B:nat]: ((minus_minus_real @ (power_power_real @ A @ B) @ one_one_real) = (times_times_real @ (minus_minus_real @ A @ one_one_real) @ (groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 185.47/93.64 thf(6789,axiom,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1570_bits__div__by__0)). 185.47/93.64 thf(30699,plain,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6789])). 185.47/93.64 thf(1167,axiom,((! [A:real]: ((topolo6980174941875973593q_real @ (^ [B:nat]: (times_times_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))) @ (power_power_real @ A @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))))) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7370_monoseq__arctan__series)). 185.47/93.64 thf(11676,plain,((! [A:real]: ((topolo6980174941875973593q_real @ (^ [B:nat]: (times_times_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))) @ (power_power_real @ A @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))))) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167])). 185.47/93.64 thf(4221,axiom,((! [A:num,B:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (bit_ri631733984087533419it_int @ (pred_numeral @ A) @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6815_signed__take__bit__numeral__bit0)). 185.47/93.64 thf(21510,plain,((! [A:num,B:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (bit_ri631733984087533419it_int @ (pred_numeral @ A) @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4221])). 185.47/93.64 thf(5936,axiom,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_one__plus__numeral)). 185.47/93.64 thf(27647,plain,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5936])). 185.47/93.64 thf(3170,axiom,((! [A:real,B:nat]: ((cos_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ pi) @ (numeral_numeral_real @ (bit0 @ one))))) = (uminus_uminus_real @ (sin_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ pi) @ (numeral_numeral_real @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7881_cos__expansion__lemma)). 185.47/93.64 thf(18207,plain,((! [A:real,B:nat]: ((cos_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ pi) @ (numeral_numeral_real @ (bit0 @ one))))) = (uminus_uminus_real @ (sin_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ pi) @ (numeral_numeral_real @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3170])). 185.47/93.64 thf(1018,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ (times_times_int @ (divide_divide_int @ A @ B) @ B) @ (modulo_modulo_int @ A @ B)) @ C) = (plus_plus_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2545_cancel__div__mod__rules_I1_J)). 185.47/93.64 thf(11215,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ (times_times_int @ (divide_divide_int @ A @ B) @ B) @ (modulo_modulo_int @ A @ B)) @ C) = (plus_plus_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018])). 185.47/93.64 thf(6908,axiom,((! [A:nat,B:rat]: (((times_times_rat @ (power_power_rat @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_rat @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2965_power__minus__mult)). 185.47/93.64 thf(31156,plain,((! [A:nat,B:rat]: (((times_times_rat @ (power_power_rat @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_rat @ B @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6908])). 185.47/93.64 thf(1977,axiom,((! [A:num,B:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (inc @ B)))) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9360_take__bit__numeral__minus__bit1)). 185.47/93.64 thf(14346,plain,((! [A:num,B:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (inc @ B)))) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977])). 185.47/93.64 thf(4159,axiom,((! [A:rat,B:rat,C:(rat > int),D:int]: ((ord_less_rat @ A @ B) => ((ord_less_int @ (C @ B) @ D) => ((! [E:rat,F:rat]: ((ord_less_int @ (C @ E) @ (C @ F)) <= (ord_less_rat @ E @ F))) => (ord_less_int @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4117_order__less__subst2)). 185.47/93.64 thf(21322,plain,((! [A:rat,B:rat,C:(rat > int),D:int]: ((ord_less_rat @ A @ B) => ((ord_less_int @ (C @ B) @ D) => ((! [E:rat,F:rat]: ((ord_less_int @ (C @ E) @ (C @ F)) | ~ (ord_less_rat @ E @ F))) => (ord_less_int @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4159])). 185.47/93.64 thf(6943,axiom,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: (((size_s6755466524823107622T_VEBT @ A) != (size_s6755466524823107622T_VEBT @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_size__neq__size__imp__neq)). 185.47/93.64 thf(31279,plain,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: ((~ ((size_s6755466524823107622T_VEBT @ A) = (size_s6755466524823107622T_VEBT @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6943])). 185.47/93.64 thf(101,axiom,((! [A:real,B:(real > real),C:(nat > real),D:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [E:real]: ((B @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (divide_divide_real @ (C @ F) @ (semiri2265585572941072030t_real @ F)) @ (power_power_real @ A @ F))) @ (set_ord_lessThan_nat @ D)) @ (times_times_real @ E @ (divide_divide_real @ (power_power_real @ A @ D) @ (semiri2265585572941072030t_real @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8079_Maclaurin__lemma)). 185.47/93.64 thf(8065,plain,((! [A:real,B:(real > real),C:(nat > real),D:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [E:real]: ((B @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (divide_divide_real @ (C @ F) @ (semiri2265585572941072030t_real @ F)) @ (power_power_real @ A @ F))) @ (set_ord_lessThan_nat @ D)) @ (times_times_real @ E @ (divide_divide_real @ (power_power_real @ A @ D) @ (semiri2265585572941072030t_real @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 185.47/93.64 thf(5965,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat,F:nat,G:nat]: ((! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ H @ B))) => ((vEBT_invar_vebt @ C @ D) => (((D = (suc @ B)) => ((E = (plus_plus_nat @ B @ D)) => ((((ord_less_eq_nat @ F @ G) => ((ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)) => (((F != G) => (! [H:nat]: ((! [I:nat]: (((ord_less_eq_nat @ I @ G) & (ord_less_nat @ F @ I)) <= (((vEBT_VEBT_high @ I @ B) = H) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ I @ B)))) & (((vEBT_VEBT_high @ G @ B) = H) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ G @ B)))) <= (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) => (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ E @ A @ C) @ E)))) <= ((F = G) => (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))))))) <= (! [H:nat]: (((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ I)) = (vEBT_V8194947554948674370ptions @ C @ H)) <= (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))))) <= ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1244_invar__vebt_Ointros_I5_J)). 185.47/93.64 thf(27746,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat,F:nat,G:nat]: ((! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ H @ B))) => ((vEBT_invar_vebt @ C @ D) => (((D = (suc @ B)) => ((E = (plus_plus_nat @ B @ D)) => (((ord_less_eq_nat @ F @ G) => ((ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)) => (((~ (F = G)) => (! [H:nat]: ((! [I:nat]: (((ord_less_eq_nat @ I @ G) & (ord_less_nat @ F @ I)) | ~ (((vEBT_VEBT_high @ I @ B) = H) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ I @ B)))) & (((vEBT_VEBT_high @ G @ B) = H) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ G @ B)))) | ~ (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) => (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ E @ A @ C) @ E)))) | ~ ((F = G) => (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)))))) | ~ (! [H:nat]: (((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ I)) = (vEBT_V8194947554948674370ptions @ C @ H)) | ~ (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))))) | ~ ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5965])). 185.47/93.64 thf(1352,axiom,((! [A:int,B:int]: ((ord_less_int @ B @ A) | (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4365_linorder__le__less__linear)). 185.47/93.64 thf(12237,plain,((! [A:int,B:int]: ((ord_less_int @ B @ A) | (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352])). 185.47/93.64 thf(1223,axiom,((! [A:real]: (ord_less_eq_real @ (plus_plus_real @ one_one_real @ A) @ (exp_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8185_exp__ge__add__one__self)). 185.47/93.64 thf(11838,plain,((! [A:real]: (ord_less_eq_real @ (plus_plus_real @ one_one_real @ A) @ (exp_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223])). 185.47/93.64 thf(1412,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2427_divide__neg__neg)). 185.47/93.64 thf(12436,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412])). 185.47/93.64 thf(5626,axiom,((! [A:rat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_rat @ one_one_rat @ (power_power_rat @ A @ B))) <= (ord_less_rat @ one_one_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2899_one__less__power)). 185.47/93.64 thf(26457,plain,((! [A:rat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_rat @ one_one_rat @ (power_power_rat @ A @ B))) | ~ (ord_less_rat @ one_one_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5626])). 185.47/93.64 thf(7599,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (~ (! [B:nat]: (A != (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4901_evenE)). 185.47/93.64 thf(33571,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (~ (! [B:nat]: ~ (A = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7599])). 185.47/93.64 thf(513,axiom,((! [A:(nat > int),B:nat,C:nat]: ((groups705719431365010083at_int @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (groups705719431365010083at_int @ (^ [D:nat]: (A @ (minus_minus_nat @ (plus_plus_nat @ C @ B) @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8865_prod_OatLeastAtMost__rev)). 185.47/93.64 thf(9457,plain,((! [A:(nat > int),B:nat,C:nat]: ((groups705719431365010083at_int @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (groups705719431365010083at_int @ (^ [D:nat]: (A @ (minus_minus_nat @ (plus_plus_nat @ C @ B) @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[513])). 185.47/93.64 thf(977,axiom,((! [A:num]: ((neg_nu8557863876264182079omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7005_dbl__inc__simps_I5_J)). 185.47/93.64 thf(11083,plain,((! [A:num]: ((neg_nu8557863876264182079omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[977])). 185.47/93.64 thf(2363,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4139_order__less__imp__not__eq2)). 185.47/93.64 thf(15554,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2363])). 185.47/93.64 thf(5850,axiom,((! [A:num]: ((size_num @ (bit0 @ A)) = (plus_plus_nat @ (size_num @ A) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9239_num_Osize__gen_I2_J)). 185.47/93.64 thf(27365,plain,((! [A:num]: ((size_num @ (bit0 @ A)) = (plus_plus_nat @ (size_num @ A) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5850])). 185.47/93.64 thf(4193,axiom,((! [A:real,B:real]: (((ord_less_real @ A @ zero_zero_real) | (ord_less_real @ B @ zero_zero_real)) <= (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2392_add__less__zeroD)). 185.47/93.64 thf(21427,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) | (ord_less_real @ B @ zero_zero_real) | ~ (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4193])). 185.47/93.64 thf(1469,axiom,((! [A:nat,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ (semiri1314217659103216013at_int @ A) @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7112_of__nat__zero__less__power__iff)). 185.47/93.64 thf(12625,plain,((! [A:nat,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ (semiri1314217659103216013at_int @ A) @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469])). 185.47/93.64 thf(4838,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ B @ C) => (ord_less_rat @ B @ (plus_plus_rat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2638_add__strict__increasing)). 185.47/93.64 thf(23539,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ B @ C) => (ord_less_rat @ B @ (plus_plus_rat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4838])). 185.47/93.64 thf(1179,axiom,((! [A:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ A) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6366_abs__le__self__iff)). 185.47/93.64 thf(11709,plain,((! [A:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ A) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179])). 185.47/93.64 thf(5315,axiom,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1355_lambda__one)). 185.47/93.64 thf(25292,plain,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5315])). 185.47/93.64 thf(4879,axiom,((! [A:num,B:num,C:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5366_semiring__norm_I172_J)). 185.47/93.64 thf(23668,plain,((! [A:num,B:num,C:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4879])). 185.47/93.64 thf(5396,axiom,((! [A:num]: ((semiri1406184849735516958ct_int @ (numeral_numeral_nat @ A)) = (times_times_int @ (numeral_numeral_int @ A) @ (semiri1406184849735516958ct_int @ (pred_numeral @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8039_fact__numeral)). 185.47/93.64 thf(25584,plain,((! [A:num]: ((semiri1406184849735516958ct_int @ (numeral_numeral_nat @ A)) = (times_times_int @ (numeral_numeral_int @ A) @ (semiri1406184849735516958ct_int @ (pred_numeral @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5396])). 185.47/93.64 thf(6162,axiom,((! [A:nat,B:real]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_real @ (uminus_uminus_real @ B) @ A) = (uminus_uminus_real @ (power_power_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5439_power__minus__odd)). 185.47/93.64 thf(28468,plain,((! [A:nat,B:real]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_real @ (uminus_uminus_real @ B) @ A) = (uminus_uminus_real @ (power_power_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6162])). 185.47/93.64 thf(4098,axiom,((! [A:num,B:num,C:(num > rat),D:rat]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_rat @ (C @ B) @ D) => ((ord_less_eq_rat @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3923_order__subst2)). 185.47/93.64 thf(21132,plain,((! [A:num,B:num,C:(num > rat),D:rat]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_rat @ (C @ B) @ D) => ((ord_less_eq_rat @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4098])). 185.47/93.64 thf(4334,axiom,((comm_s4663373288045622133er_nat = (^ [A:nat,B:nat]: (if_nat @ (B = zero_zero_nat) @ one_one_nat @ (set_fo2584398358068434914at_nat @ (^ [C:nat]: (times_times_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8605_pochhammer__code)). 185.47/93.64 thf(21884,plain,(((comm_s4663373288045622133er_nat) = (^ [A:nat,B:nat]: (if_nat @ (B = zero_zero_nat) @ one_one_nat @ (set_fo2584398358068434914at_nat @ (^ [C:nat]: (times_times_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4334])). 185.47/93.64 thf(3200,axiom,((! [A:real,B:real]: ((A != zero_zero_real) => ((divide_divide_real @ A @ (times_times_real @ B @ A)) = (divide_divide_real @ one_one_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1827_nonzero__divide__mult__cancel__right)). 185.47/93.64 thf(18301,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real)) => ((divide_divide_real @ A @ (times_times_real @ B @ A)) = (divide_divide_real @ one_one_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3200])). 185.47/93.64 thf(500,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((A = one_one_real) <= ((ln_ln_real @ A) = (minus_minus_real @ A @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6142_ln__eq__minus__one)). 185.47/93.64 thf(9415,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((A = one_one_real) | ~ ((ln_ln_real @ A) = (minus_minus_real @ A @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[500])). 185.47/93.64 thf(88,axiom,((! [A:rat,B:nat,C:rat]: ((minus_minus_rat @ (power_power_rat @ A @ (suc @ B)) @ (power_power_rat @ C @ (suc @ B))) = (times_times_rat @ (minus_minus_rat @ A @ C) @ (groups2906978787729119204at_rat @ (^ [D:nat]: (times_times_rat @ (power_power_rat @ A @ D) @ (power_power_rat @ C @ (minus_minus_nat @ B @ D)))) @ (set_ord_lessThan_nat @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7613_diff__power__eq__sum)). 185.47/93.64 thf(8018,plain,((! [A:rat,B:nat,C:rat]: ((minus_minus_rat @ (power_power_rat @ A @ (suc @ B)) @ (power_power_rat @ C @ (suc @ B))) = (times_times_rat @ (minus_minus_rat @ A @ C) @ (groups2906978787729119204at_rat @ (^ [D:nat]: (times_times_rat @ (power_power_rat @ A @ D) @ (power_power_rat @ C @ (minus_minus_nat @ B @ D)))) @ (set_ord_lessThan_nat @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 185.47/93.64 thf(4140,axiom,((! [A:int,B:int]: ((divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) = (plus_plus_real @ (ring_1_of_int_real @ (divide_divide_int @ A @ B)) @ (divide_divide_real @ (ring_1_of_int_real @ (modulo_modulo_int @ A @ B)) @ (ring_1_of_int_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7317_real__of__int__div__aux)). 185.47/93.64 thf(21261,plain,((! [A:int,B:int]: ((divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) = (plus_plus_real @ (ring_1_of_int_real @ (divide_divide_int @ A @ B)) @ (divide_divide_real @ (ring_1_of_int_real @ (modulo_modulo_int @ A @ B)) @ (ring_1_of_int_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4140])). 185.47/93.64 thf(6835,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1607_mult__0__right)). 185.47/93.64 thf(30853,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6835])). 185.47/93.64 thf(2774,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (ord_max_nat @ B @ C)) = (ord_max_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3759_nat__add__max__right)). 185.47/93.64 thf(16946,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (ord_max_nat @ B @ C)) = (ord_max_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2774])). 185.47/93.64 thf(586,axiom,((! [A:nat,B:real]: ((times_times_real @ (semiri5074537144036343181t_real @ (suc @ A)) @ (gbinomial_real @ (plus_plus_real @ B @ one_one_real) @ (suc @ A))) = (times_times_real @ (plus_plus_real @ B @ one_one_real) @ (gbinomial_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8533_Suc__times__gbinomial)). 185.47/93.64 thf(9680,plain,((! [A:nat,B:real]: ((times_times_real @ (semiri5074537144036343181t_real @ (suc @ A)) @ (gbinomial_real @ (plus_plus_real @ B @ one_one_real) @ (suc @ A))) = (times_times_real @ (plus_plus_real @ B @ one_one_real) @ (gbinomial_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[586])). 185.47/93.64 thf(6783,axiom,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit1 @ B)) = (bit0 @ (times_times_num @ A @ (bit1 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6389_semiring__norm_I14_J)). 185.47/93.64 thf(30679,plain,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit1 @ B)) = (bit0 @ (times_times_num @ A @ (bit1 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6783])). 185.47/93.64 thf(1364,axiom,((! [A:nat,B:real]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_real @ (power_power_real @ (plus_plus_real @ one_one_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A))) @ A) @ (exp_real @ B))) <= (ord_less_eq_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8268_exp__ge__one__plus__x__over__n__power__n)). 185.47/93.64 thf(12276,plain,((! [A:nat,B:real]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_real @ (power_power_real @ (plus_plus_real @ one_one_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A))) @ A) @ (exp_real @ B))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364])). 185.47/93.64 thf(6033,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ B @ one_one_nat) => ((divide_divide_nat @ A @ (times_times_nat @ B @ A)) = (divide_divide_nat @ one_one_nat @ B))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4898_is__unit__div__mult__cancel__right)). 185.47/93.64 thf(27992,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ B @ one_one_nat) => ((divide_divide_nat @ A @ (times_times_nat @ B @ A)) = (divide_divide_nat @ one_one_nat @ B))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6033])). 185.47/93.64 thf(4964,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_add__less__mono)). 185.47/93.64 thf(23983,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4964])). 185.47/93.64 thf(2402,axiom,((! [A:set_nat]: (((? [B:nat]: ((member_nat @ B @ A) & ~ (? [C:nat]: ((ord_less_nat @ C @ B) & (member_nat @ C @ A))))) <= (A != bot_bot_set_nat)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4999_ex__min__if__finite)). 185.47/93.64 thf(15678,plain,((! [A:set_nat]: (? [B:nat]: ((member_nat @ B @ A) & ~ (? [C:nat]: ((ord_less_nat @ C @ B) & (member_nat @ C @ A)))) | (A = bot_bot_set_nat) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2402])). 185.47/93.64 thf(245,axiom,((! [A:num,B:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5705_neg__numeral__less__numeral)). 185.47/93.64 thf(8511,plain,((! [A:num,B:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 185.47/93.64 thf(2840,axiom,((! [A:num,B:num]: ((ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5369_neg__numeral__le__iff)). 185.47/93.64 thf(17161,plain,((! [A:num,B:num]: ((ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2840])). 185.47/93.64 thf(4475,axiom,((! [A:complex,B:complex,C:complex]: ((((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = zero_zero_complex) <= (A = zero_zero_complex)) & ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = (divide1717551699836669952omplex @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1708_mult__divide__mult__cancel__left__if)). 185.47/93.64 thf(22325,plain,((! [A:complex,B:complex,C:complex]: ((((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = zero_zero_complex) | ~ (A = zero_zero_complex)) & ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = (divide1717551699836669952omplex @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4475])). 185.47/93.64 thf(1733,axiom,((! [A:int,B:int]: (((ord_less_eq_nat @ (nat2 @ A) @ (nat2 @ B)) = (ord_less_eq_int @ A @ B)) <= ((ord_less_eq_int @ zero_zero_int @ B) | (ord_less_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9306_nat__le__eq__zle)). 185.47/93.64 thf(13543,plain,((! [A:int,B:int]: (((ord_less_eq_nat @ (nat2 @ A) @ (nat2 @ B)) = (ord_less_eq_int @ A @ B)) | ~ ((ord_less_eq_int @ zero_zero_int @ B) | (ord_less_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1733])). 185.47/93.64 thf(3712,axiom,((! [A:int,B:int]: ((((divide_divide_int @ A @ B) = zero_zero_int) <= (ord_less_int @ A @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2181_unique__euclidean__semiring__numeral__class_Odiv__less)). 185.47/93.64 thf(19924,plain,((! [A:int,B:int]: (((divide_divide_int @ A @ B) = zero_zero_int) | ~ (ord_less_int @ A @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3712])). 185.47/93.64 thf(6059,axiom,((! [A:int]: (((! [B:nat]: ((A = (semiri1314217659103216013at_int @ B)) => (~ (ord_less_nat @ zero_zero_nat @ B)))) => (~ (! [B:nat]: ((A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ B))) => (~ (ord_less_nat @ zero_zero_nat @ B)))))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7307_int__cases3)). 185.47/93.64 thf(28065,plain,((! [A:int]: (((! [B:nat]: ((A = (semiri1314217659103216013at_int @ B)) => (~ (ord_less_nat @ zero_zero_nat @ B)))) => (~ (! [B:nat]: ((A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ B))) => (~ (ord_less_nat @ zero_zero_nat @ B)))))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6059])). 185.47/93.64 thf(1266,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((A = B) | (ord_less_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4274_order__le__less)). 185.47/93.64 thf(11971,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((A = B) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266])). 185.47/93.64 thf(1991,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (root @ B @ A)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9182_real__root__pos__pos__le)). 185.47/93.64 thf(14387,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (root @ B @ A)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1991])). 185.47/93.64 thf(6047,axiom,((! [A:num,B:num]: (((ord_less_num @ B @ A) <= (A != B)) <= (~ (ord_less_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4004_linorder__cases)). 185.47/93.64 thf(28032,plain,((! [A:num,B:num]: ((ord_less_num @ B @ A) | (A = B) | (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6047])). 185.47/93.64 thf(1944,axiom,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1530_add__cancel__right__right)). 185.47/93.64 thf(14238,plain,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1944])). 185.47/93.64 thf(6548,axiom,((! [A:option_nat]: ((A = (some_nat @ (the_nat @ A))) <= (A != none_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1226_option_Oexhaust__sel)). 185.47/93.64 thf(29833,plain,((! [A:option_nat]: ((A = (some_nat @ (the_nat @ A))) | (A = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6548])). 185.47/93.64 thf(6458,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((num_of_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_num @ (num_of_nat @ A) @ (num_of_nat @ B)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9845_num__of__nat__plus__distrib)). 185.47/93.64 thf(29508,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((num_of_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_num @ (num_of_nat @ A) @ (num_of_nat @ B)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6458])). 185.47/93.64 thf(3206,axiom,((! [A:nat,B:int]: ((bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ (bit_se2923211474154528505it_int @ A @ B))) = (bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9267_take__bit__minus)). 185.47/93.64 thf(18324,plain,((! [A:nat,B:int]: ((bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ (bit_se2923211474154528505it_int @ A @ B))) = (bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3206])). 185.47/93.64 thf(2368,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ (divide_divide_rat @ B @ A) @ one_one_rat) = (ord_less_rat @ A @ B)) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1811_divide__less__eq__1__neg)). 185.47/93.64 thf(15569,plain,((! [A:rat,B:rat]: (((ord_less_rat @ (divide_divide_rat @ B @ A) @ one_one_rat) = (ord_less_rat @ A @ B)) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2368])). 185.47/93.64 thf(617,axiom,((! [A:int,B:num,C:nat]: (((ring_1_of_int_int @ A) = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7153_of__int__eq__neg__numeral__power__cancel__iff)). 185.47/93.64 thf(9781,plain,((! [A:int,B:num,C:nat]: (((ring_1_of_int_int @ A) = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[617])). 185.47/93.64 thf(6158,axiom,((! [A:nat,B:real]: ((((power_power_real @ (sqrt @ B) @ A) = (power_power_real @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8255_real__sqrt__power__even)). 185.47/93.64 thf(28451,plain,((! [A:nat,B:real]: (((power_power_real @ (sqrt @ B) @ A) = (power_power_real @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6158])). 185.47/93.64 thf(2896,axiom,((! [A:$o,B:$o]: (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1959_invar__vebt_Ointros_I1_J)). 185.47/93.64 thf(17342,plain,((! [A:$o,B:$o]: (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2896])). 185.47/93.64 thf(5779,axiom,((! [A:nat]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ A) = (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9479_Suc__0__or__eq)). 185.47/93.64 thf(26955,plain,((! [A:nat]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ A) = (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5779])). 185.47/93.64 thf(5107,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) <= (ord_less_nat @ D @ E))) => (((! [D:nat,E:nat]: ((A @ D @ E) <= (A @ E @ D))) => (A @ B @ C)) <= (! [D:nat]: (A @ D @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4021_linorder__less__wlog)). 185.47/93.64 thf(24514,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) | ~ (ord_less_nat @ D @ E))) => (((! [D:nat,E:nat]: ((A @ D @ E) | ~ (A @ E @ D))) => (A @ B @ C)) | ~ (! [D:nat]: (A @ D @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5107])). 185.47/93.64 thf(1505,axiom,((! [A:num]: ((ring_17405671764205052669omplex @ (numeral_numeral_int @ A)) = (numera6690914467698888265omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6936_of__int__numeral)). 185.47/93.64 thf(12735,plain,((! [A:num]: ((ring_17405671764205052669omplex @ (numeral_numeral_int @ A)) = (numera6690914467698888265omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505])). 185.47/93.64 thf(3663,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (times_times_real @ B @ A) @ C) => (ord_less_eq_real @ B @ (divide_divide_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2848_mult__imp__le__div__pos)). 185.47/93.64 thf(19759,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (times_times_real @ B @ A) @ C) => (ord_less_eq_real @ B @ (divide_divide_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3663])). 185.47/93.64 thf(1291,axiom,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (divide_divide_rat @ A @ B)) = (divide_divide_rat @ A @ (uminus_uminus_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5590_minus__divide__right)). 185.47/93.64 thf(12041,plain,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (divide_divide_rat @ A @ B)) = (divide_divide_rat @ A @ (uminus_uminus_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291])). 185.47/93.64 thf(3690,axiom,((! [A:nat]: ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ semiri1314217659103216013at_int @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7345_double__gauss__sum)). 185.47/93.64 thf(19845,plain,((! [A:nat]: ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ (semiri1314217659103216013at_int) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3690])). 185.47/93.64 thf(473,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => ((! [D:nat]: (((C @ D) = zero_zero_int) <= (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups3539618377306564664at_int @ C @ B) = (groups3539618377306564664at_int @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6096_sum_Omono__neutral__left)). 185.47/93.64 thf(9319,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => ((! [D:nat]: (((C @ D) = zero_zero_int) | ~ (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups3539618377306564664at_int @ (C) @ B) = (groups3539618377306564664at_int @ (C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[473])). 185.47/93.64 thf(6904,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2919_vebt__pred_Osimps_I5_J)). 185.47/93.64 thf(31143,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6904])). 185.47/93.64 thf(879,axiom,((! [A:complex,B:complex]: ((if_complex @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Complex__Ocomplex_T)). 185.47/93.64 thf(10734,plain,((! [A:complex,B:complex]: ((if_complex @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[879])). 185.47/93.64 thf(684,axiom,((! [A:(nat > real)]: (((suminf_real @ (^ [B:nat]: (A @ (suc @ B)))) = (minus_minus_real @ (suminf_real @ A) @ (A @ zero_zero_nat))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7726_suminf__split__head)). 185.47/93.64 thf(10014,plain,((! [A:(nat > real)]: (((suminf_real @ (^ [B:nat]: (A @ (suc @ B)))) = (minus_minus_real @ (suminf_real @ (A)) @ (A @ zero_zero_nat))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[684])). 185.47/93.64 thf(6224,axiom,((! [A:real,B:nat]: (((power_power_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1842_power__eq__0__iff)). 185.47/93.64 thf(28674,plain,((! [A:real,B:nat]: (((power_power_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6224])). 185.47/93.64 thf(285,axiom,((! [A:int,B:int]: ((times_times_int @ (ring_1_of_int_int @ A) @ B) = (times_times_int @ B @ (ring_1_of_int_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7181_mult__of__int__commute)). 185.47/93.64 thf(8664,plain,((! [A:int,B:int]: ((times_times_int @ (ring_1_of_int_int @ A) @ B) = (times_times_int @ B @ (ring_1_of_int_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 185.47/93.64 thf(7689,axiom,((! [A:nat]: (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_less__exp)). 185.47/93.64 thf(33810,plain,((! [A:nat]: (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7689])). 185.47/93.64 thf(6448,axiom,(((vEBT_VEBT_set_vebt @ (nth_VEBT_VEBT @ treeList @ pr)) != bot_bot_set_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_fgh)). 185.47/93.64 thf(29477,plain,((~ ((vEBT_VEBT_set_vebt @ (nth_VEBT_VEBT @ treeList @ pr)) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6448])). 185.47/93.64 thf(6072,axiom,((! [A:num,B:num]: ((plus_plus_num @ (bit1 @ A) @ (bit0 @ B)) = (bit1 @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6388_semiring__norm_I9_J)). 185.47/93.64 thf(28109,plain,((! [A:num,B:num]: ((plus_plus_num @ (bit1 @ A) @ (bit0 @ B)) = (bit1 @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6072])). 185.47/93.64 thf(4927,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (plus_plus_nat @ B @ A)) = (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6234_neg__one__power__add__eq__neg__one__power__diff)). 185.47/93.64 thf(23860,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (plus_plus_nat @ B @ A)) = (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4927])). 185.47/93.64 thf(252,axiom,((! [A:(rat > (rat > $o)),B:set_nat,C:(nat > rat),D:(nat > rat)]: ((A @ one_one_rat @ one_one_rat) => (((finite_finite_nat @ B) => ((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups73079841787564623at_rat @ C @ B) @ (groups73079841787564623at_rat @ D @ B)))) <= (! [E:rat,F:rat,G:rat,H:rat]: ((A @ (times_times_rat @ E @ F) @ (times_times_rat @ G @ H)) <= ((A @ F @ H) & (A @ E @ G)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8810_prod_Orelated)). 185.47/93.64 thf(8532,plain,((! [A:(rat > (rat > $o)),B:set_nat,C:(nat > rat),D:(nat > rat)]: ((A @ one_one_rat @ one_one_rat) => (((finite_finite_nat @ B) => ((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups73079841787564623at_rat @ (C) @ B) @ (groups73079841787564623at_rat @ (D) @ B)))) | ~ (! [E:rat,F:rat,G:rat,H:rat]: ((A @ (times_times_rat @ E @ F) @ (times_times_rat @ G @ H)) | ~ ((A @ F @ H) & (A @ E @ G)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 185.47/93.64 thf(1419,axiom,((! [A:real,B:real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6346_abs__add__abs)). 185.47/93.64 thf(12472,plain,((! [A:real,B:real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419])). 185.47/93.64 thf(3619,axiom,((! [A:nat]: ((one_one_real = (semiri5074537144036343181t_real @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6925_of__nat__1__eq__iff)). 185.47/93.64 thf(19617,plain,((! [A:nat]: ((one_one_real = (semiri5074537144036343181t_real @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3619])). 185.47/93.64 thf(2464,axiom,((! [A:num,B:nat]: ((ord_max_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (suc @ (ord_max_nat @ (pred_numeral @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6793_max__numeral__Suc)). 185.47/93.64 thf(15893,plain,((! [A:num,B:nat]: ((ord_max_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (suc @ (ord_max_nat @ (pred_numeral @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2464])). 185.47/93.64 thf(4534,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_divide__numeral__1)). 185.47/93.64 thf(22525,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4534])). 185.47/93.64 thf(4631,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_real @ C @ B)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2347_mult__less__cancel__left__neg)). 185.47/93.64 thf(22838,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_real @ C @ B)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4631])). 185.47/93.64 thf(210,axiom,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) => (ord_less_real @ (abs_abs_real @ (tan_real @ A)) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8070_tan__bound__pi2)). 185.47/93.64 thf(8411,plain,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) => (ord_less_real @ (abs_abs_real @ (tan_real @ A)) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[210])). 185.47/93.64 thf(6028,axiom,((! [A:num]: ((one_one_int = (numeral_numeral_int @ A)) = (one = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_one__eq__numeral__iff)). 185.47/93.64 thf(27977,plain,((! [A:num]: ((one_one_int = (numeral_numeral_int @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6028])). 185.47/93.64 thf(2721,axiom,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (cos_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7845_cos__ge__minus__one)). 185.47/93.64 thf(16785,plain,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (cos_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2721])). 185.47/93.64 thf(6804,axiom,((! [A:real]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_real @ (times_times_real @ A @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6667_power3__eq__cube)). 185.47/93.64 thf(30749,plain,((! [A:real]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_real @ (times_times_real @ A @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6804])). 185.47/93.64 thf(2757,axiom,((! [A:nat]: (((semiri8010041392384452111omplex @ A) = zero_zero_complex) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6892_of__nat__eq__0__iff)). 185.47/93.64 thf(16897,plain,((! [A:nat]: (((semiri8010041392384452111omplex @ A) = zero_zero_complex) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2757])). 185.47/93.64 thf(5957,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_eq_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_850_nat__le__add__iff2)). 185.47/93.64 thf(27712,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_eq_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5957])). 185.47/93.64 thf(7380,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_real @ (root @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9167_real__root__lt__0__iff)). 185.47/93.64 thf(32859,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_real @ (root @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7380])). 185.47/93.64 thf(5168,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1652_add__less__same__cancel2)). 185.47/93.64 thf(24776,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5168])). 185.47/93.64 thf(7266,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((B = E) <= (vEBT_invar_vebt @ (vEBT_Node @ A @ B @ C @ D) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_deg__deg__n)). 185.47/93.64 thf(32484,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((B = E) | ~ (vEBT_invar_vebt @ (vEBT_Node @ A @ B @ C @ D) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7266])). 185.47/93.64 thf(3837,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_rat @ (power_power_rat @ (divide_divide_rat @ (semiri681578069525770553at_rat @ B) @ (semiri681578069525770553at_rat @ A)) @ A) @ (semiri681578069525770553at_rat @ (binomial @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8524_binomial__ge__n__over__k__pow__k)). 185.47/93.64 thf(20317,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_rat @ (power_power_rat @ (divide_divide_rat @ (semiri681578069525770553at_rat @ B) @ (semiri681578069525770553at_rat @ A)) @ A) @ (semiri681578069525770553at_rat @ (binomial @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3837])). 185.47/93.64 thf(1027,axiom,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B)) = (dvd_dvd_int @ B @ (minus_minus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4801_mod__eq__dvd__iff)). 185.47/93.64 thf(11242,plain,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B)) = (dvd_dvd_int @ B @ (minus_minus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027])). 185.47/93.64 thf(1959,axiom,((! [A:int,B:int,C:int]: ((A = (minus_minus_int @ C @ B)) <= ((plus_plus_int @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_739_add__implies__diff)). 185.47/93.64 thf(14284,plain,((! [A:int,B:int,C:int]: ((A = (minus_minus_int @ C @ B)) | ~ ((plus_plus_int @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1959])). 185.47/93.64 thf(2496,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => ((ord_less_eq_int @ A @ B) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4171_antisym__conv1)). 185.47/93.64 thf(16007,plain,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => ((ord_less_eq_int @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2496])). 185.47/93.64 thf(7667,axiom,((! [A:nat,B:num,C:num]: ((divide_divide_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_div__mult2__numeral__eq)). 185.47/93.64 thf(33754,plain,((! [A:nat,B:num,C:num]: ((divide_divide_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7667])). 185.47/93.64 thf(2411,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) = (((ord_less_int @ B @ zero_zero_int) & (ord_less_int @ A @ zero_zero_int)) | ((ord_less_int @ zero_zero_int @ A) & (ord_less_int @ zero_zero_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2338_zero__less__mult__iff)). 185.47/93.64 thf(15712,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) = (((ord_less_int @ B @ zero_zero_int) & (ord_less_int @ A @ zero_zero_int)) | ((ord_less_int @ zero_zero_int @ A) & (ord_less_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2411])). 185.47/93.64 thf(6751,axiom,((! [A:rat,B:num]: ((ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B))) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_eq_rat @ zero_zero_rat @ A)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4532_zero__le__power__eq__numeral)). 185.47/93.64 thf(30562,plain,((! [A:rat,B:num]: ((ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B))) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_eq_rat @ zero_zero_rat @ A)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6751])). 185.47/93.64 thf(7714,axiom,(((power_power_real @ zero_zero_real @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2890_zero__power2)). 185.47/93.64 thf(33881,plain,(((power_power_real @ zero_zero_real @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7714])). 185.47/93.64 thf(5058,axiom,((! [A:nat,B:nat,C:nat]: (((A = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat)) & ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1694_div__mult__mult1__if)). 185.47/93.64 thf(24362,plain,((! [A:nat,B:nat,C:nat]: (((A = zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat)) & ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5058])). 185.47/93.64 thf(1019,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ A @ B)) = (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1649_less__add__same__cancel1)). 185.47/93.64 thf(11218,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ A @ B)) = (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019])). 185.47/93.64 thf(2707,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = B) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1515_add__cancel__left__left)). 185.47/93.64 thf(16744,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = B) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2707])). 185.47/93.64 thf(5792,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_nat__le__linear)). 185.47/93.64 thf(26998,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5792])). 185.47/93.64 thf(1103,axiom,((! [A:num,B:real,C:real]: ((ord_less_real @ (numeral_numeral_real @ A) @ (divide_divide_real @ B @ C)) = (((ord_less_real @ (times_times_real @ (numeral_numeral_real @ A) @ C) @ B) <= (ord_less_real @ zero_zero_real @ C)) & ((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_real @ (numeral_numeral_real @ A) @ zero_zero_real) <= (~ (ord_less_real @ C @ zero_zero_real))) & ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ B @ (times_times_real @ (numeral_numeral_real @ A) @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2859_less__divide__eq__numeral_I1_J)). 185.47/93.64 thf(11478,plain,((! [A:num,B:real,C:real]: ((ord_less_real @ (numeral_numeral_real @ A) @ (divide_divide_real @ B @ C)) = (((ord_less_real @ (times_times_real @ (numeral_numeral_real @ A) @ C) @ B) | ~ (ord_less_real @ zero_zero_real @ C)) & ((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_real @ (numeral_numeral_real @ A) @ zero_zero_real) | (ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ B @ (times_times_real @ (numeral_numeral_real @ A) @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103])). 185.47/93.64 thf(2951,axiom,((! [A:num]: ((archim8280529875227126926d_real @ (numeral_numeral_real @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7545_round__numeral)). 185.47/93.64 thf(17513,plain,((! [A:num]: ((archim8280529875227126926d_real @ (numeral_numeral_real @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2951])). 185.47/93.64 thf(652,axiom,((! [A:nat,B:nat,C:(nat > real)]: ((((groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_real) <= (ord_less_nat @ (suc @ A) @ B)) & ((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_real @ (groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6433_sum_Ocl__ivl__Suc)). 185.47/93.64 thf(9897,plain,((! [A:nat,B:nat,C:(nat > real)]: ((((groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_real) | ~ (ord_less_nat @ (suc @ A) @ B)) & ((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_real @ (groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[652])). 185.47/93.64 thf(4561,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2420_divide__nonpos__nonpos)). 185.47/93.64 thf(22610,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4561])). 185.47/93.64 thf(6856,axiom,(((semiri5044797733671781792omplex @ zero_zero_nat) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7953_fact__0)). 185.47/93.64 thf(30974,plain,(((semiri5044797733671781792omplex @ zero_zero_nat) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6856])). 185.47/93.64 thf(2916,axiom,((! [A:int,B:int,C:int,D:int]: ((((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) <= (ord_less_eq_int @ zero_zero_int @ C))) <= (ord_less_eq_int @ C @ D)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2254_mult__mono_H)). 185.47/93.64 thf(17403,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) | ~ (ord_less_eq_int @ zero_zero_int @ C))) | ~ (ord_less_eq_int @ C @ D) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2916])). 185.47/93.64 thf(5457,axiom,((! [A:int]: ((times_times_int @ (numeral_numeral_int @ one) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_mult__numeral__1)). 185.47/93.64 thf(25813,plain,((! [A:int]: ((times_times_int @ (numeral_numeral_int @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5457])). 185.47/93.64 thf(6674,axiom,((! [A:num]: (((numera6690914467698888265omplex @ A) = one_one_complex) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_numeral__eq__one__iff)). 185.47/93.64 thf(30248,plain,((! [A:num]: (((numera6690914467698888265omplex @ A) = one_one_complex) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6674])). 185.47/93.64 thf(3595,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ A @ B)) = (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4444_dvd__add__triv__left__iff)). 185.47/93.64 thf(19546,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ A @ B)) = (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3595])). 185.47/93.64 thf(4699,axiom,((! [A:int]: ~ (ord_less_int @ (times_times_int @ A @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2316_not__square__less__zero)). 185.47/93.64 thf(23069,plain,((! [A:int]: ~ (ord_less_int @ (times_times_int @ A @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4699])). 185.47/93.64 thf(5353,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4215_order_Ostrict__trans2)). 185.47/93.64 thf(25456,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5353])). 185.47/93.64 thf(4440,axiom,((! [A:int,B:int]: ((plus_plus_int @ (times_times_int @ A @ (divide_divide_int @ B @ A)) @ (modulo_modulo_int @ B @ A)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2530_mult__div__mod__eq)). 185.47/93.64 thf(22217,plain,((! [A:int,B:int]: ((plus_plus_int @ (times_times_int @ A @ (divide_divide_int @ B @ A)) @ (modulo_modulo_int @ B @ A)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4440])). 185.47/93.64 thf(3124,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ one_one_rat @ (divide_divide_rat @ B @ A)) = (ord_less_rat @ B @ A)) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1815_less__divide__eq__1__neg)). 185.47/93.64 thf(18065,plain,((! [A:rat,B:rat]: (((ord_less_rat @ one_one_rat @ (divide_divide_rat @ B @ A)) = (ord_less_rat @ B @ A)) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3124])). 185.47/93.64 thf(6765,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4307_order__neq__le__trans)). 185.47/93.64 thf(30615,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6765])). 185.47/93.64 thf(606,axiom,((! [A:nat,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (gbinomial_complex @ (semiri8010041392384452111omplex @ C) @ A)) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (gbinomial_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ B) @ one_one_complex) @ (plus_plus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8595_gbinomial__sum__up__index)). 185.47/93.64 thf(9749,plain,((! [A:nat,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (gbinomial_complex @ (semiri8010041392384452111omplex @ C) @ A)) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (gbinomial_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ B) @ one_one_complex) @ (plus_plus_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[606])). 185.47/93.64 thf(2175,axiom,((! [A:num,B:num]: ((plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)) = (numeral_numeral_rat @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_numeral__plus__numeral)). 185.47/93.64 thf(14987,plain,((! [A:num,B:num]: ((plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)) = (numeral_numeral_rat @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2175])). 185.47/93.64 thf(2240,axiom,((! [A:(real > $o),B:real]: ((? [C:real]: (A @ (times_times_real @ B @ C))) = (? [C:real]: ((dvd_dvd_real @ B @ (plus_plus_real @ C @ zero_zero_real)) & (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4825_unity__coeff__ex)). 185.47/93.64 thf(15186,plain,((! [A:(real > $o),B:real]: ((? [C:real]: (A @ (times_times_real @ B @ C))) = (? [C:real]: ((dvd_dvd_real @ B @ (plus_plus_real @ C @ zero_zero_real)) & (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2240])). 185.47/93.64 thf(263,axiom,((ord_less_eq_int = (^ [A:int,B:int]: (B = (ord_max_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3682_max_Oorder__iff)). 185.47/93.64 thf(8595,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: (B = (ord_max_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 185.47/93.64 thf(7078,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ A @ (times_times_nat @ B @ C))) @ B) = (modulo_modulo_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1852_Suc__mod__mult__self2)). 185.47/93.64 thf(31828,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ A @ (times_times_nat @ B @ C))) @ B) = (modulo_modulo_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7078])). 185.47/93.64 thf(5099,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ (suc @ B)) @ A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2778_diff__Suc__less)). 185.47/93.64 thf(24486,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ (suc @ B)) @ A) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5099])). 185.47/93.64 thf(61,axiom,((! [A:rat,B:rat,C:nat]: ((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (times_times_rat @ (power_power_rat @ (plus_plus_rat @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_rat @ A @ D)) @ (power_power_rat @ A @ C))) @ (set_ord_lessThan_nat @ C)) = (groups2906978787729119204at_rat @ (^ [D:nat]: (times_times_rat @ (power_power_rat @ A @ D) @ (minus_minus_rat @ (power_power_rat @ (plus_plus_rat @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_rat @ A @ (minus_minus_nat @ C @ D))))) @ (set_ord_lessThan_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7609_lemma__termdiff1)). 185.47/93.64 thf(7931,plain,((! [A:rat,B:rat,C:nat]: ((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (times_times_rat @ (power_power_rat @ (plus_plus_rat @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_rat @ A @ D)) @ (power_power_rat @ A @ C))) @ (set_ord_lessThan_nat @ C)) = (groups2906978787729119204at_rat @ (^ [D:nat]: (times_times_rat @ (power_power_rat @ A @ D) @ (minus_minus_rat @ (power_power_rat @ (plus_plus_rat @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_rat @ A @ (minus_minus_nat @ C @ D))))) @ (set_ord_lessThan_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 185.47/93.64 thf(2739,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1130_ring__class_Oring__distribs_I1_J)). 185.47/93.64 thf(16841,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2739])). 185.47/93.64 thf(6819,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_trans__less__add2)). 185.47/93.64 thf(30806,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6819])). 185.47/93.64 thf(6504,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ (modulo_modulo_nat @ B @ C)) @ C) = (modulo_modulo_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1988_mod__add__right__eq)). 185.47/93.64 thf(29680,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ (modulo_modulo_nat @ B @ C)) @ C) = (modulo_modulo_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6504])). 185.47/93.64 thf(6119,axiom,((! [A:rat,B:rat,C:rat]: (((times_times_rat @ A @ B) = (times_times_rat @ A @ C)) = ((A = zero_zero_rat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1498_mult__cancel__left)). 185.47/93.64 thf(28276,plain,((! [A:rat,B:rat,C:rat]: (((times_times_rat @ A @ B) = (times_times_rat @ A @ C)) = ((A = zero_zero_rat) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6119])). 185.47/93.64 thf(7240,axiom,((! [A:num]: ((suc @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1015_Suc__numeral)). 185.47/93.64 thf(32401,plain,((! [A:num]: ((suc @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7240])). 185.47/93.64 thf(7387,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ (divide_divide_nat @ C @ A)) = (ord_less_eq_nat @ (times_times_nat @ B @ A) @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2912_less__eq__div__iff__mult__less__eq)). 185.47/93.64 thf(32882,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ (divide_divide_nat @ C @ A)) = (ord_less_eq_nat @ (times_times_nat @ B @ A) @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7387])). 185.47/93.64 thf(5390,axiom,((! [A:num,B:num]: ((times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_numeral__times__numeral)). 185.47/93.64 thf(25567,plain,((! [A:num,B:num]: ((times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (numeral_numeral_real @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5390])). 185.47/93.64 thf(1035,axiom,((! [A:nat,B:nat]: (((times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri5074537144036343181t_real @ (binomial @ B @ A))) = (divide_divide_real @ (semiri2265585572941072030t_real @ B) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ B @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8552_fact__binomial)). 185.47/93.65 thf(11265,plain,((! [A:nat,B:nat]: (((times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri5074537144036343181t_real @ (binomial @ B @ A))) = (divide_divide_real @ (semiri2265585572941072030t_real @ B) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035])). 185.47/93.65 thf(4226,axiom,((! [A:real,B:real,C:nat]: (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2445_power__mono)). 185.47/93.65 thf(21525,plain,((! [A:real,B:real,C:nat]: (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4226])). 185.47/93.65 thf(2710,axiom,((! [A:nat,B:nat]: ((dvd_dvd_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7237_of__nat__dvd__iff)). 185.47/93.65 thf(16753,plain,((! [A:nat,B:nat]: ((dvd_dvd_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2710])). 185.47/93.65 thf(4352,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (sqrt @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8164_real__sqrt__gt__zero)). 185.47/93.65 thf(21940,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (sqrt @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4352])). 185.47/93.65 thf(1410,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ (modulo_modulo_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1992_mod__add__left__eq)). 185.47/93.65 thf(12430,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ (modulo_modulo_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410])). 185.47/93.65 thf(3609,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ A @ B) => ((nat2 @ (minus_minus_int @ B @ A)) = (minus_minus_nat @ (nat2 @ B) @ (nat2 @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9314_nat__diff__distrib)). 185.47/93.65 thf(19585,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ A @ B) => ((nat2 @ (minus_minus_int @ B @ A)) = (minus_minus_nat @ (nat2 @ B) @ (nat2 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3609])). 185.47/93.65 thf(1986,axiom,((! [A:real,B:real,C:real]: ((! [D:real,E:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ D @ C)) = (dvd_dvd_real @ A @ (plus_plus_real @ (minus_minus_real @ D @ (times_times_real @ E @ B)) @ C)))) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4852_inf__period_I3_J)). 185.47/93.65 thf(14372,plain,((! [A:real,B:real,C:real]: (! [D:real,E:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ D @ C)) = (dvd_dvd_real @ A @ (plus_plus_real @ (minus_minus_real @ D @ (times_times_real @ E @ B)) @ C))) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1986])). 185.47/93.65 thf(6790,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) <= (dvd_dvd_nat @ A @ C)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4690_dvd__diff__nat)). 185.47/93.65 thf(30702,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) | ~ (dvd_dvd_nat @ A @ C) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6790])). 185.47/93.65 thf(5158,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ B @ (times_times_nat @ C @ A)) = (divide_divide_nat @ (divide_divide_nat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2185_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq)). 185.47/93.65 thf(24744,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ B @ (times_times_nat @ C @ A)) = (divide_divide_nat @ (divide_divide_nat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5158])). 185.47/93.65 thf(7496,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ B @ C) @ D) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ D)) @ (suc @ (suc @ A)) @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1249_vebt__insert_Osimps_I4_J)). 185.47/93.65 thf(33273,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ B @ C) @ D) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ D)) @ (suc @ (suc @ A)) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7496])). 185.47/93.65 thf(3929,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ C @ B)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4609_dvd__mult)). 185.47/93.65 thf(20619,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ C @ B)) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3929])). 185.47/93.65 thf(486,axiom,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (A @ (minus_minus_nat @ (plus_plus_nat @ C @ B) @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6626_sum_OatLeastAtMost__rev)). 185.47/93.65 thf(9369,plain,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (A @ (minus_minus_nat @ (plus_plus_nat @ C @ B) @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])). 185.47/93.65 thf(7539,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_VEBT_membermima @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ A) @ B @ C) @ D) = ((ord_less_nat @ (vEBT_VEBT_high @ D @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ B)) & ((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ B @ (vEBT_VEBT_high @ D @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ D @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ D @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1439_VEBT__internal_Omembermima_Osimps_I5_J)). 185.47/93.65 thf(33404,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_VEBT_membermima @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ A) @ B @ C) @ D) = ((ord_less_nat @ (vEBT_VEBT_high @ D @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ B)) & ((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ B @ (vEBT_VEBT_high @ D @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ D @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ D @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7539])). 185.47/93.65 thf(2330,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ C) => (dvd_dvd_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4581_dvd__mult__right)). 185.47/93.65 thf(15458,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ C) => (dvd_dvd_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2330])). 185.47/93.65 thf(6689,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ B @ A) <= (~ (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3959_linorder__le__cases)). 185.47/93.65 thf(30293,plain,((! [A:num,B:num]: ((ord_less_eq_num @ B @ A) | (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6689])). 185.47/93.65 thf(1375,axiom,((! [A:(nat > nat),B:nat,C:nat,D:nat]: ((groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ C) @ (plus_plus_nat @ D @ C))) = (groups3542108847815614940at_nat @ (^ [E:nat]: (A @ (plus_plus_nat @ E @ C))) @ (set_or1269000886237332187st_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6536_sum_Oshift__bounds__cl__nat__ivl)). 185.47/93.65 thf(12311,plain,((! [A:(nat > nat),B:nat,C:nat,D:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ C) @ (plus_plus_nat @ D @ C))) = (groups3542108847815614940at_nat @ (^ [E:nat]: (A @ (plus_plus_nat @ E @ C))) @ (set_or1269000886237332187st_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375])). 185.47/93.65 thf(6696,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1688_nonzero__mult__div__cancel__left)). 185.47/93.65 thf(30314,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6696])). 185.47/93.65 thf(1982,axiom,((! [A:real,B:real,C:real]: (((uminus_uminus_real @ (divide_divide_real @ A @ B)) = C) = (((B != zero_zero_real) => ((uminus_uminus_real @ A) = (times_times_real @ C @ B))) & ((C = zero_zero_real) <= (B = zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5969_minus__divide__eq__eq)). 185.47/93.65 thf(14361,plain,((! [A:real,B:real,C:real]: (((uminus_uminus_real @ (divide_divide_real @ A @ B)) = C) = (((~ (B = zero_zero_real)) => ((uminus_uminus_real @ A) = (times_times_real @ C @ B))) & ((C = zero_zero_real) | ~ (B = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1982])). 185.47/93.65 thf(5132,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_mint @ A) = B) => ((accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ A) => ((! [C:$o,D:$o]: (((((~ (C)) => (((~ (D)) => (B = none_nat)) & ((B = (some_nat @ one_one_nat)) <= (D)))) & ((C) => (B = (some_nat @ zero_zero_nat)))) => (~ (accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ (vEBT_Leaf @ C @ D)))) <= (A = (vEBT_Leaf @ C @ D)))) => ((~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)) => ((~ (accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))) <= (B = (some_nat @ C)))))) <= (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((~ (accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) <= (B = none_nat)) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8284_vebt__mint_Opelims)). 185.47/93.65 thf(24621,plain,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_mint @ A) = B) => ((accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ A) => ((! [C:$o,D:$o]: (((((~ (C)) => (((~ (D)) => (B = none_nat)) & ((B = (some_nat @ one_one_nat)) | ~ (D)))) & ((C) => (B = (some_nat @ zero_zero_nat)))) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ (vEBT_Leaf @ C @ D)))) | ~ (A = (vEBT_Leaf @ C @ D)))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)) | ~ (B = (some_nat @ C))))) | ~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (~ (accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) | ~ (B = none_nat) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5132])). 185.47/93.65 thf(3342,axiom,((! [A:int,B:int]: (((ord_less_nat @ (nat2 @ A) @ (nat2 @ B)) = (ord_less_int @ A @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9305_nat__less__eq__zless)). 185.47/93.65 thf(18737,plain,((! [A:int,B:int]: (((ord_less_nat @ (nat2 @ A) @ (nat2 @ B)) = (ord_less_int @ A @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3342])). 185.47/93.65 thf(4871,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (ord_max_nat @ A @ B) @ C) = (ord_max_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3754_max__add__distrib__left)). 185.47/93.65 thf(23643,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (ord_max_nat @ A @ B) @ C) = (ord_max_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4871])). 185.47/93.65 thf(6614,axiom,((! [A:nat,B:num,C:nat]: (((semiri681578069525770553at_rat @ A) = (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7059_real__of__nat__eq__numeral__power__cancel__iff)). 185.47/93.65 thf(30045,plain,((! [A:nat,B:num,C:nat]: (((semiri681578069525770553at_rat @ A) = (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6614])). 185.47/93.65 thf(373,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((arccos @ (cos_real @ A)) = A) <= (ord_less_eq_real @ A @ pi))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8369_arccos__cos)). 185.47/93.65 thf(8977,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((arccos @ (cos_real @ A)) = A) | ~ (ord_less_eq_real @ A @ pi))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[373])). 185.47/93.65 thf(6774,axiom,((! [A:complex]: ((uminus1482373934393186551omplex @ (uminus1482373934393186551omplex @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5027_add_Oinverse__inverse)). 185.47/93.65 thf(30653,plain,((! [A:complex]: ((uminus1482373934393186551omplex @ (uminus1482373934393186551omplex @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6774])). 185.47/93.65 thf(1850,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = ((A = B) | ~ (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4160_nless__le)). 185.47/93.65 thf(13938,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = ((A = B) | ~ (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1850])). 185.47/93.65 thf(6843,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((B = one_one_nat) & (A = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_nat__mult__eq__1__iff)). 185.47/93.65 thf(30876,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((B = one_one_nat) & (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6843])). 185.47/93.65 thf(2290,axiom,((! [A:nat,B:nat]: (((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) => ((semiri1314217659103216013at_int @ (minus_minus_nat @ A @ B)) = zero_zero_int)) & ((~ (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))) => ((semiri1314217659103216013at_int @ (minus_minus_nat @ A @ B)) = (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7316_int__ops_I6_J)). 185.47/93.65 thf(15328,plain,((! [A:nat,B:nat]: (((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) => ((semiri1314217659103216013at_int @ (minus_minus_nat @ A @ B)) = zero_zero_int)) & ((~ (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))) => ((semiri1314217659103216013at_int @ (minus_minus_nat @ A @ B)) = (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2290])). 185.47/93.65 thf(5670,axiom,((! [A:nat,B:code_integer]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ B @ A))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5443_power__minus__odd)). 185.47/93.65 thf(26603,plain,((! [A:nat,B:code_integer]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ B @ A))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5670])). 185.47/93.65 thf(2598,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ one_one_rat @ A) => (ord_less_rat @ one_one_rat @ (times_times_rat @ A @ (power_power_rat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_859_power__gt1__lemma)). 185.47/93.65 thf(16357,plain,((! [A:rat,B:nat]: ((ord_less_rat @ one_one_rat @ A) => (ord_less_rat @ one_one_rat @ (times_times_rat @ A @ (power_power_rat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2598])). 185.47/93.65 thf(1536,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1642_less__add__same__cancel2)). 185.47/93.65 thf(12824,plain,((! [A:real,B:real]: ((ord_less_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536])). 185.47/93.65 thf(5952,axiom,((! [A:nat]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9461_not__bit__Suc__0__Suc)). 185.47/93.65 thf(27697,plain,((! [A:nat]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5952])). 185.47/93.65 thf(2718,axiom,((! [A:int]: ((ord_less_int @ (abs_abs_int @ A) @ one_one_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6779_zabs__less__one__iff)). 185.47/93.65 thf(16776,plain,((! [A:int]: ((ord_less_int @ (abs_abs_int @ A) @ one_one_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2718])). 185.47/93.65 thf(1519,axiom,((! [A:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ zero_zero_int) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7012_of__nat__le__0__iff)). 185.47/93.65 thf(12777,plain,((! [A:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ zero_zero_int) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519])). 185.47/93.65 thf(324,axiom,(((tan_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8044_tan__45)). 185.47/93.65 thf(8817,plain,(((tan_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 185.47/93.65 thf(7420,axiom,((! [A:num,B:num]: ((times_times_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5337_mult__neg__numeral__simps_I3_J)). 185.47/93.65 thf(33009,plain,((! [A:num,B:num]: ((times_times_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7420])). 185.47/93.65 thf(4651,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) <= (ord_less_eq_int @ B @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2241_mult__nonpos__nonpos)). 185.47/93.65 thf(22898,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) | ~ (ord_less_eq_int @ B @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4651])). 185.47/93.65 thf(5618,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (divide_divide_nat @ B @ A) @ C) = (divide_divide_nat @ (times_times_nat @ B @ C) @ A)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4865_unit__div__commute)). 185.47/93.65 thf(26429,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (divide_divide_nat @ B @ A) @ C) = (divide_divide_nat @ (times_times_nat @ B @ C) @ A)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5618])). 185.47/93.65 thf(604,axiom,((! [A:num,B:num]: ((archim6058952711729229775r_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B))) = (divide_divide_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9080_floor__divide__eq__div__numeral)). 185.47/93.65 thf(9743,plain,((! [A:num,B:num]: ((archim6058952711729229775r_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B))) = (divide_divide_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[604])). 185.47/93.65 thf(4983,axiom,((! [A:real,B:real]: ((B = zero_zero_real) <= ((sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8224_real__sqrt__sum__squares__eq__cancel)). 185.47/93.65 thf(24033,plain,((! [A:real,B:real]: ((B = zero_zero_real) | ~ ((sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4983])). 185.47/93.65 thf(2145,axiom,((! [A:num,B:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5703_neg__numeral__less__numeral)). 185.47/93.65 thf(14874,plain,((! [A:num,B:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2145])). 185.47/93.65 thf(5169,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ A @ B)) = (times_times_nat @ (binomial @ (suc @ A) @ (suc @ B)) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8430_Suc__times__binomial__eq)). 185.47/93.65 thf(24779,plain,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ A @ B)) = (times_times_nat @ (binomial @ (suc @ A) @ (suc @ B)) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5169])). 185.47/93.65 thf(1718,axiom,((! [A:int,B:int]: ((ring_1_of_int_real @ (minus_minus_int @ A @ B)) = (minus_minus_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6976_of__int__diff)). 185.47/93.65 thf(13479,plain,((! [A:int,B:int]: ((ring_1_of_int_real @ (minus_minus_int @ A @ B)) = (minus_minus_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718])). 185.47/93.65 thf(511,axiom,((! [A:set_nat]: ((minus_minus_set_nat @ A @ A) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1300_Diff__cancel)). 185.47/93.65 thf(9452,plain,((! [A:set_nat]: ((minus_minus_set_nat @ A @ A) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[511])). 185.47/93.65 thf(6318,axiom,((! [A:nat,B:nat]: (((suc @ (minus_minus_nat @ B @ (suc @ A))) = (minus_minus_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1098_Suc__diff__Suc)). 185.47/93.65 thf(28995,plain,((! [A:nat,B:nat]: (((suc @ (minus_minus_nat @ B @ (suc @ A))) = (minus_minus_nat @ B @ A)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6318])). 185.47/93.65 thf(4577,axiom,((~ (ord_less_eq_rat @ zero_zero_rat @ (uminus_uminus_rat @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5909_le__minus__one__simps_I3_J)). 185.47/93.65 thf(22663,plain,((~ (ord_less_eq_rat @ zero_zero_rat @ (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4577])). 185.47/93.65 thf(2435,axiom,((! [A:int,B:int]: (((modulo_modulo_int @ A @ B) = A) = (((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_int @ B @ A)) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_int @ A @ B)) | (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3144_zmod__trivial__iff)). 185.47/93.65 thf(15799,plain,((! [A:int,B:int]: (((modulo_modulo_int @ A @ B) = A) = (((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_int @ B @ A)) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_int @ A @ B)) | (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2435])). 185.47/93.65 thf(7051,axiom,((! [A:num,B:num,C:int]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (times_times_int @ (numeral_numeral_int @ B) @ C)) = (times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5353_semiring__norm_I170_J)). 185.47/93.65 thf(31753,plain,((! [A:num,B:num,C:int]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (times_times_int @ (numeral_numeral_int @ B) @ C)) = (times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7051])). 185.47/93.65 thf(994,axiom,((! [A:num]: ~ (ord_less_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5953_not__numeral__less__neg__one)). 185.47/93.65 thf(11136,plain,((! [A:num]: ~ (ord_less_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[994])). 185.47/93.65 thf(2702,axiom,((! [A:int,B:int]: (((((modulo_modulo_int @ B @ A) = zero_zero_int) => ((divide_divide_int @ B @ (uminus_uminus_int @ A)) = (uminus_uminus_int @ (divide_divide_int @ B @ A)))) & (((modulo_modulo_int @ B @ A) != zero_zero_int) => ((divide_divide_int @ B @ (uminus_uminus_int @ A)) = (minus_minus_int @ (uminus_uminus_int @ (divide_divide_int @ B @ A)) @ one_one_int)))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6255_zdiv__zminus2__eq__if)). 185.47/93.65 thf(16725,plain,((! [A:int,B:int]: (((((modulo_modulo_int @ B @ A) = zero_zero_int) => ((divide_divide_int @ B @ (uminus_uminus_int @ A)) = (uminus_uminus_int @ (divide_divide_int @ B @ A)))) & ((~ ((modulo_modulo_int @ B @ A) = zero_zero_int)) => ((divide_divide_int @ B @ (uminus_uminus_int @ A)) = (minus_minus_int @ (uminus_uminus_int @ (divide_divide_int @ B @ A)) @ one_one_int)))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2702])). 185.47/93.65 thf(5087,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2230_mult__right__mono)). 185.47/93.65 thf(24450,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5087])). 185.47/93.65 thf(5207,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((divide_divide_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1797_div__less)). 185.47/93.65 thf(24894,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((divide_divide_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5207])). 185.47/93.65 thf(3333,axiom,((! [A:nat,B:int]: ((bit_se547839408752420682it_nat @ A @ (nat2 @ B)) = (nat2 @ (bit_se545348938243370406it_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9505_push__bit__nat__eq)). 185.47/93.65 thf(18710,plain,((! [A:nat,B:int]: ((bit_se547839408752420682it_nat @ A @ (nat2 @ B)) = (nat2 @ (bit_se545348938243370406it_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3333])). 185.47/93.65 thf(5920,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) | (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1492_mult__eq__0__iff)). 185.47/93.65 thf(27600,plain,((! [A:real,B:real]: (((times_times_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5920])). 185.47/93.65 thf(2347,axiom,((! [A:int,B:num,C:nat]: ((ord_le3102999989581377725nteger @ (ring_18347121197199848620nteger @ A) @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7161_of__int__le__neg__numeral__power__cancel__iff)). 185.47/93.65 thf(15505,plain,((! [A:int,B:num,C:nat]: ((ord_le3102999989581377725nteger @ (ring_18347121197199848620nteger @ A) @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2347])). 185.47/93.65 thf(5558,axiom,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1605_diff__0__eq__0)). 185.47/93.65 thf(26237,plain,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5558])). 185.47/93.65 thf(4150,axiom,((! [A:num]: ((real_V1022390504157884413omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7449_norm__neg__numeral)). 185.47/93.65 thf(21290,plain,((! [A:num]: ((real_V1022390504157884413omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4150])). 185.47/93.65 thf(54,axiom,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ A @ (set_ord_atMost_nat @ B)) = (times_times_rat @ (A @ zero_zero_nat) @ (groups73079841787564623at_rat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8771_prod_OatMost__shift)). 185.47/93.65 thf(7909,plain,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ (A) @ (set_ord_atMost_nat @ B)) = (times_times_rat @ (A @ zero_zero_nat) @ (groups73079841787564623at_rat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 185.47/93.65 thf(1279,axiom,((! [A:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5893_neg__numeral__le__zero)). 185.47/93.65 thf(12008,plain,((! [A:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279])). 185.47/93.65 thf(6425,axiom,((((=) @ real) = (^ [A:real,B:real]: ((minus_minus_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2091_eq__iff__diff__eq__0)). 185.47/93.65 thf(29398,plain,((((=) @ real) = (^ [A:real,B:real]: ((minus_minus_real @ A @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6425])). 185.47/93.65 thf(7375,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (semiri1408675320244567234ct_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8036_choose__dvd)). 185.47/93.65 thf(32844,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (semiri1408675320244567234ct_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7375])). 185.47/93.65 thf(2446,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (((plus_plus_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int)))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2286_add__nonneg__eq__0__iff)). 185.47/93.65 thf(15831,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (((plus_plus_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int)))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2446])). 185.47/93.65 thf(3848,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ B @ (plus_plus_rat @ C @ A)) <= (ord_less_eq_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2296_add__increasing2)). 185.47/93.65 thf(20358,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ B @ (plus_plus_rat @ C @ A)) | ~ (ord_less_eq_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3848])). 185.47/93.65 thf(4916,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => (((modulo_modulo_nat @ D @ B) = (modulo_modulo_nat @ E @ B)) => ((modulo_modulo_nat @ (times_times_nat @ A @ D) @ B) = (modulo_modulo_nat @ (times_times_nat @ C @ E) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1982_mod__mult__cong)). 185.47/93.65 thf(23814,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => (((modulo_modulo_nat @ D @ B) = (modulo_modulo_nat @ E @ B)) => ((modulo_modulo_nat @ (times_times_nat @ A @ D) @ B) = (modulo_modulo_nat @ (times_times_nat @ C @ E) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4916])). 185.47/93.65 thf(5148,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4364_linorder__le__less__linear)). 185.47/93.65 thf(24712,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5148])). 185.47/93.65 thf(7708,axiom,((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2903_pos2)). 185.47/93.65 thf(33866,plain,((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7708])). 185.47/93.65 thf(2294,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ B @ one_one_int)) = ((A = B) | (ord_less_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3176_zless__add1__eq)). 185.47/93.65 thf(15343,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ B @ one_one_int)) = ((A = B) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2294])). 185.47/93.65 thf(1897,axiom,((! [A:real,B:num]: ((ord_less_real @ zero_zero_real @ A) => ((powr_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9131_powr__neg__numeral)). 185.47/93.65 thf(14071,plain,((! [A:real,B:num]: ((ord_less_real @ zero_zero_real @ A) => ((powr_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897])). 185.47/93.65 thf(3228,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_rat @ (power_power_rat @ (semiri681578069525770553at_rat @ A) @ B) @ (semiri681578069525770553at_rat @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7049_of__nat__less__of__nat__power__cancel__iff)). 185.47/93.65 thf(18392,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_rat @ (power_power_rat @ (semiri681578069525770553at_rat @ A) @ B) @ (semiri681578069525770553at_rat @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3228])). 185.47/93.65 thf(4347,axiom,((! [A:rat,B:rat]: ((minus_minus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B)) = (times_times_rat @ (plus_plus_rat @ A @ B) @ (minus_minus_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1216_square__diff__square__factored)). 185.47/93.65 thf(21924,plain,((! [A:rat,B:rat]: ((minus_minus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B)) = (times_times_rat @ (plus_plus_rat @ A @ B) @ (minus_minus_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4347])). 185.47/93.65 thf(4748,axiom,((bit_se7879613467334960850it_int = (^ [A:nat,B:int]: (plus_plus_int @ B @ (times_times_int @ (zero_n2684676970156552555ol_int @ (~ (bit_se1146084159140164899it_int @ B @ A))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9441_set__bit__eq)). 185.47/93.65 thf(23223,plain,(((bit_se7879613467334960850it_int) = (^ [A:nat,B:int]: (plus_plus_int @ B @ (times_times_int @ (zero_n2684676970156552555ol_int @ (~ (bit_se1146084159140164899it_int @ B @ A))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4748])). 185.47/93.65 thf(2890,axiom,((! [A:nat,B:code_integer]: (((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_Code_integer)) => (dvd_dvd_Code_integer @ B @ (power_8256067586552552935nteger @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4916_dvd__power)). 185.47/93.65 thf(17322,plain,((! [A:nat,B:code_integer]: (((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_Code_integer)) => (dvd_dvd_Code_integer @ B @ (power_8256067586552552935nteger @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2890])). 185.47/93.65 thf(3400,axiom,((! [A:complex,B:(nat > complex),C:complex]: ((sums_complex @ (^ [D:nat]: (times_times_complex @ A @ (B @ D))) @ C) => ((A != zero_zero_complex) => (sums_complex @ B @ (divide1717551699836669952omplex @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8183_sums__mult__D)). 185.47/93.65 thf(18930,plain,((! [A:complex,B:(nat > complex),C:complex]: ((sums_complex @ (^ [D:nat]: (times_times_complex @ A @ (B @ D))) @ C) => ((~ (A = zero_zero_complex)) => (sums_complex @ (B) @ (divide1717551699836669952omplex @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3400])). 185.47/93.65 thf(3997,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_int @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3249_pinf_I5_J)). 185.47/93.65 thf(20826,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3997])). 185.47/93.65 thf(7359,axiom,(((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1712_diff__numeral__special_I9_J)). 185.47/93.65 thf(32796,plain,(((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7359])). 185.47/93.65 thf(6622,axiom,((! [A:rat]: ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) = (plus_plus_rat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_mult__2)). 185.47/93.65 thf(30077,plain,((! [A:rat]: ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) = (plus_plus_rat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6622])). 185.47/93.65 thf(3580,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = ((A != zero_zero_int) | (B != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2986_sum__power2__gt__zero__iff)). 185.47/93.65 thf(19497,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = (~ (A = zero_zero_int) | ~ (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3580])). 185.47/93.65 thf(942,axiom,(((exp_complex @ (times_times_complex @ (real_V4546457046886955230omplex @ pi) @ imaginary_unit)) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9136_exp__pi__i)). 185.47/93.65 thf(10965,plain,(((exp_complex @ (times_times_complex @ (real_V4546457046886955230omplex @ pi) @ imaginary_unit)) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[942])). 185.47/93.65 thf(1726,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B)) = (((ord_less_rat @ A @ C) <= (ord_less_eq_rat @ zero_zero_rat @ B)) & ((ord_less_rat @ C @ A) <= (ord_less_eq_rat @ B @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2595_mult__less__cancel__right)). 185.47/93.65 thf(13521,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B)) = (((ord_less_rat @ A @ C) | ~ (ord_less_eq_rat @ zero_zero_rat @ B)) & ((ord_less_rat @ C @ A) | ~ (ord_less_eq_rat @ B @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726])). 185.47/93.65 thf(6095,axiom,((! [A:real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ one)) @ A) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5975_mult__1s__ring__1_I1_J)). 185.47/93.65 thf(28188,plain,((! [A:real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ one)) @ A) = (uminus_uminus_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6095])). 185.47/93.65 thf(656,axiom,((! [A:set_nat,B:nat,C:(nat > rat)]: ((finite_finite_nat @ A) => ((((groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (B = D) @ (C @ D) @ one_one_rat)) @ A) = (C @ B)) <= (member_nat @ B @ A)) & ((~ (member_nat @ B @ A)) => ((groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (B = D) @ (C @ D) @ one_one_rat)) @ A) = one_one_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8685_prod_Odelta_H)). 185.47/93.65 thf(9914,plain,((! [A:set_nat,B:nat,C:(nat > rat)]: ((finite_finite_nat @ A) => ((((groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (B = D) @ (C @ D) @ one_one_rat)) @ A) = (C @ B)) | ~ (member_nat @ B @ A)) & ((~ (member_nat @ B @ A)) => ((groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (B = D) @ (C @ D) @ one_one_rat)) @ A) = one_one_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[656])). 185.47/93.65 thf(1238,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (times_times_real @ B @ A)) = (((ord_less_real @ B @ one_one_real) <= (ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_real @ one_one_real @ B) <= (ord_less_eq_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2824_mult__less__cancel__right1)). 185.47/93.65 thf(11885,plain,((! [A:real,B:real]: ((ord_less_real @ A @ (times_times_real @ B @ A)) = (((ord_less_real @ B @ one_one_real) | ~ (ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_real @ one_one_real @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238])). 185.47/93.65 thf(6924,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ (divide_divide_nat @ B @ A) @ C) = (dvd_dvd_nat @ B @ (times_times_nat @ C @ A)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4833_div__dvd__iff__mult)). 185.47/93.65 thf(31212,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ (divide_divide_nat @ B @ A) @ C) = (dvd_dvd_nat @ B @ (times_times_nat @ C @ A)))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6924])). 185.47/93.65 thf(7527,axiom,((! [A:num]: ((unique5055182867167087721od_nat @ one @ (bit1 @ A)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6811_divmod__algorithm__code_I4_J)). 185.47/93.65 thf(33372,plain,((! [A:num]: ((unique5055182867167087721od_nat @ one @ (bit1 @ A)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7527])). 185.47/93.65 thf(5710,axiom,((! [A:complex]: ((zero_zero_complex = (uminus1482373934393186551omplex @ A)) = (zero_zero_complex = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5052_neg__0__equal__iff__equal)). 185.47/93.65 thf(26724,plain,((! [A:complex]: ((zero_zero_complex = (uminus1482373934393186551omplex @ A)) = (zero_zero_complex = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5710])). 185.47/93.65 thf(3834,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = C) = ((vEBT_VEBT_mul @ (some_nat @ A) @ (some_nat @ B)) = (some_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_mul__shift)). 185.47/93.65 thf(20308,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = C) = ((vEBT_VEBT_mul @ (some_nat @ A) @ (some_nat @ B)) = (some_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3834])). 185.47/93.65 thf(1698,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1621_le__add__same__cancel1)). 185.47/93.65 thf(13420,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698])). 185.47/93.65 thf(3788,axiom,((! [A:rat]: ((ord_less_rat @ A @ (uminus_uminus_rat @ A)) = (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5153_less__neg__neg)). 185.47/93.65 thf(20174,plain,((! [A:rat]: ((ord_less_rat @ A @ (uminus_uminus_rat @ A)) = (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3788])). 185.47/93.65 thf(2075,axiom,((! [A:int,B:int,C:nat]: (((ring_17405671764205052669omplex @ A) = (power_power_complex @ (ring_17405671764205052669omplex @ B) @ C)) = (A = (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6982_of__int__power__eq__of__int__cancel__iff)). 185.47/93.65 thf(14658,plain,((! [A:int,B:int,C:nat]: (((ring_17405671764205052669omplex @ A) = (power_power_complex @ (ring_17405671764205052669omplex @ B) @ C)) = (A = (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2075])). 185.47/93.65 thf(4506,axiom,((! [A:nat,B:(nat > complex),C:complex]: ((! [D:nat]: (((B @ D) = zero_zero_complex) <= (ord_less_nat @ D @ A))) => ((sums_complex @ (^ [D:nat]: (B @ (plus_plus_nat @ D @ A))) @ C) = (sums_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8191_sums__zero__iff__shift)). 185.47/93.65 thf(22421,plain,((! [A:nat,B:(nat > complex),C:complex]: ((! [D:nat]: (((B @ D) = zero_zero_complex) | ~ (ord_less_nat @ D @ A))) => ((sums_complex @ (^ [D:nat]: (B @ (plus_plus_nat @ D @ A))) @ C) = (sums_complex @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4506])). 185.47/93.65 thf(769,axiom,((! [A:int]: ((ord_less_int @ (ring_1_of_int_int @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7038_of__int__less__0__iff)). 185.47/93.65 thf(10350,plain,((! [A:int]: ((ord_less_int @ (ring_1_of_int_int @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[769])). 185.47/93.65 thf(2665,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (uminus_uminus_int @ (modulo_modulo_int @ A @ B)) @ B) = (modulo_modulo_int @ (uminus_uminus_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5595_mod__minus__eq)). 185.47/93.65 thf(16562,plain,((! [A:int,B:int]: ((modulo_modulo_int @ (uminus_uminus_int @ (modulo_modulo_int @ A @ B)) @ B) = (modulo_modulo_int @ (uminus_uminus_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2665])). 185.47/93.65 thf(3739,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((? [D:real]: ((ord_less_real @ zero_zero_real @ D) & ! [E:real]: (((ord_less_eq_real @ E @ C) & (ord_less_eq_real @ A @ E)) <= (ord_less_real @ (abs_abs_real @ (minus_minus_real @ B @ E)) @ D)))) <= (ord_less_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6672_lemma__interval)). 185.47/93.65 thf(20008,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (? [D:real]: ((ord_less_real @ zero_zero_real @ D) & ! [E:real]: (((ord_less_eq_real @ E @ C) & (ord_less_eq_real @ A @ E)) | ~ (ord_less_real @ (abs_abs_real @ (minus_minus_real @ B @ E)) @ D))) | ~ (ord_less_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3739])). 185.47/93.65 thf(2503,axiom,((! [A:real,B:real]: (((divide_divide_real @ (abs_abs_real @ B) @ A) = (abs_abs_real @ (divide_divide_real @ B @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6562_abs__div__pos)). 185.47/93.65 thf(16028,plain,((! [A:real,B:real]: (((divide_divide_real @ (abs_abs_real @ B) @ A) = (abs_abs_real @ (divide_divide_real @ B @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2503])). 185.47/93.65 thf(1107,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((A != zero_zero_rat) => (((ord_less_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ D @ B)) = (ord_less_rat @ (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ D @ A)) @ (times_times_rat @ A @ B)) @ zero_zero_rat)) <= (B != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2866_frac__less__eq)). 185.47/93.65 thf(11490,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((~ (A = zero_zero_rat)) => (((ord_less_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ D @ B)) = (ord_less_rat @ (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ D @ A)) @ (times_times_rat @ A @ B)) @ zero_zero_rat)) | (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107])). 185.47/93.65 thf(2535,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D)) <= ((A = B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_add__mono__thms__linordered__semiring_I4_J)). 185.47/93.65 thf(16136,plain,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D)) | ~ ((A = B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2535])). 185.47/93.65 thf(2969,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => ((plus_plus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (plus_plus_rat @ B @ (times_times_rat @ C @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2731_divide__add__eq__iff)). 185.47/93.65 thf(17571,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => ((plus_plus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (plus_plus_rat @ B @ (times_times_rat @ C @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2969])). 185.47/93.65 thf(4848,axiom,((times_times_nat = (^ [A:nat,B:nat]: (nat2 @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9300_nat__times__as__int)). 185.47/93.65 thf(23570,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (nat2 @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4848])). 185.47/93.65 thf(4224,axiom,((minus_minus_rat = (^ [A:rat,B:rat]: (plus_plus_rat @ A @ (uminus_uminus_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5790_diff__conv__add__uminus)). 185.47/93.65 thf(21520,plain,(((minus_minus_rat) = (^ [A:rat,B:rat]: (plus_plus_rat @ A @ (uminus_uminus_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4224])). 185.47/93.65 thf(5661,axiom,((! [A:nat,B:rat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_rat @ (uminus_uminus_rat @ B) @ A) = (power_power_rat @ B @ A))) & (((power_power_rat @ (uminus_uminus_rat @ B) @ A) = (uminus_uminus_rat @ (power_power_rat @ B @ A))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6187_uminus__power__if)). 185.47/93.65 thf(26574,plain,((! [A:nat,B:rat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_rat @ (uminus_uminus_rat @ B) @ A) = (power_power_rat @ B @ A))) & (((power_power_rat @ (uminus_uminus_rat @ B) @ A) = (uminus_uminus_rat @ (power_power_rat @ B @ A))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5661])). 185.47/93.65 thf(227,axiom,((! [A:(nat > complex)]: ((summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (A @ B)))) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (suminf_complex @ A)) @ (suminf_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7728_summable__norm)). 185.47/93.65 thf(8459,plain,((! [A:(nat > complex)]: ((summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (A @ B)))) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (suminf_complex @ (A))) @ (suminf_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 185.47/93.65 thf(7447,axiom,((! [A:real,B:real]: ((power_power_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_power2__sum)). 185.47/93.65 thf(33087,plain,((! [A:real,B:real]: ((power_power_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7447])). 185.47/93.65 thf(3965,axiom,((! [A:nat,B:nat]: ((ord_less_eq_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8000_fact__mono)). 185.47/93.65 thf(20729,plain,((! [A:nat,B:nat]: ((ord_less_eq_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3965])). 185.47/93.65 thf(7363,axiom,((! [A:num,B:num]: (((A = B) | (ord_less_num @ A @ B)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4369_order__le__imp__less__or__eq)). 185.47/93.65 thf(32806,plain,((! [A:num,B:num]: ((A = B) | (ord_less_num @ A @ B) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7363])). 185.47/93.65 thf(7633,axiom,(((semiri1408675320244567234ct_nat @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7980_fact__2)). 185.47/93.65 thf(33668,plain,(((semiri1408675320244567234ct_nat @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7633])). 185.47/93.65 thf(4419,axiom,((! [A:int,B:nat,C:int]: ((ord_less_eq_int @ (power_power_int @ A @ (suc @ B)) @ (power_power_int @ C @ (suc @ B))) => ((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2757_power__le__imp__le__base)). 185.47/93.65 thf(22146,plain,((! [A:int,B:nat,C:int]: ((ord_less_eq_int @ (power_power_int @ A @ (suc @ B)) @ (power_power_int @ C @ (suc @ B))) => ((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4419])). 185.47/93.65 thf(4920,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: (B != (times_times_nat @ A @ C)))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4623_dvdE)). 185.47/93.65 thf(23829,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ~ (B = (times_times_nat @ A @ C))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4920])). 185.47/93.65 thf(5270,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2110_old_Onat_Odistinct_I2_J)). 185.47/93.65 thf(25144,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5270])). 185.47/93.65 thf(6973,axiom,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ A @ (power_power_int @ A @ B)) @ (power_power_int @ A @ B)) <= (ord_less_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2870_power__Suc__less)). 185.47/93.65 thf(31443,plain,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ A @ (power_power_int @ A @ B)) @ (power_power_int @ A @ B)) | ~ (ord_less_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6973])). 185.47/93.65 thf(946,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (arccos @ B) @ (arccos @ A)))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8362_arccos__le__arccos)). 185.47/93.65 thf(10977,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (arccos @ B) @ (arccos @ A)))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[946])). 185.47/93.65 thf(6508,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1489_mult__zero__right)). 185.47/93.65 thf(29695,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6508])). 185.47/93.65 thf(7505,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ A @ (power_power_real @ A @ B)) @ (power_power_real @ A @ B)) <= (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2867_power__Suc__less)). 185.47/93.65 thf(33302,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ A @ (power_power_real @ A @ B)) @ (power_power_real @ A @ B)) | ~ (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7505])). 185.47/93.65 thf(4466,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (times_times_rat @ C @ A) @ (times_times_rat @ C @ B)) <= (ord_less_eq_rat @ zero_zero_rat @ C)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2199_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 185.47/93.65 thf(22297,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (times_times_rat @ C @ A) @ (times_times_rat @ C @ B)) | ~ (ord_less_eq_rat @ zero_zero_rat @ C) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4466])). 185.47/93.65 thf(1548,axiom,((! [A:real,B:int]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A)))) @ (abs_abs_real @ (minus_minus_real @ A @ (ring_1_of_int_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7603_round__diff__minimal)). 185.47/93.65 thf(12860,plain,((! [A:real,B:int]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A)))) @ (abs_abs_real @ (minus_minus_real @ A @ (ring_1_of_int_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548])). 185.47/93.65 thf(5397,axiom,((! [A:num,B:num,C:num]: (((ord_less_num @ C @ A) => (ord_less_num @ C @ B)) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4035_dual__order_Ostrict__trans)). 185.47/93.65 thf(25587,plain,((! [A:num,B:num,C:num]: (((ord_less_num @ C @ A) => (ord_less_num @ C @ B)) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5397])). 185.47/93.65 thf(6721,axiom,((! [A:num]: ((ring_18347121197199848620nteger @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7299_of__int__neg__numeral)). 185.47/93.65 thf(30417,plain,((! [A:num]: ((ring_18347121197199848620nteger @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6721])). 185.47/93.65 thf(3084,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_eq_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2601_mult__le__cancel__left__pos)). 185.47/93.65 thf(17933,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_eq_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3084])). 185.47/93.65 thf(6128,axiom,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_eq_num @ B @ C) => (ord_less_num @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4318_order__less__le__trans)). 185.47/93.65 thf(28309,plain,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_eq_num @ B @ C) => (ord_less_num @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6128])). 185.47/93.65 thf(1562,axiom,((! [A:real]: (ord_less_real @ (minus_minus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7634_of__int__round__gt)). 185.47/93.65 thf(12907,plain,((! [A:real]: (ord_less_real @ (minus_minus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562])). 185.47/93.65 thf(1260,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_add__mono)). 185.47/93.65 thf(11954,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260])). 185.47/93.65 thf(5748,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((dvd_dvd_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4466_dvd__times__right__cancel__iff)). 185.47/93.65 thf(26856,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((dvd_dvd_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5748])). 185.47/93.65 thf(5568,axiom,((! [A:code_integer]: ((uminus1351360451143612070nteger @ (uminus1351360451143612070nteger @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5029_add_Oinverse__inverse)). 185.47/93.65 thf(26265,plain,((! [A:code_integer]: ((uminus1351360451143612070nteger @ (uminus1351360451143612070nteger @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5568])). 185.47/93.65 thf(346,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > $o)]: ((finite_finite_nat @ A) => ((groups6464643781859351333omplex @ B @ (collect_nat @ (^ [D:nat]: ((C @ D) & (member_nat @ D @ A))))) = (groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (C @ D) @ (B @ D) @ one_one_complex)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8775_prod_Ointer__filter)). 185.47/93.65 thf(8892,plain,((! [A:set_nat,B:(nat > complex),C:(nat > $o)]: ((finite_finite_nat @ A) => ((groups6464643781859351333omplex @ (B) @ (collect_nat @ (^ [D:nat]: ((C @ D) & (member_nat @ D @ A))))) = (groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (C @ D) @ (B @ D) @ one_one_complex)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])). 185.47/93.65 thf(5761,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2639_add__strict__increasing)). 185.47/93.65 thf(26894,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5761])). 185.47/93.65 thf(2193,axiom,((! [A:complex]: (((cos_complex @ A) != zero_zero_complex) => (((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) != zero_zero_complex) => ((tan_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (divide1717551699836669952omplex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (tan_complex @ A)) @ (minus_minus_complex @ one_one_complex @ (power_power_complex @ (tan_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7949_tan__double)). 185.47/93.65 thf(15041,plain,((! [A:complex]: ((~ ((cos_complex @ A) = zero_zero_complex)) => ((~ ((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = zero_zero_complex)) => ((tan_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (divide1717551699836669952omplex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (tan_complex @ A)) @ (minus_minus_complex @ one_one_complex @ (power_power_complex @ (tan_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2193])). 185.47/93.65 thf(7467,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_mult_Oassoc)). 185.47/93.65 thf(33170,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7467])). 185.47/93.65 thf(5510,axiom,((! [A:num]: ((plus_plus_rat @ (numeral_numeral_rat @ A) @ one_one_rat) = (numeral_numeral_rat @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_numeral__plus__one)). 185.47/93.65 thf(26080,plain,((! [A:num]: ((plus_plus_rat @ (numeral_numeral_rat @ A) @ one_one_rat) = (numeral_numeral_rat @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5510])). 185.47/93.65 thf(2517,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((A = B) & (ord_less_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_add__mono__thms__linordered__field_I2_J)). 185.47/93.65 thf(16077,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ ((A = B) & (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2517])). 185.47/93.65 thf(221,axiom,((! [A:complex]: (ord_less_eq_real @ zero_zero_real @ (re @ (csqrt @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9647_Re__csqrt)). 185.47/93.65 thf(8443,plain,((! [A:complex]: (ord_less_eq_real @ zero_zero_real @ (re @ (csqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 185.47/93.65 thf(5323,axiom,((! [A:nat,B:nat]: ((((modulo_modulo_nat @ (suc @ A) @ B) = (suc @ (modulo_modulo_nat @ A @ B))) <= ((suc @ (modulo_modulo_nat @ A @ B)) != B)) & (((modulo_modulo_nat @ (suc @ A) @ B) = zero_zero_nat) <= ((suc @ (modulo_modulo_nat @ A @ B)) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1932_mod__Suc)). 185.47/93.65 thf(25317,plain,((! [A:nat,B:nat]: ((((modulo_modulo_nat @ (suc @ A) @ B) = (suc @ (modulo_modulo_nat @ A @ B))) | ((suc @ (modulo_modulo_nat @ A @ B)) = B)) & (((modulo_modulo_nat @ (suc @ A) @ B) = zero_zero_nat) | ~ ((suc @ (modulo_modulo_nat @ A @ B)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5323])). 185.47/93.65 thf(2249,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ (plus_plus_int @ A @ C)) <= (ord_less_eq_int @ B @ C)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2640_add__strict__increasing)). 185.47/93.65 thf(15210,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ (plus_plus_int @ A @ C)) | ~ (ord_less_eq_int @ B @ C) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2249])). 185.47/93.65 thf(2674,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ (divide_divide_int @ B @ A)) = (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3056_pos__imp__zdiv__pos__iff)). 185.47/93.65 thf(16594,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ (divide_divide_int @ B @ A)) = (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2674])). 185.47/93.65 thf(3589,axiom,((~ (ord_less_rat @ one_one_rat @ (uminus_uminus_rat @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5754_less__minus__one__simps_I4_J)). 185.47/93.65 thf(19529,plain,((~ (ord_less_rat @ one_one_rat @ (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3589])). 185.47/93.65 thf(4783,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ (divide_divide_real @ (plus_plus_real @ B @ C) @ (numeral_numeral_real @ (bit0 @ one)))))) <= ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3015_arith__geo__mean)). 185.47/93.65 thf(23368,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ (divide_divide_real @ (plus_plus_real @ B @ C) @ (numeral_numeral_real @ (bit0 @ one)))))) | ~ ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4783])). 185.47/93.65 thf(996,axiom,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2250_zero__le__square)). 185.47/93.65 thf(11143,plain,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[996])). 185.47/93.65 thf(1346,axiom,((! [A:nat]: (((A != zero_zero_nat) => ((comm_s7457072308508201937r_real @ zero_zero_real @ A) = zero_zero_real)) & (((comm_s7457072308508201937r_real @ zero_zero_real @ A) = one_one_real) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8470_pochhammer__0__left)). 185.47/93.65 thf(12217,plain,((! [A:nat]: (((~ (A = zero_zero_nat)) => ((comm_s7457072308508201937r_real @ zero_zero_real @ A) = zero_zero_real)) & (((comm_s7457072308508201937r_real @ zero_zero_real @ A) = one_one_real) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346])). 185.47/93.65 thf(253,axiom,((! [A:rat,B:nat]: ((times_times_rat @ A @ (gbinomial_rat @ A @ B)) = (plus_plus_rat @ (times_times_rat @ (semiri681578069525770553at_rat @ B) @ (gbinomial_rat @ A @ B)) @ (times_times_rat @ (semiri681578069525770553at_rat @ (suc @ B)) @ (gbinomial_rat @ A @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8486_gbinomial__mult__1)). 185.47/93.65 thf(8554,plain,((! [A:rat,B:nat]: ((times_times_rat @ A @ (gbinomial_rat @ A @ B)) = (plus_plus_rat @ (times_times_rat @ (semiri681578069525770553at_rat @ B) @ (gbinomial_rat @ A @ B)) @ (times_times_rat @ (semiri681578069525770553at_rat @ (suc @ B)) @ (gbinomial_rat @ A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 185.47/93.65 thf(5033,axiom,((! [A:nat,B:nat,C:nat]: (((set_or4665077453230672383an_nat @ A @ (plus_plus_nat @ B @ C)) = (sup_sup_set_nat @ (set_or4665077453230672383an_nat @ A @ B) @ (set_or4665077453230672383an_nat @ B @ (plus_plus_nat @ B @ C)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9987_atLeastLessThan__add__Un)). 185.47/93.65 thf(24201,plain,((! [A:nat,B:nat,C:nat]: (((set_or4665077453230672383an_nat @ A @ (plus_plus_nat @ B @ C)) = (sup_sup_set_nat @ (set_or4665077453230672383an_nat @ A @ B) @ (set_or4665077453230672383an_nat @ B @ (plus_plus_nat @ B @ C)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5033])). 185.47/93.65 thf(3365,axiom,((ord_less_int = (^ [A:int,B:int]: (ord_less_int @ (minus_minus_int @ A @ B) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2426_less__iff__diff__less__0)). 185.47/93.65 thf(18814,plain,(((ord_less_int) = (^ [A:int,B:int]: (ord_less_int @ (minus_minus_int @ A @ B) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3365])). 185.47/93.65 thf(382,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ A)))) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9524_and__not__numerals_I2_J)). 185.47/93.65 thf(9007,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ A)))) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])). 185.47/93.65 thf(4515,axiom,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1358_numeral__code_I2_J)). 185.47/93.65 thf(22466,plain,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4515])). 185.47/93.65 thf(7219,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2066_mult__right__cancel)). 185.47/93.65 thf(32324,plain,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7219])). 185.47/93.65 thf(5491,axiom,(((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5405_add__neg__numeral__special_I9_J)). 185.47/93.65 thf(26021,plain,(((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5491])). 185.47/93.65 thf(2073,axiom,((! [A:rat,B:rat,C:rat]: (((divide_divide_rat @ A @ B) = (divide_divide_rat @ A @ C)) = ((A = zero_zero_rat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1582_divide__cancel__left)). 185.47/93.65 thf(14652,plain,((! [A:rat,B:rat,C:rat]: (((divide_divide_rat @ A @ B) = (divide_divide_rat @ A @ C)) = ((A = zero_zero_rat) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2073])). 185.47/93.65 thf(4130,axiom,((! [A:rat,B:(int > rat),C:int,D:int]: ((ord_less_eq_rat @ A @ (B @ C)) => (((ord_less_eq_rat @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_eq_rat @ (B @ E) @ (B @ F)) <= (ord_less_eq_int @ E @ F)))) <= (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3912_order__subst1)). 185.47/93.65 thf(21232,plain,((! [A:rat,B:(int > rat),C:int,D:int]: ((ord_less_eq_rat @ A @ (B @ C)) => ((ord_less_eq_rat @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_eq_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_int @ E @ F))) | ~ (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4130])). 185.47/93.65 thf(4272,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) => ((plus_plus_rat @ B @ (minus_minus_rat @ A @ B)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1212_linordered__semidom__class_Oadd__diff__inverse)). 185.47/93.65 thf(21665,plain,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) => ((plus_plus_rat @ B @ (minus_minus_rat @ A @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4272])). 185.47/93.65 thf(7146,axiom,((! [A:vEBT_VEBT,B:nat]: (((((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G)) => ((~ ((B = C) | (B = D) | ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G) @ B))))) => (~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E)) => ((accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E) @ B)) => (~ ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))))))))))) <= (! [C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F)) => ((accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F) @ B)) => (~ ((B = C) | (B = D))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ A @ B))) <= (vEBT_VEBT_membermima @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3183_VEBT__internal_Omembermima_Opelims_I2_J)). 185.47/93.65 thf(32055,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G)) => (~ ((B = C) | (B = D) | ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G) @ B))))) => (~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E)) => ((accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E) @ B)) => (~ ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))))))))))) | ~ (! [C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F)) => ((accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F) @ B)) => (~ ((B = C) | (B = D)))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ A @ B)) | ~ (vEBT_VEBT_membermima @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7146])). 185.47/93.65 thf(931,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ A)) => ((ord_less_eq_real @ one_one_real @ A) <= (ord_less_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6059_ln__ge__zero__imp__ge__one)). 185.47/93.65 thf(10933,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ A)) => ((ord_less_eq_real @ one_one_real @ A) | ~ (ord_less_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[931])). 185.47/93.65 thf(2745,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (ord_less_eq_real @ (plus_plus_real @ one_one_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ A)) @ (power_power_real @ (plus_plus_real @ one_one_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7335_Bernoulli__inequality)). 185.47/93.65 thf(16858,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (ord_less_eq_real @ (plus_plus_real @ one_one_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ A)) @ (power_power_real @ (plus_plus_real @ one_one_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2745])). 185.47/93.65 thf(5239,axiom,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: (((size_s6755466524823107622T_VEBT @ A) = (size_s6755466524823107622T_VEBT @ B)) => ((! [C:nat]: (((nth_VEBT_VEBT @ A @ C) = (nth_VEBT_VEBT @ B @ C)) <= (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)))) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_918_nth__equalityI)). 185.47/93.65 thf(25007,plain,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: (((size_s6755466524823107622T_VEBT @ A) = (size_s6755466524823107622T_VEBT @ B)) => ((! [C:nat]: (((nth_VEBT_VEBT @ A @ C) = (nth_VEBT_VEBT @ B @ C)) | ~ (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5239])). 185.47/93.65 thf(3494,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ C @ B) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3271_minf_I4_J)). 185.47/93.65 thf(19233,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3494])). 185.47/93.65 thf(4256,axiom,((! [A:rat]: (ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2249_zero__le__square)). 185.47/93.65 thf(21620,plain,((! [A:rat]: (ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4256])). 185.47/93.65 thf(2560,axiom,((! [A:real,B:real,C:real,D:real]: (((B != zero_zero_real) => (((divide_divide_real @ C @ A) = (divide_divide_real @ D @ B)) = ((times_times_real @ C @ B) = (times_times_real @ D @ A)))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2477_frac__eq__eq)). 185.47/93.65 thf(16219,plain,((! [A:real,B:real,C:real,D:real]: (((~ (B = zero_zero_real)) => (((divide_divide_real @ C @ A) = (divide_divide_real @ D @ B)) = ((times_times_real @ C @ B) = (times_times_real @ D @ A)))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2560])). 185.47/93.65 thf(754,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ one_one_real @ (log @ A @ B)) = (ord_less_eq_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9032_one__le__log__cancel__iff)). 185.47/93.65 thf(10256,plain,((! [A:real,B:real]: (((ord_less_eq_real @ one_one_real @ (log @ A @ B)) = (ord_less_eq_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[754])). 185.47/93.65 thf(1373,axiom,((! [A:num]: ((numeral_numeral_rat @ (bit1 @ A)) = (plus_plus_rat @ (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ A)) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6629_numeral__code_I3_J)). 185.47/93.65 thf(12306,plain,((! [A:num]: ((numeral_numeral_rat @ (bit1 @ A)) = (plus_plus_rat @ (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ A)) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373])). 185.47/93.65 thf(1838,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ C)) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2572_mult__le__cancel__right)). 185.47/93.65 thf(13891,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ C)) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1838])). 185.47/93.65 thf(1628,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_732_diff__add__eq)). 185.47/93.65 thf(13155,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628])). 185.47/93.65 thf(5813,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_div__le__dividend)). 185.47/93.65 thf(27142,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5813])). 185.47/93.65 thf(2244,axiom,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) != (modulo_modulo_int @ (numeral_numeral_int @ one) @ (numeral_numeral_int @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2161_cong__exp__iff__simps_I8_J)). 185.47/93.65 thf(15197,plain,((! [A:num,B:num]: ~ ((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (modulo_modulo_int @ (numeral_numeral_int @ one) @ (numeral_numeral_int @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2244])). 185.47/93.65 thf(7347,axiom,(((numeral_numeral_int @ one) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_833_numeral__One)). 185.47/93.65 thf(32759,plain,(((numeral_numeral_int @ one) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7347])). 185.47/93.65 thf(1556,axiom,((ord_less_eq_int @ zero_zero_int @ zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3151_less__eq__int__code_I1_J)). 185.47/93.65 thf(12892,plain,((ord_less_eq_int @ zero_zero_int @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556])). 185.47/93.65 thf(3518,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ D) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_add__strict__mono)). 185.47/93.65 thf(19310,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ D) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3518])). 185.47/93.65 thf(5530,axiom,((! [A:num,B:num]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (numera6690914467698888265omplex @ B)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5329_diff__numeral__simps_I3_J)). 185.47/93.65 thf(26148,plain,((! [A:num,B:num]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (numera6690914467698888265omplex @ B)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5530])). 185.47/93.65 thf(7661,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4935_even__two__times__div__two)). 185.47/93.65 thf(33739,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7661])). 185.47/93.65 thf(1926,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6487_abs__triangle__ineq)). 185.47/93.65 thf(14160,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1926])). 185.47/93.65 thf(7673,axiom,((! [A:real]: ((power_power_real @ (uminus_uminus_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5397_power2__minus)). 185.47/93.65 thf(33768,plain,((! [A:real]: ((power_power_real @ (uminus_uminus_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7673])). 185.47/93.65 thf(1391,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (minus_minus_int @ B @ (times_times_int @ (plus_plus_int @ (abs_abs_int @ (minus_minus_int @ B @ C)) @ one_one_int) @ A)) @ C) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6837_decr__lemma)). 185.47/93.65 thf(12375,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (minus_minus_int @ B @ (times_times_int @ (plus_plus_int @ (abs_abs_int @ (minus_minus_int @ B @ C)) @ one_one_int) @ A)) @ C) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391])). 185.47/93.65 thf(1823,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (divide_divide_int @ A @ C) @ (divide_divide_int @ B @ C)) <= (ord_less_int @ zero_zero_int @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3047_zdiv__mono1)). 185.47/93.65 thf(13838,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (divide_divide_int @ A @ C) @ (divide_divide_int @ B @ C)) | ~ (ord_less_int @ zero_zero_int @ C) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823])). 185.47/93.65 thf(7283,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (times_times_nat @ A @ B)) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6916_of__nat__mult)). 185.47/93.65 thf(32536,plain,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (times_times_nat @ A @ B)) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7283])). 185.47/93.65 thf(2666,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) <= (ord_less_real @ zero_zero_real @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2373_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)). 185.47/93.65 thf(16565,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) | ~ (ord_less_real @ zero_zero_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2666])). 185.47/93.65 thf(7135,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4570_semiring__parity__class_Oeven__mask__iff)). 185.47/93.65 thf(32023,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7135])). 185.47/93.65 thf(558,axiom,((! [A:nat,B:nat,C:rat]: (((times_times_rat @ (gbinomial_rat @ C @ B) @ (gbinomial_rat @ (semiri681578069525770553at_rat @ B) @ A)) = (times_times_rat @ (gbinomial_rat @ C @ A) @ (gbinomial_rat @ (minus_minus_rat @ C @ (semiri681578069525770553at_rat @ A)) @ (minus_minus_nat @ B @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8540_gbinomial__trinomial__revision)). 185.47/93.65 thf(9584,plain,((! [A:nat,B:nat,C:rat]: (((times_times_rat @ (gbinomial_rat @ C @ B) @ (gbinomial_rat @ (semiri681578069525770553at_rat @ B) @ A)) = (times_times_rat @ (gbinomial_rat @ C @ A) @ (gbinomial_rat @ (minus_minus_rat @ C @ (semiri681578069525770553at_rat @ A)) @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[558])). 185.47/93.65 thf(3653,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ C) <= (ord_less_eq_int @ B @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4216_order_Ostrict__trans2)). 185.47/93.65 thf(19729,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ C) | ~ (ord_less_eq_int @ B @ C) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3653])). 185.47/93.65 thf(7678,axiom,(((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2892_zero__power2)). 185.47/93.65 thf(33783,plain,(((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7678])). 185.47/93.65 thf(4407,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (divide_divide_int @ B @ C) @ (divide_divide_int @ A @ C)) <= (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ C))) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6189_verit__less__mono__div__int2)). 185.47/93.65 thf(22114,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (divide_divide_int @ B @ C) @ (divide_divide_int @ A @ C)) | ~ (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ C)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4407])). 185.47/93.65 thf(6646,axiom,((! [A:nat,B:nat]: ((((ord_less_eq_nat @ B @ one_one_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2667_mult__le__one)). 185.47/93.65 thf(30157,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ one_one_nat) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6646])). 185.47/93.65 thf(3117,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1135_distrib__left)). 185.47/93.65 thf(18047,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3117])). 185.47/93.65 thf(3282,axiom,((! [A:num]: ((semiri1408675320244567234ct_nat @ (numeral_numeral_nat @ A)) = (times_times_nat @ (numeral_numeral_nat @ A) @ (semiri1408675320244567234ct_nat @ (pred_numeral @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8041_fact__numeral)). 185.47/93.65 thf(18550,plain,((! [A:num]: ((semiri1408675320244567234ct_nat @ (numeral_numeral_nat @ A)) = (times_times_nat @ (numeral_numeral_nat @ A) @ (semiri1408675320244567234ct_nat @ (pred_numeral @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3282])). 185.47/93.65 thf(5163,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (modulo_modulo_nat @ B @ A) @ A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1922_unique__euclidean__semiring__numeral__class_Opos__mod__bound)). 185.47/93.65 thf(24762,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (modulo_modulo_nat @ B @ A) @ A) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5163])). 185.47/93.65 thf(4459,axiom,((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ one_one_Code_integer))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4903_odd__one)). 185.47/93.65 thf(22275,plain,((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4459])). 185.47/93.65 thf(1935,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (semiri681578069525770553at_rat @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7061_of__nat__power__le__of__nat__cancel__iff)). 185.47/93.65 thf(14196,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (semiri681578069525770553at_rat @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1935])). 185.47/93.65 thf(745,axiom,((! [A:nat,B:nat,C:(nat > complex)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_complex @ (groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & ((ord_less_nat @ (suc @ A) @ B) => ((groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6429_sum_Ocl__ivl__Suc)). 185.47/93.65 thf(10216,plain,((! [A:nat,B:nat,C:(nat > complex)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_complex @ (groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & ((ord_less_nat @ (suc @ A) @ B) => ((groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[745])). 185.47/93.65 thf(7009,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((semiri1406184849735516958ct_int @ A) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1406184849735516958ct_int @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8050_fact__reduce)). 185.47/93.65 thf(31586,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((semiri1406184849735516958ct_int @ A) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1406184849735516958ct_int @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7009])). 185.47/93.65 thf(2784,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => ((divide_divide_int @ C @ (times_times_int @ A @ B)) = (divide_divide_int @ (divide_divide_int @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4761_dvd__div__mult2__eq)). 185.47/93.65 thf(16978,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => ((divide_divide_int @ C @ (times_times_int @ A @ B)) = (divide_divide_int @ (divide_divide_int @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2784])). 185.47/93.65 thf(389,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_eq_real @ B @ pi) => (ord_less_eq_real @ (cos_real @ B) @ (cos_real @ A))) <= (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7844_cos__monotone__0__pi__le)). 185.47/93.65 thf(9026,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_eq_real @ B @ pi) => (ord_less_eq_real @ (cos_real @ B) @ (cos_real @ A))) | ~ (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])). 185.47/93.65 thf(5041,axiom,((! [A:complex,B:num]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus1482373934393186551omplex @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6617_power__minus__Bit1)). 185.47/93.65 thf(24302,plain,((! [A:complex,B:num]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus1482373934393186551omplex @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5041])). 185.47/93.65 thf(3129,axiom,((! [A:int,B:int]: ((ring_1_of_int_rat @ (minus_minus_int @ A @ B)) = (minus_minus_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6977_of__int__diff)). 185.47/93.65 thf(18081,plain,((! [A:int,B:int]: ((ring_1_of_int_rat @ (minus_minus_int @ A @ B)) = (minus_minus_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3129])). 185.47/93.65 thf(120,axiom,((bit_concat_bit = (^ [A:nat,B:int,C:int]: (plus_plus_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se545348938243370406it_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9516_concat__bit__eq)). 185.47/93.65 thf(8123,plain,(((bit_concat_bit) = (^ [A:nat,B:int,C:int]: (plus_plus_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se545348938243370406it_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 185.47/93.65 thf(3399,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7231_of__nat__mono)). 185.47/93.65 thf(18928,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3399])). 185.47/93.65 thf(1704,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ B @ A) @ (times_times_complex @ C @ A)) = (divide1717551699836669952omplex @ B @ C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1699_nonzero__mult__divide__mult__cancel__right)). 185.47/93.65 thf(13440,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ B @ A) @ (times_times_complex @ C @ A)) = (divide1717551699836669952omplex @ B @ C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704])). 185.47/93.65 thf(5503,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2976_power2__less__imp__less)). 185.47/93.65 thf(26060,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5503])). 185.47/93.65 thf(68,axiom,((! [A:real,B:nat,C:real]: ((minus_minus_real @ (power_power_real @ A @ B) @ (power_power_real @ C @ B)) = (times_times_real @ (minus_minus_real @ A @ C) @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (power_power_real @ C @ (minus_minus_nat @ B @ (suc @ D))) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7619_power__diff__sumr2)). 185.47/93.65 thf(7952,plain,((! [A:real,B:nat,C:real]: ((minus_minus_real @ (power_power_real @ A @ B) @ (power_power_real @ C @ B)) = (times_times_real @ (minus_minus_real @ A @ C) @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (power_power_real @ C @ (minus_minus_nat @ B @ (suc @ D))) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 185.47/93.65 thf(6346,axiom,((! [A:int,B:int,C:int]: ((((times_times_int @ A @ B) = (times_times_int @ A @ C)) = (B = C)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2062_mult__left__cancel)). 185.47/93.65 thf(29102,plain,((! [A:int,B:int,C:int]: ((((times_times_int @ A @ B) = (times_times_int @ A @ C)) = (B = C)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6346])). 185.47/93.65 thf(4486,axiom,((! [A:nat]: (((semiri1314217659103216013at_int @ A) = one_one_int) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6929_of__nat__eq__1__iff)). 185.47/93.65 thf(22361,plain,((! [A:nat]: (((semiri1314217659103216013at_int @ A) = one_one_int) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4486])). 185.47/93.65 thf(1892,axiom,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5923_neg__numeral__le__one)). 185.47/93.65 thf(14060,plain,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1892])). 185.47/93.65 thf(4172,axiom,((! [A:rat,B:rat]: ((~ (ord_less_eq_rat @ A @ B)) = (ord_less_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3102_verit__comp__simplify1_I3_J)). 185.47/93.65 thf(21357,plain,((! [A:rat,B:rat]: ((~ (ord_less_eq_rat @ A @ B)) = (ord_less_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4172])). 185.47/93.65 thf(5883,axiom,((! [A:num,B:num]: (((~ (ord_less_num @ A @ B)) = (A = B)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4175_antisym__conv2)). 185.47/93.65 thf(27474,plain,((! [A:num,B:num]: (((~ (ord_less_num @ A @ B)) = (A = B)) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5883])). 185.47/93.65 thf(6441,axiom,((! [A:nat,B:nat]: (ord_less_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9325_take__bit__nat__less__exp)). 185.47/93.65 thf(29457,plain,((! [A:nat,B:nat]: (ord_less_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6441])). 185.47/93.65 thf(890,axiom,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_real @ (A @ zero_zero_nat) @ (groups129246275422532515t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8734_prod_OatMost__Suc__shift)). 185.47/93.65 thf(10779,plain,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_real @ (A @ zero_zero_nat) @ (groups129246275422532515t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[890])). 185.47/93.65 thf(1139,axiom,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (semiri1314217659103216013at_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7210_of__nat__0__le__iff)). 185.47/93.65 thf(11597,plain,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (semiri1314217659103216013at_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139])). 185.47/93.65 thf(4978,axiom,((vEBT_is_pred_in_set = (^ [A:set_nat,B:nat,C:nat]: ((ord_less_nat @ C @ B) & ! [D:nat]: ((member_nat @ D @ A) => ((ord_less_eq_nat @ D @ C) <= (ord_less_nat @ D @ B))) & (member_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_is__pred__in__set__def)). 185.47/93.65 thf(24021,plain,(((vEBT_is_pred_in_set) = (^ [A:set_nat,B:nat,C:nat]: ((ord_less_nat @ C @ B) & ! [D:nat]: ((member_nat @ D @ A) => ((ord_less_eq_nat @ D @ C) | ~ (ord_less_nat @ D @ B))) & (member_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4978])). 185.47/93.65 thf(3931,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_eq_int @ (plus_plus_int @ A @ B) @ zero_zero_int)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2290_add__nonpos__nonpos)). 185.47/93.65 thf(20625,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_eq_int @ (plus_plus_int @ A @ B) @ zero_zero_int)) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3931])). 185.47/93.65 thf(4742,axiom,((! [A:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ A) @ A) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5731_ab__group__add__class_Oab__left__minus)). 185.47/93.65 thf(23207,plain,((! [A:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ A) @ A) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4742])). 185.47/93.65 thf(3926,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_times__divide__eq__right)). 185.47/93.65 thf(20610,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3926])). 185.47/93.65 thf(6551,axiom,((ord_less_eq_nat @ mi @ ma)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27__C4_Ohyps_C_I9_J)). 185.47/93.65 thf(29843,plain,((ord_less_eq_nat @ mi @ ma)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6551])). 185.47/93.65 thf(2195,axiom,((! [A:int,B:int]: (((times_times_int @ A @ (divide_divide_int @ B @ A)) = B) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4486_dvd__mult__div__cancel)). 185.47/93.65 thf(15046,plain,((! [A:int,B:int]: (((times_times_int @ A @ (divide_divide_int @ B @ A)) = B) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2195])). 185.47/93.65 thf(3783,axiom,((! [A:int,B:int,C:int]: ((A = C) <= ((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_add__right__imp__eq)). 185.47/93.65 thf(20157,plain,((! [A:int,B:int,C:int]: ((A = C) | ~ ((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3783])). 185.47/93.65 thf(6418,axiom,((! [A:(nat > $o),B:nat]: (((? [C:nat]: ((ord_less_nat @ C @ B) & (A @ (suc @ C)) & ! [D:nat]: ((ord_less_eq_nat @ D @ C) => (~ (A @ D))))) <= (~ (A @ zero_zero_nat))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2777_ex__least__nat__less)). 185.47/93.65 thf(29365,plain,((! [A:(nat > $o),B:nat]: (? [C:nat]: ((ord_less_nat @ C @ B) & (A @ (suc @ C)) & ! [D:nat]: ((ord_less_eq_nat @ D @ C) => (~ (A @ D)))) | (A @ zero_zero_nat) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6418])). 185.47/93.65 thf(5225,axiom,((! [A:real]: (((power_power_real @ (sqrt @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8141_real__sqrt__pow2__iff)). 185.47/93.65 thf(24950,plain,((! [A:real]: (((power_power_real @ (sqrt @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5225])). 185.47/93.65 thf(4059,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_3874_order_Otrans)). 185.47/93.65 thf(21009,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)],[4059])). 185.47/93.65 thf(2076,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (((ord_less_eq_rat @ C @ B) <= (ord_less_rat @ A @ zero_zero_rat)) & ((ord_less_eq_rat @ B @ C) <= (ord_less_rat @ zero_zero_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2570_mult__le__cancel__left)). 185.47/93.65 thf(14661,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (((ord_less_eq_rat @ C @ B) | ~ (ord_less_rat @ A @ zero_zero_rat)) & ((ord_less_eq_rat @ B @ C) | ~ (ord_less_rat @ zero_zero_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076])). 185.47/93.65 thf(5464,axiom,((! [A:complex,B:complex,C:nat]: ((power_power_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_power__mult__distrib)). 185.47/93.65 thf(25834,plain,((! [A:complex,B:complex,C:nat]: ((power_power_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5464])). 185.47/93.65 thf(1161,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ zero_zero_rat @ A) => (ord_less_rat @ zero_zero_rat @ B)) <= (ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2340_zero__less__mult__pos)). 185.47/93.65 thf(11660,plain,((! [A:rat,B:rat]: (((ord_less_rat @ zero_zero_rat @ A) => (ord_less_rat @ zero_zero_rat @ B)) | ~ (ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161])). 185.47/93.65 thf(7542,axiom,((! [A:nat]: (((divide_divide_nat @ (plus_plus_nat @ one_one_nat @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4557_even__succ__div__2)). 185.47/93.65 thf(33412,plain,((! [A:nat]: (((divide_divide_nat @ (plus_plus_nat @ one_one_nat @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7542])). 185.47/93.65 thf(7191,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((! [D:nat,E:nat]: ((A @ D @ (plus_plus_nat @ D @ E)) <= (A @ D @ E))) => (A @ B @ C)) <= (! [D:nat]: (A @ D @ zero_zero_nat))) <= (! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4397_Euclid__induct)). 185.47/93.65 thf(32222,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((A @ D @ (plus_plus_nat @ D @ E)) | ~ (A @ D @ E))) => (A @ B @ C)) | ~ (! [D:nat]: (A @ D @ zero_zero_nat)) | ~ (! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7191])). 185.47/93.65 thf(2012,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = (divide1717551699836669952omplex @ B @ C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1705_nonzero__mult__divide__mult__cancel__left)). 185.47/93.65 thf(14462,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = (divide1717551699836669952omplex @ B @ C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2012])). 185.47/93.65 thf(5541,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((suc @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4545_odd__Suc__minus__one)). 185.47/93.65 thf(26187,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((suc @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5541])). 185.47/93.65 thf(5187,axiom,((! [A:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4571_semiring__parity__class_Oeven__mask__iff)). 185.47/93.65 thf(24834,plain,((! [A:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5187])). 185.47/93.65 thf(7344,axiom,((! [A:num]: ((plus_plus_int @ one_one_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_one__plus__numeral)). 185.47/93.65 thf(32750,plain,((! [A:num]: ((plus_plus_int @ one_one_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7344])). 185.47/93.65 thf(598,axiom,((! [A:real,B:nat]: ((gbinomial_real @ (plus_plus_real @ A @ one_one_real) @ (suc @ B)) = (plus_plus_real @ (gbinomial_real @ A @ B) @ (gbinomial_real @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8461_gbinomial__Suc__Suc)). 185.47/93.65 thf(9720,plain,((! [A:real,B:nat]: ((gbinomial_real @ (plus_plus_real @ A @ one_one_real) @ (suc @ B)) = (plus_plus_real @ (gbinomial_real @ A @ B) @ (gbinomial_real @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[598])). 185.47/93.65 thf(1836,axiom,((! [A:complex,B:(nat > complex),C:complex]: ((A != zero_zero_complex) => ((sums_complex @ (^ [D:nat]: (times_times_complex @ (B @ D) @ A)) @ (times_times_complex @ C @ A)) = (sums_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8176_sums__mult2__iff)). 185.47/93.65 thf(13885,plain,((! [A:complex,B:(nat > complex),C:complex]: ((~ (A = zero_zero_complex)) => ((sums_complex @ (^ [D:nat]: (times_times_complex @ (B @ D) @ A)) @ (times_times_complex @ C @ A)) = (sums_complex @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1836])). 185.47/93.65 thf(4852,axiom,((! [A:real]: ~ (ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2314_not__square__less__zero)). 185.47/93.65 thf(23581,plain,((! [A:real]: ~ (ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4852])). 185.47/93.65 thf(4011,axiom,((! [A:rat,B:(nat > rat),C:nat,D:nat]: ((((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F)))) => (ord_less_rat @ A @ (B @ D))) <= (ord_less_nat @ C @ D)) <= (ord_less_eq_rat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4329_order__le__less__subst1)). 185.47/93.65 thf(20871,plain,((! [A:rat,B:(nat > rat),C:nat,D:nat]: (((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F)))) => (ord_less_rat @ A @ (B @ D))) | ~ (ord_less_nat @ C @ D) | ~ (ord_less_eq_rat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4011])). 185.47/93.65 thf(4200,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (sqrt @ A)) = (ord_less_eq_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8127_real__sqrt__ge__1__iff)). 185.47/93.65 thf(21445,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (sqrt @ A)) = (ord_less_eq_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4200])). 185.47/93.65 thf(7337,axiom,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ (suc @ zero_zero_nat)) = (zero_n2687167440665602831ol_nat @ (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9254_take__bit__of__Suc__0)). 185.47/93.65 thf(32728,plain,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ (suc @ zero_zero_nat)) = (zero_n2687167440665602831ol_nat @ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7337])). 185.47/93.65 thf(4445,axiom,((! [A:real,B:real]: ((minus_minus_real @ (cos_real @ A) @ (cos_real @ B)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sin_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))) @ (sin_real @ (divide_divide_real @ (minus_minus_real @ B @ A) @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7859_cos__diff__cos)). 185.47/93.65 thf(22232,plain,((! [A:real,B:real]: ((minus_minus_real @ (cos_real @ A) @ (cos_real @ B)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sin_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))) @ (sin_real @ (divide_divide_real @ (minus_minus_real @ B @ A) @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4445])). 185.47/93.65 thf(1228,axiom,((! [A:int]: ((ord_less_rat @ one_one_rat @ (ring_1_of_int_rat @ A)) = (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7087_of__int__1__less__iff)). 185.47/93.65 thf(11852,plain,((! [A:int]: ((ord_less_rat @ one_one_rat @ (ring_1_of_int_rat @ A)) = (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228])). 185.47/93.65 thf(1739,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2212_mult__nonpos__nonneg)). 185.47/93.65 thf(13564,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739])). 185.47/93.65 thf(1559,axiom,((! [A:num]: ((numeral_numeral_rat @ (bit0 @ A)) = (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_numeral__Bit0)). 185.47/93.65 thf(12898,plain,((! [A:num]: ((numeral_numeral_rat @ (bit0 @ A)) = (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559])). 185.47/93.65 thf(5726,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_mult__le__mono)). 185.47/93.65 thf(26788,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5726])). 185.47/93.65 thf(2036,axiom,((! [A:nat,B:nat,C:int]: ((ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ C) @ (bit_se2923211474154528505it_int @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9276_take__bit__tightened__less__eq__int)). 185.47/93.65 thf(14537,plain,((! [A:nat,B:nat,C:int]: ((ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ C) @ (bit_se2923211474154528505it_int @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036])). 185.47/93.65 thf(6839,axiom,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (C)) @ (set_or1269000886237332187st_nat @ A @ B)) = (divide_divide_nat @ (minus_minus_nat @ (times_times_nat @ B @ (plus_plus_nat @ B @ one_one_nat)) @ (times_times_nat @ A @ (minus_minus_nat @ A @ one_one_nat))) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6758_Sum__Icc__nat)). 185.47/93.65 thf(30865,plain,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (C)) @ (set_or1269000886237332187st_nat @ A @ B)) = (divide_divide_nat @ (minus_minus_nat @ (times_times_nat @ B @ (plus_plus_nat @ B @ one_one_nat)) @ (times_times_nat @ A @ (minus_minus_nat @ A @ one_one_nat))) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6839])). 185.47/93.65 thf(1504,axiom,((! [A:nat,B:num,C:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (numeral_numeral_int @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7119_of__nat__less__numeral__power__cancel__iff)). 185.47/93.65 thf(12732,plain,((! [A:nat,B:num,C:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (numeral_numeral_int @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504])). 185.47/93.65 thf(1927,axiom,((! [A:int,B:int]: (((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))) <= (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4908_odd__even__add)). 185.47/93.65 thf(14162,plain,((! [A:int,B:int]: (((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1927])). 185.47/93.65 thf(4365,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1806_zero__le__divide__1__iff)). 185.47/93.65 thf(21983,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4365])). 185.47/93.65 thf(2008,axiom,((! [A:real,B:(rat > real),C:rat,D:rat]: ((((ord_less_real @ A @ (B @ D)) <= (! [E:rat,F:rat]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_rat @ E @ F)))) <= (ord_less_rat @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4078_ord__eq__less__subst)). 185.47/93.65 thf(14445,plain,((! [A:real,B:(rat > real),C:rat,D:rat]: ((ord_less_real @ A @ (B @ D)) | ~ (! [E:rat,F:rat]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_rat @ E @ F))) | ~ (ord_less_rat @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2008])). 185.47/93.65 thf(4825,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((divide_divide_int @ B @ (times_times_int @ C @ A)) = (divide_divide_int @ (divide_divide_int @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3060_zdiv__zmult2__eq)). 185.47/93.65 thf(23499,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((divide_divide_int @ B @ (times_times_int @ C @ A)) = (divide_divide_int @ (divide_divide_int @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4825])). 185.47/93.65 thf(4376,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ B) = (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1628_add__le__same__cancel2)). 185.47/93.65 thf(22020,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ B) = (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4376])). 185.47/93.65 thf(3393,axiom,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ B) = (((ord_less_real @ one_one_real @ A) <= (ord_less_eq_real @ B @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2827_mult__less__cancel__right2)). 185.47/93.65 thf(18909,plain,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ B) = (((ord_less_real @ one_one_real @ A) | ~ (ord_less_eq_real @ B @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3393])). 185.47/93.65 thf(3550,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ A @ (uminus_uminus_int @ B)) = (uminus_uminus_int @ (modulo_modulo_int @ (uminus_uminus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5591_mod__minus__right)). 185.47/93.65 thf(19401,plain,((! [A:int,B:int]: ((modulo_modulo_int @ A @ (uminus_uminus_int @ B)) = (uminus_uminus_int @ (modulo_modulo_int @ (uminus_uminus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3550])). 185.47/93.65 thf(4861,axiom,((! [A:real,B:nat]: ((ord_less_real @ (power_power_real @ A @ B) @ (times_times_real @ A @ (power_power_real @ A @ B))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_power__less__power__Suc)). 185.47/93.65 thf(23607,plain,((! [A:real,B:nat]: ((ord_less_real @ (power_power_real @ A @ B) @ (times_times_real @ A @ (power_power_real @ A @ B))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4861])). 185.47/93.65 thf(7121,axiom,((! [A:real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5050_neg__0__equal__iff__equal)). 185.47/93.65 thf(31963,plain,((! [A:real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7121])). 185.47/93.65 thf(7558,axiom,((! [A:nat,B:nat]: ((suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) != (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1260_Suc__double__not__eq__double)). 185.47/93.65 thf(33456,plain,((! [A:nat,B:nat]: ~ ((suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7558])). 185.47/93.65 thf(5861,axiom,((! [A:num,B:num]: ((A != B) => ((~ (ord_less_num @ A @ B)) => (ord_less_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4050_linorder__neqE)). 185.47/93.65 thf(27404,plain,((! [A:num,B:num]: ((~ (A = B)) => ((~ (ord_less_num @ A @ B)) => (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5861])). 185.47/93.65 thf(6452,axiom,((! [A:num]: ((ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ one_one_rat)) = (A != one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5391_neg__numeral__less__neg__one__iff)). 185.47/93.65 thf(29489,plain,((! [A:num]: ((ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ one_one_rat)) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6452])). 185.47/93.65 thf(5126,axiom,((! [A:num,B:num]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_numeral__times__numeral)). 185.47/93.65 thf(24603,plain,((! [A:num,B:num]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5126])). 185.47/93.65 thf(2964,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) <= (ord_less_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2329_mult__pos__pos)). 185.47/93.65 thf(17555,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) | ~ (ord_less_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2964])). 185.47/93.65 thf(2253,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((plus_plus_rat @ (times_times_rat @ A @ B) @ (plus_plus_rat @ (times_times_rat @ C @ B) @ D)) = (plus_plus_rat @ (times_times_rat @ (plus_plus_rat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1144_combine__common__factor)). 185.47/93.65 thf(15221,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((plus_plus_rat @ (times_times_rat @ A @ B) @ (plus_plus_rat @ (times_times_rat @ C @ B) @ D)) = (plus_plus_rat @ (times_times_rat @ (plus_plus_rat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2253])). 185.47/93.65 thf(4691,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((((plus_plus_rat @ A @ B) = zero_zero_rat) = ((A = zero_zero_rat) & (B = zero_zero_rat))) <= (ord_less_eq_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2284_add__nonneg__eq__0__iff)). 185.47/93.65 thf(23033,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((((plus_plus_rat @ A @ B) = zero_zero_rat) = ((A = zero_zero_rat) & (B = zero_zero_rat))) | ~ (ord_less_eq_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4691])). 185.47/93.65 thf(5145,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:nat,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ C)) @ A @ D @ F) @ B) = (if_option_nat @ (((vEBT_vebt_mint @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_nat) & (vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ E @ B) @ (some_nat @ E) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ D @ (the_nat @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1261_pred__less__length__list)). 185.47/93.65 thf(24702,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:nat,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ C)) @ A @ D @ F) @ B) = (if_option_nat @ (~ ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) & (vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ E @ B) @ (some_nat @ E) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ D @ (the_nat @ (vEBT_vebt_pred @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5145])). 185.47/93.65 thf(5043,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2125_plus__nat_Oadd__0)). 185.47/93.65 thf(24308,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5043])). 185.47/93.65 thf(2346,axiom,((~ (ord_less_rat @ one_one_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_765_less__numeral__extra_I4_J)). 185.47/93.65 thf(15503,plain,((~ (ord_less_rat @ one_one_rat @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2346])). 185.47/93.65 thf(5191,axiom,((! [A:complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1481_mult__zero__left)). 185.47/93.65 thf(24847,plain,((! [A:complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5191])). 185.47/93.65 thf(1304,axiom,(((abs_abs_rat @ zero_zero_rat) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6326_abs__zero)). 185.47/93.65 thf(12078,plain,(((abs_abs_rat @ zero_zero_rat) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304])). 185.47/93.65 thf(841,axiom,((! [A:(rat > (rat > $o)),B:set_nat,C:(nat > rat),D:(nat > rat)]: ((A @ zero_zero_rat @ zero_zero_rat) => (((finite_finite_nat @ B) => ((A @ (groups2906978787729119204at_rat @ C @ B) @ (groups2906978787729119204at_rat @ D @ B)) <= (! [E:nat]: ((A @ (C @ E) @ (D @ E)) <= (member_nat @ E @ B))))) <= (! [E:rat,F:rat,G:rat,H:rat]: (((A @ F @ H) & (A @ E @ G)) => (A @ (plus_plus_rat @ E @ F) @ (plus_plus_rat @ G @ H)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5860_sum_Orelated)). 185.47/93.65 thf(10593,plain,((! [A:(rat > (rat > $o)),B:set_nat,C:(nat > rat),D:(nat > rat)]: ((A @ zero_zero_rat @ zero_zero_rat) => (((finite_finite_nat @ B) => ((A @ (groups2906978787729119204at_rat @ (C) @ B) @ (groups2906978787729119204at_rat @ (D) @ B)) | ~ (! [E:nat]: ((A @ (C @ E) @ (D @ E)) | ~ (member_nat @ E @ B))))) | ~ (! [E:rat,F:rat,G:rat,H:rat]: (((A @ F @ H) & (A @ E @ G)) => (A @ (plus_plus_rat @ E @ F) @ (plus_plus_rat @ G @ H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[841])). 185.47/93.65 thf(2664,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (ord_max_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3686_max_Ocobounded1)). 185.47/93.65 thf(16560,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (ord_max_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2664])). 185.47/93.65 thf(6324,axiom,((! [A:nat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ B @ A)) = (ord_less_eq_rat @ zero_zero_rat @ B)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4972_zero__le__odd__power)). 185.47/93.65 thf(29013,plain,((! [A:nat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ B @ A)) = (ord_less_eq_rat @ zero_zero_rat @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6324])). 185.47/93.65 thf(1456,axiom,((! [A:rat,B:nat]: ((times_times_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ (comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ A) @ B)) = (times_times_rat @ A @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ (uminus_uminus_rat @ A) @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8572_pochhammer__absorb__comp)). 185.47/93.65 thf(12586,plain,((! [A:rat,B:nat]: ((times_times_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ (comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ A) @ B)) = (times_times_rat @ A @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ (uminus_uminus_rat @ A) @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456])). 185.47/93.65 thf(2431,axiom,((! [A:nat,B:(nat > nat),C:nat,D:(nat > nat),E:nat]: ((! [F:nat]: (((B @ F) = zero_zero_nat) <= (ord_less_nat @ A @ F))) => (((times_times_nat @ (groups3542108847815614940at_nat @ (^ [F:nat]: (times_times_nat @ (B @ F) @ (power_power_nat @ E @ F))) @ (set_ord_atMost_nat @ A)) @ (groups3542108847815614940at_nat @ (^ [F:nat]: (times_times_nat @ (D @ F) @ (power_power_nat @ E @ F))) @ (set_ord_atMost_nat @ C))) = (groups3542108847815614940at_nat @ (^ [F:nat]: (times_times_nat @ (groups3542108847815614940at_nat @ (^ [G:nat]: (times_times_nat @ (B @ G) @ (D @ (minus_minus_nat @ F @ G)))) @ (set_ord_atMost_nat @ F)) @ (power_power_nat @ E @ F))) @ (set_ord_atMost_nat @ (plus_plus_nat @ A @ C)))) <= (! [F:nat]: (((D @ F) = zero_zero_nat) <= (ord_less_nat @ C @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8951_polynomial__product__nat)). 185.47/93.65 thf(15779,plain,((! [A:nat,B:(nat > nat),C:nat,D:(nat > nat),E:nat]: ((! [F:nat]: (((B @ F) = zero_zero_nat) | ~ (ord_less_nat @ A @ F))) => (((times_times_nat @ (groups3542108847815614940at_nat @ (^ [F:nat]: (times_times_nat @ (B @ F) @ (power_power_nat @ E @ F))) @ (set_ord_atMost_nat @ A)) @ (groups3542108847815614940at_nat @ (^ [F:nat]: (times_times_nat @ (D @ F) @ (power_power_nat @ E @ F))) @ (set_ord_atMost_nat @ C))) = (groups3542108847815614940at_nat @ (^ [F:nat]: (times_times_nat @ (groups3542108847815614940at_nat @ (^ [G:nat]: (times_times_nat @ (B @ G) @ (D @ (minus_minus_nat @ F @ G)))) @ (set_ord_atMost_nat @ F)) @ (power_power_nat @ E @ F))) @ (set_ord_atMost_nat @ (plus_plus_nat @ A @ C)))) | ~ (! [F:nat]: (((D @ F) = zero_zero_nat) | ~ (ord_less_nat @ C @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2431])). 185.47/93.65 thf(1816,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2433_divide__pos__pos)). 185.47/93.65 thf(13814,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1816])). 185.47/93.65 thf(283,axiom,((! [A:real,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (? [C:real]: ((ord_less_real @ C @ A) & ((cos_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (cos_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (cos_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))) & (ord_less_real @ zero_zero_real @ C)))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7947_Maclaurin__cos__expansion2)). 185.47/93.65 thf(8655,plain,((! [A:real,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (? [C:real]: ((ord_less_real @ C @ A) & ((cos_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (cos_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (cos_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))) & (ord_less_real @ zero_zero_real @ C)))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 185.47/93.65 thf(5394,axiom,((! [A:num,B:nat,C:nat]: (((power_power_complex @ (numera6690914467698888265omplex @ A) @ B) = (semiri8010041392384452111omplex @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7050_numeral__power__eq__of__nat__cancel__iff)). 185.47/93.65 thf(25579,plain,((! [A:num,B:nat,C:nat]: (((power_power_complex @ (numera6690914467698888265omplex @ A) @ B) = (semiri8010041392384452111omplex @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5394])). 185.47/93.65 thf(2488,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (~ (! [B:nat]: ((A = (semiri1314217659103216013at_int @ B)) => (~ (ord_less_nat @ zero_zero_nat @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7306_pos__int__cases)). 185.47/93.65 thf(15967,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (~ (! [B:nat]: ((A = (semiri1314217659103216013at_int @ B)) => (~ (ord_less_nat @ zero_zero_nat @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2488])). 185.47/93.65 thf(2134,axiom,((! [A:complex,B:complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7511_norm__triangle__ineq2)). 185.47/93.65 thf(14836,plain,((! [A:complex,B:complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2134])). 185.47/93.65 thf(1031,axiom,((! [A:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ A) @ zero_zero_rat) = (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1640_double__add__less__zero__iff__single__add__less__zero)). 185.47/93.65 thf(11253,plain,((! [A:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ A) @ zero_zero_rat) = (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031])). 185.47/93.65 thf(5449,axiom,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (((power_power_real @ B @ A) = (power_power_real @ C @ A)) = (B = C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2138_power__eq__iff__eq__base)). 185.47/93.65 thf(25789,plain,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (((power_power_real @ B @ A) = (power_power_real @ C @ A)) = (B = C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5449])). 185.47/93.65 thf(5586,axiom,((! [A:num,B:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (times_times_complex @ B @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5758_numeral__times__minus__swap)). 185.47/93.65 thf(26319,plain,((! [A:num,B:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (times_times_complex @ B @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5586])). 185.47/93.65 thf(2612,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (minus_minus_int @ A @ B)) = (ord_less_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1660_diff__gt__0__iff__gt)). 185.47/93.65 thf(16401,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (minus_minus_int @ A @ B)) = (ord_less_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2612])). 185.47/93.65 thf(5027,axiom,(((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5420_minus__1__div__2__eq)). 185.47/93.65 thf(24184,plain,(((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (uminus_uminus_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5027])). 185.47/93.65 thf(7413,axiom,((! [A:nat,B:num]: ((bit_ri631733984087533419it_int @ (suc @ A) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ (times_times_int @ (bit_ri631733984087533419it_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6448_signed__take__bit__Suc__bit1)). 185.47/93.65 thf(32986,plain,((! [A:nat,B:num]: ((bit_ri631733984087533419it_int @ (suc @ A) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ (times_times_int @ (bit_ri631733984087533419it_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7413])). 185.47/93.65 thf(3903,axiom,((! [A:int,B:int]: ((((modulo_modulo_int @ A @ B) != zero_zero_int) => ((modulo_modulo_int @ A @ (uminus_uminus_int @ B)) = (minus_minus_int @ (modulo_modulo_int @ A @ B) @ B))) & (((modulo_modulo_int @ A @ B) = zero_zero_int) => ((modulo_modulo_int @ A @ (uminus_uminus_int @ B)) = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6038_zmod__zminus2__eq__if)). 185.47/93.65 thf(20528,plain,((! [A:int,B:int]: (((~ ((modulo_modulo_int @ A @ B) = zero_zero_int)) => ((modulo_modulo_int @ A @ (uminus_uminus_int @ B)) = (minus_minus_int @ (modulo_modulo_int @ A @ B) @ B))) & (((modulo_modulo_int @ A @ B) = zero_zero_int) => ((modulo_modulo_int @ A @ (uminus_uminus_int @ B)) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3903])). 185.47/93.65 thf(7384,axiom,((! [A:(rat > $o),B:rat,C:(rat > $o)]: ((! [D:rat,E:rat]: ((A @ D) = (A @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))))) => ((! [D:rat,E:rat]: ((C @ D) = (C @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))))) => (! [D:rat,E:rat]: (((C @ D) | (A @ D)) = ((A @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))) | (C @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3327_inf__period_I2_J)). 185.47/93.65 thf(32872,plain,((! [A:(rat > $o),B:rat,C:(rat > $o)]: ((! [D:rat,E:rat]: ((A @ D) = (A @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))))) => ((! [D:rat,E:rat]: ((C @ D) = (C @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))))) => (! [D:rat,E:rat]: (((C @ D) | (A @ D)) = ((A @ (minus_minus_rat @ D @ (times_times_rat @ E @ B))) | (C @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7384])). 185.47/93.65 thf(1874,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (plus_plus_real @ B @ (times_times_real @ C @ A)) @ A)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2730_divide__add__eq__iff)). 185.47/93.65 thf(14004,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (plus_plus_real @ B @ (times_times_real @ C @ A)) @ A)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874])). 185.47/93.65 thf(6776,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B)) = (modulo_modulo_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2562_minus__div__mult__eq__mod)). 185.47/93.65 thf(30659,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B)) = (modulo_modulo_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6776])). 185.47/93.65 thf(4286,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (? [C:real]: ((ord_less_real @ C @ B) & (ord_less_real @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3974_dense)). 185.47/93.65 thf(21704,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (? [C:real]: ((ord_less_real @ C @ B) & (ord_less_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4286])). 185.47/93.65 thf(5908,axiom,((! [A:nat,B:real,C:real]: ((root @ A @ (times_times_real @ B @ C)) = (times_times_real @ (root @ A @ B) @ (root @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9177_real__root__mult)). 185.47/93.65 thf(27564,plain,((! [A:nat,B:real,C:real]: ((root @ A @ (times_times_real @ B @ C)) = (times_times_real @ (root @ A @ B) @ (root @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5908])). 185.47/93.65 thf(6407,axiom,((! [A:complex,B:num]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ B)) @ (power_power_complex @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1363_power__numeral__even)). 185.47/93.65 thf(29333,plain,((! [A:complex,B:num]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ B)) @ (power_power_complex @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6407])). 185.47/93.65 thf(3844,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_int @ A @ B)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4544_even__diff)). 185.47/93.65 thf(20348,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_int @ A @ B)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3844])). 185.47/93.65 thf(867,axiom,((! [A:(nat > real)]: ((! [B:nat]: (ord_less_eq_real @ (A @ (suc @ B)) @ (A @ B))) => (topolo6980174941875973593q_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8387_mono__SucI2)). 185.47/93.65 thf(10693,plain,((! [A:(nat > real)]: ((! [B:nat]: (ord_less_eq_real @ (A @ (suc @ B)) @ (A @ B))) => (topolo6980174941875973593q_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[867])). 185.47/93.65 thf(6971,axiom,((! [A:real,B:real]: ((times_times_real @ (uminus_uminus_real @ A) @ B) = (uminus_uminus_real @ (times_times_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5069_mult__minus__left)). 185.47/93.65 thf(31410,plain,((! [A:real,B:real]: ((times_times_real @ (uminus_uminus_real @ A) @ B) = (uminus_uminus_real @ (times_times_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6971])). 185.47/93.65 thf(198,axiom,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ (bit_ri7919022796975470100ot_int @ A) @ B) = (~ (bit_se1146084159140164899it_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9507_bit__not__int__iff)). 185.47/93.65 thf(8375,plain,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ (bit_ri7919022796975470100ot_int @ A) @ B) = (~ (bit_se1146084159140164899it_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 185.47/93.65 thf(3172,axiom,((! [A:real,B:real]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2974_power2__less__imp__less)). 185.47/93.65 thf(18212,plain,((! [A:real,B:real]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3172])). 185.47/93.65 thf(830,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se7879613467334960850it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3126_set__bit__nonnegative__int__iff)). 185.47/93.65 thf(10561,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se7879613467334960850it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[830])). 185.47/93.65 thf(6911,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ A @ C) = (member_nat @ C @ (vEBT_set_vebt @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_member__correct)). 185.47/93.65 thf(31166,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ A @ C) = (member_nat @ C @ (vEBT_set_vebt @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6911])). 185.47/93.65 thf(448,axiom,((! [A:num]: ((ring_1_of_int_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7296_of__int__neg__numeral)). 185.47/93.65 thf(9221,plain,((! [A:num]: ((ring_1_of_int_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[448])). 185.47/93.65 thf(160,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((A != one_one_real) => ((((log @ A @ (times_times_real @ B @ C)) = (plus_plus_real @ (log @ A @ B) @ (log @ A @ C))) <= (ord_less_real @ zero_zero_real @ C)) <= (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9045_log__mult)). 185.47/93.65 thf(8243,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((~ (A = one_one_real)) => (((log @ A @ (times_times_real @ B @ C)) = (plus_plus_real @ (log @ A @ B) @ (log @ A @ C))) | ~ (ord_less_real @ zero_zero_real @ C) | ~ (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 185.47/93.65 thf(508,axiom,((! [A:real,B:real]: (((((tan_real @ (minus_minus_real @ A @ B)) = (divide_divide_real @ (minus_minus_real @ (tan_real @ A) @ (tan_real @ B)) @ (plus_plus_real @ one_one_real @ (times_times_real @ (tan_real @ A) @ (tan_real @ B))))) <= ((cos_real @ (minus_minus_real @ A @ B)) != zero_zero_real)) <= ((cos_real @ B) != zero_zero_real)) <= ((cos_real @ A) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8083_tan__diff)). 185.47/93.65 thf(9440,plain,((! [A:real,B:real]: (((tan_real @ (minus_minus_real @ A @ B)) = (divide_divide_real @ (minus_minus_real @ (tan_real @ A) @ (tan_real @ B)) @ (plus_plus_real @ one_one_real @ (times_times_real @ (tan_real @ A) @ (tan_real @ B))))) | ((cos_real @ (minus_minus_real @ A @ B)) = zero_zero_real) | ((cos_real @ B) = zero_zero_real) | ((cos_real @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])). 185.47/93.65 thf(7188,axiom,((! [A:product_prod_nat_nat]: (none_P5556105721700978146at_nat != (some_P7363390416028606310at_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1161_option_Odistinct_I1_J)). 185.47/93.65 thf(32211,plain,((! [A:product_prod_nat_nat]: ~ (none_P5556105721700978146at_nat = (some_P7363390416028606310at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7188])). 185.47/93.65 thf(105,axiom,((! [A:(nat > real),B:nat,C:real]: ((minus_minus_real @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7585_sumr__diff__mult__const2)). 185.47/93.65 thf(8078,plain,((! [A:(nat > real),B:nat,C:real]: ((minus_minus_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 185.47/93.65 thf(4834,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => ((B = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ C @ A))) = ((times_times_complex @ B @ A) = (uminus1482373934393186551omplex @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5964_nonzero__neg__divide__eq__eq2)). 185.47/93.65 thf(23525,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => ((B = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ C @ A))) = ((times_times_complex @ B @ A) = (uminus1482373934393186551omplex @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4834])). 185.47/93.65 thf(4745,axiom,((tanh_real = (^ [A:real]: (divide_divide_real @ (minus_minus_real @ one_one_real @ (exp_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))) @ A))) @ (plus_plus_real @ one_one_real @ (exp_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8279_tanh__real__altdef)). 185.47/93.65 thf(23214,plain,(((tanh_real) = (^ [A:real]: (divide_divide_real @ (minus_minus_real @ one_one_real @ (exp_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))) @ A))) @ (plus_plus_real @ one_one_real @ (exp_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4745])). 185.47/93.65 thf(4166,axiom,((! [A:real,B:real,C:nat]: ((power_power_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_power__divide)). 185.47/93.65 thf(21342,plain,((! [A:real,B:real,C:nat]: ((power_power_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4166])). 185.47/93.65 thf(6704,axiom,((((=) @ complex) = (^ [A:complex,B:complex]: ((minus_minus_complex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2090_eq__iff__diff__eq__0)). 185.47/93.65 thf(30342,plain,((((=) @ complex) = (^ [A:complex,B:complex]: ((minus_minus_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6704])). 185.47/93.65 thf(3814,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (C = (plus_plus_int @ (times_times_int @ (minus_minus_int @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1220_eq__add__iff2)). 185.47/93.65 thf(20253,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (C = (plus_plus_int @ (times_times_int @ (minus_minus_int @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3814])). 185.47/93.65 thf(5117,axiom,((! [A:rat]: ((ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_rat) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1898_power2__less__eq__zero__iff)). 185.47/93.65 thf(24572,plain,((! [A:rat]: ((ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_rat) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5117])). 185.47/93.65 thf(6793,axiom,((! [A:complex,B:complex]: ((A = (uminus1482373934393186551omplex @ B)) = (B = (uminus1482373934393186551omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5498_equation__minus__iff)). 185.47/93.65 thf(30712,plain,((! [A:complex,B:complex]: ((A = (uminus1482373934393186551omplex @ B)) = (B = (uminus1482373934393186551omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6793])). 185.47/93.65 thf(5934,axiom,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (ord_less_eq_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3906_Orderings_Oorder__eq__iff)). 185.47/93.65 thf(27642,plain,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (ord_less_eq_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5934])). 185.47/93.65 thf(3363,axiom,((ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2021_le__numeral__extra_I3_J)). 185.47/93.65 thf(18809,plain,((ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3363])). 185.47/93.65 thf(6200,axiom,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3877_order__trans)). 185.47/93.65 thf(28605,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6200])). 185.47/93.65 thf(1207,axiom,((! [A:nat,B:nat,C:(nat > int)]: ((ord_less_eq_nat @ A @ B) => ((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (C @ D) @ (C @ (minus_minus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (minus_minus_int @ (C @ B) @ (C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6741_sum__telescope_H_H)). 185.47/93.65 thf(11791,plain,((! [A:nat,B:nat,C:(nat > int)]: ((ord_less_eq_nat @ A @ B) => ((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (C @ D) @ (C @ (minus_minus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (minus_minus_int @ (C @ B) @ (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207])). 185.47/93.65 thf(3079,axiom,((tan_real = (^ [A:real]: (divide_divide_real @ (sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) @ (plus_plus_real @ (cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8088_tan__half)). 185.47/93.65 thf(17919,plain,(((tan_real) = (^ [A:real]: (divide_divide_real @ (sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) @ (plus_plus_real @ (cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3079])). 185.47/93.65 thf(3235,axiom,((ring_17405671764205052669omplex = (^ [A:int]: (if_complex @ (A = zero_zero_int) @ zero_zero_complex @ (if_complex @ (ord_less_int @ A @ zero_zero_int) @ (uminus1482373934393186551omplex @ (ring_17405671764205052669omplex @ (uminus_uminus_int @ A))) @ (if_complex @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (ring_17405671764205052669omplex @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (ring_17405671764205052669omplex @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_complex))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6856_of__int__code__if)). 185.47/93.65 thf(18411,plain,(((ring_17405671764205052669omplex) = (^ [A:int]: (if_complex @ (A = zero_zero_int) @ zero_zero_complex @ (if_complex @ (ord_less_int @ A @ zero_zero_int) @ (uminus1482373934393186551omplex @ (ring_17405671764205052669omplex @ (uminus_uminus_int @ A))) @ (if_complex @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (ring_17405671764205052669omplex @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (ring_17405671764205052669omplex @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_complex))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3235])). 185.47/93.65 thf(1415,axiom,(((ord_max_nat @ zero_zero_nat @ one_one_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3627_max__0__1_I1_J)). 185.47/93.65 thf(12457,plain,(((ord_max_nat @ zero_zero_nat @ one_one_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415])). 185.47/93.65 thf(634,axiom,(((ring_1_of_int_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6967_of__int__1)). 185.47/93.65 thf(9836,plain,(((ring_1_of_int_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[634])). 185.47/93.65 thf(3180,axiom,((! [A:rat,B:nat]: ((times_times_rat @ (comm_s4028243227959126397er_rat @ A @ (suc @ B)) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ (suc @ B))) = (groups73079841787564623at_rat @ (^ [C:nat]: (plus_plus_rat @ A @ (divide_divide_rat @ (semiri681578069525770553at_rat @ C) @ (numeral_numeral_rat @ (bit0 @ one))))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8617_pochhammer__times__pochhammer__half)). 185.47/93.65 thf(18239,plain,((! [A:rat,B:nat]: ((times_times_rat @ (comm_s4028243227959126397er_rat @ A @ (suc @ B)) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ (suc @ B))) = (groups73079841787564623at_rat @ (^ [C:nat]: (plus_plus_rat @ A @ (divide_divide_rat @ (semiri681578069525770553at_rat @ C) @ (numeral_numeral_rat @ (bit0 @ one))))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3180])). 185.47/93.65 thf(3887,axiom,((! [A:complex,B:complex,C:real,D:complex,E:real]: (((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ B @ D)) @ E) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ D)) @ (plus_plus_real @ C @ E))) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7503_norm__diff__triangle__le)). 185.47/93.65 thf(20480,plain,((! [A:complex,B:complex,C:real,D:complex,E:real]: (((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ B @ D)) @ E) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ D)) @ (plus_plus_real @ C @ E))) | ~ (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3887])). 185.47/93.65 thf(381,axiom,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6646_sum_OatLeast0__atMost__Suc)). 185.47/93.65 thf(9004,plain,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])). 185.47/93.65 thf(4540,axiom,((! [A:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (semiri1314217659103216013at_int @ A)) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7117_even__of__nat)). 185.47/93.65 thf(22542,plain,((! [A:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (semiri1314217659103216013at_int @ A)) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4540])). 185.47/93.65 thf(4016,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_real @ zero_zero_real @ (ring_1_of_int_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7278_of__int__nonneg)). 185.47/93.65 thf(20886,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_real @ zero_zero_real @ (ring_1_of_int_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4016])). 185.47/93.65 thf(2093,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ B @ C) <= (dvd_dvd_rat @ (times_times_rat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4582_dvd__mult__right)). 185.47/93.65 thf(14712,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ B @ C) | ~ (dvd_dvd_rat @ (times_times_rat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2093])). 185.47/93.65 thf(4301,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) => (ord_less_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_add__less__imp__less__right)). 185.47/93.65 thf(21747,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) => (ord_less_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4301])). 185.47/93.65 thf(6215,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_trans__le__add2)). 185.47/93.65 thf(28647,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6215])). 185.47/93.65 thf(200,axiom,((! [A:(nat > real)]: (summable_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7696_summable__zero__power_H)). 185.47/93.65 thf(8382,plain,((! [A:(nat > real)]: (summable_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 185.47/93.65 thf(4184,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_eq_rat @ C @ A) <= (! [D:rat]: ((ord_less_rat @ A @ D) => ((ord_less_rat @ D @ B) => (ord_less_eq_rat @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4224_dense__ge__bounded)). 185.47/93.65 thf(21399,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_eq_rat @ C @ A) | ~ (! [D:rat]: ((ord_less_rat @ A @ D) => ((ord_less_rat @ D @ B) => (ord_less_eq_rat @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4184])). 185.47/93.65 thf(4787,axiom,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ A @ (divide1717551699836669952omplex @ B @ C)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_divide__divide__eq__right)). 185.47/93.65 thf(23380,plain,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ A @ (divide1717551699836669952omplex @ B @ C)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4787])). 185.47/93.65 thf(3160,axiom,((! [A:nat,B:num,C:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (numeral_numeral_real @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7120_of__nat__less__numeral__power__cancel__iff)). 185.47/93.65 thf(18177,plain,((! [A:nat,B:num,C:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (numeral_numeral_real @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3160])). 185.47/93.65 thf(7460,axiom,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ A @ B) @ A) = (times_times_int @ A @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_power__commutes)). 185.47/93.65 thf(33146,plain,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ A @ B) @ A) = (times_times_int @ A @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7460])). 185.47/93.65 thf(2320,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_real @ (power_power_real @ (semiri5074537144036343181t_real @ A) @ B) @ (semiri5074537144036343181t_real @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7064_of__nat__le__of__nat__power__cancel__iff)). 185.47/93.65 thf(15424,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_real @ (power_power_real @ (semiri5074537144036343181t_real @ A) @ B) @ (semiri5074537144036343181t_real @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2320])). 185.47/93.65 thf(2238,axiom,((! [A:int,B:int]: (((ord_less_int @ (modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ A) => ((modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (modulo_modulo_int @ B @ A))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2155_divmod__digit__0_I2_J)). 185.47/93.65 thf(15179,plain,((! [A:int,B:int]: (((ord_less_int @ (modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ A) => ((modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (modulo_modulo_int @ B @ A))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2238])). 185.47/93.65 thf(3265,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (ord_less_int @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3279_minf_I5_J)). 185.47/93.65 thf(18498,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (ord_less_int @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3265])). 185.47/93.65 thf(7040,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3238_pinf_I3_J)). 185.47/93.65 thf(31709,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7040])). 185.47/93.65 thf(4436,axiom,((! [A:int,B:int]: (ord_less_eq_nat @ (nat2 @ (abs_abs_int @ (plus_plus_int @ A @ B))) @ (plus_plus_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9315_nat__abs__triangle__ineq)). 185.47/93.65 thf(22204,plain,((! [A:int,B:int]: (ord_less_eq_nat @ (nat2 @ (abs_abs_int @ (plus_plus_int @ A @ B))) @ (plus_plus_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4436])). 185.47/93.65 thf(5067,axiom,(((some_nat @ maxy) = (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ pr)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637__092_060open_062Some_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_092_060close_062)). 185.47/93.65 thf(24394,plain,(((some_nat @ maxy) = (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ pr)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5067])). 185.47/93.65 thf(6744,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_nat @ A @ (power_power_nat @ (power_power_nat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1123_power__odd__eq)). 185.47/93.65 thf(30498,plain,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_nat @ A @ (power_power_nat @ (power_power_nat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6744])). 185.47/93.65 thf(1217,axiom,((! [A:real,B:real]: ((plus_plus_real @ A @ (plus_plus_real @ (uminus_uminus_real @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5084_add__minus__cancel)). 185.47/93.65 thf(11820,plain,((! [A:real,B:real]: ((plus_plus_real @ A @ (plus_plus_real @ (uminus_uminus_real @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217])). 185.47/93.65 thf(4656,axiom,((! [A:nat,B:nat]: (((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ A)) @ B) = zero_zero_rat) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8508_pochhammer__of__nat__eq__0__iff)). 185.47/93.65 thf(22916,plain,((! [A:nat,B:nat]: (((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ A)) @ B) = zero_zero_rat) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4656])). 185.47/93.65 thf(2302,axiom,((! [A:rat,B:rat,C:rat]: (((minus_minus_rat @ A @ B) = C) = (A = (plus_plus_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_diff__eq__eq)). 185.47/93.65 thf(15364,plain,((! [A:rat,B:rat,C:rat]: (((minus_minus_rat @ A @ B) = C) = (A = (plus_plus_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2302])). 185.47/93.65 thf(2424,axiom,((! [A:real,B:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ A @ B)) = (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4441_dvd__add__triv__left__iff)). 185.47/93.65 thf(15751,plain,((! [A:real,B:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ A @ B)) = (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2424])). 185.47/93.65 thf(3270,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2625_add__nonneg__pos)). 185.47/93.65 thf(18513,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3270])). 185.47/93.65 thf(3316,axiom,((! [A:complex,B:real,C:complex,D:real]: (((ord_less_real @ (real_V1022390504157884413omplex @ C) @ D) => (ord_less_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ C)) @ (plus_plus_real @ B @ D))) <= (ord_less_real @ (real_V1022390504157884413omplex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7487_norm__add__less)). 185.47/93.65 thf(18658,plain,((! [A:complex,B:real,C:complex,D:real]: (((ord_less_real @ (real_V1022390504157884413omplex @ C) @ D) => (ord_less_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ C)) @ (plus_plus_real @ B @ D))) | ~ (ord_less_real @ (real_V1022390504157884413omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3316])). 185.47/93.65 thf(2392,axiom,((! [A:rat,B:rat,C:rat]: (((divide_divide_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ A)) = (divide_divide_rat @ B @ C)) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1704_nonzero__mult__divide__mult__cancel__left2)). 185.47/93.65 thf(15642,plain,((! [A:rat,B:rat,C:rat]: (((divide_divide_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ A)) = (divide_divide_rat @ B @ C)) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2392])). 185.47/93.65 thf(3762,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4038_order_Ostrict__implies__not__eq)). 185.47/93.65 thf(20079,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3762])). 185.47/93.65 thf(1385,axiom,((! [A:int,B:nat,C:int]: (((power_power_rat @ (ring_1_of_int_rat @ A) @ B) = (ring_1_of_int_rat @ C)) = ((power_power_int @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6983_of__int__eq__of__int__power__cancel__iff)). 185.47/93.65 thf(12350,plain,((! [A:int,B:nat,C:int]: (((power_power_rat @ (ring_1_of_int_rat @ A) @ B) = (ring_1_of_int_rat @ C)) = ((power_power_int @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385])). 185.47/93.65 thf(2328,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ C)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_add__right__mono)). 185.47/93.65 thf(15449,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ C)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2328])). 185.47/93.65 thf(3318,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (abs_abs_int @ (minus_minus_int @ A @ B)) @ C) = ((ord_less_int @ (minus_minus_int @ B @ C) @ A) & (ord_less_int @ A @ (plus_plus_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6595_abs__diff__less__iff)). 185.47/93.65 thf(18664,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (abs_abs_int @ (minus_minus_int @ A @ B)) @ C) = ((ord_less_int @ (minus_minus_int @ B @ C) @ A) & (ord_less_int @ A @ (plus_plus_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3318])). 185.47/93.65 thf(4562,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (~ (ord_less_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4144_order__less__imp__not__less)). 185.47/93.65 thf(22613,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (~ (ord_less_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4562])). 185.47/93.65 thf(3707,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = ((dvd_dvd_rat @ B @ C) | (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4455_dvd__mult__cancel__left)). 185.47/93.65 thf(19903,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = ((dvd_dvd_rat @ B @ C) | (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3707])). 185.47/93.65 thf(6700,axiom,((! [A:num,B:num]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (numera6690914467698888265omplex @ B)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5344_mult__neg__numeral__simps_I2_J)). 185.47/93.65 thf(30329,plain,((! [A:num,B:num]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (numera6690914467698888265omplex @ B)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6700])). 185.47/93.65 thf(739,axiom,((! [A:real]: ((log @ A @ one_one_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9020_log__one)). 185.47/93.65 thf(10197,plain,((! [A:real]: ((log @ A @ one_one_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[739])). 185.47/93.65 thf(1667,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (ord_less_eq_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3312_pinf_I8_J)). 185.47/93.65 thf(13322,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (ord_less_eq_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667])). 185.47/93.65 thf(1408,axiom,((! [A:rat]: (((abs_abs_rat @ A) = A) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6480_abs__of__pos)). 185.47/93.65 thf(12425,plain,((! [A:rat]: (((abs_abs_rat @ A) = A) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408])). 185.47/93.65 thf(5822,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ (suc @ A)))) = ((B @ A) & ! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1031_All__less__Suc)). 185.47/93.65 thf(27265,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ (suc @ A)))) = ((B @ A) & ! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5822])). 185.47/93.65 thf(2407,axiom,((! [A:nat]: (ord_less_eq_rat @ zero_zero_rat @ (semiri773545260158071498ct_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7984_fact__ge__zero)). 185.47/93.65 thf(15697,plain,((! [A:nat]: (ord_less_eq_rat @ zero_zero_rat @ (semiri773545260158071498ct_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2407])). 185.47/93.65 thf(3895,axiom,((! [A:nat]: ((abs_abs_rat @ (semiri681578069525770553at_rat @ A)) = (semiri681578069525770553at_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6875_abs__of__nat)). 185.47/93.65 thf(20500,plain,((! [A:nat]: ((abs_abs_rat @ (semiri681578069525770553at_rat @ A)) = (semiri681578069525770553at_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3895])). 185.47/93.65 thf(5413,axiom,((divmod_nat = (^ [A:nat,B:nat]: (if_Pro6206227464963214023at_nat @ ((ord_less_nat @ A @ B) | (B = zero_zero_nat)) @ (product_Pair_nat_nat @ zero_zero_nat @ A) @ (produc2626176000494625587at_nat @ (^ [C:nat]: (product_Pair_nat_nat @ (suc @ C))) @ (divmod_nat @ (minus_minus_nat @ A @ B) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7528_divmod__nat__if)). 185.47/93.65 thf(25636,plain,(((divmod_nat) = (^ [A:nat,B:nat]: (if_Pro6206227464963214023at_nat @ ((ord_less_nat @ A @ B) | (B = zero_zero_nat)) @ (product_Pair_nat_nat @ zero_zero_nat @ A) @ (produc2626176000494625587at_nat @ (^ [C:nat]: (product_Pair_nat_nat @ (suc @ C))) @ (divmod_nat @ (minus_minus_nat @ A @ B) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5413])). 185.47/93.65 thf(7418,axiom,((! [A:rat,B:num,C:num]: ((times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ (power_power_rat @ A @ (numeral_numeral_nat @ C))) = (power_power_rat @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_power__add__numeral)). 185.47/93.65 thf(33003,plain,((! [A:rat,B:num,C:num]: ((times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ (power_power_rat @ A @ (numeral_numeral_nat @ C))) = (power_power_rat @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7418])). 185.47/93.65 thf(3670,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) <= (ord_less_eq_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2218_mult__nonneg__nonneg)). 185.47/93.65 thf(19781,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) | ~ (ord_less_eq_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3670])). 185.47/93.65 thf(63,axiom,((! [A:rat,B:nat]: ((minus_minus_rat @ one_one_rat @ (power_power_rat @ A @ B)) = (times_times_rat @ (minus_minus_rat @ one_one_rat @ A) @ (groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7593_one__diff__power__eq)). 185.47/93.65 thf(7937,plain,((! [A:rat,B:nat]: ((minus_minus_rat @ one_one_rat @ (power_power_rat @ A @ B)) = (times_times_rat @ (minus_minus_rat @ one_one_rat @ A) @ (groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[63])). 185.47/93.65 thf(443,axiom,((bit_se6526347334894502574or_int = (^ [A:int,B:int]: (bit_se1409905431419307370or_int @ (bit_se725231765392027082nd_int @ A @ (bit_ri7919022796975470100ot_int @ B)) @ (bit_se725231765392027082nd_int @ (bit_ri7919022796975470100ot_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9517_xor__int__def)). 185.47/93.65 thf(9209,plain,(((bit_se6526347334894502574or_int) = (^ [A:int,B:int]: (bit_se1409905431419307370or_int @ (bit_se725231765392027082nd_int @ A @ (bit_ri7919022796975470100ot_int @ B)) @ (bit_se725231765392027082nd_int @ (bit_ri7919022796975470100ot_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[443])). 185.47/93.65 thf(559,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => ((dvd_dvd_int @ (groups705719431365010083at_int @ C @ B) @ (groups705719431365010083at_int @ C @ A)) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8821_prod__dvd__prod__subset)). 185.47/93.65 thf(9588,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => ((dvd_dvd_int @ (groups705719431365010083at_int @ (C) @ B) @ (groups705719431365010083at_int @ (C) @ A)) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[559])). 185.47/93.65 thf(1976,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) = (divide_divide_real @ B @ C)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1700_nonzero__mult__divide__mult__cancel__right)). 185.47/93.65 thf(14342,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) = (divide_divide_real @ B @ C)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1976])). 185.47/93.65 thf(6785,axiom,((! [A:nat,B:nat]: (((semiri1408675320244567234ct_nat @ (minus_minus_nat @ (suc @ B) @ A)) = (times_times_nat @ (minus_minus_nat @ (suc @ B) @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A)))) <= (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8100_fact__diff__Suc)). 185.47/93.65 thf(30685,plain,((! [A:nat,B:nat]: (((semiri1408675320244567234ct_nat @ (minus_minus_nat @ (suc @ B) @ A)) = (times_times_nat @ (minus_minus_nat @ (suc @ B) @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6785])). 185.47/93.65 thf(5642,axiom,((! [A:rat,B:rat,C:nat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ B) => ((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_eq_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C)) = (ord_less_eq_rat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1873_power__mono__iff)). 185.47/93.65 thf(26509,plain,((! [A:rat,B:rat,C:nat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ B) => ((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_eq_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C)) = (ord_less_eq_rat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5642])). 185.47/93.65 thf(4225,axiom,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ A @ B) = (plus_plus_rat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_add__left__cancel)). 185.47/93.65 thf(21522,plain,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ A @ B) = (plus_plus_rat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4225])). 185.47/93.65 thf(5819,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((minus_minus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (divide_divide_real @ (minus_minus_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6168_minus__divide__diff__eq__iff)). 185.47/93.65 thf(27255,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((minus_minus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (divide_divide_real @ (minus_minus_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5819])). 185.47/93.65 thf(1056,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ (times_times_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_times__divide__eq__left)). 185.47/93.65 thf(11324,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ (times_times_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056])). 185.47/93.65 thf(4551,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ A @ B)) <= (ord_less_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2401_add__pos__pos)). 185.47/93.65 thf(22578,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ A @ B)) | ~ (ord_less_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4551])). 185.47/93.65 thf(5038,axiom,((! [A:num,B:num,C:num]: ((((((A = one) => (! [D:num]: ((B = (bit1 @ D)) => (C != (bit1 @ D))))) => ((((((~ (! [D:num]: ((! [E:num]: ((C != (bitM @ (bit_or_not_num_neg @ D @ E))) <= (B = (bit1 @ E)))) <= (A = (bit1 @ D))))) <= (! [D:num]: ((A = (bit1 @ D)) => (! [E:num]: ((C != (bitM @ (bit_or_not_num_neg @ D @ E))) <= (B = (bit0 @ E))))))) <= ((? [D:num]: (A = (bit1 @ D))) => ((B = one) => (C != one)))) <= (! [D:num]: ((! [E:num]: ((C != (bit0 @ (bit_or_not_num_neg @ D @ E))) <= (B = (bit1 @ E)))) <= (A = (bit0 @ D))))) <= (! [D:num]: ((! [E:num]: ((C != (bitM @ (bit_or_not_num_neg @ D @ E))) <= (B = (bit0 @ E)))) <= (A = (bit0 @ D))))) <= ((? [D:num]: (A = (bit0 @ D))) => ((B = one) => (C != (bit0 @ one)))))) <= ((! [D:num]: ((C != (bit1 @ D)) <= (B = (bit0 @ D)))) <= (A = one))) <= (((B = one) => (C != one)) <= (A = one))) <= ((bit_or_not_num_neg @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9475_or__not__num__neg_Oelims)). 185.47/93.65 thf(24216,plain,((! [A:num,B:num,C:num]: ((((A = one) => (! [D:num]: ((B = (bit1 @ D)) => (~ (C = (bit1 @ D)))))) => (~ (! [D:num]: (! [E:num]: (~ (C = (bitM @ (bit_or_not_num_neg @ D @ E))) | ~ (B = (bit1 @ E))) | ~ (A = (bit1 @ D)))) | ~ (! [D:num]: ((A = (bit1 @ D)) => (! [E:num]: (~ (C = (bitM @ (bit_or_not_num_neg @ D @ E))) | ~ (B = (bit0 @ E)))))) | ~ ((? [D:num]: (A = (bit1 @ D))) => ((B = one) => (~ (C = one)))) | ~ (! [D:num]: (! [E:num]: (~ (C = (bit0 @ (bit_or_not_num_neg @ D @ E))) | ~ (B = (bit1 @ E))) | ~ (A = (bit0 @ D)))) | ~ (! [D:num]: (! [E:num]: (~ (C = (bitM @ (bit_or_not_num_neg @ D @ E))) | ~ (B = (bit0 @ E))) | ~ (A = (bit0 @ D)))) | ~ ((? [D:num]: (A = (bit0 @ D))) => ((B = one) => (~ (C = (bit0 @ one))))))) | ~ (! [D:num]: (~ (C = (bit1 @ D)) | ~ (B = (bit0 @ D))) | ~ (A = one)) | ~ (((B = one) => (~ (C = one))) | ~ (A = one)) | ~ ((bit_or_not_num_neg @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5038])). 185.47/93.65 thf(4395,axiom,((! [A:real]: (((abs_abs_real @ A) = (uminus_uminus_real @ A)) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6403_abs__of__nonpos)). 185.47/93.65 thf(22080,plain,((! [A:real]: (((abs_abs_real @ A) = (uminus_uminus_real @ A)) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4395])). 185.47/93.65 thf(1171,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ A) = (((ord_less_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ B @ one_one_rat)) & ((ord_less_rat @ A @ zero_zero_rat) => (ord_less_eq_rat @ one_one_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2810_mult__le__cancel__left2)). 185.47/93.65 thf(11687,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ A) = (((ord_less_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ B @ one_one_rat)) & ((ord_less_rat @ A @ zero_zero_rat) => (ord_less_eq_rat @ one_one_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171])). 185.47/93.65 thf(4559,axiom,((! [A:real]: ? [B:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ B) @ A) & (ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ B @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7368_floor__exists)). 185.47/93.65 thf(22603,plain,((! [A:real]: ? [B:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ B) @ A) & (ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ B @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4559])). 185.47/93.65 thf(6179,axiom,((! [A:nat]: ((minus_minus_nat @ (suc @ A) @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_diff__Suc__1)). 185.47/93.65 thf(28525,plain,((! [A:nat]: ((minus_minus_nat @ (suc @ A) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6179])). 185.47/93.65 thf(2881,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ B @ (times_times_real @ C @ A))) = (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4477_dvd__add__times__triv__right__iff)). 185.47/93.65 thf(17289,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ B @ (times_times_real @ C @ A))) = (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2881])). 185.47/93.65 thf(2429,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) <= (ord_less_int @ E @ F))) => (? [E:int]: ! [F:int]: ((((C @ F) & (A @ F)) = ((D @ F) & (B @ F))) <= (ord_less_int @ E @ F)))) <= (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3229_pinf_I1_J)). 185.47/93.65 thf(15766,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) | ~ (ord_less_int @ E @ F))) => (? [E:int]: ! [F:int]: ((((C @ F) & (A @ F)) = ((D @ F) & (B @ F))) | ~ (ord_less_int @ E @ F)))) | ~ (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2429])). 185.47/93.65 thf(1644,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (comm_s7457072308508201937r_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8434_pochhammer__pos)). 185.47/93.65 thf(13200,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (comm_s7457072308508201937r_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644])). 185.47/93.65 thf(6125,axiom,((ord_less_nat @ pr @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31__092_060open_062pr_A_060_A2_A_094_Am_092_060close_062)). 185.47/93.65 thf(28303,plain,((ord_less_nat @ pr @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6125])). 185.47/93.65 thf(3123,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (exp_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8167_exp__ge__zero)). 185.47/93.65 thf(18063,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (exp_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3123])). 185.47/93.65 thf(4632,axiom,((! [A:int,B:int]: ? [C:int]: ! [D:int]: ((ord_less_int @ D @ C) => ((~ (dvd_dvd_int @ A @ (plus_plus_int @ D @ B))) = (~ (dvd_dvd_int @ A @ (plus_plus_int @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4707_minf_I10_J)). 185.47/93.65 thf(22842,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4632])). 185.47/93.65 thf(6679,axiom,((! [A:int,B:num,C:num]: ((power_power_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (power_power_int @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_power__mult__numeral)). 185.47/93.65 thf(30263,plain,((! [A:int,B:num,C:num]: ((power_power_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (power_power_int @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6679])). 185.47/93.65 thf(4969,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1149_left__diff__distrib)). 185.47/93.65 thf(23995,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4969])). 185.47/93.65 thf(6264,axiom,((! [A:num]: (zero_zero_complex != (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5699_zero__neq__neg__numeral)). 185.47/93.65 thf(28807,plain,((! [A:num]: ~ (zero_zero_complex = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6264])). 185.47/93.65 thf(926,axiom,((! [A:real,B:nat]: ? [C:real]: ((ord_less_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A)) & ((sin_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (sin_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (sin_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8092_Maclaurin__sin__expansion2)). 185.47/93.65 thf(10911,plain,((! [A:real,B:nat]: ? [C:real]: ((ord_less_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A)) & ((sin_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (sin_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (sin_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[926])). 185.47/93.65 thf(6865,axiom,((! [A:(real > $o),B:real,C:(real > $o)]: (((! [D:real,E:real]: ((C @ D) = (C @ (minus_minus_real @ D @ (times_times_real @ E @ B))))) => (! [D:real,E:real]: (((C @ D) | (A @ D)) = ((C @ (minus_minus_real @ D @ (times_times_real @ E @ B))) | (A @ (minus_minus_real @ D @ (times_times_real @ E @ B))))))) <= (! [D:real,E:real]: ((A @ D) = (A @ (minus_minus_real @ D @ (times_times_real @ E @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3326_inf__period_I2_J)). 185.47/93.65 thf(31007,plain,((! [A:(real > $o),B:real,C:(real > $o)]: (((! [D:real,E:real]: ((C @ D) = (C @ (minus_minus_real @ D @ (times_times_real @ E @ B))))) => (! [D:real,E:real]: (((C @ D) | (A @ D)) = ((C @ (minus_minus_real @ D @ (times_times_real @ E @ B))) | (A @ (minus_minus_real @ D @ (times_times_real @ E @ B))))))) | ~ (! [D:real,E:real]: ((A @ D) = (A @ (minus_minus_real @ D @ (times_times_real @ E @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6865])). 185.47/93.65 thf(1495,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4525_even__mod__2__iff)). 185.47/93.65 thf(12705,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1495])). 185.47/93.65 thf(4111,axiom,((! [A:nat]: ~ (ord_less_int @ (semiri1406184849735516958ct_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7989_fact__not__neg)). 185.47/93.65 thf(21174,plain,((! [A:nat]: ~ (ord_less_int @ (semiri1406184849735516958ct_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4111])). 185.47/93.65 thf(5052,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C)) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2305_add__increasing)). 185.47/93.65 thf(24335,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C)) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5052])). 185.47/93.65 thf(5545,axiom,((! [A:num]: ((plus_plus_num @ A @ one) = (inc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9380_add__One)). 185.47/93.65 thf(26197,plain,((! [A:num]: ((plus_plus_num @ A @ one) = (inc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5545])). 185.47/93.65 thf(2648,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2339_zero__less__mult__pos)). 185.47/93.65 thf(16516,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2648])). 185.47/93.65 thf(5078,axiom,((! [A:complex]: ((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit1 @ one)) @ A)) = (minus_minus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ (bit0 @ one))) @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit1 @ one)))) @ (times_times_complex @ (numera6690914467698888265omplex @ (bit1 @ one)) @ (cos_complex @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7917_cos__treble__cos)). 185.47/93.65 thf(24426,plain,((! [A:complex]: ((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit1 @ one)) @ A)) = (minus_minus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ (bit0 @ one))) @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit1 @ one)))) @ (times_times_complex @ (numera6690914467698888265omplex @ (bit1 @ one)) @ (cos_complex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5078])). 185.47/93.65 thf(5365,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4273_order__le__less)). 185.47/93.65 thf(25492,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5365])). 185.47/93.65 thf(6584,axiom,((! [A:real,B:nat]: (((ord_less_eq_real @ (power_power_real @ A @ (suc @ B)) @ A) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2871_power__Suc__le__self)). 185.47/93.65 thf(29953,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ (power_power_real @ A @ (suc @ B)) @ A) | ~ (ord_less_eq_real @ A @ one_one_real) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6584])). 185.47/93.65 thf(4890,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => ((fract @ (plus_plus_int @ B @ A) @ A) = (plus_plus_rat @ (fract @ B @ A) @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9952_Fract__add__one)). 185.47/93.65 thf(23731,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => ((fract @ (plus_plus_int @ B @ A) @ A) = (plus_plus_rat @ (fract @ B @ A) @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4890])). 185.47/93.65 thf(1320,axiom,((! [A:vEBT_VEBT]: ((! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ B @ C @ D @ E))) => (~ (! [B:$o,C:$o]: (A != (vEBT_Leaf @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2013_VEBT_Oexhaust)). 185.47/93.65 thf(12132,plain,((! [A:vEBT_VEBT]: ((! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ B @ C @ D @ E))) => (~ (! [B:$o,C:$o]: ~ (A = (vEBT_Leaf @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320])). 185.47/93.65 thf(235,axiom,((! [A:set_nat,B:(nat > rat),C:(nat > $o)]: (((groups73079841787564623at_rat @ B @ (collect_nat @ (^ [D:nat]: ((C @ D) & (member_nat @ D @ A))))) = (groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (C @ D) @ (B @ D) @ one_one_rat)) @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8783_prod_Ointer__filter)). 185.47/93.65 thf(8481,plain,((! [A:set_nat,B:(nat > rat),C:(nat > $o)]: (((groups73079841787564623at_rat @ (B) @ (collect_nat @ (^ [D:nat]: ((C @ D) & (member_nat @ D @ A))))) = (groups73079841787564623at_rat @ (^ [D:nat]: (if_rat @ (C @ D) @ (B @ D) @ one_one_rat)) @ A)) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 185.47/93.65 thf(4117,axiom,((! [A:num]: ~ (ord_less_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5903_not__zero__less__neg__numeral)). 185.47/93.65 thf(21191,plain,((! [A:num]: ~ (ord_less_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4117])). 185.47/93.65 thf(7020,axiom,((! [A:nat,B:nat,C:nat]: (((? [D:nat]: (A = (plus_plus_nat @ C @ (times_times_nat @ B @ D)))) <= (ord_less_eq_nat @ C @ A)) <= ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2175_nat__mod__eq__lemma)). 185.47/93.65 thf(31621,plain,((! [A:nat,B:nat,C:nat]: (? [D:nat]: (A = (plus_plus_nat @ C @ (times_times_nat @ B @ D))) | ~ (ord_less_eq_nat @ C @ A) | ~ ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7020])). 185.47/93.65 thf(7278,axiom,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ B)) = (times_times_complex @ A @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1069_power__Suc)). 185.47/93.65 thf(32519,plain,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ B)) = (times_times_complex @ A @ (power_power_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7278])). 185.47/93.65 thf(162,axiom,((! [A:num,B:int]: ((ord_less_int @ (numeral_numeral_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7076_of__int__numeral__less__iff)). 185.47/93.65 thf(8250,plain,((! [A:num,B:int]: ((ord_less_int @ (numeral_numeral_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 185.47/93.65 thf(3829,axiom,((! [A:int,B:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6933_of__int__le__iff)). 185.47/93.65 thf(20294,plain,((! [A:int,B:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3829])). 185.47/93.65 thf(3852,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ A) = (modulo_modulo_int @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1774_mod__mult__self4)). 185.47/93.65 thf(20370,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ A) = (modulo_modulo_int @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3852])). 185.47/93.65 thf(6261,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5467_neg__one__even__power)). 185.47/93.65 thf(28799,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6261])). 185.47/93.65 thf(589,axiom,((! [A:int]: ((ord_less_int @ (ring_1_of_int_int @ A) @ one_one_int) = (ord_less_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7091_of__int__less__1__iff)). 185.47/93.65 thf(9688,plain,((! [A:int]: ((ord_less_int @ (ring_1_of_int_int @ A) @ one_one_int) = (ord_less_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[589])). 185.47/93.65 thf(2817,axiom,((! [A:nat,B:int]: ((bit_se2159334234014336723it_int @ (suc @ A) @ B) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2159334234014336723it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3034_flip__bit__Suc)). 185.47/93.65 thf(17082,plain,((! [A:nat,B:int]: ((bit_se2159334234014336723it_int @ (suc @ A) @ B) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2159334234014336723it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2817])). 185.47/93.65 thf(7049,axiom,((! [A:nat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) != zero_zero_nat)) => (~ ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) != one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4965_parity__cases)). 185.47/93.65 thf(31741,plain,((! [A:nat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (~ ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))) => (~ ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (~ ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7049])). 185.47/93.65 thf(1342,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ (abs_abs_rat @ B)) @ zero_zero_rat) = ((B = zero_zero_rat) | (ord_less_eq_rat @ A @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6402_divide__le__0__abs__iff)). 185.47/93.65 thf(12205,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ (abs_abs_rat @ B)) @ zero_zero_rat) = ((B = zero_zero_rat) | (ord_less_eq_rat @ A @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342])). 185.47/93.65 thf(5514,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1158_right__diff__distrib_H)). 185.47/93.65 thf(26092,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5514])). 185.47/93.65 thf(2903,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ zero_zero_int @ (divide_divide_int @ B @ A)) <= (ord_less_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3053_div__positive__int)). 185.47/93.65 thf(17363,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ zero_zero_int @ (divide_divide_int @ B @ A)) | ~ (ord_less_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2903])). 185.47/93.65 thf(5272,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8003_fact__mono)). 185.47/93.65 thf(25151,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5272])). 185.47/93.65 thf(3841,axiom,((! [A:$o,B:$o,C:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_Leaf @ A @ B) @ C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2113_VEBT__internal_Omembermima_Osimps_I1_J)). 185.47/93.65 thf(20326,plain,((! [A:$o,B:$o,C:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_Leaf @ A @ B) @ C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3841])). 185.47/93.65 thf(807,axiom,((! [A:set_nat,B:(nat > nat)]: ((ord_less_nat @ zero_zero_nat @ (groups708209901874060359at_nat @ B @ A)) <= (! [C:nat]: ((ord_less_nat @ zero_zero_nat @ (B @ C)) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8757_prod__pos)). 185.47/93.65 thf(10477,plain,((! [A:set_nat,B:(nat > nat)]: ((ord_less_nat @ zero_zero_nat @ (groups708209901874060359at_nat @ (B) @ A)) | ~ (! [C:nat]: ((ord_less_nat @ zero_zero_nat @ (B @ C)) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[807])). 185.47/93.65 thf(1302,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B)) @ zero_zero_rat) = ((B = zero_zero_rat) & (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2679_sum__squares__le__zero__iff)). 185.47/93.65 thf(12073,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B)) @ zero_zero_rat) = ((B = zero_zero_rat) & (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302])). 185.47/93.65 thf(3741,axiom,((! [A:nat]: ((vEBT_invar_vebt @ (vEBT_vebt_buildup @ A) @ A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1465_buildup__gives__valid)). 185.47/93.65 thf(20015,plain,((! [A:nat]: ((vEBT_invar_vebt @ (vEBT_vebt_buildup @ A) @ A) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3741])). 185.47/93.65 thf(7186,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4203_order_Ostrict__iff__order)). 185.47/93.65 thf(32205,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7186])). 185.47/93.65 thf(3140,axiom,((! [A:rat]: (((abs_abs_rat @ A) = (uminus_uminus_rat @ A)) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6578_abs__of__neg)). 185.47/93.65 thf(18112,plain,((! [A:rat]: (((abs_abs_rat @ A) = (uminus_uminus_rat @ A)) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3140])). 185.47/93.65 thf(7379,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => (((times_times_complex @ B @ A) = (times_times_complex @ C @ A)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2063_mult__right__cancel)). 185.47/93.65 thf(32855,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => (((times_times_complex @ B @ A) = (times_times_complex @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7379])). 185.47/93.65 thf(1687,axiom,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ A @ B) = bot_bot_set_nat) = (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3204_atLeastatMost__empty__iff)). 185.47/93.65 thf(13379,plain,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ A @ B) = bot_bot_set_nat) = (~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687])). 185.47/93.65 thf(394,axiom,((! [A:nat]: ((cos_real @ (times_times_real @ pi @ (semiri5074537144036343181t_real @ A))) = (power_power_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7804_cos__npi2)). 185.47/93.65 thf(9043,plain,((! [A:nat]: ((cos_real @ (times_times_real @ pi @ (semiri5074537144036343181t_real @ A))) = (power_power_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])). 185.47/93.65 thf(6016,axiom,((! [A:nat]: (ord_less_eq_nat @ one_one_nat @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7999_fact__ge__1)). 185.47/93.65 thf(27945,plain,((! [A:nat]: (ord_less_eq_nat @ one_one_nat @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6016])). 185.47/93.65 thf(3490,axiom,((! [A:int,B:int,C:int]: ((((divide_divide_int @ (minus_minus_int @ B @ C) @ A) = (minus_minus_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A))) <= (dvd_dvd_int @ A @ C)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4500_div__diff)). 185.47/93.65 thf(19218,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (minus_minus_int @ B @ C) @ A) = (minus_minus_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A))) | ~ (dvd_dvd_int @ A @ C) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3490])). 185.47/93.65 thf(1110,axiom,((! [A:rat,B:rat,C:rat]: (((dvd_dvd_rat @ A @ (plus_plus_rat @ B @ C)) = (dvd_dvd_rat @ A @ C)) <= (dvd_dvd_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4643_dvd__add__right__iff)). 185.47/93.65 thf(11499,plain,((! [A:rat,B:rat,C:rat]: (((dvd_dvd_rat @ A @ (plus_plus_rat @ B @ C)) = (dvd_dvd_rat @ A @ C)) | ~ (dvd_dvd_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110])). 185.47/93.65 thf(3187,axiom,((! [A:num]: ((neg_nu6075765906172075777c_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (neg_nu8295874005876285629c_real @ (numeral_numeral_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7025_dbl__dec__simps_I1_J)). 185.47/93.65 thf(18261,plain,((! [A:num]: ((neg_nu6075765906172075777c_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (neg_nu8295874005876285629c_real @ (numeral_numeral_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3187])). 185.47/93.65 thf(7066,axiom,(((neg_numeral_dbl_rat @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5458_dbl__simps_I4_J)). 185.47/93.65 thf(31794,plain,(((neg_numeral_dbl_rat @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7066])). 185.47/93.65 thf(82,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ A) => ((suminf_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B)))) = (minus_minus_real @ (suminf_real @ A) @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7733_suminf__minus__initial__segment)). 185.47/93.65 thf(7999,plain,((! [A:(nat > real),B:nat]: ((summable_real @ (A)) => ((suminf_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B)))) = (minus_minus_real @ (suminf_real @ (A)) @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 185.47/93.65 thf(5186,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (((ord_less_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A)) <= (ord_less_nat @ C @ one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2881_power__strict__decreasing)). 185.47/93.65 thf(24831,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A)) | ~ (ord_less_nat @ C @ one_one_nat) | ~ (ord_less_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5186])). 185.47/93.65 thf(1177,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ B) @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7496_norm__add__leD)). 185.47/93.65 thf(11704,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ B) @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177])). 185.47/93.65 thf(6364,axiom,((! [A:nat,B:num]: ((bit_se8568078237143864401it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (bit_se8568078237143864401it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9755_drop__bit__Suc__minus__bit0)). 185.47/93.65 thf(29160,plain,((! [A:nat,B:num]: ((bit_se8568078237143864401it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (bit_se8568078237143864401it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6364])). 185.47/93.65 thf(1485,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ (plus_plus_rat @ C @ A) @ (plus_plus_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_add__strict__left__mono)). 185.47/93.65 thf(12673,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ (plus_plus_rat @ C @ A) @ (plus_plus_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485])). 185.47/93.65 thf(5274,axiom,(((uminus_uminus_int @ (numeral_numeral_int @ one)) = (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5989_uminus__numeral__One)). 185.47/93.65 thf(25156,plain,(((uminus_uminus_int @ (numeral_numeral_int @ one)) = (uminus_uminus_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5274])). 185.47/93.65 thf(1605,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7504_norm__triangle__ineq4)). 185.47/93.65 thf(13059,plain,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605])). 185.47/93.65 thf(1086,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6154_pos__minus__divide__less__eq)). 185.47/93.65 thf(11424,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086])). 185.47/93.65 thf(6299,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((A = (suc @ B)) | (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_le__Suc__eq)). 185.47/93.65 thf(28923,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((A = (suc @ B)) | (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6299])). 185.47/93.65 thf(6699,axiom,((! [A:$o]: ((ord_less_nat @ (zero_n2687167440665602831ol_nat @ A) @ one_one_nat) = (~ (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5240_of__bool__less__one__iff)). 185.47/93.65 thf(30324,plain,((! [A:$o]: ((ord_less_nat @ (zero_n2687167440665602831ol_nat @ A) @ one_one_nat) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6699])). 185.47/93.65 thf(5314,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((dvd_dvd_nat @ B @ one_one_nat) => ((divide_divide_nat @ A @ (times_times_nat @ A @ B)) = (divide_divide_nat @ one_one_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4895_is__unit__div__mult__cancel__left)). 185.47/93.65 thf(25288,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((dvd_dvd_nat @ B @ one_one_nat) => ((divide_divide_nat @ A @ (times_times_nat @ A @ B)) = (divide_divide_nat @ one_one_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5314])). 185.47/93.65 thf(5774,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) <= (ord_less_nat @ B @ zero_zero_nat)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2631_add__nonpos__neg)). 185.47/93.65 thf(26941,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_nat @ B @ zero_zero_nat) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5774])). 185.47/93.65 thf(6466,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (B = A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3892_dual__order_Oantisym)). 185.47/93.65 thf(29548,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (B = A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6466])). 185.47/93.65 thf(5683,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ (suc @ B)) = (A = B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1038_not__less__less__Suc__eq)). 185.47/93.65 thf(26645,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ (suc @ B)) = (A = B)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5683])). 185.47/93.65 thf(3096,axiom,((csqrt = (^ [A:complex]: (complex2 @ (sqrt @ (divide_divide_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ (numeral_numeral_real @ (bit0 @ one)))) @ (times_times_real @ (if_real @ ((im @ A) = zero_zero_real) @ one_one_real @ (sgn_sgn_real @ (im @ A))) @ (sqrt @ (divide_divide_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ (numeral_numeral_real @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9659_csqrt_Ocode)). 185.47/93.65 thf(17980,plain,(((csqrt) = (^ [A:complex]: (complex2 @ (sqrt @ (divide_divide_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ (numeral_numeral_real @ (bit0 @ one)))) @ (times_times_real @ (if_real @ ((im @ A) = zero_zero_real) @ one_one_real @ (sgn_sgn_real @ (im @ A))) @ (sqrt @ (divide_divide_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ (numeral_numeral_real @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3096])). 185.47/93.65 thf(5377,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4370_order__le__imp__less__or__eq)). 185.47/93.65 thf(25530,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5377])). 185.47/93.65 thf(1717,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ C @ B) <= (ord_less_eq_real @ C @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4245_dual__order_Ostrict__trans2)). 185.47/93.65 thf(13476,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ C @ B) | ~ (ord_less_eq_real @ C @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717])). 185.47/93.65 thf(2185,axiom,((! [A:real,B:nat,C:nat]: (((ord_less_nat @ B @ C) <= (ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_866_power__less__imp__less__exp)). 185.47/93.65 thf(15014,plain,((! [A:real,B:nat,C:nat]: ((ord_less_nat @ B @ C) | ~ (ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2185])). 185.47/93.65 thf(647,axiom,((! [A:(nat > real),B:set_nat,C:real]: ((divide_divide_real @ (groups6591440286371151544t_real @ A @ B) @ C) = (groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (A @ D) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5627_sum__divide__distrib)). 185.47/93.65 thf(9881,plain,((! [A:(nat > real),B:set_nat,C:real]: ((divide_divide_real @ (groups6591440286371151544t_real @ (A) @ B) @ C) = (groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (A @ D) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[647])). 185.47/93.65 thf(4661,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B) => (ord_less_eq_int @ (bit_ri631733984087533419it_int @ A @ B) @ (minus_minus_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4982_signed__take__bit__int__less__eq)). 185.47/93.65 thf(22931,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B) => (ord_less_eq_int @ (bit_ri631733984087533419it_int @ A @ B) @ (minus_minus_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4661])). 185.47/93.65 thf(7644,axiom,((sqrt = (root @ (numeral_numeral_nat @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9190_sqrt__def)). 185.47/93.65 thf(33691,plain,(((sqrt) = (root @ (numeral_numeral_nat @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7644])). 185.47/93.65 thf(4909,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_add__le__imp__le__left)). 185.47/93.65 thf(23789,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4909])). 185.47/93.65 thf(2208,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ A @ B)) @ C) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ zero_zero_real @ C) <= (~ (ord_less_real @ B @ zero_zero_real))) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ C @ B) @ (uminus_uminus_real @ A))))) & ((ord_less_real @ (uminus_uminus_real @ A) @ (times_times_real @ C @ B)) <= (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6146_minus__divide__less__eq)). 185.47/93.65 thf(15082,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ A @ B)) @ C) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ zero_zero_real @ C) | (ord_less_real @ B @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ C @ B) @ (uminus_uminus_real @ A))))) & ((ord_less_real @ (uminus_uminus_real @ A) @ (times_times_real @ C @ B)) | ~ (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2208])). 185.47/93.65 thf(3302,axiom,((! [A:$o,B:$o]: ((ord_less_eq_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B)) = ((B) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5110_of__bool__less__eq__iff)). 185.47/93.65 thf(18609,plain,((! [A:$o,B:$o]: ((ord_less_eq_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B)) = ((B) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3302])). 185.47/93.65 thf(7060,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4279_order__less__le)). 185.47/93.65 thf(31777,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7060])). 185.47/93.65 thf(6668,axiom,((! [A:int,B:num,C:nat]: (((ring_1_of_int_rat @ A) = (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7100_of__int__eq__numeral__power__cancel__iff)). 185.47/93.65 thf(30231,plain,((! [A:int,B:num,C:nat]: (((ring_1_of_int_rat @ A) = (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6668])). 185.47/93.65 thf(7437,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1644_less__add__same__cancel2)). 185.47/93.65 thf(33059,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7437])). 185.47/93.65 thf(3889,axiom,((tan_complex = (^ [A:complex]: (divide1717551699836669952omplex @ (sin_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) @ (plus_plus_complex @ (cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) @ one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8087_tan__half)). 185.47/93.65 thf(20485,plain,(((tan_complex) = (^ [A:complex]: (divide1717551699836669952omplex @ (sin_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) @ (plus_plus_complex @ (cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) @ one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3889])). 185.47/93.65 thf(246,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (ord_max_int @ A @ B) @ C) = ((ord_less_eq_int @ B @ C) & (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3559_max_Obounded__iff)). 185.47/93.65 thf(8513,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (ord_max_int @ A @ B) @ C) = ((ord_less_eq_int @ B @ C) & (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[246])). 185.47/93.65 thf(4981,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1159_right__diff__distrib_H)). 185.47/93.65 thf(24027,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4981])). 185.47/93.65 thf(4329,axiom,((minus_minus_real = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5824_minus__real__def)). 185.47/93.65 thf(21870,plain,(((minus_minus_real) = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4329])). 185.47/93.65 thf(4823,axiom,((! [A:num,B:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5689_neg__numeral__le__numeral)). 185.47/93.65 thf(23493,plain,((! [A:num,B:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4823])). 185.47/93.65 thf(3612,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (powr_real @ C @ A) @ (powr_real @ C @ B)) <= (ord_less_real @ one_one_real @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9090_powr__less__mono)). 185.47/93.65 thf(19595,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (powr_real @ C @ A) @ (powr_real @ C @ B)) | ~ (ord_less_real @ one_one_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3612])). 185.47/93.65 thf(1707,axiom,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = (ord_less_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3105_verit__comp__simplify1_I3_J)). 185.47/93.65 thf(13448,plain,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = (ord_less_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707])). 185.47/93.65 thf(5980,axiom,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2029_less__numeral__extra_I3_J)). 185.47/93.65 thf(27827,plain,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5980])). 185.47/93.65 thf(2486,axiom,((! [A:int,B:int]: ((ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_int @ A @ B) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2977_power2__less__imp__less)). 185.47/93.65 thf(15962,plain,((! [A:int,B:int]: ((ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_int @ A @ B) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2486])). 185.47/93.65 thf(5933,axiom,((! [A:nat,B:nat]: (dvd_dvd_nat @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) @ (semiri1408675320244567234ct_nat @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8022_fact__fact__dvd__fact)). 185.47/93.65 thf(27640,plain,((! [A:nat,B:nat]: (dvd_dvd_nat @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) @ (semiri1408675320244567234ct_nat @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5933])). 185.47/93.65 thf(190,axiom,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))) @ (arctan @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit1 @ (bit0 @ one)))))) @ (arctan @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit1 @ (bit1 @ (bit1 @ (bit1 @ (bit0 @ (bit1 @ (bit1 @ one))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7770_machin)). 185.47/93.65 thf(8343,plain,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))) @ (arctan @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit1 @ (bit0 @ one)))))) @ (arctan @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit1 @ (bit1 @ (bit1 @ (bit1 @ (bit0 @ (bit1 @ (bit1 @ one))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 185.47/93.65 thf(6603,axiom,((! [A:real,B:nat]: ((times_times_real @ (power_power_real @ A @ B) @ A) = (times_times_real @ A @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_power__commutes)). 185.47/93.65 thf(30015,plain,((! [A:real,B:nat]: ((times_times_real @ (power_power_real @ A @ B) @ A) = (times_times_real @ A @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6603])). 185.47/93.65 thf(4716,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A)) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6756_abs__ln__one__plus__x__minus__x__bound__nonneg)). 185.47/93.65 thf(23126,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A)) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4716])). 185.47/93.65 thf(5595,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_left__add__mult__distrib)). 185.47/93.65 thf(26351,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5595])). 185.47/93.65 thf(7258,axiom,((! [A:complex,B:complex,C:num]: (((divide1717551699836669952omplex @ A @ B) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = ((((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex) <= (B = zero_zero_complex)) & ((A = (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) @ B)) <= (B != zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6160_divide__eq__eq__numeral_I2_J)). 185.47/93.65 thf(32459,plain,((! [A:complex,B:complex,C:num]: (((divide1717551699836669952omplex @ A @ B) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = ((((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex) | ~ (B = zero_zero_complex)) & ((A = (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) @ B)) | (B = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7258])). 185.47/93.65 thf(4189,axiom,(((abs_abs_rat @ one_one_rat) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6463_abs__one)). 185.47/93.65 thf(21416,plain,(((abs_abs_rat @ one_one_rat) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4189])). 185.47/93.65 thf(7394,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ B @ (suc @ A))) = (times_times_nat @ B @ (binomial @ (minus_minus_nat @ B @ one_one_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8474_binomial__absorption)). 185.47/93.65 thf(32899,plain,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ B @ (suc @ A))) = (times_times_nat @ B @ (binomial @ (minus_minus_nat @ B @ one_one_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7394])). 185.47/93.65 thf(4618,axiom,((! [A:real]: (dvd_dvd_real @ one_one_real @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4637_one__dvd)). 185.47/93.65 thf(22791,plain,((! [A:real]: (dvd_dvd_real @ one_one_real @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4618])). 185.47/93.65 thf(4640,axiom,((! [A:rat,B:rat]: ? [C:rat]: ! [D:rat]: (((~ (dvd_dvd_rat @ A @ (plus_plus_rat @ D @ B))) = (~ (dvd_dvd_rat @ A @ (plus_plus_rat @ D @ B)))) <= (ord_less_rat @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4715_pinf_I10_J)). 185.47/93.65 thf(22867,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4640])). 185.47/93.65 thf(6144,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ A) @ B) = (minus_minus_complex @ (uminus1482373934393186551omplex @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5572_minus__diff__commute)). 185.47/93.65 thf(28367,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ A) @ B) = (minus_minus_complex @ (uminus1482373934393186551omplex @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6144])). 185.47/93.65 thf(3431,axiom,((! [A:real,B:nat]: (((comm_s7457072308508201937r_real @ A @ B) = zero_zero_real) = (? [C:nat]: ((A = (uminus_uminus_real @ (semiri5074537144036343181t_real @ C))) & (ord_less_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8502_pochhammer__eq__0__iff)). 185.47/93.65 thf(19026,plain,((! [A:real,B:nat]: (((comm_s7457072308508201937r_real @ A @ B) = zero_zero_real) = (? [C:nat]: ((A = (uminus_uminus_real @ (semiri5074537144036343181t_real @ C))) & (ord_less_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3431])). 185.47/93.65 thf(7196,axiom,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((divide_divide_nat @ one_one_nat @ (divide_divide_nat @ one_one_nat @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4494_unit__div__1__div__1)). 185.47/93.65 thf(32237,plain,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((divide_divide_nat @ one_one_nat @ (divide_divide_nat @ one_one_nat @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7196])). 185.47/93.65 thf(3857,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ B @ (bitM @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9459_or__minus__numerals_I7_J)). 185.47/93.65 thf(20390,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ B @ (bitM @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3857])). 185.47/93.65 thf(6807,axiom,((! [A:real,B:nat]: ((times_times_real @ (power_power_real @ (uminus_uminus_real @ A) @ B) @ (power_power_real @ (uminus_uminus_real @ A) @ B)) = (power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6268_minus__power__mult__self)). 185.47/93.65 thf(30759,plain,((! [A:real,B:nat]: ((times_times_real @ (power_power_real @ (uminus_uminus_real @ A) @ B) @ (power_power_real @ (uminus_uminus_real @ A) @ B)) = (power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6807])). 185.47/93.65 thf(5008,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8096_fact__mono__nat)). 185.47/93.65 thf(24130,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5008])). 185.47/93.65 thf(1795,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => ((plus_plus_rat @ (minus_minus_rat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_979_le__add__diff__inverse2)). 185.47/93.65 thf(13746,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => ((plus_plus_rat @ (minus_minus_rat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795])). 185.47/93.65 thf(2783,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ A @ C) <= (B = C)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3992_ord__less__eq__trans)). 185.47/93.65 thf(16973,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ C) | ~ (B = C) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2783])). 185.47/93.65 thf(1448,axiom,((! [A:int]: ((ord_less_nat @ (suc @ zero_zero_nat) @ (nat2 @ A)) = (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9260_one__less__nat__eq)). 185.47/93.65 thf(12561,plain,((! [A:int]: ((ord_less_nat @ (suc @ zero_zero_nat) @ (nat2 @ A)) = (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448])). 185.47/93.65 thf(6880,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => (((list_u1324408373059187874T_VEBT @ B @ A @ C) = B) = ((nth_VEBT_VEBT @ B @ A) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3781_list__update__same__conv)). 185.47/93.65 thf(31068,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => (((list_u1324408373059187874T_VEBT @ B @ A @ C) = B) = ((nth_VEBT_VEBT @ B @ A) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6880])). 185.47/93.65 thf(4180,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ zero_zero_rat) => ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2658_divide__nonpos__neg)). 185.47/93.65 thf(21384,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ zero_zero_rat) => ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4180])). 185.47/93.65 thf(1062,axiom,((! [A:int,B:int]: (((nat2 @ (times_times_int @ A @ B)) = (times_times_nat @ (nat2 @ A) @ (nat2 @ B))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9311_nat__mult__distrib)). 185.47/93.65 thf(11339,plain,((! [A:int,B:int]: (((nat2 @ (times_times_int @ A @ B)) = (times_times_nat @ (nat2 @ A) @ (nat2 @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062])). 185.47/93.65 thf(1465,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((B @ D) != zero_zero_real))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((C @ D) != zero_zero_real) & (member_nat @ D @ A))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((plus_plus_real @ (B @ D) @ (C @ D)) != zero_zero_real))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3547_sum_Ofinite__Collect__op)). 185.47/93.65 thf(12613,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((B @ D) = zero_zero_real))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((C @ D) = zero_zero_real) & (member_nat @ D @ A))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((plus_plus_real @ (B @ D) @ (C @ D)) = zero_zero_real))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465])). 185.47/93.65 thf(1699,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((C != A) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3244_pinf_I4_J)). 185.47/93.65 thf(13423,plain,((! [A:int]: ? [B:int]: ! [C:int]: (~ (C = A) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699])). 185.47/93.65 thf(465,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (ord_max_int @ B @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3741_max_Ostrict__coboundedI1)). 185.47/93.65 thf(9296,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (ord_max_int @ B @ C)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])). 185.47/93.65 thf(5056,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_le__iff__add)). 185.47/93.65 thf(24358,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5056])). 185.47/93.65 thf(166,axiom,((! [A:complex,B:complex]: ((im @ (plus_plus_complex @ A @ B)) = (plus_plus_real @ (im @ A) @ (im @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9672_plus__complex_Osimps_I2_J)). 185.47/93.65 thf(8265,plain,((! [A:complex,B:complex]: ((im @ (plus_plus_complex @ A @ B)) = (plus_plus_real @ (im @ A) @ (im @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 185.47/93.65 thf(313,axiom,((! [A:rat,B:nat]: ((times_times_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ (gbinomial_rat @ A @ B)) = (times_times_rat @ A @ (gbinomial_rat @ (minus_minus_rat @ A @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8480_gbinomial__absorb__comp)). 185.47/93.65 thf(8778,plain,((! [A:rat,B:nat]: ((times_times_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ (gbinomial_rat @ A @ B)) = (times_times_rat @ A @ (gbinomial_rat @ (minus_minus_rat @ A @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 185.47/93.65 thf(2746,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((~ (ord_less_eq_rat @ A @ C)) <= (ord_less_rat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3319_minf_I8_J)). 185.47/93.65 thf(16861,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: (~ (ord_less_eq_rat @ A @ C) | ~ (ord_less_rat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2746])). 185.47/93.65 thf(4240,axiom,((! [A:num,B:(int > num),C:int,D:int]: (((ord_less_eq_int @ C @ D) => ((! [E:int,F:int]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_int @ E @ F))) => (ord_less_eq_num @ A @ (B @ D)))) <= (ord_less_eq_num @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3916_order__subst1)). 185.47/93.65 thf(21567,plain,((! [A:num,B:(int > num),C:int,D:int]: (((ord_less_eq_int @ C @ D) => ((! [E:int,F:int]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_int @ E @ F))) => (ord_less_eq_num @ A @ (B @ D)))) | ~ (ord_less_eq_num @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4240])). 185.47/93.65 thf(5453,axiom,((! [A:num,B:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ one) @ (numeral_numeral_nat @ (bit0 @ A))) = (modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ B)) @ (numeral_numeral_nat @ (bit0 @ A)))) = ((modulo_modulo_nat @ (numeral_numeral_nat @ B) @ (numeral_numeral_nat @ A)) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6701_cong__exp__iff__simps_I7_J)). 185.47/93.65 thf(25802,plain,((! [A:num,B:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ one) @ (numeral_numeral_nat @ (bit0 @ A))) = (modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ B)) @ (numeral_numeral_nat @ (bit0 @ A)))) = ((modulo_modulo_nat @ (numeral_numeral_nat @ B) @ (numeral_numeral_nat @ A)) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5453])). 185.47/93.65 thf(537,axiom,((! [A:nat,B:nat,C:(nat > rat),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6694_sum_Oub__add__nat)). 185.47/93.65 thf(9522,plain,((! [A:nat,B:nat,C:(nat > rat),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[537])). 185.47/93.65 thf(5760,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((dvd_dvd_nat @ A @ B) = (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4812_less__eq__dvd__minus)). 185.47/93.65 thf(26891,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((dvd_dvd_nat @ A @ B) = (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5760])). 185.47/93.65 thf(5902,axiom,(((neg_nu7009210354673126013omplex @ one_one_complex) = (numera6690914467698888265omplex @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3804_dbl__simps_I3_J)). 185.47/93.65 thf(27547,plain,(((neg_nu7009210354673126013omplex @ one_one_complex) = (numera6690914467698888265omplex @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5902])). 185.47/93.65 thf(6811,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (uminus_uminus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6237_realpow__square__minus__le)). 185.47/93.65 thf(30778,plain,((! [A:real,B:real]: (ord_less_eq_real @ (uminus_uminus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6811])). 185.47/93.65 thf(7015,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (~ (! [D:nat]: (A != (plus_plus_nat @ C @ (times_times_nat @ B @ D)))))) <= ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2177_mod__eq__nat1E)). 185.47/93.65 thf(31606,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (~ (! [D:nat]: ~ (A = (plus_plus_nat @ C @ (times_times_nat @ B @ D)))))) | ~ ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7015])). 185.47/93.65 thf(42,axiom,((! [A:num]: ((set_ord_lessThan_nat @ (numeral_numeral_nat @ A)) = (insert_nat @ (pred_numeral @ A) @ (set_ord_lessThan_nat @ (pred_numeral @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9430_lessThan__nat__numeral)). 185.47/93.65 thf(7870,plain,((! [A:num]: ((set_ord_lessThan_nat @ (numeral_numeral_nat @ A)) = (insert_nat @ (pred_numeral @ A) @ (set_ord_lessThan_nat @ (pred_numeral @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[42])). 185.47/93.65 thf(4647,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((C != A) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3269_minf_I3_J)). 185.47/93.65 thf(22884,plain,((! [A:int]: ? [B:int]: ! [C:int]: (~ (C = A) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4647])). 185.47/93.65 thf(3167,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_724_add__diff__eq)). 185.47/93.65 thf(18200,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3167])). 185.47/93.65 thf(641,axiom,((! [A:real,B:nat]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ pi))) = (tan_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7974_tan__periodic__nat)). 185.47/93.65 thf(9861,plain,((! [A:real,B:nat]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ pi))) = (tan_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[641])). 185.47/93.65 thf(7499,axiom,((! [A:num,B:num]: ((times_times_num @ (bit1 @ A) @ (bit0 @ B)) = (bit0 @ (times_times_num @ (bit1 @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6390_semiring__norm_I15_J)). 185.47/93.65 thf(33282,plain,((! [A:num,B:num]: ((times_times_num @ (bit1 @ A) @ (bit0 @ B)) = (bit0 @ (times_times_num @ (bit1 @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7499])). 185.47/93.65 thf(4911,axiom,((! [A:real]: ((exp_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (power_power_real @ (exp_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8235_exp__double)). 185.47/93.65 thf(23795,plain,((! [A:real]: ((exp_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (power_power_real @ (exp_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4911])). 185.47/93.65 thf(5668,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4120_order__less__not__sym)). 185.47/93.65 thf(26599,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5668])). 185.47/93.65 thf(7330,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_int @ (times_times_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ (minus_minus_nat @ B @ A))) @ (semiri1406184849735516958ct_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8034_choose__dvd)). 185.47/93.65 thf(32707,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_int @ (times_times_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ (minus_minus_nat @ B @ A))) @ (semiri1406184849735516958ct_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7330])). 185.47/93.65 thf(5817,axiom,((! [A:int,B:num]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ B))) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) | ((ord_less_eq_int @ zero_zero_int @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4533_zero__le__power__eq__numeral)). 185.47/93.65 thf(27248,plain,((! [A:int,B:num]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ B))) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) | ((ord_less_eq_int @ zero_zero_int @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5817])). 185.47/93.65 thf(6851,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_755_diff__le__mono2)). 185.47/93.65 thf(30937,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6851])). 185.47/93.65 thf(4482,axiom,((comm_s2602460028002588243omplex = (^ [A:complex,B:nat]: (if_complex @ (B = zero_zero_nat) @ one_one_complex @ (set_fo1517530859248394432omplex @ (^ [C:nat]: (times_times_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8601_pochhammer__code)). 185.47/93.65 thf(22351,plain,(((comm_s2602460028002588243omplex) = (^ [A:complex,B:nat]: (if_complex @ (B = zero_zero_nat) @ one_one_complex @ (set_fo1517530859248394432omplex @ (^ [C:nat]: (times_times_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4482])). 185.47/93.65 thf(5875,axiom,((! [A:int,B:nat]: (((power_power_int @ A @ B) = zero_zero_int) = ((A = zero_zero_int) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1843_power__eq__0__iff)). 185.47/93.65 thf(27445,plain,((! [A:int,B:nat]: (((power_power_int @ A @ B) = zero_zero_int) = ((A = zero_zero_int) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5875])). 185.47/93.65 thf(2450,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ B) = (((ord_less_eq_rat @ B @ zero_zero_rat) => (ord_less_rat @ one_one_rat @ A)) & ((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ one_one_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2828_mult__less__cancel__right2)). 185.47/93.65 thf(15843,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ B) = (((ord_less_eq_rat @ B @ zero_zero_rat) => (ord_less_rat @ one_one_rat @ A)) & ((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ one_one_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2450])). 185.47/93.65 thf(6057,axiom,(((abs_abs_real @ (uminus_uminus_real @ one_one_real)) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6379_abs__neg__one)). 185.47/93.65 thf(28060,plain,(((abs_abs_real @ (uminus_uminus_real @ one_one_real)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6057])). 185.47/93.65 thf(4614,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ D))) @ (plus_plus_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ C)) @ (abs_abs_rat @ (minus_minus_rat @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6586_abs__diff__triangle__ineq)). 185.47/93.65 thf(22773,plain,((! [A:rat,B:rat,C:rat,D:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ D))) @ (plus_plus_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ C)) @ (abs_abs_rat @ (minus_minus_rat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4614])). 185.47/93.65 thf(5765,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((plus_plus_nat @ (times_times_nat @ A @ C) @ D) = (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (D = (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_852_nat__eq__add__iff2)). 185.47/93.65 thf(26906,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((plus_plus_nat @ (times_times_nat @ A @ C) @ D) = (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (D = (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5765])). 185.47/93.65 thf(1660,axiom,(((mi = ma) => (! [A:vEBT_VEBT]: ((~ (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B))) <= (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178__C4_Ohyps_C_I8_J)). 185.47/93.65 thf(13301,plain,(((mi = ma) => (! [A:vEBT_VEBT]: (~ (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B)) | ~ (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660])). 185.47/93.65 thf(378,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_real @ A @ one_one_real) => ((cos_real @ (arcsin @ A)) != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8319_cos__arcsin__nonzero)). 185.47/93.65 thf(8994,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_real @ A @ one_one_real) => (~ ((cos_real @ (arcsin @ A)) = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])). 185.47/93.65 thf(1199,axiom,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ (binomial @ B @ A)) = (divide_divide_real @ (semiri2265585572941072030t_real @ B) @ (times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ B @ A))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8555_binomial__fact)). 185.47/93.65 thf(11768,plain,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ (binomial @ B @ A)) = (divide_divide_real @ (semiri2265585572941072030t_real @ B) @ (times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ B @ A))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199])). 185.47/93.65 thf(6914,axiom,((! [A:rat]: ((times_times_rat @ (numeral_numeral_rat @ one) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_mult__numeral__1)). 185.47/93.65 thf(31176,plain,((! [A:rat]: ((times_times_rat @ (numeral_numeral_rat @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6914])). 185.47/93.65 thf(6461,axiom,((! [A:nat,B:nat]: ((((divide_divide_nat @ B @ A) = zero_zero_nat) = (B = zero_zero_nat)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4727_dvd__div__eq__0__iff)). 185.47/93.65 thf(29526,plain,((! [A:nat,B:nat]: ((((divide_divide_nat @ B @ A) = zero_zero_nat) = (B = zero_zero_nat)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6461])). 185.47/93.65 thf(3113,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ (minus_minus_real @ (uminus_uminus_real @ A) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (ln_ln_real @ (minus_minus_real @ one_one_real @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6238_ln__one__minus__pos__lower__bound)). 185.47/93.65 thf(18036,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ (minus_minus_real @ (uminus_uminus_real @ A) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (ln_ln_real @ (minus_minus_real @ one_one_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3113])). 185.47/93.65 thf(7004,axiom,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) != zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6664_cong__exp__iff__simps_I3_J)). 185.47/93.65 thf(31564,plain,((! [A:num,B:num]: ~ ((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7004])). 185.47/93.65 thf(2113,axiom,((! [A:(int > (int > $o)),B:int,C:int]: (((A @ B @ C) <= (! [D:int,E:int]: ((A @ E @ D) => (A @ D @ E)))) <= (! [D:int,E:int]: ((ord_less_eq_int @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3883_linorder__wlog)). 185.47/93.65 thf(14766,plain,((! [A:(int > (int > $o)),B:int,C:int]: ((A @ B @ C) | ~ (! [D:int,E:int]: ((A @ E @ D) => (A @ D @ E))) | ~ (! [D:int,E:int]: ((ord_less_eq_int @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2113])). 185.47/93.65 thf(3457,axiom,(((neg_numeral_dbl_real @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3822_dbl__simps_I2_J)). 185.47/93.65 thf(19099,plain,(((neg_numeral_dbl_real @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3457])). 185.47/93.65 thf(3337,axiom,((ring_1_of_int_real = (^ [A:int]: (if_real @ (A = zero_zero_int) @ zero_zero_real @ (if_real @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_real @ (ring_1_of_int_real @ (uminus_uminus_int @ A))) @ (if_real @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (ring_1_of_int_real @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (ring_1_of_int_real @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_real))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6854_of__int__code__if)). 185.47/93.65 thf(18722,plain,(((ring_1_of_int_real) = (^ [A:int]: (if_real @ (A = zero_zero_int) @ zero_zero_real @ (if_real @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_real @ (ring_1_of_int_real @ (uminus_uminus_int @ A))) @ (if_real @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (ring_1_of_int_real @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (ring_1_of_int_real @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3337])). 185.47/93.65 thf(1970,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2452_zero__le__power)). 185.47/93.65 thf(14323,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1970])). 185.47/93.65 thf(3809,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1134_comm__semiring__class_Odistrib)). 185.47/93.65 thf(20240,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3809])). 185.47/93.65 thf(3604,axiom,((! [A:num]: ~ (ord_less_rat @ one_one_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5957_not__one__less__neg__numeral)). 185.47/93.65 thf(19571,plain,((! [A:num]: ~ (ord_less_rat @ one_one_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3604])). 185.47/93.65 thf(3591,axiom,((! [A:real]: ? [B:int]: (ord_less_real @ (ring_1_of_int_real @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7438_ex__of__int__less)). 185.47/93.65 thf(19534,plain,((! [A:real]: ? [B:int]: (ord_less_real @ (ring_1_of_int_real @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3591])). 185.47/93.65 thf(3913,axiom,((! [A:num]: ((plus_plus_rat @ one_one_rat @ (numeral_numeral_rat @ A)) = (plus_plus_rat @ (numeral_numeral_rat @ A) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_826_one__plus__numeral__commute)). 185.47/93.65 thf(20565,plain,((! [A:num]: ((plus_plus_rat @ one_one_rat @ (numeral_numeral_rat @ A)) = (plus_plus_rat @ (numeral_numeral_rat @ A) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3913])). 185.47/93.65 thf(6853,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((((B != none_nat) <= (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ (! [C:nat,D:nat]: ((B != (some_nat @ D)) <= (? [E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))))))) <= (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((D) => (B = (some_nat @ one_one_nat))) & ((((~ (C)) => (B = none_nat)) & ((C) => (B = (some_nat @ zero_zero_nat)))) <= (~ (D)))))))) <= ((vEBT_vebt_maxt @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2893_vebt__maxt_Oelims)). 185.47/93.65 thf(30943,plain,((! [A:vEBT_VEBT,B:option_nat]: (((~ (B = none_nat) | ~ (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ (! [C:nat,D:nat]: (~ (B = (some_nat @ D)) | ~ (? [E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))))))) | ~ (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((D) => (B = (some_nat @ one_one_nat))) & ((((~ (C)) => (B = none_nat)) & ((C) => (B = (some_nat @ zero_zero_nat)))) | (D)))))) | ~ ((vEBT_vebt_maxt @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6853])). 185.47/93.65 thf(6496,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (times_times_nat @ (modulo_modulo_nat @ A @ B) @ (modulo_modulo_nat @ C @ B)) @ B) = (modulo_modulo_nat @ (times_times_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1985_mod__mult__eq)). 185.47/93.65 thf(29650,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (times_times_nat @ (modulo_modulo_nat @ A @ B) @ (modulo_modulo_nat @ C @ B)) @ B) = (modulo_modulo_nat @ (times_times_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6496])). 185.47/93.65 thf(5580,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_nat @ (minus_minus_nat @ B @ C) @ (minus_minus_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_907_diff__le__diff__pow)). 185.47/93.65 thf(26302,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_nat @ (minus_minus_nat @ B @ C) @ (minus_minus_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5580])). 185.47/93.65 thf(5997,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (((plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ one_one_nat) = (divide_divide_nat @ A @ B)) <= (ord_less_eq_nat @ B @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2801_divmod__digit__1_I1_J)). 185.47/93.65 thf(27882,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (((plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ one_one_nat) = (divide_divide_nat @ A @ B)) | ~ (ord_less_eq_nat @ B @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5997])). 185.47/93.65 thf(7050,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3931_order__eq__refl)). 185.47/93.65 thf(31749,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7050])). 185.47/93.65 thf(4880,axiom,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ A) @ B) = (times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5549_minus__mult__commute)). 185.47/93.65 thf(23671,plain,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ A) @ B) = (times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4880])). 185.47/93.65 thf(7427,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_eq_nat @ A @ B) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4170_antisym__conv1)). 185.47/93.65 thf(33031,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_eq_nat @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7427])). 185.47/93.65 thf(1147,axiom,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ A @ (suc @ B)) = (times_times_rat @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ (comm_s4028243227959126397er_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8500_pochhammer__rec_H)). 185.47/93.65 thf(11619,plain,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ A @ (suc @ B)) = (times_times_rat @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ (comm_s4028243227959126397er_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147])). 185.47/93.65 thf(2632,axiom,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ A @ B) = (insert_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9429_Icc__eq__insert__lb__nat)). 185.47/93.65 thf(16460,plain,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ A @ B) = (insert_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2632])). 185.47/93.65 thf(869,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (? [B:real]: ((ord_less_real @ A @ (tan_real @ B)) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8054_lemma__tan__total)). 185.47/93.65 thf(10699,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (? [B:real]: ((ord_less_real @ A @ (tan_real @ B)) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[869])). 185.47/93.65 thf(4030,axiom,((! [A:rat]: (ord_less_eq_rat @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A)) @ (plus_plus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7631_of__int__round__le)). 185.47/93.65 thf(20931,plain,((! [A:rat]: (ord_less_eq_rat @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A)) @ (plus_plus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4030])). 185.47/93.65 thf(2525,axiom,((! [A:rat,B:rat,C:(rat > rat),D:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (C @ B) @ D) => ((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_rat @ (C @ E) @ (C @ F)))) => (ord_less_rat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4114_order__less__subst2)). 185.47/93.65 thf(16104,plain,((! [A:rat,B:rat,C:(rat > rat),D:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (C @ B) @ D) => ((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_rat @ (C @ E) @ (C @ F)))) => (ord_less_rat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2525])). 185.47/93.65 thf(3682,axiom,((! [A:rat,B:rat]: (((abs_abs_rat @ (divide_divide_rat @ B @ A)) = (divide_divide_rat @ (abs_abs_rat @ B) @ (abs_abs_rat @ A))) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6507_nonzero__abs__divide)). 185.47/93.65 thf(19813,plain,((! [A:rat,B:rat]: (((abs_abs_rat @ (divide_divide_rat @ B @ A)) = (divide_divide_rat @ (abs_abs_rat @ B) @ (abs_abs_rat @ A))) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3682])). 185.47/93.65 thf(2164,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ (cos_complex @ A) @ (cos_complex @ B)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (cos_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (cos_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7894_cos__plus__cos)). 185.47/93.65 thf(14943,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ (cos_complex @ A) @ (cos_complex @ B)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (cos_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (cos_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2164])). 185.47/93.65 thf(6105,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_780_nat__mult__1)). 185.47/93.65 thf(28235,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6105])). 185.47/93.65 thf(1281,axiom,((ord_less_eq_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2274_linordered__nonzero__semiring__class_Ozero__le__one)). 185.47/93.65 thf(12012,plain,((ord_less_eq_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281])). 185.47/93.65 thf(4700,axiom,((! [A:rat,B:rat]: (((~ (ord_less_rat @ A @ B)) => (ord_less_rat @ B @ A)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4049_linorder__neqE)). 185.47/93.65 thf(23072,plain,((! [A:rat,B:rat]: (((~ (ord_less_rat @ A @ B)) => (ord_less_rat @ B @ A)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4700])). 185.47/93.65 thf(1091,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (ord_max_nat @ B @ C)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3722_less__max__iff__disj)). 185.47/93.65 thf(11439,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (ord_max_nat @ B @ C)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091])). 185.47/93.65 thf(6798,axiom,((! [A:nat]: (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = (uminus_uminus_rat @ one_one_rat))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6230_minus__one__power__iff)). 185.47/93.65 thf(30727,plain,((! [A:nat]: (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = (uminus_uminus_rat @ one_one_rat))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6798])). 185.47/93.65 thf(4132,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_eq_set_nat @ (nat_set_decode @ A) @ (nat_set_decode @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4915_subset__decode__imp__le)). 185.47/93.65 thf(21238,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_set_nat @ (nat_set_decode @ A) @ (nat_set_decode @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4132])). 185.47/93.65 thf(6787,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (times_times_nat @ B @ (semiri1316708129612266289at_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7184_mult__of__nat__commute)). 185.47/93.65 thf(30691,plain,((! [A:nat,B:nat]: ((times_times_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (times_times_nat @ B @ (semiri1316708129612266289at_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6787])). 185.47/93.65 thf(2323,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ A @ (divide_divide_rat @ (plus_plus_rat @ A @ B) @ (numeral_numeral_rat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_field__less__half__sum)). 185.47/93.65 thf(15434,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ A @ (divide_divide_rat @ (plus_plus_rat @ A @ B) @ (numeral_numeral_rat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2323])). 185.47/93.65 thf(4545,axiom,((! [A:(nat > nat),B:nat]: ((! [C:nat]: (ord_less_eq_nat @ C @ (A @ C))) => (finite_finite_nat @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ (A @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3402_finite__less__ub)). 185.47/93.65 thf(22559,plain,((! [A:(nat > nat),B:nat]: ((! [C:nat]: (ord_less_eq_nat @ C @ (A @ C))) => (finite_finite_nat @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ (A @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4545])). 185.47/93.65 thf(4052,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_int @ C @ B) => ((ord_less_eq_int @ zero_zero_int @ D) => ((ord_less_eq_int @ zero_zero_int @ E) => (((plus_plus_int @ D @ E) = one_one_int) => (ord_less_int @ (plus_plus_int @ (times_times_int @ D @ A) @ (times_times_int @ E @ C)) @ B))))) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2922_convex__bound__lt)). 185.47/93.65 thf(20989,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_int @ C @ B) => ((ord_less_eq_int @ zero_zero_int @ D) => ((ord_less_eq_int @ zero_zero_int @ E) => (((plus_plus_int @ D @ E) = one_one_int) => (ord_less_int @ (plus_plus_int @ (times_times_int @ D @ A) @ (times_times_int @ E @ C)) @ B))))) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4052])). 185.47/93.65 thf(4218,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ (sin_complex @ A) @ (sin_complex @ B)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sin_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (cos_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7856_sin__diff__sin)). 185.47/93.65 thf(21502,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ (sin_complex @ A) @ (sin_complex @ B)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sin_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (cos_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4218])). 185.47/93.65 thf(3380,axiom,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ B)) = (uminus1351360451143612070nteger @ (times_3573771949741848930nteger @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5083_mult__minus__right)). 185.47/93.65 thf(18864,plain,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ B)) = (uminus1351360451143612070nteger @ (times_3573771949741848930nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3380])). 185.47/93.65 thf(46,axiom,((! [A:rat,B:nat,C:rat]: ((minus_minus_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ C @ B)) = (times_times_rat @ (minus_minus_rat @ A @ C) @ (groups2906978787729119204at_rat @ (^ [D:nat]: (times_times_rat @ (power_power_rat @ C @ (minus_minus_nat @ B @ (suc @ D))) @ (power_power_rat @ A @ D))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7617_power__diff__sumr2)). 185.47/93.65 thf(7881,plain,((! [A:rat,B:nat,C:rat]: ((minus_minus_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ C @ B)) = (times_times_rat @ (minus_minus_rat @ A @ C) @ (groups2906978787729119204at_rat @ (^ [D:nat]: (times_times_rat @ (power_power_rat @ C @ (minus_minus_nat @ B @ (suc @ D))) @ (power_power_rat @ A @ D))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 185.47/93.65 thf(6176,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (binomial @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8426_zero__less__binomial__iff)). 185.47/93.65 thf(28515,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (binomial @ A @ B)) = (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6176])). 185.47/93.65 thf(1183,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ C @ B))) = ((B = D) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6288_crossproduct__eq)). 185.47/93.65 thf(11719,plain,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ C @ B))) = ((B = D) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183])). 185.47/93.65 thf(7453,axiom,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (plus_plus_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) @ (divide_divide_nat @ (plus_plus_nat @ (modulo_modulo_nat @ A @ C) @ (modulo_modulo_nat @ B @ C)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2165_div__add1__eq)). 185.47/93.65 thf(33104,plain,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (plus_plus_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) @ (divide_divide_nat @ (plus_plus_nat @ (modulo_modulo_nat @ A @ C) @ (modulo_modulo_nat @ B @ C)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7453])). 185.47/93.65 thf(3991,axiom,((! [A:real,B:real,C:real]: ((((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ B @ A))) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9092_powr__mono2_H)). 185.47/93.65 thf(20807,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ B @ A))) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3991])). 185.47/93.65 thf(1936,axiom,((! [A:int,B:int,C:nat,D:nat]: (((~ (((sgn_sgn_int @ A) = zero_zero_int) | (C = zero_zero_nat) | ((sgn_sgn_int @ B) = zero_zero_int))) => ((((modulo_modulo_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ (modulo_modulo_nat @ D @ C)))) <= ((sgn_sgn_int @ B) = (sgn_sgn_int @ A))) & (((modulo_modulo_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (times_times_int @ (sgn_sgn_int @ A) @ (minus_minus_int @ (semiri1314217659103216013at_int @ (times_times_nat @ C @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ C @ D))))) @ (semiri1314217659103216013at_int @ (modulo_modulo_nat @ D @ C))))) <= ((sgn_sgn_int @ B) != (sgn_sgn_int @ A))))) & ((((sgn_sgn_int @ A) = zero_zero_int) | ((sgn_sgn_int @ B) = zero_zero_int) | (C = zero_zero_nat)) => ((modulo_modulo_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9211_modulo__int__unfold)). 185.47/93.65 thf(14199,plain,((! [A:int,B:int,C:nat,D:nat]: (((~ (((sgn_sgn_int @ A) = zero_zero_int) | (C = zero_zero_nat) | ((sgn_sgn_int @ B) = zero_zero_int))) => ((((modulo_modulo_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ (modulo_modulo_nat @ D @ C)))) | ~ ((sgn_sgn_int @ B) = (sgn_sgn_int @ A))) & (((modulo_modulo_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (times_times_int @ (sgn_sgn_int @ A) @ (minus_minus_int @ (semiri1314217659103216013at_int @ (times_times_nat @ C @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ C @ D))))) @ (semiri1314217659103216013at_int @ (modulo_modulo_nat @ D @ C))))) | ((sgn_sgn_int @ B) = (sgn_sgn_int @ A))))) & ((((sgn_sgn_int @ A) = zero_zero_int) | ((sgn_sgn_int @ B) = zero_zero_int) | (C = zero_zero_nat)) => ((modulo_modulo_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1936])). 185.47/93.65 thf(4873,axiom,((! [A:num]: ~ (ord_less_rat @ zero_zero_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5905_not__zero__less__neg__numeral)). 185.47/93.65 thf(23649,plain,((! [A:num]: ~ (ord_less_rat @ zero_zero_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4873])). 185.47/93.65 thf(1105,axiom,((! [A:rat]: (ord_less_eq_rat @ (minus_minus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7633_of__int__round__ge)). 185.47/93.65 thf(11484,plain,((! [A:rat]: (ord_less_eq_rat @ (minus_minus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105])). 185.47/93.65 thf(5788,axiom,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_real @ one_one_real @ (power_power_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2898_one__less__power)). 185.47/93.65 thf(26983,plain,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_real @ one_one_real @ (power_power_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5788])). 185.47/93.65 thf(2555,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (uminus_uminus_real @ B)) = (ord_less_real @ B @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5518_less__minus__iff)). 185.47/93.65 thf(16205,plain,((! [A:real,B:real]: ((ord_less_real @ A @ (uminus_uminus_real @ B)) = (ord_less_real @ B @ (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2555])). 185.47/93.65 thf(4938,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ A) @ B) = (times_times_complex @ A @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5547_minus__mult__commute)). 185.47/93.65 thf(23903,plain,((! [A:complex,B:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ A) @ B) = (times_times_complex @ A @ (uminus1482373934393186551omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4938])). 185.47/93.65 thf(2607,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_real @ B @ (times_times_real @ C @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2703_pos__divide__less__eq)). 185.47/93.65 thf(16386,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_real @ B @ (times_times_real @ C @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2607])). 185.47/93.65 thf(7180,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2613_mult__le__less__imp__less)). 185.47/93.65 thf(32186,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7180])). 185.47/93.65 thf(5629,axiom,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit1 @ one))) => (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6759_odd__mod__4__div__2)). 185.47/93.65 thf(26467,plain,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit1 @ one))) => (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5629])). 185.47/93.65 thf(3726,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1574_division__ring__divide__zero)). 185.47/93.65 thf(19967,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3726])). 185.47/93.65 thf(1551,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4093_order__less__irrefl)). 185.47/93.65 thf(12878,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551])). 185.47/93.65 thf(3881,axiom,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o),C:vEBT_VEBT]: (((B @ C) <= (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A))) <= (! [D:nat]: ((B @ (nth_VEBT_VEBT @ A @ D)) <= (ord_less_nat @ D @ (size_s6755466524823107622T_VEBT @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_all__nth__imp__all__set)). 185.47/93.65 thf(20459,plain,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o),C:vEBT_VEBT]: ((B @ C) | ~ (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A)) | ~ (! [D:nat]: ((B @ (nth_VEBT_VEBT @ A @ D)) | ~ (ord_less_nat @ D @ (size_s6755466524823107622T_VEBT @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3881])). 185.47/93.65 thf(6541,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2789_nat__mult__le__cancel1)). 185.47/93.65 thf(29811,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6541])). 185.47/93.65 thf(1337,axiom,((! [A:real,B:(rat > real),C:rat,D:rat]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_rat @ E @ F))) => (ord_less_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4099_order__less__subst1)). 185.47/93.65 thf(12190,plain,((! [A:real,B:(rat > real),C:rat,D:rat]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_rat @ E @ F))) => (ord_less_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337])). 185.47/93.65 thf(1854,axiom,((! [A:int,B:num,C:nat]: ((ord_le6747313008572928689nteger @ (ring_18347121197199848620nteger @ A) @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (ord_less_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7171_of__int__less__neg__numeral__power__cancel__iff)). 185.47/93.65 thf(13949,plain,((! [A:int,B:num,C:nat]: ((ord_le6747313008572928689nteger @ (ring_18347121197199848620nteger @ A) @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (ord_less_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854])). 185.47/93.65 thf(3354,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (uminus_uminus_int @ B)) = (ord_less_int @ B @ (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5519_less__minus__iff)). 185.47/93.65 thf(18784,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (uminus_uminus_int @ B)) = (ord_less_int @ B @ (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3354])). 185.47/93.65 thf(1231,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_is__num__normalize_I1_J)). 185.47/93.65 thf(11865,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231])). 185.47/93.65 thf(3781,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => ((ord_less_eq_int @ B @ one_one_int) => (ord_less_eq_int @ (times_times_int @ A @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2671_mult__right__le__one__le)). 185.47/93.65 thf(20152,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => ((ord_less_eq_int @ B @ one_one_int) => (ord_less_eq_int @ (times_times_int @ A @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3781])). 185.47/93.65 thf(4239,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ (minus_minus_rat @ B @ C)) = (ord_less_rat @ (plus_plus_rat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_less__diff__eq)). 185.47/93.65 thf(21564,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ (minus_minus_rat @ B @ C)) = (ord_less_rat @ (plus_plus_rat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4239])). 185.47/93.65 thf(2998,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((dvd_dvd_rat @ A @ B) => ((dvd_dvd_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)) <= (dvd_dvd_rat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4587_mult__dvd__mono)). 185.47/93.65 thf(17670,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((dvd_dvd_rat @ A @ B) => ((dvd_dvd_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)) | ~ (dvd_dvd_rat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2998])). 185.47/93.65 thf(908,axiom,((topolo6980174941875973593q_real = (^ [A:(nat > real)]: (! [B:nat]: (ord_less_eq_real @ (A @ B) @ (A @ (suc @ B))) | ! [B:nat]: (ord_less_eq_real @ (A @ (suc @ B)) @ (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8381_monoseq__Suc)). 185.47/93.65 thf(10843,plain,(((topolo6980174941875973593q_real) = (^ [A:(nat > real)]: (! [B:nat]: (ord_less_eq_real @ (A @ B) @ (A @ (suc @ B))) | ! [B:nat]: (ord_less_eq_real @ (A @ (suc @ B)) @ (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[908])). 185.47/93.65 thf(568,axiom,((! [A:nat]: (((archim6058952711729229775r_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A))) = (plus_plus_int @ (archim6058952711729229775r_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ one_one_int)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9132_floor__log2__div2)). 185.47/93.65 thf(9618,plain,((! [A:nat]: (((archim6058952711729229775r_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A))) = (plus_plus_int @ (archim6058952711729229775r_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ one_one_int)) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[568])). 185.47/93.65 thf(2172,axiom,((! [A:nat,B:nat]: ((ord_max_nat @ (suc @ A) @ (suc @ B)) = (suc @ (ord_max_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3592_max__Suc__Suc)). 185.47/93.65 thf(14978,plain,((! [A:nat,B:nat]: ((ord_max_nat @ (suc @ A) @ (suc @ B)) = (suc @ (ord_max_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2172])). 185.47/93.65 thf(6312,axiom,(((minus_minus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = (numeral_numeral_int @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5416_diff__numeral__special_I11_J)). 185.47/93.65 thf(28963,plain,(((minus_minus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = (numeral_numeral_int @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6312])). 185.47/93.65 thf(6010,axiom,((! [A:num,B:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6663_cong__exp__iff__simps_I3_J)). 185.47/93.65 thf(27926,plain,((! [A:num,B:num]: ~ ((modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6010])). 185.47/93.65 thf(5781,axiom,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (minus_minus_rat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_diff__right__commute)). 185.47/93.65 thf(26961,plain,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (minus_minus_rat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5781])). 185.47/93.65 thf(5632,axiom,((! [A:num]: ~ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2196_not__numeral__le__zero)). 185.47/93.65 thf(26477,plain,((! [A:num]: ~ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5632])). 185.47/93.65 thf(32,axiom,((! [A:real,B:nat]: ((ord_less_eq_nat @ (nat2 @ (archim7802044766580827645g_real @ A)) @ B) = (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9259_nat__ceiling__le__eq)). 185.47/93.65 thf(7834,plain,((! [A:real,B:nat]: ((ord_less_eq_nat @ (nat2 @ (archim7802044766580827645g_real @ A)) @ B) = (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 185.47/93.65 thf(6244,axiom,((! [A:real]: ((^ [B:real]: (times_times_real @ B @ A)) = (times_times_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1334_mult__commute__abs)). 185.47/93.65 thf(28743,plain,((! [A:real]: ((^ [B:real]: (times_times_real @ B @ A)) = (times_times_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6244])). 185.47/93.65 thf(3033,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_eq_real @ B @ (times_times_real @ C @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2842_pos__divide__le__eq)). 185.47/93.65 thf(17773,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_eq_real @ B @ (times_times_real @ C @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3033])). 185.47/93.65 thf(6593,axiom,((! [A:int,B:num,C:num]: ((times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ (power_power_int @ A @ (numeral_numeral_nat @ C))) = (power_power_int @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_power__add__numeral)). 185.47/93.65 thf(29985,plain,((! [A:int,B:num,C:num]: ((times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ (power_power_int @ A @ (numeral_numeral_nat @ C))) = (power_power_int @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6593])). 185.47/93.65 thf(5809,axiom,((! [A:num]: ((~ (ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)))) = (A != one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5377_not__neg__one__le__neg__numeral__iff)). 185.47/93.65 thf(27127,plain,((! [A:num]: ((~ (ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)))) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5809])). 185.47/93.65 thf(3425,axiom,((! [A:rat,B:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ B @ A)) = (dvd_dvd_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4437_dvd__add__triv__right__iff)). 185.47/93.65 thf(19006,plain,((! [A:rat,B:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ B @ A)) = (dvd_dvd_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3425])). 185.47/93.65 thf(3002,axiom,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ B) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1653_add__less__same__cancel2)). 185.47/93.65 thf(17683,plain,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ B) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3002])). 185.47/93.65 thf(3957,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (ord_max_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3740_max_Ostrict__coboundedI1)). 185.47/93.65 thf(20706,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (ord_max_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3957])). 185.47/93.65 thf(5485,axiom,((! [A:int]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_int) = (ord_less_eq_int @ (abs_abs_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6717_abs__square__le__1)). 185.47/93.65 thf(26000,plain,((! [A:int]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_int) = (ord_less_eq_int @ (abs_abs_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5485])). 185.47/93.65 thf(4151,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2978_sum__power2__le__zero__iff)). 185.47/93.65 thf(21293,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4151])). 185.47/93.65 thf(3793,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = ((ord_less_real @ B @ A) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4028_not__less__iff__gr__or__eq)). 185.47/93.65 thf(20188,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = ((ord_less_real @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3793])). 185.47/93.65 thf(1898,axiom,((! [A:num,B:nat]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7020_numeral__le__real__of__nat__iff)). 185.47/93.65 thf(14075,plain,((! [A:num,B:nat]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1898])). 185.47/93.65 thf(5091,axiom,((! [A:int]: ((uminus_uminus_int @ (uminus_uminus_int @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5026_add_Oinverse__inverse)). 185.47/93.65 thf(24461,plain,((! [A:int]: ((uminus_uminus_int @ (uminus_uminus_int @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5091])). 185.47/93.65 thf(7189,axiom,((! [A:num]: (((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = (uminus_uminus_rat @ one_one_rat)) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5289_numeral__eq__neg__one__iff)). 185.47/93.65 thf(32215,plain,((! [A:num]: (((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = (uminus_uminus_rat @ one_one_rat)) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7189])). 185.47/93.65 thf(3348,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B)) = (ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6684_abs__le__square__iff)). 185.47/93.65 thf(18767,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B)) = (ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3348])). 185.47/93.65 thf(7721,axiom,((! [A:num]: ((num_of_nat @ (numeral_numeral_nat @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9840_num__of__nat__numeral__eq)). 185.47/93.65 thf(33901,plain,((! [A:num]: ((num_of_nat @ (numeral_numeral_nat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7721])). 185.47/93.65 thf(3437,axiom,((! [A:real,B:real]: ((A = (abs_abs_real @ B)) = ((ord_less_eq_real @ zero_zero_real @ A) & ((B = A) | (B = (uminus_uminus_real @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6550_eq__abs__iff_H)). 185.47/93.65 thf(19043,plain,((! [A:real,B:real]: ((A = (abs_abs_real @ B)) = ((ord_less_eq_real @ zero_zero_real @ A) & ((B = A) | (B = (uminus_uminus_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3437])). 185.47/93.65 thf(2220,axiom,((! [A:rat]: ((ord_less_eq_rat @ A @ (uminus_uminus_rat @ A)) = (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5145_less__eq__neg__nonpos)). 185.47/93.65 thf(15118,plain,((! [A:rat]: ((ord_less_eq_rat @ A @ (uminus_uminus_rat @ A)) = (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2220])). 185.47/93.65 thf(7434,axiom,((semiri1316708129612266289at_nat = (^ [A:nat]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8957_of__nat__id)). 185.47/93.65 thf(33050,plain,(((semiri1316708129612266289at_nat) = (^ [A:nat]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7434])). 185.47/93.65 thf(3511,axiom,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1573_bits__div__0)). 185.47/93.65 thf(19290,plain,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3511])). 185.47/93.65 thf(3755,axiom,((! [A:nat]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ semiri5074537144036343181t_real @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7348_double__gauss__sum)). 185.47/93.65 thf(20057,plain,((! [A:nat]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ (semiri5074537144036343181t_real) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3755])). 185.47/93.65 thf(6960,axiom,((! [A:nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1769_power__Suc0__right)). 185.47/93.65 thf(31378,plain,((! [A:nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6960])). 185.47/93.65 thf(4713,axiom,((! [A:rat]: ((ord_less_rat @ (uminus_uminus_rat @ A) @ zero_zero_rat) = (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5165_neg__less__0__iff__less)). 185.47/93.65 thf(23116,plain,((! [A:rat]: ((ord_less_rat @ (uminus_uminus_rat @ A) @ zero_zero_rat) = (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4713])). 185.47/93.65 thf(2592,axiom,((! [A:nat]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ semiri8010041392384452111omplex @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7344_double__gauss__sum)). 185.47/93.65 thf(16339,plain,((! [A:nat]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ (semiri8010041392384452111omplex) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2592])). 185.47/93.65 thf(4265,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (minus_minus_rat @ C @ B) @ (minus_minus_rat @ C @ A)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_diff__left__mono)). 185.47/93.65 thf(21646,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (minus_minus_rat @ C @ B) @ (minus_minus_rat @ C @ A)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4265])). 185.47/93.65 thf(6753,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (vEBT_VEBT_lesseq @ (some_nat @ A) @ (some_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_lesseq__shift)). 185.47/93.65 thf(30567,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: (vEBT_VEBT_lesseq @ (some_nat @ A) @ (some_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6753])). 185.47/93.65 thf(6430,axiom,((! [A:num]: ((numera6690914467698888265omplex @ A) != (uminus1482373934393186551omplex @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5774_numeral__neq__neg__one)). 185.47/93.65 thf(29413,plain,((! [A:num]: ~ ((numera6690914467698888265omplex @ A) = (uminus1482373934393186551omplex @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6430])). 185.47/93.65 thf(6599,axiom,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) != (suc @ zero_zero_nat)) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1912_not__mod2__eq__Suc__0__eq__0)). 185.47/93.65 thf(30002,plain,((! [A:nat]: ((~ ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ zero_zero_nat))) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6599])). 185.47/93.65 thf(1543,axiom,((! [A:(nat > $o)]: ((bot_bot_set_nat = (collect_nat @ A)) = (! [B:nat]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1267_empty__Collect__eq)). 185.47/93.65 thf(12846,plain,((! [A:(nat > $o)]: ((bot_bot_set_nat = (collect_nat @ (A))) = (! [B:nat]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543])). 185.47/93.65 thf(5159,axiom,((! [A:real,B:real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5020_neg__equal__iff__equal)). 185.47/93.65 thf(24748,plain,((! [A:real,B:real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5159])). 185.47/93.65 thf(2748,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (plus_plus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_726_add__diff__eq)). 185.47/93.65 thf(16865,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (plus_plus_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2748])). 185.47/93.65 thf(2315,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (bit1 @ A)) = (plus_plus_complex @ (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A)) @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6627_numeral__code_I3_J)). 185.47/93.65 thf(15407,plain,((! [A:num]: ((numera6690914467698888265omplex @ (bit1 @ A)) = (plus_plus_complex @ (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A)) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2315])). 185.47/93.65 thf(3383,axiom,((! [A:rat,B:rat]: ((~ (ord_less_eq_rat @ A @ B)) = ((B != A) & (ord_less_eq_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3842_nle__le)). 185.47/93.65 thf(18873,plain,((! [A:rat,B:rat]: ((~ (ord_less_eq_rat @ A @ B)) = (~ (B = A) & (ord_less_eq_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3383])). 185.47/93.65 thf(5969,axiom,((! [A:int,B:num,C:nat]: (((nat2 @ A) = (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9258_nat__eq__numeral__power__cancel__iff)). 185.47/93.65 thf(27795,plain,((! [A:int,B:num,C:nat]: (((nat2 @ A) = (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5969])). 185.47/93.65 thf(4830,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ A @ B)) @ C) = ((ord_less_eq_int @ A @ (plus_plus_int @ B @ C)) & (ord_less_eq_int @ (minus_minus_int @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6591_abs__diff__le__iff)). 185.47/93.65 thf(23514,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ A @ B)) @ C) = ((ord_less_eq_int @ A @ (plus_plus_int @ B @ C)) & (ord_less_eq_int @ (minus_minus_int @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4830])). 185.47/93.65 thf(2536,axiom,((! [A:num,B:nat,C:nat]: ((ord_less_eq_rat @ (power_power_rat @ (numeral_numeral_rat @ A) @ B) @ (semiri681578069525770553at_rat @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7132_numeral__power__le__of__nat__cancel__iff)). 185.47/93.65 thf(16140,plain,((! [A:num,B:nat,C:nat]: ((ord_less_eq_rat @ (power_power_rat @ (numeral_numeral_rat @ A) @ B) @ (semiri681578069525770553at_rat @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2536])). 185.47/93.65 thf(5005,axiom,((! [A:int]: ((A = (uminus_uminus_int @ A)) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5042_equal__neg__zero)). 185.47/93.65 thf(24120,plain,((! [A:int]: ((A = (uminus_uminus_int @ A)) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5005])). 185.47/93.65 thf(3291,axiom,((! [A:nat]: ((semiri681578069525770553at_rat @ (suc @ A)) = (plus_plus_rat @ one_one_rat @ (semiri681578069525770553at_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7017_of__nat__Suc)). 185.47/93.65 thf(18576,plain,((! [A:nat]: ((semiri681578069525770553at_rat @ (suc @ A)) = (plus_plus_rat @ one_one_rat @ (semiri681578069525770553at_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3291])). 185.47/93.65 thf(1489,axiom,((! [A:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ one_one_real) = (ord_less_eq_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7083_of__int__le__1__iff)). 185.47/93.65 thf(12687,plain,((! [A:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ one_one_real) = (ord_less_eq_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489])). 185.47/93.65 thf(4428,axiom,((! [A:real,B:real]: ((dvd_dvd_real @ A @ B) => ((divide_divide_real @ B @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (divide_divide_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5807_dvd__div__neg)). 185.47/93.65 thf(22176,plain,((! [A:real,B:real]: ((dvd_dvd_real @ A @ B) => ((divide_divide_real @ B @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (divide_divide_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4428])). 185.47/93.65 thf(3951,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_add__diff__cancel__left_H)). 185.47/93.65 thf(20689,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3951])). 185.47/93.65 thf(5567,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_895_nat__less__add__iff1)). 185.47/93.65 thf(26261,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5567])). 185.47/93.65 thf(1649,axiom,((! [A:real,B:real]: (((A = B) | (ord_less_real @ A @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4366_order__le__imp__less__or__eq)). 185.47/93.65 thf(13218,plain,((! [A:real,B:real]: ((A = B) | (ord_less_real @ A @ B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649])). 185.47/93.65 thf(5228,axiom,(((mi != ma) => (! [A:nat]: (((((vEBT_VEBT_high @ ma @ na) = A) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ ma @ na))) & ! [B:nat]: (((ord_less_eq_nat @ B @ ma) & (ord_less_nat @ mi @ B)) <= (((vEBT_VEBT_high @ B @ na) = A) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ B @ na))))) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99__C4_Ohyps_C_I11_J)). 185.47/93.65 thf(24964,plain,(((~ (mi = ma)) => (! [A:nat]: (((((vEBT_VEBT_high @ ma @ na) = A) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ ma @ na))) & ! [B:nat]: (((ord_less_eq_nat @ B @ ma) & (ord_less_nat @ mi @ B)) | ~ (((vEBT_VEBT_high @ B @ na) = A) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ B @ na))))) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5228])). 185.47/93.65 thf(1477,axiom,((! [A:int,B:nat,C:nat]: (((ord_less_int @ A @ one_one_int) => ((ord_less_eq_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (ord_less_eq_nat @ C @ B))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1892_power__decreasing__iff)). 185.47/93.65 thf(12650,plain,((! [A:int,B:nat,C:nat]: (((ord_less_int @ A @ one_one_int) => ((ord_less_eq_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (ord_less_eq_nat @ C @ B))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477])). 185.47/93.65 thf(2114,axiom,((! [A:real,B:real]: (((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1816_less__divide__eq__1__pos)). 185.47/93.65 thf(14772,plain,((! [A:real,B:real]: (((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2114])). 185.47/93.65 thf(712,axiom,((! [A:num]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (A != one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5392_neg__numeral__less__neg__one__iff)). 185.47/93.65 thf(10102,plain,((! [A:num]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[712])). 185.47/93.65 thf(5105,axiom,(((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1888_one__div__two__eq__zero)). 185.47/93.65 thf(24508,plain,(((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5105])). 185.47/93.65 thf(2851,axiom,((! [A:real,B:real,C:num]: ((ord_less_real @ (divide_divide_real @ A @ B) @ (numeral_numeral_real @ C)) = (((ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ C) @ B)) <= (ord_less_real @ zero_zero_real @ B)) & ((((ord_less_real @ zero_zero_real @ (numeral_numeral_real @ C)) <= (~ (ord_less_real @ B @ zero_zero_real))) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ (numeral_numeral_real @ C) @ B) @ A))) <= (~ (ord_less_real @ zero_zero_real @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2861_divide__less__eq__numeral_I1_J)). 185.47/93.65 thf(17193,plain,((! [A:real,B:real,C:num]: ((ord_less_real @ (divide_divide_real @ A @ B) @ (numeral_numeral_real @ C)) = (((ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ C) @ B)) | ~ (ord_less_real @ zero_zero_real @ B)) & ((((ord_less_real @ zero_zero_real @ (numeral_numeral_real @ C)) | (ord_less_real @ B @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ (numeral_numeral_real @ C) @ B) @ A))) | (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2851])). 185.47/93.65 thf(6531,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_group__cancel_Oadd1)). 185.47/93.65 thf(29779,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((A = (plus_plus_nat @ B @ C)) => ((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6531])). 185.47/93.65 thf(5756,axiom,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_774_comm__monoid__mult__class_Omult__1)). 185.47/93.65 thf(26879,plain,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5756])). 185.47/93.65 thf(2928,axiom,((! [A:num]: (imaginary_unit != (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9002_complex__i__not__neg__numeral)). 185.47/93.65 thf(17440,plain,((! [A:num]: ~ (imaginary_unit = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2928])). 185.47/93.65 thf(106,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ A @ B) @ C) => (((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((archim7802044766580827645g_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ C))) = (plus_plus_int @ (semiri1314217659103216013at_int @ B) @ one_one_int))) <= (ord_less_eq_nat @ C @ (power_power_nat @ A @ (plus_plus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9063_ceiling__log__nat__eq__if)). 185.47/93.65 thf(8081,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ A @ B) @ C) => (((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((archim7802044766580827645g_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ C))) = (plus_plus_int @ (semiri1314217659103216013at_int @ B) @ one_one_int))) | ~ (ord_less_eq_nat @ C @ (power_power_nat @ A @ (plus_plus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 185.47/93.65 thf(3990,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2216_mult__nonneg__nonpos)). 185.47/93.65 thf(20804,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3990])). 185.47/93.65 thf(780,axiom,((! [A:int,B:real]: ((ord_less_real @ (ring_1_of_int_real @ A) @ B) => (((archim6058952711729229775r_real @ B) = A) <= (ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9111_floor__eq)). 185.47/93.65 thf(10394,plain,((! [A:int,B:real]: ((ord_less_real @ (ring_1_of_int_real @ A) @ B) => (((archim6058952711729229775r_real @ B) = A) | ~ (ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[780])). 185.47/93.65 thf(5471,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ C @ (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_790_le__add__diff)). 185.47/93.65 thf(25944,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ C @ (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5471])). 185.47/93.65 thf(6992,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3878_order__trans)). 185.47/93.65 thf(31520,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6992])). 185.47/93.65 thf(705,axiom,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: ((if_Pro6206227464963214023at_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T)). 185.47/93.65 thf(10084,plain,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: ((if_Pro6206227464963214023at_nat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[705])). 185.47/93.65 thf(5334,axiom,((! [A:rat,B:num]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ (power_power_rat @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1365_power__numeral__even)). 185.47/93.65 thf(25360,plain,((! [A:rat,B:num]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ (power_power_rat @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5334])). 185.47/93.65 thf(6833,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1479_le__zero__eq)). 185.47/93.65 thf(30847,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6833])). 185.47/93.65 thf(5606,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) != zero_zero_nat) => ((B != zero_zero_nat) & (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2046_mult__not__zero)). 185.47/93.65 thf(26382,plain,((! [A:nat,B:nat]: ((~ ((times_times_nat @ A @ B) = zero_zero_nat)) => (~ (B = zero_zero_nat) & ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5606])). 185.47/93.65 thf(3826,axiom,((! [A:int,B:int,C:int]: ((B = C) <= ((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_add__left__imp__eq)). 185.47/93.65 thf(20284,plain,((! [A:int,B:int,C:int]: ((B = C) | ~ ((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3826])). 185.47/93.65 thf(3267,axiom,((! [A:set_nat]: ((~ (finite_finite_nat @ A)) = (! [B:nat]: ? [C:nat]: ((member_nat @ C @ A) & (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7921_infinite__nat__iff__unbounded__le)). 185.47/93.65 thf(18503,plain,((! [A:set_nat]: ((~ (finite_finite_nat @ A)) = (! [B:nat]: ? [C:nat]: ((member_nat @ C @ A) & (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3267])). 185.47/93.65 thf(348,axiom,((! [A:real,B:real,C:(nat > complex),D:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((summable_real @ (^ [E:nat]: (times_times_real @ (real_V1022390504157884413omplex @ (C @ E)) @ (power_power_real @ A @ E)))) <= (! [E:nat]: (ord_less_eq_real @ (times_times_real @ (real_V1022390504157884413omplex @ (C @ E)) @ (power_power_real @ B @ E)) @ D))) <= (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7751_Abel__lemma)). 185.47/93.65 thf(8899,plain,((! [A:real,B:real,C:(nat > complex),D:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((summable_real @ (^ [E:nat]: (times_times_real @ (real_V1022390504157884413omplex @ (C @ E)) @ (power_power_real @ A @ E)))) | ~ (! [E:nat]: (ord_less_eq_real @ (times_times_real @ (real_V1022390504157884413omplex @ (C @ E)) @ (power_power_real @ B @ E)) @ D)) | ~ (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 185.47/93.65 thf(3064,axiom,((! [A:int]: ((ord_less_int @ (plus_plus_int @ A @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1641_double__add__less__zero__iff__single__add__less__zero)). 185.47/93.65 thf(17876,plain,((! [A:int]: ((ord_less_int @ (plus_plus_int @ A @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3064])). 185.47/93.65 thf(7623,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & ((F = A) | (F = B) | ((ord_less_nat @ F @ B) & (ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) & (vEBT_vebt_member @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) & (ord_less_nat @ A @ F)))) <= (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_member__inv)). 185.47/93.65 thf(33632,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & ((F = A) | (F = B) | ((ord_less_nat @ F @ B) & (ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) & (vEBT_vebt_member @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) & (ord_less_nat @ A @ F)))) | ~ (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7623])). 185.47/93.65 thf(3851,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => (ord_less_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_700_diff__strict__mono)). 185.47/93.65 thf(20367,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => (ord_less_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3851])). 185.47/93.65 thf(6740,axiom,((! [A:num,B:(num > num),C:num,D:num]: ((((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))) <= (ord_less_eq_num @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3943_ord__eq__le__subst)). 185.47/93.65 thf(30479,plain,((! [A:num,B:(num > num),C:num,D:num]: (((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))) | ~ (ord_less_eq_num @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6740])). 185.47/93.65 thf(7458,axiom,((! [A:vEBT_VEBT,B:nat]: ((((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((((C) <= (B = zero_zero_nat)) & (((B = one_one_nat) & ((D) <= (B = one_one_nat))) <= (B != zero_zero_nat))) <= (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B))))) => ((! [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((~ (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ zero_zero_nat @ D @ E) @ B))) <= (A = (vEBT_Node @ C @ zero_zero_nat @ D @ E)))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ (suc @ D) @ E @ F)) => ((accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ (suc @ D) @ E @ F) @ B)) => (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ A @ B))) <= (~ (vEBT_V5719532721284313246member @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3120_VEBT__internal_Onaive__member_Opelims_I3_J)). 185.47/93.65 thf(33119,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((((C) | ~ (B = zero_zero_nat)) & (((B = one_one_nat) & ((D) | ~ (B = one_one_nat))) | (B = zero_zero_nat))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B))))) => ((! [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ zero_zero_nat @ D @ E) @ B)) | ~ (A = (vEBT_Node @ C @ zero_zero_nat @ D @ E)))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ (suc @ D) @ E @ F)) => ((accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ (suc @ D) @ E @ F) @ B)) => (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))))))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ A @ B)) | (vEBT_V5719532721284313246member @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7458])). 185.47/93.65 thf(1313,axiom,((! [A:real,B:num,C:real]: ((ord_less_real @ (divide_divide_real @ A @ (numeral_numeral_real @ B)) @ C) = (ord_less_real @ A @ (times_times_real @ C @ (numeral_numeral_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_divide__less__eq__numeral1_I1_J)). 185.47/93.65 thf(12115,plain,((! [A:real,B:num,C:real]: ((ord_less_real @ (divide_divide_real @ A @ (numeral_numeral_real @ B)) @ C) = (ord_less_real @ A @ (times_times_real @ C @ (numeral_numeral_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313])). 185.47/93.65 thf(2366,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_real @ (times_times_real @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2705_pos__less__divide__eq)). 185.47/93.65 thf(15563,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_real @ (times_times_real @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2366])). 185.47/93.65 thf(6729,axiom,((! [A:num,B:num]: (((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5068_neg__numeral__eq__iff)). 185.47/93.65 thf(30443,plain,((! [A:num,B:num]: (((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6729])). 185.47/93.65 thf(1245,axiom,((! [A:int,B:num,C:nat]: ((ord_less_nat @ (nat2 @ A) @ (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9263_nat__less__numeral__power__cancel__iff)). 185.47/93.65 thf(11908,plain,((! [A:int,B:num,C:nat]: ((ord_less_nat @ (nat2 @ A) @ (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245])). 185.47/93.65 thf(4480,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ B) <= (ord_less_eq_rat @ (abs_abs_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6514_abs__le__D2)). 185.47/93.65 thf(22346,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ B) | ~ (ord_less_eq_rat @ (abs_abs_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4480])). 185.47/93.65 thf(5177,axiom,((! [A:num]: ((plus_plus_rat @ one_one_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_rat @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_one__plus__numeral)). 185.47/93.65 thf(24803,plain,((! [A:num]: ((plus_plus_rat @ one_one_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_rat @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5177])). 185.47/93.65 thf(2019,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) <= (ord_less_int @ zero_zero_int @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3143_zmult__zless__mono2)). 185.47/93.65 thf(14484,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) | ~ (ord_less_int @ zero_zero_int @ C) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2019])). 185.47/93.65 thf(4357,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (modulo_modulo_int @ A @ B) @ A) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3149_zmod__le__nonneg__dividend)). 185.47/93.65 thf(21958,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (modulo_modulo_int @ A @ B) @ A) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4357])). 185.47/93.65 thf(53,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7552_sum_OlessThan__Suc)). 185.47/93.65 thf(7906,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 185.47/93.65 thf(4511,axiom,((! [A:rat,B:rat,C:(rat > num),D:num]: ((((ord_less_num @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F))))) <= ((C @ B) = D)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4090_ord__less__eq__subst)). 185.47/93.65 thf(22447,plain,((! [A:rat,B:rat,C:(rat > num),D:num]: ((ord_less_num @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4511])). 185.47/93.65 thf(5539,axiom,((! [A:nat]: (dvd_dvd_nat @ one_one_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4639_one__dvd)). 185.47/93.65 thf(26182,plain,((! [A:nat]: (dvd_dvd_nat @ one_one_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5539])). 185.47/93.65 thf(4723,axiom,((minus_minus_complex = (^ [A:complex,B:complex]: (plus_plus_complex @ A @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5789_diff__conv__add__uminus)). 185.47/93.65 thf(23148,plain,(((minus_minus_complex) = (^ [A:complex,B:complex]: (plus_plus_complex @ A @ (uminus1482373934393186551omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4723])). 185.47/93.65 thf(5423,axiom,((! [A:nat,B:num]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_nat @ (times_times_nat @ A @ (power_power_nat @ A @ (numeral_numeral_nat @ B))) @ (power_power_nat @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6635_power__numeral__odd)). 185.47/93.65 thf(25664,plain,((! [A:nat,B:num]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_nat @ (times_times_nat @ A @ (power_power_nat @ A @ (numeral_numeral_nat @ B))) @ (power_power_nat @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5423])). 185.47/93.65 thf(1010,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (uminus_uminus_real @ (divide_divide_real @ B @ C))) = (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B))) & ((((ord_less_real @ A @ zero_zero_real) <= (~ (ord_less_real @ C @ zero_zero_real))) & ((ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C)) <= (ord_less_real @ C @ zero_zero_real))) <= (~ (ord_less_real @ zero_zero_real @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6144_less__minus__divide__eq)). 185.47/93.65 thf(11191,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (uminus_uminus_real @ (divide_divide_real @ B @ C))) = (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B))) & ((((ord_less_real @ A @ zero_zero_real) | (ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C)) | ~ (ord_less_real @ C @ zero_zero_real))) | (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010])). 185.47/93.65 thf(3368,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_add__left__mono)). 185.47/93.65 thf(18821,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3368])). 185.47/93.65 thf(2753,axiom,((! [A:rat,B:rat,C:(rat > nat),D:nat]: ((ord_less_eq_rat @ A @ B) => (((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3950_ord__le__eq__subst)). 185.47/93.65 thf(16880,plain,((! [A:rat,B:rat,C:(rat > nat),D:nat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2753])). 185.47/93.65 thf(3548,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2441_divide__strict__right__mono)). 185.47/93.65 thf(19396,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3548])). 185.47/93.65 thf(2157,axiom,((! [A:real,B:num,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B))) @ C) = (ord_less_eq_real @ (times_times_real @ C @ (uminus_uminus_real @ (numeral_numeral_real @ B))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5381_divide__le__eq__numeral1_I2_J)). 185.47/93.65 thf(14921,plain,((! [A:real,B:num,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B))) @ C) = (ord_less_eq_real @ (times_times_real @ C @ (uminus_uminus_real @ (numeral_numeral_real @ B))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2157])). 185.47/93.65 thf(2583,axiom,((! [A:int,B:(real > int),C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_less_int @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_int @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4077_ord__eq__less__subst)). 185.47/93.65 thf(16307,plain,((! [A:int,B:(real > int),C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_less_int @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_int @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2583])). 185.47/93.65 thf(6642,axiom,((! [A:nat,B:nat]: (((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((A = B) <= (ord_less_eq_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2939_power2__eq__imp__eq)). 185.47/93.65 thf(30139,plain,((! [A:nat,B:nat]: (((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((A = B) | ~ (ord_less_eq_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6642])). 185.47/93.65 thf(2106,axiom,(((neg_numeral_dbl_int @ zero_zero_int) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3824_dbl__simps_I2_J)). 185.47/93.65 thf(14745,plain,(((neg_numeral_dbl_int @ zero_zero_int) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2106])). 185.47/93.65 thf(5512,axiom,((! [A:real,B:nat]: (((ord_less_real @ A @ one_one_real) => (ord_less_real @ (power_power_real @ A @ (suc @ B)) @ one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2875_power__Suc__less__one)). 185.47/93.65 thf(26086,plain,((! [A:real,B:nat]: (((ord_less_real @ A @ one_one_real) => (ord_less_real @ (power_power_real @ A @ (suc @ B)) @ one_one_real)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5512])). 185.47/93.65 thf(2325,axiom,((! [A:int,B:nat]: ((ord_less_int @ one_one_int @ (power_power_int @ A @ (suc @ B))) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1112_power__gt1)). 185.47/93.65 thf(15439,plain,((! [A:int,B:nat]: ((ord_less_int @ one_one_int @ (power_power_int @ A @ (suc @ B))) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2325])). 185.47/93.65 thf(1137,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((~ (ord_less_eq_real @ C @ A)) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3303_pinf_I6_J)). 185.47/93.65 thf(11592,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (ord_less_eq_real @ C @ A) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137])). 185.47/93.65 thf(6438,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ B @ (power_power_nat @ B @ A)) <= ((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4918_dvd__power)). 185.47/93.65 thf(29436,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ B @ (power_power_nat @ B @ A)) | ~ ((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6438])). 185.47/93.65 thf(6653,axiom,((! [A:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ A @ A) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1719_div__self)). 185.47/93.65 thf(30178,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ A @ A) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6653])). 185.47/93.65 thf(7590,axiom,(((semiri5044797733671781792omplex @ (numeral_numeral_nat @ (bit0 @ one))) = (numera6690914467698888265omplex @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7976_fact__2)). 185.47/93.65 thf(33540,plain,(((semiri5044797733671781792omplex @ (numeral_numeral_nat @ (bit0 @ one))) = (numera6690914467698888265omplex @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7590])). 185.47/93.65 thf(3087,axiom,(((ring_1_of_int_real @ one_one_int) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6968_of__int__1)). 185.47/93.65 thf(17945,plain,(((ring_1_of_int_real @ one_one_int) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3087])). 185.47/93.65 thf(1008,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_740_diff__diff__eq)). 185.47/93.65 thf(11185,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008])). 185.47/93.65 thf(5878,axiom,((! [A:int,B:int]: ((A = (times_times_int @ B @ A)) = ((B = one_one_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1672_mult__cancel__right1)). 185.47/93.65 thf(27454,plain,((! [A:int,B:int]: ((A = (times_times_int @ B @ A)) = ((B = one_one_int) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5878])). 185.47/93.65 thf(1958,axiom,((! [A:rat,B:nat,C:nat]: (((comm_s4028243227959126397er_rat @ A @ B) = zero_zero_rat) => ((ord_less_eq_nat @ B @ C) => ((comm_s4028243227959126397er_rat @ A @ C) = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8440_pochhammer__eq__0__mono)). 185.47/93.65 thf(14280,plain,((! [A:rat,B:nat,C:nat]: (((comm_s4028243227959126397er_rat @ A @ B) = zero_zero_rat) => ((ord_less_eq_nat @ B @ C) => ((comm_s4028243227959126397er_rat @ A @ C) = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1958])). 185.47/93.65 thf(6877,axiom,((! [A:int,B:nat,C:nat]: ((A != zero_zero_int) => ((ord_less_eq_nat @ B @ C) => ((power_power_int @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2908_power__diff)). 185.47/93.65 thf(31058,plain,((! [A:int,B:nat,C:nat]: ((~ (A = zero_zero_int)) => ((ord_less_eq_nat @ B @ C) => ((power_power_int @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_int @ (power_power_int @ A @ C) @ (power_power_int @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6877])). 185.47/93.65 thf(6703,axiom,((! [A:nat]: ? [B:list_VEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_883_Ex__list__of__length)). 185.47/93.65 thf(30339,plain,((! [A:nat]: ? [B:list_VEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6703])). 185.47/93.65 thf(434,axiom,((! [A:num]: ((ord_max_int @ (numeral_numeral_int @ A) @ one_one_int) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3634_max__0__1_I6_J)). 185.47/93.65 thf(9177,plain,((! [A:num]: ((ord_max_int @ (numeral_numeral_int @ A) @ one_one_int) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[434])). 185.47/93.65 thf(272,axiom,((! [A:nat,B:real]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B) => ((ord_less_real @ B @ (semiri5074537144036343181t_real @ (suc @ A))) => ((nat2 @ (archim6058952711729229775r_real @ B)) = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9336_floor__eq4)). 185.47/93.65 thf(8623,plain,((! [A:nat,B:real]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B) => ((ord_less_real @ B @ (semiri5074537144036343181t_real @ (suc @ A))) => ((nat2 @ (archim6058952711729229775r_real @ B)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 185.47/93.65 thf(512,axiom,((! [A:real]: ((summable_real @ (power_power_real @ A)) <= (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7724_complete__algebra__summable__geometric)). 185.47/93.65 thf(9455,plain,((! [A:real]: ((summable_real @ (power_power_real @ A)) | ~ (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[512])). 185.47/93.65 thf(1095,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1139_distrib__right)). 185.47/93.65 thf(11452,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095])). 185.47/93.65 thf(7253,axiom,((! [A:rat]: ((A = (uminus_uminus_rat @ A)) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5043_equal__neg__zero)). 185.47/93.65 thf(32441,plain,((! [A:rat]: ((A = (uminus_uminus_rat @ A)) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7253])). 185.47/93.65 thf(3719,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2089_add_Ogroup__left__neutral)). 185.47/93.65 thf(19946,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3719])). 185.47/93.65 thf(462,axiom,((! [A:(complex > (complex > $o)),B:set_nat,C:(nat > complex),D:(nat > complex)]: ((((finite_finite_nat @ B) => ((! [E:nat]: ((A @ (C @ E) @ (D @ E)) <= (member_nat @ E @ B))) => (A @ (groups2073611262835488442omplex @ C @ B) @ (groups2073611262835488442omplex @ D @ B)))) <= (! [E:complex,F:complex,G:complex,H:complex]: (((A @ F @ H) & (A @ E @ G)) => (A @ (plus_plus_complex @ E @ F) @ (plus_plus_complex @ G @ H))))) <= (A @ zero_zero_complex @ zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5856_sum_Orelated)). 185.47/93.65 thf(9264,plain,((! [A:(complex > (complex > $o)),B:set_nat,C:(nat > complex),D:(nat > complex)]: (((finite_finite_nat @ B) => ((! [E:nat]: ((A @ (C @ E) @ (D @ E)) | ~ (member_nat @ E @ B))) => (A @ (groups2073611262835488442omplex @ (C) @ B) @ (groups2073611262835488442omplex @ (D) @ B)))) | ~ (! [E:complex,F:complex,G:complex,H:complex]: (((A @ F @ H) & (A @ E @ G)) => (A @ (plus_plus_complex @ E @ F) @ (plus_plus_complex @ G @ H)))) | ~ (A @ zero_zero_complex @ zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[462])). 185.47/93.65 thf(2083,axiom,((! [A:nat,B:nat]: (((ord_less_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B)) <= (ord_less_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8012_fact__less__mono)). 185.47/93.65 thf(14680,plain,((! [A:nat,B:nat]: ((ord_less_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B)) | ~ (ord_less_nat @ A @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2083])). 185.47/93.65 thf(1629,axiom,((ord_less_eq_rat = (^ [A:rat,B:rat]: ((A = B) | (ord_less_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4271_order__le__less)). 185.47/93.65 thf(13158,plain,(((ord_less_eq_rat) = (^ [A:rat,B:rat]: ((A = B) | (ord_less_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629])). 185.47/93.65 thf(875,axiom,((! [A:complex]: ? [B:complex,C:real]: (A = (times_times_complex @ (real_V4546457046886955230omplex @ C) @ (exp_complex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9139_complex__exp__exists)). 185.47/93.65 thf(10721,plain,((! [A:complex]: ? [B:complex,C:real]: (A = (times_times_complex @ (real_V4546457046886955230omplex @ C) @ (exp_complex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[875])). 185.47/93.65 thf(1735,axiom,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (power_power_nat @ A @ B)) = (power_power_real @ (semiri5074537144036343181t_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6959_of__nat__power)). 185.47/93.65 thf(13551,plain,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (power_power_nat @ A @ B)) = (power_power_real @ (semiri5074537144036343181t_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735])). 185.47/93.65 thf(3027,axiom,((abs_abs_real = (^ [A:real]: (if_real @ (ord_less_real @ A @ zero_zero_real) @ (uminus_uminus_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6568_abs__if__raw)). 185.47/93.65 thf(17755,plain,(((abs_abs_real) = (^ [A:real]: (if_real @ (ord_less_real @ A @ zero_zero_real) @ (uminus_uminus_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3027])). 185.47/93.65 thf(4267,axiom,((! [A:real,B:real,C:real]: ((divide_divide_real @ A @ (powr_real @ B @ C)) = (times_times_real @ A @ (powr_real @ B @ (uminus_uminus_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9102_divide__powr__uminus)). 185.47/93.65 thf(21651,plain,((! [A:real,B:real,C:real]: ((divide_divide_real @ A @ (powr_real @ B @ C)) = (times_times_real @ A @ (powr_real @ B @ (uminus_uminus_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4267])). 185.47/93.65 thf(5681,axiom,((! [A:nat,B:complex]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_complex @ (power_power_complex @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_complex @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2963_power__minus__mult)). 185.47/93.65 thf(26637,plain,((! [A:nat,B:complex]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_complex @ (power_power_complex @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_complex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5681])). 185.47/93.65 thf(756,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9528_int__numeral__or__not__num__neg)). 185.47/93.65 thf(10263,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[756])). 185.47/93.65 thf(1473,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (uminus_uminus_rat @ B)) = (ord_less_eq_rat @ B @ (uminus_uminus_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5508_le__minus__iff)). 185.47/93.65 thf(12640,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (uminus_uminus_rat @ B)) = (ord_less_eq_rat @ B @ (uminus_uminus_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473])). 185.47/93.65 thf(323,axiom,((! [A:nat,B:nat,C:(nat > int)]: ((((groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_int) <= (ord_less_nat @ (suc @ A) @ B)) & (((groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_int @ (groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) <= (~ (ord_less_nat @ (suc @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8708_prod_Ocl__ivl__Suc)). 185.47/93.65 thf(8810,plain,((! [A:nat,B:nat,C:(nat > int)]: ((((groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_int) | ~ (ord_less_nat @ (suc @ A) @ B)) & (((groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_int @ (groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) | (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[323])). 185.47/93.65 thf(872,axiom,((! [A:int,B:num]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (numeral_numeral_int @ B)) = (ord_less_int @ A @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7079_of__int__less__numeral__iff)). 185.47/93.65 thf(10710,plain,((! [A:int,B:num]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (numeral_numeral_int @ B)) = (ord_less_int @ A @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[872])). 185.47/93.65 thf(4381,axiom,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5947_neg__one__less__numeral)). 185.47/93.65 thf(22035,plain,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4381])). 185.47/93.65 thf(5160,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2510_nat__mult__less__cancel1)). 185.47/93.65 thf(24751,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5160])). 185.47/93.65 thf(5988,axiom,((! [A:int]: (((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) != zero_zero_int) = ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1910_not__mod__2__eq__0__eq__1)). 185.47/93.65 thf(27854,plain,((! [A:int]: ((~ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)) = ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5988])). 185.47/93.65 thf(2853,axiom,((! [A:rat,B:rat,C:(rat > num),D:num]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3920_order__subst2)). 185.47/93.65 thf(17200,plain,((! [A:rat,B:rat,C:(rat > num),D:num]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2853])). 185.47/93.65 thf(3402,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ (times_times_rat @ B @ C)) <= (dvd_dvd_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4602_dvd__mult2)). 185.47/93.65 thf(18937,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ (times_times_rat @ B @ C)) | ~ (dvd_dvd_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3402])). 185.47/93.65 thf(2726,axiom,((! [A:real,B:int]: ((ord_less_real @ (minus_minus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (ring_1_of_int_real @ B)) => ((ord_less_eq_real @ (ring_1_of_int_real @ B) @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))) => ((archim8280529875227126926d_real @ A) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7530_round__unique)). 185.47/93.65 thf(16801,plain,((! [A:real,B:int]: ((ord_less_real @ (minus_minus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (ring_1_of_int_real @ B)) => ((ord_less_eq_real @ (ring_1_of_int_real @ B) @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))) => ((archim8280529875227126926d_real @ A) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2726])). 185.47/93.65 thf(5035,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ B @ A)) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4009_dual__order_Oasym)). 185.47/93.65 thf(24209,plain,((! [A:num,B:num]: (~ (ord_less_num @ B @ A) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5035])). 185.47/93.65 thf(3506,axiom,((! [A:real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3024_double__eq__0__iff)). 185.47/93.65 thf(19273,plain,((! [A:real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3506])). 185.47/93.65 thf(6481,axiom,(((^ [A:int]: (A)) = (times_times_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1356_lambda__one)). 185.47/93.65 thf(29593,plain,(((^ [A:int]: (A)) = (times_times_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6481])). 185.47/93.65 thf(6792,axiom,((! [A:nat]: (((A != (suc @ zero_zero_nat)) => (~ (! [B:nat]: (A != (suc @ (suc @ B)))))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2112_vebt__buildup_Ocases)). 185.47/93.65 thf(30708,plain,((! [A:nat]: (((~ (A = (suc @ zero_zero_nat))) => (~ (! [B:nat]: ~ (A = (suc @ (suc @ B)))))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6792])). 185.47/93.65 thf(6421,axiom,((! [A:int,B:nat]: ((power_power_int @ (uminus_uminus_int @ A) @ B) = (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5994_power__minus)). 185.47/93.65 thf(29385,plain,((! [A:int,B:nat]: ((power_power_int @ (uminus_uminus_int @ A) @ B) = (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6421])). 185.47/93.65 thf(2224,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (times_times_int @ C @ B) @ (times_times_int @ C @ A)) <= (ord_less_eq_int @ C @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2244_mult__left__mono__neg)). 185.47/93.65 thf(15129,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (times_times_int @ C @ B) @ (times_times_int @ C @ A)) | ~ (ord_less_eq_int @ C @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2224])). 185.47/93.65 thf(934,axiom,((! [A:real,B:num]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ B) @ pi))) = (tan_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7973_tan__periodic__n)). 185.47/93.65 thf(10939,plain,((! [A:real,B:num]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ B) @ pi))) = (tan_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[934])). 185.47/93.65 thf(3131,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_max_nat @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3706_max_Oabsorb__iff2)). 185.47/93.65 thf(18087,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_max_nat @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3131])). 185.47/93.65 thf(3586,axiom,((! [A:num]: ~ (ord_le3102999989581377725nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5940_not__one__le__neg__numeral)). 185.47/93.65 thf(19519,plain,((! [A:num]: ~ (ord_le3102999989581377725nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3586])). 185.47/93.65 thf(6290,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (modulo_modulo_nat @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1940_unique__euclidean__semiring__numeral__class_Opos__mod__sign)). 185.47/93.65 thf(28895,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (modulo_modulo_nat @ B @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6290])). 185.47/93.65 thf(548,axiom,((! [A:(nat > real),B:real]: ((summable_real @ A) => (summable_real @ (^ [C:nat]: (times_times_real @ B @ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7663_summable__mult)). 185.47/93.65 thf(9554,plain,((! [A:(nat > real),B:real]: ((summable_real @ (A)) => (summable_real @ (^ [C:nat]: (times_times_real @ B @ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[548])). 185.47/93.65 thf(1132,axiom,((! [A:rat,B:rat]: ((A = (plus_plus_rat @ A @ B)) = (B = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6279_add__0__iff)). 185.47/93.65 thf(11570,plain,((! [A:rat,B:rat]: ((A = (plus_plus_rat @ A @ B)) = (B = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132])). 185.47/93.65 thf(3546,axiom,((! [A:complex,B:complex,C:complex]: ((A = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ C))) = ((((times_times_complex @ A @ C) = (uminus1482373934393186551omplex @ B)) <= (C != zero_zero_complex)) & ((C = zero_zero_complex) => (A = zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5973_eq__minus__divide__eq)). 185.47/93.65 thf(19390,plain,((! [A:complex,B:complex,C:complex]: ((A = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ C))) = ((((times_times_complex @ A @ C) = (uminus1482373934393186551omplex @ B)) | (C = zero_zero_complex)) & ((C = zero_zero_complex) => (A = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3546])). 185.47/93.65 thf(2690,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (sin_complex @ A) @ (sin_complex @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (cos_complex @ (minus_minus_complex @ A @ B)) @ (cos_complex @ (plus_plus_complex @ A @ B))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7848_sin__times__sin)). 185.47/93.65 thf(16687,plain,((! [A:complex,B:complex]: ((times_times_complex @ (sin_complex @ A) @ (sin_complex @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (cos_complex @ (minus_minus_complex @ A @ B)) @ (cos_complex @ (plus_plus_complex @ A @ B))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2690])). 185.47/93.65 thf(7159,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ (power_power_nat @ A @ (suc @ B))) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1111_power__gt1)). 185.47/93.65 thf(32116,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ (power_power_nat @ A @ (suc @ B))) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7159])). 185.47/93.65 thf(3313,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5147_neg__less__eq__nonneg)). 185.47/93.65 thf(18649,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3313])). 185.47/93.65 thf(3995,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= (ord_less_real @ C @ D)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_add__strict__mono)). 185.47/93.65 thf(20819,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ (ord_less_real @ C @ D) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3995])). 185.47/93.65 thf(4772,axiom,((! [A:(nat > real),B:real,C:(nat > real),D:real]: (((sums_real @ (^ [E:nat]: (minus_minus_real @ (A @ E) @ (C @ E))) @ (minus_minus_real @ B @ D)) <= (sums_real @ C @ D)) <= (sums_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8161_sums__diff)). 185.47/93.65 thf(23336,plain,((! [A:(nat > real),B:real,C:(nat > real),D:real]: ((sums_real @ (^ [E:nat]: (minus_minus_real @ (A @ E) @ (C @ E))) @ (minus_minus_real @ B @ D)) | ~ (sums_real @ (C) @ D) | ~ (sums_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4772])). 185.47/93.65 thf(96,axiom,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (minus_minus_rat @ (A @ (suc @ C)) @ (A @ C))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_rat @ (A @ B) @ (A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7589_sum__lessThan__telescope)). 185.47/93.65 thf(8048,plain,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (minus_minus_rat @ (A @ (suc @ C)) @ (A @ C))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_rat @ (A @ B) @ (A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 185.47/93.65 thf(3666,axiom,((! [A:real,B:real,C:real]: ((((uminus_uminus_real @ (divide_divide_real @ B @ A)) = C) = ((uminus_uminus_real @ B) = (times_times_real @ C @ A))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5966_nonzero__neg__divide__eq__eq)). 185.47/93.65 thf(19768,plain,((! [A:real,B:real,C:real]: ((((uminus_uminus_real @ (divide_divide_real @ B @ A)) = C) = ((uminus_uminus_real @ B) = (times_times_real @ C @ A))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3666])). 185.47/93.65 thf(34,axiom,((! [A:int,B:nat]: ((minus_minus_int @ one_one_int @ (power_power_int @ A @ B)) = (times_times_int @ (minus_minus_int @ one_one_int @ A) @ (groups3539618377306564664at_int @ (^ [C:nat]: (power_power_int @ A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7627_one__diff__power__eq_H)). 185.47/93.65 thf(7842,plain,((! [A:int,B:nat]: ((minus_minus_int @ one_one_int @ (power_power_int @ A @ B)) = (times_times_int @ (minus_minus_int @ one_one_int @ A) @ (groups3539618377306564664at_int @ (^ [C:nat]: (power_power_int @ A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[34])). 185.47/93.65 thf(3210,axiom,((! [A:code_integer,B:code_integer]: (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4590_dvd__triv__left)). 185.47/93.65 thf(18340,plain,((! [A:code_integer,B:code_integer]: (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3210])). 185.47/93.65 thf(4639,axiom,((! [A:num]: ((semiri8010041392384452111omplex @ (numeral_numeral_nat @ A)) = (numera6690914467698888265omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6901_of__nat__numeral)). 185.47/93.65 thf(22864,plain,((! [A:num]: ((semiri8010041392384452111omplex @ (numeral_numeral_nat @ A)) = (numera6690914467698888265omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4639])). 185.47/93.65 thf(6519,axiom,((! [A:num]: ((minus_minus_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (numeral_numeral_int @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5445_diff__numeral__special_I3_J)). 185.47/93.65 thf(29733,plain,((! [A:num]: ((minus_minus_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (numeral_numeral_int @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6519])). 185.47/93.65 thf(2982,axiom,((! [A:int,B:int]: ((ring_1_of_int_rat @ (plus_plus_int @ A @ B)) = (plus_plus_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6975_of__int__add)). 185.47/93.65 thf(17623,plain,((! [A:int,B:int]: ((ring_1_of_int_rat @ (plus_plus_int @ A @ B)) = (plus_plus_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2982])). 185.47/93.65 thf(3465,axiom,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_one__plus__numeral__commute)). 185.47/93.65 thf(19139,plain,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3465])). 185.47/93.65 thf(6394,axiom,((! [A:nat,B:nat,C:real]: (((ord_less_nat @ A @ B) => ((ord_less_real @ (root @ B @ C) @ (root @ A @ C)) <= (ord_less_real @ one_one_real @ C))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9189_real__root__strict__decreasing)). 185.47/93.65 thf(29261,plain,((! [A:nat,B:nat,C:real]: (((ord_less_nat @ A @ B) => ((ord_less_real @ (root @ B @ C) @ (root @ A @ C)) | ~ (ord_less_real @ one_one_real @ C))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6394])). 185.47/93.65 thf(5002,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C)) @ B) = (modulo_modulo_nat @ (suc @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1853_Suc__mod__mult__self3)). 185.47/93.65 thf(24111,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C)) @ B) = (modulo_modulo_nat @ (suc @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5002])). 185.47/93.65 thf(1325,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: ((? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))) <= (? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) <= (ord_less_int @ F @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3264_minf_I2_J)). 185.47/93.65 thf(12147,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: ((? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((A @ F) = (B @ F)))) => (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F)))) | ~ (? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) | ~ (ord_less_int @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325])). 185.47/93.65 thf(6817,axiom,((! [A:nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ A) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1800_power__Suc__0)). 185.47/93.65 thf(30800,plain,((! [A:nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ A) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6817])). 185.47/93.65 thf(3784,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (minus_minus_int @ B @ one_one_int)) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3131_zle__diff1__eq)). 185.47/93.65 thf(20161,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (minus_minus_int @ B @ one_one_int)) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3784])). 185.47/93.65 thf(2653,axiom,((! [A:num]: ((neg_nu5219082963157363817nc_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_rat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7007_dbl__inc__simps_I5_J)). 185.47/93.65 thf(16529,plain,((! [A:num]: ((neg_nu5219082963157363817nc_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_rat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2653])). 185.47/93.65 thf(7683,axiom,(((power_power_int @ one_one_int @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_904_one__power2)). 185.47/93.65 thf(33795,plain,(((power_power_int @ one_one_int @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7683])). 185.47/93.65 thf(1384,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real) => (? [C:real]: ((B = (cos_real @ C)) & (A = (sin_real @ C)) & (ord_less_eq_real @ C @ pi) & (ord_less_eq_real @ zero_zero_real @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7869_sincos__total__pi)). 185.47/93.65 thf(12340,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real) => (? [C:real]: ((B = (cos_real @ C)) & (A = (sin_real @ C)) & (ord_less_eq_real @ C @ pi) & (ord_less_eq_real @ zero_zero_real @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384])). 185.47/93.65 thf(5061,axiom,((! [A:real]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) = (ord_less_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6719_abs__square__less__1)). 185.47/93.65 thf(24377,plain,((! [A:real]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) = (ord_less_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5061])). 185.47/93.65 thf(4840,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ A @ D) = (plus_plus_int @ B @ (plus_plus_int @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_group__cancel_Oadd1)). 185.47/93.65 thf(23546,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ A @ D) = (plus_plus_int @ B @ (plus_plus_int @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4840])). 185.47/93.65 thf(128,axiom,((! [A:real]: (((cos_real @ A) = one_one_real) = (? [B:int]: (A = (times_times_real @ (times_times_real @ (ring_1_of_int_real @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ pi)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7909_cos__one__2pi__int)). 185.47/93.65 thf(8145,plain,((! [A:real]: (((cos_real @ A) = one_one_real) = (? [B:int]: (A = (times_times_real @ (times_times_real @ (ring_1_of_int_real @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ pi)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 185.47/93.65 thf(2354,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_diff__left__mono)). 185.47/93.65 thf(15527,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2354])). 185.47/93.65 thf(1815,axiom,((! [A:rat,B:nat,C:nat]: ((((power_power_rat @ A @ B) = (power_power_rat @ A @ C)) = (B = C)) <= (ord_less_rat @ one_one_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_power__inject__exp)). 185.47/93.65 thf(13810,plain,((! [A:rat,B:nat,C:nat]: ((((power_power_rat @ A @ B) = (power_power_rat @ A @ C)) = (B = C)) | ~ (ord_less_rat @ one_one_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1815])). 185.47/93.65 thf(12,axiom,((! [A:real,B:nat,C:(nat > (int > real))]: (((B != zero_zero_nat) => ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_int) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_int))) <= (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8078_Maclaurin__zero)). 185.47/93.65 thf(7762,plain,((! [A:real,B:nat,C:(nat > (int > real))]: (((~ (B = zero_zero_nat)) => ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_int) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_int))) | ~ (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 185.47/93.65 thf(584,axiom,((! [A:set_nat,B:set_nat]: (((~ (finite_finite_nat @ (minus_minus_set_nat @ B @ A))) <= (~ (finite_finite_nat @ B))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3497_Diff__infinite__finite)). 185.47/93.65 thf(9671,plain,((! [A:set_nat,B:set_nat]: (~ (finite_finite_nat @ (minus_minus_set_nat @ B @ A)) | (finite_finite_nat @ B) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[584])). 185.47/93.65 thf(6577,axiom,((! [A:nat,B:nat]: ((A = (suc @ B)) => (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2108_nat_OdiscI)). 185.47/93.65 thf(29930,plain,((! [A:nat,B:nat]: ((A = (suc @ B)) => (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6577])). 185.47/93.65 thf(4763,axiom,((! [A:num,B:num]: ((plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_numeral__plus__numeral)). 185.47/93.65 thf(23308,plain,((! [A:num,B:num]: ((plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4763])). 185.47/93.65 thf(1753,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_743_diff__diff__eq)). 185.47/93.65 thf(13612,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753])). 185.47/93.65 thf(5418,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_759_diff__add__inverse2)). 185.47/93.65 thf(25649,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5418])). 185.47/93.65 thf(6490,axiom,((! [A:nat,B:int]: (((power_power_int @ (uminus_uminus_int @ B) @ A) = (uminus_uminus_int @ (power_power_int @ B @ A))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5440_power__minus__odd)). 185.47/93.65 thf(29633,plain,((! [A:nat,B:int]: (((power_power_int @ (uminus_uminus_int @ B) @ A) = (uminus_uminus_int @ (power_power_int @ B @ A))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6490])). 185.47/93.65 thf(6294,axiom,((! [A:rat]: ((minus_minus_rat @ A @ zero_zero_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1554_diff__0__right)). 185.47/93.65 thf(28908,plain,((! [A:rat]: ((minus_minus_rat @ A @ zero_zero_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6294])). 185.47/93.65 thf(5195,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_diff__diff__left)). 185.47/93.65 thf(24858,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5195])). 185.47/93.65 thf(2003,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((((modulo_modulo_int @ (times_times_int @ A @ D) @ B) = (modulo_modulo_int @ (times_times_int @ C @ E) @ B)) <= ((modulo_modulo_int @ D @ B) = (modulo_modulo_int @ E @ B))) <= ((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1983_mod__mult__cong)). 185.47/93.65 thf(14430,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((modulo_modulo_int @ (times_times_int @ A @ D) @ B) = (modulo_modulo_int @ (times_times_int @ C @ E) @ B)) | ~ ((modulo_modulo_int @ D @ B) = (modulo_modulo_int @ E @ B)) | ~ ((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2003])). 185.47/93.65 thf(4804,axiom,((plus_plus_int = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_add_Ocommute)). 185.47/93.65 thf(23432,plain,(((plus_plus_int) = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4804])). 185.47/93.65 thf(1731,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7252_int__ops_I7_J)). 185.47/93.65 thf(13536,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731])). 185.47/93.65 thf(1845,axiom,(((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5272_add__neg__numeral__special_I8_J)). 185.47/93.65 thf(13924,plain,(((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1845])). 185.47/93.65 thf(4667,axiom,((! [A:real]: ((times_times_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8193_exp__minus__inverse)). 185.47/93.65 thf(22948,plain,((! [A:real]: ((times_times_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4667])). 185.47/93.65 thf(775,axiom,((! [A:nat,B:nat,C:(nat > nat)]: ((((groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_nat) <= (ord_less_nat @ (suc @ A) @ B)) & (((groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_nat @ (groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) <= (~ (ord_less_nat @ (suc @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8707_prod_Ocl__ivl__Suc)). 185.47/93.65 thf(10369,plain,((! [A:nat,B:nat,C:(nat > nat)]: ((((groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_nat) | ~ (ord_less_nat @ (suc @ A) @ B)) & (((groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_nat @ (groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) | (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[775])). 185.47/93.65 thf(2994,axiom,((! [A:nat,B:(rat > nat),C:rat,D:rat]: ((((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:rat,F:rat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_rat @ E @ F)))) <= (ord_less_eq_rat @ C @ D)) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3917_order__subst1)). 185.47/93.65 thf(17659,plain,((! [A:nat,B:(rat > nat),C:rat,D:rat]: ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:rat,F:rat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_rat @ E @ F))) | ~ (ord_less_eq_rat @ C @ D) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2994])). 185.47/93.65 thf(6062,axiom,((bit_se2925701944663578781it_nat = (^ [A:nat,B:nat]: (modulo_modulo_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9327_take__bit__nat__def)). 185.47/93.65 thf(28080,plain,(((bit_se2925701944663578781it_nat) = (^ [A:nat,B:nat]: (modulo_modulo_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6062])). 185.47/93.65 thf(6982,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (modulo_modulo_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4682_dvd__mod)). 185.47/93.65 thf(31492,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (modulo_modulo_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6982])). 185.47/93.65 thf(1811,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1540_add__0)). 185.47/93.65 thf(13799,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811])). 185.47/93.65 thf(5872,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_V5719532721284313246member @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2522_VEBT__internal_Onaive__member_Osimps_I2_J)). 185.47/93.65 thf(27436,plain,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_V5719532721284313246member @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5872])). 185.47/93.65 thf(4528,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)) <= (ord_less_rat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_add__strict__mono)). 185.47/93.65 thf(22505,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)) | ~ (ord_less_rat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4528])). 185.47/93.65 thf(7448,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4633_unit__imp__dvd)). 185.47/93.65 thf(33090,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7448])). 185.47/93.65 thf(4384,axiom,(((neg_nu5219082963157363817nc_rat @ zero_zero_rat) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6993_dbl__inc__simps_I2_J)). 185.47/93.65 thf(22046,plain,(((neg_nu5219082963157363817nc_rat @ zero_zero_rat) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4384])). 185.47/93.65 thf(7567,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_pow__sum)). 185.47/93.65 thf(33480,plain,((! [A:nat,B:nat]: ((divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7567])). 185.47/93.65 thf(2764,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_ab__semigroup__add__class_Oadd__ac_I1_J)). 185.47/93.65 thf(16916,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2764])). 185.47/93.65 thf(3962,axiom,((! [A:real,B:real]: ((! [C:real]: ((ord_less_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ (plus_plus_real @ B @ C)))) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2619_field__le__epsilon)). 185.47/93.65 thf(20721,plain,((! [A:real,B:real]: ((! [C:real]: ((ord_less_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ (plus_plus_real @ B @ C)))) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3962])). 185.47/93.65 thf(751,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_real @ (groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6649_sum_OatLeast0__atMost__Suc)). 185.47/93.65 thf(10247,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_real @ (groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[751])). 185.47/93.65 thf(334,axiom,((! [A:set_nat,B:(nat > real)]: ((ord_less_eq_real @ one_one_real @ (groups129246275422532515t_real @ B @ A)) <= (! [C:nat]: ((ord_less_eq_real @ one_one_real @ (B @ C)) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8760_prod__ge__1)). 185.47/93.65 thf(8852,plain,((! [A:set_nat,B:(nat > real)]: ((ord_less_eq_real @ one_one_real @ (groups129246275422532515t_real @ (B) @ A)) | ~ (! [C:nat]: ((ord_less_eq_real @ one_one_real @ (B @ C)) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 185.47/93.65 thf(5467,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:nat,F:vEBT_VEBT]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ (size_s6755466524823107622T_VEBT @ D) @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ C)) @ A @ D @ F) @ B) = none_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_pred__list__to__short)). 185.47/93.65 thf(25844,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:nat,F:vEBT_VEBT]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_eq_nat @ B @ C) => ((ord_less_eq_nat @ (size_s6755466524823107622T_VEBT @ D) @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ C)) @ A @ D @ F) @ B) = none_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5467])). 185.47/93.65 thf(4388,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= ((C = D) & (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_add__mono__thms__linordered__field_I1_J)). 185.47/93.65 thf(22060,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ ((C = D) & (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4388])). 185.47/93.65 thf(1609,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ A @ (plus_plus_int @ B @ C)) = (minus_minus_int @ (minus_minus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_735_diff__add__eq__diff__diff__swap)). 185.47/93.65 thf(13070,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ A @ (plus_plus_int @ B @ C)) = (minus_minus_int @ (minus_minus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609])). 185.47/93.65 thf(837,axiom,((! [A:complex]: (ord_less_eq_real @ (re @ A) @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9641_complex__Re__le__cmod)). 185.47/93.65 thf(10583,plain,((! [A:complex]: (ord_less_eq_real @ (re @ A) @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[837])). 185.47/93.65 thf(7608,axiom,((! [A:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1869_zero__eq__power2)). 185.47/93.65 thf(33595,plain,((! [A:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7608])). 185.47/93.65 thf(609,axiom,((~ (ord_le6747313008572928689nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5755_less__minus__one__simps_I4_J)). 185.47/93.65 thf(9758,plain,((~ (ord_le6747313008572928689nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[609])). 185.47/93.65 thf(89,axiom,((! [A:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((archim7802044766580827645g_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A))) = (plus_plus_int @ (archim7802044766580827645g_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (divide_divide_nat @ (minus_minus_nat @ A @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9064_ceiling__log2__div2)). 185.47/93.65 thf(8021,plain,((! [A:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((archim7802044766580827645g_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A))) = (plus_plus_int @ (archim7802044766580827645g_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (divide_divide_nat @ (minus_minus_nat @ A @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 185.47/93.65 thf(6042,axiom,((! [A:rat]: ((uminus_uminus_rat @ (uminus_uminus_rat @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5028_add_Oinverse__inverse)). 185.47/93.65 thf(28019,plain,((! [A:rat]: ((uminus_uminus_rat @ (uminus_uminus_rat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6042])). 185.47/93.65 thf(5276,axiom,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: (((B @ A @ C) <= (A = none_P5556105721700978146at_nat)) => (((C = none_P5556105721700978146at_nat) => (B @ A @ C)) => ((! [D:product_prod_nat_nat,E:product_prod_nat_nat]: ((A = (some_P7363390416028606310at_nat @ D)) => ((C = (some_P7363390416028606310at_nat @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1176_combine__options__cases)). 185.47/93.65 thf(25161,plain,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: (((B @ A @ C) | ~ (A = none_P5556105721700978146at_nat)) => (((C = none_P5556105721700978146at_nat) => (B @ A @ C)) => ((! [D:product_prod_nat_nat,E:product_prod_nat_nat]: ((A = (some_P7363390416028606310at_nat @ D)) => ((C = (some_P7363390416028606310at_nat @ E)) => (B @ A @ C)))) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5276])). 185.47/93.65 thf(4744,axiom,((! [A:rat,B:nat,C:rat]: (((ord_less_eq_rat @ A @ C) <= (ord_less_eq_rat @ zero_zero_rat @ C)) <= (ord_less_eq_rat @ (power_power_rat @ A @ (suc @ B)) @ (power_power_rat @ C @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2755_power__le__imp__le__base)). 185.47/93.65 thf(23212,plain,((! [A:rat,B:nat,C:rat]: ((ord_less_eq_rat @ A @ C) | ~ (ord_less_eq_rat @ zero_zero_rat @ C) | ~ (ord_less_eq_rat @ (power_power_rat @ A @ (suc @ B)) @ (power_power_rat @ C @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4744])). 185.47/93.65 thf(1552,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5526_verit__negate__coefficient_I2_J)). 185.47/93.65 thf(12881,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552])). 185.47/93.65 thf(5887,axiom,((! [A:complex]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_complex @ (times_times_complex @ A @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6666_power3__eq__cube)). 185.47/93.65 thf(27489,plain,((! [A:complex]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_complex @ (times_times_complex @ A @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5887])). 185.47/93.65 thf(6449,axiom,((! [A:num,B:num]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (uminus_uminus_real @ (numeral_numeral_real @ B))) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5064_neg__numeral__eq__iff)). 185.47/93.65 thf(29480,plain,((! [A:num,B:num]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (uminus_uminus_real @ (numeral_numeral_real @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6449])). 185.47/93.65 thf(3703,axiom,((! [A:nat,B:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6898_of__nat__less__iff)). 185.47/93.65 thf(19886,plain,((! [A:nat,B:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3703])). 185.47/93.65 thf(6139,axiom,((! [A:complex]: ((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (minus_minus_complex @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7860_cos__double)). 185.47/93.65 thf(28350,plain,((! [A:complex]: ((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (minus_minus_complex @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6139])). 185.47/93.65 thf(5927,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ A) = (modulo_modulo_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1773_mod__mult__self4)). 185.47/93.65 thf(27621,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ A) = (modulo_modulo_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5927])). 185.47/93.65 thf(4847,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6503_abs__triangle__ineq2)). 185.47/93.65 thf(23568,plain,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4847])). 185.47/93.65 thf(2227,axiom,(((neg_nu6511756317524482435omplex @ one_one_complex) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6775_dbl__dec__simps_I3_J)). 185.47/93.65 thf(15137,plain,(((neg_nu6511756317524482435omplex @ one_one_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2227])). 185.47/93.65 thf(2502,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ A @ B) & (ord_less_rat @ C @ D)) => (ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_add__mono__thms__linordered__field_I5_J)). 185.47/93.65 thf(16026,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ A @ B) & (ord_less_rat @ C @ D)) => (ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2502])). 185.47/93.65 thf(3481,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (minus_minus_int @ A @ B) @ B) = (modulo_modulo_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1600_minus__mod__self2)). 185.47/93.65 thf(19190,plain,((! [A:int,B:int]: ((modulo_modulo_int @ (minus_minus_int @ A @ B) @ B) = (modulo_modulo_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3481])). 185.47/93.65 thf(2917,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ A @ A)) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1613_zero__le__double__add__iff__zero__le__single__add)). 185.47/93.65 thf(17406,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ A @ A)) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2917])). 185.47/93.65 thf(6257,axiom,((! [A:(nat > nat),B:nat]: ((size_option_nat @ A @ (some_nat @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4421_option_Osize__gen_I2_J)). 185.47/93.65 thf(28785,plain,((! [A:(nat > nat),B:nat]: ((size_option_nat @ (A) @ (some_nat @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6257])). 185.47/93.65 thf(7041,axiom,((! [A:num,B:nat,C:int]: (((power_power_nat @ (numeral_numeral_nat @ A) @ B) = (nat2 @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9257_numeral__power__eq__nat__cancel__iff)). 185.47/93.65 thf(31713,plain,((! [A:num,B:nat,C:int]: (((power_power_nat @ (numeral_numeral_nat @ A) @ B) = (nat2 @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7041])). 185.47/93.65 thf(3321,axiom,((bit_se2923211474154528505it_int = (^ [A:nat,B:int]: (modulo_modulo_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9333_take__bit__int__def)). 185.47/93.65 thf(18673,plain,(((bit_se2923211474154528505it_int) = (^ [A:nat,B:int]: (modulo_modulo_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3321])). 185.47/93.65 thf(4432,axiom,((! [A:real]: ? [B:int]: (ord_less_real @ A @ (ring_1_of_int_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7440_ex__less__of__int)). 185.47/93.65 thf(22186,plain,((! [A:real]: ? [B:int]: (ord_less_real @ A @ (ring_1_of_int_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4432])). 185.47/93.65 thf(21,axiom,((! [A:real,B:nat]: (((? [C:real]: ((ord_less_real @ zero_zero_real @ (abs_abs_real @ C)) & ((exp_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (power_power_real @ A @ D) @ (semiri2265585572941072030t_real @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (exp_real @ C) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))) & (ord_less_real @ (abs_abs_real @ C) @ (abs_abs_real @ A)))) <= (ord_less_nat @ zero_zero_nat @ B)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8104_Maclaurin__exp__lt)). 185.47/93.65 thf(7794,plain,((! [A:real,B:nat]: (? [C:real]: ((ord_less_real @ zero_zero_real @ (abs_abs_real @ C)) & ((exp_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (power_power_real @ A @ D) @ (semiri2265585572941072030t_real @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (exp_real @ C) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))) & (ord_less_real @ (abs_abs_real @ C) @ (abs_abs_real @ A))) | ~ (ord_less_nat @ zero_zero_nat @ B) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 185.47/93.65 thf(7160,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_eq_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_add__mono__thms__linordered__field_I3_J)). 185.47/93.65 thf(32119,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_eq_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7160])). 185.47/93.65 thf(6866,axiom,((! [A:$o,B:$o,C:nat]: ((((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ one_one_nat)) <= (A)) & ((~ (A)) => ((((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = none_nat) <= (~ (B))) & (((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ zero_zero_nat)) <= (B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2520_vebt__pred_Osimps_I3_J)). 185.47/93.65 thf(31011,plain,((! [A:$o,B:$o,C:nat]: ((((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ one_one_nat)) | ~ (A)) & ((~ (A)) => ((((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = none_nat) | (B)) & (((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ zero_zero_nat)) | ~ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6866])). 185.47/93.65 thf(6104,axiom,((! [A:option_nat,B:(option_nat > (option_nat > $o)),C:option_nat]: (((A = none_nat) => (B @ A @ C)) => (((B @ A @ C) <= (C = none_nat)) => ((! [D:nat,E:nat]: ((A = (some_nat @ D)) => ((B @ A @ C) <= (C = (some_nat @ E))))) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1180_combine__options__cases)). 185.47/93.65 thf(28218,plain,((! [A:option_nat,B:(option_nat > (option_nat > $o)),C:option_nat]: (((A = none_nat) => (B @ A @ C)) => (((B @ A @ C) | ~ (C = none_nat)) => ((! [D:nat,E:nat]: ((A = (some_nat @ D)) => ((B @ A @ C) | ~ (C = (some_nat @ E))))) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6104])). 185.47/93.65 thf(5526,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((? [D:nat]: ((A @ D) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E)))) <= (! [D:nat]: ((ord_less_eq_nat @ D @ C) <= (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_Nat_Oex__has__greatest__nat)). 185.47/93.65 thf(26130,plain,((! [A:(nat > $o),B:nat,C:nat]: (? [D:nat]: ((A @ D) & ! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E))) | ~ (! [D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (A @ D))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5526])). 185.47/93.65 thf(4408,axiom,((! [A:real,B:real]: ((minus_minus_real @ A @ (uminus_uminus_real @ B)) = (plus_plus_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5202_diff__minus__eq__add)). 185.47/93.65 thf(22117,plain,((! [A:real,B:real]: ((minus_minus_real @ A @ (uminus_uminus_real @ B)) = (plus_plus_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4408])). 185.47/93.65 thf(6631,axiom,((! [A:rat,B:nat,C:nat]: ((power_power_rat @ A @ (plus_plus_nat @ B @ C)) = (times_times_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_power__add)). 185.47/93.65 thf(30106,plain,((! [A:rat,B:nat,C:nat]: ((power_power_rat @ A @ (plus_plus_nat @ B @ C)) = (times_times_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6631])). 185.47/93.65 thf(7027,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ (suc @ A) @ B) @ (times_times_nat @ (suc @ A) @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1102_Suc__mult__le__cancel1)). 185.47/93.65 thf(31670,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ (suc @ A) @ B) @ (times_times_nat @ (suc @ A) @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7027])). 185.47/93.65 thf(7267,axiom,((! [A:rat]: ((times_times_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))) = (plus_plus_rat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_mult__2__right)). 185.47/93.65 thf(32487,plain,((! [A:rat]: ((times_times_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))) = (plus_plus_rat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7267])). 185.47/93.65 thf(5555,axiom,((! [A:real]: ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (minus_minus_real @ one_one_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7863_cos__double__sin)). 185.47/93.65 thf(26229,plain,((! [A:real]: ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (minus_minus_real @ one_one_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5555])). 185.47/93.65 thf(503,axiom,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ ($true) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1949_VEBT__internal_OminNull_Osimps_I2_J)). 185.47/93.65 thf(9423,plain,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ ($true) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[503])). 185.47/93.65 thf(3539,axiom,((ord_less_eq_rat @ zero_zero_rat @ one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2272_linordered__nonzero__semiring__class_Ozero__le__one)). 185.47/93.65 thf(19369,plain,((ord_less_eq_rat @ zero_zero_rat @ one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3539])). 185.47/93.65 thf(7484,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1480_not__gr__zero)). 185.47/93.65 thf(33222,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7484])). 185.47/93.65 thf(422,axiom,((! [A:num,B:num]: ((((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ A))) <= (~ (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)))) & ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) => ((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5315_max__number__of_I3_J)). 185.47/93.65 thf(9132,plain,((! [A:num,B:num]: ((((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ A))) | (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B))) & ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) => ((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])). 185.47/93.65 thf(681,axiom,((! [A:num]: ((ring_1_of_int_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6939_of__int__numeral)). 185.47/93.65 thf(10006,plain,((! [A:num]: ((ring_1_of_int_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[681])). 185.47/93.65 thf(7198,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4946_odd__pos)). 185.47/93.65 thf(32243,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7198])). 185.47/93.65 thf(774,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ (plus_plus_real @ A @ (inverse_inverse_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8975_plus__inverse__ge__2)). 185.47/93.65 thf(10367,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ (plus_plus_real @ A @ (inverse_inverse_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[774])). 185.47/93.65 thf(1604,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_eq_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2598_mult__le__cancel__left__neg)). 185.47/93.65 thf(13055,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_eq_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604])). 185.47/93.65 thf(1929,axiom,((! [A:rat,B:rat]: ((one_one_rat = (divide_divide_rat @ A @ B)) = ((A = B) & (B != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1737_one__eq__divide__iff)). 185.47/93.65 thf(14167,plain,((! [A:rat,B:rat]: ((one_one_rat = (divide_divide_rat @ A @ B)) = ((A = B) & ~ (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929])). 185.47/93.65 thf(1702,axiom,((imaginary_unit = (complex2 @ zero_zero_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9008_imaginary__unit_Ocode)). 185.47/93.65 thf(13433,plain,((imaginary_unit = (complex2 @ zero_zero_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702])). 185.47/93.65 thf(5912,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (minus_minus_nat @ B @ A) @ C) = (ord_less_nat @ B @ (plus_plus_nat @ C @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_less__diff__conv2)). 185.47/93.65 thf(27576,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (minus_minus_nat @ B @ A) @ C) = (ord_less_nat @ B @ (plus_plus_nat @ C @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5912])). 185.47/93.65 thf(369,axiom,((! [A:set_nat,B:set_nat,C:(nat > rat)]: (((ord_less_eq_set_nat @ B @ A) => ((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => (ord_less_eq_rat @ zero_zero_rat @ (C @ D)))) => (ord_less_eq_rat @ (groups2906978787729119204at_rat @ C @ B) @ (groups2906978787729119204at_rat @ C @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6195_sum__mono2)). 185.47/93.65 thf(8964,plain,((! [A:set_nat,B:set_nat,C:(nat > rat)]: (((ord_less_eq_set_nat @ B @ A) => ((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => (ord_less_eq_rat @ zero_zero_rat @ (C @ D)))) => (ord_less_eq_rat @ (groups2906978787729119204at_rat @ (C) @ B) @ (groups2906978787729119204at_rat @ (C) @ A)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])). 185.47/93.65 thf(6122,axiom,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (((root @ A @ C) = B) <= ((power_power_real @ B @ A) = C))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9198_real__root__pos__unique)). 185.47/93.65 thf(28291,plain,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (((root @ A @ C) = B) | ~ ((power_power_real @ B @ A) = C))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6122])). 185.47/93.65 thf(6303,axiom,((! [A:nat]: ((bit_se545348938243370406it_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9541_push__bit__minus__one)). 185.47/93.65 thf(28935,plain,((! [A:nat]: ((bit_se545348938243370406it_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6303])). 185.47/93.65 thf(1156,axiom,((sgn_sgn_real = (^ [A:real]: (if_real @ (A = zero_zero_real) @ zero_zero_real @ (if_real @ (ord_less_real @ zero_zero_real @ A) @ one_one_real @ (uminus_uminus_real @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9304_sgn__real__def)). 185.47/93.65 thf(11646,plain,(((sgn_sgn_real) = (^ [A:real]: (if_real @ (A = zero_zero_real) @ zero_zero_real @ (if_real @ (ord_less_real @ zero_zero_real @ A) @ one_one_real @ (uminus_uminus_real @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156])). 185.47/93.65 thf(2680,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (A = (ord_max_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3666_max_OorderI)). 185.47/93.65 thf(16661,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | ~ (A = (ord_max_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2680])). 185.47/93.65 thf(1544,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D))) <= (ord_less_eq_int @ zero_zero_int @ A)) <= (ord_less_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2593_mult__strict__mono_H)). 185.47/93.65 thf(12849,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => (((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D))) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544])). 185.47/93.65 thf(5879,axiom,((! [A:nat,B:nat]: ((binomial @ (suc @ A) @ (suc @ B)) = (plus_plus_nat @ (binomial @ A @ B) @ (binomial @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8419_binomial__Suc__Suc)). 185.47/93.65 thf(27457,plain,((! [A:nat,B:nat]: ((binomial @ (suc @ A) @ (suc @ B)) = (plus_plus_nat @ (binomial @ A @ B) @ (binomial @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5879])). 185.47/93.65 thf(1822,axiom,((! [A:num]: ((plus_plus_complex @ one_one_complex @ (numera6690914467698888265omplex @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_one__plus__numeral__commute)). 185.47/93.65 thf(13835,plain,((! [A:num]: ((plus_plus_complex @ one_one_complex @ (numera6690914467698888265omplex @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1822])). 185.47/93.65 thf(2149,axiom,((! [A:int]: (ord_less_eq_int @ (uminus_uminus_int @ (abs_abs_int @ A)) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6561_abs__minus__le__zero)). 185.47/93.65 thf(14894,plain,((! [A:int]: (ord_less_eq_int @ (uminus_uminus_int @ (abs_abs_int @ A)) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2149])). 185.47/93.65 thf(1864,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (minus_minus_rat @ A @ B) @ C) = (ord_less_eq_rat @ A @ (plus_plus_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_796_diff__le__eq)). 185.47/93.65 thf(13976,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (minus_minus_rat @ A @ B) @ C) = (ord_less_eq_rat @ A @ (plus_plus_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1864])). 185.47/93.65 thf(4424,axiom,((! [A:complex,B:complex,C:nat]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ (^ [D:nat]: (plus_plus_complex @ A @ (times_times_complex @ (semiri8010041392384452111omplex @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ C) @ one_one_complex) @ (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ (times_times_complex @ (semiri8010041392384452111omplex @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7339_double__arith__series)). 185.47/93.65 thf(22159,plain,((! [A:complex,B:complex,C:nat]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ (^ [D:nat]: (plus_plus_complex @ A @ (times_times_complex @ (semiri8010041392384452111omplex @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ C) @ one_one_complex) @ (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ (times_times_complex @ (semiri8010041392384452111omplex @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4424])). 185.47/93.65 thf(2579,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((divide_divide_int @ (plus_plus_int @ A @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4555_even__succ__div__two)). 185.47/93.65 thf(16274,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((divide_divide_int @ (plus_plus_int @ A @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2579])). 185.47/93.65 thf(1165,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ B @ C)) => (? [D:int,E:int]: ((dvd_dvd_int @ E @ C) & (dvd_dvd_int @ D @ B) & (A = (times_times_int @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4626_division__decomp)). 185.47/93.65 thf(11670,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ B @ C)) => (? [D:int,E:int]: ((dvd_dvd_int @ E @ C) & (dvd_dvd_int @ D @ B) & (A = (times_times_int @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165])). 185.47/93.65 thf(7417,axiom,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus_nat @ B @ C)) => ((suc @ A) = (plus_plus_nat @ B @ (suc @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1049_nat__arith_Osuc1)). 185.47/93.65 thf(32999,plain,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus_nat @ B @ C)) => ((suc @ A) = (plus_plus_nat @ B @ (suc @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7417])). 185.47/93.65 thf(62,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (^ [C:nat]: (minus_minus_int @ (A @ (suc @ C)) @ (A @ C))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_int @ (A @ B) @ (A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7590_sum__lessThan__telescope)). 185.47/93.65 thf(7934,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (^ [C:nat]: (minus_minus_int @ (A @ (suc @ C)) @ (A @ C))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_int @ (A @ B) @ (A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 185.47/93.65 thf(7010,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_738_add__implies__diff)). 185.47/93.65 thf(31589,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7010])). 185.47/93.65 thf(1570,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => ((divide_divide_rat @ (times_times_rat @ B @ A) @ (times_times_rat @ C @ A)) = (divide_divide_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1701_nonzero__mult__divide__mult__cancel__right)). 185.47/93.65 thf(12930,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => ((divide_divide_rat @ (times_times_rat @ B @ A) @ (times_times_rat @ C @ A)) = (divide_divide_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570])). 185.47/93.65 thf(2571,axiom,((! [A:num,B:complex,C:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ B) @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_distrib__left__numeral)). 185.47/93.65 thf(16252,plain,((! [A:num,B:complex,C:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ B) @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2571])). 185.47/93.65 thf(1258,axiom,((! [A:num,B:num,C:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) @ C)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5324_semiring__norm_I168_J)). 185.47/93.65 thf(11948,plain,((! [A:num,B:num,C:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) @ C)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258])). 185.47/93.65 thf(6248,axiom,((! [A:complex]: ((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (minus_minus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7910_cos__double__cos)). 185.47/93.65 thf(28753,plain,((! [A:complex]: ((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (minus_minus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6248])). 185.47/93.65 thf(5121,axiom,((! [A:nat,B:nat]: ((((modulo_modulo_nat @ A @ B) = A) <= (ord_less_nat @ A @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1937_unique__euclidean__semiring__numeral__class_Omod__less)). 185.47/93.65 thf(24582,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = A) | ~ (ord_less_nat @ A @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5121])). 185.47/93.65 thf(4673,axiom,((! [A:num,B:num]: ((((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit1 @ B)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit1 @ A)))) <= (ord_less_num @ A @ B)) & (((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit1 @ B)) = (unique5026877609467782581ep_nat @ (bit1 @ B) @ (unique5055182867167087721od_nat @ (bit1 @ A) @ (bit0 @ (bit1 @ B))))) <= (~ (ord_less_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6766_divmod__algorithm__code_I8_J)). 185.47/93.65 thf(22967,plain,((! [A:num,B:num]: ((((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit1 @ B)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit1 @ A)))) | ~ (ord_less_num @ A @ B)) & (((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit1 @ B)) = (unique5026877609467782581ep_nat @ (bit1 @ B) @ (unique5055182867167087721od_nat @ (bit1 @ A) @ (bit0 @ (bit1 @ B))))) | (ord_less_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4673])). 185.47/93.65 thf(4860,axiom,((! [A:real,B:real,C:real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ A @ (times_times_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_divide__divide__eq__left_H)). 185.47/93.65 thf(23604,plain,((! [A:real,B:real,C:real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ A @ (times_times_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4860])). 185.47/93.65 thf(6460,axiom,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: ((? [E:num]: ! [F:num]: ((ord_less_num @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:num]: ! [F:num]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) <= (ord_less_num @ F @ E))) <= (? [E:num]: ! [F:num]: ((ord_less_num @ F @ E) => ((C @ F) = (D @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3257_minf_I1_J)). 185.47/93.65 thf(29516,plain,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: ((? [E:num]: ! [F:num]: ((ord_less_num @ F @ E) => ((A @ F) = (B @ F)))) => (? [E:num]: ! [F:num]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) | ~ (ord_less_num @ F @ E)) | ~ (? [E:num]: ! [F:num]: ((ord_less_num @ F @ E) => ((C @ F) = (D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6460])). 185.47/93.65 thf(3203,axiom,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (plus_plus_real @ (times_times_real @ C @ B) @ D)) = (plus_plus_real @ (times_times_real @ (plus_plus_real @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_combine__common__factor)). 185.47/93.65 thf(18315,plain,((! [A:real,B:real,C:real,D:real]: ((plus_plus_real @ (times_times_real @ A @ B) @ (plus_plus_real @ (times_times_real @ C @ B) @ D)) = (plus_plus_real @ (times_times_real @ (plus_plus_real @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3203])). 185.47/93.65 thf(5826,axiom,((! [A:code_integer,B:num]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6002_power__minus__Bit0)). 185.47/93.65 thf(27277,plain,((! [A:code_integer,B:num]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5826])). 185.47/93.65 thf(2391,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ C) = (ord_less_eq_rat @ (times_times_rat @ C @ A) @ B)) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2839_neg__divide__le__eq)). 185.47/93.65 thf(15638,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ C) = (ord_less_eq_rat @ (times_times_rat @ C @ A) @ B)) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2391])). 185.47/93.65 thf(5830,axiom,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_semiring__norm_I6_J)). 185.47/93.65 thf(27287,plain,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5830])). 185.47/93.65 thf(2802,axiom,((! [A:(nat > real),B:real,C:real]: ((sums_real @ (^ [D:nat]: (divide_divide_real @ (A @ D) @ C)) @ (divide_divide_real @ B @ C)) <= (sums_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8163_sums__divide)). 185.47/93.65 thf(17037,plain,((! [A:(nat > real),B:real,C:real]: ((sums_real @ (^ [D:nat]: (divide_divide_real @ (A @ D) @ C)) @ (divide_divide_real @ B @ C)) | ~ (sums_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2802])). 185.47/93.65 thf(2785,axiom,(((neg_nu8557863876264182079omplex @ zero_zero_complex) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6991_dbl__inc__simps_I2_J)). 185.47/93.65 thf(16981,plain,(((neg_nu8557863876264182079omplex @ zero_zero_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2785])). 185.47/93.65 thf(2360,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) | (ord_less_eq_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3934_linorder__linear)). 185.47/93.65 thf(15546,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) | (ord_less_eq_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2360])). 185.47/93.65 thf(4925,axiom,((! [A:nat]: ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5463_power__minus1__even)). 185.47/93.65 thf(23854,plain,((! [A:nat]: ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4925])). 185.47/93.65 thf(963,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ A)))) = (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9533_or__not__numerals_I3_J)). 185.47/93.65 thf(11042,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ A)))) = (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[963])). 185.47/93.65 thf(7617,axiom,((vEBT_invar_vebt @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ na)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_abc)). 185.47/93.65 thf(33618,plain,((vEBT_invar_vebt @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7617])). 185.47/93.65 thf(2399,axiom,((! [A:int]: (ord_less_eq_int @ A @ (abs_abs_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6452_abs__ge__self)). 185.47/93.65 thf(15670,plain,((! [A:int]: (ord_less_eq_int @ A @ (abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2399])). 185.47/93.65 thf(3994,axiom,((! [A:real,B:real]: ((? [C:nat]: (ord_less_real @ B @ (power_power_real @ A @ C))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_962_real__arch__pow)). 185.47/93.65 thf(20816,plain,((! [A:real,B:real]: (? [C:nat]: (ord_less_real @ B @ (power_power_real @ A @ C)) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3994])). 185.47/93.65 thf(3936,axiom,((! [A:int,B:int,C:int,D:int]: (((((fract @ C @ A) = (fract @ D @ B)) = ((times_times_int @ C @ B) = (times_times_int @ D @ A))) <= (B != zero_zero_int)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9939_eq__rat_I1_J)). 185.47/93.65 thf(20637,plain,((! [A:int,B:int,C:int,D:int]: ((((fract @ C @ A) = (fract @ D @ B)) = ((times_times_int @ C @ B) = (times_times_int @ D @ A))) | (B = zero_zero_int) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3936])). 185.47/93.65 thf(4930,axiom,((ord_less_nat @ mi @ res)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23__092_060open_062mi_A_060_Ares_092_060close_062)). 185.47/93.65 thf(23868,plain,((ord_less_nat @ mi @ res)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4930])). 185.47/93.65 thf(38,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (groups3542108847815614940at_nat @ A @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7574_sum_Onat__diff__reindex)). 185.47/93.65 thf(7853,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (groups3542108847815614940at_nat @ (A) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 185.47/93.65 thf(6409,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4145_order__less__imp__not__less)). 185.47/93.65 thf(29340,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6409])). 185.47/93.65 thf(6743,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ A) = (plus_plus_nat @ B @ (divide_divide_nat @ C @ A))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1832_div__mult__self4)). 185.47/93.65 thf(30494,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ A) = (plus_plus_nat @ B @ (divide_divide_nat @ C @ A))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6743])). 185.47/93.65 thf(1149,axiom,((! [A:num]: ((real_V7735802525324610683m_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7452_norm__numeral)). 185.47/93.65 thf(11624,plain,((! [A:num]: ((real_V7735802525324610683m_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149])). 185.47/93.65 thf(5909,axiom,((! [A:complex,B:complex,C:nat]: (((times_times_complex @ (power_power_complex @ A @ C) @ B) = (times_times_complex @ B @ (power_power_complex @ A @ C))) <= ((times_times_complex @ A @ B) = (times_times_complex @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_power__commuting__commutes)). 185.47/93.65 thf(27567,plain,((! [A:complex,B:complex,C:nat]: (((times_times_complex @ (power_power_complex @ A @ C) @ B) = (times_times_complex @ B @ (power_power_complex @ A @ C))) | ~ ((times_times_complex @ A @ B) = (times_times_complex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5909])). 185.47/93.65 thf(405,axiom,((! [A:complex,B:nat,C:set_nat]: ((groups2073611262835488442omplex @ (^ [D:nat]: (power_power_complex @ A @ (plus_plus_nat @ B @ D))) @ C) = (times_times_complex @ (power_power_complex @ A @ B) @ (groups2073611262835488442omplex @ (power_power_complex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6621_sum__power__add)). 185.47/93.65 thf(9080,plain,((! [A:complex,B:nat,C:set_nat]: ((groups2073611262835488442omplex @ (^ [D:nat]: (power_power_complex @ A @ (plus_plus_nat @ B @ D))) @ C) = (times_times_complex @ (power_power_complex @ A @ B) @ (groups2073611262835488442omplex @ (power_power_complex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[405])). 185.47/93.65 thf(4413,axiom,((! [A:nat,B:nat,C:(nat > rat),D:rat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_rat @ (C @ B) @ D) => ((ord_less_eq_rat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3927_order__subst2)). 185.47/93.65 thf(22129,plain,((! [A:nat,B:nat,C:(nat > rat),D:rat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_rat @ (C @ B) @ D) => ((ord_less_eq_rat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4413])). 185.47/93.65 thf(1141,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ (real_V7735802525324610683m_real @ C) @ D) => (ord_less_real @ (real_V7735802525324610683m_real @ (times_times_real @ A @ C)) @ (times_times_real @ B @ D))) <= (ord_less_real @ (real_V7735802525324610683m_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7480_norm__mult__less)). 185.47/93.65 thf(11602,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ (real_V7735802525324610683m_real @ C) @ D) => (ord_less_real @ (real_V7735802525324610683m_real @ (times_times_real @ A @ C)) @ (times_times_real @ B @ D))) | ~ (ord_less_real @ (real_V7735802525324610683m_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141])). 185.47/93.65 thf(2318,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((C != A) <= (ord_less_real @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3270_minf_I4_J)). 185.47/93.65 thf(15417,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (C = A) | ~ (ord_less_real @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2318])). 185.47/93.65 thf(1876,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_add__diff__cancel__right_H)). 185.47/93.65 thf(14011,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1876])). 185.47/93.65 thf(7451,axiom,(((neg_numeral_dbl_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3805_dbl__simps_I3_J)). 185.47/93.65 thf(33099,plain,(((neg_numeral_dbl_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7451])). 185.47/93.65 thf(1906,axiom,((! [A:complex,B:complex,C:complex]: (((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = C) = (((C = zero_zero_complex) <= (B = zero_zero_complex)) & (((uminus1482373934393186551omplex @ A) = (times_times_complex @ C @ B)) <= (B != zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5970_minus__divide__eq__eq)). 185.47/93.65 thf(14100,plain,((! [A:complex,B:complex,C:complex]: (((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = C) = (((C = zero_zero_complex) | ~ (B = zero_zero_complex)) & (((uminus1482373934393186551omplex @ A) = (times_times_complex @ C @ B)) | (B = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1906])). 185.47/93.65 thf(2269,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_add__mono)). 185.47/93.65 thf(15266,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2269])). 185.47/93.65 thf(2415,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_real @ (power_power_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A)) @ A) @ (semiri5074537144036343181t_real @ (binomial @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8523_binomial__ge__n__over__k__pow__k)). 185.47/93.65 thf(15724,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_real @ (power_power_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A)) @ A) @ (semiri5074537144036343181t_real @ (binomial @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2415])). 185.47/93.65 thf(4797,axiom,((! [A:nat,B:int]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7177_of__nat__less__of__int__iff)). 185.47/93.65 thf(23412,plain,((! [A:nat,B:int]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4797])). 185.47/93.65 thf(6863,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_809_add__diff__inverse__nat)). 185.47/93.65 thf(31001,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6863])). 185.47/93.65 thf(2599,axiom,((! [A:int,B:nat,C:int]: (((power_power_complex @ (ring_17405671764205052669omplex @ A) @ B) = (ring_17405671764205052669omplex @ C)) = ((power_power_int @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6986_of__int__eq__of__int__power__cancel__iff)). 185.47/93.65 thf(16360,plain,((! [A:int,B:nat,C:int]: (((power_power_complex @ (ring_17405671764205052669omplex @ A) @ B) = (ring_17405671764205052669omplex @ C)) = ((power_power_int @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2599])). 185.47/93.65 thf(13,axiom,((! [A:(nat > real),B:real,C:nat]: ((sums_real @ A @ B) => (sums_real @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ C))) @ (minus_minus_real @ B @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8211_sums__split__initial__segment)). 185.47/93.65 thf(7767,plain,((! [A:(nat > real),B:real,C:nat]: ((sums_real @ (A) @ B) => (sums_real @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ C))) @ (minus_minus_real @ B @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 185.47/93.65 thf(1827,axiom,((! [A:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (exp_real @ A)) @ (numeral_numeral_real @ (bit0 @ one))) <= (ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8249_exp__bound__half)). 185.47/93.65 thf(13853,plain,((! [A:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (exp_real @ A)) @ (numeral_numeral_real @ (bit0 @ one))) | ~ (ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827])). 185.47/93.65 thf(6036,axiom,(((sqrt @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8116_real__sqrt__one)). 185.47/93.65 thf(28002,plain,(((sqrt @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6036])). 185.47/93.65 thf(631,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ A)))) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9534_and__not__numerals_I3_J)). 185.47/93.65 thf(9829,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ A)))) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[631])). 185.47/93.65 thf(6153,axiom,((! [A:nat,B:num]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ (inc @ B)))) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9361_take__bit__Suc__minus__bit1)). 185.47/93.65 thf(28395,plain,((! [A:nat,B:num]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ (inc @ B)))) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6153])). 185.47/93.65 thf(6363,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_849_nat__diff__add__eq1)). 185.47/93.65 thf(29156,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6363])). 185.47/93.65 thf(1015,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_rat @ zero_zero_rat @ (ring_1_of_int_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7286_of__int__pos)). 185.47/93.65 thf(11206,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_rat @ zero_zero_rat @ (ring_1_of_int_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015])). 185.47/93.65 thf(7489,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = ((ord_less_num @ B @ A) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4030_not__less__iff__gr__or__eq)). 185.47/93.65 thf(33250,plain,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = ((ord_less_num @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7489])). 185.47/93.65 thf(6044,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6280_add__0__iff)). 185.47/93.65 thf(28024,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6044])). 185.47/93.65 thf(5415,axiom,((! [A:int,B:nat,C:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ (times_times_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ C))) = (((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ C @ B)))) & (ord_less_eq_nat @ B @ C)) | ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ C) = zero_zero_int) | (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4995_even__mult__exp__div__exp__iff)). 185.47/93.65 thf(25640,plain,((! [A:int,B:nat,C:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ (times_times_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ C))) = (((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ C @ B)))) & (ord_less_eq_nat @ B @ C)) | ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ C) = zero_zero_int) | (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5415])). 185.47/93.65 thf(836,axiom,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2159334234014336723it_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) != (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4956_even__flip__bit__iff)). 185.47/93.65 thf(10580,plain,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2159334234014336723it_int @ A @ B)) = (~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) = (A = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[836])). 185.47/93.65 thf(1691,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((A = (plus_plus_rat @ B @ C)) => ((minus_minus_rat @ A @ D) = (plus_plus_rat @ B @ (minus_minus_rat @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_group__cancel_Osub1)). 185.47/93.65 thf(13391,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((A = (plus_plus_rat @ B @ C)) => ((minus_minus_rat @ A @ D) = (plus_plus_rat @ B @ (minus_minus_rat @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691])). 185.47/93.65 thf(6487,axiom,((! [A:real,B:num,C:num,D:real]: ((times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ (times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_power__add__numeral2)). 185.47/93.65 thf(29626,plain,((! [A:real,B:num,C:num,D:real]: ((times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ (times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6487])). 185.47/93.65 thf(5557,axiom,((! [A:nat,B:nat]: (A = (plus_plus_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ (modulo_modulo_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3029_div__mod__decomp)). 185.47/93.65 thf(26234,plain,((! [A:nat,B:nat]: (A = (plus_plus_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ (modulo_modulo_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5557])). 185.47/93.65 thf(5741,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se7882103937844011126it_nat @ A @ B)) = ((A != zero_zero_nat) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4954_even__set__bit__iff)). 185.47/93.65 thf(26832,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se7882103937844011126it_nat @ A @ B)) = (~ (A = zero_zero_nat) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5741])). 185.47/93.65 thf(4028,axiom,((! [A:int]: (((nat2 @ A) = zero_zero_nat) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9250_nat__le__0)). 185.47/93.65 thf(20925,plain,((! [A:int]: (((nat2 @ A) = zero_zero_nat) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4028])). 185.47/93.65 thf(3677,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_less__eq__real__def)). 185.47/93.65 thf(19800,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3677])). 185.47/93.65 thf(1111,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_real @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1237_less__add__iff1)). 185.47/93.65 thf(11503,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_real @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111])). 185.47/93.65 thf(5407,axiom,((! [A:int,B:num,C:nat]: (((ring_1_of_int_real @ A) = (power_power_real @ (numeral_numeral_real @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7099_of__int__eq__numeral__power__cancel__iff)). 185.47/93.65 thf(25617,plain,((! [A:int,B:num,C:nat]: (((ring_1_of_int_real @ A) = (power_power_real @ (numeral_numeral_real @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5407])). 185.47/93.65 thf(3366,axiom,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ A) => (ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2930_half__gt__zero)). 185.47/93.65 thf(18816,plain,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ A) => (ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3366])). 185.47/93.65 thf(4457,axiom,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: (((plus_plus_rat @ (times_times_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (C = (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1219_eq__add__iff2)). 185.47/93.65 thf(22269,plain,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: (((plus_plus_rat @ (times_times_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (C = (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4457])). 185.47/93.65 thf(4937,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1137_distrib__left)). 185.47/93.65 thf(23900,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4937])). 185.47/93.65 thf(410,axiom,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) = (divide_divide_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8231_cos__45)). 185.47/93.65 thf(9095,plain,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) = (divide_divide_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[410])). 185.47/93.65 thf(2505,axiom,(((abs_abs_Code_integer @ one_one_Code_integer) = one_one_Code_integer)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6461_abs__one)). 185.47/93.65 thf(16040,plain,(((abs_abs_Code_integer @ one_one_Code_integer) = one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2505])). 185.47/93.65 thf(1917,axiom,((! [A:(nat > real),B:nat,C:nat]: ((! [D:nat]: (ord_less_real @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_real @ (A @ B) @ (A @ C)) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1054_lift__Suc__mono__less)). 185.47/93.65 thf(14135,plain,((! [A:(nat > real),B:nat,C:nat]: ((! [D:nat]: (ord_less_real @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_real @ (A @ B) @ (A @ C)) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1917])). 185.47/93.65 thf(4567,axiom,((! [A:(nat > int)]: ((groups3539618377306564664at_int @ A @ bot_bot_set_nat) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5219_sum_Oempty)). 185.47/93.65 thf(22630,plain,((! [A:(nat > int)]: ((groups3539618377306564664at_int @ (A) @ bot_bot_set_nat) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4567])). 185.47/93.65 thf(1390,axiom,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) <= ((plus_plus_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5733_add_Oinverse__unique)). 185.47/93.65 thf(12372,plain,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) | ~ ((plus_plus_real @ A @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390])). 185.47/93.65 thf(5243,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3960_linorder__le__cases)). 185.47/93.65 thf(25021,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5243])). 185.47/93.65 thf(5955,axiom,((! [A:int,B:num,C:nat]: (((ring_1_of_int_real @ A) = (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7152_of__int__eq__neg__numeral__power__cancel__iff)). 185.47/93.65 thf(27705,plain,((! [A:int,B:num,C:nat]: (((ring_1_of_int_real @ A) = (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5955])). 185.47/93.65 thf(6377,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((A = C) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1609_mult__cancel2)). 185.47/93.65 thf(29205,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((A = C) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6377])). 185.47/93.65 thf(1475,axiom,((zero_n2684676970156552555ol_int = (^ [A:$o]: (if_int @ A @ one_one_int @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5687_of__bool__def)). 185.47/93.65 thf(12645,plain,(((zero_n2684676970156552555ol_int) = (^ [A:$o]: (if_int @ A @ one_one_int @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1475])). 185.47/93.65 thf(1407,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ A)) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1638_zero__less__double__add__iff__zero__less__single__add)). 185.47/93.65 thf(12422,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ A)) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407])). 185.47/93.65 thf(628,axiom,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => ((~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D)))) <= (A != (vEBT_Leaf @ ($false) @ ($false))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2482_VEBT__internal_OminNull_Oelims_I2_J)). 185.47/93.65 thf(9814,plain,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) | (A = (vEBT_Leaf @ ($false) @ ($false))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[628])). 185.47/93.65 thf(7324,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ (divide_divide_nat @ C @ A) @ (divide_divide_nat @ B @ A))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4778_div__plus__div__distrib__dvd__right)). 185.47/93.65 thf(32679,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ (divide_divide_nat @ C @ A) @ (divide_divide_nat @ B @ A))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7324])). 185.47/93.65 thf(4751,axiom,((! [A:rat,B:rat,C:rat]: ((! [D:rat,E:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ D @ C)) = (dvd_dvd_rat @ A @ (plus_plus_rat @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)) @ C)))) <= (dvd_dvd_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4853_inf__period_I3_J)). 185.47/93.65 thf(23231,plain,((! [A:rat,B:rat,C:rat]: (! [D:rat,E:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ D @ C)) = (dvd_dvd_rat @ A @ (plus_plus_rat @ (minus_minus_rat @ D @ (times_times_rat @ E @ B)) @ C))) | ~ (dvd_dvd_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4751])). 185.47/93.65 thf(3818,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (semiri681578069525770553at_rat @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7045_of__nat__power__less__of__nat__cancel__iff)). 185.47/93.65 thf(20264,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (semiri681578069525770553at_rat @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3818])). 185.47/93.65 thf(5248,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1849_div__mult__self__is__m)). 185.47/93.65 thf(25034,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5248])). 185.47/93.65 thf(3049,axiom,((! [A:rat,B:rat,C:nat]: ((ord_less_rat @ A @ B) => (((ord_less_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ C)) <= (ord_less_eq_rat @ zero_zero_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2172_power__strict__mono)). 185.47/93.65 thf(17827,plain,((! [A:rat,B:rat,C:nat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_rat @ zero_zero_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3049])). 185.47/93.65 thf(5124,axiom,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => ((vEBT_vebt_mint @ A) = none_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_953_minNullmin)). 185.47/93.65 thf(24597,plain,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => ((vEBT_vebt_mint @ A) = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5124])). 185.47/93.65 thf(3882,axiom,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B)) => (~ (! [D:int]: (C != (plus_plus_int @ A @ (times_times_int @ B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2163_mod__eqE)). 185.47/93.65 thf(20463,plain,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B)) => (~ (! [D:int]: ~ (C = (plus_plus_int @ A @ (times_times_int @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3882])). 185.47/93.65 thf(1713,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_eq_real @ C @ (times_times_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2840_neg__le__divide__eq)). 185.47/93.65 thf(13463,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_eq_real @ C @ (times_times_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713])). 185.47/93.65 thf(7210,axiom,((! [A:nat,B:complex]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (power_power_complex @ B @ A))) & (((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (power_power_complex @ B @ A))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6186_uminus__power__if)). 185.47/93.65 thf(32290,plain,((! [A:nat,B:complex]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (power_power_complex @ B @ A))) & (((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (power_power_complex @ B @ A))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7210])). 185.47/93.65 thf(4758,axiom,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((vEBT_vebt_insert @ A @ B) = C) => (((((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((C != (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ (suc @ (suc @ D)) @ E @ F)) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F)))) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)) => (C != (if_VEBT_VEBT @ ((ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ~ ((B = E) | (B = D))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (ord_less_nat @ B @ D) @ B @ D) @ (ord_max_nat @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ H @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ H)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H))))))) <= (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((C != (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)) <= (A = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F))))) <= (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ D @ zero_zero_nat @ E @ F)) => (C != (vEBT_Node @ D @ zero_zero_nat @ E @ F))))) <= (! [D:$o,E:$o]: ((~ (((((C = (vEBT_Leaf @ D @ ($true))) <= (B = one_one_nat)) & ((B != one_one_nat) => (C = (vEBT_Leaf @ D @ E)))) <= (B != zero_zero_nat)) & ((C = (vEBT_Leaf @ ($true) @ E)) <= (B = zero_zero_nat)))) <= (A = (vEBT_Leaf @ D @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3790_vebt__insert_Oelims)). 185.47/93.65 thf(23254,plain,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((vEBT_vebt_insert @ A @ B) = C) => (((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ (C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ (suc @ (suc @ D)) @ E @ F)) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F)))) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)) => (~ (C = (if_VEBT_VEBT @ ((ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ~ ((B = E) | (B = D))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (ord_less_nat @ B @ D) @ B @ D) @ (ord_max_nat @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ H @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ H)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))))))) | ~ (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ (C = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)) | ~ (A = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)))) | ~ (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ D @ zero_zero_nat @ E @ F)) => (~ (C = (vEBT_Node @ D @ zero_zero_nat @ E @ F))))) | ~ (! [D:$o,E:$o]: (~ (((((C = (vEBT_Leaf @ D @ ($true))) | ~ (B = one_one_nat)) & ((~ (B = one_one_nat)) => (C = (vEBT_Leaf @ D @ E)))) | (B = zero_zero_nat)) & ((C = (vEBT_Leaf @ ($true) @ E)) | ~ (B = zero_zero_nat))) | ~ (A = (vEBT_Leaf @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4758])). 185.47/93.65 thf(1435,axiom,((! [A:nat]: ((divide_divide_int @ (bit_se2000444600071755411sk_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = (bit_se2000444600071755411sk_int @ (minus_minus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9233_mask__half__int)). 185.47/93.65 thf(12521,plain,((! [A:nat]: ((divide_divide_int @ (bit_se2000444600071755411sk_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = (bit_se2000444600071755411sk_int @ (minus_minus_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435])). 185.47/93.65 thf(6096,axiom,((! [A:nat,B:nat]: (((power_power_real @ (uminus_uminus_real @ one_one_real) @ (plus_plus_nat @ B @ A)) = (power_power_real @ (uminus_uminus_real @ one_one_real) @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6232_neg__one__power__add__eq__neg__one__power__diff)). 185.47/93.65 thf(28191,plain,((! [A:nat,B:nat]: (((power_power_real @ (uminus_uminus_real @ one_one_real) @ (plus_plus_nat @ B @ A)) = (power_power_real @ (uminus_uminus_real @ one_one_real) @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6096])). 185.47/93.65 thf(232,axiom,((! [A:real]: ((tan_real @ (minus_minus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ A)) = (inverse_inverse_real @ (tan_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8977_tan__cot)). 185.47/93.65 thf(8471,plain,((! [A:real]: ((tan_real @ (minus_minus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ A)) = (inverse_inverse_real @ (tan_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 185.47/93.65 thf(1386,axiom,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2081_add_Ocomm__neutral)). 185.47/93.65 thf(12353,plain,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386])). 185.47/93.65 thf(2860,axiom,((! [A:real]: ((ord_less_eq_real @ (sqrt @ A) @ one_one_real) = (ord_less_eq_real @ A @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8128_real__sqrt__le__1__iff)). 185.47/93.65 thf(17225,plain,((! [A:real]: ((ord_less_eq_real @ (sqrt @ A) @ one_one_real) = (ord_less_eq_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2860])). 185.47/93.65 thf(6629,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4678_dvd__power__same)). 185.47/93.65 thf(30099,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6629])). 185.47/93.65 thf(941,axiom,((! [A:int,B:(nat > nat),C:set_nat]: ((power_power_int @ A @ (groups3542108847815614940at_nat @ B @ C)) = (groups705719431365010083at_int @ (^ [D:nat]: (power_power_int @ A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8789_power__sum)). 185.47/93.65 thf(10962,plain,((! [A:int,B:(nat > nat),C:set_nat]: ((power_power_int @ A @ (groups3542108847815614940at_nat @ (B) @ C)) = (groups705719431365010083at_int @ (^ [D:nat]: (power_power_int @ A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[941])). 185.47/93.65 thf(5536,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (((divide_divide_nat @ A @ B) = zero_zero_nat) <= (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2180_unique__euclidean__semiring__numeral__class_Odiv__less)). 185.47/93.65 thf(26173,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (((divide_divide_nat @ A @ B) = zero_zero_nat) | ~ (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5536])). 185.47/93.65 thf(6521,axiom,(((neg_numeral_dbl_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5455_dbl__simps_I4_J)). 185.47/93.65 thf(29739,plain,(((neg_numeral_dbl_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6521])). 185.47/93.65 thf(1068,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ (modulo_modulo_int @ A @ B) @ (modulo_modulo_int @ C @ B)) @ B) = (modulo_modulo_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1998_mod__add__eq)). 185.47/93.65 thf(11356,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ (modulo_modulo_int @ A @ B) @ (modulo_modulo_int @ C @ B)) @ B) = (modulo_modulo_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068])). 185.47/93.65 thf(6284,axiom,((! [A:num]: ~ (ord_less_nat @ (numeral_numeral_nat @ A) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_822_not__numeral__less__one)). 185.47/93.65 thf(28876,plain,((! [A:num]: ~ (ord_less_nat @ (numeral_numeral_nat @ A) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6284])). 185.47/93.65 thf(3672,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (ord_max_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3691_max_Ocobounded2)). 185.47/93.65 thf(19786,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (ord_max_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3672])). 185.47/93.65 thf(910,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ A)))) = (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9526_or__not__numerals_I2_J)). 185.47/93.65 thf(10848,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ A)))) = (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[910])). 185.47/93.65 thf(2676,axiom,((! [A:rat]: ? [B:int]: ((ord_less_rat @ A @ (ring_1_of_int_rat @ (plus_plus_int @ B @ one_one_int))) & (ord_less_eq_rat @ (ring_1_of_int_rat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7369_floor__exists)). 185.47/93.65 thf(16601,plain,((! [A:rat]: ? [B:int]: ((ord_less_rat @ A @ (ring_1_of_int_rat @ (plus_plus_int @ B @ one_one_int))) & (ord_less_eq_rat @ (ring_1_of_int_rat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2676])). 185.47/93.65 thf(4739,axiom,((! [A:rat,B:rat,C:rat]: ((((plus_plus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (plus_plus_rat @ B @ (times_times_rat @ C @ A)) @ A)) <= (A != zero_zero_rat)) & (((plus_plus_rat @ (divide_divide_rat @ B @ A) @ C) = C) <= (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2749_add__divide__eq__if__simps_I2_J)). 185.47/93.65 thf(23195,plain,((! [A:rat,B:rat,C:rat]: ((((plus_plus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (plus_plus_rat @ B @ (times_times_rat @ C @ A)) @ A)) | (A = zero_zero_rat)) & (((plus_plus_rat @ (divide_divide_rat @ B @ A) @ C) = C) | ~ (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4739])). 185.47/93.65 thf(6272,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_mult_Oright__neutral)). 185.47/93.65 thf(28844,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6272])). 185.47/93.65 thf(5751,axiom,((! [A:real]: ((times_times_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5197_mult__minus1)). 185.47/93.65 thf(26864,plain,((! [A:real]: ((times_times_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5751])). 185.47/93.65 thf(1620,axiom,((! [A:(rat > (rat > $o)),B:rat,C:rat]: (((! [D:rat]: (A @ D @ D)) => ((A @ B @ C) <= (! [D:rat,E:rat]: ((A @ D @ E) <= (A @ E @ D))))) <= (! [D:rat,E:rat]: ((ord_less_rat @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4019_linorder__less__wlog)). 185.47/93.65 thf(13116,plain,((! [A:(rat > (rat > $o)),B:rat,C:rat]: (((! [D:rat]: (A @ D @ D)) => ((A @ B @ C) | ~ (! [D:rat,E:rat]: ((A @ D @ E) | ~ (A @ E @ D))))) | ~ (! [D:rat,E:rat]: ((ord_less_rat @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620])). 185.47/93.65 thf(600,axiom,((! [A:num,B:num]: ((archim6058952711729229775r_real @ (uminus_uminus_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)))) = (divide_divide_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9083_floor__minus__divide__eq__div__numeral)). 185.47/93.65 thf(9730,plain,((! [A:num,B:num]: ((archim6058952711729229775r_real @ (uminus_uminus_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)))) = (divide_divide_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[600])). 185.47/93.65 thf(7142,axiom,(((neg_nu3811975205180677377ec_int @ zero_zero_int) = (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6795_dbl__dec__simps_I2_J)). 185.47/93.65 thf(32042,plain,(((neg_nu3811975205180677377ec_int @ zero_zero_int) = (uminus_uminus_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7142])). 185.47/93.65 thf(1587,axiom,((! [A:nat]: ((zero_zero_complex = (semiri8010041392384452111omplex @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6887_of__nat__0__eq__iff)). 185.47/93.65 thf(12987,plain,((! [A:nat]: ((zero_zero_complex = (semiri8010041392384452111omplex @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587])). 185.47/93.65 thf(4393,axiom,((! [A:real,B:real,C:real]: ((A = (plus_plus_real @ B @ C)) => ((uminus_uminus_real @ A) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5560_group__cancel_Oneg1)). 185.47/93.65 thf(22073,plain,((! [A:real,B:real,C:real]: ((A = (plus_plus_real @ B @ C)) => ((uminus_uminus_real @ A) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4393])). 185.47/93.65 thf(6143,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((divide_divide_nat @ A @ B) = A) = (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2799_div__eq__dividend__iff)). 185.47/93.65 thf(28363,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((divide_divide_nat @ A @ B) = A) = (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6143])). 185.47/93.65 thf(7480,axiom,((! [A:nat]: ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus1482373934393186551omplex @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6295_power__minus1__odd)). 185.47/93.65 thf(33210,plain,((! [A:nat]: ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus1482373934393186551omplex @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7480])). 185.47/93.65 thf(4517,axiom,((! [A:rat,B:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (plus_plus_rat @ A @ B)) @ (plus_plus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6488_abs__triangle__ineq)). 185.47/93.65 thf(22473,plain,((! [A:rat,B:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (plus_plus_rat @ A @ B)) @ (plus_plus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4517])). 185.47/93.65 thf(2260,axiom,((! [A:int]: (dvd_dvd_int @ one_one_int @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4640_one__dvd)). 185.47/93.65 thf(15243,plain,((! [A:int]: (dvd_dvd_int @ one_one_int @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2260])). 185.47/93.65 thf(6339,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6912_of__nat__add)). 185.47/93.65 thf(29060,plain,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6339])). 185.47/93.65 thf(2762,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1636_zero__less__double__add__iff__zero__less__single__add)). 185.47/93.65 thf(16910,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2762])). 185.47/93.65 thf(993,axiom,((! [A:real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1723_one__divide__eq__0__iff)). 185.47/93.65 thf(11133,plain,((! [A:real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[993])). 185.47/93.65 thf(2887,axiom,((neg_nu3811975205180677377ec_int = (^ [A:int]: (minus_minus_int @ (plus_plus_int @ A @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6836_dbl__dec__def)). 185.47/93.65 thf(17314,plain,(((neg_nu3811975205180677377ec_int) = (^ [A:int]: (minus_minus_int @ (plus_plus_int @ A @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2887])). 185.47/93.65 thf(4820,axiom,((! [A:rat]: (ord_less_eq_rat @ zero_zero_rat @ (abs_abs_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6476_abs__ge__zero)). 185.47/93.65 thf(23480,plain,((! [A:rat]: (ord_less_eq_rat @ zero_zero_rat @ (abs_abs_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4820])). 185.47/93.65 thf(2420,axiom,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3106_verit__sum__simplify)). 185.47/93.65 thf(15739,plain,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2420])). 185.47/93.65 thf(7327,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:vEBT_VEBT]: ((A != B) => ((list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ C @ A @ D) @ B @ E) = (list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ C @ B @ E) @ A @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3652_list__update__swap)). 185.47/93.65 thf(32689,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:vEBT_VEBT]: ((~ (A = B)) => ((list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ C @ A @ D) @ B @ E) = (list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ C @ B @ E) @ A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7327])). 185.47/93.65 thf(6513,axiom,((! [A:list_VEBT_VEBT,B:nat,C:nat]: ((! [D:vEBT_VEBT]: ((vEBT_invar_vebt @ D @ B) <= (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)))) => ((ord_less_eq_nat @ one_one_nat @ B) <= ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_set__n__deg__not__0)). 185.47/93.65 thf(29711,plain,((! [A:list_VEBT_VEBT,B:nat,C:nat]: ((! [D:vEBT_VEBT]: ((vEBT_invar_vebt @ D @ B) | ~ (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)))) => ((ord_less_eq_nat @ one_one_nat @ B) | ~ ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6513])). 185.47/93.65 thf(7475,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_768_diff__mult__distrib)). 185.47/93.65 thf(33195,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7475])). 185.47/93.65 thf(6396,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((modulo_modulo_nat @ (modulo_modulo_nat @ C @ B) @ A) = (modulo_modulo_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4685_mod__mod__cancel)). 185.47/93.65 thf(29266,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((modulo_modulo_nat @ (modulo_modulo_nat @ C @ B) @ A) = (modulo_modulo_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6396])). 185.47/93.65 thf(6952,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = one_one_int) = (((B = one_one_int) & (A = one_one_int)) | ((B = (uminus_uminus_int @ one_one_int)) & (A = (uminus_uminus_int @ one_one_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5821_zmult__eq__1__iff)). 185.47/93.65 thf(31309,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = one_one_int) = (((B = one_one_int) & (A = one_one_int)) | ((B = (uminus_uminus_int @ one_one_int)) & (A = (uminus_uminus_int @ one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6952])). 185.47/93.65 thf(2636,axiom,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2082_add_Ocomm__neutral)). 185.47/93.65 thf(16472,plain,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2636])). 185.47/93.65 thf(4273,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) => (ord_less_eq_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_add__le__imp__le__right)). 185.47/93.65 thf(21668,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) => (ord_less_eq_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4273])). 185.47/93.65 thf(4552,axiom,((! [A:num]: ((pred_numeral @ (bit1 @ A)) = (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6787_pred__numeral__simps_I3_J)). 185.47/93.65 thf(22581,plain,((! [A:num]: ((pred_numeral @ (bit1 @ A)) = (numeral_numeral_nat @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4552])). 185.47/93.65 thf(5607,axiom,((suc = (plus_plus_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1105_Suc__eq__plus1__left)). 185.47/93.65 thf(26389,plain,(((suc) = (plus_plus_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5607])). 185.47/93.65 thf(5864,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ (times_times_nat @ B @ C)) @ C) = (modulo_modulo_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1782_mod__mult__self1)). 185.47/93.65 thf(27413,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ (times_times_nat @ B @ C)) @ C) = (modulo_modulo_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5864])). 185.47/93.65 thf(5998,axiom,((! [A:rat]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_rat @ (times_times_rat @ A @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6668_power3__eq__cube)). 185.47/93.65 thf(27886,plain,((! [A:rat]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_rat @ (times_times_rat @ A @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5998])). 185.47/93.65 thf(3102,axiom,((! [A:nat,B:int,C:int]: ((bit_concat_bit @ (suc @ A) @ B @ C) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_concat_bit @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3803_concat__bit__Suc)). 185.47/93.65 thf(17999,plain,((! [A:nat,B:int,C:int]: ((bit_concat_bit @ (suc @ A) @ B @ C) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_concat_bit @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3102])). 185.47/93.65 thf(5828,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_semiring__norm_I71_J)). 185.47/93.65 thf(27282,plain,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5828])). 185.47/93.65 thf(6648,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ B) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9338_take__bit__nat__less__self__iff)). 185.47/93.65 thf(30163,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ B) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6648])). 185.47/93.65 thf(4535,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1126_ring__class_Oring__distribs_I2_J)). 185.47/93.65 thf(22528,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4535])). 185.47/93.65 thf(6782,axiom,((! [A:num,B:int,C:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ (numeral_numeral_int @ A) @ B) @ (times_times_int @ (numeral_numeral_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_right__diff__distrib__numeral)). 185.47/93.65 thf(30676,plain,((! [A:num,B:int,C:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ (numeral_numeral_int @ A) @ B) @ (times_times_int @ (numeral_numeral_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6782])). 185.47/93.65 thf(921,axiom,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ A @ (uminus1351360451143612070nteger @ B)) = (ord_le6747313008572928689nteger @ B @ (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5521_less__minus__iff)). 185.47/93.65 thf(10887,plain,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ A @ (uminus1351360451143612070nteger @ B)) = (ord_le6747313008572928689nteger @ B @ (uminus1351360451143612070nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[921])). 185.47/93.65 thf(5392,axiom,((! [A:rat,B:rat,C:num]: ((times_times_rat @ (minus_minus_rat @ A @ B) @ (numeral_numeral_rat @ C)) = (minus_minus_rat @ (times_times_rat @ A @ (numeral_numeral_rat @ C)) @ (times_times_rat @ B @ (numeral_numeral_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_left__diff__distrib__numeral)). 185.47/93.65 thf(25573,plain,((! [A:rat,B:rat,C:num]: ((times_times_rat @ (minus_minus_rat @ A @ B) @ (numeral_numeral_rat @ C)) = (minus_minus_rat @ (times_times_rat @ A @ (numeral_numeral_rat @ C)) @ (times_times_rat @ B @ (numeral_numeral_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5392])). 185.47/93.65 thf(4139,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ zero_zero_rat @ C) => ((ord_less_eq_rat @ C @ D) => (ord_less_eq_rat @ (plus_plus_rat @ A @ (divide_divide_rat @ (times_times_rat @ C @ (minus_minus_rat @ B @ A)) @ D)) @ B))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2932_scaling__mono)). 185.47/93.65 thf(21258,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ zero_zero_rat @ C) => ((ord_less_eq_rat @ C @ D) => (ord_less_eq_rat @ (plus_plus_rat @ A @ (divide_divide_rat @ (times_times_rat @ C @ (minus_minus_rat @ B @ A)) @ D)) @ B))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4139])). 185.47/93.65 thf(3280,axiom,((! [A:num,B:rat,C:rat]: ((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (divide_divide_rat @ B @ C)) = (((ord_less_eq_rat @ (times_times_rat @ (numeral_numeral_rat @ A) @ C) @ B) <= (ord_less_rat @ zero_zero_rat @ C)) & ((((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ zero_zero_rat) <= (~ (ord_less_rat @ C @ zero_zero_rat))) & ((ord_less_eq_rat @ B @ (times_times_rat @ (numeral_numeral_rat @ A) @ C)) <= (ord_less_rat @ C @ zero_zero_rat))) <= (~ (ord_less_rat @ zero_zero_rat @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2926_le__divide__eq__numeral_I1_J)). 185.47/93.65 thf(18545,plain,((! [A:num,B:rat,C:rat]: ((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (divide_divide_rat @ B @ C)) = (((ord_less_eq_rat @ (times_times_rat @ (numeral_numeral_rat @ A) @ C) @ B) | ~ (ord_less_rat @ zero_zero_rat @ C)) & ((((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ zero_zero_rat) | (ord_less_rat @ C @ zero_zero_rat)) & ((ord_less_eq_rat @ B @ (times_times_rat @ (numeral_numeral_rat @ A) @ C)) | ~ (ord_less_rat @ C @ zero_zero_rat))) | (ord_less_rat @ zero_zero_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3280])). 185.47/93.65 thf(2713,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (divide_divide_int @ B @ C)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1691_div__mult__mult1)). 185.47/93.65 thf(16761,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (divide_divide_int @ B @ C)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2713])). 185.47/93.65 thf(2433,axiom,((! [A:complex,B:complex]: (((((tan_complex @ (plus_plus_complex @ A @ B)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (tan_complex @ A) @ (tan_complex @ B)) @ (minus_minus_complex @ one_one_complex @ (times_times_complex @ (tan_complex @ A) @ (tan_complex @ B))))) <= ((cos_complex @ (plus_plus_complex @ A @ B)) != zero_zero_complex)) <= ((cos_complex @ B) != zero_zero_complex)) <= ((cos_complex @ A) != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8084_tan__add)). 185.47/93.65 thf(15792,plain,((! [A:complex,B:complex]: (((tan_complex @ (plus_plus_complex @ A @ B)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (tan_complex @ A) @ (tan_complex @ B)) @ (minus_minus_complex @ one_one_complex @ (times_times_complex @ (tan_complex @ A) @ (tan_complex @ B))))) | ((cos_complex @ (plus_plus_complex @ A @ B)) = zero_zero_complex) | ((cos_complex @ B) = zero_zero_complex) | ((cos_complex @ A) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2433])). 185.47/93.65 thf(7070,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C)) @ A) = (modulo_modulo_nat @ (suc @ C) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1854_Suc__mod__mult__self4)). 185.47/93.65 thf(31805,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C)) @ A) = (modulo_modulo_nat @ (suc @ C) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7070])). 185.47/93.65 thf(2775,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: (((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((C @ D) != one_one_real))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((times_times_real @ (B @ D) @ (C @ D)) != one_one_real)))))) <= (finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((B @ D) != one_one_real) & (member_nat @ D @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3537_prod_Ofinite__Collect__op)). 185.47/93.65 thf(16949,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: (((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((C @ D) = one_one_real))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((times_times_real @ (B @ D) @ (C @ D)) = one_one_real)))))) | ~ (finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((B @ D) = one_one_real) & (member_nat @ D @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2775])). 185.47/93.65 thf(2339,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (cos_complex @ A) @ (cos_complex @ B)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (cos_complex @ (minus_minus_complex @ A @ B)) @ (cos_complex @ (plus_plus_complex @ A @ B))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7892_cos__times__cos)). 185.47/93.65 thf(15481,plain,((! [A:complex,B:complex]: ((times_times_complex @ (cos_complex @ A) @ (cos_complex @ B)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (cos_complex @ (minus_minus_complex @ A @ B)) @ (cos_complex @ (plus_plus_complex @ A @ B))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2339])). 185.47/93.65 thf(949,axiom,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ A @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups73079841787564623at_rat @ (^ [C:nat]: (times_times_rat @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) @ (set_ord_atMost_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8844_prod_Oin__pairs__0)). 185.47/93.65 thf(10986,plain,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ (A) @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups73079841787564623at_rat @ (^ [C:nat]: (times_times_rat @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) @ (set_ord_atMost_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[949])). 185.47/93.65 thf(3710,axiom,((! [A:int]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ one_one_rat) = (ord_less_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7090_of__int__less__1__iff)). 185.47/93.65 thf(19918,plain,((! [A:int]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ one_one_rat) = (ord_less_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3710])). 185.47/93.65 thf(85,axiom,(((set_ord_lessThan_nat @ zero_zero_nat) = bot_bot_set_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7547_lessThan__0)). 185.47/93.65 thf(8009,plain,(((set_ord_lessThan_nat @ zero_zero_nat) = bot_bot_set_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 185.47/93.65 thf(718,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (ord_max_int @ A @ B) @ C) = ((ord_less_int @ A @ C) & (ord_less_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3575_max__less__iff__conj)). 185.47/93.65 thf(10126,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (ord_max_int @ A @ B) @ C) = ((ord_less_int @ A @ C) & (ord_less_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[718])). 185.47/93.65 thf(3714,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((ord_max_nat @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3580_max_Oabsorb4)). 185.47/93.65 thf(19931,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((ord_max_nat @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3714])). 185.47/93.65 thf(3983,axiom,((abs_abs_rat = (^ [A:rat]: (if_rat @ (ord_less_rat @ A @ zero_zero_rat) @ (uminus_uminus_rat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6570_abs__if__raw)). 185.47/93.65 thf(20787,plain,(((abs_abs_rat) = (^ [A:rat]: (if_rat @ (ord_less_rat @ A @ zero_zero_rat) @ (uminus_uminus_rat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3983])). 185.47/93.65 thf(481,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (arctan @ A) @ (arctan @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6817_arctan__monotone_H)). 185.47/93.65 thf(9355,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (arctan @ A) @ (arctan @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])). 185.47/93.65 thf(5799,axiom,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ (comm_s4663373288045622133er_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8499_pochhammer__rec_H)). 185.47/93.65 thf(27095,plain,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ (comm_s4663373288045622133er_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5799])). 185.47/93.65 thf(4217,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (((plus_plus_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2279_add__nonpos__eq__0__iff)). 185.47/93.65 thf(21498,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (((plus_plus_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4217])). 185.47/93.65 thf(7108,axiom,((! [A:num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2261_zero__less__numeral)). 185.47/93.65 thf(31923,plain,((! [A:num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7108])). 185.47/93.65 thf(4397,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ C) => (ord_less_int @ B @ (plus_plus_int @ A @ C))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2398_pos__add__strict)). 185.47/93.65 thf(22085,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ C) => (ord_less_int @ B @ (plus_plus_int @ A @ C))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4397])). 185.47/93.65 thf(7519,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_add__less__cancel__left)). 185.47/93.65 thf(33342,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7519])). 185.47/93.65 thf(2781,axiom,((zero_n2687167440665602831ol_nat = (^ [A:$o]: (if_nat @ A @ one_one_nat @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5686_of__bool__def)). 185.47/93.65 thf(16968,plain,(((zero_n2687167440665602831ol_nat) = (^ [A:$o]: (if_nat @ A @ one_one_nat @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2781])). 185.47/93.65 thf(5727,axiom,(((plus_plus_int @ one_one_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_one__add__one)). 185.47/93.65 thf(26791,plain,(((plus_plus_int @ one_one_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5727])). 185.47/93.65 thf(6725,axiom,((! [A:num,B:real,C:real]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (divide_divide_real @ B @ C)) = ((((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) = B) <= (C != zero_zero_real)) & ((C = zero_zero_real) => ((uminus_uminus_real @ (numeral_numeral_real @ A)) = zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6156_eq__divide__eq__numeral_I2_J)). 185.47/93.65 thf(30430,plain,((! [A:num,B:real,C:real]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (divide_divide_real @ B @ C)) = ((((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) = B) | (C = zero_zero_real)) & ((C = zero_zero_real) => ((uminus_uminus_real @ (numeral_numeral_real @ A)) = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6725])). 185.47/93.65 thf(1181,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (B = (ord_max_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3681_max_Oorder__iff)). 185.47/93.65 thf(11715,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: (B = (ord_max_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181])). 185.47/93.65 thf(4474,axiom,((! [A:int,B:int]: ((ord_less_nat @ (nat2 @ A) @ (nat2 @ B)) = ((ord_less_int @ A @ B) & (ord_less_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9251_zless__nat__conj)). 185.47/93.65 thf(22322,plain,((! [A:int,B:int]: ((ord_less_nat @ (nat2 @ A) @ (nat2 @ B)) = ((ord_less_int @ A @ B) & (ord_less_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4474])). 185.47/93.65 thf(2736,axiom,((~ (ord_less_eq_real @ one_one_real @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2267_not__one__le__zero)). 185.47/93.65 thf(16833,plain,((~ (ord_less_eq_real @ one_one_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2736])). 185.47/93.65 thf(7346,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4984_even__mask__div__iff_H)). 185.47/93.65 thf(32756,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7346])). 185.47/93.65 thf(4067,axiom,(((neg_nu5851722552734809277nc_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7001_dbl__inc__simps_I4_J)). 185.47/93.65 thf(21034,plain,(((neg_nu5851722552734809277nc_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4067])). 185.47/93.65 thf(6193,axiom,((! [A:num,B:num]: ((minus_minus_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (numeral_numeral_real @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5332_diff__numeral__simps_I2_J)). 185.47/93.65 thf(28586,plain,((! [A:num,B:num]: ((minus_minus_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (numeral_numeral_real @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6193])). 185.47/93.65 thf(7182,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1141_distrib__right)). 185.47/93.65 thf(32192,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7182])). 185.47/93.65 thf(455,axiom,((tan_real = (^ [A:real]: (divide_divide_real @ (sin_real @ A) @ (cos_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8031_tan__def)). 185.47/93.65 thf(9245,plain,(((tan_real) = (^ [A:real]: (divide_divide_real @ (sin_real @ A) @ (cos_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])). 185.47/93.65 thf(1635,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (modulo_modulo_int @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1921_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend)). 185.47/93.65 thf(13173,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (modulo_modulo_int @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635])). 185.47/93.65 thf(662,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((arccos @ (uminus_uminus_real @ A)) = (minus_minus_real @ pi @ (arccos @ A))) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8376_arccos__minus)). 185.47/93.65 thf(9945,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((arccos @ (uminus_uminus_real @ A)) = (minus_minus_real @ pi @ (arccos @ A))) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[662])). 185.47/93.65 thf(3947,axiom,((! [A:rat,B:rat,C:(rat > rat),D:rat]: ((((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F)))) => (ord_less_rat @ (C @ A) @ D)) <= (ord_less_rat @ (C @ B) @ D)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4332_order__le__less__subst2)). 185.47/93.65 thf(20678,plain,((! [A:rat,B:rat,C:(rat > rat),D:rat]: (((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F)))) => (ord_less_rat @ (C @ A) @ D)) | ~ (ord_less_rat @ (C @ B) @ D) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3947])). 185.47/93.65 thf(188,axiom,((bit_se6528837805403552850or_nat = (^ [A:nat,B:nat]: (nat2 @ (bit_se6526347334894502574or_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9492_xor__nat__def)). 185.47/93.65 thf(8339,plain,(((bit_se6528837805403552850or_nat) = (^ [A:nat,B:nat]: (nat2 @ (bit_se6526347334894502574or_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 185.47/93.65 thf(878,axiom,((! [A:int,B:int,C:nat]: (((ring_1_of_int_int @ A) = (power_power_int @ (ring_1_of_int_int @ B) @ C)) = (A = (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6981_of__int__power__eq__of__int__cancel__iff)). 185.47/93.65 thf(10731,plain,((! [A:int,B:int,C:nat]: (((ring_1_of_int_int @ A) = (power_power_int @ (ring_1_of_int_int @ B) @ C)) = (A = (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[878])). 185.47/93.65 thf(981,axiom,((! [A:num,B:nat,C:int]: ((ord_less_eq_real @ (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7164_neg__numeral__power__le__of__int__cancel__iff)). 185.47/93.65 thf(11096,plain,((! [A:num,B:nat,C:int]: ((ord_less_eq_real @ (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[981])). 185.47/93.65 thf(650,axiom,((! [A:real,B:real]: (((cos_real @ A) != zero_zero_real) => (((cos_real @ B) != zero_zero_real) => ((plus_plus_real @ (tan_real @ A) @ (tan_real @ B)) = (divide_divide_real @ (sin_real @ (plus_plus_real @ A @ B)) @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8064_add__tan__eq)). 185.47/93.65 thf(9889,plain,((! [A:real,B:real]: ((~ ((cos_real @ A) = zero_zero_real)) => ((~ ((cos_real @ B) = zero_zero_real)) => ((plus_plus_real @ (tan_real @ A) @ (tan_real @ B)) = (divide_divide_real @ (sin_real @ (plus_plus_real @ A @ B)) @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[650])). 185.47/93.65 thf(475,axiom,((! [A:(nat > real),B:set_nat,C:real]: ((times_times_real @ (groups6591440286371151544t_real @ A @ B) @ C) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5614_sum__distrib__right)). 185.47/93.65 thf(9328,plain,((! [A:(nat > real),B:set_nat,C:real]: ((times_times_real @ (groups6591440286371151544t_real @ (A) @ B) @ C) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[475])). 185.47/93.65 thf(2526,axiom,((! [A:real]: ((cos_real @ (arctan @ A)) = (divide_divide_real @ one_one_real @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8270_cos__arctan)). 185.47/93.65 thf(16108,plain,((! [A:real]: ((cos_real @ (arctan @ A)) = (divide_divide_real @ one_one_real @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2526])). 185.47/93.65 thf(1443,axiom,((! [A:real]: (((cos_real @ A) = one_one_real) = (? [B:nat]: (A = (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ pi)) | ? [B:nat]: (A = (uminus_uminus_real @ (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ pi))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7929_cos__one__2pi)). 185.47/93.65 thf(12546,plain,((! [A:real]: (((cos_real @ A) = one_one_real) = (? [B:nat]: (A = (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ pi)) | ? [B:nat]: (A = (uminus_uminus_real @ (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ pi))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443])). 185.47/93.65 thf(1979,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_add__less__cancel__left)). 185.47/93.65 thf(14353,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1979])). 185.47/93.65 thf(6828,axiom,((! [A:int]: (((abs_abs_int @ A) = zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6323_abs__eq__0)). 185.47/93.65 thf(30832,plain,((! [A:int]: (((abs_abs_int @ A) = zero_zero_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6828])). 185.47/93.65 thf(3260,axiom,(((plus_plus_rat @ (uminus_uminus_rat @ one_one_rat) @ one_one_rat) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5274_add__neg__numeral__special_I8_J)). 185.47/93.65 thf(18480,plain,(((plus_plus_rat @ (uminus_uminus_rat @ one_one_rat) @ one_one_rat) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3260])). 185.47/93.65 thf(5133,axiom,((! [A:rat]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ one)) @ A) = (uminus_uminus_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5978_mult__1s__ring__1_I1_J)). 185.47/93.65 thf(24655,plain,((! [A:rat]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ one)) @ A) = (uminus_uminus_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5133])). 185.47/93.65 thf(7316,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4267_dual__order_Ostrict__implies__order)). 185.47/93.65 thf(32657,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7316])). 185.47/93.65 thf(2465,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_3879_order__trans)). 185.47/93.65 thf(15896,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)],[2465])). 185.47/93.65 thf(1430,axiom,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (plus_plus_rat @ A @ B)) = (plus_plus_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5097_minus__add__distrib)). 185.47/93.65 thf(12506,plain,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (plus_plus_rat @ A @ B)) = (plus_plus_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430])). 185.47/93.65 thf(2542,axiom,((! [A:rat,B:rat,C:num]: ((A = (divide_divide_rat @ B @ (numeral_numeral_rat @ C))) = ((((numeral_numeral_rat @ C) = zero_zero_rat) => (A = zero_zero_rat)) & (((times_times_rat @ A @ (numeral_numeral_rat @ C)) = B) <= ((numeral_numeral_rat @ C) != zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1822_eq__divide__eq__numeral1_I1_J)). 185.47/93.65 thf(16163,plain,((! [A:rat,B:rat,C:num]: ((A = (divide_divide_rat @ B @ (numeral_numeral_rat @ C))) = ((((numeral_numeral_rat @ C) = zero_zero_rat) => (A = zero_zero_rat)) & (((times_times_rat @ A @ (numeral_numeral_rat @ C)) = B) | ((numeral_numeral_rat @ C) = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2542])). 185.47/93.65 thf(2243,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6364_abs__le__self__iff)). 185.47/93.65 thf(15194,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2243])). 185.47/93.65 thf(1283,axiom,((! [A:product_prod_nat_nat]: ((nat2 @ (abs_Integ @ A)) = (produc6842872674320459806at_nat @ minus_minus_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9815_nat_Oabs__eq)). 185.47/93.65 thf(12016,plain,((! [A:product_prod_nat_nat]: ((nat2 @ (abs_Integ @ A)) = (produc6842872674320459806at_nat @ (minus_minus_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283])). 185.47/93.65 thf(5675,axiom,((! [A:nat]: ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus_uminus_rat @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6296_power__minus1__odd)). 185.47/93.65 thf(26620,plain,((! [A:nat]: ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5675])). 185.47/93.65 thf(7046,axiom,((! [A:nat,B:nat]: ((A = B) | (ord_less_nat @ B @ A) | (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4131_linorder__less__linear)). 185.47/93.65 thf(31734,plain,((! [A:nat,B:nat]: ((A = B) | (ord_less_nat @ B @ A) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7046])). 185.47/93.65 thf(5837,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_807_less__diff__iff)). 185.47/93.65 thf(27309,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5837])). 185.47/93.65 thf(3780,axiom,((! [A:int,B:int,C:(int > real),D:real]: ((((ord_less_real @ (C @ A) @ D) <= (! [E:int,F:int]: ((ord_less_real @ (C @ E) @ (C @ F)) <= (ord_less_int @ E @ F)))) <= (ord_less_eq_real @ (C @ B) @ D)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4355_order__less__le__subst2)). 185.47/93.65 thf(20148,plain,((! [A:int,B:int,C:(int > real),D:real]: ((ord_less_real @ (C @ A) @ D) | ~ (! [E:int,F:int]: ((ord_less_real @ (C @ E) @ (C @ F)) | ~ (ord_less_int @ E @ F))) | ~ (ord_less_eq_real @ (C @ B) @ D) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3780])). 185.47/93.65 thf(182,axiom,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ zero_zero_nat @ (B @ C)))) => (ord_less_eq_nat @ zero_zero_nat @ (groups708209901874060359at_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8744_prod__nonneg)). 185.47/93.65 thf(8319,plain,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ zero_zero_nat @ (B @ C)))) => (ord_less_eq_nat @ zero_zero_nat @ (groups708209901874060359at_nat @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 185.47/93.65 thf(6888,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ A))) = (? [C:nat]: ((member_nat @ C @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) & (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9562_ex__nat__less__eq)). 185.47/93.65 thf(31093,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ A))) = (? [C:nat]: ((member_nat @ C @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) & (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6888])). 185.47/93.65 thf(1020,axiom,((! [A:rat,B:rat,C:num]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))) = (((((~ (ord_less_rat @ B @ zero_zero_rat)) => (ord_less_rat @ zero_zero_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)))) & ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B) @ A))) <= (~ (ord_less_rat @ zero_zero_rat @ B))) & ((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6219_divide__less__eq__numeral_I2_J)). 185.47/93.65 thf(11221,plain,((! [A:rat,B:rat,C:num]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))) = (((((~ (ord_less_rat @ B @ zero_zero_rat)) => (ord_less_rat @ zero_zero_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)))) & ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B) @ A))) | (ord_less_rat @ zero_zero_rat @ B)) & ((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020])). 185.47/93.65 thf(509,axiom,((! [A:(nat > real),B:(nat > real)]: ((? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (A @ D)) @ (B @ D)))) => ((summable_real @ B) => (summable_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7657_summable__comparison__test)). 185.47/93.65 thf(9444,plain,((! [A:(nat > real),B:(nat > real)]: ((? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (A @ D)) @ (B @ D)))) => ((summable_real @ (B)) => (summable_real @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])). 185.47/93.65 thf(6308,axiom,((vEBT_VEBT_max_in_set = (^ [A:set_nat,B:nat]: ((member_nat @ B @ A) & ! [C:nat]: ((ord_less_eq_nat @ C @ B) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_max__in__set__def)). 185.47/93.65 thf(28952,plain,(((vEBT_VEBT_max_in_set) = (^ [A:set_nat,B:nat]: ((member_nat @ B @ A) & ! [C:nat]: ((ord_less_eq_nat @ C @ B) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6308])). 185.47/93.65 thf(757,axiom,(((exp_complex @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ pi))) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9135_exp__pi__i_H)). 185.47/93.65 thf(10266,plain,(((exp_complex @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ pi))) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[757])). 185.47/93.65 thf(2495,axiom,((! [A:nat,B:real]: ((exp_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ B)) = (power_power_real @ (exp_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8198_exp__of__nat__mult)). 185.47/93.65 thf(16004,plain,((! [A:nat,B:real]: ((exp_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ B)) = (power_power_real @ (exp_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2495])). 185.47/93.65 thf(5787,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_add__le__mono1)). 185.47/93.65 thf(26980,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5787])). 185.47/93.65 thf(4774,axiom,((! [A:num,B:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5690_neg__numeral__le__numeral)). 185.47/93.65 thf(23341,plain,((! [A:num,B:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4774])). 185.47/93.65 thf(5166,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ A @ (semiri1408675320244567234ct_nat @ B))) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8099_dvd__fact)). 185.47/93.65 thf(24771,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ A @ (semiri1408675320244567234ct_nat @ B))) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5166])). 185.47/93.65 thf(3169,axiom,((ord_max_nat = (^ [A:nat,B:nat]: (if_nat @ (ord_less_eq_nat @ A @ B) @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4414_max__def)). 185.47/93.65 thf(18205,plain,(((ord_max_nat) = (^ [A:nat,B:nat]: (if_nat @ (ord_less_eq_nat @ A @ B) @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3169])). 185.47/93.65 thf(3905,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (dvd_dvd_int @ B @ C)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4467_dvd__times__right__cancel__iff)). 185.47/93.65 thf(20538,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (dvd_dvd_int @ B @ C)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3905])). 185.47/93.65 thf(3214,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C) @ D) = (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2803_vebt__insert_Osimps_I3_J)). 185.47/93.65 thf(18351,plain,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C) @ D) = (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3214])). 185.47/93.65 thf(358,axiom,((! [A:real,B:(nat > real),C:set_nat]: ((times_times_real @ A @ (groups6591440286371151544t_real @ B @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5618_sum__distrib__left)). 185.47/93.65 thf(8931,plain,((! [A:real,B:(nat > real),C:set_nat]: ((times_times_real @ A @ (groups6591440286371151544t_real @ (B) @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])). 185.47/93.65 thf(7357,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_maxt @ A) = (some_nat @ C)) <= (vEBT_VEBT_max_in_set @ (vEBT_VEBT_set_vebt @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_946_maxt__sound)). 185.47/93.65 thf(32788,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_maxt @ A) = (some_nat @ C)) | ~ (vEBT_VEBT_max_in_set @ (vEBT_VEBT_set_vebt @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7357])). 185.47/93.65 thf(375,axiom,((! [A:nat,B:nat,C:(nat > real)]: (((groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_real @ (C @ A) @ (groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6657_sum_OatLeast__Suc__atMost)). 185.47/93.65 thf(8984,plain,((! [A:nat,B:nat,C:(nat > real)]: (((groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_real @ (C @ A) @ (groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])). 185.47/93.65 thf(271,axiom,((! [A:real,B:real]: ((((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) => ((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_eq_real @ (tan_real @ A) @ (tan_real @ B)) = (ord_less_eq_real @ A @ B)))) <= (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8068_tan__mono__le__eq)). 185.47/93.65 thf(8619,plain,((! [A:real,B:real]: (((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) => ((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_eq_real @ (tan_real @ A) @ (tan_real @ B)) = (ord_less_eq_real @ A @ B)))) | ~ (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[271])). 185.47/93.65 thf(7508,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((semiri773545260158071498ct_rat @ A) = (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8051_fact__reduce)). 185.47/93.65 thf(33310,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((semiri773545260158071498ct_rat @ A) = (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7508])). 185.47/93.65 thf(94,axiom,((! [A:(nat > int),B:nat,C:int]: ((minus_minus_int @ (groups3539618377306564664at_int @ A @ (set_ord_lessThan_nat @ B)) @ (times_times_int @ (semiri1314217659103216013at_int @ B) @ C)) = (groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7583_sumr__diff__mult__const2)). 185.47/93.65 thf(8041,plain,((! [A:(nat > int),B:nat,C:int]: ((minus_minus_int @ (groups3539618377306564664at_int @ (A) @ (set_ord_lessThan_nat @ B)) @ (times_times_int @ (semiri1314217659103216013at_int @ B) @ C)) = (groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 185.47/93.65 thf(4665,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => (((uminus_uminus_rat @ (divide_divide_rat @ B @ A)) = C) = ((uminus_uminus_rat @ B) = (times_times_rat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5968_nonzero__neg__divide__eq__eq)). 185.47/93.65 thf(22941,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => (((uminus_uminus_rat @ (divide_divide_rat @ B @ A)) = C) = ((uminus_uminus_rat @ B) = (times_times_rat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4665])). 185.47/93.65 thf(968,axiom,((! [A:real,B:nat]: ((gbinomial_real @ A @ (suc @ B)) = (plus_plus_real @ (gbinomial_real @ (minus_minus_real @ A @ one_one_real) @ (suc @ B)) @ (gbinomial_real @ (minus_minus_real @ A @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8476_gbinomial__addition__formula)). 185.47/93.65 thf(11057,plain,((! [A:real,B:nat]: ((gbinomial_real @ A @ (suc @ B)) = (plus_plus_real @ (gbinomial_real @ (minus_minus_real @ A @ one_one_real) @ (suc @ B)) @ (gbinomial_real @ (minus_minus_real @ A @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[968])). 185.47/93.65 thf(3515,axiom,((! [A:int,B:int]: (ord_less_eq_real @ (minus_minus_real @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) @ (ring_1_of_int_real @ (divide_divide_int @ A @ B))) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7326_real__of__int__div3)). 185.47/93.65 thf(19302,plain,((! [A:int,B:int]: (ord_less_eq_real @ (minus_minus_real @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) @ (ring_1_of_int_real @ (divide_divide_int @ A @ B))) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3515])). 185.47/93.65 thf(2026,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) <= (((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ zero_zero_real @ B)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2245_split__mult__pos__le)). 185.47/93.65 thf(14505,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) | ~ (((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ zero_zero_real @ B)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2026])). 185.47/93.65 thf(87,axiom,((! [A:(nat > real),B:nat,C:nat]: ((summable_real @ A) => ((! [D:nat]: ((ord_less_eq_nat @ B @ D) => (ord_less_eq_real @ zero_zero_real @ (A @ D)))) => ((ord_less_eq_nat @ B @ C) => ((ord_less_real @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B)) @ (suminf_real @ A)) <= (ord_less_real @ zero_zero_real @ (A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7756_sum__less__suminf2)). 185.47/93.65 thf(8014,plain,((! [A:(nat > real),B:nat,C:nat]: ((summable_real @ (A)) => ((! [D:nat]: ((ord_less_eq_nat @ B @ D) => (ord_less_eq_real @ zero_zero_real @ (A @ D)))) => ((ord_less_eq_nat @ B @ C) => ((ord_less_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B)) @ (suminf_real @ (A))) | ~ (ord_less_real @ zero_zero_real @ (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 185.47/93.65 thf(659,axiom,((! [A:set_nat,B:set_nat]: (((finite_finite_nat @ (minus_minus_set_nat @ B @ A)) = (finite_finite_nat @ B)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3458_finite__Diff2)). 185.47/93.65 thf(9936,plain,((! [A:set_nat,B:set_nat]: (((finite_finite_nat @ (minus_minus_set_nat @ B @ A)) = (finite_finite_nat @ B)) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[659])). 185.47/93.65 thf(4473,axiom,((! [A:rat,B:rat,C:num]: ((ord_less_eq_rat @ A @ (divide_divide_rat @ B @ (numeral_numeral_rat @ C))) = (ord_less_eq_rat @ (times_times_rat @ A @ (numeral_numeral_rat @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_le__divide__eq__numeral1_I1_J)). 185.47/93.65 thf(22319,plain,((! [A:rat,B:rat,C:num]: ((ord_less_eq_rat @ A @ (divide_divide_rat @ B @ (numeral_numeral_rat @ C))) = (ord_less_eq_rat @ (times_times_rat @ A @ (numeral_numeral_rat @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4473])). 185.47/93.65 thf(3379,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((A != zero_zero_rat) => ((B != zero_zero_rat) => ((minus_minus_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ D @ B)) = (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ D @ A)) @ (times_times_rat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2770_diff__frac__eq)). 185.47/93.65 thf(18860,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((~ (A = zero_zero_rat)) => ((~ (B = zero_zero_rat)) => ((minus_minus_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ D @ B)) = (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ D @ A)) @ (times_times_rat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3379])). 185.47/93.65 thf(570,axiom,((! [A:complex,B:complex]: ((((((re @ A) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ (im @ A))) | (ord_less_real @ zero_zero_real @ (re @ A))) => ((csqrt @ B) = A)) <= ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9699_csqrt__unique)). 185.47/93.65 thf(9624,plain,((! [A:complex,B:complex]: ((((((re @ A) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ (im @ A))) | (ord_less_real @ zero_zero_real @ (re @ A))) => ((csqrt @ B) = A)) | ~ ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[570])). 185.47/93.65 thf(765,axiom,((! [A:num,B:nat,C:int]: ((ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7167_neg__numeral__power__le__of__int__cancel__iff)). 185.47/93.65 thf(10335,plain,((! [A:num,B:nat,C:int]: ((ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[765])). 185.47/93.65 thf(4162,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_eq_int @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3307_pinf_I6_J)). 185.47/93.65 thf(21332,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_eq_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4162])). 185.47/93.65 thf(6120,axiom,((! [A:nat,B:nat,C:(nat > int),D:int]: ((! [E:nat]: (((ord_less_nat @ E @ B) & (ord_less_eq_nat @ A @ E)) => (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (C @ (suc @ E)) @ (C @ E))) @ one_one_int))) => ((((? [E:nat]: ((ord_less_eq_nat @ A @ E) & ((C @ E) = D) & (ord_less_eq_nat @ E @ B))) <= (ord_less_eq_int @ D @ (C @ B))) <= (ord_less_eq_int @ (C @ A) @ D)) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6832_nat__intermed__int__val)). 185.47/93.65 thf(28279,plain,((! [A:nat,B:nat,C:(nat > int),D:int]: ((! [E:nat]: (((ord_less_nat @ E @ B) & (ord_less_eq_nat @ A @ E)) => (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (C @ (suc @ E)) @ (C @ E))) @ one_one_int))) => (? [E:nat]: ((ord_less_eq_nat @ A @ E) & ((C @ E) = D) & (ord_less_eq_nat @ E @ B)) | ~ (ord_less_eq_int @ D @ (C @ B)) | ~ (ord_less_eq_int @ (C @ A) @ D) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6120])). 185.47/93.65 thf(225,axiom,((! [A:real,B:real,C:real]: ((((ord_less_eq_real @ (powr_real @ A @ C) @ B) = (ord_less_eq_real @ C @ (log @ A @ B))) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9118_powr__le__iff)). 185.47/93.65 thf(8451,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (powr_real @ A @ C) @ B) = (ord_less_eq_real @ C @ (log @ A @ B))) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 185.47/93.65 thf(3224,axiom,((! [A:nat,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ (semiri5074537144036343181t_real @ A) @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7113_of__nat__zero__less__power__iff)). 185.47/93.65 thf(18379,plain,((! [A:nat,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ (semiri5074537144036343181t_real @ A) @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3224])). 185.47/93.65 thf(2520,axiom,((! [A:rat]: ((plus_plus_rat @ A @ zero_zero_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1508_add_Oright__neutral)). 185.47/93.65 thf(16087,plain,((! [A:rat]: ((plus_plus_rat @ A @ zero_zero_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2520])). 185.47/93.65 thf(4752,axiom,((! [A:int]: (((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)) & ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4963_mod2__eq__if)). 185.47/93.65 thf(23235,plain,((! [A:int]: (((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)) & ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4752])). 185.47/93.65 thf(6003,axiom,((code_integer_of_num = numera6620942414471956472nteger)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9621_integer__of__num__def)). 185.47/93.65 thf(27909,plain,(((code_integer_of_num) = (numera6620942414471956472nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6003])). 185.47/93.65 thf(5517,axiom,(((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ one_one_int)) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5282_diff__numeral__special_I12_J)). 185.47/93.65 thf(26101,plain,(((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ one_one_int)) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5517])). 185.47/93.65 thf(343,axiom,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se4203085406695923979it_int @ A @ B)) = ((A = zero_zero_nat) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4950_even__unset__bit__iff)). 185.47/93.65 thf(8884,plain,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se4203085406695923979it_int @ A @ B)) = ((A = zero_zero_nat) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 185.47/93.65 thf(4906,axiom,((! [A:int,B:int]: ((plus_plus_int @ A @ (plus_plus_int @ (uminus_uminus_int @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5085_add__minus__cancel)). 185.47/93.65 thf(23780,plain,((! [A:int,B:int]: ((plus_plus_int @ A @ (plus_plus_int @ (uminus_uminus_int @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4906])). 185.47/93.65 thf(6636,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (divide_divide_nat @ B @ A) @ B)) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2798_div__less__dividend)). 185.47/93.65 thf(30121,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (divide_divide_nat @ B @ A) @ B)) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6636])). 185.47/93.65 thf(4542,axiom,((! [A:nat,B:complex]: (((gbinomial_complex @ B @ A) = (times_times_complex @ (divide1717551699836669952omplex @ B @ (semiri8010041392384452111omplex @ A)) @ (gbinomial_complex @ (minus_minus_complex @ B @ one_one_complex) @ (minus_minus_nat @ A @ one_one_nat)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8598_gbinomial__absorption_H)). 185.47/93.65 thf(22548,plain,((! [A:nat,B:complex]: (((gbinomial_complex @ B @ A) = (times_times_complex @ (divide1717551699836669952omplex @ B @ (semiri8010041392384452111omplex @ A)) @ (gbinomial_complex @ (minus_minus_complex @ B @ one_one_complex) @ (minus_minus_nat @ A @ one_one_nat)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4542])). 185.47/93.65 thf(7014,axiom,((! [A:nat,B:nat,C:real]: ((((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ C @ one_one_real) => (ord_less_eq_real @ (root @ A @ C) @ (root @ B @ C)))) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9202_real__root__increasing)). 185.47/93.65 thf(31603,plain,((! [A:nat,B:nat,C:real]: (((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ C @ one_one_real) => (ord_less_eq_real @ (root @ A @ C) @ (root @ B @ C)))) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7014])). 185.47/93.65 thf(7241,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (modulo_modulo_nat @ A @ B) @ A) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1920_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend)). 185.47/93.65 thf(32404,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (modulo_modulo_nat @ A @ B) @ A) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7241])). 185.47/93.65 thf(5139,axiom,((((~ (((vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_nat) & (vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (if_option_nat @ ((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ mi @ xa) @ (some_nat @ mi) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) & (((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) <= ((vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1245__C1_C)). 185.47/93.65 thf(24670,plain,((((~ (~ ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) & (vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (if_option_nat @ ((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ mi @ xa) @ (some_nat @ mi) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) & (((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) | ~ ((vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) & ~ ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5139])). 185.47/93.65 thf(4290,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6036_real__add__le__0__iff)). 185.47/93.65 thf(21715,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4290])). 185.47/93.65 thf(6462,axiom,((! [A:real,B:real]: (((times_times_real @ A @ A) = (times_times_real @ B @ B)) = ((A = (uminus_uminus_real @ B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5540_square__eq__iff)). 185.47/93.65 thf(29529,plain,((! [A:real,B:real]: (((times_times_real @ A @ A) = (times_times_real @ B @ B)) = ((A = (uminus_uminus_real @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6462])). 185.47/93.65 thf(4634,axiom,((! [A:num]: (((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ one_one_Code_integer)) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5290_numeral__eq__neg__one__iff)). 185.47/93.65 thf(22845,plain,((! [A:num]: (((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ one_one_Code_integer)) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4634])). 185.47/93.65 thf(2141,axiom,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: (((? [E:real]: ! [F:real]: ((((C @ F) & (A @ F)) = ((B @ F) & (D @ F))) <= (ord_less_real @ E @ F))) <= (? [E:real]: ! [F:real]: ((ord_less_real @ E @ F) => ((C @ F) = (D @ F))))) <= (? [E:real]: ! [F:real]: ((ord_less_real @ E @ F) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3225_pinf_I1_J)). 185.47/93.65 thf(14855,plain,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: (? [E:real]: ! [F:real]: ((((C @ F) & (A @ F)) = ((B @ F) & (D @ F))) | ~ (ord_less_real @ E @ F)) | ~ (? [E:real]: ! [F:real]: ((ord_less_real @ E @ F) => ((C @ F) = (D @ F)))) | ~ (? [E:real]: ! [F:real]: ((ord_less_real @ E @ F) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2141])). 185.47/93.65 thf(5640,axiom,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & (dvd_dvd_nat @ C @ B) & (((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ A @ E) @ C)) | ((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4815_bezout__add__nat)). 185.47/93.65 thf(26499,plain,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & (dvd_dvd_nat @ C @ B) & (((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ A @ E) @ C)) | ((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5640])). 185.47/93.65 thf(1913,axiom,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (times_times_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))) = (bit_se2923211474154528505it_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9268_take__bit__mult)). 185.47/93.65 thf(14121,plain,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (times_times_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))) = (bit_se2923211474154528505it_int @ A @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1913])). 185.47/93.65 thf(1632,axiom,((! [A:int,B:int]: (((nat2 @ (divide_divide_int @ A @ B)) = (divide_divide_nat @ (nat2 @ A) @ (nat2 @ B))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9316_nat__div__distrib)). 185.47/93.65 thf(13163,plain,((! [A:int,B:int]: (((nat2 @ (divide_divide_int @ A @ B)) = (divide_divide_nat @ (nat2 @ A) @ (nat2 @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632])). 185.47/93.65 thf(726,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ B)))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9542_or__not__numerals_I5_J)). 185.47/93.65 thf(10152,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ B)))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[726])). 185.47/93.65 thf(5404,axiom,((! [A:num,B:num,C:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (times_times_int @ (numeral_numeral_int @ B) @ C)) = (times_times_int @ (numeral_numeral_int @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_mult__numeral__left__semiring__numeral)). 185.47/93.65 thf(25608,plain,((! [A:num,B:num,C:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (times_times_int @ (numeral_numeral_int @ B) @ C)) = (times_times_int @ (numeral_numeral_int @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5404])). 185.47/93.65 thf(2333,axiom,((! [A:rat,B:rat]: ((A = (abs_abs_rat @ B)) = ((ord_less_eq_rat @ zero_zero_rat @ A) & ((B = A) | (B = (uminus_uminus_rat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6552_eq__abs__iff_H)). 185.47/93.65 thf(15466,plain,((! [A:rat,B:rat]: ((A = (abs_abs_rat @ B)) = ((ord_less_eq_rat @ zero_zero_rat @ A) & ((B = A) | (B = (uminus_uminus_rat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2333])). 185.47/93.65 thf(1989,axiom,((! [A:int,B:int]: ((nat2 @ (abs_abs_int @ (times_times_int @ A @ B))) = (times_times_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9298_nat__abs__mult__distrib)). 185.47/93.65 thf(14381,plain,((! [A:int,B:int]: ((nat2 @ (abs_abs_int @ (times_times_int @ A @ B))) = (times_times_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1989])). 185.47/93.65 thf(992,axiom,((! [A:real,B:real,C:real]: ((! [D:real,E:real]: ((~ (dvd_dvd_real @ A @ (plus_plus_real @ D @ C))) = (~ (dvd_dvd_real @ A @ (plus_plus_real @ (minus_minus_real @ D @ (times_times_real @ E @ B)) @ C))))) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4848_inf__period_I4_J)). 185.47/93.65 thf(11128,plain,((! [A:real,B:real,C:real]: (! [D:real,E:real]: ((~ (dvd_dvd_real @ A @ (plus_plus_real @ D @ C))) = (~ (dvd_dvd_real @ A @ (plus_plus_real @ (minus_minus_real @ D @ (times_times_real @ E @ B)) @ C)))) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[992])). 185.47/93.65 thf(2241,axiom,((arctan = (^ [A:real]: (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (arctan @ (divide_divide_real @ A @ (plus_plus_real @ one_one_real @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8278_arctan__half)). 185.47/93.65 thf(15189,plain,(((arctan) = (^ [A:real]: (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (arctan @ (divide_divide_real @ A @ (plus_plus_real @ one_one_real @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2241])). 185.47/93.65 thf(6918,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) = (? [D:nat,E:nat]: ((plus_plus_nat @ A @ (times_times_nat @ B @ D)) = (plus_plus_nat @ C @ (times_times_nat @ B @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2132_nat__mod__eq__iff)). 185.47/93.65 thf(31189,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) = (? [D:nat,E:nat]: ((plus_plus_nat @ A @ (times_times_nat @ B @ D)) = (plus_plus_nat @ C @ (times_times_nat @ B @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6918])). 185.47/93.65 thf(4103,axiom,((! [A:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5938_not__numeral__le__neg__one)). 185.47/93.65 thf(21150,plain,((! [A:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4103])). 185.47/93.65 thf(2136,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (ord_less_rat @ (times_times_rat @ C @ A) @ (uminus_uminus_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6151_neg__minus__divide__less__eq)). 185.47/93.65 thf(14840,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (ord_less_rat @ (times_times_rat @ C @ A) @ (uminus_uminus_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2136])). 185.47/93.65 thf(2963,axiom,((! [A:real,B:real,C:real]: (((B = C) => (ord_less_real @ A @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3991_ord__less__eq__trans)). 185.47/93.65 thf(17550,plain,((! [A:real,B:real,C:real]: (((B = C) => (ord_less_real @ A @ C)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2963])). 185.47/93.65 thf(276,axiom,((! [A:num,B:nat,C:int]: ((ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7140_numeral__power__le__of__int__cancel__iff)). 185.47/93.65 thf(8636,plain,((! [A:num,B:nat,C:int]: ((ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 185.47/93.65 thf(4706,axiom,((! [A:int,B:int,C:$o]: ((ord_less_int @ A @ B) => ((C) <= (ord_less_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4127_order__less__imp__triv)). 185.47/93.65 thf(23094,plain,((! [A:int,B:int,C:$o]: ((ord_less_int @ A @ B) => ((C) | ~ (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4706])). 185.47/93.65 thf(3362,axiom,((! [A:num,B:num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (ord_less_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5371_neg__numeral__less__iff)). 185.47/93.65 thf(18806,plain,((! [A:num,B:num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (ord_less_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3362])). 185.47/93.65 thf(791,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (ring_1_of_int_int @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7333_even__of__int__iff)). 185.47/93.65 thf(10430,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (ring_1_of_int_int @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[791])). 185.47/93.65 thf(2218,axiom,((! [A:rat,B:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ A @ B)) = (dvd_dvd_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4442_dvd__add__triv__left__iff)). 185.47/93.65 thf(15114,plain,((! [A:rat,B:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ A @ B)) = (dvd_dvd_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2218])). 185.47/93.65 thf(2057,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((times_times_rat @ (divide_divide_rat @ A @ B) @ (divide_divide_rat @ C @ D)) = (divide_divide_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_times__divide__times__eq)). 185.47/93.65 thf(14601,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((times_times_rat @ (divide_divide_rat @ A @ B) @ (divide_divide_rat @ C @ D)) = (divide_divide_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2057])). 185.47/93.65 thf(2168,axiom,((! [A:num,B:num,C:(num > int),D:int]: ((((! [E:num,F:num]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D)) <= (ord_less_eq_int @ (C @ B) @ D)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3926_order__subst2)). 185.47/93.65 thf(14953,plain,((! [A:num,B:num,C:(num > int),D:int]: (((! [E:num,F:num]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D)) | ~ (ord_less_eq_int @ (C @ B) @ D) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2168])). 185.47/93.65 thf(4387,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => (((divide_divide_real @ B @ A) = C) = (B = (times_times_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2462_nonzero__divide__eq__eq)). 185.47/93.65 thf(22056,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => (((divide_divide_real @ B @ A) = C) = (B = (times_times_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4387])). 185.47/93.65 thf(2811,axiom,((unique5026877609467782581ep_nat = (^ [A:num]: (produc2626176000494625587at_nat @ (^ [B:nat,C:nat]: (if_Pro6206227464963214023at_nat @ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ C) @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat) @ (minus_minus_nat @ C @ (numeral_numeral_nat @ A))) @ (product_Pair_nat_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7336_divmod__step__nat__def)). 185.47/93.65 thf(17065,plain,(((unique5026877609467782581ep_nat) = (^ [A:num]: (produc2626176000494625587at_nat @ (^ [B:nat,C:nat]: (if_Pro6206227464963214023at_nat @ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ C) @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat) @ (minus_minus_nat @ C @ (numeral_numeral_nat @ A))) @ (product_Pair_nat_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2811])). 185.47/93.65 thf(3421,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_real @ (times_times_real @ C @ A) @ (uminus_uminus_real @ B))) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6150_neg__minus__divide__less__eq)). 185.47/93.65 thf(18994,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_real @ (times_times_real @ C @ A) @ (uminus_uminus_real @ B))) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3421])). 185.47/93.65 thf(4821,axiom,((! [A:$o]: ((zero_n2684676970156552555ol_int @ (~ (A))) = (minus_minus_int @ one_one_int @ (zero_n2684676970156552555ol_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5247_of__bool__not__iff)). 185.47/93.65 thf(23482,plain,((! [A:$o]: ((zero_n2684676970156552555ol_int @ (~ (A))) = (minus_minus_int @ one_one_int @ (zero_n2684676970156552555ol_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4821])). 185.47/93.65 thf(2176,axiom,(((real_V1022390504157884413omplex @ one_one_complex) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7455_norm__one)). 185.47/93.65 thf(14990,plain,(((real_V1022390504157884413omplex @ one_one_complex) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2176])). 185.47/93.65 thf(6544,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_less__SucI)). 185.47/93.65 thf(29821,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6544])). 185.47/93.65 thf(6491,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1847_mult__le__cancel2)). 185.47/93.65 thf(29637,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6491])). 185.47/93.65 thf(3823,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ B) <= (ord_less_real @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4033_dual__order_Ostrict__trans)). 185.47/93.65 thf(20277,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ B) | ~ (ord_less_real @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3823])). 185.47/93.65 thf(1775,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ (divide_divide_rat @ C @ A)) = (ord_less_eq_rat @ C @ (times_times_rat @ B @ A))) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2841_neg__le__divide__eq)). 185.47/93.65 thf(13676,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ (divide_divide_rat @ C @ A)) = (ord_less_eq_rat @ C @ (times_times_rat @ B @ A))) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775])). 185.47/93.65 thf(1525,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) => (ord_less_eq_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_add__le__imp__le__left)). 185.47/93.65 thf(12796,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) => (ord_less_eq_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525])). 185.47/93.65 thf(979,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (plus_plus_real @ C @ (times_times_real @ B @ A)) @ A)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2736_add__num__frac)). 185.47/93.65 thf(11089,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (plus_plus_real @ C @ (times_times_real @ B @ A)) @ A)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[979])). 185.47/93.65 thf(2245,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (ord_max_nat @ A @ B) @ C) = ((ord_less_eq_nat @ A @ C) & (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3558_max_Obounded__iff)). 185.47/93.65 thf(15201,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (ord_max_nat @ A @ B) @ C) = ((ord_less_eq_nat @ A @ C) & (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2245])). 185.47/93.65 thf(5923,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_le__square)). 185.47/93.65 thf(27610,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5923])). 185.47/93.65 thf(1984,axiom,((! [A:real]: ((ord_less_real @ one_one_real @ (exp_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8134_one__less__exp__iff)). 185.47/93.65 thf(14366,plain,((! [A:real]: ((ord_less_real @ one_one_real @ (exp_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1984])). 185.47/93.65 thf(3330,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_int @ B @ zero_zero_int) => (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2407_add__neg__neg)). 185.47/93.65 thf(18701,plain,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_int @ B @ zero_zero_int) => (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3330])). 185.47/93.65 thf(6858,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2102_Zero__neq__Suc)). 185.47/93.65 thf(30979,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6858])). 185.47/93.65 thf(6990,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = ((B @ zero_zero_nat) & ! [C:nat]: ((ord_less_nat @ C @ A) => (B @ (suc @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2493_All__less__Suc2)). 185.47/93.65 thf(31514,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = ((B @ zero_zero_nat) & ! [C:nat]: ((ord_less_nat @ C @ A) => (B @ (suc @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6990])). 185.47/93.65 thf(6431,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (power_power_nat @ (modulo_modulo_nat @ A @ B) @ C) @ B) = (modulo_modulo_nat @ (power_power_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2008_power__mod)). 185.47/93.65 thf(29417,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (power_power_nat @ (modulo_modulo_nat @ A @ B) @ C) @ B) = (modulo_modulo_nat @ (power_power_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6431])). 185.47/93.65 thf(1675,axiom,((bit_se2161824704523386999it_nat = (^ [A:nat,B:nat]: (bit_se6528837805403552850or_nat @ B @ (bit_se547839408752420682it_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9510_flip__bit__nat__def)). 185.47/93.65 thf(13344,plain,(((bit_se2161824704523386999it_nat) = (^ [A:nat,B:nat]: (bit_se6528837805403552850or_nat @ B @ (bit_se547839408752420682it_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675])). 185.47/93.65 thf(4657,axiom,((! [A:complex,B:nat]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (power_power_complex @ A @ B)) @ (power_power_real @ (real_V1022390504157884413omplex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7489_norm__power__ineq)). 185.47/93.65 thf(22919,plain,((! [A:complex,B:nat]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (power_power_complex @ A @ B)) @ (power_power_real @ (real_V1022390504157884413omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4657])). 185.47/93.65 thf(1539,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((A = (times_3573771949741848930nteger @ B @ C)) => (dvd_dvd_Code_integer @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4615_dvdI)). 185.47/93.65 thf(12834,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((A = (times_3573771949741848930nteger @ B @ C)) => (dvd_dvd_Code_integer @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1539])). 185.47/93.65 thf(1711,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((~ (ord_less_rat @ C @ A)) <= (ord_less_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3246_pinf_I5_J)). 185.47/93.65 thf(13458,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: (~ (ord_less_rat @ C @ A) | ~ (ord_less_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711])). 185.47/93.65 thf(7404,axiom,((! [A:num,B:rat,C:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (times_times_rat @ (numeral_numeral_rat @ A) @ B) @ (times_times_rat @ (numeral_numeral_rat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_right__diff__distrib__numeral)). 185.47/93.65 thf(32936,plain,((! [A:num,B:rat,C:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (times_times_rat @ (numeral_numeral_rat @ A) @ B) @ (times_times_rat @ (numeral_numeral_rat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7404])). 185.47/93.65 thf(3575,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ A @ (times_times_complex @ A @ B)) = (divide1717551699836669952omplex @ one_one_complex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1829_nonzero__divide__mult__cancel__left)). 185.47/93.65 thf(19478,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ A @ (times_times_complex @ A @ B)) = (divide1717551699836669952omplex @ one_one_complex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3575])). 185.47/93.65 thf(6404,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((B = none_nat) => (~ (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)) => ((B = (some_nat @ D)) => (~ (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))))))) <= (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((((D) => (B = (some_nat @ one_one_nat))) & ((((C) => (B = (some_nat @ zero_zero_nat))) & ((~ (C)) => (B = none_nat))) <= (~ (D)))) => (~ (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ (vEBT_Leaf @ C @ D))))))) <= (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ A)) <= ((vEBT_vebt_maxt @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8283_vebt__maxt_Opelims)). 185.47/93.65 thf(29293,plain,((! [A:vEBT_VEBT,B:option_nat]: (((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((B = none_nat) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)) => ((B = (some_nat @ D)) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))))))) | ~ (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((((D) => (B = (some_nat @ one_one_nat))) & ((((C) => (B = (some_nat @ zero_zero_nat))) & ((~ (C)) => (B = none_nat))) | (D))) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ (vEBT_Leaf @ C @ D)))))) | ~ (accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ A) | ~ ((vEBT_vebt_maxt @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6404])). 185.47/93.65 thf(2417,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (sqrt @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (sqrt @ A) @ (sqrt @ B))) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8182_sqrt__add__le__add__sqrt)). 185.47/93.65 thf(15729,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (sqrt @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (sqrt @ A) @ (sqrt @ B))) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2417])). 185.47/93.65 thf(653,axiom,((! [A:nat,B:int]: ((ord_less_int @ (bit_se7879613467334960850it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3129_set__bit__negative__int__iff)). 185.47/93.65 thf(9904,plain,((! [A:nat,B:int]: ((ord_less_int @ (bit_se7879613467334960850it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[653])). 185.47/93.65 thf(4174,axiom,((! [A:nat]: (ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7321_of__nat__less__two__power)). 185.47/93.65 thf(21364,plain,((! [A:nat]: (ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4174])). 185.47/93.65 thf(6621,axiom,((! [A:rat,B:rat,C:nat]: ((power_power_rat @ (times_times_rat @ A @ B) @ C) = (times_times_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_power__mult__distrib)). 185.47/93.65 thf(30074,plain,((! [A:rat,B:rat,C:nat]: ((power_power_rat @ (times_times_rat @ A @ B) @ C) = (times_times_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6621])). 185.47/93.65 thf(4410,axiom,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_diff__eq__diff__less__eq)). 185.47/93.65 thf(22122,plain,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((ord_less_eq_int @ A @ B) = (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4410])). 185.47/93.65 thf(3602,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ A @ (divide_divide_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4764_dvd__mult__imp__div)). 185.47/93.65 thf(19566,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ A @ (divide_divide_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3602])). 185.47/93.65 thf(885,axiom,((! [A:nat,B:real]: (((ord_less_real @ B @ zero_zero_real) => (? [C:real]: (((cos_real @ B) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (cos_coeff @ D) @ (power_power_real @ B @ D))) @ (set_ord_lessThan_nat @ A)) @ (times_times_real @ (divide_divide_real @ (cos_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ A)) @ pi))) @ (semiri2265585572941072030t_real @ A)) @ (power_power_real @ B @ A)))) & (ord_less_real @ C @ zero_zero_real) & (ord_less_real @ B @ C)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7946_Maclaurin__minus__cos__expansion)). 185.47/93.65 thf(10760,plain,((! [A:nat,B:real]: (((ord_less_real @ B @ zero_zero_real) => (? [C:real]: (((cos_real @ B) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (cos_coeff @ D) @ (power_power_real @ B @ D))) @ (set_ord_lessThan_nat @ A)) @ (times_times_real @ (divide_divide_real @ (cos_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ A)) @ pi))) @ (semiri2265585572941072030t_real @ A)) @ (power_power_real @ B @ A)))) & (ord_less_real @ C @ zero_zero_real) & (ord_less_real @ B @ C)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[885])). 185.47/93.65 thf(7470,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8008_fact__dvd)). 185.47/93.65 thf(33178,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7470])). 185.47/93.65 thf(2274,axiom,((! [A:real,B:real,C:real]: ((A = (uminus_uminus_real @ (divide_divide_real @ B @ C))) = ((((times_times_real @ A @ C) = (uminus_uminus_real @ B)) <= (C != zero_zero_real)) & ((A = zero_zero_real) <= (C = zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5972_eq__minus__divide__eq)). 185.47/93.65 thf(15281,plain,((! [A:real,B:real,C:real]: ((A = (uminus_uminus_real @ (divide_divide_real @ B @ C))) = ((((times_times_real @ A @ C) = (uminus_uminus_real @ B)) | (C = zero_zero_real)) & ((A = zero_zero_real) | ~ (C = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2274])). 185.47/93.65 thf(3072,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (ord_max_nat @ A @ B) @ C) => (~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3671_max_OboundedE)). 185.47/93.65 thf(17898,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (ord_max_nat @ A @ B) @ C) => (~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3072])). 185.47/93.65 thf(126,axiom,((! [A:set_nat,B:(nat > real)]: (((groups129246275422532515t_real @ B @ A) = one_one_real) <= (~ (finite_finite_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8654_prod_Oinfinite)). 185.47/93.65 thf(8138,plain,((! [A:set_nat,B:(nat > real)]: (((groups129246275422532515t_real @ (B) @ A) = one_one_real) | (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 185.47/93.65 thf(7214,axiom,((! [A:complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1556_diff__self)). 185.47/93.65 thf(32307,plain,((! [A:complex]: ((minus_minus_complex @ A @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7214])). 185.47/93.65 thf(696,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((((groups2073611262835488442omplex @ (^ [D:nat]: (divide1717551699836669952omplex @ (times_times_complex @ (B @ D) @ (power_power_complex @ zero_zero_complex @ D)) @ (C @ D))) @ A) = zero_zero_complex) <= (~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A)))) & (((groups2073611262835488442omplex @ (^ [D:nat]: (divide1717551699836669952omplex @ (times_times_complex @ (B @ D) @ (power_power_complex @ zero_zero_complex @ D)) @ (C @ D))) @ A) = (divide1717551699836669952omplex @ (B @ zero_zero_nat) @ (C @ zero_zero_nat))) <= ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6444_sum__zero__power_H)). 185.47/93.65 thf(10052,plain,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((((groups2073611262835488442omplex @ (^ [D:nat]: (divide1717551699836669952omplex @ (times_times_complex @ (B @ D) @ (power_power_complex @ zero_zero_complex @ D)) @ (C @ D))) @ A) = zero_zero_complex) | ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))) & (((groups2073611262835488442omplex @ (^ [D:nat]: (divide1717551699836669952omplex @ (times_times_complex @ (B @ D) @ (power_power_complex @ zero_zero_complex @ D)) @ (C @ D))) @ A) = (divide1717551699836669952omplex @ (B @ zero_zero_nat) @ (C @ zero_zero_nat))) | ~ ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[696])). 185.47/93.65 thf(1583,axiom,((! [A:num]: ((neg_numeral_dbl_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (neg_numeral_dbl_int @ (numeral_numeral_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5267_dbl__simps_I1_J)). 185.47/93.65 thf(12974,plain,((! [A:num]: ((neg_numeral_dbl_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (neg_numeral_dbl_int @ (numeral_numeral_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583])). 185.47/93.65 thf(5072,axiom,((! [A:nat]: ((modulo_modulo_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1586_bits__mod__0)). 185.47/93.65 thf(24409,plain,((! [A:nat]: ((modulo_modulo_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5072])). 185.47/93.65 thf(614,axiom,((! [A:real]: (((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ zero_zero_real @ (sin_real @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7896_sin__gt__zero2)). 185.47/93.65 thf(9772,plain,((! [A:real]: (((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ zero_zero_real @ (sin_real @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[614])). 185.47/93.65 thf(1235,axiom,((! [A:nat]: (ord_less_eq_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7274_negative__zle__0)). 185.47/93.65 thf(11877,plain,((! [A:nat]: (ord_less_eq_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235])). 185.47/93.65 thf(741,axiom,((! [A:real,B:real,C:int]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ B) => (((archim6058952711729229775r_real @ (log @ B @ A)) = C) = ((ord_less_eq_real @ (powr_real @ B @ (ring_1_of_int_real @ C)) @ A) & (ord_less_real @ A @ (powr_real @ B @ (ring_1_of_int_real @ (plus_plus_int @ C @ one_one_int)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9105_floor__log__eq__powr__iff)). 185.47/93.65 thf(10203,plain,((! [A:real,B:real,C:int]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ B) => (((archim6058952711729229775r_real @ (log @ B @ A)) = C) = ((ord_less_eq_real @ (powr_real @ B @ (ring_1_of_int_real @ C)) @ A) & (ord_less_real @ A @ (powr_real @ B @ (ring_1_of_int_real @ (plus_plus_int @ C @ one_one_int)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[741])). 185.47/93.65 thf(1344,axiom,((! [A:num]: ((neg_nu5219082963157363817nc_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (uminus_uminus_rat @ (neg_nu3179335615603231917ec_rat @ (numeral_numeral_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6865_dbl__inc__simps_I1_J)). 185.47/93.65 thf(12211,plain,((! [A:num]: ((neg_nu5219082963157363817nc_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (uminus_uminus_rat @ (neg_nu3179335615603231917ec_rat @ (numeral_numeral_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344])). 185.47/93.65 thf(5630,axiom,((! [A:num]: ((bit_or_not_num_neg @ one @ (bit0 @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9471_or__not__num__neg_Osimps_I2_J)). 185.47/93.65 thf(26470,plain,((! [A:num]: ((bit_or_not_num_neg @ one @ (bit0 @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5630])). 185.47/93.65 thf(4875,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((set_or1269000886237332187st_nat @ A @ B) = (set_or1269000886237332187st_nat @ C @ D)) = (((A = C) & (B = D)) | (~ (ord_less_eq_nat @ C @ D) & ~ (ord_less_eq_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3212_Icc__eq__Icc)). 185.47/93.65 thf(23656,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((set_or1269000886237332187st_nat @ A @ B) = (set_or1269000886237332187st_nat @ C @ D)) = (((A = C) & (B = D)) | (~ (ord_less_eq_nat @ C @ D) & ~ (ord_less_eq_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4875])). 185.47/93.65 thf(3510,axiom,((! [A:nat,B:nat,C:int]: (((ord_less_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)) <= (ord_less_int @ one_one_int @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_power__strict__increasing)). 185.47/93.65 thf(19287,plain,((! [A:nat,B:nat,C:int]: ((ord_less_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)) | ~ (ord_less_int @ one_one_int @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3510])). 185.47/93.65 thf(6623,axiom,((! [A:int]: (((times_times_int @ A @ A) = one_one_int) = ((A = one_one_int) | (A = (uminus_uminus_int @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5778_square__eq__1__iff)). 185.47/93.65 thf(30080,plain,((! [A:int]: (((times_times_int @ A @ A) = one_one_int) = ((A = one_one_int) | (A = (uminus_uminus_int @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6623])). 185.47/93.65 thf(316,axiom,((ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7740_pi__ge__two)). 185.47/93.65 thf(8792,plain,((ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 185.47/93.65 thf(3209,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ one_one_int) @ B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3169_zless__imp__add1__zle)). 185.47/93.65 thf(18338,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ one_one_int) @ B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3209])). 185.47/93.65 thf(5433,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2935_power2__le__imp__le)). 185.47/93.65 thf(25697,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5433])). 185.47/93.65 thf(552,axiom,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) = (divide_divide_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8232_sin__45)). 185.47/93.65 thf(9566,plain,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) = (divide_divide_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[552])). 185.47/93.65 thf(3243,axiom,((! [A:int,B:int,C:nat]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2448_power__mono)). 185.47/93.65 thf(18433,plain,((! [A:int,B:int,C:nat]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3243])). 185.47/93.65 thf(5180,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_less__or__eq__imp__le)). 185.47/93.65 thf(24812,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5180])). 185.47/93.65 thf(6655,axiom,(((size_size_option_nat @ none_nat) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2503_option_Osize_I3_J)). 185.47/93.65 thf(30185,plain,(((size_size_option_nat @ none_nat) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6655])). 185.47/93.65 thf(6635,axiom,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((B = one_one_nat) & (A = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_nat__1__eq__mult__iff)). 185.47/93.65 thf(30118,plain,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((B = one_one_nat) & (A = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6635])). 185.47/93.65 thf(6092,axiom,((! [A:num,B:num]: ((ord_less_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_semiring__norm_I78_J)). 185.47/93.65 thf(28179,plain,((! [A:num,B:num]: ((ord_less_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6092])). 185.47/93.65 thf(7320,axiom,((zero_zero_complex != one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2071_zero__neq__one)). 185.47/93.65 thf(32667,plain,((~ (zero_zero_complex = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7320])). 185.47/93.65 thf(1210,axiom,((! [A:(int > $o),B:$o]: ((A @ (zero_n2684676970156552555ol_int @ B)) = (((A @ one_one_int) <= (B)) & ((~ (B)) => (A @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5681_split__of__bool)). 185.47/93.65 thf(11801,plain,((! [A:(int > $o),B:$o]: ((A @ (zero_n2684676970156552555ol_int @ B)) = (((A @ one_one_int) | ~ (B)) & ((~ (B)) => (A @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210])). 185.47/93.65 thf(2427,axiom,((! [A:int]: ((modulo_modulo_int @ A @ (uminus_uminus_int @ one_one_int)) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5306_mod__minus1__right)). 185.47/93.65 thf(15760,plain,((! [A:int]: ((modulo_modulo_int @ A @ (uminus_uminus_int @ one_one_int)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2427])). 185.47/93.65 thf(3620,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7249_int__plus)). 185.47/93.65 thf(19620,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3620])). 185.47/93.65 thf(5022,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (ord_less_nat @ A @ B)) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4176_antisym__conv2)). 185.47/93.65 thf(24170,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (ord_less_nat @ A @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5022])). 185.47/93.65 thf(2065,axiom,((! [A:real,B:real,C:real,D:real]: ((A != zero_zero_real) => (((ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ D @ B)) = (ord_less_real @ (divide_divide_real @ (minus_minus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A)) @ (times_times_real @ A @ B)) @ zero_zero_real)) <= (B != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2865_frac__less__eq)). 185.47/93.65 thf(14623,plain,((! [A:real,B:real,C:real,D:real]: ((~ (A = zero_zero_real)) => (((ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ D @ B)) = (ord_less_real @ (divide_divide_real @ (minus_minus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A)) @ (times_times_real @ A @ B)) @ zero_zero_real)) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065])). 185.47/93.65 thf(4829,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (semiri1314217659103216013at_int @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7063_of__nat__power__le__of__nat__cancel__iff)). 185.47/93.65 thf(23511,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (semiri1314217659103216013at_int @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4829])). 185.47/93.65 thf(5077,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ B @ C) & (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1794_nat__mult__less__cancel__disj)). 185.47/93.65 thf(24423,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ B @ C) & (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5077])). 185.47/93.65 thf(6130,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_753_diff__le__self)). 185.47/93.65 thf(28314,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6130])). 185.47/93.65 thf(5307,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1090_less__Suc__eq__le)). 185.47/93.65 thf(25265,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5307])). 185.47/93.65 thf(2186,axiom,((! [A:num]: (ord_less_eq_real @ zero_zero_real @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2190_zero__le__numeral)). 185.47/93.65 thf(15017,plain,((! [A:num]: (ord_less_eq_real @ zero_zero_real @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2186])). 185.47/93.65 thf(4006,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_group__cancel_Oadd2)). 185.47/93.65 thf(20855,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4006])). 185.47/93.65 thf(6671,axiom,((! [A:nat,B:nat]: ((((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (modulo_modulo_nat @ B @ A)) <= (ord_less_nat @ (modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2154_divmod__digit__0_I2_J)). 185.47/93.65 thf(30239,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (modulo_modulo_nat @ B @ A)) | ~ (ord_less_nat @ (modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ A) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6671])). 185.47/93.65 thf(3861,axiom,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2263_not__numeral__less__zero)). 185.47/93.65 thf(20402,plain,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3861])). 185.47/93.65 thf(1122,axiom,((! [A:num]: (ord_less_eq_int @ one_one_int @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_819_one__le__numeral)). 185.47/93.65 thf(11536,plain,((! [A:num]: (ord_less_eq_int @ one_one_int @ (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122])). 185.47/93.65 thf(2731,axiom,((bit_se6526347334894502574or_int = (^ [A:int,B:int]: (plus_plus_int @ (zero_n2684676970156552555ol_int @ ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) != (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se6526347334894502574or_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9495_xor__int__rec)). 185.47/93.65 thf(16815,plain,(((bit_se6526347334894502574or_int) = (^ [A:int,B:int]: (plus_plus_int @ (zero_n2684676970156552555ol_int @ (~ ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se6526347334894502574or_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2731])). 185.47/93.65 thf(6216,axiom,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ (uminus_uminus_int @ A) @ B) @ (power_power_int @ (uminus_uminus_int @ A) @ B)) = (power_power_int @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6269_minus__power__mult__self)). 185.47/93.65 thf(28650,plain,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ (uminus_uminus_int @ A) @ B) @ (power_power_int @ (uminus_uminus_int @ A) @ B)) = (power_power_int @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6216])). 185.47/93.65 thf(4430,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((ord_less_eq_int @ A @ B) & (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_add__mono__thms__linordered__semiring_I1_J)). 185.47/93.65 thf(22181,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ ((ord_less_eq_int @ A @ B) & (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4430])). 185.47/93.65 thf(2005,axiom,(((neg_nu3811975205180677377ec_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6778_dbl__dec__simps_I3_J)). 185.47/93.65 thf(14437,plain,(((neg_nu3811975205180677377ec_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2005])). 185.47/93.65 thf(5740,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3242_pinf_I4_J)). 185.47/93.65 thf(26828,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5740])). 185.47/93.65 thf(1204,axiom,((! [A:real,B:real]: ((ord_less_real @ (sqrt @ A) @ (sqrt @ B)) = (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8114_real__sqrt__less__iff)). 185.47/93.65 thf(11782,plain,((! [A:real,B:real]: ((ord_less_real @ (sqrt @ A) @ (sqrt @ B)) = (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204])). 185.47/93.65 thf(5199,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (A = C))) <= ((power_power_nat @ A @ (suc @ B)) = (power_power_nat @ C @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2752_power__inject__base)). 185.47/93.65 thf(24870,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (A = C))) | ~ ((power_power_nat @ A @ (suc @ B)) = (power_power_nat @ C @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5199])). 185.47/93.65 thf(329,axiom,((! [A:real]: (((divide_divide_real @ (sqrt @ A) @ A) = (inverse_inverse_real @ (sqrt @ A))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8972_sqrt__divide__self__eq)). 185.47/93.65 thf(8835,plain,((! [A:real]: (((divide_divide_real @ (sqrt @ A) @ A) = (inverse_inverse_real @ (sqrt @ A))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 185.47/93.65 thf(1762,axiom,((! [A:int,B:int]: (((ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int) <= (ord_less_int @ B @ zero_zero_int)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2632_add__nonpos__neg)). 185.47/93.65 thf(13635,plain,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int) | ~ (ord_less_int @ B @ zero_zero_int) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762])). 185.47/93.65 thf(1000,axiom,((! [A:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5935_not__numeral__le__neg__one)). 185.47/93.65 thf(11157,plain,((! [A:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000])). 185.47/93.65 thf(2198,axiom,((ord_less_eq_rat = (^ [A:rat,B:rat]: (ord_less_eq_rat @ (minus_minus_rat @ A @ B) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2378_le__iff__diff__le__0)). 185.47/93.65 thf(15054,plain,(((ord_less_eq_rat) = (^ [A:rat,B:rat]: (ord_less_eq_rat @ (minus_minus_rat @ A @ B) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2198])). 185.47/93.65 thf(3812,axiom,((ring_1_of_int_rat = (^ [A:int]: (if_rat @ (A = zero_zero_int) @ zero_zero_rat @ (if_rat @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_rat @ (ring_1_of_int_rat @ (uminus_uminus_int @ A))) @ (if_rat @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (ring_1_of_int_rat @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (ring_1_of_int_rat @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_rat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6857_of__int__code__if)). 185.47/93.65 thf(20248,plain,(((ring_1_of_int_rat) = (^ [A:int]: (if_rat @ (A = zero_zero_int) @ zero_zero_rat @ (if_rat @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_rat @ (ring_1_of_int_rat @ (uminus_uminus_int @ A))) @ (if_rat @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (ring_1_of_int_rat @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (ring_1_of_int_rat @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_rat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3812])). 185.47/93.65 thf(5468,axiom,((! [A:num,B:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_numeral__plus__numeral)). 185.47/93.65 thf(25848,plain,((! [A:num,B:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5468])). 185.47/93.65 thf(4048,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4259_order_Ostrict__implies__order)). 185.47/93.65 thf(20979,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4048])). 185.47/93.65 thf(3977,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (uminus_uminus_rat @ B)) = (ord_less_rat @ B @ (uminus_uminus_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5520_less__minus__iff)). 185.47/93.65 thf(20771,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (uminus_uminus_rat @ B)) = (ord_less_rat @ B @ (uminus_uminus_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3977])). 185.47/93.65 thf(3022,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) => ((ord_less_int @ zero_zero_int @ A) <= (ord_less_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2346_zero__less__mult__pos2)). 185.47/93.65 thf(17742,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) => ((ord_less_int @ zero_zero_int @ A) | ~ (ord_less_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3022])). 185.47/93.65 thf(7147,axiom,((! [A:num,B:num,C:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) @ C)) = (times_times_complex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5364_semiring__norm_I172_J)). 185.47/93.65 thf(32073,plain,((! [A:num,B:num,C:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) @ C)) = (times_times_complex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7147])). 185.47/93.65 thf(6907,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1608_mult__cancel1)). 185.47/93.65 thf(31153,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6907])). 185.47/93.65 thf(5963,axiom,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3886_dual__order_Oeq__iff)). 185.47/93.65 thf(27741,plain,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5963])). 185.47/93.65 thf(1516,axiom,((! [A:rat,B:nat,C:nat]: (((comm_s4028243227959126397er_rat @ A @ B) != zero_zero_rat) => ((ord_less_eq_nat @ C @ B) => ((comm_s4028243227959126397er_rat @ A @ C) != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8443_pochhammer__neq__0__mono)). 185.47/93.65 thf(12768,plain,((! [A:rat,B:nat,C:nat]: ((~ ((comm_s4028243227959126397er_rat @ A @ B) = zero_zero_rat)) => ((ord_less_eq_nat @ C @ B) => (~ ((comm_s4028243227959126397er_rat @ A @ C) = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516])). 185.47/93.65 thf(2316,axiom,((! [A:real]: ~ (ord_less_real @ (abs_abs_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6483_abs__not__less__zero)). 185.47/93.65 thf(15410,plain,((! [A:real]: ~ (ord_less_real @ (abs_abs_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2316])). 185.47/93.65 thf(7555,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1360_numeral__code_I2_J)). 185.47/93.65 thf(33448,plain,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7555])). 185.47/93.65 thf(15,axiom,((! [A:real,B:nat]: ? [C:real]: ((ord_less_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A)) & ((exp_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (power_power_real @ A @ D) @ (semiri2265585572941072030t_real @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (exp_real @ C) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8274_Maclaurin__exp__le)). 185.47/93.65 thf(7774,plain,((! [A:real,B:nat]: ? [C:real]: ((ord_less_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A)) & ((exp_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (power_power_real @ A @ D) @ (semiri2265585572941072030t_real @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (exp_real @ C) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 185.47/93.65 thf(2787,axiom,((! [A:int,B:int]: (((ord_less_int @ B @ zero_zero_int) | (ord_less_int @ A @ zero_zero_int)) <= (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2394_add__less__zeroD)). 185.47/93.65 thf(16986,plain,((! [A:int,B:int]: ((ord_less_int @ B @ zero_zero_int) | (ord_less_int @ A @ zero_zero_int) | ~ (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2787])). 185.47/93.65 thf(115,axiom,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((finite_finite_nat @ A) => ((! [D:nat]: ((ord_less_eq_rat @ (B @ D) @ (C @ D)) <= (member_nat @ D @ A))) => ((ord_less_rat @ (groups2906978787729119204at_rat @ B @ A) @ (groups2906978787729119204at_rat @ C @ A)) <= (? [D:nat]: ((member_nat @ D @ A) & (ord_less_rat @ (B @ D) @ (C @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5848_sum__strict__mono__ex1)). 185.47/93.65 thf(8105,plain,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((finite_finite_nat @ A) => ((! [D:nat]: ((ord_less_eq_rat @ (B @ D) @ (C @ D)) | ~ (member_nat @ D @ A))) => ((ord_less_rat @ (groups2906978787729119204at_rat @ (B) @ A) @ (groups2906978787729119204at_rat @ (C) @ A)) | ~ (? [D:nat]: ((member_nat @ D @ A) & (ord_less_rat @ (B @ D) @ (C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 185.47/93.65 thf(575,axiom,((! [A:set_nat]: ((groups705719431365010083at_int @ (^ [B:nat]: (one_one_int)) @ A) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8639_prod_Oneutral__const)). 185.47/93.65 thf(9640,plain,((! [A:set_nat]: ((groups705719431365010083at_int @ (^ [B:nat]: (one_one_int)) @ A) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[575])). 185.47/93.65 thf(2604,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((divide_divide_int @ (plus_plus_int @ C @ B) @ A) = (plus_plus_int @ (divide_divide_int @ C @ A) @ (divide_divide_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4779_div__plus__div__distrib__dvd__right)). 185.47/93.65 thf(16375,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((divide_divide_int @ (plus_plus_int @ C @ B) @ A) = (plus_plus_int @ (divide_divide_int @ C @ A) @ (divide_divide_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2604])). 185.47/93.65 thf(4469,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (power_power_int @ A @ B) @ one_one_int) <= (ord_less_eq_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2722_power__le__one)). 185.47/93.65 thf(22306,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (power_power_int @ A @ B) @ one_one_int) | ~ (ord_less_eq_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4469])). 185.47/93.65 thf(5004,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ B) = (modulo_modulo_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1776_mod__mult__self3)). 185.47/93.65 thf(24117,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ B) = (modulo_modulo_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5004])). 185.47/93.65 thf(904,axiom,((! [A:nat,B:nat,C:(nat > rat)]: ((ord_less_eq_nat @ A @ B) => ((groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_rat @ (C @ A) @ (groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6654_sum_OatLeast__Suc__atMost)). 185.47/93.65 thf(10830,plain,((! [A:nat,B:nat,C:(nat > rat)]: ((ord_less_eq_nat @ A @ B) => ((groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_rat @ (C @ A) @ (groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[904])). 185.47/93.65 thf(5282,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_add__mono)). 185.47/93.65 thf(25192,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5282])). 185.47/93.65 thf(6716,axiom,((~ (ord_less_nat @ one_one_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2382_not__one__less__zero)). 185.47/93.65 thf(30379,plain,((~ (ord_less_nat @ one_one_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6716])). 185.47/93.65 thf(4351,axiom,((! [A:int,B:int]: (((B = A) <= (ord_less_eq_int @ B @ A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3893_dual__order_Oantisym)). 185.47/93.65 thf(21937,plain,((! [A:int,B:int]: ((B = A) | ~ (ord_less_eq_int @ B @ A) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4351])). 185.47/93.65 thf(3934,axiom,((ord_less_real = (^ [A:real,B:real]: ((B != A) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4233_dual__order_Ostrict__iff__order)). 185.47/93.65 thf(20633,plain,(((ord_less_real) = (^ [A:real,B:real]: (~ (B = A) & (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3934])). 185.47/93.65 thf(3226,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ B @ (times_times_rat @ C @ A))) = (dvd_dvd_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4478_dvd__add__times__triv__right__iff)). 185.47/93.65 thf(18386,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ B @ (times_times_rat @ C @ A))) = (dvd_dvd_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3226])). 185.47/93.65 thf(6416,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7238_of__nat__dvd__iff)). 185.47/93.65 thf(29357,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6416])). 185.47/93.65 thf(2236,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((comm_s2602460028002588243omplex @ zero_zero_complex @ A) = one_one_complex)) & ((A != zero_zero_nat) => ((comm_s2602460028002588243omplex @ zero_zero_complex @ A) = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8469_pochhammer__0__left)). 185.47/93.65 thf(15168,plain,((! [A:nat]: (((A = zero_zero_nat) => ((comm_s2602460028002588243omplex @ zero_zero_complex @ A) = one_one_complex)) & ((~ (A = zero_zero_nat)) => ((comm_s2602460028002588243omplex @ zero_zero_complex @ A) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2236])). 185.47/93.65 thf(2532,axiom,((! [A:num,B:num]: ((ord_less_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_numeral__less__iff)). 185.47/93.65 thf(16127,plain,((! [A:num,B:num]: ((ord_less_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2532])). 185.47/93.65 thf(1777,axiom,((! [A:real,B:real,C:nat]: (((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2171_power__strict__mono)). 185.47/93.65 thf(13682,plain,((! [A:real,B:real,C:nat]: (((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777])). 185.47/93.65 thf(3449,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4149_leD)). 185.47/93.65 thf(19075,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3449])). 185.47/93.65 thf(5059,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4730_unit__mult__right__cancel)). 185.47/93.65 thf(24370,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5059])). 185.47/93.65 thf(4799,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_int @ (power_power_int @ (semiri1314217659103216013at_int @ A) @ B) @ (semiri1314217659103216013at_int @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7067_of__nat__le__of__nat__power__cancel__iff)). 185.47/93.65 thf(23418,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_int @ (power_power_int @ (semiri1314217659103216013at_int @ A) @ B) @ (semiri1314217659103216013at_int @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4799])). 185.47/93.65 thf(655,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_eq_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)) = (ord_less_eq_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5229_ln__le__cancel__iff)). 185.47/93.65 thf(9910,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_eq_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)) = (ord_less_eq_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[655])). 185.47/93.65 thf(1581,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ C) = (ord_less_eq_rat @ B @ (times_times_rat @ C @ A))) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2843_pos__divide__le__eq)). 185.47/93.65 thf(12967,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ C) = (ord_less_eq_rat @ B @ (times_times_rat @ C @ A))) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581])). 185.47/93.66 thf(4254,axiom,((! [A:nat]: ((zero_zero_int = (semiri1314217659103216013at_int @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6888_of__nat__0__eq__iff)). 185.47/93.66 thf(21615,plain,((! [A:nat]: ((zero_zero_int = (semiri1314217659103216013at_int @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4254])). 185.47/93.66 thf(6647,axiom,((! [A:num]: ((abs_abs_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6375_abs__neg__numeral)). 185.47/93.66 thf(30160,plain,((! [A:num]: ((abs_abs_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6647])). 185.47/93.66 thf(6391,axiom,((! [A:num,B:num,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_mult__numeral__left__semiring__numeral)). 185.47/93.66 thf(29249,plain,((! [A:num,B:num,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6391])). 185.47/93.66 thf(5700,axiom,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ (abs_abs_real @ B) @ (abs_abs_real @ C)) => (ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A))) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6723_power__mono__even)). 185.47/93.66 thf(26695,plain,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ (abs_abs_real @ B) @ (abs_abs_real @ C)) => (ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A))) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5700])). 185.47/93.66 thf(735,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ pi) @ A) => (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_real @ (cos_real @ A) @ (cos_real @ B))) <= (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7886_cos__monotone__minus__pi__0)). 185.47/93.66 thf(10185,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ pi) @ A) => (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_real @ (cos_real @ A) @ (cos_real @ B))) | ~ (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[735])). 185.47/93.66 thf(5489,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1151_right__diff__distrib)). 185.47/93.66 thf(26011,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5489])). 185.47/93.66 thf(2049,axiom,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5934_neg__numeral__le__neg__one)). 185.47/93.66 thf(14580,plain,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2049])). 185.47/93.66 thf(7685,axiom,(((semiri1406184849735516958ct_int @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_int @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7978_fact__2)). 185.47/93.66 thf(33799,plain,(((semiri1406184849735516958ct_int @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_int @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7685])). 185.47/93.66 thf(3463,axiom,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ B) = zero_zero_rat) = ((B = zero_zero_rat) | (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1585_divide__eq__0__iff)). 185.47/93.66 thf(19114,plain,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ B) = zero_zero_rat) = ((B = zero_zero_rat) | (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3463])). 185.47/93.66 thf(3711,axiom,((! [A:num]: ((ord_max_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3638_max__0__1_I5_J)). 185.47/93.66 thf(19921,plain,((! [A:num]: ((ord_max_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3711])). 185.47/93.66 thf(4479,axiom,((! [A:rat,B:rat]: (((~ (ord_less_rat @ A @ B)) = (A = B)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4174_antisym__conv2)). 185.47/93.66 thf(22343,plain,((! [A:rat,B:rat]: (((~ (ord_less_rat @ A @ B)) = (A = B)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4479])). 185.47/93.66 thf(7352,axiom,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (bit0 @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_semiring__norm_I13_J)). 185.47/93.66 thf(32775,plain,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (bit0 @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7352])). 185.47/93.66 thf(2939,axiom,((! [A:num,B:num,C:real]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ (numeral_numeral_real @ B) @ C)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_add__numeral__left)). 185.47/93.66 thf(17478,plain,((! [A:num,B:num,C:real]: ((plus_plus_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ (numeral_numeral_real @ B) @ C)) = (plus_plus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2939])). 185.47/93.66 thf(5294,axiom,((ord_less_num = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4202_order_Ostrict__iff__order)). 185.47/93.66 thf(25233,plain,(((ord_less_num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5294])). 185.47/93.66 thf(5104,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (times_times_nat @ B @ (divide_divide_nat @ A @ B))) = (modulo_modulo_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2553_minus__mult__div__eq__mod)). 185.47/93.66 thf(24505,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (times_times_nat @ B @ (divide_divide_nat @ A @ B))) = (modulo_modulo_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5104])). 185.47/93.66 thf(2852,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (dvd_dvd_int @ B @ C)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4464_dvd__times__left__cancel__iff)). 185.47/93.66 thf(17196,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (dvd_dvd_int @ B @ C)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2852])). 185.47/93.66 thf(1966,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ (times_times_int @ C @ A))) = (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4480_dvd__add__times__triv__right__iff)). 185.47/93.66 thf(14313,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ (times_times_int @ C @ A))) = (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1966])). 185.47/93.66 thf(7222,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ A @ C) <= ((vEBT_vebt_mint @ A) = (some_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_954_mint__member)). 185.47/93.66 thf(32349,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ A @ C) | ~ ((vEBT_vebt_mint @ A) = (some_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7222])). 185.47/93.66 thf(1284,axiom,((! [A:code_integer,B:code_integer,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ B @ D))) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4796_dvd__power__le)). 185.47/93.66 thf(12019,plain,((! [A:code_integer,B:code_integer,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ B @ D))) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284])). 185.47/93.66 thf(6845,axiom,((! [A:int]: ((times_times_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5193_mult__minus1__right)). 185.47/93.66 thf(30919,plain,((! [A:int]: ((times_times_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6845])). 185.47/93.66 thf(4672,axiom,((! [A:int,B:int]: (((ord_less_nat @ (nat2 @ B) @ (nat2 @ A)) = (ord_less_int @ B @ A)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9289_nat__mono__iff)). 185.47/93.66 thf(22963,plain,((! [A:int,B:int]: (((ord_less_nat @ (nat2 @ B) @ (nat2 @ A)) = (ord_less_int @ B @ A)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4672])). 185.47/93.66 thf(5295,axiom,((vEBT_invar_vebt @ summary @ m)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47__C4_Ohyps_C_I2_J)). 185.47/93.66 thf(25235,plain,((vEBT_invar_vebt @ summary @ m)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5295])). 185.47/93.66 thf(4063,axiom,((! [A:int,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((modulo_modulo_int @ (plus_plus_int @ one_one_int @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (plus_plus_int @ one_one_int @ (modulo_modulo_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))) <= (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4418_even__succ__mod__exp)). 185.47/93.66 thf(21020,plain,((! [A:int,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((modulo_modulo_int @ (plus_plus_int @ one_one_int @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (plus_plus_int @ one_one_int @ (modulo_modulo_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4063])). 185.47/93.66 thf(3030,axiom,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one)))) = (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2928_half__gt__zero__iff)). 185.47/93.66 thf(17763,plain,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one)))) = (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3030])). 185.47/93.66 thf(4298,axiom,((! [A:rat,B:rat,C:rat]: (((divide_divide_rat @ A @ B) = C) = (((B != zero_zero_rat) => (A = (times_times_rat @ C @ B))) & ((C = zero_zero_rat) <= (B = zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2475_divide__eq__eq)). 185.47/93.66 thf(21737,plain,((! [A:rat,B:rat,C:rat]: (((divide_divide_rat @ A @ B) = C) = (((~ (B = zero_zero_rat)) => (A = (times_times_rat @ C @ B))) & ((C = zero_zero_rat) | ~ (B = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4298])). 185.47/93.66 thf(2229,axiom,((! [A:rat,B:nat,C:nat]: (((ord_less_rat @ A @ one_one_rat) => ((ord_less_eq_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) = (ord_less_eq_nat @ C @ B))) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1890_power__decreasing__iff)). 185.47/93.66 thf(15141,plain,((! [A:rat,B:nat,C:nat]: (((ord_less_rat @ A @ one_one_rat) => ((ord_less_eq_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) = (ord_less_eq_nat @ C @ B))) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2229])). 185.47/93.66 thf(5560,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2605_mult__left__le__imp__le)). 185.47/93.66 thf(26242,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ B @ C)) | ~ (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5560])). 185.47/93.66 thf(3071,axiom,((! [A:rat,B:rat,C:num]: (((divide_divide_rat @ A @ B) = (numeral_numeral_rat @ C)) = ((((numeral_numeral_rat @ C) = zero_zero_rat) <= (B = zero_zero_rat)) & ((B != zero_zero_rat) => (A = (times_times_rat @ (numeral_numeral_rat @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2728_divide__eq__eq__numeral_I1_J)). 185.47/93.66 thf(17895,plain,((! [A:rat,B:rat,C:num]: (((divide_divide_rat @ A @ B) = (numeral_numeral_rat @ C)) = ((((numeral_numeral_rat @ C) = zero_zero_rat) | ~ (B = zero_zero_rat)) & ((~ (B = zero_zero_rat)) => (A = (times_times_rat @ (numeral_numeral_rat @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3071])). 185.47/93.66 thf(7299,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) <= (ord_less_eq_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2592_mult__strict__mono_H)). 185.47/93.66 thf(32596,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7299])). 185.47/93.66 thf(812,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat)]: (((dvd_dvd_nat @ (groups708209901874060359at_nat @ C @ B) @ (groups708209901874060359at_nat @ C @ A)) <= (ord_less_eq_set_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8820_prod__dvd__prod__subset)). 185.47/93.66 thf(10498,plain,((! [A:set_nat,B:set_nat,C:(nat > nat)]: ((dvd_dvd_nat @ (groups708209901874060359at_nat @ (C) @ B) @ (groups708209901874060359at_nat @ (C) @ A)) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[812])). 185.47/93.66 thf(4317,axiom,((! [A:(int > $o),B:int,C:int]: (((! [D:int]: ((ord_less_eq_int @ B @ D) => ((A @ (plus_plus_int @ D @ one_one_int)) <= (A @ D)))) => ((! [D:int]: ((ord_less_eq_int @ D @ B) => ((A @ (minus_minus_int @ D @ one_one_int)) <= (A @ D)))) => (A @ C))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3134_int__induct)). 185.47/93.66 thf(21792,plain,((! [A:(int > $o),B:int,C:int]: (((! [D:int]: ((ord_less_eq_int @ B @ D) => ((A @ (plus_plus_int @ D @ one_one_int)) | ~ (A @ D)))) => ((! [D:int]: ((ord_less_eq_int @ D @ B) => ((A @ (minus_minus_int @ D @ one_one_int)) | ~ (A @ D)))) => (A @ C))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4317])). 185.47/93.66 thf(4701,axiom,((! [A:nat,B:complex]: (sums_complex @ (^ [C:nat]: (times_times_complex @ (if_complex @ (C = A) @ one_one_complex @ zero_zero_complex) @ (power_power_complex @ B @ C))) @ (power_power_complex @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8199_powser__sums__if)). 185.47/93.66 thf(23075,plain,((! [A:nat,B:complex]: (sums_complex @ (^ [C:nat]: (times_times_complex @ (if_complex @ (C = A) @ one_one_complex @ zero_zero_complex) @ (power_power_complex @ B @ C))) @ (power_power_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4701])). 185.47/93.66 thf(2595,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_add__right__mono)). 185.47/93.66 thf(16348,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2595])). 185.47/93.66 thf(2056,axiom,((! [A:real]: ((ord_less_real @ (sqrt @ A) @ one_one_real) = (ord_less_real @ A @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8125_real__sqrt__lt__1__iff)). 185.47/93.66 thf(14598,plain,((! [A:real]: ((ord_less_real @ (sqrt @ A) @ one_one_real) = (ord_less_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056])). 185.47/93.66 thf(3005,axiom,(((nat2 @ one_one_int) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9248_nat__1)). 185.47/93.66 thf(17692,plain,(((nat2 @ one_one_int) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3005])). 185.47/93.66 thf(2995,axiom,((~ (ord_less_real @ zero_zero_real @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2027_less__numeral__extra_I3_J)). 185.47/93.66 thf(17663,plain,((~ (ord_less_real @ zero_zero_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2995])). 185.47/93.66 thf(596,axiom,(((arcsin @ one_one_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8309_arcsin__1)). 185.47/93.66 thf(9714,plain,(((arcsin @ one_one_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[596])). 185.47/93.66 thf(800,axiom,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (divide_divide_real @ (A @ C) @ B))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7660_summable__divide)). 185.47/93.66 thf(10458,plain,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (divide_divide_real @ (A @ C) @ B))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[800])). 185.47/93.66 thf(2833,axiom,((vEBT_set_vebt = (^ [A:vEBT_VEBT]: (collect_nat @ (vEBT_V8194947554948674370ptions @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1362_set__vebt__def)). 185.47/93.66 thf(17133,plain,(((vEBT_set_vebt) = (^ [A:vEBT_VEBT]: (collect_nat @ (vEBT_V8194947554948674370ptions @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2833])). 185.47/93.66 thf(1924,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((A != zero_zero_rat) => ((B != zero_zero_rat) => ((plus_plus_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ D @ B)) = (divide_divide_rat @ (plus_plus_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ D @ A)) @ (times_times_rat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2743_add__frac__eq)). 185.47/93.66 thf(14153,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((~ (A = zero_zero_rat)) => ((~ (B = zero_zero_rat)) => ((plus_plus_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ D @ B)) = (divide_divide_rat @ (plus_plus_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ D @ A)) @ (times_times_rat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1924])). 185.47/93.66 thf(5219,axiom,((! [A:num]: ((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = (fract @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9958_rat__number__expand_I5_J)). 185.47/93.66 thf(24931,plain,((! [A:num]: ((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = (fract @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5219])). 185.47/93.66 thf(4323,axiom,((! [A:set_nat]: (((? [B:nat]: (! [C:nat]: (((B = C) <= (ord_less_eq_nat @ C @ B)) <= (member_nat @ C @ A)) & (member_nat @ B @ A))) <= (A != bot_bot_set_nat)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3522_finite__has__minimal)). 185.47/93.66 thf(21851,plain,((! [A:set_nat]: (? [B:nat]: (! [C:nat]: ((B = C) | ~ (ord_less_eq_nat @ C @ B) | ~ (member_nat @ C @ A)) & (member_nat @ B @ A)) | (A = bot_bot_set_nat) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4323])). 185.47/93.66 thf(768,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (? [B:real]: ((ord_less_eq_real @ B @ pi) & ! [C:real]: ((C = B) <= ((ord_less_eq_real @ C @ pi) & ((cos_real @ C) = A) & (ord_less_eq_real @ zero_zero_real @ C))) & ((cos_real @ B) = A) & (ord_less_eq_real @ zero_zero_real @ B)))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7887_cos__total)). 185.47/93.66 thf(10342,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (? [B:real]: ((ord_less_eq_real @ B @ pi) & ! [C:real]: ((C = B) | ~ ((ord_less_eq_real @ C @ pi) & ((cos_real @ C) = A) & (ord_less_eq_real @ zero_zero_real @ C))) & ((cos_real @ B) = A) & (ord_less_eq_real @ zero_zero_real @ B)))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[768])). 185.47/93.66 thf(2485,axiom,((! [A:nat]: ((ord_max_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3597_max__0L)). 185.47/93.66 thf(15959,plain,((! [A:nat]: ((ord_max_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2485])). 185.47/93.66 thf(2667,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)) | ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2412_zero__le__divide__iff)). 185.47/93.66 thf(16568,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)) | ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2667])). 185.47/93.66 thf(666,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ A) => (summable_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7667_summable__ignore__initial__segment)). 185.47/93.66 thf(9957,plain,((! [A:(nat > real),B:nat]: ((summable_real @ (A)) => (summable_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[666])). 185.47/93.66 thf(1509,axiom,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ C))) = (ord_less_eq_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_le__divide__eq__numeral1_I1_J)). 185.47/93.66 thf(12746,plain,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ C))) = (ord_less_eq_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509])). 185.47/93.66 thf(6658,axiom,((! [A:nat,B:nat]: (((times_times_nat @ B @ (divide_divide_nat @ one_one_nat @ A)) = (divide_divide_nat @ B @ A)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4506_unit__mult__div__div)). 185.47/93.66 thf(30192,plain,((! [A:nat,B:nat]: (((times_times_nat @ B @ (divide_divide_nat @ one_one_nat @ A)) = (divide_divide_nat @ B @ A)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6658])). 185.47/93.66 thf(6296,axiom,((! [A:num,B:num,C:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ (numeral_numeral_nat @ B) @ C)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_add__numeral__left)). 185.47/93.66 thf(28913,plain,((! [A:num,B:num,C:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ (numeral_numeral_nat @ B) @ C)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6296])). 185.47/93.66 thf(7627,axiom,(((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1019_Suc__1)). 185.47/93.66 thf(33650,plain,(((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7627])). 185.47/93.66 thf(2384,axiom,((! [A:rat]: ((comm_s4028243227959126397er_rat @ A @ zero_zero_nat) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8422_pochhammer__0)). 185.47/93.66 thf(15619,plain,((! [A:rat]: ((comm_s4028243227959126397er_rat @ A @ zero_zero_nat) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2384])). 185.47/93.66 thf(3880,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_ring__class_Oring__distribs_I1_J)). 185.47/93.66 thf(20456,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3880])). 185.47/93.66 thf(4628,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ C) = (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ (times_times_rat @ C @ B))) & ((((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (times_times_rat @ C @ B) @ A)) & ((ord_less_rat @ zero_zero_rat @ C) <= (~ (ord_less_rat @ B @ zero_zero_rat)))) <= (~ (ord_less_rat @ zero_zero_rat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2696_divide__less__eq)). 185.47/93.66 thf(22828,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ C) = (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ (times_times_rat @ C @ B))) & ((((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (times_times_rat @ C @ B) @ A)) & ((ord_less_rat @ zero_zero_rat @ C) | (ord_less_rat @ B @ zero_zero_rat))) | (ord_less_rat @ zero_zero_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4628])). 185.47/93.66 thf(4084,axiom,((! [A:rat,B:rat]: (((~ (ord_less_rat @ B @ A)) = (B = A)) <= (~ (ord_less_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3998_antisym__conv3)). 185.47/93.66 thf(21091,plain,((! [A:rat,B:rat]: (((~ (ord_less_rat @ B @ A)) = (B = A)) | (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4084])). 185.47/93.66 thf(7663,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_minNull @ A) => (~ (vEBT_vebt_member @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_min__Null__member)). 185.47/93.66 thf(33745,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_minNull @ A) => (~ (vEBT_vebt_member @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7663])). 185.47/93.66 thf(7140,axiom,((! [A:complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1486_mult__zero__right)). 185.47/93.66 thf(32037,plain,((! [A:complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7140])). 185.47/93.66 thf(5013,axiom,((! [A:real]: ((times_times_real @ (sqrt @ A) @ (sqrt @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8130_real__sqrt__mult__self)). 185.47/93.66 thf(24144,plain,((! [A:real]: ((times_times_real @ (sqrt @ A) @ (sqrt @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5013])). 185.47/93.66 thf(859,axiom,((! [A:int,B:int]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6946_of__int__less__iff)). 185.47/93.66 thf(10671,plain,((! [A:int,B:int]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[859])). 185.47/93.66 thf(2759,axiom,((! [A:complex]: (ord_less_eq_real @ zero_zero_real @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7459_norm__ge__zero)). 185.47/93.66 thf(16903,plain,((! [A:complex]: (ord_less_eq_real @ zero_zero_real @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2759])). 185.47/93.66 thf(4728,axiom,((ord_less_eq_int = (^ [A:int,B:int]: (ord_less_eq_int @ (minus_minus_int @ A @ B) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2379_le__iff__diff__le__0)). 185.47/93.66 thf(23163,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: (ord_less_eq_int @ (minus_minus_int @ A @ B) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4728])). 185.47/93.66 thf(5519,axiom,((! [A:int,B:num]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ (power_power_int @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1367_power__numeral__even)). 185.47/93.66 thf(26111,plain,((! [A:int,B:num]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ (power_power_int @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5519])). 185.47/93.66 thf(2870,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ C @ B) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3266_minf_I3_J)). 185.47/93.66 thf(17254,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2870])). 185.47/93.66 thf(5229,axiom,((! [A:real,B:num,C:real]: (((divide_divide_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = C) = (((C = zero_zero_real) <= ((uminus_uminus_real @ (numeral_numeral_real @ B)) = zero_zero_real)) & (((uminus_uminus_real @ (numeral_numeral_real @ B)) != zero_zero_real) => (A = (times_times_real @ C @ (uminus_uminus_real @ (numeral_numeral_real @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5386_divide__eq__eq__numeral1_I2_J)). 185.47/93.66 thf(24974,plain,((! [A:real,B:num,C:real]: (((divide_divide_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = C) = (((C = zero_zero_real) | ~ ((uminus_uminus_real @ (numeral_numeral_real @ B)) = zero_zero_real)) & ((~ ((uminus_uminus_real @ (numeral_numeral_real @ B)) = zero_zero_real)) => (A = (times_times_real @ C @ (uminus_uminus_real @ (numeral_numeral_real @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5229])). 185.47/93.66 thf(4079,axiom,((! [A:real,B:real]: ? [C:real]: ! [D:real]: ((ord_less_real @ C @ D) => ((~ (dvd_dvd_real @ A @ (plus_plus_real @ D @ B))) = (~ (dvd_dvd_real @ A @ (plus_plus_real @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4714_pinf_I10_J)). 185.47/93.66 thf(21070,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4079])). 185.47/93.66 thf(5119,axiom,((m = na)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__C4_Ohyps_C_I5_J)). 185.47/93.66 thf(24578,plain,((m = na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5119])). 185.47/93.66 thf(646,axiom,((! [A:real]: ((sin_real @ (minus_minus_real @ pi @ A)) = (sin_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7782_sin__pi__minus)). 185.47/93.66 thf(9878,plain,((! [A:real]: ((sin_real @ (minus_minus_real @ pi @ A)) = (sin_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[646])). 185.47/93.66 thf(2651,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ (times_times_real @ (sin_real @ A) @ (sin_real @ B)) @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)))) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7834_sin__cos__le1)). 185.47/93.66 thf(16524,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ (times_times_real @ (sin_real @ A) @ (sin_real @ B)) @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)))) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2651])). 185.47/93.66 thf(5597,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_times__div__less__eq__dividend)). 185.47/93.66 thf(26357,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5597])). 185.47/93.66 thf(3747,axiom,((! [A:real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5143_less__eq__neg__nonpos)). 185.47/93.66 thf(20033,plain,((! [A:real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3747])). 185.47/93.66 thf(2671,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1861_le__divide__eq__1__pos)). 185.47/93.66 thf(16583,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2671])). 185.47/93.66 thf(3982,axiom,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ (plus_plus_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8585_pochhammer__minus_H)). 185.47/93.66 thf(20784,plain,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ (plus_plus_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3982])). 185.47/93.66 thf(1023,axiom,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ one_one_real) = ((B = zero_zero_real) | ((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ B @ A)) | ((ord_less_real @ A @ B) & (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2715_divide__less__eq__1)). 185.47/93.66 thf(11229,plain,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ one_one_real) = ((B = zero_zero_real) | ((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ B @ A)) | ((ord_less_real @ A @ B) & (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023])). 185.47/93.66 thf(7211,axiom,((! [A:option4927543243414619207at_nat]: ((! [B:product_prod_nat_nat]: (A != (some_P7363390416028606310at_nat @ B))) = (A = none_P5556105721700978146at_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_not__Some__eq)). 185.47/93.66 thf(32297,plain,((! [A:option4927543243414619207at_nat]: ((! [B:product_prod_nat_nat]: ~ (A = (some_P7363390416028606310at_nat @ B))) = (A = none_P5556105721700978146at_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7211])). 185.47/93.66 thf(4118,axiom,((! [A:int]: (((ring_1_of_int_rat @ A) = one_one_rat) = (A = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6965_of__int__eq__1__iff)). 185.47/93.66 thf(21194,plain,((! [A:int]: (((ring_1_of_int_rat @ A) = one_one_rat) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4118])). 185.47/93.66 thf(1860,axiom,((! [A:nat]: ((ord_max_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3594_max__nat_Oleft__neutral)). 185.47/93.66 thf(13964,plain,((! [A:nat]: ((ord_max_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1860])). 185.47/93.66 thf(6205,axiom,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4126_order__less__imp__triv)). 185.47/93.66 thf(28618,plain,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6205])). 185.47/93.66 thf(2858,axiom,((! [A:complex,B:complex]: ((A = (uminus1482373934393186551omplex @ B)) = ((plus_plus_complex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5740_eq__neg__iff__add__eq__0)). 185.47/93.66 thf(17218,plain,((! [A:complex,B:complex]: ((A = (uminus1482373934393186551omplex @ B)) = ((plus_plus_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2858])). 185.47/93.66 thf(6555,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_add__strict__mono)). 185.47/93.66 thf(29853,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6555])). 185.47/93.66 thf(7516,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4739_dvd__mult__unit__iff_H)). 185.47/93.66 thf(33332,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7516])). 185.47/93.66 thf(5994,axiom,((! [A:nat]: ((modulo_modulo_nat @ A @ one_one_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1757_mod__by__1)). 185.47/93.66 thf(27874,plain,((! [A:nat]: ((modulo_modulo_nat @ A @ one_one_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5994])). 185.47/93.66 thf(7118,axiom,(((neg_nu5219082963157363817nc_rat @ one_one_rat) = (numeral_numeral_rat @ (bit1 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6850_dbl__inc__simps_I3_J)). 185.47/93.66 thf(31955,plain,(((neg_nu5219082963157363817nc_rat @ one_one_rat) = (numeral_numeral_rat @ (bit1 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7118])). 185.47/93.66 thf(169,axiom,((ln_ln_real = (log @ (exp_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9040_log__ln)). 185.47/93.66 thf(8275,plain,(((ln_ln_real) = (log @ (exp_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 185.47/93.66 thf(2661,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ C @ D) => (((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D))) <= (ord_less_eq_int @ zero_zero_int @ B))) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2258_mult__mono)). 185.47/93.66 thf(16551,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ C @ D) => (((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D))) | ~ (ord_less_eq_int @ zero_zero_int @ B))) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2661])). 185.47/93.66 thf(1566,axiom,((! [A:real,B:nat,C:nat]: (((comm_s7457072308508201937r_real @ A @ B) != zero_zero_real) => ((ord_less_eq_nat @ C @ B) => ((comm_s7457072308508201937r_real @ A @ C) != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8442_pochhammer__neq__0__mono)). 185.47/93.66 thf(12917,plain,((! [A:real,B:nat,C:nat]: ((~ ((comm_s7457072308508201937r_real @ A @ B) = zero_zero_real)) => ((ord_less_eq_nat @ C @ B) => (~ ((comm_s7457072308508201937r_real @ A @ C) = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566])). 185.47/93.66 thf(6035,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4061_linorder__neq__iff)). 185.47/93.66 thf(27999,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6035])). 185.47/93.66 thf(124,axiom,((! [A:int,B:num,C:nat]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (numeral_numeral_int @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7137_of__int__le__numeral__power__cancel__iff)). 185.47/93.66 thf(8132,plain,((! [A:int,B:num,C:nat]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (numeral_numeral_int @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 185.47/93.66 thf(6098,axiom,((vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ res)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371__092_060open_062vebt__member_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ares_092_060close_062)). 185.47/93.66 thf(28197,plain,((vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ res)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6098])). 185.47/93.66 thf(4182,axiom,((! [A:nat]: (ord_less_eq_rat @ one_one_rat @ (semiri773545260158071498ct_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7996_fact__ge__1)). 185.47/93.66 thf(21389,plain,((! [A:nat]: (ord_less_eq_rat @ one_one_rat @ (semiri773545260158071498ct_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4182])). 185.47/93.66 thf(4864,axiom,((! [A:rat,B:(num > rat),C:num,D:num]: ((((ord_less_rat @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_rat @ (B @ E) @ (B @ F)) <= (ord_less_num @ E @ F)))) <= (ord_less_num @ C @ D)) <= (ord_less_rat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4105_order__less__subst1)). 185.47/93.66 thf(23616,plain,((! [A:rat,B:(num > rat),C:num,D:num]: ((ord_less_rat @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_num @ E @ F))) | ~ (ord_less_num @ C @ D) | ~ (ord_less_rat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4864])). 185.47/93.66 thf(902,axiom,((! [A:set_nat,B:set_nat,C:(nat > real)]: ((finite_finite_nat @ A) => (((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_real))) => ((groups129246275422532515t_real @ C @ A) = (groups129246275422532515t_real @ C @ B))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8937_prod_Omono__neutral__right)). 185.47/93.66 thf(10823,plain,((! [A:set_nat,B:set_nat,C:(nat > real)]: ((finite_finite_nat @ A) => (((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_real))) => ((groups129246275422532515t_real @ (C) @ A) = (groups129246275422532515t_real @ (C) @ B))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[902])). 185.47/93.66 thf(5479,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (times_times_nat @ A @ B)) = ((B = (suc @ zero_zero_nat)) & (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1789_one__eq__mult__iff)). 185.47/93.66 thf(25968,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (times_times_nat @ A @ B)) = ((B = (suc @ zero_zero_nat)) & (A = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5479])). 185.47/93.66 thf(4843,axiom,((! [A:nat,B:vEBT_VEBT,C:(vEBT_VEBT > $o)]: ((? [D:vEBT_VEBT]: ((C @ D) & (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ A @ B))))) = ((C @ B) & (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5257_Bex__set__replicate)). 185.47/93.66 thf(23556,plain,((! [A:nat,B:vEBT_VEBT,C:(vEBT_VEBT > $o)]: ((? [D:vEBT_VEBT]: ((C @ D) & (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ A @ B))))) = ((C @ B) & ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4843])). 185.47/93.66 thf(5724,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ A @ (times_times_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2780_n__less__m__mult__n)). 185.47/93.66 thf(26783,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ A @ (times_times_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5724])). 185.47/93.66 thf(3303,axiom,((! [A:int,B:num]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (numeral_numeral_rat @ B)) = (ord_less_eq_int @ A @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7072_of__int__le__numeral__iff)). 185.47/93.66 thf(18618,plain,((! [A:int,B:num]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (numeral_numeral_rat @ B)) = (ord_less_eq_int @ A @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3303])). 185.47/93.66 thf(7184,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_add_Oassoc)). 185.47/93.66 thf(32198,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7184])). 185.47/93.66 thf(4609,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ (minus_minus_int @ A @ D) @ B) @ C) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1233_ordered__ring__class_Ole__add__iff1)). 185.47/93.66 thf(22758,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ (minus_minus_int @ A @ D) @ B) @ C) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4609])). 185.47/93.66 thf(370,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((ord_max_int @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3707_max_Oabsorb__iff2)). 185.47/93.66 thf(8968,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((ord_max_int @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[370])). 185.47/93.66 thf(4694,axiom,((! [A:rat]: (((abs_abs_rat @ A) = zero_zero_rat) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6322_abs__eq__0)). 185.47/93.66 thf(23043,plain,((! [A:rat]: (((abs_abs_rat @ A) = zero_zero_rat) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4694])). 185.47/93.66 thf(6240,axiom,((! [A:nat]: ((((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = one_one_real) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6227_minus__one__power__iff)). 185.47/93.66 thf(28727,plain,((! [A:nat]: ((((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = one_one_real) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6240])). 185.47/93.66 thf(7386,axiom,((! [A:nat]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6297_power__minus1__odd)). 185.47/93.66 thf(32879,plain,((! [A:nat]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7386])). 185.47/93.66 thf(2740,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4007_dual__order_Oasym)). 185.47/93.66 thf(16844,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2740])). 185.47/93.66 thf(1092,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4286_linorder__not__less)). 185.47/93.66 thf(11442,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092])). 185.47/93.66 thf(2828,axiom,((! [A:int]: ((ord_less_nat @ zero_zero_nat @ (nat2 @ A)) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9255_zero__less__nat__eq)). 185.47/93.66 thf(17118,plain,((! [A:int]: ((ord_less_nat @ zero_zero_nat @ (nat2 @ A)) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2828])). 185.47/93.66 thf(865,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ (sgn_sgn_int @ B)) @ C) = (((C = zero_zero_int) <= (B = zero_zero_int)) & (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9216_mult__sgn__dvd__iff)). 185.47/93.66 thf(10688,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ (sgn_sgn_int @ B)) @ C) = (((C = zero_zero_int) | ~ (B = zero_zero_int)) & (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[865])). 185.47/93.66 thf(7651,axiom,(((sqr @ one) = one)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9847_sqr_Osimps_I1_J)). 185.47/93.66 thf(33712,plain,(((sqr @ one) = one)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7651])). 185.47/93.66 thf(3196,axiom,((! [A:nat]: ((one_one_rat = (semiri681578069525770553at_rat @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6927_of__nat__1__eq__iff)). 185.47/93.66 thf(18289,plain,((! [A:nat]: ((one_one_rat = (semiri681578069525770553at_rat @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3196])). 185.47/93.66 thf(7079,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (divide_divide_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1692_div__mult__mult2)). 185.47/93.66 thf(31831,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (divide_divide_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7079])). 185.47/93.66 thf(7597,axiom,((vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_abe)). 185.47/93.66 thf(33567,plain,((vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7597])). 185.47/93.66 thf(4762,axiom,((! [A:nat,B:num,C:nat]: ((ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7128_of__nat__le__numeral__power__cancel__iff)). 185.47/93.66 thf(23305,plain,((! [A:nat,B:num,C:nat]: ((ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4762])). 185.47/93.66 thf(6027,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = B) = ((A = one_one_complex) | (B = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1673_mult__cancel__right2)). 185.47/93.66 thf(27974,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = B) = ((A = one_one_complex) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6027])). 185.47/93.66 thf(1201,axiom,((! [A:real,B:real]: ((divide_divide_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (divide_divide_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5585_minus__divide__divide)). 185.47/93.66 thf(11774,plain,((! [A:real,B:real]: ((divide_divide_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (divide_divide_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201])). 185.47/93.66 thf(7676,axiom,((! [A:complex]: ((power_power_complex @ (csqrt @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9174_power2__csqrt)). 185.47/93.66 thf(33777,plain,((! [A:complex]: ((power_power_complex @ (csqrt @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7676])). 185.47/93.66 thf(7390,axiom,((ord_less_num = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4278_order__less__le)). 185.47/93.66 thf(32890,plain,(((ord_less_num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7390])). 185.47/93.66 thf(6495,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_diff__diff__eq)). 185.47/93.66 thf(29647,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6495])). 185.47/93.66 thf(1639,axiom,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_real @ (root @ A @ B) @ (root @ A @ C)) = (ord_less_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9162_real__root__less__iff)). 185.47/93.66 thf(13184,plain,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_real @ (root @ A @ B) @ (root @ A @ C)) = (ord_less_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639])). 185.47/93.66 thf(5816,axiom,((! [A:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_rat) = ((A = one_one_rat) | (A = (uminus_uminus_rat @ one_one_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6225_power2__eq__1__iff)). 185.47/93.66 thf(27245,plain,((! [A:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_rat) = ((A = one_one_rat) | (A = (uminus_uminus_rat @ one_one_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5816])). 185.47/93.66 thf(2272,axiom,((! [A:int,B:num,C:nat]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7162_of__int__le__neg__numeral__power__cancel__iff)). 185.47/93.66 thf(15275,plain,((! [A:int,B:num,C:nat]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2272])). 185.47/93.66 thf(6239,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4096_order__less__irrefl)). 185.47/93.66 thf(28724,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6239])). 185.47/93.66 thf(203,axiom,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_rat @ (A @ zero_zero_nat) @ (groups73079841787564623at_rat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8735_prod_OatMost__Suc__shift)). 185.47/93.66 thf(8390,plain,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_rat @ (A @ zero_zero_nat) @ (groups73079841787564623at_rat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 185.47/93.66 thf(6445,axiom,((! [A:code_integer,B:nat]: ((times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ B) @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ B)) = (power_8256067586552552935nteger @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6272_minus__power__mult__self)). 185.47/93.66 thf(29468,plain,((! [A:code_integer,B:nat]: ((times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ B) @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ B)) = (power_8256067586552552935nteger @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6445])). 185.47/93.66 thf(3035,axiom,((! [A:int,B:int]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6934_of__int__le__iff)). 185.47/93.66 thf(17780,plain,((! [A:int,B:int]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3035])). 185.47/93.66 thf(5991,axiom,((zero_zero_rat != one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2073_zero__neq__one)). 185.47/93.66 thf(27864,plain,((~ (zero_zero_rat = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5991])). 185.47/93.66 thf(3416,axiom,((! [A:real,B:real]: ((times_times_real @ (cos_real @ A) @ (cos_real @ B)) = (divide_divide_real @ (plus_plus_real @ (cos_real @ (minus_minus_real @ A @ B)) @ (cos_real @ (plus_plus_real @ A @ B))) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7893_cos__times__cos)). 185.47/93.66 thf(18978,plain,((! [A:real,B:real]: ((times_times_real @ (cos_real @ A) @ (cos_real @ B)) = (divide_divide_real @ (plus_plus_real @ (cos_real @ (minus_minus_real @ A @ B)) @ (cos_real @ (plus_plus_real @ A @ B))) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3416])). 185.47/93.66 thf(4858,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ A) @ (collect_nat @ B)) = (! [C:nat]: ((B @ C) <= (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1404_Collect__mono__iff)). 185.47/93.66 thf(23599,plain,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) = (! [C:nat]: ((B @ C) | ~ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4858])). 185.47/93.66 thf(5011,axiom,((! [A:real,B:real]: ((power_power_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_909_power2__diff)). 185.47/93.66 thf(24138,plain,((! [A:real,B:real]: ((power_power_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5011])). 185.47/93.66 thf(2223,axiom,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se545348938243370406it_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ B @ (minus_minus_nat @ C @ A)) & (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9514_bit__push__bit__iff__int)). 185.47/93.66 thf(15126,plain,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se545348938243370406it_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ B @ (minus_minus_nat @ C @ A)) & (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2223])). 185.47/93.66 thf(729,axiom,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_real @ (groups129246275422532515t_real @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8700_prod_OatMost__Suc)). 185.47/93.66 thf(10163,plain,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_real @ (groups129246275422532515t_real @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[729])). 185.47/93.66 thf(3534,axiom,(((neg_nu5851722552734809277nc_int @ zero_zero_int) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6994_dbl__inc__simps_I2_J)). 185.47/93.66 thf(19358,plain,(((neg_nu5851722552734809277nc_int @ zero_zero_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3534])). 185.47/93.66 thf(2629,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_real @ (power_power_real @ (semiri5074537144036343181t_real @ A) @ B) @ (semiri5074537144036343181t_real @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7047_of__nat__less__of__nat__power__cancel__iff)). 185.47/93.66 thf(16451,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_real @ (power_power_real @ (semiri5074537144036343181t_real @ A) @ B) @ (semiri5074537144036343181t_real @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2629])). 185.47/93.66 thf(1663,axiom,((! [A:rat,B:rat,C:(rat > nat),D:nat]: ((ord_less_rat @ A @ B) => (((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) <= (ord_less_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4116_order__less__subst2)). 185.47/93.66 thf(13309,plain,((! [A:rat,B:rat,C:(rat > nat),D:nat]: ((ord_less_rat @ A @ B) => (((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) | ~ (ord_less_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663])). 185.47/93.66 thf(6411,axiom,((ord_less_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_4221_order_Ostrict__iff__not)). 185.47/93.66 thf(29344,plain,(((ord_less_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)],[6411])). 185.47/93.66 thf(5801,axiom,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ B)) = (((ord_less_int @ zero_zero_int @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A != zero_zero_int)) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4981_zero__less__power__eq)). 185.47/93.66 thf(27101,plain,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ B)) = (((ord_less_int @ zero_zero_int @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & ~ (A = zero_zero_int)) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5801])). 185.47/93.66 thf(3578,axiom,((! [A:rat,B:nat,C:rat]: (((ord_less_rat @ A @ C) <= (ord_less_eq_rat @ zero_zero_rat @ C)) <= (ord_less_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2682_power__less__imp__less__base)). 185.47/93.66 thf(19488,plain,((! [A:rat,B:nat,C:rat]: ((ord_less_rat @ A @ C) | ~ (ord_less_eq_rat @ zero_zero_rat @ C) | ~ (ord_less_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3578])). 185.47/93.66 thf(5544,axiom,((power_power_real = (^ [A:real,B:nat]: (if_real @ (B = zero_zero_nat) @ one_one_real @ (times_times_real @ A @ (power_power_real @ A @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2959_power__eq__if)). 185.47/93.66 thf(26195,plain,(((power_power_real) = (^ [A:real,B:nat]: (if_real @ (B = zero_zero_nat) @ one_one_real @ (times_times_real @ A @ (power_power_real @ A @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5544])). 185.47/93.66 thf(6786,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ (power_power_rat @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ zero_zero_rat) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3009_odd__power__less__zero)). 185.47/93.66 thf(30688,plain,((! [A:rat,B:nat]: ((ord_less_rat @ (power_power_rat @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ zero_zero_rat) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6786])). 185.47/93.66 thf(2898,axiom,((abs_abs_rat = (^ [A:rat]: (if_rat @ (ord_less_rat @ A @ zero_zero_rat) @ (uminus_uminus_rat @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6574_abs__if)). 185.47/93.66 thf(17350,plain,(((abs_abs_rat) = (^ [A:rat]: (if_rat @ (ord_less_rat @ A @ zero_zero_rat) @ (uminus_uminus_rat @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2898])). 185.47/93.66 thf(1158,axiom,((! [A:rat,B:rat]: ((A = B) | (ord_less_rat @ B @ A) | (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4129_linorder__less__linear)). 185.47/93.66 thf(11651,plain,((! [A:rat,B:rat]: ((A = B) | (ord_less_rat @ B @ A) | (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158])). 185.47/93.66 thf(6341,axiom,((! [A:num]: ((times_times_num @ one @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_semiring__norm_I12_J)). 185.47/93.66 thf(29066,plain,((! [A:num]: ((times_times_num @ one @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6341])). 185.47/93.66 thf(493,axiom,((! [A:real]: ((tan_real @ (plus_plus_real @ A @ pi)) = (tan_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7952_tan__periodic__pi)). 185.47/93.66 thf(9392,plain,((! [A:real]: ((tan_real @ (plus_plus_real @ A @ pi)) = (tan_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])). 185.47/93.66 thf(1584,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (times_times_rat @ A @ B)) = (((ord_less_eq_rat @ zero_zero_rat @ A) => (ord_less_rat @ one_one_rat @ B)) & ((ord_less_rat @ B @ one_one_rat) <= (ord_less_eq_rat @ A @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2819_mult__less__cancel__left1)). 185.47/93.66 thf(12977,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (times_times_rat @ A @ B)) = (((ord_less_eq_rat @ zero_zero_rat @ A) => (ord_less_rat @ one_one_rat @ B)) & ((ord_less_rat @ B @ one_one_rat) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584])). 185.47/93.66 thf(770,axiom,((! [A:nat,B:int]: ((bit_concat_bit @ A @ zero_zero_int @ B) = (bit_se545348938243370406it_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9499_concat__bit__of__zero__1)). 185.47/93.66 thf(10353,plain,((! [A:nat,B:int]: ((bit_concat_bit @ A @ zero_zero_int @ B) = (bit_se545348938243370406it_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[770])). 185.47/93.66 thf(7052,axiom,(((minus_minus_int @ one_one_int @ one_one_int) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1714_diff__numeral__special_I9_J)). 185.47/93.66 thf(31756,plain,(((minus_minus_int @ one_one_int @ one_one_int) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7052])). 185.47/93.66 thf(230,axiom,((! [A:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (plus_plus_real @ (abs_abs_real @ (re @ A)) @ (abs_abs_real @ (im @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9684_cmod__le)). 185.47/93.66 thf(8467,plain,((! [A:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (plus_plus_real @ (abs_abs_real @ (re @ A)) @ (abs_abs_real @ (im @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 185.47/93.66 thf(2319,axiom,((! [A:nat]: ((groups3539618377306564664at_int @ semiri1314217659103216013at_int @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A)) = (divide_divide_int @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6852_gauss__sum__from__Suc__0)). 185.47/93.66 thf(15421,plain,((! [A:nat]: ((groups3539618377306564664at_int @ (semiri1314217659103216013at_int) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A)) = (divide_divide_int @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2319])). 185.47/93.66 thf(6896,axiom,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1901_zero__less__power2)). 185.47/93.66 thf(31121,plain,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (~ (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6896])). 185.47/93.66 thf(709,axiom,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ A) @ B) = (bit_se1146084159140164899it_int @ (bit_ri7919022796975470100ot_int @ (minus_minus_int @ A @ one_one_int)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9527_bit__minus__int__iff)). 185.47/93.66 thf(10094,plain,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ A) @ B) = (bit_se1146084159140164899it_int @ (bit_ri7919022796975470100ot_int @ (minus_minus_int @ A @ one_one_int)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[709])). 185.47/93.66 thf(28,axiom,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_rat @ (A @ zero_zero_nat) @ (groups2906978787729119204at_rat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7579_sum_OlessThan__Suc__shift)). 185.47/93.66 thf(7821,plain,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_rat @ (A @ zero_zero_nat) @ (groups2906978787729119204at_rat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 185.47/93.66 thf(5599,axiom,(((bit_or_not_num_neg @ one @ one) = one)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9460_or__not__num__neg_Osimps_I1_J)). 185.47/93.66 thf(26362,plain,(((bit_or_not_num_neg @ one @ one) = one)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5599])). 185.47/93.66 thf(1468,axiom,((! [A:real]: ((ord_less_real @ (exp_real @ A) @ one_one_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8133_exp__less__one__iff)). 185.47/93.66 thf(12622,plain,((! [A:real]: ((ord_less_real @ (exp_real @ A) @ one_one_real) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468])). 185.47/93.66 thf(7353,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4026_order_Ostrict__trans)). 185.47/93.66 thf(32778,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7353])). 185.47/93.66 thf(5982,axiom,((! [A:num,B:num]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (numera6690914467698888265omplex @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5349_mult__neg__numeral__simps_I1_J)). 185.47/93.66 thf(27832,plain,((! [A:num,B:num]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (numera6690914467698888265omplex @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5982])). 185.47/93.66 thf(3713,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ B @ D)) @ E) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ D)) @ (plus_plus_real @ C @ E))) <= (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7502_norm__diff__triangle__le)). 185.47/93.66 thf(19928,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ B @ D)) @ E) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ D)) @ (plus_plus_real @ C @ E))) | ~ (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3713])). 185.47/93.66 thf(1240,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (divide_divide_real @ B @ C)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1706_nonzero__mult__divide__mult__cancel__left)). 185.47/93.66 thf(11892,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (divide_divide_real @ B @ C)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240])). 185.47/93.66 thf(2501,axiom,((! [A:int,B:num,C:nat]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7142_of__int__less__numeral__power__cancel__iff)). 185.47/93.66 thf(16023,plain,((! [A:int,B:num,C:nat]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2501])). 185.47/93.66 thf(6981,axiom,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_mult__numeral__1__right)). 185.47/93.66 thf(31489,plain,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6981])). 185.47/93.66 thf(1690,axiom,((! [A:real,B:real]: ((((plus_plus_real @ (arctan @ A) @ (arctan @ B)) = (arctan @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (minus_minus_real @ one_one_real @ (times_times_real @ A @ B))))) <= (ord_less_real @ (abs_abs_real @ B) @ one_one_real)) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6841_arctan__add)). 185.47/93.66 thf(13387,plain,((! [A:real,B:real]: (((plus_plus_real @ (arctan @ A) @ (arctan @ B)) = (arctan @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (minus_minus_real @ one_one_real @ (times_times_real @ A @ B))))) | ~ (ord_less_real @ (abs_abs_real @ B) @ one_one_real) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690])). 185.47/93.66 thf(1376,axiom,((! [A:rat,B:rat,C:rat]: ((A = (minus_minus_rat @ B @ C)) = ((plus_plus_rat @ A @ C) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_722_eq__diff__eq)). 185.47/93.66 thf(12314,plain,((! [A:rat,B:rat,C:rat]: ((A = (minus_minus_rat @ B @ C)) = ((plus_plus_rat @ A @ C) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376])). 185.47/93.66 thf(1732,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ C @ (plus_plus_int @ D @ B)) => (((ord_less_eq_int @ (minus_minus_int @ C @ B) @ D) <= (ord_less_eq_int @ C @ (plus_plus_int @ D @ B))) <= (ord_less_eq_int @ (plus_plus_int @ A @ B) @ C))) <= (ord_less_eq_int @ (plus_plus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1198_add__le__add__imp__diff__le)). 185.47/93.66 thf(13539,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ C @ (plus_plus_int @ D @ B)) => ((ord_less_eq_int @ (minus_minus_int @ C @ B) @ D) | ~ (ord_less_eq_int @ C @ (plus_plus_int @ D @ B)) | ~ (ord_less_eq_int @ (plus_plus_int @ A @ B) @ C))) | ~ (ord_less_eq_int @ (plus_plus_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732])). 185.47/93.66 thf(4206,axiom,((! [A:real,B:real]: (ord_less_eq_real @ A @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8226_real__sqrt__sum__squares__ge1)). 185.47/93.66 thf(21463,plain,((! [A:real,B:real]: (ord_less_eq_real @ A @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4206])). 185.47/93.66 thf(5768,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1603_Nat_Oadd__0__right)). 185.47/93.66 thf(26915,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5768])). 185.47/93.66 thf(3148,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((((modulo_modulo_int @ D @ B) = (modulo_modulo_int @ E @ B)) => ((modulo_modulo_int @ (minus_minus_int @ A @ D) @ B) = (modulo_modulo_int @ (minus_minus_int @ C @ E) @ B))) <= ((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2004_mod__diff__cong)). 185.47/93.66 thf(18137,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((((modulo_modulo_int @ D @ B) = (modulo_modulo_int @ E @ B)) => ((modulo_modulo_int @ (minus_minus_int @ A @ D) @ B) = (modulo_modulo_int @ (minus_minus_int @ C @ E) @ B))) | ~ ((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3148])). 185.47/93.66 thf(4803,axiom,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ B) = (ord_less_real @ (uminus_uminus_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5522_minus__less__iff)). 185.47/93.66 thf(23429,plain,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ B) = (ord_less_real @ (uminus_uminus_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4803])). 185.47/93.66 thf(3708,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: ((? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))) <= (? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) <= (ord_less_int @ E @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3234_pinf_I2_J)). 185.47/93.66 thf(19906,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: ((? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => ((A @ F) = (B @ F)))) => (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F)))) | ~ (? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) | ~ (ord_less_int @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3708])). 185.47/93.66 thf(1029,axiom,((semiri5044797733671781792omplex = (comm_s2602460028002588243omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8444_pochhammer__fact)). 185.47/93.66 thf(11248,plain,(((semiri5044797733671781792omplex) = (comm_s2602460028002588243omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029])). 185.47/93.66 thf(4251,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (exp_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8136_one__le__exp__iff)). 185.47/93.66 thf(21604,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (exp_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4251])). 185.47/93.66 thf(1968,axiom,((! [A:nat,B:nat]: (dvd_dvd_int @ (times_times_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B)) @ (semiri1406184849735516958ct_int @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8020_fact__fact__dvd__fact)). 185.47/93.66 thf(14318,plain,((! [A:nat,B:nat]: (dvd_dvd_int @ (times_times_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B)) @ (semiri1406184849735516958ct_int @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1968])). 185.47/93.66 thf(3497,axiom,((! [A:rat,B:rat,C:(rat > int),D:int]: ((((C @ B) = D) => ((! [E:rat,F:rat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_rat @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3951_ord__le__eq__subst)). 185.47/93.66 thf(19241,plain,((! [A:rat,B:rat,C:(rat > int),D:int]: ((((C @ B) = D) => ((! [E:rat,F:rat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_rat @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3497])). 185.47/93.66 thf(3774,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (times_times_rat @ B @ A)) = (((ord_less_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ one_one_rat @ B)) & ((ord_less_rat @ A @ zero_zero_rat) => (ord_less_eq_rat @ B @ one_one_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2813_mult__le__cancel__right1)). 185.47/93.66 thf(20129,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (times_times_rat @ B @ A)) = (((ord_less_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ one_one_rat @ B)) & ((ord_less_rat @ A @ zero_zero_rat) => (ord_less_eq_rat @ B @ one_one_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3774])). 185.47/93.66 thf(2180,axiom,((bit_se1146084159140164899it_int = (^ [A:int,B:nat]: ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9437_bit__int__def)). 185.47/93.66 thf(15001,plain,(((bit_se1146084159140164899it_int) = (^ [A:int,B:nat]: ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2180])). 185.47/93.66 thf(4993,axiom,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6313_abs__idempotent)). 185.47/93.66 thf(24079,plain,((! [A:real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4993])). 185.47/93.66 thf(6741,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) => ((B = zero_zero_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2052_divisors__zero)). 185.47/93.66 thf(30487,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) => ((B = zero_zero_int) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6741])). 185.47/93.66 thf(2262,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ B @ C)) = (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_792_le__diff__eq)). 185.47/93.66 thf(15247,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ B @ C)) = (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2262])). 185.47/93.66 thf(4616,axiom,((! [A:int]: ((divide_divide_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5212_div__minus1__right)). 185.47/93.66 thf(22778,plain,((! [A:int]: ((divide_divide_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4616])). 185.47/93.66 thf(440,axiom,((! [A:complex,B:nat]: ((times_times_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ (gbinomial_complex @ A @ B)) = (times_times_complex @ A @ (gbinomial_complex @ (minus_minus_complex @ A @ one_one_complex) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8478_gbinomial__absorb__comp)). 185.47/93.66 thf(9200,plain,((! [A:complex,B:nat]: ((times_times_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ (gbinomial_complex @ A @ B)) = (times_times_complex @ A @ (gbinomial_complex @ (minus_minus_complex @ A @ one_one_complex) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[440])). 185.47/93.66 thf(2771,axiom,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ one)) = (modulo_modulo_int @ (numeral_numeral_int @ B) @ (numeral_numeral_int @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2069_cong__exp__iff__simps_I4_J)). 185.47/93.66 thf(16937,plain,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ one)) = (modulo_modulo_int @ (numeral_numeral_int @ B) @ (numeral_numeral_int @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2771])). 185.47/93.66 thf(5358,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ (times_times_nat @ A @ B) @ A) = (B = one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4925_dvd__mult__cancel1)). 185.47/93.66 thf(25470,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ (times_times_nat @ A @ B) @ A) = (B = one_one_nat)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5358])). 185.47/93.66 thf(834,axiom,((! [A:complex]: (ord_less_eq_real @ (plus_plus_real @ (abs_abs_real @ (re @ A)) @ (abs_abs_real @ (im @ A))) @ (times_times_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (real_V1022390504157884413omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9703_complex__abs__le__norm)). 185.47/93.66 thf(10575,plain,((! [A:complex]: (ord_less_eq_real @ (plus_plus_real @ (abs_abs_real @ (re @ A)) @ (abs_abs_real @ (im @ A))) @ (times_times_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (real_V1022390504157884413omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[834])). 185.47/93.66 thf(5549,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_trans__less__add1)). 185.47/93.66 thf(26210,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5549])). 185.47/93.66 thf(1865,axiom,((! [A:real,B:nat]: (((powr_real @ A @ (semiri5074537144036343181t_real @ B)) = (power_power_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9106_powr__realpow)). 185.47/93.66 thf(13979,plain,((! [A:real,B:nat]: (((powr_real @ A @ (semiri5074537144036343181t_real @ B)) = (power_power_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865])). 185.47/93.66 thf(2755,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ B @ A)) & (ord_less_int @ (modulo_modulo_int @ B @ A) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3142_pos__mod__conj)). 185.47/93.66 thf(16889,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ B @ A)) & (ord_less_int @ (modulo_modulo_int @ B @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2755])). 185.47/93.66 thf(4526,axiom,((! [A:$o]: (ord_less_eq_int @ zero_zero_int @ (zero_n2684676970156552555ol_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5664_zero__less__eq__of__bool)). 185.47/93.66 thf(22499,plain,((! [A:$o]: (ord_less_eq_int @ zero_zero_int @ (zero_n2684676970156552555ol_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4526])). 185.47/93.66 thf(5577,axiom,((! [A:nat,B:num]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ B)) @ (power_power_nat @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1366_power__numeral__even)). 185.47/93.66 thf(26293,plain,((! [A:nat,B:num]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ B)) @ (power_power_nat @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5577])). 185.47/93.66 thf(4394,axiom,((! [A:int,B:nat]: ((ord_less_int @ A @ (bit_ri631733984087533419it_int @ B @ A)) = (ord_less_int @ A @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6241_signed__take__bit__int__greater__self__iff)). 185.47/93.66 thf(22077,plain,((! [A:int,B:nat]: ((ord_less_int @ A @ (bit_ri631733984087533419it_int @ B @ A)) = (ord_less_int @ A @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4394])). 185.47/93.66 thf(7468,axiom,(((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5406_add__neg__numeral__special_I9_J)). 185.47/93.66 thf(33173,plain,(((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7468])). 185.47/93.66 thf(6988,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((dvd_dvd_nat @ (power_power_nat @ A @ D) @ C) <= (ord_less_eq_nat @ D @ B)) <= (dvd_dvd_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4792_power__le__dvd)). 185.47/93.66 thf(31509,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ D) @ C) | ~ (ord_less_eq_nat @ D @ B) | ~ (dvd_dvd_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6988])). 185.47/93.66 thf(4167,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) <= (ord_less_eq_real @ zero_zero_real @ C)))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2255_mult__mono)). 185.47/93.66 thf(21345,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) | ~ (ord_less_eq_real @ zero_zero_real @ C)))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4167])). 185.47/93.66 thf(6570,axiom,((! [A:$o,B:$o]: ((zero_n2687167440665602831ol_nat @ ((A) & (B))) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5503_of__bool__conj)). 185.47/93.66 thf(29902,plain,((! [A:$o,B:$o]: ((zero_n2687167440665602831ol_nat @ ((A) & (B))) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6570])). 185.47/93.66 thf(5885,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((divide_divide_nat @ B @ A) = (suc @ (divide_divide_nat @ (minus_minus_nat @ B @ A) @ A))) <= (~ (ord_less_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2568_div__geq)). 185.47/93.66 thf(27482,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((divide_divide_nat @ B @ A) = (suc @ (divide_divide_nat @ (minus_minus_nat @ B @ A) @ A))) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5885])). 185.47/93.66 thf(2577,axiom,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ A @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_divide__divide__eq__left)). 185.47/93.66 thf(16269,plain,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ A @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2577])). 185.47/93.66 thf(4137,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = (divide_divide_real @ A @ C)) = ((A = zero_zero_real) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1581_divide__cancel__left)). 185.47/93.66 thf(21252,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = (divide_divide_real @ A @ C)) = ((A = zero_zero_real) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4137])). 185.47/93.66 thf(1143,axiom,((! [A:rat,B:rat]: (ord_less_eq_rat @ zero_zero_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2982_sum__power2__ge__zero)). 185.47/93.66 thf(11608,plain,((! [A:rat,B:rat]: (ord_less_eq_rat @ zero_zero_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143])). 185.47/93.66 thf(2455,axiom,((! [A:complex,B:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (times_times_complex @ A @ B)) @ (times_times_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7483_norm__mult__ineq)). 185.47/93.66 thf(15867,plain,((! [A:complex,B:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (times_times_complex @ A @ B)) @ (times_times_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2455])). 185.47/93.66 thf(288,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_ri7919022796975470100ot_int @ A)) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9500_not__nonnegative__int__iff)). 185.47/93.66 thf(8673,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_ri7919022796975470100ot_int @ A)) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 185.47/93.66 thf(1577,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_add_Oassoc)). 185.47/93.66 thf(12955,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577])). 185.47/93.66 thf(6219,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((~ (ord_less_num @ C @ A)) <= (ord_less_num @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3247_pinf_I5_J)). 185.47/93.66 thf(28660,plain,((! [A:num]: ? [B:num]: ! [C:num]: (~ (ord_less_num @ C @ A) | ~ (ord_less_num @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6219])). 185.47/93.66 thf(7442,axiom,((! [A:nat]: ((power_power_complex @ one_one_complex @ A) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_power__one)). 185.47/93.66 thf(33074,plain,((! [A:nat]: ((power_power_complex @ one_one_complex @ A) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7442])). 185.47/93.66 thf(5753,axiom,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_mult__2)). 185.47/93.66 thf(26870,plain,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5753])). 185.47/93.66 thf(2835,axiom,((! [A:(rat > $o),B:(rat > $o),C:(rat > $o),D:(rat > $o)]: ((? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F))))) <= (? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => ((C @ F) = (D @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3261_minf_I2_J)). 185.47/93.66 thf(17138,plain,((! [A:(rat > $o),B:(rat > $o),C:(rat > $o),D:(rat > $o)]: ((? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => ((A @ F) = (B @ F)))) => (? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F)))) | ~ (? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => ((C @ F) = (D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2835])). 185.47/93.66 thf(2372,axiom,((! [A:real]: ((~ (! [B:nat]: ~ (ord_less_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (suc @ B))) @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7364_nat__approx__posE)). 185.47/93.66 thf(15582,plain,((! [A:real]: (~ (! [B:nat]: ~ (ord_less_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (suc @ B))) @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2372])). 185.47/93.66 thf(1696,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2659_divide__nonpos__pos)). 185.47/93.66 thf(13415,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696])). 185.47/93.66 thf(5749,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: (vEBT_VEBT_minNull @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1463_VEBT__internal_OminNull_Osimps_I4_J)). 185.47/93.66 thf(26860,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: (vEBT_VEBT_minNull @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5749])). 185.47/93.66 thf(152,axiom,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (bit_ri7919022796975470100ot_int @ (bit_se1409905431419307370or_int @ (minus_minus_int @ (numeral_numeral_int @ A) @ one_one_int) @ (minus_minus_int @ (numeral_numeral_int @ B) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9503_and__minus__minus__numerals)). 185.47/93.66 thf(8219,plain,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (bit_ri7919022796975470100ot_int @ (bit_se1409905431419307370or_int @ (minus_minus_int @ (numeral_numeral_int @ A) @ one_one_int) @ (minus_minus_int @ (numeral_numeral_int @ B) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 185.47/93.66 thf(3405,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ B @ A)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4064_order__less__asym_H)). 185.47/93.66 thf(18946,plain,((! [A:rat,B:rat]: (~ (ord_less_rat @ B @ A) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3405])). 185.47/93.66 thf(6348,axiom,((! [A:rat,B:rat]: (((times_times_rat @ A @ B) = zero_zero_rat) = ((B = zero_zero_rat) | (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1493_mult__eq__0__iff)). 185.47/93.66 thf(29109,plain,((! [A:rat,B:rat]: (((times_times_rat @ A @ B) = zero_zero_rat) = ((B = zero_zero_rat) | (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6348])). 185.47/93.66 thf(6572,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) <= (ord_less_eq_real @ (sqrt @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8214_sqrt__le__D)). 185.47/93.66 thf(29917,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (ord_less_eq_real @ (sqrt @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6572])). 185.47/93.66 thf(6175,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:vEBT_VEBT]: ((list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ A @ B @ C) @ B @ D) = (list_u1324408373059187874T_VEBT @ A @ B @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3554_list__update__overwrite)). 185.47/93.66 thf(28512,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:vEBT_VEBT]: ((list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ A @ B @ C) @ B @ D) = (list_u1324408373059187874T_VEBT @ A @ B @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6175])). 185.47/93.66 thf(1922,axiom,((! [A:nat,B:real]: ((times_times_real @ (semiri5074537144036343181t_real @ A) @ B) = (times_times_real @ B @ (semiri5074537144036343181t_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7183_mult__of__nat__commute)). 185.47/93.66 thf(14148,plain,((! [A:nat,B:real]: ((times_times_real @ (semiri5074537144036343181t_real @ A) @ B) = (times_times_real @ B @ (semiri5074537144036343181t_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922])). 185.47/93.66 thf(7699,axiom,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_semiring__norm_I87_J)). 185.47/93.66 thf(33841,plain,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7699])). 185.47/93.66 thf(4624,axiom,((! [A:int,B:(int > (int > $o)),C:int]: (((B @ (divide_divide_int @ C @ A) @ (modulo_modulo_int @ C @ A)) = (! [D:int,E:int]: (((ord_less_eq_int @ zero_zero_int @ E) & (ord_less_int @ E @ A) & (C = (plus_plus_int @ (times_times_int @ A @ D) @ E))) => (B @ D @ E)))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3064_split__pos__lemma)). 185.47/93.66 thf(22814,plain,((! [A:int,B:(int > (int > $o)),C:int]: (((B @ (divide_divide_int @ C @ A) @ (modulo_modulo_int @ C @ A)) = (! [D:int,E:int]: (((ord_less_eq_int @ zero_zero_int @ E) & (ord_less_int @ E @ A) & (C = (plus_plus_int @ (times_times_int @ A @ D) @ E))) => (B @ D @ E)))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4624])). 185.47/93.66 thf(6976,axiom,((((=) @ rat) = (^ [A:rat,B:rat]: ((minus_minus_rat @ A @ B) = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2092_eq__iff__diff__eq__0)). 185.47/93.66 thf(31474,plain,((((=) @ rat) = (^ [A:rat,B:rat]: ((minus_minus_rat @ A @ B) = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6976])). 185.47/93.66 thf(384,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (ord_max_nat @ A @ B)) = (ord_max_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7256_of__nat__max)). 185.47/93.66 thf(9012,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (ord_max_nat @ A @ B)) = (ord_max_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])). 185.47/93.66 thf(7105,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ (suc @ B) @ (suc @ A))) = (times_times_nat @ (suc @ B) @ (binomial @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8429_Suc__times__binomial)). 185.47/93.66 thf(31914,plain,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ (suc @ B) @ (suc @ A))) = (times_times_nat @ (suc @ B) @ (binomial @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7105])). 185.47/93.66 thf(2902,axiom,((! [A:nat]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ semiri5074537144036343181t_real @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7360_double__gauss__sum__from__Suc__0)). 185.47/93.66 thf(17360,plain,((! [A:nat]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ (semiri5074537144036343181t_real) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2902])). 185.47/93.66 thf(220,axiom,((ord_less_eq_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7759_pi__half__le__two)). 185.47/93.66 thf(8442,plain,((ord_less_eq_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 185.47/93.66 thf(788,axiom,((gbinomial_complex = (^ [A:complex,B:nat]: (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (gbinomial_complex @ (minus_minus_complex @ (minus_minus_complex @ (semiri8010041392384452111omplex @ B) @ A) @ one_one_complex) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8565_gbinomial__negated__upper)). 185.47/93.66 thf(10423,plain,(((gbinomial_complex) = (^ [A:complex,B:nat]: (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (gbinomial_complex @ (minus_minus_complex @ (minus_minus_complex @ (semiri8010041392384452111omplex @ B) @ A) @ one_one_complex) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[788])). 185.47/93.66 thf(2397,axiom,((! [A:int]: ((fract @ A @ zero_zero_int) = (fract @ zero_zero_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9941_eq__rat_I2_J)). 185.47/93.66 thf(15664,plain,((! [A:int]: ((fract @ A @ zero_zero_int) = (fract @ zero_zero_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2397])). 185.47/93.66 thf(6854,axiom,(((minus_minus_rat @ (uminus_uminus_rat @ one_one_rat) @ one_one_rat) = (uminus_uminus_rat @ (numeral_numeral_rat @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5413_diff__numeral__special_I10_J)). 185.47/93.66 thf(30968,plain,(((minus_minus_rat @ (uminus_uminus_rat @ one_one_rat) @ one_one_rat) = (uminus_uminus_rat @ (numeral_numeral_rat @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6854])). 185.47/93.66 thf(45,axiom,((! [A:int,B:nat]: ((minus_minus_int @ (power_power_int @ A @ B) @ one_one_int) = (times_times_int @ (minus_minus_int @ A @ one_one_int) @ (groups3539618377306564664at_int @ (power_power_int @ A) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7598_power__diff__1__eq)). 185.47/93.66 thf(7878,plain,((! [A:int,B:nat]: ((minus_minus_int @ (power_power_int @ A @ B) @ one_one_int) = (times_times_int @ (minus_minus_int @ A @ one_one_int) @ (groups3539618377306564664at_int @ (power_power_int @ A) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 185.47/93.66 thf(3434,axiom,((! [A:num]: ((plus_plus_num @ one @ (bitM @ A)) = (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8968_one__plus__BitM)). 185.47/93.66 thf(19034,plain,((! [A:num]: ((plus_plus_num @ one @ (bitM @ A)) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3434])). 185.47/93.66 thf(2118,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((powr_real @ A @ (uminus_uminus_real @ one_one_real)) = (divide_divide_real @ one_one_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9116_powr__neg__one)). 185.47/93.66 thf(14784,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((powr_real @ A @ (uminus_uminus_real @ one_one_real)) = (divide_divide_real @ one_one_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2118])). 185.47/93.66 thf(2808,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ C) => (ord_less_eq_rat @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3856_ord__eq__le__trans)). 185.47/93.66 thf(17054,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ C) => (ord_less_eq_rat @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2808])). 185.47/93.66 thf(4604,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ B @ A)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3982_order_Oasym)). 185.47/93.66 thf(22746,plain,((! [A:rat,B:rat]: (~ (ord_less_rat @ B @ A) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4604])). 185.47/93.66 thf(1422,axiom,((! [A:nat,B:code_integer]: ((times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) @ (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5305_left__minus__one__mult__self)). 185.47/93.66 thf(12481,plain,((! [A:nat,B:code_integer]: ((times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) @ (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422])). 185.47/93.66 thf(5432,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_nat @ A @ (binomial @ B @ A)) = (times_times_nat @ B @ (binomial @ (minus_minus_nat @ B @ one_one_nat) @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8531_times__binomial__minus1__eq)). 185.47/93.66 thf(25693,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_nat @ A @ (binomial @ B @ A)) = (times_times_nat @ B @ (binomial @ (minus_minus_nat @ B @ one_one_nat) @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5432])). 185.47/93.66 thf(4939,axiom,(((neg_nu8295874005876285629c_real @ one_one_real) = (numeral_numeral_real @ (bit1 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6849_dbl__inc__simps_I3_J)). 185.47/93.66 thf(23906,plain,(((neg_nu8295874005876285629c_real @ one_one_real) = (numeral_numeral_real @ (bit1 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4939])). 185.47/93.66 thf(4695,axiom,((! [A:real,B:real]: ((((? [C:real]: ((ord_less_eq_real @ zero_zero_real @ C) & (A = (cos_real @ C)) & (B = (sin_real @ C)) & (ord_less_eq_real @ C @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) <= ((plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real)) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7888_sincos__total__pi__half)). 185.47/93.66 thf(23046,plain,((! [A:real,B:real]: (? [C:real]: ((ord_less_eq_real @ zero_zero_real @ C) & (A = (cos_real @ C)) & (B = (sin_real @ C)) & (ord_less_eq_real @ C @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) | ~ ((plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4695])). 185.47/93.66 thf(1398,axiom,((set_fo2584398358068434914at_nat = (^ [A:(nat > (nat > nat)),B:nat,C:nat,D:nat]: (if_nat @ (ord_less_nat @ C @ B) @ D @ (set_fo2584398358068434914at_nat @ A @ (plus_plus_nat @ B @ one_one_nat) @ C @ (A @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8318_fold__atLeastAtMost__nat_Osimps)). 185.47/93.66 thf(12393,plain,(((set_fo2584398358068434914at_nat) = (^ [A:(nat > (nat > nat)),B:nat,C:nat,D:nat]: (if_nat @ (ord_less_nat @ C @ B) @ D @ (set_fo2584398358068434914at_nat @ A @ (plus_plus_nat @ B @ one_one_nat) @ C @ (A @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398])). 185.47/93.66 thf(6382,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ one_one_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9369_and__minus__numerals_I5_J)). 185.47/93.66 thf(29220,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ one_one_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6382])). 185.47/93.66 thf(3572,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1510_add_Oright__neutral)). 185.47/93.66 thf(19471,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3572])). 185.47/93.66 thf(103,axiom,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (minus_minus_rat @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_rat @ (A @ zero_zero_nat) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7586_sum__lessThan__telescope_H)). 185.47/93.66 thf(8072,plain,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (minus_minus_rat @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_rat @ (A @ zero_zero_nat) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 185.47/93.66 thf(6963,axiom,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_766_less__numeral__extra_I4_J)). 185.47/93.66 thf(31386,plain,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6963])). 185.47/93.66 thf(5711,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((((C @ A) <= (! [D:nat]: (((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D))) <= (ord_less_eq_nat @ A @ D)))) <= (C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1087_inc__induct)). 185.47/93.66 thf(26727,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((C @ A) | ~ (! [D:nat]: (((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D))) | ~ (ord_less_eq_nat @ A @ D))) | ~ (C @ B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5711])). 185.47/93.66 thf(7145,axiom,((! [A:int,B:int,C:nat]: (((times_times_int @ (power_power_int @ A @ C) @ B) = (times_times_int @ B @ (power_power_int @ A @ C))) <= ((times_times_int @ A @ B) = (times_times_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_power__commuting__commutes)). 185.47/93.66 thf(32051,plain,((! [A:int,B:int,C:nat]: (((times_times_int @ (power_power_int @ A @ C) @ B) = (times_times_int @ B @ (power_power_int @ A @ C))) | ~ ((times_times_int @ A @ B) = (times_times_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7145])). 185.47/93.66 thf(6246,axiom,((! [A:nat]: ((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6275_minus__1__div__exp__eq__int)). 185.47/93.66 thf(28748,plain,((! [A:nat]: ((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6246])). 185.47/93.66 thf(5833,axiom,((! [A:nat,B:(nat > (vEBT_VEBT > $o))]: ((! [C:nat]: ((? [D:vEBT_VEBT]: (B @ C @ D)) <= (ord_less_nat @ C @ A))) = (? [C:list_VEBT_VEBT]: (! [D:nat]: ((B @ D @ (nth_VEBT_VEBT @ C @ D)) <= (ord_less_nat @ D @ A)) & ((size_s6755466524823107622T_VEBT @ C) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_922_Skolem__list__nth)). 185.47/93.66 thf(27296,plain,((! [A:nat,B:(nat > (vEBT_VEBT > $o))]: ((! [C:nat]: (? [D:vEBT_VEBT]: (B @ C @ D) | ~ (ord_less_nat @ C @ A))) = (? [C:list_VEBT_VEBT]: (! [D:nat]: ((B @ D @ (nth_VEBT_VEBT @ C @ D)) | ~ (ord_less_nat @ D @ A)) & ((size_s6755466524823107622T_VEBT @ C) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5833])). 185.47/93.66 thf(6758,axiom,((divide_divide_nat = (^ [A:nat,B:nat]: (if_nat @ ((B = zero_zero_nat) | (ord_less_nat @ A @ B)) @ zero_zero_nat @ (suc @ (divide_divide_nat @ (minus_minus_nat @ A @ B) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2909_div__if)). 185.47/93.66 thf(30595,plain,(((divide_divide_nat) = (^ [A:nat,B:nat]: (if_nat @ ((B = zero_zero_nat) | (ord_less_nat @ A @ B)) @ zero_zero_nat @ (suc @ (divide_divide_nat @ (minus_minus_nat @ A @ B) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6758])). 185.47/93.66 thf(4689,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)) <= (ord_less_int @ zero_zero_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2369_mult__strict__right__mono)). 185.47/93.66 thf(23027,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)) | ~ (ord_less_int @ zero_zero_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4689])). 185.47/93.66 thf(3145,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (times_times_real @ B @ A) @ A)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2672_mult__left__le__one__le)). 185.47/93.66 thf(18127,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (times_times_real @ B @ A) @ A)) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3145])). 185.47/93.66 thf(905,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4403_max__absorb2)). 185.47/93.66 thf(10834,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[905])). 185.47/93.66 thf(4926,axiom,((! [A:rat,B:num]: ((power_power_rat @ (uminus_uminus_rat @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus_uminus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6618_power__minus__Bit1)). 185.47/93.66 thf(23857,plain,((! [A:rat,B:num]: ((power_power_rat @ (uminus_uminus_rat @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus_uminus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4926])). 185.47/93.66 thf(6045,axiom,(((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5410_diff__numeral__special_I10_J)). 185.47/93.66 thf(28027,plain,(((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6045])). 185.47/93.66 thf(3478,axiom,((! [A:int,B:int,C:int]: ((((ord_less_eq_int @ (divide_divide_int @ A @ C) @ (divide_divide_int @ A @ B)) <= (ord_less_eq_int @ B @ C)) <= (ord_less_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3048_zdiv__mono2)). 185.47/93.66 thf(19181,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (divide_divide_int @ A @ C) @ (divide_divide_int @ A @ B)) | ~ (ord_less_eq_int @ B @ C) | ~ (ord_less_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3478])). 185.47/93.66 thf(3758,axiom,((! [A:real,B:real]: (((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2629_add__nonpos__neg)). 185.47/93.66 thf(20064,plain,((! [A:real,B:real]: (((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3758])). 185.47/93.66 thf(3547,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (ord_max_nat @ B @ C)) = (ord_max_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3750_max__add__distrib__right)). 185.47/93.66 thf(19393,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (ord_max_nat @ B @ C)) = (ord_max_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3547])). 185.47/93.66 thf(2074,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5163_neg__less__0__iff__less)). 185.47/93.66 thf(14655,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2074])). 185.47/93.66 thf(1985,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = ((dvd_dvd_int @ A @ C) | (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4461_dvd__mult__cancel__right)). 185.47/93.66 thf(14369,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = ((dvd_dvd_int @ A @ C) | (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1985])). 185.47/93.66 thf(4917,axiom,((! [A:int,B:nat]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ (power_power_int @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3010_odd__power__less__zero)). 185.47/93.66 thf(23818,plain,((! [A:int,B:nat]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ (power_power_int @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4917])). 185.47/93.66 thf(893,axiom,((! [A:nat]: ((sin_real @ (times_times_real @ pi @ (semiri5074537144036343181t_real @ A))) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7794_sin__npi2)). 185.47/93.66 thf(10787,plain,((! [A:nat]: ((sin_real @ (times_times_real @ pi @ (semiri5074537144036343181t_real @ A))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[893])). 185.47/93.66 thf(3790,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ B) @ E)) = ((plus_plus_int @ (times_times_int @ (minus_minus_int @ A @ D) @ B) @ C) = E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1223_eq__add__iff1)). 185.47/93.66 thf(20180,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ B) @ E)) = ((plus_plus_int @ (times_times_int @ (minus_minus_int @ A @ D) @ B) @ C) = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3790])). 185.47/93.66 thf(2691,axiom,((! [A:num,B:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5702_neg__numeral__less__numeral)). 185.47/93.66 thf(16690,plain,((! [A:num,B:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2691])). 185.47/93.66 thf(7093,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ C) => ((divide_divide_nat @ C @ (divide_divide_nat @ B @ A)) = (times_times_nat @ (divide_divide_nat @ C @ B) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4757_div__div__eq__right)). 185.47/93.66 thf(31878,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ C) => ((divide_divide_nat @ C @ (divide_divide_nat @ B @ A)) = (times_times_nat @ (divide_divide_nat @ C @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7093])). 185.47/93.66 thf(6013,axiom,((! [A:nat]: ((order_mono_nat_nat @ (times_times_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10171_mono__times__nat)). 185.47/93.66 thf(27936,plain,((! [A:nat]: ((order_mono_nat_nat @ (times_times_nat @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6013])). 185.47/93.66 thf(73,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_int @ (groups3539618377306564664at_int @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7551_sum_OlessThan__Suc)). 185.47/93.66 thf(7966,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_int @ (groups3539618377306564664at_int @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 185.47/93.66 thf(4569,axiom,((! [A:num]: ~ (ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5895_not__zero__le__neg__numeral)). 185.47/93.66 thf(22641,plain,((! [A:num]: ~ (ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4569])). 185.47/93.66 thf(4232,axiom,(((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5271_add__neg__numeral__special_I8_J)). 185.47/93.66 thf(21543,plain,(((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4232])). 185.47/93.66 thf(308,axiom,((! [A:complex]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ zero_zero_real) = ((re @ A) = (uminus_uminus_real @ (real_V1022390504157884413omplex @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9656_cmod__plus__Re__le__0__iff)). 185.47/93.66 thf(8764,plain,((! [A:complex]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ zero_zero_real) = ((re @ A) = (uminus_uminus_real @ (real_V1022390504157884413omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 185.47/93.66 thf(6424,axiom,((! [A:nat,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((power_power_real @ (root @ A @ B) @ A) = B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9175_real__root__pow__pos2)). 185.47/93.66 thf(29394,plain,((! [A:nat,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((power_power_real @ (root @ A @ B) @ A) = B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6424])). 185.47/93.66 thf(1392,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2655_divide__nonneg__pos)). 185.47/93.66 thf(12378,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392])). 185.47/93.66 thf(3063,axiom,((! [A:int,B:int]: ((minus_minus_int @ A @ (modulo_modulo_int @ A @ B)) = (times_times_int @ (divide_divide_int @ A @ B) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2560_minus__mod__eq__div__mult)). 185.47/93.66 thf(17873,plain,((! [A:int,B:int]: ((minus_minus_int @ A @ (modulo_modulo_int @ A @ B)) = (times_times_int @ (divide_divide_int @ A @ B) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3063])). 185.47/93.66 thf(2288,axiom,((! [A:rat,B:nat]: ((power_power_rat @ (divide_divide_rat @ one_one_rat @ A) @ B) = (divide_divide_rat @ one_one_rat @ (power_power_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_845_power__one__over)). 185.47/93.66 thf(15322,plain,((! [A:rat,B:nat]: ((power_power_rat @ (divide_divide_rat @ one_one_rat @ A) @ B) = (divide_divide_rat @ one_one_rat @ (power_power_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2288])). 185.47/93.66 thf(6020,axiom,((! [A:nat]: ((suc @ (suc @ (suc @ A))) = (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6673_Suc3__eq__add__3)). 185.47/93.66 thf(27954,plain,((! [A:nat]: ((suc @ (suc @ (suc @ A))) = (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6020])). 185.47/93.66 thf(6135,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ (plus_plus_nat @ A @ B) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2760_div__add__self1)). 185.47/93.66 thf(28327,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ (plus_plus_nat @ A @ B) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6135])). 185.47/93.66 thf(5638,axiom,((! [A:complex,B:nat]: ((times_times_complex @ (power_power_complex @ A @ B) @ A) = (times_times_complex @ A @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_power__commutes)). 185.47/93.66 thf(26492,plain,((! [A:complex,B:nat]: ((times_times_complex @ (power_power_complex @ A @ B) @ A) = (times_times_complex @ A @ (power_power_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5638])). 185.47/93.66 thf(6315,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: (((? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C))) <= (~ (A @ C))) <= (ord_less_nat @ zero_zero_nat @ C))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2120_infinite__descent0)). 185.47/93.66 thf(28972,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C)) | (A @ C) | ~ (ord_less_nat @ zero_zero_nat @ C))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6315])). 185.47/93.66 thf(5290,axiom,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1563_div__by__0)). 185.47/93.66 thf(25220,plain,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5290])). 185.47/93.66 thf(4096,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3090_verit__comp__simplify1_I2_J)). 185.47/93.66 thf(21127,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4096])). 185.47/93.66 thf(2447,axiom,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ A @ (plus_plus_rat @ B @ C)) = (plus_plus_rat @ B @ (plus_plus_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_add_Oleft__commute)). 185.47/93.66 thf(15835,plain,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ A @ (plus_plus_rat @ B @ C)) = (plus_plus_rat @ B @ (plus_plus_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2447])). 185.47/93.66 thf(7204,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_3868_order__antisym)). 185.47/93.66 thf(32265,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)],[7204])). 185.47/93.66 thf(651,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ one_one_real) => (((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_eq_real @ B @ (arcsin @ A)) = (ord_less_eq_real @ (sin_real @ B) @ A))) <= (ord_less_eq_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ B))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8337_le__arcsin__iff)). 185.47/93.66 thf(9893,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ one_one_real) => (((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_eq_real @ B @ (arcsin @ A)) = (ord_less_eq_real @ (sin_real @ B) @ A))) | ~ (ord_less_eq_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ B))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[651])). 185.47/93.66 thf(6073,axiom,((! [A:rat,B:rat]: (((times_times_rat @ A @ B) != zero_zero_rat) => ((B != zero_zero_rat) & (A != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2045_mult__not__zero)). 185.47/93.66 thf(28112,plain,((! [A:rat,B:rat]: ((~ ((times_times_rat @ A @ B) = zero_zero_rat)) => (~ (B = zero_zero_rat) & ~ (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6073])). 185.47/93.66 thf(4435,axiom,((! [A:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5174_ab__left__minus)). 185.47/93.66 thf(22201,plain,((! [A:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4435])). 185.47/93.66 thf(7717,axiom,((! [A:num]: ((pow @ A @ one) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9425_pow_Osimps_I1_J)). 185.47/93.66 thf(33888,plain,((! [A:num]: ((pow @ A @ one) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7717])). 185.47/93.66 thf(2326,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (times_times_real @ A @ B)) = (((ord_less_real @ A @ zero_zero_real) => (ord_less_eq_real @ B @ one_one_real)) & ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ one_one_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2806_mult__le__cancel__left1)). 185.47/93.66 thf(15442,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (times_times_real @ A @ B)) = (((ord_less_real @ A @ zero_zero_real) => (ord_less_eq_real @ B @ one_one_real)) & ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ one_one_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2326])). 185.47/93.66 thf(5249,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) <= (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3897_dual__order_Otrans)). 185.47/93.66 thf(25038,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5249])). 185.47/93.66 thf(5416,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ (suc @ (suc @ (suc @ A))) @ B) = (divide_divide_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6704_Suc__div__eq__add3__div)). 185.47/93.66 thf(25643,plain,((! [A:nat,B:nat]: ((divide_divide_nat @ (suc @ (suc @ (suc @ A))) @ B) = (divide_divide_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5416])). 185.47/93.66 thf(6029,axiom,((! [A:num]: ((ring_1_of_int_real @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7295_of__int__neg__numeral)). 185.47/93.66 thf(27980,plain,((! [A:num]: ((ring_1_of_int_real @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6029])). 185.47/93.66 thf(5795,axiom,((! [A:num,B:num]: ((times_times_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_numeral__times__numeral)). 185.47/93.66 thf(27005,plain,((! [A:num,B:num]: ((times_times_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5795])). 185.47/93.66 thf(6350,axiom,((! [A:complex]: ((power_power_complex @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_power__one__right)). 185.47/93.66 thf(29114,plain,((! [A:complex]: ((power_power_complex @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6350])). 185.47/93.66 thf(2848,axiom,((! [A:nat]: (ord_less_eq_real @ zero_zero_real @ (semiri5074537144036343181t_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7207_of__nat__0__le__iff)). 185.47/93.66 thf(17186,plain,((! [A:nat]: (ord_less_eq_real @ zero_zero_real @ (semiri5074537144036343181t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2848])). 185.47/93.66 thf(603,axiom,((! [A:vEBT_VEBT]: (((((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E))))) <= (! [B:$o]: (A != (vEBT_Leaf @ B @ ($true))))) <= (! [B:$o]: (A != (vEBT_Leaf @ ($true) @ B)))) <= (A != (vEBT_Leaf @ ($false) @ ($false)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2187_VEBT__internal_OminNull_Ocases)). 185.47/93.66 thf(9739,plain,((! [A:vEBT_VEBT]: (((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E))))) | ~ (! [B:$o]: ~ (A = (vEBT_Leaf @ B @ ($true)))) | ~ (! [B:$o]: ~ (A = (vEBT_Leaf @ ($true) @ B))) | (A = (vEBT_Leaf @ ($false) @ ($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[603])). 185.47/93.66 thf(4487,axiom,((! [A:nat]: ~ (ord_less_rat @ (semiri773545260158071498ct_rat @ A) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7988_fact__not__neg)). 185.47/93.66 thf(22364,plain,((! [A:nat]: ~ (ord_less_rat @ (semiri773545260158071498ct_rat @ A) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4487])). 185.47/93.66 thf(175,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_real @ zero_zero_real @ (log @ A @ B)) = (ord_less_real @ one_one_real @ B)) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9028_zero__less__log__cancel__iff)). 185.47/93.66 thf(8294,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_real @ zero_zero_real @ (log @ A @ B)) = (ord_less_real @ one_one_real @ B)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 185.47/93.66 thf(4146,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_729_diff__diff__eq2)). 185.47/93.66 thf(21279,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4146])). 185.47/93.66 thf(4135,axiom,((! [A:real,B:real]: ((times_times_complex @ imaginary_unit @ (complex2 @ A @ B)) = (complex2 @ (uminus_uminus_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9010_i__mult__Complex)). 185.47/93.66 thf(21246,plain,((! [A:real,B:real]: ((times_times_complex @ imaginary_unit @ (complex2 @ A @ B)) = (complex2 @ (uminus_uminus_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4135])). 185.47/93.66 thf(4,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (minus_minus_real @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_real @ (A @ zero_zero_nat) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7588_sum__lessThan__telescope_H)). 185.47/93.66 thf(7738,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (minus_minus_real @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_real @ (A @ zero_zero_nat) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 185.47/93.66 thf(1278,axiom,((! [A:int,B:int,C:int]: ((((dvd_dvd_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A)) = (dvd_dvd_int @ B @ C)) <= (dvd_dvd_int @ A @ C)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4449_div__dvd__div)). 185.47/93.66 thf(12004,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A)) = (dvd_dvd_int @ B @ C)) | ~ (dvd_dvd_int @ A @ C) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278])). 185.47/93.66 thf(1297,axiom,((! [A:int,B:int,C:int]: (((minus_minus_int @ A @ B) = C) = (A = (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_720_diff__eq__eq)). 185.47/93.66 thf(12059,plain,((! [A:int,B:int,C:int]: (((minus_minus_int @ A @ B) = C) = (A = (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297])). 185.47/93.66 thf(4223,axiom,((! [A:int,B:int]: (((divide_divide_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (divide_divide_int @ (plus_plus_int @ B @ one_one_int) @ A)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3081_neg__zdiv__mult__2)). 185.47/93.66 thf(21516,plain,((! [A:int,B:int]: (((divide_divide_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (divide_divide_int @ (plus_plus_int @ B @ one_one_int) @ A)) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4223])). 185.47/93.66 thf(5451,axiom,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4578_dvd__triv__right)). 185.47/93.66 thf(25797,plain,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5451])). 185.47/93.66 thf(5615,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = B) = ((A = one_one_int) | (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1676_mult__cancel__right2)). 185.47/93.66 thf(26419,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = B) = ((A = one_one_int) | (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5615])). 185.47/93.66 thf(1239,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_eq_real @ C @ B)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2597_mult__le__cancel__left__neg)). 185.47/93.66 thf(11888,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_eq_real @ C @ B)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239])). 185.47/93.66 thf(4617,axiom,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: ((? [E:real]: ! [F:real]: (((A @ F) = (B @ F)) <= (ord_less_real @ F @ E))) => ((? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F))))) <= (? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) <= (ord_less_real @ F @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3255_minf_I1_J)). 185.47/93.66 thf(22781,plain,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: ((? [E:real]: ! [F:real]: (((A @ F) = (B @ F)) | ~ (ord_less_real @ F @ E))) => (? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F)))) | ~ (? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) | ~ (ord_less_real @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4617])). 185.47/93.66 thf(3258,axiom,((! [A:num]: (ord_less_eq_int @ zero_zero_int @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2193_zero__le__numeral)). 185.47/93.66 thf(18476,plain,((! [A:num]: (ord_less_eq_int @ zero_zero_int @ (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3258])). 185.47/93.66 thf(3116,axiom,((! [A:nat,B:nat]: (((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B) = zero_zero_real) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8512_pochhammer__of__nat__eq__0__lemma)). 185.47/93.66 thf(18044,plain,((! [A:nat,B:nat]: (((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B) = zero_zero_real) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3116])). 185.47/93.66 thf(1447,axiom,((! [A:num]: ((ord_max_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3633_max__0__1_I6_J)). 185.47/93.66 thf(12558,plain,((! [A:num]: ((ord_max_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1447])). 185.47/93.66 thf(6400,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => (((times_times_rat @ B @ A) = (times_times_rat @ C @ A)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2065_mult__right__cancel)). 185.47/93.66 thf(29280,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => (((times_times_rat @ B @ A) = (times_times_rat @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6400])). 185.47/93.66 thf(5247,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (modulo_modulo_nat @ B @ C)) = (((A @ B) <= (C = zero_zero_nat)) & ((! [D:nat,E:nat]: ((ord_less_nat @ E @ C) => ((B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)) => (A @ E)))) <= (C != zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2137_split__mod)). 185.47/93.66 thf(25031,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (modulo_modulo_nat @ B @ C)) = (((A @ B) | ~ (C = zero_zero_nat)) & (! [D:nat,E:nat]: ((ord_less_nat @ E @ C) => ((B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)) => (A @ E))) | (C = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5247])). 185.47/93.66 thf(2365,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1125_ring__class_Oring__distribs_I2_J)). 185.47/93.66 thf(15560,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2365])). 185.47/93.66 thf(5971,axiom,((! [A:int,B:num,C:nat]: (((ring_1_of_int_rat @ A) = (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7155_of__int__eq__neg__numeral__power__cancel__iff)). 185.47/93.66 thf(27801,plain,((! [A:int,B:num,C:nat]: (((ring_1_of_int_rat @ A) = (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5971])). 185.47/93.66 thf(2701,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ A @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2336_zero__less__mult__iff)). 185.47/93.66 thf(16722,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ A @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2701])). 185.47/93.66 thf(4044,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = (uminus1482373934393186551omplex @ one_one_complex)) = ((B != zero_zero_complex) & (A = (uminus1482373934393186551omplex @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5986_divide__eq__minus__1__iff)). 185.47/93.66 thf(20967,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = (uminus1482373934393186551omplex @ one_one_complex)) = (~ (B = zero_zero_complex) & (A = (uminus1482373934393186551omplex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4044])). 185.47/93.66 thf(5029,axiom,((! [A:num,B:num]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ B)) = (numera6690914467698888265omplex @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_numeral__times__numeral)). 185.47/93.66 thf(24189,plain,((! [A:num,B:num]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ B)) = (numera6690914467698888265omplex @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5029])). 185.47/93.66 thf(5445,axiom,((! [A:nat]: ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5462_power__minus1__even)). 185.47/93.66 thf(25778,plain,((! [A:nat]: ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5445])). 185.47/93.66 thf(1831,axiom,((! [A:rat,B:rat]: ((abs_abs_rat @ (plus_plus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))) = (plus_plus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6347_abs__add__abs)). 185.47/93.66 thf(13868,plain,((! [A:rat,B:rat]: ((abs_abs_rat @ (plus_plus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))) = (plus_plus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831])). 185.47/93.66 thf(4134,axiom,((! [A:int]: ((ord_less_eq_rat @ zero_zero_rat @ (ring_1_of_int_rat @ A)) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7031_of__int__0__le__iff)). 185.47/93.66 thf(21243,plain,((! [A:int]: ((ord_less_eq_rat @ zero_zero_rat @ (ring_1_of_int_rat @ A)) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4134])). 185.47/93.66 thf(4427,axiom,((! [A:real,B:real,C:(real > int),D:int]: ((ord_less_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_int @ (C @ E) @ (C @ F)))) => (ord_less_int @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4087_ord__less__eq__subst)). 185.47/93.66 thf(22168,plain,((! [A:real,B:real,C:(real > int),D:int]: ((ord_less_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_int @ (C @ E) @ (C @ F)))) => (ord_less_int @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4427])). 185.47/93.66 thf(6093,axiom,((! [A:rat]: ((minus_minus_rat @ zero_zero_rat @ A) = (uminus_uminus_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5185_verit__minus__simplify_I3_J)). 185.47/93.66 thf(28182,plain,((! [A:rat]: ((minus_minus_rat @ zero_zero_rat @ A) = (uminus_uminus_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6093])). 185.47/93.66 thf(5073,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ C) = (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_815_le__diff__conv)). 185.47/93.66 thf(24412,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ C) = (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5073])). 185.47/93.66 thf(799,axiom,((! [A:int,B:num]: (((ring_1_of_int_int @ A) = (numeral_numeral_int @ B)) = (A = (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6943_of__int__eq__numeral__iff)). 185.47/93.66 thf(10455,plain,((! [A:int,B:num]: (((ring_1_of_int_int @ A) = (numeral_numeral_int @ B)) = (A = (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[799])). 185.47/93.66 thf(8,axiom,((! [A:real,B:nat,C:real]: ((minus_minus_real @ (power_power_real @ A @ (suc @ B)) @ (power_power_real @ C @ (suc @ B))) = (times_times_real @ (minus_minus_real @ A @ C) @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (power_power_real @ A @ D) @ (power_power_real @ C @ (minus_minus_nat @ B @ D)))) @ (set_ord_lessThan_nat @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7615_diff__power__eq__sum)). 185.47/93.66 thf(7749,plain,((! [A:real,B:nat,C:real]: ((minus_minus_real @ (power_power_real @ A @ (suc @ B)) @ (power_power_real @ C @ (suc @ B))) = (times_times_real @ (minus_minus_real @ A @ C) @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (power_power_real @ A @ D) @ (power_power_real @ C @ (minus_minus_nat @ B @ D)))) @ (set_ord_lessThan_nat @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 185.47/93.66 thf(2097,axiom,(((pred_numeral @ one) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6780_pred__numeral__simps_I1_J)). 185.47/93.66 thf(14721,plain,(((pred_numeral @ one) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2097])). 185.47/93.66 thf(7288,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: (B != (suc @ (plus_plus_nat @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1097_less__natE)). 185.47/93.66 thf(32550,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: ~ (B = (suc @ (plus_plus_nat @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7288])). 185.47/93.66 thf(3704,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_add_Oassoc)). 185.47/93.66 thf(19889,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3704])). 185.47/93.66 thf(742,axiom,((! [A:real]: (((ord_less_real @ (tan_real @ A) @ zero_zero_real) <= (ord_less_real @ A @ zero_zero_real)) <= (ord_less_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8067_tan__less__zero)). 185.47/93.66 thf(10207,plain,((! [A:real]: ((ord_less_real @ (tan_real @ A) @ zero_zero_real) | ~ (ord_less_real @ A @ zero_zero_real) | ~ (ord_less_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[742])). 185.47/93.66 thf(415,axiom,((! [A:int,B:int,C:nat]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (ring_1_of_int_int @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7094_of__int__power__le__of__int__cancel__iff)). 185.47/93.66 thf(9112,plain,((! [A:int,B:int,C:nat]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (ring_1_of_int_int @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])). 185.47/93.66 thf(5162,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3273_minf_I4_J)). 185.47/93.66 thf(24758,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5162])). 185.47/93.66 thf(219,axiom,((! [A:int]: ((ord_less_int @ (bit_ri7919022796975470100ot_int @ A) @ zero_zero_int) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9501_not__negative__int__iff)). 185.47/93.66 thf(8439,plain,((! [A:int]: ((ord_less_int @ (bit_ri7919022796975470100ot_int @ A) @ zero_zero_int) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 185.47/93.66 thf(3110,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (minus_minus_int @ A @ (modulo_modulo_int @ B @ C)) @ C) = (modulo_modulo_int @ (minus_minus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2000_mod__diff__right__eq)). 185.47/93.66 thf(18027,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (minus_minus_int @ A @ (modulo_modulo_int @ B @ C)) @ C) = (modulo_modulo_int @ (minus_minus_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3110])). 185.47/93.66 thf(3640,axiom,((! [A:real,B:real,C:real,D:real]: ((A != zero_zero_real) => (((ord_less_eq_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ D @ B)) = (ord_less_eq_real @ (divide_divide_real @ (minus_minus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A)) @ (times_times_real @ A @ B)) @ zero_zero_real)) <= (B != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2863_frac__le__eq)). 185.47/93.66 thf(19684,plain,((! [A:real,B:real,C:real,D:real]: ((~ (A = zero_zero_real)) => (((ord_less_eq_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ D @ B)) = (ord_less_eq_real @ (divide_divide_real @ (minus_minus_real @ (times_times_real @ C @ B) @ (times_times_real @ D @ A)) @ (times_times_real @ A @ B)) @ zero_zero_real)) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3640])). 185.47/93.66 thf(817,axiom,((! [A:real,B:real]: ((if_real @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Real__Oreal_T)). 185.47/93.66 thf(10518,plain,((! [A:real,B:real]: ((if_real @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[817])). 185.47/93.66 thf(6805,axiom,((! [A:rat,B:nat,C:nat]: (((ord_less_rat @ A @ one_one_rat) => ((ord_less_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) = (ord_less_nat @ C @ B))) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1864_power__strict__decreasing__iff)). 185.47/93.66 thf(30752,plain,((! [A:rat,B:nat,C:nat]: (((ord_less_rat @ A @ one_one_rat) => ((ord_less_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) = (ord_less_nat @ C @ B))) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6805])). 185.47/93.66 thf(386,axiom,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => (((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ (tan_real @ A) @ (tan_real @ B))) <= (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8057_tan__monotone)). 185.47/93.66 thf(9017,plain,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => (((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ (tan_real @ A) @ (tan_real @ B))) | ~ (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])). 185.47/93.66 thf(6848,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9396_and__nat__numerals_I4_J)). 185.47/93.66 thf(30929,plain,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6848])). 185.47/93.66 thf(4399,axiom,((! [A:nat,B:int]: ((ord_less_nat @ A @ (nat2 @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9292_zless__nat__eq__int__zless)). 185.47/93.66 thf(22090,plain,((! [A:nat,B:int]: ((ord_less_nat @ A @ (nat2 @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4399])). 185.47/93.66 thf(347,axiom,((! [A:real]: (((arccos @ (cos_real @ A)) = (abs_abs_real @ A)) <= (ord_less_eq_real @ (abs_abs_real @ A) @ pi)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8371_arccos__cos__eq__abs)). 185.47/93.66 thf(8896,plain,((! [A:real]: (((arccos @ (cos_real @ A)) = (abs_abs_real @ A)) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 185.47/93.66 thf(717,axiom,((! [A:nat,B:nat,C:complex]: ((ord_less_eq_nat @ A @ B) => ((times_times_complex @ (minus_minus_complex @ one_one_complex @ C) @ (groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ A @ B))) = (minus_minus_complex @ (power_power_complex @ C @ A) @ (power_power_complex @ C @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6745_sum__gp__multiplied)). 185.47/93.66 thf(10122,plain,((! [A:nat,B:nat,C:complex]: ((ord_less_eq_nat @ A @ B) => ((times_times_complex @ (minus_minus_complex @ one_one_complex @ C) @ (groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ A @ B))) = (minus_minus_complex @ (power_power_complex @ C @ A) @ (power_power_complex @ C @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[717])). 185.47/93.66 thf(4093,axiom,((! [A:rat,B:rat]: ((plus_plus_rat @ A @ (plus_plus_rat @ (uminus_uminus_rat @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5087_add__minus__cancel)). 185.47/93.66 thf(21119,plain,((! [A:rat,B:rat]: ((plus_plus_rat @ A @ (plus_plus_rat @ (uminus_uminus_rat @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4093])). 185.47/93.66 thf(2861,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ B @ A)) => ((exp_complex @ (plus_plus_complex @ A @ B)) = (times_times_complex @ (exp_complex @ A) @ (exp_complex @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8172_exp__add__commuting)). 185.47/93.66 thf(17228,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ B @ A)) => ((exp_complex @ (plus_plus_complex @ A @ B)) = (times_times_complex @ (exp_complex @ A) @ (exp_complex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2861])). 185.47/93.66 thf(4543,axiom,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = (bit_se2000444600071755411sk_int @ A)) = (dvd_dvd_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (plus_plus_int @ B @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9351_take__bit__eq__mask__iff__exp__dvd)). 185.47/93.66 thf(22552,plain,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = (bit_se2000444600071755411sk_int @ A)) = (dvd_dvd_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (plus_plus_int @ B @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4543])). 185.47/93.66 thf(1776,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_nat @ (nat2 @ A) @ (nat2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9282_nat__mono)). 185.47/93.66 thf(13680,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_nat @ (nat2 @ A) @ (nat2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776])). 185.47/93.66 thf(4710,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (comm_s7457072308508201937r_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8465_pochhammer__nonneg)). 185.47/93.66 thf(23107,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (comm_s7457072308508201937r_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4710])). 185.47/93.66 thf(2696,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((((ord_less_eq_rat @ C @ D) => (ord_less_eq_rat @ (divide_divide_rat @ B @ D) @ (divide_divide_rat @ A @ C))) <= (ord_less_rat @ zero_zero_rat @ C)) <= (ord_less_eq_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2646_frac__le)). 185.47/93.66 thf(16705,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => (((ord_less_eq_rat @ C @ D) => (ord_less_eq_rat @ (divide_divide_rat @ B @ D) @ (divide_divide_rat @ A @ C))) | ~ (ord_less_rat @ zero_zero_rat @ C) | ~ (ord_less_eq_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2696])). 185.47/93.66 thf(3573,axiom,((abs_abs_int = (^ [A:int]: (if_int @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_int @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6573_abs__if)). 185.47/93.66 thf(19474,plain,(((abs_abs_int) = (^ [A:int]: (if_int @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_int @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3573])). 185.47/93.66 thf(2305,axiom,((! [A:(nat > int),B:set_nat,C:(nat > int),D:nat]: (((groups3539618377306564664at_int @ A @ B) = (groups3539618377306564664at_int @ C @ B)) => (((member_nat @ D @ B) => (((A @ D) = (C @ D)) <= (finite_finite_nat @ B))) <= (! [E:nat]: ((ord_less_eq_int @ (A @ E) @ (C @ E)) <= (member_nat @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5659_sum__mono__inv)). 185.47/93.66 thf(15374,plain,((! [A:(nat > int),B:set_nat,C:(nat > int),D:nat]: (((groups3539618377306564664at_int @ (A) @ B) = (groups3539618377306564664at_int @ (C) @ B)) => (((member_nat @ D @ B) => (((A @ D) = (C @ D)) | ~ (finite_finite_nat @ B))) | ~ (! [E:nat]: ((ord_less_eq_int @ (A @ E) @ (C @ E)) | ~ (member_nat @ E @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2305])). 185.47/93.66 thf(1708,axiom,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ A @ (plus_plus_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_is__num__normalize_I1_J)). 185.47/93.66 thf(13451,plain,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ A @ (plus_plus_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708])). 185.47/93.66 thf(695,axiom,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ one_one_real) => (? [B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) @ B) & ((tan_real @ B) = A) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8086_tan__total__pi4)). 185.47/93.66 thf(10047,plain,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ one_one_real) => (? [B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) @ B) & ((tan_real @ B) = A) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[695])). 185.47/93.66 thf(1759,axiom,((! [A:real,B:real]: ? [C:real]: ! [D:real]: (((dvd_dvd_real @ A @ (plus_plus_real @ D @ B)) = (dvd_dvd_real @ A @ (plus_plus_real @ D @ B))) <= (ord_less_real @ D @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4709_minf_I9_J)). 185.47/93.66 thf(13629,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759])). 185.47/93.66 thf(1665,axiom,((! [A:int,B:real]: (((ord_less_real @ one_one_real @ B) | (A = zero_zero_int)) <= (ord_less_real @ (abs_abs_real @ (ring_1_of_int_real @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7289_of__int__lessD)). 185.47/93.66 thf(13316,plain,((! [A:int,B:real]: ((ord_less_real @ one_one_real @ B) | (A = zero_zero_int) | ~ (ord_less_real @ (abs_abs_real @ (ring_1_of_int_real @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665])). 185.47/93.66 thf(7562,axiom,((! [A:num]: (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4845_even__numeral)). 185.47/93.66 thf(33467,plain,((! [A:num]: (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7562])). 185.47/93.66 thf(7197,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7114_of__nat__zero__less__power__iff)). 185.47/93.66 thf(32240,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7197])). 185.47/93.66 thf(2509,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_add__diff__cancel__right)). 185.47/93.66 thf(16051,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (minus_minus_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2509])). 185.47/93.66 thf(821,axiom,((! [A:num,B:num]: ((((ord_max_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (numeral_numeral_int @ A)) <= (~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))))) & ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) => ((ord_max_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5319_max__number__of_I2_J)). 185.47/93.66 thf(10533,plain,((! [A:num,B:num]: ((((ord_max_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (numeral_numeral_int @ A)) | (ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B)))) & ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) => ((ord_max_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[821])). 185.47/93.66 thf(260,axiom,((! [A:(nat > real),B:set_nat]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (groups6591440286371151544t_real @ A @ B)) @ (groups6591440286371151544t_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (A @ C))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7473_norm__sum)). 185.47/93.66 thf(8587,plain,((! [A:(nat > real),B:set_nat]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (groups6591440286371151544t_real @ (A) @ B)) @ (groups6591440286371151544t_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (A @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[260])). 185.47/93.66 thf(1060,axiom,((ord_less_rat @ (uminus_uminus_rat @ one_one_rat) @ one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5750_less__minus__one__simps_I2_J)). 185.47/93.66 thf(11336,plain,((ord_less_rat @ (uminus_uminus_rat @ one_one_rat) @ one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060])). 185.47/93.66 thf(3906,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2351_mult__less__cancel__left__pos)). 185.47/93.66 thf(20542,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3906])). 185.47/93.66 thf(7338,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (((ord_less_eq_nat @ A @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ B)) | ((ord_less_eq_nat @ B @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2223_split__mult__neg__le)). 185.47/93.66 thf(32731,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (((ord_less_eq_nat @ A @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ B)) | ((ord_less_eq_nat @ B @ zero_zero_nat) & (ord_less_eq_nat @ zero_zero_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7338])). 185.47/93.66 thf(4921,axiom,((! [A:$o,B:$o]: ((((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = none_nat) <= (~ (A))) & (((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (some_nat @ zero_zero_nat)) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2184_vebt__pred_Osimps_I2_J)). 185.47/93.66 thf(23833,plain,((! [A:$o,B:$o]: ((((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = none_nat) | (A)) & (((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (some_nat @ zero_zero_nat)) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4921])). 185.47/93.66 thf(6608,axiom,(((plus_plus_rat @ one_one_rat @ one_one_rat) = (numeral_numeral_rat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_one__add__one)). 185.47/93.66 thf(30029,plain,(((plus_plus_rat @ one_one_rat @ one_one_rat) = (numeral_numeral_rat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6608])). 185.47/93.66 thf(1633,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_add__le__cancel__right)). 185.47/93.66 thf(13167,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) = (ord_less_eq_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633])). 185.47/93.66 thf(7358,axiom,((! [A:int]: ((~ (! [B:int]: (A != (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))) <= (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4902_evenE)). 185.47/93.66 thf(32792,plain,((! [A:int]: (~ (! [B:int]: ~ (A = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7358])). 185.47/93.66 thf(2121,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ C @ B) => (~ (ord_less_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3281_minf_I7_J)). 185.47/93.66 thf(14794,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ C @ B) => (~ (ord_less_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2121])). 185.47/93.66 thf(5966,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (minus_minus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_diff__right__commute)). 185.47/93.66 thf(27786,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (minus_minus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5966])). 185.47/93.66 thf(312,axiom,((! [A:(nat > rat)]: ((groups2906978787729119204at_rat @ A @ bot_bot_set_nat) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5218_sum_Oempty)). 185.47/93.66 thf(8775,plain,((! [A:(nat > rat)]: ((groups2906978787729119204at_rat @ (A) @ bot_bot_set_nat) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 185.47/93.66 thf(760,axiom,((! [A:real]: (((ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ A)) = (ord_less_eq_real @ one_one_real @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5321_ln__ge__zero__iff)). 185.47/93.66 thf(10302,plain,((! [A:real]: (((ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ A)) = (ord_less_eq_real @ one_one_real @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[760])). 185.47/93.66 thf(226,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (log @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9027_log__less__zero__cancel__iff)). 185.47/93.66 thf(8455,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (log @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 185.47/93.66 thf(7064,axiom,((! [A:nat]: ((modulo_modulo_int @ one_one_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (zero_n2684676970156552555ol_int @ (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5484_one__mod__2__pow__eq)). 185.47/93.66 thf(31788,plain,((! [A:nat]: ((modulo_modulo_int @ one_one_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (zero_n2684676970156552555ol_int @ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7064])). 185.47/93.66 thf(6041,axiom,((! [A:int,B:nat,C:nat]: ((divide_divide_int @ (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ C)) = (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_div__exp__eq)). 185.47/93.66 thf(28016,plain,((! [A:int,B:nat,C:nat]: ((divide_divide_int @ (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ C)) = (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6041])). 185.47/93.66 thf(6859,axiom,((! [A:real,B:num]: ((power_power_real @ (uminus_uminus_real @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5998_power__minus__Bit0)). 185.47/93.66 thf(30983,plain,((! [A:real,B:num]: ((power_power_real @ (uminus_uminus_real @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6859])). 185.47/93.66 thf(2110,axiom,((! [A:rat,B:nat,C:nat]: ((comm_s4028243227959126397er_rat @ A @ (plus_plus_nat @ B @ C)) = (times_times_rat @ (comm_s4028243227959126397er_rat @ A @ B) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8522_pochhammer__product_H)). 185.47/93.66 thf(14757,plain,((! [A:rat,B:nat,C:nat]: ((comm_s4028243227959126397er_rat @ A @ (plus_plus_nat @ B @ C)) = (times_times_rat @ (comm_s4028243227959126397er_rat @ A @ B) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2110])). 185.47/93.66 thf(3360,axiom,((~ (ord_less_int @ one_one_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_767_less__numeral__extra_I4_J)). 185.47/93.66 thf(18802,plain,((~ (ord_less_int @ one_one_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3360])). 185.47/93.66 thf(845,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((ln_ln_real @ (root @ A @ B)) = (divide_divide_real @ (ln_ln_real @ B) @ (semiri5074537144036343181t_real @ A))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9204_ln__root)). 185.47/93.66 thf(10629,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((ln_ln_real @ (root @ A @ B)) = (divide_divide_real @ (ln_ln_real @ B) @ (semiri5074537144036343181t_real @ A))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[845])). 185.47/93.66 thf(215,axiom,((! [A:set_nat,B:set_nat,C:(nat > rat)]: (((ord_less_eq_set_nat @ B @ A) => (((groups73079841787564623at_rat @ C @ B) = (groups73079841787564623at_rat @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_rat))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8928_prod_Omono__neutral__left)). 185.47/93.66 thf(8425,plain,((! [A:set_nat,B:set_nat,C:(nat > rat)]: (((ord_less_eq_set_nat @ B @ A) => (((groups73079841787564623at_rat @ (C) @ B) = (groups73079841787564623at_rat @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_rat))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 185.47/93.66 thf(4620,axiom,((pred_numeral = (^ [A:num]: (minus_minus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6823_pred__numeral__def)). 185.47/93.66 thf(22797,plain,(((pred_numeral) = (^ [A:num]: (minus_minus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4620])). 185.47/93.66 thf(7654,axiom,((! [A:char]: ((comm_s629917340098488124ar_nat @ (ascii_of @ A)) = (bit_se2925701944663578781it_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (comm_s629917340098488124ar_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9980_String_Ochar__of__ascii__of)). 185.47/93.66 thf(33718,plain,((! [A:char]: ((comm_s629917340098488124ar_nat @ (ascii_of @ A)) = (bit_se2925701944663578781it_nat @ (numeral_numeral_nat @ (bit1 @ (bit1 @ one))) @ (comm_s629917340098488124ar_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7654])). 185.47/93.66 thf(3038,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (ord_max_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3595_max__nat_Oneutr__eq__iff)). 185.47/93.66 thf(17793,plain,((! [A:nat,B:nat]: ((zero_zero_nat = (ord_max_nat @ A @ B)) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3038])). 185.47/93.66 thf(6872,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2683_power__less__imp__less__base)). 185.47/93.66 thf(31044,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6872])). 185.47/93.66 thf(1439,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1859_le__divide__eq__1__neg)). 185.47/93.66 thf(12533,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439])). 185.47/93.66 thf(2813,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ zero_zero_rat @ C) => ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ B @ A)) => (ord_less_rat @ (divide_divide_rat @ C @ B) @ (divide_divide_rat @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2712_divide__strict__left__mono)). 185.47/93.66 thf(17069,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ zero_zero_rat @ C) => ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ B @ A)) => (ord_less_rat @ (divide_divide_rat @ C @ B) @ (divide_divide_rat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2813])). 185.47/93.66 thf(564,axiom,((! [A:real,B:nat]: ((times_times_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ (gbinomial_real @ A @ B)) = (times_times_real @ A @ (gbinomial_real @ (minus_minus_real @ A @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8479_gbinomial__absorb__comp)). 185.47/93.66 thf(9607,plain,((! [A:real,B:nat]: ((times_times_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ (gbinomial_real @ A @ B)) = (times_times_real @ A @ (gbinomial_real @ (minus_minus_real @ A @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[564])). 185.47/93.66 thf(6288,axiom,((! [A:nat,B:nat]: (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) != zero_zero_nat) => ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2951_exp__not__zero__imp__exp__diff__not__zero)). 185.47/93.66 thf(28888,plain,((! [A:nat,B:nat]: ((~ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = zero_zero_nat)) => (~ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6288])). 185.47/93.66 thf(3183,axiom,((! [A:int,B:int]: (((divide_divide_int @ (plus_plus_int @ B @ A) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ one_one_int)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2759_div__add__self2)). 185.47/93.66 thf(18248,plain,((! [A:int,B:int]: (((divide_divide_int @ (plus_plus_int @ B @ A) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ one_one_int)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3183])). 185.47/93.66 thf(826,axiom,((! [A:(nat > real),B:(nat > real)]: ((? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (abs_abs_real @ (A @ D)) @ (B @ D)))) => ((summable_real @ B) => (summable_real @ (^ [C:nat]: (abs_abs_real @ (A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7708_summable__rabs__comparison__test)). 185.47/93.66 thf(10550,plain,((! [A:(nat > real),B:(nat > real)]: ((? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (abs_abs_real @ (A @ D)) @ (B @ D)))) => ((summable_real @ (B)) => (summable_real @ (^ [C:nat]: (abs_abs_real @ (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[826])). 185.47/93.66 thf(4355,axiom,((! [A:int,B:int]: (((abs_abs_int @ (times_times_int @ A @ B)) = (times_times_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))) <= (((ord_less_eq_int @ A @ zero_zero_int) | (ord_less_eq_int @ zero_zero_int @ A)) & ((ord_less_eq_int @ zero_zero_int @ B) | (ord_less_eq_int @ B @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6549_abs__eq__mult)). 185.47/93.66 thf(21947,plain,((! [A:int,B:int]: (((abs_abs_int @ (times_times_int @ A @ B)) = (times_times_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))) | ~ (((ord_less_eq_int @ A @ zero_zero_int) | (ord_less_eq_int @ zero_zero_int @ A)) & ((ord_less_eq_int @ zero_zero_int @ B) | (ord_less_eq_int @ B @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4355])). 185.47/93.66 thf(5882,axiom,((! [A:rat]: ((minus_minus_rat @ A @ zero_zero_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1548_diff__zero)). 185.47/93.66 thf(27471,plain,((! [A:rat]: ((minus_minus_rat @ A @ zero_zero_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5882])). 185.47/93.66 thf(109,axiom,((! [A:real]: (((ord_less_real @ zero_zero_real @ (tan_real @ A)) <= (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8055_tan__gt__zero)). 185.47/93.66 thf(8090,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (tan_real @ A)) | ~ (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 185.47/93.66 thf(6397,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1914_mod2__gr__0)). 185.47/93.66 thf(29270,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6397])). 185.47/93.66 thf(7680,axiom,(((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1885_bits__1__div__2)). 185.47/93.66 thf(33787,plain,(((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7680])). 185.47/93.66 thf(1144,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) <= (ord_less_eq_real @ zero_zero_real @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2579_mult__strict__mono)). 185.47/93.66 thf(11610,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) | ~ (ord_less_eq_real @ zero_zero_real @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144])). 185.47/93.66 thf(6351,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1157_right__diff__distrib_H)). 185.47/93.66 thf(29117,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6351])). 185.47/93.66 thf(3415,axiom,((! [A:real]: (((sin_real @ A) = zero_zero_real) <= ((cos_real @ A) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7821_cos__one__sin__zero)). 185.47/93.66 thf(18975,plain,((! [A:real]: (((sin_real @ A) = zero_zero_real) | ~ ((cos_real @ A) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3415])). 185.47/93.66 thf(815,axiom,((! [A:real]: (((cos_real @ A) = (divide_divide_real @ one_one_real @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ (tan_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))) <= (ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8103_cos__tan)). 185.47/93.66 thf(10513,plain,((! [A:real]: (((cos_real @ A) = (divide_divide_real @ one_one_real @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ (tan_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))) | ~ (ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[815])). 185.47/93.66 thf(5254,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4071_order__less__trans)). 185.47/93.66 thf(25053,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5254])). 185.47/93.66 thf(2332,axiom,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ A @ (suc @ B)) = (insert_nat @ (suc @ B) @ (set_or1269000886237332187st_nat @ A @ B))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9428_atLeastAtMostSuc__conv)). 185.47/93.66 thf(15463,plain,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ A @ (suc @ B)) = (insert_nat @ (suc @ B) @ (set_or1269000886237332187st_nat @ A @ B))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2332])). 185.47/93.66 thf(5098,axiom,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5491_minus__equation__iff)). 185.47/93.66 thf(24483,plain,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5098])). 185.47/93.66 thf(5417,axiom,((! [A:real,B:real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5496_equation__minus__iff)). 185.47/93.66 thf(25646,plain,((! [A:real,B:real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5417])). 185.47/93.66 thf(1527,axiom,((! [A:int,B:int]: (ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) @ (ring_1_of_int_real @ (divide_divide_int @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7325_real__of__int__div2)). 185.47/93.66 thf(12800,plain,((! [A:int,B:int]: (ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) @ (ring_1_of_int_real @ (divide_divide_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527])). 185.47/93.66 thf(2192,axiom,((! [A:complex,B:complex,C:complex,D:complex]: (((B != zero_zero_complex) => (((divide1717551699836669952omplex @ C @ A) = (divide1717551699836669952omplex @ D @ B)) = ((times_times_complex @ C @ B) = (times_times_complex @ D @ A)))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2476_frac__eq__eq)). 185.47/93.66 thf(15037,plain,((! [A:complex,B:complex,C:complex,D:complex]: (((~ (B = zero_zero_complex)) => (((divide1717551699836669952omplex @ C @ A) = (divide1717551699836669952omplex @ D @ B)) = ((times_times_complex @ C @ B) = (times_times_complex @ D @ A)))) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2192])). 185.47/93.66 thf(6613,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) <= (ord_less_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2581_mult__strict__mono)). 185.47/93.66 thf(30042,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) | ~ (ord_less_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6613])). 185.47/93.66 thf(127,axiom,((! [A:real,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (gbinomial_real @ A @ C) @ (minus_minus_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (times_times_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (numeral_numeral_real @ (bit0 @ one))) @ (gbinomial_real @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8411_gchoose__row__sum__weighted)). 185.47/93.66 thf(8142,plain,((! [A:real,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (gbinomial_real @ A @ C) @ (minus_minus_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (times_times_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (numeral_numeral_real @ (bit0 @ one))) @ (gbinomial_real @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 185.47/93.66 thf(4724,axiom,((! [A:real,B:nat,C:real]: ((((real_V7735802525324610683m_real @ A) = (real_V7735802525324610683m_real @ C)) <= (ord_less_nat @ zero_zero_nat @ B)) <= ((power_power_real @ A @ B) = (power_power_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7478_power__eq__imp__eq__norm)). 185.47/93.66 thf(23150,plain,((! [A:real,B:nat,C:real]: (((real_V7735802525324610683m_real @ A) = (real_V7735802525324610683m_real @ C)) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ ((power_power_real @ A @ B) = (power_power_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4724])). 185.47/93.66 thf(1779,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((modulo_modulo_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (minus_minus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ (plus_plus_int @ B @ one_one_int) @ A)) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3070_neg__zmod__mult__2)). 185.47/93.66 thf(13693,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((modulo_modulo_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (minus_minus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ (plus_plus_int @ B @ one_one_int) @ A)) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779])). 185.47/93.66 thf(2615,axiom,((! [A:num,B:num]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5346_mult__neg__numeral__simps_I2_J)). 185.47/93.66 thf(16410,plain,((! [A:num,B:num]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2615])). 185.47/93.66 thf(3234,axiom,((! [A:nat,B:rat]: ((times_times_rat @ (semiri681578069525770553at_rat @ A) @ B) = (times_times_rat @ B @ (semiri681578069525770553at_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7185_mult__of__nat__commute)). 185.47/93.66 thf(18408,plain,((! [A:nat,B:rat]: ((times_times_rat @ (semiri681578069525770553at_rat @ A) @ B) = (times_times_rat @ B @ (semiri681578069525770553at_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3234])). 185.47/93.66 thf(5134,axiom,((cos_coeff = (^ [A:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (divide_divide_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri2265585572941072030t_real @ A)) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8089_cos__coeff__def)). 185.47/93.66 thf(24658,plain,(((cos_coeff) = (^ [A:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (divide_divide_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri2265585572941072030t_real @ A)) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5134])). 185.47/93.66 thf(3058,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2201_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 185.47/93.66 thf(17858,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3058])). 185.47/93.66 thf(3647,axiom,((! [A:set_nat,B:set_nat]: (((finite_finite_nat @ B) => (finite_finite_nat @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3486_finite__subset)). 185.47/93.66 thf(19708,plain,((! [A:set_nat,B:set_nat]: (((finite_finite_nat @ B) => (finite_finite_nat @ A)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3647])). 185.47/93.66 thf(4874,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((((divide_divide_real @ B @ A) = (divide_divide_real @ C @ A)) = (B = C)) <= (dvd_dvd_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4664_dvd__div__eq__iff)). 185.47/93.66 thf(23652,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((((divide_divide_real @ B @ A) = (divide_divide_real @ C @ A)) = (B = C)) | ~ (dvd_dvd_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4874])). 185.47/93.66 thf(980,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) <= (! [C:rat]: ((ord_less_eq_rat @ C @ B) <= (ord_less_rat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4181_dense__le)). 185.47/93.66 thf(11093,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) | ~ (! [C:rat]: ((ord_less_eq_rat @ C @ B) | ~ (ord_less_rat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[980])). 185.47/93.66 thf(6661,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ B @ (divide_divide_nat @ C @ A)) = (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4775_dvd__div__unit__iff)). 185.47/93.66 thf(30202,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ B @ (divide_divide_nat @ C @ A)) = (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6661])). 185.47/93.66 thf(7701,axiom,(((finite_card_o @ top_top_set_o) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9971_card__UNIV__bool)). 185.47/93.66 thf(33846,plain,(((finite_card_o @ top_top_set_o) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7701])). 185.47/93.66 thf(2477,axiom,((! [A:nat]: ((semiri773545260158071498ct_rat @ (suc @ A)) = (times_times_rat @ (semiri681578069525770553at_rat @ (suc @ A)) @ (semiri773545260158071498ct_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7969_fact__Suc)). 185.47/93.66 thf(15934,plain,((! [A:nat]: ((semiri773545260158071498ct_rat @ (suc @ A)) = (times_times_rat @ (semiri681578069525770553at_rat @ (suc @ A)) @ (semiri773545260158071498ct_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2477])). 185.47/93.66 thf(3422,axiom,((! [A:num,B:num]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (uminus1482373934393186551omplex @ (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5189_add__neg__numeral__simps_I3_J)). 185.47/93.66 thf(18998,plain,((! [A:num,B:num]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (uminus1482373934393186551omplex @ (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3422])). 185.47/93.66 thf(374,axiom,((! [A:set_nat,B:nat,C:(nat > rat)]: ((finite_finite_nat @ A) => ((member_nat @ B @ A) => (((ord_less_rat @ one_one_rat @ (groups73079841787564623at_rat @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_rat @ one_one_rat @ (C @ D))))) <= (ord_less_rat @ one_one_rat @ (C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8876_less__1__prod2)). 185.47/93.66 thf(8980,plain,((! [A:set_nat,B:nat,C:(nat > rat)]: ((finite_finite_nat @ A) => ((member_nat @ B @ A) => ((ord_less_rat @ one_one_rat @ (groups73079841787564623at_rat @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_rat @ one_one_rat @ (C @ D)))) | ~ (ord_less_rat @ one_one_rat @ (C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])). 185.47/93.66 thf(4143,axiom,((! [A:rat]: ((zero_zero_rat = (abs_abs_rat @ A)) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6318_abs__0__eq)). 185.47/93.66 thf(21270,plain,((! [A:rat]: ((zero_zero_rat = (abs_abs_rat @ A)) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4143])). 185.47/93.66 thf(3026,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real) <= (ord_less_eq_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2205_mult__nonneg__nonpos2)). 185.47/93.66 thf(17752,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real) | ~ (ord_less_eq_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3026])). 185.47/93.66 thf(1038,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ D) @ (times_times_real @ C @ B))) = ((A = C) | (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6285_crossproduct__eq)). 185.47/93.66 thf(11274,plain,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ D) @ (times_times_real @ C @ B))) = ((A = C) | (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038])). 185.47/93.66 thf(5901,axiom,((! [A:rat]: (((uminus_uminus_rat @ A) = A) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5039_neg__equal__zero)). 185.47/93.66 thf(27544,plain,((! [A:rat]: (((uminus_uminus_rat @ A) = A) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5901])). 185.47/93.66 thf(661,axiom,((! [A:(nat > complex),B:nat,C:nat]: ((groups2073611262835488442omplex @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo1517530859248394432omplex @ (^ [D:nat]: (plus_plus_complex @ (A @ D))) @ B @ C @ zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8320_sum__atLeastAtMost__code)). 185.47/93.66 thf(9942,plain,((! [A:(nat > complex),B:nat,C:nat]: ((groups2073611262835488442omplex @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo1517530859248394432omplex @ (^ [D:nat]: (plus_plus_complex @ (A @ D))) @ B @ C @ zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[661])). 185.47/93.66 thf(3192,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ A) = (ord_less_eq_rat @ B @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1630_add__le__same__cancel1)). 185.47/93.66 thf(18276,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ A) = (ord_less_eq_rat @ B @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3192])). 185.47/93.66 thf(7024,axiom,(((abs_abs_int @ zero_zero_int) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6327_abs__zero)). 185.47/93.66 thf(31634,plain,(((abs_abs_int @ zero_zero_int) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7024])). 185.47/93.66 thf(6706,axiom,((! [A:nat,B:nat]: (A = (plus_plus_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ (modulo_modulo_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2541_mod__div__decomp)). 185.47/93.66 thf(30347,plain,((! [A:nat,B:nat]: (A = (plus_plus_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ (modulo_modulo_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6706])). 185.47/93.66 thf(3093,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ B @ (times_times_rat @ C @ A)) => (ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2847_mult__imp__div__pos__le)). 185.47/93.66 thf(17967,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ B @ (times_times_rat @ C @ A)) => (ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3093])). 185.47/93.66 thf(6695,axiom,((! [A:num]: (((uminus_uminus_int @ (numeral_numeral_int @ A)) = (uminus_uminus_int @ one_one_int)) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5287_numeral__eq__neg__one__iff)). 185.47/93.66 thf(30311,plain,((! [A:num]: (((uminus_uminus_int @ (numeral_numeral_int @ A)) = (uminus_uminus_int @ one_one_int)) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6695])). 185.47/93.66 thf(6164,axiom,((! [A:real,B:real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6466_abs__minus__commute)). 185.47/93.66 thf(28476,plain,((! [A:real,B:real]: ((abs_abs_real @ (minus_minus_real @ A @ B)) = (abs_abs_real @ (minus_minus_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6164])). 185.47/93.66 thf(3944,axiom,((! [A:real,B:real,C:num]: ((ord_less_real @ (divide_divide_real @ A @ B) @ (uminus_uminus_real @ (numeral_numeral_real @ C))) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B) @ A)) & ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ C))) <= (~ (ord_less_real @ B @ zero_zero_real))))) & ((ord_less_real @ A @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B)) <= (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6218_divide__less__eq__numeral_I2_J)). 185.47/93.66 thf(20669,plain,((! [A:real,B:real,C:num]: ((ord_less_real @ (divide_divide_real @ A @ B) @ (uminus_uminus_real @ (numeral_numeral_real @ C))) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B) @ A)) & ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ C))) | (ord_less_real @ B @ zero_zero_real)))) & ((ord_less_real @ A @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B)) | ~ (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3944])). 185.47/93.66 thf(4306,axiom,(((bitM @ one) = one)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8961_semiring__norm_I26_J)). 185.47/93.66 thf(21761,plain,(((bitM @ one) = one)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4306])). 185.47/93.66 thf(7233,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4036_dual__order_Ostrict__trans)). 185.47/93.66 thf(32380,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7233])). 185.47/93.66 thf(487,axiom,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((finite_finite_nat @ A) => (((! [D:nat]: (((C @ D) = one_one_rat) <= (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups73079841787564623at_rat @ C @ A) = (groups73079841787564623at_rat @ C @ B))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8938_prod_Omono__neutral__right)). 185.47/93.66 thf(9372,plain,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((finite_finite_nat @ A) => (((! [D:nat]: (((C @ D) = one_one_rat) | ~ (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups73079841787564623at_rat @ (C) @ A) = (groups73079841787564623at_rat @ (C) @ B))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[487])). 185.47/93.66 thf(2286,axiom,(((csqrt @ imaginary_unit) = (divide1717551699836669952omplex @ (plus_plus_complex @ one_one_complex @ imaginary_unit) @ (real_V4546457046886955230omplex @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9151_csqrt__ii)). 185.47/93.66 thf(15317,plain,(((csqrt @ imaginary_unit) = (divide1717551699836669952omplex @ (plus_plus_complex @ one_one_complex @ imaginary_unit) @ (real_V4546457046886955230omplex @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2286])). 185.47/93.66 thf(6201,axiom,((res = (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ pr) @ maxy))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308__092_060open_062res_A_061_A2_A_094_A_Ideg_Adiv_A2_J_A_K_Apr_A_L_Amaxy_092_060close_062)). 185.47/93.66 thf(28608,plain,((res = (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ pr) @ maxy))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6201])). 185.47/93.66 thf(401,axiom,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((ord_less_eq_rat @ (groups73079841787564623at_rat @ B @ A) @ (groups73079841787564623at_rat @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ A) => ((ord_less_eq_rat @ zero_zero_rat @ (B @ D)) & (ord_less_eq_rat @ (B @ D) @ (C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8751_prod__mono)). 185.47/93.66 thf(9068,plain,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((ord_less_eq_rat @ (groups73079841787564623at_rat @ (B) @ A) @ (groups73079841787564623at_rat @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ A) => ((ord_less_eq_rat @ zero_zero_rat @ (B @ D)) & (ord_less_eq_rat @ (B @ D) @ (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])). 185.47/93.66 thf(4279,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_diff__right__mono)). 185.47/93.66 thf(21683,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4279])). 185.47/93.66 thf(4326,axiom,((! [A:nat,B:int]: (ord_less_int @ (bit_ri631733984087533419it_int @ A @ B) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4948_signed__take__bit__int__less__exp)). 185.47/93.66 thf(21862,plain,((! [A:nat,B:int]: (ord_less_int @ (bit_ri631733984087533419it_int @ A @ B) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4326])). 185.47/93.66 thf(7045,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F))))) <= (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ E @ F)))) <= (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3228_pinf_I1_J)). 185.47/93.66 thf(31724,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F)))) | ~ (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ E @ F))) | ~ (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7045])). 185.47/93.66 thf(723,axiom,((! [A:real,B:nat]: ((gbinomial_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (gbinomial_real @ (minus_minus_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8580_gbinomial__minus)). 185.47/93.66 thf(10143,plain,((! [A:real,B:nat]: ((gbinomial_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (gbinomial_real @ (minus_minus_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[723])). 185.47/93.66 thf(2626,axiom,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5931_neg__numeral__le__neg__one)). 185.47/93.66 thf(16445,plain,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2626])). 185.47/93.66 thf(6720,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1095_less__add__Suc2)). 185.47/93.66 thf(30415,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6720])). 185.47/93.66 thf(4043,axiom,((! [A:num,B:nat,C:int]: ((ord_less_eq_rat @ (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7166_neg__numeral__power__le__of__int__cancel__iff)). 185.47/93.66 thf(20964,plain,((! [A:num,B:nat,C:int]: ((ord_less_eq_rat @ (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_eq_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4043])). 185.47/93.66 thf(3092,axiom,((! [A:rat,B:(nat > rat),C:nat,D:nat]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F)))) => (ord_less_eq_rat @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_rat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3911_order__subst1)). 185.47/93.66 thf(17963,plain,((! [A:rat,B:(nat > rat),C:nat,D:nat]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F)))) => (ord_less_eq_rat @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_rat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3092])). 185.47/93.66 thf(2102,axiom,((ord_less_rat = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4201_order_Ostrict__iff__order)). 185.47/93.66 thf(14734,plain,(((ord_less_rat) = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2102])). 185.47/93.66 thf(2589,axiom,((! [A:int,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((divide_divide_int @ (plus_plus_int @ one_one_int @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))) <= (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4425_even__succ__div__exp)). 185.47/93.66 thf(16328,plain,((! [A:int,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((divide_divide_int @ (plus_plus_int @ one_one_int @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2589])). 185.47/93.66 thf(5772,axiom,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_770_comm__monoid__mult__class_Omult__1)). 185.47/93.66 thf(26935,plain,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5772])). 185.47/93.66 thf(3568,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri681578069525770553at_rat @ (minus_minus_nat @ B @ A)) = (minus_minus_rat @ (semiri681578069525770553at_rat @ B) @ (semiri681578069525770553at_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7265_of__nat__diff)). 185.47/93.66 thf(19459,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri681578069525770553at_rat @ (minus_minus_nat @ B @ A)) = (minus_minus_rat @ (semiri681578069525770553at_rat @ B) @ (semiri681578069525770553at_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3568])). 185.47/93.66 thf(1848,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ B) => ((ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((bit_ri631733984087533419it_int @ A @ B) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6273_signed__take__bit__int__eq__self)). 185.47/93.66 thf(13932,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ B) => ((ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((bit_ri631733984087533419it_int @ A @ B) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848])). 185.47/93.66 thf(5039,axiom,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (plus_plus_nat @ B @ C)) = (times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_power__add)). 185.47/93.66 thf(24298,plain,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (plus_plus_nat @ B @ C)) = (times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5039])). 185.47/93.66 thf(1355,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ A)) = (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5138_neg__0__le__iff__le)). 185.47/93.66 thf(12250,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ A)) = (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355])). 185.47/93.66 thf(122,axiom,((! [A:complex]: ((im @ (times_times_complex @ imaginary_unit @ A)) = (re @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9663_Im__i__times)). 185.47/93.66 thf(8127,plain,((! [A:complex]: ((im @ (times_times_complex @ imaginary_unit @ A)) = (re @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 185.47/93.66 thf(3382,axiom,((! [A:int]: ((bit_ri631733984087533419it_int @ zero_zero_nat @ A) = (uminus_uminus_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5476_signed__take__bit__0)). 185.47/93.66 thf(18870,plain,((! [A:int]: ((bit_ri631733984087533419it_int @ zero_zero_nat @ A) = (uminus_uminus_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3382])). 185.47/93.66 thf(2791,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) <= (ord_less_rat @ B @ zero_zero_rat)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2432_divide__pos__neg)). 185.47/93.66 thf(16996,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) | ~ (ord_less_rat @ B @ zero_zero_rat) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2791])). 185.47/93.66 thf(784,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat)]: (((ord_less_eq_set_nat @ B @ A) => ((dvd_dvd_nat @ (groups708209901874060359at_nat @ C @ B) @ (groups708209901874060359at_nat @ D @ A)) <= (! [E:nat]: ((dvd_dvd_nat @ (C @ E) @ (D @ E)) <= (member_nat @ E @ B))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8832_prod__dvd__prod__subset2)). 185.47/93.66 thf(10406,plain,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat)]: (((ord_less_eq_set_nat @ B @ A) => ((dvd_dvd_nat @ (groups708209901874060359at_nat @ (C) @ B) @ (groups708209901874060359at_nat @ (D) @ A)) | ~ (! [E:nat]: ((dvd_dvd_nat @ (C @ E) @ (D @ E)) | ~ (member_nat @ E @ B))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[784])). 185.47/93.66 thf(4844,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_eq_int @ C @ B)) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2599_mult__le__cancel__left__neg)). 185.47/93.66 thf(23559,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_eq_int @ C @ B)) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4844])). 185.47/93.66 thf(6380,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_Nat_Ole__diff__conv2)). 185.47/93.66 thf(29213,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6380])). 185.47/93.66 thf(5582,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))) <= (ord_less_eq_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2173_power__strict__mono)). 185.47/93.66 thf(26307,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5582])). 185.47/93.66 thf(4643,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ A @ C) <= (ord_less_real @ B @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4023_order_Ostrict__trans)). 185.47/93.66 thf(22873,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ C) | ~ (ord_less_real @ B @ C) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4643])). 185.47/93.66 thf(6252,axiom,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: ((? [E:num]: ! [F:num]: (((A @ F) = (B @ F)) <= (ord_less_num @ F @ E))) => ((? [E:num]: ! [F:num]: (((C @ F) = (D @ F)) <= (ord_less_num @ F @ E))) => (? [E:num]: ! [F:num]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) <= (ord_less_num @ F @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3262_minf_I2_J)). 185.47/93.66 thf(28763,plain,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: ((? [E:num]: ! [F:num]: (((A @ F) = (B @ F)) | ~ (ord_less_num @ F @ E))) => ((? [E:num]: ! [F:num]: (((C @ F) = (D @ F)) | ~ (ord_less_num @ F @ E))) => (? [E:num]: ! [F:num]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) | ~ (ord_less_num @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6252])). 185.47/93.66 thf(4081,axiom,((! [A:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5728_ab__group__add__class_Oab__left__minus)). 185.47/93.66 thf(21074,plain,((! [A:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4081])). 185.47/93.66 thf(5309,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2107_old_Onat_Oexhaust)). 185.47/93.66 thf(25271,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5309])). 185.47/93.66 thf(851,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: (((ord_less_eq_set_nat @ B @ A) => ((groups3539618377306564664at_int @ C @ (minus_minus_set_nat @ A @ B)) = (minus_minus_int @ (groups3539618377306564664at_int @ C @ A) @ (groups3539618377306564664at_int @ C @ B)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6134_sum__diff)). 185.47/93.66 thf(10651,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: (((ord_less_eq_set_nat @ B @ A) => ((groups3539618377306564664at_int @ (C) @ (minus_minus_set_nat @ A @ B)) = (minus_minus_int @ (groups3539618377306564664at_int @ (C) @ A) @ (groups3539618377306564664at_int @ (C) @ B)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[851])). 185.47/93.66 thf(4366,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_real @ A @ (plus_plus_real @ B @ C)) & (ord_less_real @ (minus_minus_real @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6593_abs__diff__less__iff)). 185.47/93.66 thf(21986,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_real @ A @ (plus_plus_real @ B @ C)) & (ord_less_real @ (minus_minus_real @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4366])). 185.47/93.66 thf(3533,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ A @ (plus_plus_real @ B @ C)) = (dvd_dvd_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4642_dvd__add__right__iff)). 185.47/93.66 thf(19354,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ A @ (plus_plus_real @ B @ C)) = (dvd_dvd_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3533])). 185.47/93.66 thf(541,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => (((sin_real @ (arccos @ A)) != zero_zero_real) <= (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8374_sin__arccos__nonzero)). 185.47/93.66 thf(9534,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => (~ ((sin_real @ (arccos @ A)) = zero_zero_real) | ~ (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[541])). 185.47/93.66 thf(3940,axiom,((! [A:nat]: ~ (ord_less_rat @ (semiri681578069525770553at_rat @ A) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7214_of__nat__less__0__iff)). 185.47/93.66 thf(20656,plain,((! [A:nat]: ~ (ord_less_rat @ (semiri681578069525770553at_rat @ A) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3940])). 185.47/93.66 thf(318,axiom,((bit_se4203085406695923979it_int = (^ [A:nat,B:int]: (bit_se725231765392027082nd_int @ B @ (bit_ri7919022796975470100ot_int @ (bit_se545348938243370406it_int @ A @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9506_unset__bit__int__def)). 185.47/93.66 thf(8796,plain,(((bit_se4203085406695923979it_int) = (^ [A:nat,B:int]: (bit_se725231765392027082nd_int @ B @ (bit_ri7919022796975470100ot_int @ (bit_se545348938243370406it_int @ A @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 185.47/93.66 thf(3310,axiom,((! [A:int,B:rat]: ((times_times_rat @ (ring_1_of_int_rat @ A) @ B) = (times_times_rat @ B @ (ring_1_of_int_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7180_mult__of__int__commute)). 185.47/93.66 thf(18640,plain,((! [A:int,B:rat]: ((times_times_rat @ (ring_1_of_int_rat @ A) @ B) = (times_times_rat @ B @ (ring_1_of_int_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3310])). 185.47/93.66 thf(7065,axiom,((! [A:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_rat) = ((abs_abs_rat @ A) = one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6687_abs__square__eq__1)). 185.47/93.66 thf(31791,plain,((! [A:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_rat) = ((abs_abs_rat @ A) = one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7065])). 185.47/93.66 thf(1335,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_real @ (semiri5074537144036343181t_real @ A) @ B) = (semiri5074537144036343181t_real @ C)) = ((power_power_nat @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6954_of__nat__eq__of__nat__power__cancel__iff)). 185.47/93.66 thf(12183,plain,((! [A:nat,B:nat,C:nat]: (((power_power_real @ (semiri5074537144036343181t_real @ A) @ B) = (semiri5074537144036343181t_real @ C)) = ((power_power_nat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335])). 185.47/93.66 thf(4735,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ A) = (((ord_less_eq_int @ one_one_int @ B) <= (ord_less_int @ A @ zero_zero_int)) & ((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ B @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2811_mult__le__cancel__left2)). 185.47/93.66 thf(23182,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ A) = (((ord_less_eq_int @ one_one_int @ B) | ~ (ord_less_int @ A @ zero_zero_int)) & ((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ B @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4735])). 185.47/93.66 thf(3491,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_eq_rat @ A @ C) <= (ord_less_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3309_pinf_I8_J)). 185.47/93.66 thf(19222,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_eq_rat @ A @ C) | ~ (ord_less_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3491])). 185.47/93.66 thf(5627,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_758_diff__add__inverse)). 185.47/93.66 thf(26460,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5627])). 185.47/93.66 thf(1340,axiom,((! [A:int,B:int]: (ord_less_eq_int @ (minus_minus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) @ (abs_abs_int @ (minus_minus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6505_abs__triangle__ineq2)). 185.47/93.66 thf(12201,plain,((! [A:int,B:int]: (ord_less_eq_int @ (minus_minus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) @ (abs_abs_int @ (minus_minus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340])). 185.47/93.66 thf(7540,axiom,((! [A:int]: ((abs_abs_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6425_abs__power2)). 185.47/93.66 thf(33407,plain,((! [A:int]: ((abs_abs_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7540])). 185.47/93.66 thf(2763,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_3869_order__antisym)). 185.47/93.66 thf(16913,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)],[2763])). 185.47/93.66 thf(5174,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3811_order__refl)). 185.47/93.66 thf(24795,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5174])). 185.47/93.66 thf(5319,axiom,((! [A:nat]: ((power_power_int @ (uminus_uminus_int @ one_one_int) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5461_power__minus1__even)). 185.47/93.66 thf(25303,plain,((! [A:nat]: ((power_power_int @ (uminus_uminus_int @ one_one_int) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5319])). 185.47/93.66 thf(3832,axiom,((! [A:rat]: (ord_less_eq_rat @ (uminus_uminus_rat @ A) @ (abs_abs_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6522_abs__ge__minus__self)). 185.47/93.66 thf(20303,plain,((! [A:rat]: (ord_less_eq_rat @ (uminus_uminus_rat @ A) @ (abs_abs_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3832])). 185.47/93.66 thf(3564,axiom,(((abs_abs_Code_integer @ one_one_Code_integer) = one_one_Code_integer)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6340_abs__1)). 185.47/93.66 thf(19447,plain,(((abs_abs_Code_integer @ one_one_Code_integer) = one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3564])). 185.47/93.66 thf(5338,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (~ (ord_less_eq_num @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3320_minf_I8_J)). 185.47/93.66 thf(25371,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (~ (ord_less_eq_num @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5338])). 185.47/93.66 thf(2221,axiom,((! [A:complex,B:complex,C:real,D:complex,E:real]: (((ord_less_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ B @ D)) @ E) => (ord_less_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ D)) @ (plus_plus_real @ C @ E))) <= (ord_less_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7499_norm__diff__triangle__less)). 185.47/93.66 thf(15121,plain,((! [A:complex,B:complex,C:real,D:complex,E:real]: (((ord_less_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ B @ D)) @ E) => (ord_less_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ D)) @ (plus_plus_real @ C @ E))) | ~ (ord_less_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2221])). 185.47/93.66 thf(4001,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ A @ B)) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2294_add__nonneg__nonneg)). 185.47/93.66 thf(20840,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ A @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4001])). 185.47/93.66 thf(5268,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A)))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9415_or__minus__numerals_I2_J)). 185.47/93.66 thf(25139,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A)))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5268])). 185.47/93.66 thf(1701,axiom,((! [A:num,B:nat]: (((numeral_numeral_nat @ A) = (suc @ B)) = ((pred_numeral @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6781_eq__numeral__Suc)). 185.47/93.66 thf(13430,plain,((! [A:num,B:nat]: (((numeral_numeral_nat @ A) = (suc @ B)) = ((pred_numeral @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701])). 185.47/93.66 thf(7073,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_mult_Oassoc)). 185.47/93.66 thf(31814,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7073])). 185.47/93.66 thf(4074,axiom,((! [A:int]: (((plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) @ one_one_int) = A) <= (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4565_odd__two__times__div__two__succ)). 185.47/93.66 thf(21055,plain,((! [A:int]: (((plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) @ one_one_int) = A) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4074])). 185.47/93.66 thf(269,axiom,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7798_sin__pi__half)). 185.47/93.66 thf(8614,plain,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[269])). 185.47/93.66 thf(7190,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4136_order__less__imp__not__eq)). 185.47/93.66 thf(32218,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7190])). 185.47/93.66 thf(2921,axiom,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ A @ (suc @ B)) = (times_times_rat @ A @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ A @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8490_pochhammer__rec)). 185.47/93.66 thf(17419,plain,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ A @ (suc @ B)) = (times_times_rat @ A @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ A @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2921])). 185.47/93.66 thf(3925,axiom,((! [A:rat,B:rat,C:(rat > nat),D:nat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_rat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4334_order__le__less__subst2)). 185.47/93.66 thf(20606,plain,((! [A:rat,B:rat,C:(rat > nat),D:nat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_rat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3925])). 185.47/93.66 thf(1617,axiom,((! [A:nat,B:nat,C:(nat > nat)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & (((groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_nat) <= (ord_less_nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6432_sum_Ocl__ivl__Suc)). 185.47/93.66 thf(13103,plain,((! [A:nat,B:nat,C:(nat > nat)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & (((groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_nat) | ~ (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617])). 185.47/93.66 thf(6468,axiom,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1467_valid__0__not)). 185.47/93.66 thf(29554,plain,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6468])). 185.47/93.66 thf(6559,axiom,((! [A:real,B:real,C:real]: ((((minus_minus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (minus_minus_real @ B @ (times_times_real @ C @ A)) @ A)) <= (A != zero_zero_real)) & (((minus_minus_real @ (divide_divide_real @ B @ A) @ C) = (uminus_uminus_real @ C)) <= (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6171_add__divide__eq__if__simps_I5_J)). 185.47/93.66 thf(29866,plain,((! [A:real,B:real,C:real]: ((((minus_minus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (minus_minus_real @ B @ (times_times_real @ C @ A)) @ A)) | (A = zero_zero_real)) & (((minus_minus_real @ (divide_divide_real @ B @ A) @ C) = (uminus_uminus_real @ C)) | ~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6559])). 185.47/93.66 thf(6683,axiom,((! [A:rat]: (((uminus_uminus_rat @ A) = zero_zero_rat) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5048_neg__equal__0__iff__equal)). 185.47/93.66 thf(30275,plain,((! [A:rat]: (((uminus_uminus_rat @ A) = zero_zero_rat) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6683])). 185.47/93.66 thf(5435,axiom,((! [A:vEBT_VEBT,B:nat]: ((~ (vEBT_vebt_member @ A @ B)) => ((((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E) @ B))))) => (((~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G)) => ((accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G) @ B)) => (((B != D) => (~ (ord_less_nat @ B @ C) & ((~ (ord_less_nat @ B @ C)) => (((~ (ord_less_nat @ D @ B)) => (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)))) & ~ (ord_less_nat @ D @ B))))) <= (B != C)))))) <= (! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ (suc @ zero_zero_nat) @ D @ E) @ B))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ (suc @ zero_zero_nat) @ D @ E))))) <= (! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ zero_zero_nat @ D @ E) @ B))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ zero_zero_nat @ D @ E)))))) <= (! [C:$o,D:$o]: (((accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => ((((B = one_one_nat) & ((B = one_one_nat) => (D))) <= (B != zero_zero_nat)) & ((C) <= (B = zero_zero_nat)))) <= (A = (vEBT_Leaf @ C @ D))))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3117_vebt__member_Opelims_I3_J)). 185.47/93.66 thf(25701,plain,((! [A:vEBT_VEBT,B:nat]: ((~ (vEBT_vebt_member @ A @ B)) => (((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E) @ B))))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G)) => ((accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G) @ B)) => (((~ (B = D)) => (~ (ord_less_nat @ B @ C) & ((~ (ord_less_nat @ B @ C)) => (((~ (ord_less_nat @ D @ B)) => (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)))) & ~ (ord_less_nat @ D @ B))))) | (B = C))))) | ~ (! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ (suc @ zero_zero_nat) @ D @ E) @ B)) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ (suc @ zero_zero_nat) @ D @ E)))) | ~ (! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ zero_zero_nat @ D @ E) @ B)) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ zero_zero_nat @ D @ E)))))) | ~ (! [C:$o,D:$o]: (((accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => ((((B = one_one_nat) & ((B = one_one_nat) => (D))) | (B = zero_zero_nat)) & ((C) | ~ (B = zero_zero_nat)))) | ~ (A = (vEBT_Leaf @ C @ D)))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5435])). 185.47/93.66 thf(1012,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = one_one_real) = ((B != zero_zero_real) & (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1727_divide__eq__eq__1)). 185.47/93.66 thf(11197,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = one_one_real) = (~ (B = zero_zero_real) & (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012])). 185.47/93.66 thf(6935,axiom,((! [A:nat]: ((ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = ((A = zero_zero_nat) | (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2955_less__2__cases__iff)). 185.47/93.66 thf(31253,plain,((! [A:nat]: ((ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = ((A = zero_zero_nat) | (A = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6935])). 185.47/93.66 thf(4549,axiom,((! [A:real]: (((abs_abs_real @ A) = A) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6479_abs__of__pos)). 185.47/93.66 thf(22572,plain,((! [A:real]: (((abs_abs_real @ A) = A) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4549])). 185.47/93.66 thf(999,axiom,((! [A:nat,B:nat,C:vEBT_VEBT]: ((ord_less_nat @ A @ B) => ((nth_VEBT_VEBT @ (replicate_VEBT_VEBT @ B @ C) @ A) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5265_nth__replicate)). 185.47/93.66 thf(11153,plain,((! [A:nat,B:nat,C:vEBT_VEBT]: ((ord_less_nat @ A @ B) => ((nth_VEBT_VEBT @ (replicate_VEBT_VEBT @ B @ C) @ A) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[999])). 185.47/93.66 thf(2170,axiom,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4576_dvd__triv__right)). 185.47/93.66 thf(14961,plain,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2170])). 185.47/93.66 thf(4270,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (plus_plus_rat @ B @ C)) = (plus_plus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1129_ring__class_Oring__distribs_I1_J)). 185.47/93.66 thf(21659,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (plus_plus_rat @ B @ C)) = (plus_plus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4270])). 185.47/93.66 thf(930,axiom,((! [A:complex,B:complex,C:nat]: ((A != zero_zero_complex) => ((minus_minus_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ (power_power_complex @ (plus_plus_complex @ B @ A) @ C) @ (power_power_complex @ B @ C)) @ A) @ (times_times_complex @ (semiri8010041392384452111omplex @ C) @ (power_power_complex @ B @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))) = (times_times_complex @ A @ (groups2073611262835488442omplex @ (^ [D:nat]: (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (power_power_complex @ (plus_plus_complex @ B @ A) @ E) @ (power_power_complex @ B @ (minus_minus_nat @ (minus_minus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ E)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat)) @ D)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7532_lemma__termdiff2)). 185.47/93.66 thf(10929,plain,((! [A:complex,B:complex,C:nat]: ((~ (A = zero_zero_complex)) => ((minus_minus_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ (power_power_complex @ (plus_plus_complex @ B @ A) @ C) @ (power_power_complex @ B @ C)) @ A) @ (times_times_complex @ (semiri8010041392384452111omplex @ C) @ (power_power_complex @ B @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))) = (times_times_complex @ A @ (groups2073611262835488442omplex @ (^ [D:nat]: (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (power_power_complex @ (plus_plus_complex @ B @ A) @ E) @ (power_power_complex @ B @ (minus_minus_nat @ (minus_minus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ E)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat)) @ D)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[930])). 185.47/93.66 thf(14,axiom,((! [A:real,B:nat]: (((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)) = (divide_divide_real @ (minus_minus_real @ (power_power_real @ A @ B) @ one_one_real) @ (minus_minus_real @ A @ one_one_real))) <= (A != one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7602_geometric__sum)). 185.47/93.66 thf(7770,plain,((! [A:real,B:nat]: (((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)) = (divide_divide_real @ (minus_minus_real @ (power_power_real @ A @ B) @ one_one_real) @ (minus_minus_real @ A @ one_one_real))) | (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 185.47/93.66 thf(1736,axiom,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: (((ord_less_rat @ C @ B) => ((ord_less_eq_rat @ zero_zero_rat @ D) => ((ord_less_eq_rat @ zero_zero_rat @ E) => (((plus_plus_rat @ D @ E) = one_one_rat) => (ord_less_rat @ (plus_plus_rat @ (times_times_rat @ D @ A) @ (times_times_rat @ E @ C)) @ B))))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2921_convex__bound__lt)). 185.47/93.66 thf(13554,plain,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: (((ord_less_rat @ C @ B) => ((ord_less_eq_rat @ zero_zero_rat @ D) => ((ord_less_eq_rat @ zero_zero_rat @ E) => (((plus_plus_rat @ D @ E) = one_one_rat) => (ord_less_rat @ (plus_plus_rat @ (times_times_rat @ D @ A) @ (times_times_rat @ E @ C)) @ B))))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736])). 185.47/93.66 thf(3105,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_linordered__field__no__ub)). 185.47/93.66 thf(18012,plain,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3105])). 185.47/93.66 thf(4963,axiom,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4434_nat__dvd__1__iff__1)). 185.47/93.66 thf(23980,plain,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4963])). 185.47/93.66 thf(161,axiom,((! [A:set_nat,B:(nat > rat)]: ((ord_less_eq_rat @ (groups2906978787729119204at_rat @ B @ A) @ zero_zero_rat) <= (! [C:nat]: ((ord_less_eq_rat @ (B @ C) @ zero_zero_rat) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5633_sum__nonpos)). 185.47/93.66 thf(8247,plain,((! [A:set_nat,B:(nat > rat)]: ((ord_less_eq_rat @ (groups2906978787729119204at_rat @ (B) @ A) @ zero_zero_rat) | ~ (! [C:nat]: ((ord_less_eq_rat @ (B @ C) @ zero_zero_rat) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 185.47/93.66 thf(2824,axiom,((! [A:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ zero_zero_rat) = (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5141_neg__le__0__iff__le)). 185.47/93.66 thf(17106,plain,((! [A:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ zero_zero_rat) = (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2824])). 185.47/93.66 thf(766,axiom,(((tan_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit1 @ one))))) = (divide_divide_real @ one_one_real @ (sqrt @ (numeral_numeral_real @ (bit1 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8258_tan__30)). 185.47/93.66 thf(10338,plain,(((tan_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit1 @ one))))) = (divide_divide_real @ one_one_real @ (sqrt @ (numeral_numeral_real @ (bit1 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[766])). 185.47/93.66 thf(2946,axiom,((! [A:nat,B:num,C:nat]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7122_of__nat__less__numeral__power__cancel__iff)). 185.47/93.66 thf(17499,plain,((! [A:nat,B:num,C:nat]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2946])). 185.47/93.66 thf(6254,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (modulo_modulo_nat @ A @ B)) = (times_times_nat @ (divide_divide_nat @ A @ B) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2559_minus__mod__eq__div__mult)). 185.47/93.66 thf(28776,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (modulo_modulo_nat @ A @ B)) = (times_times_nat @ (divide_divide_nat @ A @ B) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6254])). 185.47/93.66 thf(1072,axiom,((! [A:int,B:int]: ((((divide_divide_int @ A @ (times_times_int @ A @ B)) = (divide_divide_int @ one_one_int @ B)) <= (dvd_dvd_int @ B @ one_one_int)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4896_is__unit__div__mult__cancel__left)). 185.47/93.66 thf(11368,plain,((! [A:int,B:int]: (((divide_divide_int @ A @ (times_times_int @ A @ B)) = (divide_divide_int @ one_one_int @ B)) | ~ (dvd_dvd_int @ B @ one_one_int) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072])). 185.47/93.66 thf(4705,axiom,((! [A:rat,B:rat,C:(rat > rat),D:rat]: ((ord_less_rat @ A @ B) => (((ord_less_rat @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_rat @ (C @ E) @ (C @ F)) <= (ord_less_rat @ E @ F)))) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4089_ord__less__eq__subst)). 185.47/93.66 thf(23086,plain,((! [A:rat,B:rat,C:(rat > rat),D:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_rat @ E @ F))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4705])). 185.47/93.66 thf(1521,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2654_divide__nonneg__neg)). 185.47/93.66 thf(12783,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521])). 185.47/93.66 thf(5346,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4191_not__le__imp__less)). 185.47/93.66 thf(25393,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5346])). 185.47/93.66 thf(2906,axiom,((! [A:real,B:(nat > real),C:real]: ((sums_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ C) => ((sums_real @ B @ (divide_divide_real @ C @ A)) <= (A != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8184_sums__mult__D)). 185.47/93.66 thf(17370,plain,((! [A:real,B:(nat > real),C:real]: ((sums_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ C) => ((sums_real @ (B) @ (divide_divide_real @ C @ A)) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2906])). 185.47/93.66 thf(5297,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_980_le__add__diff__inverse2)). 185.47/93.66 thf(25239,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5297])). 185.47/93.66 thf(5698,axiom,((! [A:rat,B:nat]: (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2991_zero__le__even__power_H)). 185.47/93.66 thf(26691,plain,((! [A:rat,B:nat]: (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5698])). 185.47/93.66 thf(6446,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) = (B = A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3965_order__antisym__conv)). 185.47/93.66 thf(29471,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) = (B = A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6446])). 185.47/93.66 thf(5183,axiom,((! [A:num]: ((size_size_num @ (bit1 @ A)) = (plus_plus_nat @ (size_size_num @ A) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6690_num_Osize_I6_J)). 185.47/93.66 thf(24822,plain,((! [A:num]: ((size_size_num @ (bit1 @ A)) = (plus_plus_nat @ (size_size_num @ A) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5183])). 185.47/93.66 thf(668,axiom,((invers8013647133539491842omplex = (^ [A:complex]: (complex2 @ (divide_divide_real @ (re @ A) @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (divide_divide_real @ (uminus_uminus_real @ (im @ A)) @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9705_inverse__complex_Ocode)). 185.47/93.66 thf(9964,plain,(((invers8013647133539491842omplex) = (^ [A:complex]: (complex2 @ (divide_divide_real @ (re @ A) @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (divide_divide_real @ (uminus_uminus_real @ (im @ A)) @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[668])). 185.47/93.66 thf(1933,axiom,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5952_not__numeral__less__neg__one)). 185.47/93.66 thf(14180,plain,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1933])). 185.47/93.66 thf(1785,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int) = (((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ A @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ B @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2227_mult__le__0__iff)). 185.47/93.66 thf(13714,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int) = (((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ A @ zero_zero_int)) | ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ B @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785])). 185.47/93.66 thf(2660,axiom,((! [A:real]: ((plus_plus_real @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7805_sin__cos__squared__add)). 185.47/93.66 thf(16548,plain,((! [A:real]: ((plus_plus_real @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2660])). 185.47/93.66 thf(1555,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ B @ A) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_eq_real @ (divide_divide_real @ B @ D) @ (divide_divide_real @ A @ C)) <= (ord_less_eq_real @ C @ D)))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2645_frac__le)). 185.47/93.66 thf(12889,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ B @ A) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_eq_real @ (divide_divide_real @ B @ D) @ (divide_divide_real @ A @ C)) | ~ (ord_less_eq_real @ C @ D)))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1555])). 185.47/93.66 thf(1925,axiom,((! [A:num,B:num]: ((plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ B)) = (numera6690914467698888265omplex @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_numeral__plus__numeral)). 185.47/93.66 thf(14157,plain,((! [A:num,B:num]: ((plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ B)) = (numera6690914467698888265omplex @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1925])). 185.47/93.66 thf(6916,axiom,((! [A:nat,B:nat]: ((B != zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2033_gr__implies__not__zero)). 185.47/93.66 thf(31182,plain,((! [A:nat,B:nat]: (~ (B = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6916])). 185.47/93.66 thf(5611,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ (times_times_nat @ B @ A) @ A) = (B = one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4924_dvd__mult__cancel2)). 185.47/93.66 thf(26402,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ (times_times_nat @ B @ A) @ A) = (B = one_one_nat)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5611])). 185.47/93.66 thf(3044,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3182_int__distrib_I1_J)). 185.47/93.66 thf(17812,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3044])). 185.47/93.66 thf(1875,axiom,((! [A:num,B:num]: ((bit_or_not_num_neg @ (bit1 @ A) @ (bit1 @ B)) = (bitM @ (bit_or_not_num_neg @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9469_or__not__num__neg_Osimps_I9_J)). 185.47/93.66 thf(14008,plain,((! [A:num,B:num]: ((bit_or_not_num_neg @ (bit1 @ A) @ (bit1 @ B)) = (bitM @ (bit_or_not_num_neg @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1875])). 185.47/93.66 thf(5950,axiom,((! [A:num,B:num]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5343_mult__neg__numeral__simps_I2_J)). 185.47/93.66 thf(27691,plain,((! [A:num,B:num]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5950])). 185.47/93.66 thf(5226,axiom,((! [A:nat,B:real]: ((((power_power_real @ (uminus_uminus_real @ B) @ A) = (uminus_uminus_real @ (power_power_real @ B @ A))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_real @ (uminus_uminus_real @ B) @ A) = (power_power_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6184_uminus__power__if)). 185.47/93.66 thf(24953,plain,((! [A:nat,B:real]: ((((power_power_real @ (uminus_uminus_real @ B) @ A) = (uminus_uminus_real @ (power_power_real @ B @ A))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_real @ (uminus_uminus_real @ B) @ A) = (power_power_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5226])). 185.47/93.66 thf(4212,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3160_plus__int__code_I1_J)). 185.47/93.66 thf(21485,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4212])). 185.47/93.66 thf(1118,axiom,((! [A:int]: ((modulo_modulo_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1587_bits__mod__0)). 185.47/93.66 thf(11524,plain,((! [A:int]: ((modulo_modulo_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118])). 185.47/93.66 thf(597,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ pi) => (((ord_less_eq_real @ B @ pi) => ((ord_less_real @ (cos_real @ A) @ (cos_real @ B)) = (ord_less_real @ B @ A))) <= (ord_less_eq_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7865_cos__mono__less__eq)). 185.47/93.66 thf(9716,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ pi) => (((ord_less_eq_real @ B @ pi) => ((ord_less_real @ (cos_real @ A) @ (cos_real @ B)) = (ord_less_real @ B @ A))) | ~ (ord_less_eq_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[597])). 185.47/93.66 thf(4367,axiom,((! [A:real,B:real]: ((ord_less_real @ (abs_abs_real @ A) @ B) = ((ord_less_real @ (uminus_uminus_real @ A) @ B) & (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6524_abs__less__iff)). 185.47/93.66 thf(21989,plain,((! [A:real,B:real]: ((ord_less_real @ (abs_abs_real @ A) @ B) = ((ord_less_real @ (uminus_uminus_real @ A) @ B) & (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4367])). 185.47/93.66 thf(3221,axiom,((! [A:complex]: ((sums_complex @ (power_power_complex @ A) @ (divide1717551699836669952omplex @ one_one_complex @ (minus_minus_complex @ one_one_complex @ A))) <= (ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8237_geometric__sums)). 185.47/93.66 thf(18371,plain,((! [A:complex]: ((sums_complex @ (power_power_complex @ A) @ (divide1717551699836669952omplex @ one_one_complex @ (minus_minus_complex @ one_one_complex @ A))) | ~ (ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3221])). 185.47/93.66 thf(3483,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C)) <= (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_diff__mono)). 185.47/93.66 thf(19198,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C)) | ~ (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3483])). 185.47/93.66 thf(5823,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ A) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9397_Suc__0__and__eq)). 185.47/93.66 thf(27268,plain,((! [A:nat]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ A) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5823])). 185.47/93.66 thf(2528,axiom,((! [A:real,B:real]: ((? [C:nat]: (ord_less_real @ B @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7373_ex__less__of__nat__mult)). 185.47/93.66 thf(16115,plain,((! [A:real,B:real]: (? [C:nat]: (ord_less_real @ B @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2528])). 185.47/93.66 thf(7523,axiom,((! [A:num,B:num]: (((~ (ord_less_num @ B @ A)) = (B = A)) <= (~ (ord_less_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3999_antisym__conv3)). 185.47/93.66 thf(33356,plain,((! [A:num,B:num]: (((~ (ord_less_num @ B @ A)) = (B = A)) | (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7523])). 185.47/93.66 thf(5046,axiom,((! [A:complex]: ((minus_minus_complex @ zero_zero_complex @ A) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5179_diff__0)). 185.47/93.66 thf(24320,plain,((! [A:complex]: ((minus_minus_complex @ zero_zero_complex @ A) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5046])). 185.47/93.66 thf(2239,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ A @ (minus_minus_real @ B @ C)) <= (dvd_dvd_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4659_dvd__diff)). 185.47/93.66 thf(15183,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ A @ (minus_minus_real @ B @ C)) | ~ (dvd_dvd_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2239])). 185.47/93.66 thf(853,axiom,((divide1717551699836669952omplex = (^ [A:complex,B:complex]: (complex2 @ (divide_divide_real @ (plus_plus_real @ (times_times_real @ (re @ A) @ (re @ B)) @ (times_times_real @ (im @ A) @ (im @ B))) @ (plus_plus_real @ (power_power_real @ (re @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ B) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (divide_divide_real @ (minus_minus_real @ (times_times_real @ (im @ A) @ (re @ B)) @ (times_times_real @ (re @ A) @ (im @ B))) @ (plus_plus_real @ (power_power_real @ (re @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9706_Complex__divide)). 185.47/93.66 thf(10656,plain,(((divide1717551699836669952omplex) = (^ [A:complex,B:complex]: (complex2 @ (divide_divide_real @ (plus_plus_real @ (times_times_real @ (re @ A) @ (re @ B)) @ (times_times_real @ (im @ A) @ (im @ B))) @ (plus_plus_real @ (power_power_real @ (re @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ B) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (divide_divide_real @ (minus_minus_real @ (times_times_real @ (im @ A) @ (re @ B)) @ (times_times_real @ (re @ A) @ (im @ B))) @ (plus_plus_real @ (power_power_real @ (re @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[853])). 185.47/93.66 thf(214,axiom,((! [A:int,B:nat,C:int]: ((ord_less_int @ (power_power_int @ (ring_1_of_int_int @ A) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7111_of__int__less__of__int__power__cancel__iff)). 185.47/93.66 thf(8422,plain,((! [A:int,B:nat,C:int]: ((ord_less_int @ (power_power_int @ (ring_1_of_int_int @ A) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_int @ (power_power_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 185.47/93.66 thf(6268,axiom,((! [A:num,B:num]: ((minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (plus_plus_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5328_diff__numeral__simps_I3_J)). 185.47/93.66 thf(28820,plain,((! [A:num,B:num]: ((minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (uminus_uminus_int @ (numeral_numeral_int @ (plus_plus_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6268])). 185.47/93.66 thf(5780,axiom,((! [A:nat]: ((A != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2031_gr__zeroI)). 185.47/93.66 thf(26958,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5780])). 185.47/93.66 thf(3959,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ (plus_plus_complex @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5091_minus__add__cancel)). 185.47/93.66 thf(20713,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ (plus_plus_complex @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3959])). 185.47/93.66 thf(2872,axiom,((! [A:nat]: ((semiri5074537144036343181t_real @ (suc @ A)) != zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7217_of__nat__neq__0)). 185.47/93.66 thf(17261,plain,((! [A:nat]: ~ ((semiri5074537144036343181t_real @ (suc @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2872])). 185.47/93.66 thf(338,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > real)]: ((! [D:nat]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (B @ D)) @ (C @ D)) <= (member_nat @ D @ A))) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (groups2073611262835488442omplex @ B @ A)) @ (groups6591440286371151544t_real @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7466_sum__norm__le)). 185.47/93.66 thf(8871,plain,((! [A:set_nat,B:(nat > complex),C:(nat > real)]: ((! [D:nat]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (B @ D)) @ (C @ D)) | ~ (member_nat @ D @ A))) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (groups2073611262835488442omplex @ (B) @ A)) @ (groups6591440286371151544t_real @ (C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 185.47/93.66 thf(5060,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ (plus_plus_nat @ B @ A)) = (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6235_neg__one__power__add__eq__neg__one__power__diff)). 185.47/93.66 thf(24374,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ (plus_plus_nat @ B @ A)) = (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5060])). 185.47/93.66 thf(4692,axiom,((! [A:code_integer]: ((times_3573771949741848930nteger @ (abs_abs_Code_integer @ A) @ (abs_abs_Code_integer @ A)) = (times_3573771949741848930nteger @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6336_abs__mult__self__eq)). 185.47/93.66 thf(23037,plain,((! [A:code_integer]: ((times_3573771949741848930nteger @ (abs_abs_Code_integer @ A) @ (abs_abs_Code_integer @ A)) = (times_3573771949741848930nteger @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4692])). 185.47/93.66 thf(700,axiom,((! [A:real,B:real,C:nat]: ((ord_less_real @ zero_zero_real @ A) => ((log @ B @ (power_power_real @ A @ C)) = (times_times_real @ (semiri5074537144036343181t_real @ C) @ (log @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9049_log__nat__power)). 185.47/93.66 thf(10069,plain,((! [A:real,B:real,C:nat]: ((ord_less_real @ zero_zero_real @ A) => ((log @ B @ (power_power_real @ A @ C)) = (times_times_real @ (semiri5074537144036343181t_real @ C) @ (log @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[700])). 185.47/93.66 thf(4595,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ B @ zero_zero_rat) => (ord_less_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2622_add__neg__nonpos)). 185.47/93.66 thf(22714,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ B @ zero_zero_rat) => (ord_less_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4595])). 185.47/93.66 thf(4416,axiom,((! [A:real,B:real]: ((times_times_real @ (sin_real @ A) @ (sin_real @ B)) = (divide_divide_real @ (minus_minus_real @ (cos_real @ (minus_minus_real @ A @ B)) @ (cos_real @ (plus_plus_real @ A @ B))) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7849_sin__times__sin)). 185.47/93.66 thf(22137,plain,((! [A:real,B:real]: ((times_times_real @ (sin_real @ A) @ (sin_real @ B)) = (divide_divide_real @ (minus_minus_real @ (cos_real @ (minus_minus_real @ A @ B)) @ (cos_real @ (plus_plus_real @ A @ B))) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4416])). 185.47/93.66 thf(7224,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ C)) <= (dvd_dvd_nat @ A @ B)) <= (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4811_dvd__diffD1)). 185.47/93.66 thf(32355,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ C)) | ~ (dvd_dvd_nat @ A @ B) | ~ (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7224])). 185.47/93.66 thf(7254,axiom,((! [A:num,B:num]: ((times_times_num @ (bit1 @ A) @ (bit1 @ B)) = (bit1 @ (plus_plus_num @ (plus_plus_num @ A @ B) @ (bit0 @ (times_times_num @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6416_semiring__norm_I16_J)). 185.47/93.66 thf(32444,plain,((! [A:num,B:num]: ((times_times_num @ (bit1 @ A) @ (bit1 @ B)) = (bit1 @ (plus_plus_num @ (plus_plus_num @ A @ B) @ (bit0 @ (times_times_num @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7254])). 185.47/93.66 thf(1255,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (minus_minus_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_add__diff__cancel__left)). 185.47/93.66 thf(11940,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (minus_minus_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255])). 185.47/93.66 thf(901,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((((archim6058952711729229775r_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))) = (semiri1314217659103216013at_int @ C)) = ((ord_less_eq_nat @ (power_power_nat @ A @ C) @ B) & (ord_less_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))))) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9068_floor__log__nat__eq__powr__iff)). 185.47/93.66 thf(10819,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((((archim6058952711729229775r_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))) = (semiri1314217659103216013at_int @ C)) = ((ord_less_eq_nat @ (power_power_nat @ A @ C) @ B) & (ord_less_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))))) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[901])). 185.47/93.66 thf(3150,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ (plus_plus_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (bit_se2923211474154528505it_int @ B @ A)) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9354_take__bit__int__greater__eq)). 185.47/93.66 thf(18144,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ (plus_plus_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (bit_se2923211474154528505it_int @ B @ A)) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3150])). 185.47/93.66 thf(2393,axiom,((! [A:num,B:num,C:(num > int),D:int]: ((((ord_less_eq_int @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F)))) <= ((C @ B) = D)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3955_ord__le__eq__subst)). 185.47/93.66 thf(15646,plain,((! [A:num,B:num,C:(num > int),D:int]: ((ord_less_eq_int @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2393])). 185.47/93.66 thf(2423,axiom,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ B @ (times_times_int @ C @ A)) = (plus_plus_int @ (times_times_int @ C @ (modulo_modulo_int @ (divide_divide_int @ B @ C) @ A)) @ (modulo_modulo_int @ B @ C))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3062_zmod__zmult2__eq)). 185.47/93.66 thf(15747,plain,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ B @ (times_times_int @ C @ A)) = (plus_plus_int @ (times_times_int @ C @ (modulo_modulo_int @ (divide_divide_int @ B @ C) @ A)) @ (modulo_modulo_int @ B @ C))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2423])). 185.47/93.66 thf(4730,axiom,((! [A:int,B:int]: ((ring_1_of_int_real @ (plus_plus_int @ A @ B)) = (plus_plus_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6974_of__int__add)). 185.47/93.66 thf(23167,plain,((! [A:int,B:int]: ((ring_1_of_int_real @ (plus_plus_int @ A @ B)) = (plus_plus_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4730])). 185.47/93.66 thf(2508,axiom,((! [A:nat]: (((semiri1314217659103216013at_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6893_of__nat__eq__0__iff)). 185.47/93.66 thf(16048,plain,((! [A:nat]: (((semiri1314217659103216013at_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2508])). 185.47/93.66 thf(3381,axiom,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri631733984087533419it_int @ A @ B)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4699_even__signed__take__bit__iff)). 185.47/93.66 thf(18867,plain,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri631733984087533419it_int @ A @ B)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3381])). 185.47/93.66 thf(6870,axiom,((! [A:code_integer,B:code_integer]: ((A = (uminus1351360451143612070nteger @ B)) = (B = (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5500_equation__minus__iff)). 185.47/93.66 thf(31038,plain,((! [A:code_integer,B:code_integer]: ((A = (uminus1351360451143612070nteger @ B)) = (B = (uminus1351360451143612070nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6870])). 185.47/93.66 thf(5856,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (suc @ B)) @ (power_power_nat @ C @ (suc @ B))) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2756_power__le__imp__le__base)). 185.47/93.66 thf(27383,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (suc @ B)) @ (power_power_nat @ C @ (suc @ B))) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5856])). 185.47/93.66 thf(5521,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((~ (ord_less_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3248_pinf_I5_J)). 185.47/93.66 thf(26117,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (ord_less_nat @ C @ A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5521])). 185.47/93.66 thf(204,axiom,((! [A:(nat > real)]: ((groups129246275422532515t_real @ A @ bot_bot_set_nat) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8642_prod_Oempty)). 185.47/93.66 thf(8393,plain,((! [A:(nat > real)]: ((groups129246275422532515t_real @ (A) @ bot_bot_set_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 185.47/93.66 thf(5054,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat]: (((vEBT_invar_vebt @ C @ D) => (((D = (suc @ B)) => ((((vEBT_invar_vebt @ (vEBT_Node @ none_P5556105721700978146at_nat @ E @ A @ C) @ E) <= (! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)) => (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)))))) <= (~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ C @ F)))) <= (E = (plus_plus_nat @ B @ D)))) <= ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)))) <= (! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ F @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_invar__vebt_Ointros_I3_J)). 185.47/93.66 thf(24341,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat]: (((vEBT_invar_vebt @ C @ D) => (((D = (suc @ B)) => ((vEBT_invar_vebt @ (vEBT_Node @ none_P5556105721700978146at_nat @ E @ A @ C) @ E) | ~ (! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)) => (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))))) | ? [F:nat]: (vEBT_V8194947554948674370ptions @ C @ F) | ~ (E = (plus_plus_nat @ B @ D)))) | ~ ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)))) | ~ (! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ F @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5054])). 185.47/93.66 thf(4957,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = (uminus_uminus_rat @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5473_neg__one__odd__power)). 185.47/93.66 thf(23963,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = (uminus_uminus_rat @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4957])). 185.47/93.66 thf(4612,axiom,((! [A:real,B:nat,C:real]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ C)) <= (ord_less_eq_real @ (power_power_real @ A @ (suc @ B)) @ (power_power_real @ C @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2754_power__le__imp__le__base)). 185.47/93.66 thf(22768,plain,((! [A:real,B:nat,C:real]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ C)) | ~ (ord_less_eq_real @ (power_power_real @ A @ (suc @ B)) @ (power_power_real @ C @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4612])). 185.47/93.66 thf(2459,axiom,((! [A:real,B:real]: (((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1814_less__divide__eq__1__neg)). 185.47/93.66 thf(15877,plain,((! [A:real,B:real]: (((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2459])). 185.47/93.66 thf(5785,axiom,((! [A:num,B:num]: ((bit0 @ A) != (bit1 @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6329_semiring__norm_I88_J)). 185.47/93.66 thf(26973,plain,((! [A:num,B:num]: ~ ((bit0 @ A) = (bit1 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5785])). 185.47/93.66 thf(4769,axiom,((! [A:rat,B:rat,C:(rat > int),D:int]: ((((! [E:rat,F:rat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_rat @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D)) <= (ord_less_eq_int @ (C @ B) @ D)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3922_order__subst2)). 185.47/93.66 thf(23327,plain,((! [A:rat,B:rat,C:(rat > int),D:int]: (((! [E:rat,F:rat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_rat @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D)) | ~ (ord_less_eq_int @ (C @ B) @ D) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4769])). 185.47/93.66 thf(7017,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) = (ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6683_abs__le__square__iff)). 185.47/93.66 thf(31613,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)) = (ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7017])). 185.47/93.66 thf(1424,axiom,(((set_ord_atMost_nat @ zero_zero_nat) = (insert_nat @ zero_zero_nat @ bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9410_atMost__0)). 185.47/93.66 thf(12486,plain,(((set_ord_atMost_nat @ zero_zero_nat) = (insert_nat @ zero_zero_nat @ bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424])). 185.47/93.66 thf(1357,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_eq_int @ B @ C) => (ord_less_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4320_order__less__le__trans)). 185.47/93.66 thf(12255,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_eq_int @ B @ C) => (ord_less_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357])). 185.47/93.66 thf(5789,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_vebt_mint @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1446_vebt__mint_Osimps_I2_J)). 185.47/93.66 thf(26986,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_vebt_mint @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5789])). 185.47/93.66 thf(445,axiom,(((im @ imaginary_unit) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9670_imaginary__unit_Osimps_I2_J)). 185.47/93.66 thf(9213,plain,(((im @ imaginary_unit) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[445])). 185.47/93.66 thf(6901,axiom,((! [A:num]: ((semiri5044797733671781792omplex @ (numeral_numeral_nat @ A)) = (times_times_complex @ (numera6690914467698888265omplex @ A) @ (semiri5044797733671781792omplex @ (pred_numeral @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8037_fact__numeral)). 185.47/93.66 thf(31134,plain,((! [A:num]: ((semiri5044797733671781792omplex @ (numeral_numeral_nat @ A)) = (times_times_complex @ (numera6690914467698888265omplex @ A) @ (semiri5044797733671781792omplex @ (pred_numeral @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6901])). 185.47/93.66 thf(7639,axiom,((! [A:code_integer]: ((power_8256067586552552935nteger @ (abs_abs_Code_integer @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6426_power2__abs)). 185.47/93.66 thf(33682,plain,((! [A:code_integer]: ((power_8256067586552552935nteger @ (abs_abs_Code_integer @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7639])). 185.47/93.66 thf(6844,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat,F:nat,G:nat]: ((! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ H @ B))) => ((vEBT_invar_vebt @ C @ D) => (((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((((! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ I)) = (vEBT_V8194947554948674370ptions @ C @ H)))) => (((! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))))) <= (F = G)) => ((ord_less_eq_nat @ F @ G) => ((ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)) => (((! [H:nat]: ((((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ G @ B)) <= ((vEBT_VEBT_high @ G @ B) = H)) & ! [I:nat]: ((((vEBT_VEBT_high @ I @ B) = H) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ I @ B))) => ((ord_less_eq_nat @ I @ G) & (ord_less_nat @ F @ I)))) <= (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)))) <= (F != G)) => (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ E @ A @ C) @ E)))))) <= (E = (plus_plus_nat @ B @ D))) <= (D = B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_invar__vebt_Ointros_I4_J)). 185.47/93.66 thf(30879,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat,F:nat,G:nat]: ((! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ H @ B))) => ((vEBT_invar_vebt @ C @ D) => (((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => (((! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ I)) = (vEBT_V8194947554948674370ptions @ C @ H)))) => ((! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)))) | ~ (F = G)) => ((ord_less_eq_nat @ F @ G) => ((ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)) => ((! [H:nat]: ((((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ G @ B)) | ~ ((vEBT_VEBT_high @ G @ B) = H)) & ! [I:nat]: ((((vEBT_VEBT_high @ I @ B) = H) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ I @ B))) => ((ord_less_eq_nat @ I @ G) & (ord_less_nat @ F @ I)))) | ~ (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) | (F = G)) => (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ E @ A @ C) @ E)))))) | ~ (E = (plus_plus_nat @ B @ D)) | ~ (D = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6844])). 185.47/93.66 thf(1903,axiom,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ (abs_abs_real @ A)) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6558_abs__minus__le__zero)). 185.47/93.66 thf(14092,plain,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ (abs_abs_real @ A)) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903])). 185.47/93.66 thf(814,axiom,((! [A:set_nat,B:(nat > rat),C:(nat > rat),D:rat,E:rat]: ((((groups2906978787729119204at_rat @ B @ A) = one_one_rat) => ((! [F:nat]: ((member_nat @ F @ A) => (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (C @ F) @ D)) @ E))) => (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (groups2906978787729119204at_rat @ (^ [F:nat]: (times_times_rat @ (C @ F) @ (B @ F))) @ A) @ D)) @ E))) <= (! [F:nat]: ((member_nat @ F @ A) => (ord_less_eq_rat @ zero_zero_rat @ (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6733_convex__sum__bound__le)). 185.47/93.66 thf(10503,plain,((! [A:set_nat,B:(nat > rat),C:(nat > rat),D:rat,E:rat]: ((((groups2906978787729119204at_rat @ (B) @ A) = one_one_rat) => ((! [F:nat]: ((member_nat @ F @ A) => (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (C @ F) @ D)) @ E))) => (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (groups2906978787729119204at_rat @ (^ [F:nat]: (times_times_rat @ (C @ F) @ (B @ F))) @ A) @ D)) @ E))) | ~ (! [F:nat]: ((member_nat @ F @ A) => (ord_less_eq_rat @ zero_zero_rat @ (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[814])). 185.47/93.66 thf(433,axiom,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => (((groups2906978787729119204at_rat @ C @ A) = (groups2906978787729119204at_rat @ C @ B)) <= (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = zero_zero_rat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6085_sum_Omono__neutral__right)). 185.47/93.66 thf(9171,plain,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => (((groups2906978787729119204at_rat @ (C) @ A) = (groups2906978787729119204at_rat @ (C) @ B)) | ~ (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = zero_zero_rat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[433])). 185.47/93.66 thf(6996,axiom,((! [A:int]: ~ (! [B:nat]: ((! [C:nat]: (((bit_se1146084159140164899it_int @ A @ C) = (bit_se1146084159140164899it_int @ A @ B)) <= (ord_less_eq_nat @ B @ C))) => (~ (((bit_se1146084159140164899it_int @ A @ (minus_minus_nat @ B @ one_one_nat)) = (~ (bit_se1146084159140164899it_int @ A @ B))) <= (ord_less_nat @ zero_zero_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9435_int__bit__bound)). 185.47/93.66 thf(31538,plain,((! [A:int]: ~ (! [B:nat]: ((! [C:nat]: (((bit_se1146084159140164899it_int @ A @ C) = (bit_se1146084159140164899it_int @ A @ B)) | ~ (ord_less_eq_nat @ B @ C))) => (~ (((bit_se1146084159140164899it_int @ A @ (minus_minus_nat @ B @ one_one_nat)) = (~ (bit_se1146084159140164899it_int @ A @ B))) | ~ (ord_less_nat @ zero_zero_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6996])). 185.47/93.66 thf(4071,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sqrt @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8123_real__sqrt__ge__0__iff)). 185.47/93.66 thf(21046,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sqrt @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4071])). 185.47/93.66 thf(3345,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = ((B != zero_zero_rat) | (A != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2985_sum__power2__gt__zero__iff)). 185.47/93.66 thf(18757,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = (~ (B = zero_zero_rat) | ~ (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3345])). 185.47/93.66 thf(3216,axiom,((! [A:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ A) @ zero_zero_int) = (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1616_double__add__le__zero__iff__single__add__le__zero)). 185.47/93.66 thf(18357,plain,((! [A:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ A) @ zero_zero_int) = (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3216])). 185.47/93.66 thf(1243,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_real @ (sin_real @ A) @ (sin_real @ B)) = (ord_less_real @ A @ B))) <= (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7924_sin__mono__less__eq)). 185.47/93.66 thf(11901,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_real @ (sin_real @ A) @ (sin_real @ B)) = (ord_less_real @ A @ B))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243])). 185.47/93.66 thf(4485,axiom,((! [A:vEBT_VEBT,B:list_VEBT_VEBT]: ((member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ B)) = (? [C:nat]: ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ B)) & ((nth_VEBT_VEBT @ B @ C) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_in__set__conv__nth)). 185.47/93.66 thf(22358,plain,((! [A:vEBT_VEBT,B:list_VEBT_VEBT]: ((member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ B)) = (? [C:nat]: ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ B)) & ((nth_VEBT_VEBT @ B @ C) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4485])). 185.47/93.66 thf(4555,axiom,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: (((dvd_dvd_Code_integer @ C @ D) => (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ C) @ (times_3573771949741848930nteger @ B @ D))) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4585_mult__dvd__mono)). 185.47/93.66 thf(22590,plain,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: (((dvd_dvd_Code_integer @ C @ D) => (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ C) @ (times_3573771949741848930nteger @ B @ D))) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4555])). 185.47/93.66 thf(7392,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = ((B != A) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3844_nle__le)). 185.47/93.66 thf(32894,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (~ (B = A) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7392])). 185.47/93.66 thf(6808,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_add__mono__thms__linordered__field_I2_J)). 185.47/93.66 thf(30762,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((A = B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6808])). 185.47/93.66 thf(1202,axiom,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (times_3573771949741848930nteger @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5078_minus__mult__minus)). 185.47/93.66 thf(11777,plain,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (times_3573771949741848930nteger @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202])). 185.47/93.66 thf(3454,axiom,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ (plus_plus_nat @ A @ C) @ C)) @ (set_ord_atMost_nat @ B)) = (binomial @ (suc @ (plus_plus_nat @ A @ B)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8942_sum__choose__lower)). 185.47/93.66 thf(19090,plain,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ (plus_plus_nat @ A @ C) @ C)) @ (set_ord_atMost_nat @ B)) = (binomial @ (suc @ (plus_plus_nat @ A @ B)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3454])). 185.47/93.66 thf(938,axiom,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_real @ A @ B) = (ord_less_real @ (tan_real @ A) @ (tan_real @ B)))) <= (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8058_tan__monotone_H)). 185.47/93.66 thf(10951,plain,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_real @ A @ B) = (ord_less_real @ (tan_real @ A) @ (tan_real @ B)))) | ~ (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[938])). 185.47/93.66 thf(5439,axiom,((! [A:nat]: ((power_power_int @ one_one_int @ A) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_power__one)). 185.47/93.66 thf(25757,plain,((! [A:nat]: ((power_power_int @ one_one_int @ A) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5439])). 185.47/93.66 thf(1622,axiom,((! [A:rat,B:num,C:rat]: (((divide_divide_rat @ A @ (numeral_numeral_rat @ B)) = C) = ((((numeral_numeral_rat @ B) != zero_zero_rat) => (A = (times_times_rat @ C @ (numeral_numeral_rat @ B)))) & ((C = zero_zero_rat) <= ((numeral_numeral_rat @ B) = zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1825_divide__eq__eq__numeral1_I1_J)). 185.47/93.66 thf(13137,plain,((! [A:rat,B:num,C:rat]: (((divide_divide_rat @ A @ (numeral_numeral_rat @ B)) = C) = (((~ ((numeral_numeral_rat @ B) = zero_zero_rat)) => (A = (times_times_rat @ C @ (numeral_numeral_rat @ B)))) & ((C = zero_zero_rat) | ~ ((numeral_numeral_rat @ B) = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1622])). 185.47/93.66 thf(267,axiom,((! [A:real,B:int]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (ring_1_of_int_real @ B) @ pi))) = (tan_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7975_tan__periodic__int)). 185.47/93.66 thf(8609,plain,((! [A:real,B:int]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (ring_1_of_int_real @ B) @ pi))) = (tan_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 185.47/93.66 thf(6124,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((modulo_modulo_nat @ (plus_plus_nat @ A @ D) @ B) = (modulo_modulo_nat @ (plus_plus_nat @ C @ E) @ B)) <= ((modulo_modulo_nat @ D @ B) = (modulo_modulo_nat @ E @ B))) <= ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1994_mod__add__cong)). 185.47/93.66 thf(28299,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((modulo_modulo_nat @ (plus_plus_nat @ A @ D) @ B) = (modulo_modulo_nat @ (plus_plus_nat @ C @ E) @ B)) | ~ ((modulo_modulo_nat @ D @ B) = (modulo_modulo_nat @ E @ B)) | ~ ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6124])). 185.47/93.66 thf(2544,axiom,((! [A:rat]: ? [B:rat]: (ord_less_rat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_linordered__field__no__ub)). 185.47/93.66 thf(16169,plain,((! [A:rat]: ? [B:rat]: (ord_less_rat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2544])). 185.47/93.66 thf(5257,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1610_mod__less)). 185.47/93.66 thf(25075,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5257])). 185.47/93.66 thf(3344,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ (plus_plus_real @ (real_V7735802525324610683m_real @ B) @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7506_norm__triangle__sub)). 185.47/93.66 thf(18755,plain,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ (plus_plus_real @ (real_V7735802525324610683m_real @ B) @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3344])). 185.47/93.66 thf(6217,axiom,((! [A:nat,B:nat]: (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)) != zero_zero_int) <= ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2952_exp__not__zero__imp__exp__diff__not__zero)). 185.47/93.66 thf(28653,plain,((! [A:nat,B:nat]: (~ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)) = zero_zero_int) | ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6217])). 185.47/93.66 thf(3628,axiom,((! [A:int,B:int]: (((divide_divide_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (divide_divide_int @ B @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3080_pos__zdiv__mult__2)). 185.47/93.66 thf(19644,plain,((! [A:int,B:int]: (((divide_divide_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (divide_divide_int @ B @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3628])). 185.47/93.66 thf(4375,axiom,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ B) = zero_zero_rat) => ((uminus_uminus_rat @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5736_add_Oinverse__unique)). 185.47/93.66 thf(22017,plain,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ B) = zero_zero_rat) => ((uminus_uminus_rat @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4375])). 185.47/93.66 thf(199,axiom,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ B) => ((plus_plus_real @ (suminf_real @ A) @ (suminf_real @ B)) = (suminf_real @ (^ [C:nat]: (plus_plus_real @ (A @ C) @ (B @ C)))))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7678_suminf__add)). 185.47/93.66 thf(8378,plain,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ (B)) => ((plus_plus_real @ (suminf_real @ (A)) @ (suminf_real @ (B))) = (suminf_real @ (^ [C:nat]: (plus_plus_real @ (A @ C) @ (B @ C)))))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 185.47/93.66 thf(40,axiom,((! [A:real,B:nat]: ((minus_minus_real @ one_one_real @ (power_power_real @ A @ B)) = (times_times_real @ (minus_minus_real @ one_one_real @ A) @ (groups6591440286371151544t_real @ (^ [C:nat]: (power_power_real @ A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7628_one__diff__power__eq_H)). 185.47/93.66 thf(7863,plain,((! [A:real,B:nat]: ((minus_minus_real @ one_one_real @ (power_power_real @ A @ B)) = (times_times_real @ (minus_minus_real @ one_one_real @ A) @ (groups6591440286371151544t_real @ (^ [C:nat]: (power_power_real @ A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 185.47/93.66 thf(6178,axiom,((! [A:int,B:int]: (((dvd_dvd_int @ (times_times_int @ A @ B) @ A) = ((abs_abs_int @ B) = one_one_int)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6824_zdvd__mult__cancel1)). 185.47/93.66 thf(28521,plain,((! [A:int,B:int]: (((dvd_dvd_int @ (times_times_int @ A @ B) @ A) = ((abs_abs_int @ B) = one_one_int)) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6178])). 185.47/93.66 thf(6801,axiom,((! [A:int]: ((zero_zero_int = (abs_abs_int @ A)) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6319_abs__0__eq)). 185.47/93.66 thf(30740,plain,((! [A:int]: ((zero_zero_int = (abs_abs_int @ A)) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6801])). 185.47/93.66 thf(4944,axiom,((! [A:code_integer,B:code_integer]: (((uminus1351360451143612070nteger @ A) = (uminus1351360451143612070nteger @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5024_neg__equal__iff__equal)). 185.47/93.66 thf(23921,plain,((! [A:code_integer,B:code_integer]: (((uminus1351360451143612070nteger @ A) = (uminus1351360451143612070nteger @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4944])). 185.47/93.66 thf(707,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (bit_ri7919022796975470100ot_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9525_or__not__numerals_I4_J)). 185.47/93.66 thf(10090,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (bit_ri7919022796975470100ot_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[707])). 185.47/93.66 thf(3771,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2213_mult__nonneg__nonpos)). 185.47/93.66 thf(20120,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3771])). 185.47/93.66 thf(1317,axiom,((! [A:rat,B:rat,C:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_rat @ B @ C)) => ((ord_less_eq_rat @ zero_zero_rat @ B) => ((ord_less_eq_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ A @ (divide_divide_rat @ (plus_plus_rat @ B @ C) @ (numeral_numeral_rat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3016_arith__geo__mean)). 185.47/93.66 thf(12123,plain,((! [A:rat,B:rat,C:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_rat @ B @ C)) => ((ord_less_eq_rat @ zero_zero_rat @ B) => ((ord_less_eq_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ A @ (divide_divide_rat @ (plus_plus_rat @ B @ C) @ (numeral_numeral_rat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317])). 185.47/93.66 thf(432,axiom,((! [A:int,B:int]: ((ord_less_int @ (bit_se6526347334894502574or_int @ A @ B) @ zero_zero_int) = ((ord_less_int @ A @ zero_zero_int) != (ord_less_int @ B @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9489_xor__negative__int__iff)). 185.47/93.66 thf(9168,plain,((! [A:int,B:int]: ((ord_less_int @ (bit_se6526347334894502574or_int @ A @ B) @ zero_zero_int) = (~ ((ord_less_int @ A @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[432])). 185.47/93.66 thf(7410,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_788_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc)). 185.47/93.66 thf(32975,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7410])). 185.47/93.66 thf(6076,axiom,(((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5411_diff__numeral__special_I10_J)). 185.47/93.66 thf(28124,plain,(((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6076])). 185.47/93.66 thf(6117,axiom,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_779_mult_Ocomm__neutral)). 185.47/93.66 thf(28271,plain,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6117])). 185.47/93.66 thf(4636,axiom,((! [A:num,B:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5693_not__numeral__le__neg__numeral)). 185.47/93.66 thf(22856,plain,((! [A:num,B:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4636])). 185.47/93.66 thf(3227,axiom,((! [A:real,B:real]: ~ (ord_less_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2685_not__sum__squares__lt__zero)). 185.47/93.66 thf(18389,plain,((! [A:real,B:real]: ~ (ord_less_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3227])). 185.47/93.66 thf(911,axiom,((! [A:int,B:int]: ((bit_concat_bit @ zero_zero_nat @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3820_concat__bit__0)). 185.47/93.66 thf(10851,plain,((! [A:int,B:int]: ((bit_concat_bit @ zero_zero_nat @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[911])). 185.47/93.66 thf(4897,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) <= (ord_less_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2657_divide__nonpos__neg)). 185.47/93.66 thf(23753,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) | ~ (ord_less_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4897])). 185.47/93.66 thf(3623,axiom,((! [A:rat,B:(real > rat),C:real,D:real]: ((ord_less_eq_rat @ A @ (B @ C)) => (((ord_less_rat @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F))))) <= (ord_less_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4326_order__le__less__subst1)). 185.47/93.66 thf(19627,plain,((! [A:rat,B:(real > rat),C:real,D:real]: ((ord_less_eq_rat @ A @ (B @ C)) => ((ord_less_rat @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F)))) | ~ (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3623])). 185.47/93.66 thf(5845,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1850_div__mult__self1__is__m)). 185.47/93.66 thf(27349,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5845])). 185.47/93.66 thf(4201,axiom,((! [A:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4941_odd__iff__mod__2__eq__one)). 185.47/93.66 thf(21448,plain,((! [A:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4201])). 185.47/93.66 thf(1773,axiom,((! [A:nat,B:nat,C:(nat > int)]: ((((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_int @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat)))) <= (ord_less_eq_nat @ A @ B)) & (((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = zero_zero_int) <= (~ (ord_less_eq_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6738_sum__natinterval__diff)). 185.47/93.66 thf(13667,plain,((! [A:nat,B:nat,C:(nat > int)]: ((((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_int @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat)))) | ~ (ord_less_eq_nat @ A @ B)) & (((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = zero_zero_int) | (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773])). 185.47/93.66 thf(3157,axiom,((! [A:nat]: (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7320_of__nat__less__two__power)). 185.47/93.66 thf(18169,plain,((! [A:nat]: (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3157])). 185.47/93.66 thf(3520,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (minus_minus_int @ C @ B) @ (minus_minus_int @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_diff__left__mono)). 185.47/93.66 thf(19315,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (minus_minus_int @ C @ B) @ (minus_minus_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3520])). 185.47/93.66 thf(4599,axiom,((! [A:set_nat,B:set_nat,C:nat,D:(nat > int)]: ((finite_finite_nat @ A) => (((((ord_less_int @ (groups3539618377306564664at_int @ D @ B) @ (groups3539618377306564664at_int @ D @ A)) <= (! [E:nat]: ((ord_less_eq_int @ zero_zero_int @ (D @ E)) <= (member_nat @ E @ A)))) <= (ord_less_int @ zero_zero_int @ (D @ C))) <= (member_nat @ C @ (minus_minus_set_nat @ A @ B))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6253_sum__strict__mono2)). 185.47/93.66 thf(22731,plain,((! [A:set_nat,B:set_nat,C:nat,D:(nat > int)]: ((finite_finite_nat @ A) => ((ord_less_int @ (groups3539618377306564664at_int @ (D) @ B) @ (groups3539618377306564664at_int @ (D) @ A)) | ~ (! [E:nat]: ((ord_less_eq_int @ zero_zero_int @ (D @ E)) | ~ (member_nat @ E @ A))) | ~ (ord_less_int @ zero_zero_int @ (D @ C)) | ~ (member_nat @ C @ (minus_minus_set_nat @ A @ B)) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4599])). 185.47/93.66 thf(2766,axiom,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5928_neg__one__le__numeral)). 185.47/93.66 thf(16923,plain,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2766])). 185.47/93.66 thf(75,axiom,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (^ [C:nat]: (A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (groups705719431365010083at_int @ A @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8858_prod_Onat__diff__reindex)). 185.47/93.66 thf(7972,plain,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (^ [C:nat]: (A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (groups705719431365010083at_int @ (A) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 185.47/93.66 thf(6775,axiom,((! [A:(nat > num),B:nat,C:nat]: ((! [D:nat]: (ord_less_num @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_num @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_lift__Suc__mono__less)). 185.47/93.66 thf(30656,plain,((! [A:(nat > num),B:nat,C:nat]: ((! [D:nat]: (ord_less_num @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_num @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6775])). 185.47/93.66 thf(22,axiom,((! [A:real,B:nat]: ((minus_minus_real @ one_one_real @ (power_power_real @ A @ B)) = (times_times_real @ (minus_minus_real @ one_one_real @ A) @ (groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7595_one__diff__power__eq)). 185.47/93.66 thf(7802,plain,((! [A:real,B:nat]: ((minus_minus_real @ one_one_real @ (power_power_real @ A @ B)) = (times_times_real @ (minus_minus_real @ one_one_real @ A) @ (groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 185.47/93.66 thf(6931,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_real @ A @ (power_power_real @ (power_power_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1121_power__odd__eq)). 185.47/93.66 thf(31236,plain,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_real @ A @ (power_power_real @ (power_power_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6931])). 185.47/93.66 thf(4119,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6696_sum_Oub__add__nat)). 185.47/93.66 thf(21197,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4119])). 185.47/93.66 thf(3668,axiom,((! [A:real]: ((power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_real @ one_one_real @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7836_cos__squared__eq)). 185.47/93.66 thf(19775,plain,((! [A:real]: ((power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_real @ one_one_real @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3668])). 185.47/93.66 thf(5975,axiom,((! [A:complex,B:num,C:num]: ((times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ B)) @ (power_power_complex @ A @ (numeral_numeral_nat @ C))) = (power_power_complex @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_power__add__numeral)). 185.47/93.66 thf(27814,plain,((! [A:complex,B:num,C:num]: ((times_times_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ B)) @ (power_power_complex @ A @ (numeral_numeral_nat @ C))) = (power_power_complex @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5975])). 185.47/93.66 thf(7153,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((root @ A @ (times_times_real @ (sgn_sgn_real @ B) @ (power_power_real @ (abs_abs_real @ B) @ A))) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9341_root__sgn__power)). 185.47/93.66 thf(32094,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((root @ A @ (times_times_real @ (sgn_sgn_real @ B) @ (power_power_real @ (abs_abs_real @ B) @ A))) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7153])). 185.47/93.66 thf(5000,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) = (dvd_dvd_nat @ A @ C)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4644_dvd__add__right__iff)). 185.47/93.66 thf(24104,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) = (dvd_dvd_nat @ A @ C)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5000])). 185.47/93.66 thf(4391,axiom,((ord_less_eq_set_nat = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) <= (member_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1418_subset__iff)). 185.47/93.66 thf(22068,plain,(((ord_less_eq_set_nat) = (^ [A:set_nat,B:set_nat]: ! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4391])). 185.47/93.66 thf(2923,axiom,((! [A:real,B:(rat > real),C:rat,D:rat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_rat @ E @ F))) => (ord_less_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4322_order__le__less__subst1)). 185.47/93.66 thf(17426,plain,((! [A:real,B:(rat > real),C:rat,D:rat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_rat @ E @ F))) => (ord_less_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2923])). 185.47/93.66 thf(3616,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (ord_max_nat @ B @ C)) = (ord_max_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3761_nat__mult__max__right)). 185.47/93.66 thf(19607,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (ord_max_nat @ B @ C)) = (ord_max_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3616])). 185.47/93.66 thf(5487,axiom,((! [A:nat]: ((semiri1316708129612266289at_nat @ (suc @ A)) = (plus_plus_nat @ one_one_nat @ (semiri1316708129612266289at_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7016_of__nat__Suc)). 185.47/93.66 thf(26005,plain,((! [A:nat]: ((semiri1316708129612266289at_nat @ (suc @ A)) = (plus_plus_nat @ one_one_nat @ (semiri1316708129612266289at_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5487])). 185.47/93.66 thf(7648,axiom,(((modulo_modulo_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1876_bits__one__mod__two__eq__one)). 185.47/93.66 thf(33703,plain,(((modulo_modulo_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7648])). 185.47/93.66 thf(4888,axiom,((! [A:num,B:num]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5372_neg__numeral__less__iff)). 185.47/93.66 thf(23725,plain,((! [A:num,B:num]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4888])). 185.47/93.66 thf(2352,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) = (ord_less_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3371_mult__less__iff1)). 185.47/93.66 thf(15520,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) = (ord_less_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2352])). 185.47/93.66 thf(4676,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((A = (plus_plus_rat @ B @ C)) => ((minus_minus_rat @ D @ A) = (plus_plus_rat @ (uminus_uminus_rat @ B) @ (minus_minus_rat @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5785_group__cancel_Osub2)). 185.47/93.66 thf(22980,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((A = (plus_plus_rat @ B @ C)) => ((minus_minus_rat @ D @ A) = (plus_plus_rat @ (uminus_uminus_rat @ B) @ (minus_minus_rat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4676])). 185.47/93.66 thf(423,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (cos_real @ A) @ (cos_real @ B)))) <= (ord_less_eq_real @ (uminus_uminus_real @ pi) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7867_cos__monotone__minus__pi__0_H)). 185.47/93.66 thf(9139,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (cos_real @ A) @ (cos_real @ B)))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ pi) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[423])). 185.47/93.66 thf(7206,axiom,((! [A:nat]: ((((power_power_complex @ zero_zero_complex @ A) = one_one_complex) <= (A = zero_zero_nat)) & ((A != zero_zero_nat) => ((power_power_complex @ zero_zero_complex @ A) = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1964_power__0__left)). 185.47/93.66 thf(32272,plain,((! [A:nat]: ((((power_power_complex @ zero_zero_complex @ A) = one_one_complex) | ~ (A = zero_zero_nat)) & ((~ (A = zero_zero_nat)) => ((power_power_complex @ zero_zero_complex @ A) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7206])). 185.47/93.66 thf(3638,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => (((divide1717551699836669952omplex @ B @ A) = C) = (B = (times_times_complex @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2461_nonzero__divide__eq__eq)). 185.47/93.66 thf(19676,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => (((divide1717551699836669952omplex @ B @ A) = C) = (B = (times_times_complex @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3638])). 185.47/93.66 thf(273,axiom,(((vEBT_vebt_buildup @ (suc @ zero_zero_nat)) = (vEBT_Leaf @ ($false) @ ($false)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2011_vebt__buildup_Osimps_I2_J)). 185.47/93.66 thf(8626,plain,(((vEBT_vebt_buildup @ (suc @ zero_zero_nat)) = (vEBT_Leaf @ ($false) @ ($false)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 185.47/93.66 thf(6862,axiom,((! [A:nat,B:(num > nat),C:num,D:num]: ((A = (B @ C)) => (((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))) <= (ord_less_eq_num @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3944_ord__eq__le__subst)). 185.47/93.66 thf(30993,plain,((! [A:nat,B:(num > nat),C:num,D:num]: ((A = (B @ C)) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6862])). 185.47/93.66 thf(7185,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_real @ (abs_abs_real @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6711_power2__le__iff__abs__le)). 185.47/93.66 thf(32201,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_real @ (abs_abs_real @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7185])). 185.47/93.66 thf(551,axiom,((! [A:nat,B:nat,C:(nat > real),D:nat]: (((groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_real @ (groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D))))) <= (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6697_sum_Oub__add__nat)). 185.47/93.66 thf(9562,plain,((! [A:nat,B:nat,C:(nat > real),D:nat]: (((groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_real @ (groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D))))) | ~ (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[551])). 185.47/93.66 thf(4405,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ B)) @ A) != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8518_pochhammer__of__nat__eq__0__lemma_H)). 185.47/93.66 thf(22109,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ ((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ B)) @ A) = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4405])). 185.47/93.66 thf(3349,axiom,((! [A:num]: ((nat2 @ (numeral_numeral_int @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9247_nat__numeral)). 185.47/93.66 thf(18770,plain,((! [A:num]: ((nat2 @ (numeral_numeral_int @ A)) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3349])). 185.47/93.66 thf(3526,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) => ((ord_less_rat @ B @ A) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4003_linorder__cases)). 185.47/93.66 thf(19333,plain,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) => ((ord_less_rat @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3526])). 185.47/93.66 thf(5674,axiom,((! [A:option_nat]: ((A != none_nat) = (? [B:nat]: (A = (some_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1006_not__None__eq)). 185.47/93.66 thf(26617,plain,((! [A:option_nat]: ((~ (A = none_nat)) = (? [B:nat]: (A = (some_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5674])). 185.47/93.66 thf(6018,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) & (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_add__mono__thms__linordered__field_I4_J)). 185.47/93.66 thf(27949,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) & (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6018])). 185.47/93.66 thf(7477,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_add__le__less__mono)). 185.47/93.66 thf(33201,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7477])). 185.47/93.66 thf(6915,axiom,((! [A:complex,B:nat]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_complex @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5428_Power_Oring__1__class_Opower__minus__even)). 185.47/93.66 thf(31179,plain,((! [A:complex,B:nat]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_complex @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6915])). 185.47/93.66 thf(7047,axiom,((! [A:rat,B:rat,C:num]: ((A = (divide_divide_rat @ B @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)))) = ((((uminus_uminus_rat @ (numeral_numeral_rat @ C)) != zero_zero_rat) => ((times_times_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))) = B)) & ((A = zero_zero_rat) <= ((uminus_uminus_rat @ (numeral_numeral_rat @ C)) = zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5385_eq__divide__eq__numeral1_I2_J)). 185.47/93.66 thf(31737,plain,((! [A:rat,B:rat,C:num]: ((A = (divide_divide_rat @ B @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)))) = (((~ ((uminus_uminus_rat @ (numeral_numeral_rat @ C)) = zero_zero_rat)) => ((times_times_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))) = B)) & ((A = zero_zero_rat) | ~ ((uminus_uminus_rat @ (numeral_numeral_rat @ C)) = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7047])). 185.47/93.66 thf(4759,axiom,((! [A:real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & (((divide_divide_real @ A @ A) = one_one_real) <= (A != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1730_divide__self__if)). 185.47/93.66 thf(23291,plain,((! [A:real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & (((divide_divide_real @ A @ A) = one_one_real) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4759])). 185.47/93.66 thf(948,axiom,((! [A:complex,B:complex]: ((im @ (divide1717551699836669952omplex @ A @ B)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ (im @ A) @ (re @ B)) @ (times_times_real @ (re @ A) @ (im @ B))) @ (plus_plus_real @ (power_power_real @ (re @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9702_Im__divide)). 185.47/93.66 thf(10983,plain,((! [A:complex,B:complex]: ((im @ (divide1717551699836669952omplex @ A @ B)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ (im @ A) @ (re @ B)) @ (times_times_real @ (re @ A) @ (im @ B))) @ (plus_plus_real @ (power_power_real @ (re @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[948])). 185.47/93.66 thf(459,axiom,((tan_complex = (^ [A:complex]: (divide1717551699836669952omplex @ (sin_complex @ A) @ (cos_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8030_tan__def)). 185.47/93.66 thf(9256,plain,(((tan_complex) = (^ [A:complex]: (divide1717551699836669952omplex @ (sin_complex @ A) @ (cos_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[459])). 185.47/93.66 thf(3509,axiom,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (plus_plus_rat @ (times_times_rat @ B @ A) @ C) @ A)) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2734_add__divide__eq__iff)). 185.47/93.66 thf(19283,plain,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (plus_plus_rat @ (times_times_rat @ B @ A) @ C) @ A)) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3509])). 185.47/93.66 thf(6101,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((power_power_int @ zero_zero_int @ A) = one_one_int)) & ((A != zero_zero_nat) => ((power_power_int @ zero_zero_int @ A) = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1963_power__0__left)). 185.47/93.66 thf(28204,plain,((! [A:nat]: (((A = zero_zero_nat) => ((power_power_int @ zero_zero_int @ A) = one_one_int)) & ((~ (A = zero_zero_nat)) => ((power_power_int @ zero_zero_int @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6101])). 185.47/93.66 thf(989,axiom,((! [A:complex,B:real,C:complex,D:real]: ((ord_less_real @ (real_V1022390504157884413omplex @ A) @ B) => ((ord_less_real @ (real_V1022390504157884413omplex @ (times_times_complex @ A @ C)) @ (times_times_real @ B @ D)) <= (ord_less_real @ (real_V1022390504157884413omplex @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7481_norm__mult__less)). 185.47/93.66 thf(11120,plain,((! [A:complex,B:real,C:complex,D:real]: ((ord_less_real @ (real_V1022390504157884413omplex @ A) @ B) => ((ord_less_real @ (real_V1022390504157884413omplex @ (times_times_complex @ A @ C)) @ (times_times_real @ B @ D)) | ~ (ord_less_real @ (real_V1022390504157884413omplex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[989])). 185.47/93.66 thf(4719,axiom,((! [A:real,B:nat]: (((ord_less_eq_real @ (power_power_real @ A @ B) @ one_one_real) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2719_power__le__one)). 185.47/93.66 thf(23135,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ (power_power_real @ A @ B) @ one_one_real) | ~ (ord_less_eq_real @ A @ one_one_real) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4719])). 185.47/93.66 thf(2863,axiom,((zero_zero_int = (abs_Integ @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9816_zero__int__def)). 185.47/93.66 thf(17235,plain,((zero_zero_int = (abs_Integ @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2863])). 185.47/93.66 thf(4891,axiom,((! [A:rat,B:rat]: (ord_less_eq_rat @ (minus_minus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B)) @ (abs_abs_rat @ (minus_minus_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6504_abs__triangle__ineq2)). 185.47/93.66 thf(23735,plain,((! [A:rat,B:rat]: (ord_less_eq_rat @ (minus_minus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B)) @ (abs_abs_rat @ (minus_minus_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4891])). 185.47/93.66 thf(3819,axiom,((! [A:real,B:real,C:real,D:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ C @ D) => (dvd_dvd_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4586_mult__dvd__mono)). 185.47/93.66 thf(20267,plain,((! [A:real,B:real,C:real,D:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ C @ D) => (dvd_dvd_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3819])). 185.47/93.66 thf(6141,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_899_power__le__imp__le__exp)). 185.47/93.66 thf(28358,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6141])). 185.47/93.66 thf(4546,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2600_mult__le__cancel__left__pos)). 185.47/93.66 thf(22562,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4546])). 185.47/93.66 thf(1689,axiom,((! [A:real,B:real]: ((! [C:real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ C @ one_one_real) => (ord_less_eq_real @ (times_times_real @ C @ A) @ B)))) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2830_field__le__mult__one__interval)). 185.47/93.66 thf(13383,plain,((! [A:real,B:real]: ((! [C:real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ C @ one_one_real) => (ord_less_eq_real @ (times_times_real @ C @ A) @ B)))) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1689])). 185.47/93.66 thf(6794,axiom,((! [A:nat,B:rat]: (((power_power_rat @ (uminus_uminus_rat @ B) @ A) = (uminus_uminus_rat @ (power_power_rat @ B @ A))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5442_power__minus__odd)). 185.47/93.66 thf(30715,plain,((! [A:nat,B:rat]: (((power_power_rat @ (uminus_uminus_rat @ B) @ A) = (uminus_uminus_rat @ (power_power_rat @ B @ A))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6794])). 185.47/93.66 thf(1459,axiom,((! [A:rat,B:rat,C:rat]: (((dvd_dvd_rat @ B @ A) => ((dvd_dvd_rat @ B @ C) => (A = C))) <= ((divide_divide_rat @ A @ B) = (divide_divide_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4671_dvd__div__eq__cancel)). 185.47/93.66 thf(12596,plain,((! [A:rat,B:rat,C:rat]: (((dvd_dvd_rat @ B @ A) => ((dvd_dvd_rat @ B @ C) => (A = C))) | ~ ((divide_divide_rat @ A @ B) = (divide_divide_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459])). 185.47/93.66 thf(1470,axiom,((ord_less_eq_rat = (^ [A:rat,B:rat]: ((A = B) | (ord_less_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9549_less__eq__rat__def)). 185.47/93.66 thf(12628,plain,(((ord_less_eq_rat) = (^ [A:rat,B:rat]: ((A = B) | (ord_less_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470])). 185.47/93.66 thf(6000,axiom,((! [A:nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((ord_less_nat @ E @ A) => (ord_less_eq_nat @ (B @ D) @ (B @ E))))) => ((! [D:nat,E:nat]: (((ord_less_eq_nat @ (C @ E) @ (C @ D)) <= (ord_less_nat @ E @ A)) <= (ord_less_eq_nat @ D @ E))) => (ord_less_eq_nat @ (times_times_nat @ A @ (groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ (B @ D) @ (C @ D))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A))) @ (times_times_nat @ (groups3542108847815614940at_nat @ B @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) @ (groups3542108847815614940at_nat @ C @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9572_Chebyshev__sum__upper__nat)). 185.47/93.66 thf(27894,plain,((! [A:nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => ((ord_less_nat @ E @ A) => (ord_less_eq_nat @ (B @ D) @ (B @ E))))) => ((! [D:nat,E:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ D)) | ~ (ord_less_nat @ E @ A) | ~ (ord_less_eq_nat @ D @ E))) => (ord_less_eq_nat @ (times_times_nat @ A @ (groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ (B @ D) @ (C @ D))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A))) @ (times_times_nat @ (groups3542108847815614940at_nat @ (B) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) @ (groups3542108847815614940at_nat @ (C) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6000])). 185.47/93.66 thf(4572,axiom,((! [A:num,B:rat,C:rat]: ((ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (divide_divide_rat @ B @ C)) = (((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C) @ B)) & ((~ (ord_less_rat @ zero_zero_rat @ C)) => (((~ (ord_less_rat @ C @ zero_zero_rat)) => (ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ zero_zero_rat)) & ((ord_less_rat @ B @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C)) <= (ord_less_rat @ C @ zero_zero_rat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6221_less__divide__eq__numeral_I2_J)). 185.47/93.66 thf(22650,plain,((! [A:num,B:rat,C:rat]: ((ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (divide_divide_rat @ B @ C)) = (((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C) @ B)) & ((~ (ord_less_rat @ zero_zero_rat @ C)) => (((~ (ord_less_rat @ C @ zero_zero_rat)) => (ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ zero_zero_rat)) & ((ord_less_rat @ B @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C)) | ~ (ord_less_rat @ C @ zero_zero_rat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4572])). 185.47/93.66 thf(4648,axiom,((! [A:int]: ((ord_less_eq_rat @ one_one_rat @ (ring_1_of_int_rat @ A)) = (ord_less_eq_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7081_of__int__1__le__iff)). 185.47/93.66 thf(22888,plain,((! [A:int]: ((ord_less_eq_rat @ one_one_rat @ (ring_1_of_int_rat @ A)) = (ord_less_eq_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4648])). 185.47/93.66 thf(6966,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) => ((A = B) <= ((minus_minus_nat @ B @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2127_diffs0__imp__equal)). 185.47/93.66 thf(31393,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) => ((A = B) | ~ ((minus_minus_nat @ B @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6966])). 185.47/93.66 thf(4458,axiom,((! [A:rat,B:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_add__diff__cancel)). 185.47/93.66 thf(22272,plain,((! [A:rat,B:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4458])). 185.47/93.66 thf(2321,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_int @ C @ B)) & ((ord_less_int @ B @ C) <= (ord_less_eq_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2585_mult__less__cancel__left)). 185.47/93.66 thf(15427,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_int @ C @ B)) & ((ord_less_int @ B @ C) | ~ (ord_less_eq_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2321])). 185.47/93.66 thf(2822,axiom,((! [A:code_integer,B:nat,C:code_integer,D:nat]: ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ B) @ C) => ((ord_less_eq_nat @ D @ B) => (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4791_power__le__dvd)). 185.47/93.66 thf(17101,plain,((! [A:code_integer,B:nat,C:code_integer,D:nat]: ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ B) @ C) => ((ord_less_eq_nat @ D @ B) => (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2822])). 185.47/93.66 thf(2973,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ zero_zero_rat) => ((((plus_plus_rat @ A @ B) = zero_zero_rat) = ((B = zero_zero_rat) & (A = zero_zero_rat))) <= (ord_less_eq_rat @ B @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2280_add__nonpos__eq__0__iff)). 185.47/93.66 thf(17587,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ zero_zero_rat) => ((((plus_plus_rat @ A @ B) = zero_zero_rat) = ((B = zero_zero_rat) & (A = zero_zero_rat))) | ~ (ord_less_eq_rat @ B @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2973])). 185.47/93.66 thf(3680,axiom,((! [A:set_nat]: ((! [B:nat]: ~ (member_nat @ B @ A)) = (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1276_all__not__in__conv)). 185.47/93.66 thf(19807,plain,((! [A:set_nat]: ((! [B:nat]: ~ (member_nat @ B @ A)) = (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3680])). 185.47/93.66 thf(7111,axiom,((! [A:num,B:num]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (numeral_numeral_int @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5348_mult__neg__numeral__simps_I1_J)). 185.47/93.66 thf(31931,plain,((! [A:num,B:num]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (numeral_numeral_int @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7111])). 185.47/93.66 thf(3543,axiom,((! [A:nat,B:nat,C:(nat > nat)]: (((plus_plus_nat @ (groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_nat @ (C @ A) @ (groups3542108847815614940at_nat @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6676_sum_OSuc__reindex__ivl)). 185.47/93.66 thf(19380,plain,((! [A:nat,B:nat,C:(nat > nat)]: (((plus_plus_nat @ (groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_nat @ (C @ A) @ (groups3542108847815614940at_nat @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3543])). 185.47/93.66 thf(150,axiom,((! [A:nat,B:rat]: ((times_times_rat @ (semiri681578069525770553at_rat @ (suc @ A)) @ (gbinomial_rat @ B @ (suc @ A))) = (times_times_rat @ B @ (gbinomial_rat @ (minus_minus_rat @ B @ one_one_rat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8537_gbinomial__absorption)). 185.47/93.66 thf(8215,plain,((! [A:nat,B:rat]: ((times_times_rat @ (semiri681578069525770553at_rat @ (suc @ A)) @ (gbinomial_rat @ B @ (suc @ A))) = (times_times_rat @ B @ (gbinomial_rat @ (minus_minus_rat @ B @ one_one_rat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 185.47/93.66 thf(4822,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (ord_less_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3373_mult__less__iff1)). 185.47/93.66 thf(23489,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (ord_less_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4822])). 185.47/93.66 thf(4106,axiom,((! [A:real,B:nat,C:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_power__strict__increasing__iff)). 185.47/93.66 thf(21159,plain,((! [A:real,B:nat,C:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4106])). 185.47/93.66 thf(1705,axiom,(((plus_plus_rat @ one_one_rat @ (uminus_uminus_rat @ one_one_rat)) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5279_add__neg__numeral__special_I7_J)). 185.47/93.66 thf(13444,plain,(((plus_plus_rat @ one_one_rat @ (uminus_uminus_rat @ one_one_rat)) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1705])). 185.47/93.66 thf(7139,axiom,((! [A:nat]: ((modulo_modulo_nat @ A @ one_one_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1760_bits__mod__by__1)). 185.47/93.66 thf(32034,plain,((! [A:nat]: ((modulo_modulo_nat @ A @ one_one_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7139])). 185.47/93.66 thf(5931,axiom,((! [A:complex,B:complex]: ((A = (times_times_complex @ B @ A)) = ((B = one_one_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1669_mult__cancel__right1)). 185.47/93.66 thf(27634,plain,((! [A:complex,B:complex]: ((A = (times_times_complex @ B @ A)) = ((B = one_one_complex) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5931])). 185.47/93.66 thf(3634,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ B) => (((ord_less_eq_real @ zero_zero_real @ E) => ((ord_less_real @ (plus_plus_real @ (times_times_real @ D @ A) @ (times_times_real @ E @ C)) @ B) <= ((plus_plus_real @ D @ E) = one_one_real))) <= (ord_less_eq_real @ zero_zero_real @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2920_convex__bound__lt)). 185.47/93.66 thf(19662,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ B) => (((ord_less_eq_real @ zero_zero_real @ E) => ((ord_less_real @ (plus_plus_real @ (times_times_real @ D @ A) @ (times_times_real @ E @ C)) @ B) | ~ ((plus_plus_real @ D @ E) = one_one_real))) | ~ (ord_less_eq_real @ zero_zero_real @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3634])). 185.47/93.66 thf(7287,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = ((B = zero_zero_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1491_mult__eq__0__iff)). 185.47/93.66 thf(32547,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = ((B = zero_zero_complex) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7287])). 185.47/93.66 thf(2931,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (plus_plus_real @ (times_times_real @ B @ A) @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2733_add__divide__eq__iff)). 185.47/93.66 thf(17454,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (plus_plus_real @ (times_times_real @ B @ A) @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2931])). 185.47/93.66 thf(5886,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_power__add)). 185.47/93.66 thf(27486,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5886])). 185.47/93.66 thf(414,axiom,((! [A:complex]: (((((im @ A) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ (re @ A))) | (ord_less_real @ (im @ A) @ zero_zero_real)) => ((csqrt @ (uminus1482373934393186551omplex @ A)) = (times_times_complex @ imaginary_unit @ (csqrt @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9668_csqrt__minus)). 185.47/93.66 thf(9107,plain,((! [A:complex]: (((((im @ A) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ (re @ A))) | (ord_less_real @ (im @ A) @ zero_zero_real)) => ((csqrt @ (uminus1482373934393186551omplex @ A)) = (times_times_complex @ imaginary_unit @ (csqrt @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[414])). 185.47/93.66 thf(3728,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ one_one_rat @ (divide_divide_rat @ B @ A)) = (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1862_le__divide__eq__1__pos)). 185.47/93.66 thf(19972,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ one_one_rat @ (divide_divide_rat @ B @ A)) = (ord_less_eq_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3728])). 185.47/93.66 thf(186,axiom,((! [A:complex,B:nat]: ((gbinomial_complex @ (plus_plus_complex @ A @ one_one_complex) @ (suc @ B)) = (plus_plus_complex @ (gbinomial_complex @ A @ B) @ (gbinomial_complex @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8460_gbinomial__Suc__Suc)). 185.47/93.66 thf(8333,plain,((! [A:complex,B:nat]: ((gbinomial_complex @ (plus_plus_complex @ A @ one_one_complex) @ (suc @ B)) = (plus_plus_complex @ (gbinomial_complex @ A @ B) @ (gbinomial_complex @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 185.47/93.66 thf(4380,axiom,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (uminus_uminus_rat @ A)) = (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5161_neg__0__less__iff__less)). 185.47/93.66 thf(22032,plain,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (uminus_uminus_rat @ A)) = (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4380])). 185.47/93.66 thf(1942,axiom,((! [A:int,B:int]: (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))) @ (abs_abs_int @ (minus_minus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6501_abs__triangle__ineq3)). 185.47/93.66 thf(14231,plain,((! [A:int,B:int]: (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))) @ (abs_abs_int @ (minus_minus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1942])). 185.47/93.66 thf(5995,axiom,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) <= ((vEBT_vebt_mint @ A) = none_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_952_minminNull)). 185.47/93.66 thf(27877,plain,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) | ~ ((vEBT_vebt_mint @ A) = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5995])). 185.47/93.66 thf(4642,axiom,((! [A:nat]: (ord_less_eq_int @ one_one_int @ (semiri1406184849735516958ct_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7997_fact__ge__1)). 185.47/93.66 thf(22871,plain,((! [A:nat]: (ord_less_eq_int @ one_one_int @ (semiri1406184849735516958ct_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4642])). 185.47/93.66 thf(3166,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ A) = B) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1685_nonzero__mult__div__cancel__left)). 185.47/93.66 thf(18196,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ A) = B) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3166])). 185.47/93.66 thf(5495,axiom,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4503_triangle__Suc)). 185.47/93.66 thf(26032,plain,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5495])). 185.47/93.66 thf(1530,axiom,((! [A:int,B:nat,C:nat]: ((modulo_modulo_int @ (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ C)) = (divide_divide_int @ (modulo_modulo_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ B @ C))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2971_div__exp__mod__exp__eq)). 185.47/93.66 thf(12808,plain,((! [A:int,B:nat,C:nat]: ((modulo_modulo_int @ (divide_divide_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ C)) = (divide_divide_int @ (modulo_modulo_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ B @ C))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530])). 185.47/93.66 thf(870,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ln_ln_real @ (sqrt @ A)) = (divide_divide_real @ (ln_ln_real @ A) @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8245_ln__sqrt)). 185.47/93.66 thf(10703,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ln_ln_real @ (sqrt @ A)) = (divide_divide_real @ (ln_ln_real @ A) @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[870])). 185.47/93.66 thf(183,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (minus_minus_set_nat @ B @ C)) = ((member_nat @ A @ B) & ~ (member_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1296_Diff__iff)). 185.47/93.66 thf(8322,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (minus_minus_set_nat @ B @ C)) = ((member_nat @ A @ B) & ~ (member_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 185.47/93.66 thf(828,axiom,((! [A:real,B:real]: (((ord_less_real @ A @ B) => ((ord_less_real @ (cos_real @ B) @ (cos_real @ A)) <= (ord_less_eq_real @ B @ pi))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7866_cos__monotone__0__pi)). 185.47/93.66 thf(10556,plain,((! [A:real,B:real]: (((ord_less_real @ A @ B) => ((ord_less_real @ (cos_real @ B) @ (cos_real @ A)) | ~ (ord_less_eq_real @ B @ pi))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[828])). 185.47/93.66 thf(4544,axiom,((! [A:rat,B:rat,C:(rat > rat),D:rat]: (((ord_less_eq_rat @ (C @ B) @ D) => ((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_rat @ (C @ E) @ (C @ F)))) => (ord_less_rat @ (C @ A) @ D))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4357_order__less__le__subst2)). 185.47/93.66 thf(22555,plain,((! [A:rat,B:rat,C:(rat > rat),D:rat]: (((ord_less_eq_rat @ (C @ B) @ D) => ((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_rat @ (C @ E) @ (C @ F)))) => (ord_less_rat @ (C @ A) @ D))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4544])). 185.47/93.66 thf(7271,axiom,((~ (dvd_dvd_nat @ zero_zero_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4701_not__is__unit__0)). 185.47/93.66 thf(32500,plain,((~ (dvd_dvd_nat @ zero_zero_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7271])). 185.47/93.66 thf(1370,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((modulo_modulo_int @ B @ (times_times_int @ C @ A)) = (plus_plus_int @ (times_times_int @ C @ (modulo_modulo_int @ (divide_divide_int @ B @ C) @ A)) @ (modulo_modulo_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2136_unique__euclidean__semiring__numeral__class_Omod__mult2__eq)). 185.47/93.66 thf(12295,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((modulo_modulo_int @ B @ (times_times_int @ C @ A)) = (plus_plus_int @ (times_times_int @ C @ (modulo_modulo_int @ (divide_divide_int @ B @ C) @ A)) @ (modulo_modulo_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370])). 185.47/93.66 thf(393,axiom,((! [A:int,B:int]: ((if_int @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Int__Oint_T)). 185.47/93.66 thf(9040,plain,((! [A:int,B:int]: ((if_int @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[393])). 185.47/93.66 thf(1112,axiom,((! [A:int,B:int,C:nat]: ((ord_less_int @ A @ B) => ((ord_less_int @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ A) @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ B)) <= (ord_less_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7310_zmult__zless__mono2__lemma)). 185.47/93.66 thf(11506,plain,((! [A:int,B:int,C:nat]: ((ord_less_int @ A @ B) => ((ord_less_int @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ A) @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112])). 185.47/93.66 thf(6637,axiom,((! [A:num,B:num]: ((times_times_num @ A @ (inc @ B)) = (plus_plus_num @ (times_times_num @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9386_mult__inc)). 185.47/93.66 thf(30124,plain,((! [A:num,B:num]: ((times_times_num @ A @ (inc @ B)) = (plus_plus_num @ (times_times_num @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6637])). 185.47/93.66 thf(6994,axiom,((! [A:num]: (((uminus_uminus_int @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ A))) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5292_neg__one__eq__numeral__iff)). 185.47/93.66 thf(31533,plain,((! [A:num]: (((uminus_uminus_int @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ A))) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6994])). 185.47/93.66 thf(2070,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ B @ C) @ (times_times_real @ A @ C))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2363_mult__strict__right__mono__neg)). 185.47/93.66 thf(14638,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ B @ C) @ (times_times_real @ A @ C))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2070])). 185.47/93.66 thf(907,axiom,((! [A:real,B:real]: ((if_real @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Real__Oreal_T)). 185.47/93.66 thf(10840,plain,((! [A:real,B:real]: ((if_real @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[907])). 185.47/93.66 thf(2128,axiom,((! [A:num,B:num]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (uminus_uminus_real @ (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5187_add__neg__numeral__simps_I3_J)). 185.47/93.66 thf(14816,plain,((! [A:num,B:num]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (uminus_uminus_real @ (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2128])). 185.47/93.66 thf(6006,axiom,((! [A:complex]: ((one_one_complex = A) = (A = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_one__reorient)). 185.47/93.66 thf(27917,plain,((! [A:complex]: ((one_one_complex = A) = (A = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6006])). 185.47/93.66 thf(7405,axiom,((! [A:num]: ~ (ord_less_eq_num @ (bit1 @ A) @ one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6394_semiring__norm_I70_J)). 185.47/93.66 thf(32939,plain,((! [A:num]: ~ (ord_less_eq_num @ (bit1 @ A) @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7405])). 185.47/93.66 thf(1173,axiom,((((=) @ int) = (^ [A:int,B:int]: (((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) & ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4911_bit__eq__rec)). 185.47/93.66 thf(11692,plain,((((=) @ int) = (^ [A:int,B:int]: (((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) & ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173])). 185.47/93.66 thf(1547,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ (cos_complex @ A) @ (cos_complex @ B)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sin_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (sin_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ B @ A) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7858_cos__diff__cos)). 185.47/93.66 thf(12857,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ (cos_complex @ A) @ (cos_complex @ B)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sin_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (sin_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ B @ A) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547])). 185.47/93.66 thf(6651,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_le__cube)). 185.47/93.66 thf(30172,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6651])). 185.47/93.66 thf(4321,axiom,((! [A:rat]: ? [B:int]: (ord_less_rat @ A @ (ring_1_of_int_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7441_ex__less__of__int)). 185.47/93.66 thf(21845,plain,((! [A:rat]: ? [B:int]: (ord_less_rat @ A @ (ring_1_of_int_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4321])). 185.47/93.66 thf(2367,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) => ((ord_less_real @ A @ C) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2586_mult__right__less__imp__less)). 185.47/93.66 thf(15567,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) => ((ord_less_real @ A @ C) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2367])). 185.47/93.66 thf(3232,axiom,((! [A:int,B:int]: (((ord_less_int @ A @ B) <= (ord_less_eq_int @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4308_order__neq__le__trans)). 185.47/93.66 thf(18403,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) | ~ (ord_less_eq_int @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3232])). 185.47/93.66 thf(3042,axiom,((! [A:nat,B:(nat > nat),C:set_nat]: ((times_times_nat @ A @ (groups3542108847815614940at_nat @ B @ C)) = (groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5617_sum__distrib__left)). 185.47/93.66 thf(17806,plain,((! [A:nat,B:(nat > nat),C:set_nat]: ((times_times_nat @ A @ (groups3542108847815614940at_nat @ (B) @ C)) = (groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3042])). 185.47/93.66 thf(5851,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ (modulo_modulo_nat @ A @ B) @ B) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1763_bits__mod__div__trivial)). 185.47/93.66 thf(27368,plain,((! [A:nat,B:nat]: ((divide_divide_nat @ (modulo_modulo_nat @ A @ B) @ B) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5851])). 185.47/93.66 thf(833,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((((minus_minus_set_nat @ B @ (minus_minus_set_nat @ C @ A)) = A) <= (ord_less_eq_set_nat @ B @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1414_double__diff)). 185.47/93.66 thf(10571,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((minus_minus_set_nat @ B @ (minus_minus_set_nat @ C @ A)) = A) | ~ (ord_less_eq_set_nat @ B @ C) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[833])). 185.47/93.66 thf(3470,axiom,(((cos_coeff @ zero_zero_nat) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7648_cos__coeff__0)). 185.47/93.66 thf(19154,plain,(((cos_coeff @ zero_zero_nat) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3470])). 185.47/93.66 thf(3756,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8242_sqrt__sum__squares__le__sum__abs)). 185.47/93.66 thf(20060,plain,((! [A:real,B:real]: (ord_less_eq_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3756])). 185.47/93.66 thf(3185,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2231_mult__right__mono)). 185.47/93.66 thf(18255,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3185])). 185.47/93.66 thf(1192,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ one_one_real) => (((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (times_times_real @ A @ B) @ one_one_real)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2665_mult__le__one)). 185.47/93.66 thf(11747,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ one_one_real) => (((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (times_times_real @ A @ B) @ one_one_real)) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192])). 185.47/93.66 thf(7441,axiom,((! [A:num]: ~ (ord_less_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2265_not__numeral__less__zero)). 185.47/93.66 thf(33071,plain,((! [A:num]: ~ (ord_less_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7441])). 185.47/93.66 thf(7619,axiom,((! [A:num]: ((bit_or_not_num_neg @ (bit0 @ A) @ one) = (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9463_or__not__num__neg_Osimps_I4_J)). 185.47/93.66 thf(33622,plain,((! [A:num]: ((bit_or_not_num_neg @ (bit0 @ A) @ one) = (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7619])). 185.47/93.66 thf(1330,axiom,((! [A:nat]: ((one_one_int = (semiri1314217659103216013at_int @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6924_of__nat__1__eq__iff)). 185.47/93.66 thf(12168,plain,((! [A:nat]: ((one_one_int = (semiri1314217659103216013at_int @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330])). 185.47/93.66 thf(962,axiom,((! [A:set_nat,B:(nat > real)]: ((((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (B @ C) @ (power_power_real @ zero_zero_real @ C))) @ A) = zero_zero_real) <= (~ ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A)))) & (((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (B @ C) @ (power_power_real @ zero_zero_real @ C))) @ A) = (B @ zero_zero_nat)) <= ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6436_sum__zero__power)). 185.47/93.66 thf(11033,plain,((! [A:set_nat,B:(nat > real)]: ((((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (B @ C) @ (power_power_real @ zero_zero_real @ C))) @ A) = zero_zero_real) | ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A))) & (((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (B @ C) @ (power_power_real @ zero_zero_real @ C))) @ A) = (B @ zero_zero_nat)) | ~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[962])). 185.47/93.66 thf(278,axiom,((! [A:num,B:nat,C:int]: ((ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7173_neg__numeral__power__less__of__int__cancel__iff)). 185.47/93.66 thf(8641,plain,((! [A:num,B:nat,C:int]: ((ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 185.47/93.66 thf(6722,axiom,((power_power_int = (^ [A:int,B:nat]: (if_int @ (B = zero_zero_nat) @ one_one_int @ (times_times_int @ A @ (power_power_int @ A @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2962_power__eq__if)). 185.47/93.66 thf(30420,plain,(((power_power_int) = (^ [A:int,B:nat]: (if_int @ (B = zero_zero_nat) @ one_one_int @ (times_times_int @ A @ (power_power_int @ A @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6722])). 185.47/93.66 thf(4585,axiom,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2266_not__numeral__less__zero)). 185.47/93.66 thf(22686,plain,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4585])). 185.47/93.66 thf(2524,axiom,((! [A:real,B:real]: ((dvd_dvd_real @ A @ B) => (~ (! [C:real]: (B != (times_times_real @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4621_dvdE)). 185.47/93.66 thf(16100,plain,((! [A:real,B:real]: ((dvd_dvd_real @ A @ B) => (~ (! [C:real]: ~ (B = (times_times_real @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2524])). 185.47/93.66 thf(4025,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ A @ C)) <= (ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2608_mult__right__le__imp__le)). 185.47/93.66 thf(20918,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ A @ C)) | ~ (ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4025])). 185.47/93.66 thf(5648,axiom,(((nat2 @ (numeral_numeral_int @ (bit0 @ one))) = (suc @ (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9328_nat__2)). 185.47/93.66 thf(26528,plain,(((nat2 @ (numeral_numeral_int @ (bit0 @ one))) = (suc @ (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5648])). 185.47/93.66 thf(1670,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) <= (ord_less_int @ zero_zero_int @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2359_mult__strict__left__mono)). 185.47/93.66 thf(13331,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) | ~ (ord_less_int @ zero_zero_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670])). 185.47/93.66 thf(111,axiom,((! [A:num]: ~ (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5962_not__neg__one__less__neg__numeral)). 185.47/93.66 thf(8095,plain,((! [A:num]: ~ (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 185.47/93.66 thf(7202,axiom,((! [A:complex,B:complex]: (((A != zero_zero_complex) & (B != zero_zero_complex)) <= ((times_times_complex @ A @ B) != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2043_mult__not__zero)). 185.47/93.66 thf(32255,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex) & ~ (B = zero_zero_complex)) | ((times_times_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7202])). 185.47/93.66 thf(5212,axiom,((! [A:int,B:num,C:nat]: (((ring_17405671764205052669omplex @ A) = (power_power_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7154_of__int__eq__neg__numeral__power__cancel__iff)). 185.47/93.66 thf(24910,plain,((! [A:int,B:num,C:nat]: (((ring_17405671764205052669omplex @ A) = (power_power_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) @ C)) = (A = (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5212])). 185.47/93.66 thf(2165,axiom,((! [A:complex]: ((minus_minus_complex @ (times_times_complex @ A @ A) @ one_one_complex) = (times_times_complex @ (plus_plus_complex @ A @ one_one_complex) @ (minus_minus_complex @ A @ one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1240_square__diff__one__factored)). 185.47/93.66 thf(14946,plain,((! [A:complex]: ((minus_minus_complex @ (times_times_complex @ A @ A) @ one_one_complex) = (times_times_complex @ (plus_plus_complex @ A @ one_one_complex) @ (minus_minus_complex @ A @ one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2165])). 185.47/93.66 thf(41,axiom,((! [A:real,B:real,C:nat]: (((minus_minus_real @ (divide_divide_real @ (minus_minus_real @ (power_power_real @ (plus_plus_real @ B @ A) @ C) @ (power_power_real @ B @ C)) @ A) @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ (power_power_real @ B @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))) = (times_times_real @ A @ (groups6591440286371151544t_real @ (^ [D:nat]: (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (power_power_real @ (plus_plus_real @ B @ A) @ E) @ (power_power_real @ B @ (minus_minus_nat @ (minus_minus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ E)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat)) @ D)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat)))))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7534_lemma__termdiff2)). 185.47/93.66 thf(7866,plain,((! [A:real,B:real,C:nat]: (((minus_minus_real @ (divide_divide_real @ (minus_minus_real @ (power_power_real @ (plus_plus_real @ B @ A) @ C) @ (power_power_real @ B @ C)) @ A) @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ (power_power_real @ B @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))) = (times_times_real @ A @ (groups6591440286371151544t_real @ (^ [D:nat]: (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (power_power_real @ (plus_plus_real @ B @ A) @ E) @ (power_power_real @ B @ (minus_minus_nat @ (minus_minus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ E)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat)) @ D)))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ C @ (suc @ zero_zero_nat)))))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 185.47/93.66 thf(2382,axiom,((! [A:num]: ((archim7778729529865785530nd_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7546_round__numeral)). 185.47/93.66 thf(15614,plain,((! [A:num]: ((archim7778729529865785530nd_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2382])). 185.47/93.66 thf(6136,axiom,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ A @ B) => (~ (ord_less_eq_num @ B @ C))) => (((~ (ord_less_eq_num @ A @ C)) <= (ord_less_eq_num @ B @ A)) => ((((ord_less_eq_num @ C @ B) => (~ (ord_less_eq_num @ B @ A))) => ((~ ((~ (ord_less_eq_num @ A @ B)) <= (ord_less_eq_num @ C @ A))) <= ((ord_less_eq_num @ B @ C) => (~ (ord_less_eq_num @ C @ A))))) <= ((~ (ord_less_eq_num @ C @ B)) <= (ord_less_eq_num @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3847_le__cases3)). 185.47/93.66 thf(28331,plain,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ A @ B) => (~ (ord_less_eq_num @ B @ C))) => ((~ (ord_less_eq_num @ A @ C) | ~ (ord_less_eq_num @ B @ A)) => ((((ord_less_eq_num @ C @ B) => (~ (ord_less_eq_num @ B @ A))) => (~ (~ (ord_less_eq_num @ A @ B) | ~ (ord_less_eq_num @ C @ A)) | ~ ((ord_less_eq_num @ B @ C) => (~ (ord_less_eq_num @ C @ A))))) | ~ (~ (ord_less_eq_num @ C @ B) | ~ (ord_less_eq_num @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6136])). 185.47/93.66 thf(6282,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (minus_minus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4562_odd__two__times__div__two__nat)). 185.47/93.66 thf(28871,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (minus_minus_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6282])). 185.47/93.66 thf(5367,axiom,((! [A:nat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ B @ A)) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4975_zero__le__even__power)). 185.47/93.66 thf(25498,plain,((! [A:nat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ B @ A)) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5367])). 185.47/93.66 thf(5766,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4010_dual__order_Oasym)). 185.47/93.66 thf(26910,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5766])). 185.47/93.66 thf(1868,axiom,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) = (B = (uminus1482373934393186551omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5725_add__eq__0__iff)). 185.47/93.66 thf(13989,plain,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) = (B = (uminus1482373934393186551omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1868])). 185.47/93.66 thf(5566,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_add_Ocommute)). 185.47/93.66 thf(26259,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5566])). 185.47/93.66 thf(7473,axiom,((! [A:nat,B:int]: (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_int @ (uminus_uminus_int @ B) @ A) = (uminus_uminus_int @ (power_power_int @ B @ A)))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_int @ (uminus_uminus_int @ B) @ A) = (power_power_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6185_uminus__power__if)). 185.47/93.66 thf(33186,plain,((! [A:nat,B:int]: (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_int @ (uminus_uminus_int @ B) @ A) = (uminus_uminus_int @ (power_power_int @ B @ A)))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_int @ (uminus_uminus_int @ B) @ A) = (power_power_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7473])). 185.47/93.66 thf(7092,axiom,((! [A:num]: ((bit1 @ A) != one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6330_semiring__norm_I86_J)). 185.47/93.66 thf(31874,plain,((! [A:num]: ~ ((bit1 @ A) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7092])). 185.47/93.66 thf(6005,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ A @ C) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1792_mult__less__cancel2)). 185.47/93.66 thf(27914,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ A @ C) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6005])). 185.47/93.66 thf(5260,axiom,((! [A:nat]: ((power_power_rat @ zero_zero_rat @ (suc @ A)) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1741_power__0__Suc)). 185.47/93.66 thf(25085,plain,((! [A:nat]: ((power_power_rat @ zero_zero_rat @ (suc @ A)) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5260])). 185.47/93.66 thf(2401,axiom,((! [A:int,B:int]: (((plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1679_sum__squares__eq__zero__iff)). 185.47/93.66 thf(15675,plain,((! [A:int,B:int]: (((plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2401])). 185.47/93.66 thf(7132,axiom,((! [A:nat]: ((groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) = (divide_divide_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7355_gauss__sum)). 185.47/93.66 thf(32014,plain,((! [A:nat]: ((groups3542108847815614940at_nat @ (semiri1316708129612266289at_nat) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) = (divide_divide_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7132])). 185.47/93.66 thf(5401,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ A) @ B @ C) = ((vEBT_vebt_member @ A @ C) & (ord_less_nat @ C @ B) & ! [D:nat]: (((ord_less_nat @ D @ B) & (vEBT_vebt_member @ A @ D)) => (ord_less_eq_nat @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_pred__member)). 185.47/93.66 thf(25598,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ A) @ B @ C) = ((vEBT_vebt_member @ A @ C) & (ord_less_nat @ C @ B) & ! [D:nat]: (((ord_less_nat @ D @ B) & (vEBT_vebt_member @ A @ D)) => (ord_less_eq_nat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5401])). 185.47/93.66 thf(3355,axiom,((! [A:nat,B:int,C:int]: ((ord_less_nat @ zero_zero_nat @ A) => ((dvd_dvd_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) = (dvd_dvd_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4514_pow__divides__pow__iff)). 185.47/93.66 thf(18787,plain,((! [A:nat,B:int,C:int]: ((ord_less_nat @ zero_zero_nat @ A) => ((dvd_dvd_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) = (dvd_dvd_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3355])). 185.47/93.66 thf(3657,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ C @ D) => (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_add__mono)). 185.47/93.66 thf(19740,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ C @ D) => (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3657])). 185.47/93.66 thf(4915,axiom,((! [A:rat,B:rat,C:rat]: ((((minus_minus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (minus_minus_rat @ B @ (times_times_rat @ C @ A)) @ A)) <= (A != zero_zero_rat)) & ((A = zero_zero_rat) => ((minus_minus_rat @ (divide_divide_rat @ B @ A) @ C) = (uminus_uminus_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6173_add__divide__eq__if__simps_I5_J)). 185.47/93.66 thf(23807,plain,((! [A:rat,B:rat,C:rat]: ((((minus_minus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (minus_minus_rat @ B @ (times_times_rat @ C @ A)) @ A)) | (A = zero_zero_rat)) & ((A = zero_zero_rat) => ((minus_minus_rat @ (divide_divide_rat @ B @ A) @ C) = (uminus_uminus_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4915])). 185.47/93.66 thf(4782,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => (((ord_less_real @ (sin_real @ A) @ (sin_real @ B)) <= (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7925_sin__monotone__2pi)). 185.47/93.66 thf(23365,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_real @ (sin_real @ A) @ (sin_real @ B)) | ~ (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4782])). 185.47/93.66 thf(1949,axiom,((! [A:real,B:real,C:real]: (((B = (divide_divide_real @ C @ A)) = ((times_times_real @ B @ A) = C)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2459_nonzero__eq__divide__eq)). 185.47/93.66 thf(14254,plain,((! [A:real,B:real,C:real]: (((B = (divide_divide_real @ C @ A)) = ((times_times_real @ B @ A) = C)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949])). 185.47/93.66 thf(5344,axiom,((bit_se547839408752420682it_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9537_push__bit__nat__def)). 185.47/93.66 thf(25388,plain,(((bit_se547839408752420682it_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5344])). 185.47/93.66 thf(3251,axiom,((! [A:real]: ((summable_real @ (^ [B:nat]: (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (times_times_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))) @ (power_power_real @ A @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))))) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7646_summable__arctan__series)). 185.47/93.66 thf(18455,plain,((! [A:real]: ((summable_real @ (^ [B:nat]: (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (times_times_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))) @ (power_power_real @ A @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))))) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3251])). 185.47/93.66 thf(7028,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3983_order_Oasym)). 185.47/93.66 thf(31673,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7028])). 185.47/93.66 thf(7528,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) != (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1259_double__not__eq__Suc__double)). 185.47/93.66 thf(33375,plain,((! [A:nat,B:nat]: ~ ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7528])). 185.47/93.66 thf(441,axiom,((! [A:int,B:int]: (((divide_divide_int @ B @ A) = (times_times_int @ (times_times_int @ (sgn_sgn_int @ B) @ (sgn_sgn_int @ A)) @ (divide_divide_int @ (abs_abs_int @ B) @ (abs_abs_int @ A)))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9227_div__dvd__sgn__abs)). 185.47/93.66 thf(9203,plain,((! [A:int,B:int]: (((divide_divide_int @ B @ A) = (times_times_int @ (times_times_int @ (sgn_sgn_int @ B) @ (sgn_sgn_int @ A)) @ (divide_divide_int @ (abs_abs_int @ B) @ (abs_abs_int @ A)))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])). 185.47/93.66 thf(6160,axiom,((! [A:rat]: ((times_times_rat @ A @ zero_zero_rat) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1488_mult__zero__right)). 185.47/93.66 thf(28462,plain,((! [A:rat]: ((times_times_rat @ A @ zero_zero_rat) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6160])). 185.47/93.66 thf(3644,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ A @ B) & (ord_less_eq_rat @ C @ D)) => (ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_add__mono__thms__linordered__field_I3_J)). 185.47/93.66 thf(19699,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ A @ B) & (ord_less_eq_rat @ C @ D)) => (ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3644])). 185.47/93.66 thf(594,axiom,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A)) <= (ord_le6747313008572928689nteger @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5529_verit__negate__coefficient_I2_J)). 185.47/93.66 thf(9709,plain,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A)) | ~ (ord_le6747313008572928689nteger @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[594])). 185.47/93.66 thf(3283,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) = (((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ zero_zero_rat @ B)) | ((ord_less_rat @ B @ zero_zero_rat) & (ord_less_rat @ A @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2440_zero__less__divide__iff)). 185.47/93.66 thf(18553,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) = (((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ zero_zero_rat @ B)) | ((ord_less_rat @ B @ zero_zero_rat) & (ord_less_rat @ A @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3283])). 185.47/93.66 thf(4949,axiom,((! [A:nat]: (ord_less_eq_nat @ (suc @ zero_zero_nat) @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8098_fact__ge__Suc__0__nat)). 185.47/93.66 thf(23938,plain,((! [A:nat]: (ord_less_eq_nat @ (suc @ zero_zero_nat) @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4949])). 185.47/93.66 thf(3608,axiom,((bit_se1412395901928357646or_nat = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ B @ (if_nat @ (B = zero_zero_nat) @ A @ (plus_plus_nat @ (ord_max_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9484_or__nat__unfold)). 185.47/93.66 thf(19583,plain,(((bit_se1412395901928357646or_nat) = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ B @ (if_nat @ (B = zero_zero_nat) @ A @ (plus_plus_nat @ (ord_max_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3608])). 185.47/93.66 thf(556,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (tanh_real @ A) @ (tanh_real @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6356_tanh__real__le__iff)). 185.47/93.66 thf(9577,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (tanh_real @ A) @ (tanh_real @ B)) = (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[556])). 185.47/93.66 thf(1480,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((A = B) | (ord_less_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4371_order__le__imp__less__or__eq)). 185.47/93.66 thf(12660,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((A = B) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480])). 185.47/93.66 thf(5049,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((B != zero_zero_nat) => ((times_times_nat @ A @ B) != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2056_no__zero__divisors)). 185.47/93.66 thf(24326,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((~ (B = zero_zero_nat)) => (~ ((times_times_nat @ A @ B) = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5049])). 185.47/93.66 thf(689,axiom,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ A @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8692_sum_OatMost__Suc)). 185.47/93.66 thf(10030,plain,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[689])). 185.47/93.66 thf(6886,axiom,((vEBT_VEBT_bit_concat = (^ [A:nat,B:nat,C:nat]: (plus_plus_nat @ (times_times_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_bit__concat__def)). 185.47/93.66 thf(31087,plain,(((vEBT_VEBT_bit_concat) = (^ [A:nat,B:nat,C:nat]: (plus_plus_nat @ (times_times_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6886])). 185.47/93.66 thf(1840,axiom,((! [A:(int > $o),B:int]: (((A @ B) <= (! [C:int,D:$o]: ((A @ C) => (((divide_divide_int @ (plus_plus_int @ (zero_n2684676970156552555ol_int @ D) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ C)) @ (numeral_numeral_int @ (bit0 @ one))) = C) => (A @ (plus_plus_int @ (zero_n2684676970156552555ol_int @ D) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ C))))))) <= (! [C:int]: ((A @ C) <= ((divide_divide_int @ C @ (numeral_numeral_int @ (bit0 @ one))) = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6258_bits__induct)). 185.47/93.66 thf(13896,plain,((! [A:(int > $o),B:int]: ((A @ B) | ~ (! [C:int,D:$o]: ((A @ C) => (((divide_divide_int @ (plus_plus_int @ (zero_n2684676970156552555ol_int @ D) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ C)) @ (numeral_numeral_int @ (bit0 @ one))) = C) => (A @ (plus_plus_int @ (zero_n2684676970156552555ol_int @ D) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ C)))))) | ~ (! [C:int]: ((A @ C) | ~ ((divide_divide_int @ C @ (numeral_numeral_int @ (bit0 @ one))) = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1840])). 185.47/93.66 thf(31,axiom,((! [A:(nat > real),B:nat,C:real]: ((sums_real @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ B))) @ C) = (sums_real @ A @ (plus_plus_real @ C @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8209_sums__iff__shift)). 185.47/93.66 thf(7831,plain,((! [A:(nat > real),B:nat,C:real]: ((sums_real @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ B))) @ C) = (sums_real @ (A) @ (plus_plus_real @ C @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 185.47/93.66 thf(4846,axiom,((! [A:int,B:int]: (ord_less_eq_real @ (ring_1_of_int_real @ (divide_divide_int @ A @ B)) @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7267_real__of__int__div4)). 185.47/93.66 thf(23566,plain,((! [A:int,B:int]: (ord_less_eq_real @ (ring_1_of_int_real @ (divide_divide_int @ A @ B)) @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4846])). 185.47/93.66 thf(5583,axiom,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit1 @ B)) = (bit1 @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6387_semiring__norm_I7_J)). 185.47/93.66 thf(26310,plain,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit1 @ B)) = (bit1 @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5583])). 185.47/93.66 thf(5525,axiom,((! [A:rat]: ((zero_zero_rat = A) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1927_zero__reorient)). 185.47/93.66 thf(26127,plain,((! [A:rat]: ((zero_zero_rat = A) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5525])). 185.47/93.66 thf(1052,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ (minus_minus_rat @ C @ B)) <= (ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1200_add__le__imp__le__diff)). 185.47/93.66 thf(11311,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ (minus_minus_rat @ C @ B)) | ~ (ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052])). 185.47/93.66 thf(6366,axiom,((bit_se2002935070580805687sk_nat = (^ [A:nat]: (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9232_mask__nat__def)). 185.47/93.66 thf(29166,plain,(((bit_se2002935070580805687sk_nat) = (^ [A:nat]: (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6366])). 185.47/93.66 thf(2574,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A != zero_zero_nat) => (ord_less_eq_rat @ (divide_divide_rat @ one_one_rat @ (semiri681578069525770553at_rat @ B)) @ (divide_divide_rat @ one_one_rat @ (semiri681578069525770553at_rat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7323_inverse__of__nat__le)). 185.47/93.66 thf(16260,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (A = zero_zero_nat)) => (ord_less_eq_rat @ (divide_divide_rat @ one_one_rat @ (semiri681578069525770553at_rat @ B)) @ (divide_divide_rat @ one_one_rat @ (semiri681578069525770553at_rat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2574])). 185.47/93.66 thf(4282,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_int @ (semiri1314217659103216013at_int @ A) @ B) = (semiri1314217659103216013at_int @ C)) = ((power_power_nat @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6953_of__nat__eq__of__nat__power__cancel__iff)). 185.47/93.66 thf(21692,plain,((! [A:nat,B:nat,C:nat]: (((power_power_int @ (semiri1314217659103216013at_int @ A) @ B) = (semiri1314217659103216013at_int @ C)) = ((power_power_nat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4282])). 185.47/93.66 thf(2644,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_int @ (groups3539618377306564664at_int @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6647_sum_OatLeast0__atMost__Suc)). 185.47/93.66 thf(16505,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_int @ (groups3539618377306564664at_int @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2644])). 185.47/93.66 thf(1189,axiom,((! [A:nat,B:nat,C:int]: (((times_times_int @ (minus_minus_int @ one_one_int @ C) @ (groups3539618377306564664at_int @ (power_power_int @ C) @ (set_or1269000886237332187st_nat @ A @ B))) = (minus_minus_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ (suc @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6747_sum__gp__multiplied)). 185.47/93.66 thf(11737,plain,((! [A:nat,B:nat,C:int]: (((times_times_int @ (minus_minus_int @ one_one_int @ C) @ (groups3539618377306564664at_int @ (power_power_int @ C) @ (set_or1269000886237332187st_nat @ A @ B))) = (minus_minus_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ (suc @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189])). 185.47/93.66 thf(6378,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7209_of__nat__0__le__iff)). 185.47/93.66 thf(29208,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6378])). 185.47/93.66 thf(2442,axiom,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7272_int__ops_I4_J)). 185.47/93.66 thf(15820,plain,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2442])). 185.47/93.66 thf(1059,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => (! [D:int,E:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ D @ C)) = (dvd_dvd_int @ A @ (plus_plus_int @ (minus_minus_int @ D @ (times_times_int @ E @ B)) @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4854_inf__period_I3_J)). 185.47/93.66 thf(11332,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => (! [D:int,E:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ D @ C)) = (dvd_dvd_int @ A @ (plus_plus_int @ (minus_minus_int @ D @ (times_times_int @ E @ B)) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059])). 185.47/93.66 thf(2064,axiom,((! [A:rat,B:rat]: (((abs_abs_rat @ A) = B) = (((A = (uminus_uminus_rat @ B)) | (A = B)) & (ord_less_eq_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6556_abs__eq__iff_H)). 185.47/93.66 thf(14620,plain,((! [A:rat,B:rat]: (((abs_abs_rat @ A) = B) = (((A = (uminus_uminus_rat @ B)) | (A = B)) & (ord_less_eq_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2064])). 185.47/93.66 thf(7513,axiom,((! [A:num]: ((ord_less_real @ one_one_real @ (numeral_numeral_real @ A)) = (ord_less_num @ one @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_one__less__numeral__iff)). 185.47/93.66 thf(33323,plain,((! [A:num]: ((ord_less_real @ one_one_real @ (numeral_numeral_real @ A)) = (ord_less_num @ one @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7513])). 185.47/93.66 thf(6413,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ one_one_nat) @ (plus_plus_nat @ B @ one_one_nat)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1205_add__mono1)). 185.47/93.66 thf(29348,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ one_one_nat) @ (plus_plus_nat @ B @ one_one_nat)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6413])). 185.47/93.66 thf(418,axiom,(((arccos @ (uminus_uminus_real @ one_one_real)) = pi)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8359_arccos__minus__1)). 185.47/93.66 thf(9122,plain,(((arccos @ (uminus_uminus_real @ one_one_real)) = pi)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[418])). 185.47/93.66 thf(4401,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_5033_neg__le__iff__le)). 185.47/93.66 thf(22096,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)],[4401])). 185.47/93.66 thf(1315,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) & (ord_less_eq_real @ A @ B)) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_add__mono__thms__linordered__field_I4_J)). 185.47/93.66 thf(12119,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) & (ord_less_eq_real @ A @ B)) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315])). 185.47/93.66 thf(2608,axiom,((! [A:(nat > nat),B:nat,C:set_nat]: ((modulo_modulo_nat @ (groups3542108847815614940at_nat @ (^ [D:nat]: (modulo_modulo_nat @ (A @ D) @ B)) @ C) @ B) = (modulo_modulo_nat @ (groups3542108847815614940at_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5629_mod__sum__eq)). 185.47/93.66 thf(16390,plain,((! [A:(nat > nat),B:nat,C:set_nat]: ((modulo_modulo_nat @ (groups3542108847815614940at_nat @ (^ [D:nat]: (modulo_modulo_nat @ (A @ D) @ B)) @ C) @ B) = (modulo_modulo_nat @ (groups3542108847815614940at_nat @ (A) @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2608])). 185.47/93.66 thf(5447,axiom,((divmod_nat = (^ [A:nat,B:nat]: (product_Pair_nat_nat @ (divide_divide_nat @ A @ B) @ (modulo_modulo_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7624_divmod__nat__def)). 185.47/93.66 thf(25784,plain,(((divmod_nat) = (^ [A:nat,B:nat]: (product_Pair_nat_nat @ (divide_divide_nat @ A @ B) @ (modulo_modulo_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5447])). 185.47/93.66 thf(7301,axiom,((! [A:nat]: ((binomial @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ (times_times_nat @ A @ (minus_minus_nat @ A @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8578_choose__two)). 185.47/93.66 thf(32603,plain,((! [A:nat]: ((binomial @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ (times_times_nat @ A @ (minus_minus_nat @ A @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7301])). 185.47/93.66 thf(7564,axiom,((! [A:num]: ((divide_divide_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6658_numeral__Bit1__div__2)). 185.47/93.66 thf(33471,plain,((! [A:num]: ((divide_divide_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7564])). 185.47/93.66 thf(5071,axiom,((! [A:num]: ((plus_plus_complex @ one_one_complex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_one__plus__numeral)). 185.47/93.66 thf(24406,plain,((! [A:num]: ((plus_plus_complex @ one_one_complex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5071])). 185.47/93.66 thf(2705,axiom,((! [A:complex,B:complex,C:complex]: (((B = (times_times_complex @ C @ A)) => ((divide1717551699836669952omplex @ B @ A) = C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2467_divide__eq__imp)). 185.47/93.66 thf(16737,plain,((! [A:complex,B:complex,C:complex]: (((B = (times_times_complex @ C @ A)) => ((divide1717551699836669952omplex @ B @ A) = C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2705])). 185.47/93.66 thf(1336,axiom,((! [A:int,B:int]: ((((divide_divide_int @ B @ A) = zero_zero_int) = (B = zero_zero_int)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4843_unit__div__eq__0__iff)). 185.47/93.66 thf(12186,plain,((! [A:int,B:int]: ((((divide_divide_int @ B @ A) = zero_zero_int) = (B = zero_zero_int)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336])). 185.47/93.66 thf(5336,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1023_Suc__lessD)). 185.47/93.66 thf(25366,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5336])). 185.47/93.66 thf(3912,axiom,((! [A:int,B:int]: (((dvd_dvd_int @ B @ A) => (ord_less_eq_int @ (abs_abs_int @ B) @ (abs_abs_int @ A))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6821_dvd__imp__le__int)). 185.47/93.66 thf(20561,plain,((! [A:int,B:int]: (((dvd_dvd_int @ B @ A) => (ord_less_eq_int @ (abs_abs_int @ B) @ (abs_abs_int @ A))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3912])). 185.47/93.66 thf(998,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((((D != E) & (B = C)) => ((plus_plus_int @ B @ (times_times_int @ A @ D)) != (plus_plus_int @ C @ (times_times_int @ A @ E)))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5014_add__scale__eq__noteq)). 185.47/93.66 thf(11148,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((~ (D = E) & (B = C)) => (~ ((plus_plus_int @ B @ (times_times_int @ A @ D)) = (plus_plus_int @ C @ (times_times_int @ A @ E))))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[998])). 185.47/93.66 thf(693,axiom,(((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7799_cos__two__pi)). 185.47/93.66 thf(10043,plain,(((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[693])). 185.47/93.66 thf(561,axiom,((! [A:nat]: ((cos_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = (power_power_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7803_cos__npi)). 185.47/93.66 thf(9594,plain,((! [A:nat]: ((cos_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = (power_power_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[561])). 185.47/93.66 thf(5444,axiom,((! [A:nat]: (none_nat != (some_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1162_option_Odistinct_I1_J)). 185.47/93.66 thf(25774,plain,((! [A:nat]: ~ (none_nat = (some_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5444])). 185.47/93.66 thf(1488,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_real @ (exp_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A))) @ A) = (exp_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8218_exp__divide__power__eq)). 185.47/93.66 thf(12683,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_real @ (exp_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A))) @ A) = (exp_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488])). 185.47/93.66 thf(1964,axiom,((! [A:real,B:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ A) = (ord_less_real @ B @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1654_add__less__same__cancel1)). 185.47/93.66 thf(14303,plain,((! [A:real,B:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ A) = (ord_less_real @ B @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1964])). 185.47/93.66 thf(5375,axiom,((! [A:nat,B:complex]: ((times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5303_left__minus__one__mult__self)). 185.47/93.66 thf(25524,plain,((! [A:nat,B:complex]: ((times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5375])). 185.47/93.66 thf(1744,axiom,((! [A:nat]: ((cos_real @ (divide_divide_real @ (times_times_real @ pi @ (semiri5074537144036343181t_real @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))) @ (numeral_numeral_real @ (bit0 @ one)))) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7774_cos__pi__eq__zero)). 185.47/93.66 thf(13579,plain,((! [A:nat]: ((cos_real @ (divide_divide_real @ (times_times_real @ pi @ (semiri5074537144036343181t_real @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))) @ (numeral_numeral_real @ (bit0 @ one)))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744])). 185.47/93.66 thf(2708,axiom,((! [A:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ A) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5156_neg__less__pos)). 185.47/93.66 thf(16747,plain,((! [A:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ A) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2708])). 185.47/93.66 thf(3505,axiom,((! [A:num,B:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ (times_times_int @ (bit_ri631733984087533419it_int @ (pred_numeral @ A) @ (minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ one_one_int)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6760_signed__take__bit__numeral__minus__bit1)). 185.47/93.66 thf(19270,plain,((! [A:num,B:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ (times_times_int @ (bit_ri631733984087533419it_int @ (pred_numeral @ A) @ (minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ one_one_int)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3505])). 185.47/93.66 thf(7533,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (ord_less_nat @ (binomial @ B @ A) @ (binomial @ B @ (suc @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8545_binomial__less__binomial__Suc)). 185.47/93.66 thf(33388,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (ord_less_nat @ (binomial @ B @ A) @ (binomial @ B @ (suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7533])). 185.47/93.66 thf(5602,axiom,((! [A:code_integer]: (((power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_Code_integer) = ((A = (uminus1351360451143612070nteger @ one_one_Code_integer)) | (A = one_one_Code_integer))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6226_power2__eq__1__iff)). 185.47/93.66 thf(26370,plain,((! [A:code_integer]: (((power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_Code_integer) = ((A = (uminus1351360451143612070nteger @ one_one_Code_integer)) | (A = one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5602])). 185.47/93.66 thf(5419,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1539_add__0)). 185.47/93.66 thf(25652,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5419])). 185.47/93.66 thf(4660,axiom,((! [A:num,B:num]: ~ (ord_less_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5708_not__numeral__less__neg__numeral)). 185.47/93.66 thf(22928,plain,((! [A:num,B:num]: ~ (ord_less_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4660])). 185.47/93.66 thf(5472,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4654_dvd__add)). 185.47/93.66 thf(25947,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5472])). 185.47/93.66 thf(3504,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (times_times_real @ A @ B)) @ (times_times_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7482_norm__mult__ineq)). 185.47/93.66 thf(19268,plain,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (times_times_real @ A @ B)) @ (times_times_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3504])). 185.47/93.66 thf(117,axiom,((! [A:set_nat,B:set_nat]: ((minus_minus_set_nat @ (minus_minus_set_nat @ A @ B) @ B) = (minus_minus_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1297_Diff__idemp)). 185.47/93.66 thf(8112,plain,((! [A:set_nat,B:set_nat]: ((minus_minus_set_nat @ (minus_minus_set_nat @ A @ B) @ B) = (minus_minus_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 185.47/93.66 thf(3537,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ A @ B) <= (ord_less_int @ zero_zero_int @ B)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4883_zdvd__imp__le)). 185.47/93.66 thf(19365,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | ~ (ord_less_int @ zero_zero_int @ B) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3537])). 185.47/93.66 thf(762,axiom,((minus_minus_set_nat = (^ [A:set_nat,B:set_nat]: (collect_nat @ (^ [C:nat]: (~ (member_nat @ C @ B) & (member_nat @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1328_set__diff__eq)). 185.47/93.66 thf(10327,plain,(((minus_minus_set_nat) = (^ [A:set_nat,B:set_nat]: (collect_nat @ (^ [C:nat]: (~ (member_nat @ C @ B) & (member_nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[762])). 185.47/93.66 thf(5458,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_add__le__cancel__left)). 185.47/93.66 thf(25816,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5458])). 185.47/93.66 thf(6275,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1042_Suc__le__D)). 185.47/93.66 thf(28852,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6275])). 185.47/93.66 thf(3907,axiom,((! [A:set_nat]: ((~ (finite_finite_nat @ A)) = (! [B:nat]: ? [C:nat]: ((ord_less_nat @ B @ C) & (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7920_infinite__nat__iff__unbounded)). 185.47/93.66 thf(20546,plain,((! [A:set_nat]: ((~ (finite_finite_nat @ A)) = (! [B:nat]: ? [C:nat]: ((ord_less_nat @ B @ C) & (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3907])). 185.47/93.66 thf(6736,axiom,((vEBT_V8194947554948674370ptions = (^ [A:vEBT_VEBT,B:nat]: ((vEBT_V5719532721284313246member @ A @ B) | (vEBT_VEBT_membermima @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1264_both__member__options__def)). 185.47/93.66 thf(30470,plain,(((vEBT_V8194947554948674370ptions) = (^ [A:vEBT_VEBT,B:nat]: ((vEBT_V5719532721284313246member @ A @ B) | (vEBT_VEBT_membermima @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6736])). 185.47/93.66 thf(5631,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2103_Suc__neq__Zero)). 185.47/93.66 thf(26473,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5631])). 185.47/93.66 thf(1478,axiom,((! [A:int,B:int]: (((times_times_int @ (divide_divide_int @ B @ A) @ A) = B) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4483_dvd__div__mult__self)). 185.47/93.66 thf(12654,plain,((! [A:int,B:int]: (((times_times_int @ (divide_divide_int @ B @ A) @ A) = B) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478])). 185.47/93.66 thf(640,axiom,((! [A:set_nat,B:set_nat,C:(nat > rat),D:(nat > nat),E:(nat > rat)]: ((finite_finite_nat @ A) => ((finite_finite_nat @ B) => (((ord_less_eq_rat @ (groups2906978787729119204at_rat @ E @ A) @ (groups2906978787729119204at_rat @ C @ B)) <= (! [F:nat]: ((? [G:nat]: ((member_nat @ G @ B) & (ord_less_eq_rat @ (E @ F) @ (C @ G)) & ((D @ G) = F))) <= (member_nat @ F @ A)))) <= (! [F:nat]: ((member_nat @ F @ B) => (ord_less_eq_rat @ zero_zero_rat @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5840_sum__le__included)). 185.47/93.66 thf(9853,plain,((! [A:set_nat,B:set_nat,C:(nat > rat),D:(nat > nat),E:(nat > rat)]: ((finite_finite_nat @ A) => ((finite_finite_nat @ B) => ((ord_less_eq_rat @ (groups2906978787729119204at_rat @ (E) @ A) @ (groups2906978787729119204at_rat @ (C) @ B)) | ~ (! [F:nat]: (? [G:nat]: ((member_nat @ G @ B) & (ord_less_eq_rat @ (E @ F) @ (C @ G)) & ((D @ G) = F)) | ~ (member_nat @ F @ A))) | ~ (! [F:nat]: ((member_nat @ F @ B) => (ord_less_eq_rat @ zero_zero_rat @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[640])). 185.47/93.66 thf(4287,axiom,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1519_add__cancel__left__right)). 185.47/93.66 thf(21707,plain,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4287])). 185.47/93.66 thf(4441,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ (times_times_int @ B @ A) @ B) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2664_mult__left__le)). 185.47/93.66 thf(22220,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ B @ A) @ B) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4441])). 185.47/93.66 thf(573,axiom,((! [A:set_nat]: ((groups708209901874060359at_nat @ (^ [B:nat]: (one_one_nat)) @ A) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8638_prod_Oneutral__const)). 185.47/93.66 thf(9635,plain,((! [A:set_nat]: ((groups708209901874060359at_nat @ (^ [B:nat]: (one_one_nat)) @ A) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[573])). 185.47/93.66 thf(7005,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((B = (divide_divide_nat @ C @ A)) = ((times_times_nat @ B @ A) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4859_unit__eq__div2)). 185.47/93.66 thf(31568,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((B = (divide_divide_nat @ C @ A)) = ((times_times_nat @ B @ A) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7005])). 185.47/93.66 thf(4032,axiom,((! [A:int]: ((ord_less_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3044_half__negative__int__iff)). 185.47/93.66 thf(20935,plain,((! [A:int]: ((ord_less_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4032])). 185.47/93.66 thf(7056,axiom,((bit_se2000444600071755411sk_int = (^ [A:nat]: (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9234_mask__int__def)). 185.47/93.66 thf(31766,plain,(((bit_se2000444600071755411sk_int) = (^ [A:nat]: (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7056])). 185.47/93.66 thf(3331,axiom,((! [A:real,B:num]: ((real_V7735802525324610683m_real @ (times_times_real @ A @ (numeral_numeral_real @ B))) = (times_times_real @ (real_V7735802525324610683m_real @ A) @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7444_norm__mult__numeral2)). 185.47/93.66 thf(18704,plain,((! [A:real,B:num]: ((real_V7735802525324610683m_real @ (times_times_real @ A @ (numeral_numeral_real @ B))) = (times_times_real @ (real_V7735802525324610683m_real @ A) @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3331])). 185.47/93.66 thf(3286,axiom,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (times_times_real @ (comm_s7457072308508201937r_real @ A @ B) @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8494_pochhammer__Suc)). 185.47/93.66 thf(18562,plain,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (times_times_real @ (comm_s7457072308508201937r_real @ A @ B) @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3286])). 185.47/93.66 thf(2336,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) => (ord_less_eq_real @ (abs_abs_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6508_abs__leI)). 185.47/93.66 thf(15474,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) => (ord_less_eq_real @ (abs_abs_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2336])). 185.47/93.66 thf(1063,axiom,((~ (ord_less_eq_int @ one_one_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2270_not__one__le__zero)). 185.47/93.66 thf(11343,plain,((~ (ord_less_eq_int @ one_one_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063])). 185.47/93.66 thf(5303,axiom,(((semiri1316708129612266289at_nat @ one_one_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6921_of__nat__1)). 185.47/93.66 thf(25256,plain,(((semiri1316708129612266289at_nat @ one_one_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5303])). 185.47/93.66 thf(970,axiom,((! [A:real,B:nat]: (((ln_ln_real @ (power_power_real @ A @ B)) = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (ln_ln_real @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7331_ln__realpow)). 185.47/93.66 thf(11063,plain,((! [A:real,B:nat]: (((ln_ln_real @ (power_power_real @ A @ B)) = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (ln_ln_real @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[970])). 185.47/93.66 thf(6464,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2492_gr0__conv__Suc)). 185.47/93.66 thf(29535,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6464])). 185.47/93.66 thf(1672,axiom,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ (minus_minus_rat @ B @ A)) = B) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_975_le__add__diff__inverse)). 185.47/93.66 thf(13336,plain,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ (minus_minus_rat @ B @ A)) = B) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672])). 185.47/93.66 thf(6820,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1154_left__diff__distrib_H)). 185.47/93.66 thf(30809,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6820])). 185.47/93.66 thf(2641,axiom,((! [A:rat]: ~ (ord_less_rat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4013_dual__order_Oirrefl)). 185.47/93.66 thf(16496,plain,((! [A:rat]: ~ (ord_less_rat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2641])). 185.47/93.66 thf(6615,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => (((A @ B) <= (! [C:nat]: ((A @ (plus_plus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) <= (A @ C)))) <= (A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2957_nat__induct2)). 185.47/93.66 thf(30048,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ (plus_plus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (A @ C))) | ~ (A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6615])). 185.47/93.66 thf(3134,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (ord_less_eq_int @ B @ C)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3345_mult__le__cancel__iff1)). 185.47/93.66 thf(18095,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (ord_less_eq_int @ B @ C)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3134])). 185.47/93.66 thf(1295,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ C @ A)) <= (ord_less_eq_rat @ C @ zero_zero_rat)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2243_mult__left__mono__neg)). 185.47/93.66 thf(12052,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ C @ A)) | ~ (ord_less_eq_rat @ C @ zero_zero_rat) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295])). 185.47/93.66 thf(2412,axiom,((! [A:num]: ((numeral_numeral_rat @ (bit1 @ A)) = (plus_plus_rat @ (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ A)) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6602_numeral__Bit1)). 185.47/93.66 thf(15715,plain,((! [A:num]: ((numeral_numeral_rat @ (bit1 @ A)) = (plus_plus_rat @ (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ A)) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2412])). 185.47/93.66 thf(1826,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((C != A) <= (ord_less_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3236_pinf_I3_J)). 185.47/93.66 thf(13849,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: (~ (C = A) | ~ (ord_less_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826])). 185.47/93.66 thf(5333,axiom,((! [A:real,B:real,C:nat]: (((times_times_real @ A @ B) = (times_times_real @ B @ A)) => ((times_times_real @ (power_power_real @ A @ C) @ B) = (times_times_real @ B @ (power_power_real @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_power__commuting__commutes)). 185.47/93.66 thf(25356,plain,((! [A:real,B:real,C:nat]: (((times_times_real @ A @ B) = (times_times_real @ B @ A)) => ((times_times_real @ (power_power_real @ A @ C) @ B) = (times_times_real @ B @ (power_power_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5333])). 185.47/93.66 thf(7203,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1966_zero__power)). 185.47/93.66 thf(32262,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7203])). 185.47/93.66 thf(18,axiom,((! [A:complex,B:nat]: ((minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ B)) = (times_times_complex @ (minus_minus_complex @ one_one_complex @ A) @ (groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7592_one__diff__power__eq)). 185.47/93.66 thf(7785,plain,((! [A:complex,B:nat]: ((minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ B)) = (times_times_complex @ (minus_minus_complex @ one_one_complex @ A) @ (groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[18])). 185.47/93.66 thf(2513,axiom,((! [A:rat,B:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))) @ (abs_abs_rat @ (minus_minus_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6500_abs__triangle__ineq3)). 185.47/93.66 thf(16063,plain,((! [A:rat,B:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))) @ (abs_abs_rat @ (minus_minus_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2513])). 185.47/93.66 thf(5429,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_less__imp__le__nat)). 185.47/93.66 thf(25684,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5429])). 185.47/93.66 thf(5217,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_778_mult_Ocomm__neutral)). 185.47/93.66 thf(24925,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5217])). 185.47/93.66 thf(4293,axiom,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2981_sum__power2__ge__zero)). 185.47/93.66 thf(21724,plain,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4293])). 185.47/93.66 thf(3687,axiom,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: (((? [E:real]: ! [F:real]: ((((C @ F) | (A @ F)) = ((B @ F) | (D @ F))) <= (ord_less_real @ F @ E))) <= (? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) <= (ord_less_real @ F @ E)))) <= (? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3260_minf_I2_J)). 185.47/93.66 thf(19828,plain,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: (? [E:real]: ! [F:real]: ((((C @ F) | (A @ F)) = ((B @ F) | (D @ F))) | ~ (ord_less_real @ F @ E)) | ~ (? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) | ~ (ord_less_real @ F @ E))) | ~ (? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3687])). 185.47/93.66 thf(3181,axiom,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_rat @ (plus_plus_rat @ (times_times_rat @ A @ B) @ C) @ (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (ord_less_rat @ (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ A @ D) @ B) @ C) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1238_less__add__iff1)). 185.47/93.66 thf(18242,plain,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_rat @ (plus_plus_rat @ (times_times_rat @ A @ B) @ C) @ (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (ord_less_rat @ (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ A @ D) @ B) @ C) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3181])). 185.47/93.66 thf(3827,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (times_times_real @ A @ B)) = (((ord_less_real @ B @ one_one_real) <= (ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ one_one_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2818_mult__less__cancel__left1)). 185.47/93.66 thf(20288,plain,((! [A:real,B:real]: ((ord_less_real @ A @ (times_times_real @ A @ B)) = (((ord_less_real @ B @ one_one_real) | ~ (ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ one_one_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3827])). 185.47/93.66 thf(4318,axiom,((! [A:nat]: ((semiri681578069525770553at_rat @ (suc @ A)) != zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7219_of__nat__neq__0)). 185.47/93.66 thf(21830,plain,((! [A:nat]: ~ ((semiri681578069525770553at_rat @ (suc @ A)) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4318])). 185.47/93.66 thf(2927,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ one_one_rat) = (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1856_divide__le__eq__1__neg)). 185.47/93.66 thf(17436,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ one_one_rat) = (ord_less_eq_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2927])). 185.47/93.66 thf(339,axiom,(((re @ one_one_complex) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9642_one__complex_Osimps_I1_J)). 185.47/93.66 thf(8874,plain,(((re @ one_one_complex) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 185.47/93.66 thf(4236,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ B @ one_one_int)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3130_zle__add1__eq__le)). 185.47/93.66 thf(21555,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ B @ one_one_int)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4236])). 185.47/93.66 thf(3304,axiom,((! [A:int]: ((ord_less_eq_int @ A @ zero_zero_int) => (~ (! [B:nat]: (A != (uminus_uminus_int @ (semiri1314217659103216013at_int @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7275_nonpos__int__cases)). 185.47/93.66 thf(18621,plain,((! [A:int]: ((ord_less_eq_int @ A @ zero_zero_int) => (~ (! [B:nat]: ~ (A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3304])). 185.47/93.66 thf(4263,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ B)) @ C) = ((ord_less_eq_rat @ A @ (plus_plus_rat @ B @ C)) & (ord_less_eq_rat @ (minus_minus_rat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6590_abs__diff__le__iff)). 185.47/93.66 thf(21640,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ B)) @ C) = ((ord_less_eq_rat @ A @ (plus_plus_rat @ B @ C)) & (ord_less_eq_rat @ (minus_minus_rat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4263])). 185.47/93.66 thf(5592,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (times_times_nat @ B @ C)) => (~ (! [D:nat,E:nat]: (((~ (dvd_dvd_nat @ E @ C)) <= (dvd_dvd_nat @ D @ B)) <= (A = (times_times_nat @ D @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4627_dvd__productE)). 185.47/93.66 thf(26339,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (times_times_nat @ B @ C)) => (~ (! [D:nat,E:nat]: (~ (dvd_dvd_nat @ E @ C) | ~ (dvd_dvd_nat @ D @ B) | ~ (A = (times_times_nat @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5592])). 185.47/93.66 thf(2115,axiom,((! [A:int,B:int]: ((((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ A @ zero_zero_int)) | ((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ A))) => (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2224_split__mult__neg__le)). 185.47/93.66 thf(14776,plain,((! [A:int,B:int]: ((((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ A @ zero_zero_int)) | ((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ A))) => (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2115])). 185.47/93.66 thf(1130,axiom,((bit_se1409905431419307370or_int = (^ [A:int,B:int]: (plus_plus_int @ (zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9440_or__int__rec)). 185.47/93.66 thf(11561,plain,(((bit_se1409905431419307370or_int) = (^ [A:int,B:int]: (plus_plus_int @ (zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130])). 185.47/93.66 thf(2752,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ C @ B)) <= ((plus_plus_real @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_add__implies__diff)). 185.47/93.66 thf(16876,plain,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ C @ B)) | ~ ((plus_plus_real @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2752])). 185.47/93.66 thf(3373,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (cos_complex @ A) @ (sin_complex @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (sin_complex @ (plus_plus_complex @ A @ B)) @ (sin_complex @ (minus_minus_complex @ A @ B))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7852_cos__times__sin)). 185.47/93.66 thf(18841,plain,((! [A:complex,B:complex]: ((times_times_complex @ (cos_complex @ A) @ (sin_complex @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (sin_complex @ (plus_plus_complex @ A @ B)) @ (sin_complex @ (minus_minus_complex @ A @ B))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3373])). 185.47/93.66 thf(5327,axiom,((! [A:int,B:nat]: ((abs_abs_int @ (power_power_int @ A @ B)) = (power_power_int @ (abs_abs_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6471_power__abs)). 185.47/93.66 thf(25340,plain,((! [A:int,B:nat]: ((abs_abs_int @ (power_power_int @ A @ B)) = (power_power_int @ (abs_abs_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5327])). 185.47/93.66 thf(4083,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((divide_divide_int @ B @ A) = (divide_divide_int @ C @ A)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4770_unit__div__cancel)). 185.47/93.66 thf(21087,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((divide_divide_int @ B @ A) = (divide_divide_int @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4083])). 185.47/93.66 thf(5871,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (modulo_modulo_nat @ B @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1933_mod__less__divisor)). 185.47/93.66 thf(27433,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (modulo_modulo_nat @ B @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5871])). 185.47/93.66 thf(6929,axiom,((! [A:rat,B:nat]: ((ord_less_eq_rat @ (power_power_rat @ A @ B) @ zero_zero_rat) = (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_rat @ A @ zero_zero_rat)) | ((A = zero_zero_rat) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4987_power__le__zero__eq)). 185.47/93.66 thf(31228,plain,((! [A:rat,B:nat]: ((ord_less_eq_rat @ (power_power_rat @ A @ B) @ zero_zero_rat) = (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_rat @ A @ zero_zero_rat)) | ((A = zero_zero_rat) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6929])). 185.47/93.66 thf(5715,axiom,((! [A:real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5045_neg__equal__0__iff__equal)). 185.47/93.66 thf(26755,plain,((! [A:real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5715])). 185.47/93.66 thf(3685,axiom,((ord_less_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_4217_order_Ostrict__iff__not)). 185.47/93.66 thf(19822,plain,(((ord_less_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)],[3685])). 185.47/93.66 thf(7167,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B)) @ (power_power_nat @ A @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2869_power__Suc__less)). 185.47/93.66 thf(32147,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B)) @ (power_power_nat @ A @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7167])). 185.47/93.66 thf(4249,axiom,((! [A:int,B:int]: (dvd_dvd_int @ A @ (minus_minus_int @ B @ (modulo_modulo_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4804_dvd__minus__mod)). 185.47/93.66 thf(21600,plain,((! [A:int,B:int]: (dvd_dvd_int @ A @ (minus_minus_int @ B @ (modulo_modulo_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4249])). 185.47/93.66 thf(922,axiom,((! [A:set_nat,B:(nat > real)]: ((finite_finite_nat @ A) => ((A != bot_bot_set_nat) => ((ord_less_real @ one_one_real @ (groups129246275422532515t_real @ B @ A)) <= (! [C:nat]: ((ord_less_real @ one_one_real @ (B @ C)) <= (member_nat @ C @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8882_less__1__prod)). 185.47/93.66 thf(10890,plain,((! [A:set_nat,B:(nat > real)]: ((finite_finite_nat @ A) => ((~ (A = bot_bot_set_nat)) => ((ord_less_real @ one_one_real @ (groups129246275422532515t_real @ (B) @ A)) | ~ (! [C:nat]: ((ord_less_real @ one_one_real @ (B @ C)) | ~ (member_nat @ C @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[922])). 185.47/93.66 thf(956,axiom,((! [A:int,B:real]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ B) => (((archim6058952711729229775r_real @ B) = A) <= (ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9122_floor__eq2)). 185.47/93.66 thf(11011,plain,((! [A:int,B:real]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ B) => (((archim6058952711729229775r_real @ B) = A) | ~ (ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[956])). 185.47/93.66 thf(7545,axiom,((! [A:real,B:real]: ((power_power_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ (minus_minus_real @ B @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_892_power2__commute)). 185.47/93.66 thf(33420,plain,((! [A:real,B:real]: ((power_power_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ (minus_minus_real @ B @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7545])). 185.47/93.66 thf(3744,axiom,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5566_add_Oinverse__distrib__swap)). 185.47/93.66 thf(20024,plain,((! [A:int,B:int]: ((uminus_uminus_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3744])). 185.47/93.66 thf(6542,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ (ord_less_nat @ A @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6282_exp__mod__exp)). 185.47/93.66 thf(29815,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ (ord_less_nat @ A @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6542])). 185.47/93.66 thf(6694,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_less__not__refl2)). 185.47/93.66 thf(30307,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6694])). 185.47/93.66 thf(4527,axiom,((! [A:nat]: ((times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A)) = one_one_Code_integer))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5300_minus__one__mult__self)). 185.47/93.66 thf(22502,plain,((! [A:nat]: ((times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A)) = one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4527])). 185.47/93.66 thf(3223,axiom,((! [A:nat]: ((bit_ri631733984087533419it_int @ (suc @ A) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4501_signed__take__bit__Suc__1)). 185.47/93.66 thf(18376,plain,((! [A:nat]: ((bit_ri631733984087533419it_int @ (suc @ A) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3223])). 185.47/93.66 thf(917,axiom,((! [A:(nat > real),B:set_nat]: (((groups129246275422532515t_real @ A @ B) != one_one_real) => (~ (! [C:nat]: (((A @ C) = one_one_real) <= (member_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8716_prod_Onot__neutral__contains__not__neutral)). 185.47/93.66 thf(10872,plain,((! [A:(nat > real),B:set_nat]: ((~ ((groups129246275422532515t_real @ (A) @ B) = one_one_real)) => (~ (! [C:nat]: (((A @ C) = one_one_real) | ~ (member_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[917])). 185.47/93.66 thf(7687,axiom,((! [A:code_integer,B:code_integer]: (((power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_8256067586552552935nteger @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = (uminus1351360451143612070nteger @ B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6183_power2__eq__iff)). 185.47/93.66 thf(33804,plain,((! [A:code_integer,B:code_integer]: (((power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_8256067586552552935nteger @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = (uminus1351360451143612070nteger @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7687])). 185.47/93.66 thf(3477,axiom,((! [A:int,B:nat,C:int]: ((ord_less_rat @ (power_power_rat @ (ring_1_of_int_rat @ A) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7110_of__int__less__of__int__power__cancel__iff)). 185.47/93.66 thf(19178,plain,((! [A:int,B:nat,C:int]: ((ord_less_rat @ (power_power_rat @ (ring_1_of_int_rat @ A) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_int @ (power_power_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3477])). 185.47/93.66 thf(4283,axiom,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6278_add__0__iff)). 185.47/93.66 thf(21695,plain,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4283])). 185.47/93.66 thf(3024,axiom,((ord_less_eq_real @ zero_zero_real @ zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2020_le__numeral__extra_I3_J)). 185.47/93.66 thf(17748,plain,((ord_less_eq_real @ zero_zero_real @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3024])). 185.47/93.66 thf(1537,axiom,((! [A:(nat > real),B:real,C:real]: ((sums_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ C)) @ (times_times_real @ B @ C)) <= (sums_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8156_sums__mult2)). 185.47/93.66 thf(12827,plain,((! [A:(nat > real),B:real,C:real]: ((sums_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ C)) @ (times_times_real @ B @ C)) | ~ (sums_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537])). 185.47/93.66 thf(4378,axiom,((! [A:nat,B:int]: ((bit_ri631733984087533419it_int @ (suc @ A) @ B) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri631733984087533419it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4427_signed__take__bit__Suc)). 185.47/93.66 thf(22027,plain,((! [A:nat,B:int]: ((bit_ri631733984087533419it_int @ (suc @ A) @ B) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri631733984087533419it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4378])). 185.47/93.66 thf(6221,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4066_order__less__asym_H)). 185.47/93.66 thf(28665,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6221])). 185.47/93.66 thf(7652,axiom,(((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1887_one__div__two__eq__zero)). 185.47/93.66 thf(33714,plain,(((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7652])). 185.47/93.66 thf(322,axiom,((! [A:complex]: ((im @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (re @ A)) @ (im @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9692_Im__power2)). 185.47/93.66 thf(8807,plain,((! [A:complex]: ((im @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (re @ A)) @ (im @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 185.47/93.66 thf(5016,axiom,((! [A:int,B:num]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ zero_zero_int) = ((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ B)) & (((ord_less_eq_int @ A @ zero_zero_int) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (A = zero_zero_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4568_power__le__zero__eq__numeral)). 185.47/93.66 thf(24153,plain,((! [A:int,B:num]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ zero_zero_int) = ((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ B)) & (((ord_less_eq_int @ A @ zero_zero_int) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (A = zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5016])). 185.47/93.66 thf(7013,axiom,((! [A:complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2487_power__0)). 185.47/93.66 thf(31600,plain,((! [A:complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7013])). 185.47/93.66 thf(7232,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ A @ one_one_nat)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4630_dvd__unit__imp__unit)). 185.47/93.66 thf(32378,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ A @ one_one_nat)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7232])). 185.47/93.66 thf(6149,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ one_one_nat @ C) => (ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_876_power__increasing)). 185.47/93.66 thf(28383,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ one_one_nat @ C) => (ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6149])). 185.47/93.66 thf(4207,axiom,((ord_less_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_4187_less__le__not__le)). 185.47/93.66 thf(21465,plain,(((ord_less_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)],[4207])). 185.47/93.66 thf(3326,axiom,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ D @ E) @ F)) => ((ord_less_int @ F @ D) => ((((ord_less_eq_int @ D @ A) => (ord_less_eq_int @ B @ E)) <= (ord_less_int @ zero_zero_int @ D)) <= (ord_less_eq_int @ zero_zero_int @ C)))) <= ((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ E) @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3168_zdiv__mono2__lemma)). 185.47/93.66 thf(18689,plain,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ D @ E) @ F)) => ((ord_less_int @ F @ D) => (((ord_less_eq_int @ D @ A) => (ord_less_eq_int @ B @ E)) | ~ (ord_less_int @ zero_zero_int @ D) | ~ (ord_less_eq_int @ zero_zero_int @ C)))) | ~ ((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ E) @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3326])). 185.47/93.66 thf(858,axiom,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_rat @ (groups73079841787564623at_rat @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8701_prod_OatMost__Suc)). 185.47/93.66 thf(10668,plain,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_rat @ (groups73079841787564623at_rat @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[858])). 185.47/93.66 thf(5654,axiom,((! [A:num,B:num]: ((ord_less_num @ B @ A) | (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4363_linorder__le__less__linear)). 185.47/93.66 thf(26545,plain,((! [A:num,B:num]: ((ord_less_num @ B @ A) | (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5654])). 185.47/93.66 thf(5703,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3816_dual__order_Orefl)). 185.47/93.66 thf(26704,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5703])). 185.47/93.66 thf(2709,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (modulo_modulo_int @ B @ A)) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3152_neg__mod__bound)). 185.47/93.66 thf(16750,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (modulo_modulo_int @ B @ A)) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2709])). 185.47/93.66 thf(6258,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4947_dvd__power__iff__le)). 185.47/93.66 thf(28788,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6258])). 185.47/93.66 thf(5786,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1160_right__diff__distrib_H)). 185.47/93.66 thf(26977,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5786])). 185.47/93.66 thf(1287,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_add__left__cancel)). 185.47/93.66 thf(12028,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287])). 185.47/93.66 thf(1784,axiom,((! [A:int,B:int]: (((ord_less_int @ A @ B) => ((modulo_modulo_int @ A @ B) = A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3133_mod__pos__pos__trivial)). 185.47/93.66 thf(13710,plain,((! [A:int,B:int]: (((ord_less_int @ A @ B) => ((modulo_modulo_int @ A @ B) = A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1784])). 185.47/93.66 thf(4958,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9395_and__nat__numerals_I2_J)). 185.47/93.66 thf(23966,plain,((! [A:num]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4958])). 185.47/93.66 thf(4629,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ (powr_real @ B @ A) @ (powr_real @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9093_powr__less__mono2)). 185.47/93.66 thf(22831,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ (powr_real @ B @ A) @ (powr_real @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4629])). 185.47/93.66 thf(264,axiom,((! [A:real]: ((((cos_real @ (arccos @ A)) = A) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8360_cos__arccos)). 185.47/93.66 thf(8597,plain,((! [A:real]: (((cos_real @ (arccos @ A)) = A) | ~ (ord_less_eq_real @ A @ one_one_real) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 185.47/93.66 thf(3856,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ B @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4067_order__less__asym_H)). 185.47/93.66 thf(20388,plain,((! [A:int,B:int]: (~ (ord_less_int @ B @ A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3856])). 185.47/93.66 thf(1863,axiom,((! [A:rat,B:rat]: (((A = B) <= (ord_less_eq_rat @ B @ A)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3866_order__antisym)). 185.47/93.66 thf(13973,plain,((! [A:rat,B:rat]: ((A = B) | ~ (ord_less_eq_rat @ B @ A) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1863])). 185.47/93.66 thf(501,axiom,(((ord_max_int @ one_one_int @ zero_zero_int) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3624_max__0__1_I2_J)). 185.47/93.66 thf(9418,plain,(((ord_max_int @ one_one_int @ zero_zero_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])). 185.47/93.66 thf(2203,axiom,(((ord_max_nat @ one_one_nat @ zero_zero_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3622_max__0__1_I2_J)). 185.47/93.66 thf(15070,plain,(((ord_max_nat @ one_one_nat @ zero_zero_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2203])). 185.47/93.66 thf(5356,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((((vEBT_vebt_member @ (vEBT_vebt_insert @ A @ C) @ D) => ((C = D) | (vEBT_vebt_member @ A @ D))) <= (ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) <= (ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_post__member__pre__member)). 185.47/93.66 thf(25464,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((vEBT_vebt_member @ (vEBT_vebt_insert @ A @ C) @ D) => ((C = D) | (vEBT_vebt_member @ A @ D))) | ~ (ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ (ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5356])). 185.47/93.66 thf(2968,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_rat) = ((A = zero_zero_rat) & (B = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2979_sum__power2__le__zero__iff)). 185.47/93.66 thf(17568,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_rat) = ((A = zero_zero_rat) & (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2968])). 185.47/93.66 thf(6276,axiom,((! [A:real]: ((minus_minus_real @ zero_zero_real @ A) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5177_diff__0)). 185.47/93.66 thf(28855,plain,((! [A:real]: ((minus_minus_real @ zero_zero_real @ A) = (uminus_uminus_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6276])). 185.47/93.66 thf(4655,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_974_le__add__diff__inverse)). 185.47/93.66 thf(22913,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4655])). 185.47/93.66 thf(789,axiom,(((nat_set_encode @ bot_bot_set_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9214_set__encode__empty)). 185.47/93.66 thf(10425,plain,(((nat_set_encode @ bot_bot_set_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[789])). 185.47/93.66 thf(2493,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (plus_plus_rat @ A @ B)) = (ord_less_eq_rat @ zero_zero_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1622_le__add__same__cancel1)). 185.47/93.66 thf(15998,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (plus_plus_rat @ A @ B)) = (ord_less_eq_rat @ zero_zero_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2493])). 185.47/93.66 thf(6998,axiom,((! [A:real]: (((times_times_real @ A @ A) = one_one_real) = ((A = (uminus_uminus_real @ one_one_real)) | (A = one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5777_square__eq__1__iff)). 185.47/93.66 thf(31547,plain,((! [A:real]: (((times_times_real @ A @ A) = one_one_real) = ((A = (uminus_uminus_real @ one_one_real)) | (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6998])). 185.47/93.66 thf(5636,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ B @ A) => (A = B)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5489_dvd__antisym)). 185.47/93.66 thf(26486,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ B @ A) => (A = B)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5636])). 185.47/93.66 thf(727,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arctan @ A)) & (ord_less_real @ (arctan @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7766_arctan__bounded)). 185.47/93.66 thf(10155,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arctan @ A)) & (ord_less_real @ (arctan @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[727])). 185.47/93.66 thf(4607,axiom,((! [A:num]: ~ (ord_less_eq_rat @ zero_zero_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5897_not__zero__le__neg__numeral)). 185.47/93.66 thf(22753,plain,((! [A:num]: ~ (ord_less_eq_rat @ zero_zero_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4607])). 185.47/93.66 thf(6917,axiom,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ (bit0 @ one))) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_mult__2__right)). 185.47/93.66 thf(31186,plain,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ (bit0 @ one))) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6917])). 185.47/93.66 thf(5713,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ C @ B)) = (dvd_dvd_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4649_dvd__add__left__iff)). 185.47/93.66 thf(26748,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ C @ B)) = (dvd_dvd_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5713])). 185.47/93.66 thf(4541,axiom,((! [A:nat,B:int]: ((ord_less_int @ (bit_ri631733984087533419it_int @ A @ B) @ zero_zero_int) = (bit_se1146084159140164899it_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9412_signed__take__bit__negative__iff)). 185.47/93.66 thf(22545,plain,((! [A:nat,B:int]: ((ord_less_int @ (bit_ri631733984087533419it_int @ A @ B) @ zero_zero_int) = (bit_se1146084159140164899it_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4541])). 185.47/93.66 thf(623,axiom,((! [A:int]: ((ord_less_eq_int @ one_one_int @ (ring_1_of_int_int @ A)) = (ord_less_eq_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7082_of__int__1__le__iff)). 185.47/93.66 thf(9798,plain,((! [A:int]: ((ord_less_eq_int @ one_one_int @ (ring_1_of_int_int @ A)) = (ord_less_eq_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[623])). 185.47/93.66 thf(1821,axiom,((! [A:nat,B:rat,C:rat]: (((ord_less_eq_rat @ (abs_abs_rat @ B) @ (abs_abs_rat @ C)) => (ord_less_eq_rat @ (power_power_rat @ B @ A) @ (power_power_rat @ C @ A))) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6724_power__mono__even)). 185.47/93.66 thf(13832,plain,((! [A:nat,B:rat,C:rat]: (((ord_less_eq_rat @ (abs_abs_rat @ B) @ (abs_abs_rat @ C)) => (ord_less_eq_rat @ (power_power_rat @ B @ A) @ (power_power_rat @ C @ A))) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1821])). 185.47/93.66 thf(5304,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4121_order__less__not__sym)). 185.47/93.66 thf(25258,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5304])). 185.47/93.66 thf(1271,axiom,((! [A:real,B:real]: (((plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = zero_zero_real) = ((B = zero_zero_real) & (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1677_sum__squares__eq__zero__iff)). 185.47/93.66 thf(11983,plain,((! [A:real,B:real]: (((plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = zero_zero_real) = ((B = zero_zero_real) & (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271])). 185.47/93.66 thf(2219,axiom,((ord_less_rat @ zero_zero_rat @ one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2389_less__numeral__extra_I1_J)). 185.47/93.66 thf(15117,plain,((ord_less_rat @ zero_zero_rat @ one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2219])). 185.47/93.66 thf(4571,axiom,((! [A:nat]: ((ord_less_nat @ A @ (bit_se2002935070580805687sk_nat @ A)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9224_less__mask)). 185.47/93.66 thf(22648,plain,((! [A:nat]: ((ord_less_nat @ A @ (bit_se2002935070580805687sk_nat @ A)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4571])). 185.47/93.66 thf(738,axiom,((! [A:real]: ((cos_real @ (minus_minus_real @ A @ pi)) = (uminus_uminus_real @ (cos_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7789_cos__minus__pi)). 185.47/93.66 thf(10194,plain,((! [A:real]: ((cos_real @ (minus_minus_real @ A @ pi)) = (uminus_uminus_real @ (cos_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[738])). 185.47/93.66 thf(4698,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_eq_int @ E @ zero_zero_int) => ((ord_less_int @ A @ E) => ((ord_less_int @ A @ C) => (ord_less_eq_int @ D @ B)))) <= (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ A @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3164_unique__quotient__lemma__neg)). 185.47/93.66 thf(23067,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_eq_int @ E @ zero_zero_int) => ((ord_less_int @ A @ E) => ((ord_less_int @ A @ C) => (ord_less_eq_int @ D @ B)))) | ~ (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ A @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4698])). 185.47/93.66 thf(4907,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ (divide_divide_rat @ B @ A) @ C) = (ord_less_rat @ B @ (times_times_rat @ C @ A))) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2704_pos__divide__less__eq)). 185.47/93.66 thf(23783,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ (divide_divide_rat @ B @ A) @ C) = (ord_less_rat @ B @ (times_times_rat @ C @ A))) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4907])). 185.47/93.66 thf(3877,axiom,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = B) = ((plus_plus_complex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5745_neg__eq__iff__add__eq__0)). 185.47/93.66 thf(20447,plain,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = B) = ((plus_plus_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3877])). 185.47/93.66 thf(5144,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat]: ((! [F:vEBT_VEBT]: ((vEBT_invar_vebt @ F @ B) <= (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)))) => (((((((! [F:vEBT_VEBT]: ((~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) <= (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)))) => (vEBT_invar_vebt @ (vEBT_Node @ none_P5556105721700978146at_nat @ E @ A @ C) @ E)) <= (~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ C @ F)))) <= (E = (plus_plus_nat @ B @ D))) <= (D = B)) <= ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) <= (vEBT_invar_vebt @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1224_invar__vebt_Ointros_I2_J)). 185.47/93.66 thf(24688,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat]: ((! [F:vEBT_VEBT]: ((vEBT_invar_vebt @ F @ B) | ~ (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)))) => (((! [F:vEBT_VEBT]: (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)) | ~ (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)))) => (vEBT_invar_vebt @ (vEBT_Node @ none_P5556105721700978146at_nat @ E @ A @ C) @ E)) | ? [F:nat]: (vEBT_V8194947554948674370ptions @ C @ F) | ~ (E = (plus_plus_nat @ B @ D)) | ~ (D = B) | ~ ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) | ~ (vEBT_invar_vebt @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5144])). 185.47/93.66 thf(4666,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_3150_verit__la__generic)). 185.47/93.66 thf(22945,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)],[4666])). 185.47/93.66 thf(4092,axiom,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: (dvd_dvd_nat @ C @ A))) @ (collect_nat @ (^ [C:nat]: (dvd_dvd_nat @ C @ B)))) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4695_subset__divisors__dvd)). 185.47/93.66 thf(21116,plain,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (collect_nat @ (^ [C:nat]: (dvd_dvd_nat @ C @ A))) @ (collect_nat @ (^ [C:nat]: (dvd_dvd_nat @ C @ B)))) = (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4092])). 185.47/93.66 thf(5742,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => ((? [G:nat]: ((ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ F @ (divide_divide_nat @ F @ (numeral_numeral_nat @ (bit0 @ one)))))) & ((some_nat @ G) = (vEBT_vebt_mint @ E))) & (ord_less_nat @ A @ B)) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_941_mintlistlength)). 185.47/93.66 thf(26835,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => ((? [G:nat]: ((ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ F @ (divide_divide_nat @ F @ (numeral_numeral_nat @ (bit0 @ one)))))) & ((some_nat @ G) = (vEBT_vebt_mint @ E))) & (ord_less_nat @ A @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5742])). 185.47/93.66 thf(5403,axiom,((! [A:nat]: (((num_of_nat @ (plus_plus_nat @ A @ A)) = (bit0 @ (num_of_nat @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9844_num__of__nat__double)). 185.47/93.66 thf(25605,plain,((! [A:nat]: (((num_of_nat @ (plus_plus_nat @ A @ A)) = (bit0 @ (num_of_nat @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5403])). 185.47/93.66 thf(1921,axiom,((! [A:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (exp_complex @ A)) @ (exp_real @ (real_V1022390504157884413omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8150_norm__exp)). 185.47/93.66 thf(14146,plain,((! [A:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (exp_complex @ A)) @ (exp_real @ (real_V1022390504157884413omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1921])). 185.47/93.66 thf(3275,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D)) <= ((A = B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_add__mono__thms__linordered__semiring_I4_J)). 185.47/93.66 thf(18529,plain,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D)) | ~ ((A = B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3275])). 185.47/93.66 thf(4584,axiom,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2086_add_Ogroup__left__neutral)). 185.47/93.66 thf(22683,plain,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4584])). 185.47/93.66 thf(7403,axiom,((! [A:real]: (((real_V7735802525324610683m_real @ A) = one_one_real) <= ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7518_square__norm__one)). 185.47/93.66 thf(32933,plain,((! [A:real]: (((real_V7735802525324610683m_real @ A) = one_one_real) | ~ ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7403])). 185.47/93.66 thf(4996,axiom,((! [A:nat,B:nat,C:int]: (((modulo_modulo_int @ (times_times_int @ C @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (times_times_int @ (modulo_modulo_int @ C @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ B @ A))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2997_mult__exp__mod__exp__eq)). 185.47/93.66 thf(24089,plain,((! [A:nat,B:nat,C:int]: (((modulo_modulo_int @ (times_times_int @ C @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (times_times_int @ (modulo_modulo_int @ C @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ B @ A))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4996])). 185.47/93.66 thf(1152,axiom,((! [A:int,B:nat,C:int]: ((ord_less_eq_rat @ (power_power_rat @ (ring_1_of_int_rat @ A) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_eq_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7096_of__int__le__of__int__power__cancel__iff)). 185.47/93.66 thf(11633,plain,((! [A:int,B:nat,C:int]: ((ord_less_eq_rat @ (power_power_rat @ (ring_1_of_int_rat @ A) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_eq_int @ (power_power_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152])). 185.47/93.66 thf(1089,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ A @ C) <= (ord_less_eq_rat @ zero_zero_rat @ B)) <= (ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2587_mult__right__less__imp__less)). 185.47/93.66 thf(11434,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ C) | ~ (ord_less_eq_rat @ zero_zero_rat @ B) | ~ (ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089])). 185.47/93.66 thf(2907,axiom,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2456_zero__less__power)). 185.47/93.66 thf(17373,plain,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ B)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2907])). 185.47/93.66 thf(4711,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ A) @ one_one_real) @ (power_power_real @ (plus_plus_real @ A @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7334_linear__plus__1__le__power)). 185.47/93.66 thf(23110,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ A) @ one_one_real) @ (power_power_real @ (plus_plus_real @ A @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4711])). 185.47/93.66 thf(2862,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_int @ C @ B)) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2349_mult__less__cancel__left__neg)). 185.47/93.66 thf(17231,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_int @ C @ B)) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2862])). 185.47/93.66 thf(5456,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_Suc__leI)). 185.47/93.66 thf(25811,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5456])). 185.47/93.66 thf(3498,axiom,((! [A:num]: ((archim6058952711729229775r_real @ (uminus_uminus_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A)))) = (divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9085_floor__minus__one__divide__eq__div__numeral)). 185.47/93.66 thf(19249,plain,((! [A:num]: ((archim6058952711729229775r_real @ (uminus_uminus_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A)))) = (divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3498])). 185.47/93.66 thf(2013,axiom,(((size_num @ one) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9228_num_Osize__gen_I1_J)). 185.47/93.66 thf(14466,plain,(((size_num @ one) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013])). 185.47/93.66 thf(2865,axiom,((! [A:num]: ((nat2 @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9252_nat__neg__numeral)). 185.47/93.66 thf(17241,plain,((! [A:num]: ((nat2 @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2865])). 185.47/93.66 thf(383,axiom,((bit_se6526347334894502574or_int = (^ [A:int,B:int]: (if_int @ (A = (uminus_uminus_int @ one_one_int)) @ (bit_ri7919022796975470100ot_int @ B) @ (if_int @ (B = (uminus_uminus_int @ one_one_int)) @ (bit_ri7919022796975470100ot_int @ A) @ (if_int @ (A = zero_zero_int) @ B @ (if_int @ (B = zero_zero_int) @ A @ (plus_plus_int @ (abs_abs_int @ (minus_minus_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se6526347334894502574or_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9496_xor__int__unfold)). 185.47/93.66 thf(9010,plain,(((bit_se6526347334894502574or_int) = (^ [A:int,B:int]: (if_int @ (A = (uminus_uminus_int @ one_one_int)) @ (bit_ri7919022796975470100ot_int @ B) @ (if_int @ (B = (uminus_uminus_int @ one_one_int)) @ (bit_ri7919022796975470100ot_int @ A) @ (if_int @ (A = zero_zero_int) @ B @ (if_int @ (B = zero_zero_int) @ A @ (plus_plus_int @ (abs_abs_int @ (minus_minus_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se6526347334894502574or_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])). 185.47/93.66 thf(5473,axiom,((! [A:(nat > complex)]: ((suminf_complex @ (^ [B:nat]: (times_times_complex @ (A @ B) @ (power_power_complex @ zero_zero_complex @ B)))) = (A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7556_powser__zero)). 185.47/93.66 thf(25950,plain,((! [A:(nat > complex)]: ((suminf_complex @ (^ [B:nat]: (times_times_complex @ (A @ B) @ (power_power_complex @ zero_zero_complex @ B)))) = (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5473])). 185.47/93.66 thf(165,axiom,((! [A:set_nat,B:(nat > rat)]: (((! [C:nat]: ((ord_less_eq_rat @ zero_zero_rat @ (B @ C)) <= (member_nat @ C @ A))) => (((groups2906978787729119204at_rat @ B @ A) = zero_zero_rat) = (! [C:nat]: ((member_nat @ C @ A) => ((B @ C) = zero_zero_rat))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5830_sum__nonneg__eq__0__iff)). 185.47/93.66 thf(8259,plain,((! [A:set_nat,B:(nat > rat)]: (((! [C:nat]: ((ord_less_eq_rat @ zero_zero_rat @ (B @ C)) | ~ (member_nat @ C @ A))) => (((groups2906978787729119204at_rat @ (B) @ A) = zero_zero_rat) = (! [C:nat]: ((member_nat @ C @ A) => ((B @ C) = zero_zero_rat))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 185.47/93.66 thf(5693,axiom,((! [A:num,B:num,C:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) @ C)) = (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5359_semiring__norm_I171_J)). 185.47/93.66 thf(26676,plain,((! [A:num,B:num,C:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) @ C)) = (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5693])). 185.47/93.66 thf(1905,axiom,((! [A:int]: ((ord_less_eq_int @ one_one_int @ A) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3166_int__one__le__iff__zero__less)). 185.47/93.66 thf(14097,plain,((! [A:int]: ((ord_less_eq_int @ one_one_int @ A) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1905])). 185.47/93.66 thf(1096,axiom,((! [A:int,B:int]: ((A != B) = ((ord_less_int @ B @ A) | (ord_less_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4062_linorder__neq__iff)). 185.47/93.66 thf(11455,plain,((! [A:int,B:int]: ((~ (A = B)) = ((ord_less_int @ B @ A) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096])). 185.47/93.66 thf(2111,axiom,((! [A:(int > $o),B:$o]: ((A @ (zero_n2684676970156552555ol_int @ B)) = (~ ((~ (A @ zero_zero_int) & ~ (B)) | ((B) & ~ (A @ one_one_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5675_split__of__bool__asm)). 185.47/93.66 thf(14760,plain,((! [A:(int > $o),B:$o]: ((A @ (zero_n2684676970156552555ol_int @ B)) = (~ ((~ (A @ zero_zero_int) & ~ (B)) | ((B) & ~ (A @ one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111])). 185.47/93.66 thf(2469,axiom,((! [A:int,B:(rat > int),C:rat,D:rat]: ((ord_less_int @ A @ (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) <= (ord_less_eq_rat @ E @ F))) => (ord_less_int @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4345_order__less__le__subst1)). 185.47/93.66 thf(15909,plain,((! [A:int,B:(rat > int),C:rat,D:rat]: ((ord_less_int @ A @ (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_rat @ E @ F))) => (ord_less_int @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2469])). 185.47/93.66 thf(5846,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_nat__le__iff__add)). 185.47/93.66 thf(27353,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5846])). 185.47/93.66 thf(984,axiom,((! [A:nat,B:int,C:int]: ((bit_ri631733984087533419it_int @ A @ (plus_plus_int @ (bit_ri631733984087533419it_int @ A @ B) @ (bit_ri631733984087533419it_int @ A @ C))) = (bit_ri631733984087533419it_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4689_signed__take__bit__add)). 185.47/93.66 thf(11105,plain,((! [A:nat,B:int,C:int]: ((bit_ri631733984087533419it_int @ A @ (plus_plus_int @ (bit_ri631733984087533419it_int @ A @ B) @ (bit_ri631733984087533419it_int @ A @ C))) = (bit_ri631733984087533419it_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[984])). 185.47/93.66 thf(7332,axiom,((! [A:nat,B:nat,C:nat]: ((((divide_divide_nat @ B @ A) = (divide_divide_nat @ C @ A)) = (B = C)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4769_unit__div__cancel)). 185.47/93.66 thf(32712,plain,((! [A:nat,B:nat,C:nat]: ((((divide_divide_nat @ B @ A) = (divide_divide_nat @ C @ A)) = (B = C)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7332])). 185.47/93.66 thf(3908,axiom,((! [A:real,B:real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (uminus_uminus_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5582_minus__divide__left)). 185.47/93.66 thf(20549,plain,((! [A:real,B:real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (uminus_uminus_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3908])). 185.47/93.66 thf(1683,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (bit0 @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_numeral__Bit0)). 185.47/93.66 thf(13368,plain,((! [A:num]: ((numera6690914467698888265omplex @ (bit0 @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683])). 185.47/93.66 thf(7296,axiom,((! [A:int,B:int]: (((plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1905_sum__power2__eq__zero__iff)). 185.47/93.66 thf(32589,plain,((! [A:int,B:int]: (((plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7296])). 185.47/93.66 thf(424,axiom,((! [A:nat,B:nat,C:(nat > rat)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (C @ (suc @ D)) @ (C @ D))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_rat @ (C @ (suc @ B)) @ (C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6678_sum__Suc__diff)). 185.47/93.66 thf(9142,plain,((! [A:nat,B:nat,C:(nat > rat)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (C @ (suc @ D)) @ (C @ D))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_rat @ (C @ (suc @ B)) @ (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])). 185.47/93.66 thf(6001,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (divide_divide_nat @ B @ A)) <= (ord_less_nat @ (modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2488_divmod__digit__0_I1_J)). 185.47/93.66 thf(27902,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (divide_divide_nat @ B @ A)) | ~ (ord_less_nat @ (modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6001])). 185.47/93.66 thf(4309,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ B) = (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5511_minus__le__iff)). 185.47/93.66 thf(21770,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ B) = (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4309])). 185.47/93.66 thf(1040,axiom,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((B @ D) != zero_zero_rat) & (member_nat @ D @ A))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((C @ D) != zero_zero_rat) & (member_nat @ D @ A))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((plus_plus_rat @ (B @ D) @ (C @ D)) != zero_zero_rat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3551_sum_Ofinite__Collect__op)). 185.47/93.66 thf(11279,plain,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((B @ D) = zero_zero_rat) & (member_nat @ D @ A))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((C @ D) = zero_zero_rat) & (member_nat @ D @ A))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((plus_plus_rat @ (B @ D) @ (C @ D)) = zero_zero_rat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040])). 185.47/93.66 thf(3182,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ C @ B)) <= (ord_less_eq_real @ one_one_real @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9091_powr__mono)). 185.47/93.66 thf(18245,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ C @ B)) | ~ (ord_less_eq_real @ one_one_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3182])). 185.47/93.66 thf(825,axiom,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_int @ (A @ zero_zero_nat) @ (groups705719431365010083at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8737_prod_OatMost__Suc__shift)). 185.47/93.66 thf(10547,plain,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_int @ (A @ zero_zero_nat) @ (groups705719431365010083at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[825])). 185.47/93.66 thf(5898,axiom,((! [A:option4927543243414619207at_nat,B:product_prod_nat_nat]: ((A = (some_P7363390416028606310at_nat @ B)) => (A != none_P5556105721700978146at_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1164_option_OdiscI)). 185.47/93.66 thf(27531,plain,((! [A:option4927543243414619207at_nat,B:product_prod_nat_nat]: ((A = (some_P7363390416028606310at_nat @ B)) => (~ (A = none_P5556105721700978146at_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5898])). 185.47/93.66 thf(3040,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2403_add__pos__pos)). 185.47/93.66 thf(17800,plain,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3040])). 185.47/93.66 thf(4718,axiom,((! [A:int]: ((modulo_modulo_int @ A @ one_one_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1758_mod__by__1)). 185.47/93.66 thf(23132,plain,((! [A:int]: ((modulo_modulo_int @ A @ one_one_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4718])). 185.47/93.66 thf(2004,axiom,((! [A:int,B:int]: ((ord_less_int @ (bit_se725231765392027082nd_int @ A @ B) @ zero_zero_int) = ((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ B @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9364_and__negative__int__iff)). 185.47/93.66 thf(14434,plain,((! [A:int,B:int]: ((ord_less_int @ (bit_se725231765392027082nd_int @ A @ B) @ zero_zero_int) = ((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ B @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004])). 185.47/93.66 thf(5903,axiom,((! [A:list_VEBT_VEBT,B:vEBT_VEBT,C:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ A @ B) @ C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2804_VEBT__internal_Omembermima_Osimps_I2_J)). 185.47/93.66 thf(27549,plain,((! [A:list_VEBT_VEBT,B:vEBT_VEBT,C:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ A @ B) @ C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5903])). 185.47/93.66 thf(4389,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ zero_zero_real @ (cos_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7928_cos__ge__zero)). 185.47/93.66 thf(22064,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ zero_zero_real @ (cos_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4389])). 185.47/93.66 thf(740,axiom,((! [A:nat,B:complex]: ((times_times_complex @ (semiri8010041392384452111omplex @ (suc @ A)) @ (gbinomial_complex @ B @ (suc @ A))) = (times_times_complex @ B @ (gbinomial_complex @ (minus_minus_complex @ B @ one_one_complex) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8535_gbinomial__absorption)). 185.47/93.66 thf(10200,plain,((! [A:nat,B:complex]: ((times_times_complex @ (semiri8010041392384452111omplex @ (suc @ A)) @ (gbinomial_complex @ B @ (suc @ A))) = (times_times_complex @ B @ (gbinomial_complex @ (minus_minus_complex @ B @ one_one_complex) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[740])). 185.47/93.66 thf(2190,axiom,((! [A:rat,B:(rat > rat),C:rat,D:rat]: ((ord_less_eq_rat @ A @ (B @ C)) => (((! [E:rat,F:rat]: ((ord_less_eq_rat @ (B @ E) @ (B @ F)) <= (ord_less_eq_rat @ E @ F))) => (ord_less_eq_rat @ A @ (B @ D))) <= (ord_less_eq_rat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3909_order__subst1)). 185.47/93.66 thf(15030,plain,((! [A:rat,B:(rat > rat),C:rat,D:rat]: ((ord_less_eq_rat @ A @ (B @ C)) => (((! [E:rat,F:rat]: ((ord_less_eq_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_rat @ E @ F))) => (ord_less_eq_rat @ A @ (B @ D))) | ~ (ord_less_eq_rat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2190])). 185.47/93.66 thf(6081,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((B = A) <= (ord_less_nat @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1033_less__antisym)). 185.47/93.66 thf(28139,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((B = A) | ~ (ord_less_nat @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6081])). 185.47/93.66 thf(3683,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((~ (ord_less_eq_rat @ C @ A)) <= (ord_less_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3304_pinf_I6_J)). 185.47/93.66 thf(19817,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: (~ (ord_less_eq_rat @ C @ A) | ~ (ord_less_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3683])). 185.47/93.66 thf(6813,axiom,((! [A:nat,B:real]: (((ord_less_eq_real @ zero_zero_real @ (root @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9169_real__root__ge__0__iff)). 185.47/93.66 thf(30787,plain,((! [A:nat,B:real]: (((ord_less_eq_real @ zero_zero_real @ (root @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6813])). 185.47/93.66 thf(5981,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1145_combine__common__factor)). 185.47/93.66 thf(27829,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5981])). 185.47/93.66 thf(4514,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) = (A = B)) <= (~ (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4166_antisym__conv1)). 185.47/93.66 thf(22463,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) = (A = B)) | (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4514])). 185.47/93.66 thf(601,axiom,((! [A:real]: (((arctan @ (divide_divide_real @ one_one_real @ A)) = (minus_minus_real @ (divide_divide_real @ (times_times_real @ (sgn_sgn_real @ A) @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ (arctan @ A))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9359_arctan__inverse)). 185.47/93.66 thf(9733,plain,((! [A:real]: (((arctan @ (divide_divide_real @ one_one_real @ A)) = (minus_minus_real @ (divide_divide_real @ (times_times_real @ (sgn_sgn_real @ A) @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ (arctan @ A))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[601])). 185.47/93.66 thf(2878,axiom,((! [A:real,B:real,C:num]: ((A = (divide_divide_real @ B @ (numeral_numeral_real @ C))) = (((A = zero_zero_real) <= ((numeral_numeral_real @ C) = zero_zero_real)) & (((times_times_real @ A @ (numeral_numeral_real @ C)) = B) <= ((numeral_numeral_real @ C) != zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1821_eq__divide__eq__numeral1_I1_J)). 185.47/93.66 thf(17280,plain,((! [A:real,B:real,C:num]: ((A = (divide_divide_real @ B @ (numeral_numeral_real @ C))) = (((A = zero_zero_real) | ~ ((numeral_numeral_real @ C) = zero_zero_real)) & (((times_times_real @ A @ (numeral_numeral_real @ C)) = B) | ((numeral_numeral_real @ C) = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2878])). 185.47/93.66 thf(6401,axiom,((! [A:rat]: ((times_times_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = (uminus_uminus_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5200_mult__minus1)). 185.47/93.66 thf(29284,plain,((! [A:rat]: ((times_times_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = (uminus_uminus_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6401])). 185.47/93.66 thf(1244,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (((ord_less_int @ B @ C) & (ord_less_int @ zero_zero_int @ A)) | ((ord_less_int @ C @ B) & (ord_less_int @ A @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2362_mult__less__cancel__left__disj)). 185.47/93.66 thf(11905,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (((ord_less_int @ B @ C) & (ord_less_int @ zero_zero_int @ A)) | ((ord_less_int @ C @ B) & (ord_less_int @ A @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244])). 185.47/93.66 thf(3008,axiom,((! [A:int,B:int]: (((modulo_modulo_int @ (uminus_uminus_int @ B) @ A) = (minus_minus_int @ (minus_minus_int @ A @ one_one_int) @ (modulo_modulo_int @ (minus_minus_int @ B @ one_one_int) @ A))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6242_minus__mod__int__eq)). 185.47/93.66 thf(17700,plain,((! [A:int,B:int]: (((modulo_modulo_int @ (uminus_uminus_int @ B) @ A) = (minus_minus_int @ (minus_minus_int @ A @ one_one_int) @ (modulo_modulo_int @ (minus_minus_int @ B @ one_one_int) @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3008])). 185.47/93.66 thf(4685,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ A @ one_one_int) @ (plus_plus_int @ B @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1206_add__mono1)). 185.47/93.66 thf(23017,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ A @ one_one_int) @ (plus_plus_int @ B @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4685])). 185.47/93.66 thf(6826,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1051_add__Suc__shift)). 185.47/93.66 thf(30826,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6826])). 185.47/93.66 thf(7113,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (divide_divide_nat @ B @ A) @ C) = (ord_less_nat @ B @ (times_times_nat @ C @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2797_div__less__iff__less__mult)). 185.47/93.66 thf(31941,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (divide_divide_nat @ B @ A) @ C) = (ord_less_nat @ B @ (times_times_nat @ C @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7113])). 185.47/93.66 thf(1290,axiom,((! [A:int,B:nat]: ((ring_1_of_int_rat @ (power_power_int @ A @ B)) = (power_power_rat @ (ring_1_of_int_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6987_of__int__power)). 185.47/93.66 thf(12038,plain,((! [A:int,B:nat]: ((ring_1_of_int_rat @ (power_power_int @ A @ B)) = (power_power_rat @ (ring_1_of_int_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290])). 185.47/93.66 thf(1377,axiom,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (sin_real @ A)) @ (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7833_abs__sin__x__le__abs__x)). 185.47/93.66 thf(12317,plain,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (sin_real @ A)) @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377])). 185.47/93.66 thf(4433,axiom,((! [A:nat,B:nat,C:(nat > real),D:(nat > real)]: ((ord_less_eq_nat @ one_one_nat @ A) => (((groups129246275422532515t_real @ (^ [E:nat]: (if_real @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_real @ (E = B) @ one_one_real @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups129246275422532515t_real @ (^ [E:nat]: (if_real @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8867_prod_Ozero__middle)). 185.47/93.66 thf(22188,plain,((! [A:nat,B:nat,C:(nat > real),D:(nat > real)]: ((ord_less_eq_nat @ one_one_nat @ A) => (((groups129246275422532515t_real @ (^ [E:nat]: (if_real @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_real @ (E = B) @ one_one_real @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups129246275422532515t_real @ (^ [E:nat]: (if_real @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4433])). 185.47/93.66 thf(4505,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_linordered__field__no__lb)). 185.47/93.66 thf(22419,plain,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4505])). 185.47/93.66 thf(1350,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (ord_le3102999989581377725nteger @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5034_neg__le__iff__le)). 185.47/93.66 thf(12231,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (ord_le3102999989581377725nteger @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350])). 185.47/93.66 thf(5019,axiom,((! [A:nat]: ((bit_se7882103937844011126it_nat @ zero_zero_nat @ A) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3022_set__bit__0)). 185.47/93.66 thf(24161,plain,((! [A:nat]: ((bit_se7882103937844011126it_nat @ zero_zero_nat @ A) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5019])). 185.47/93.66 thf(1872,axiom,(((neg_nu6075765906172075777c_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6776_dbl__dec__simps_I3_J)). 185.47/93.66 thf(13999,plain,(((neg_nu6075765906172075777c_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1872])). 185.47/93.66 thf(2897,axiom,((! [A:complex]: ((sin_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sin_complex @ A)) @ (cos_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7827_sin__double)). 185.47/93.66 thf(17347,plain,((! [A:complex]: ((sin_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sin_complex @ A)) @ (cos_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2897])). 185.47/93.66 thf(7548,axiom,((~ (? [A:nat]: ((ord_less_nat @ A @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) & (vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26__C33_C)). 185.47/93.66 thf(33428,plain,((~ (? [A:nat]: ((ord_less_nat @ A @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) & (vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7548])). 185.47/93.66 thf(3114,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (plus_plus_rat @ B @ A)) = (ord_less_eq_rat @ zero_zero_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1618_le__add__same__cancel2)). 185.47/93.66 thf(18038,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ (plus_plus_rat @ B @ A)) = (ord_less_eq_rat @ zero_zero_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3114])). 185.47/93.66 thf(1211,axiom,((! [A:rat,B:rat]: (((divide_divide_rat @ B @ (uminus_uminus_rat @ A)) = (uminus_uminus_rat @ (divide_divide_rat @ B @ A))) <= (dvd_dvd_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5810_dvd__div__neg)). 185.47/93.66 thf(11804,plain,((! [A:rat,B:rat]: (((divide_divide_rat @ B @ (uminus_uminus_rat @ A)) = (uminus_uminus_rat @ (divide_divide_rat @ B @ A))) | ~ (dvd_dvd_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211])). 185.47/93.66 thf(3676,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ A @ B)) @ C) = (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (uminus_uminus_real @ A) @ (times_times_real @ C @ B))) & ((((~ (ord_less_real @ B @ zero_zero_real)) => (ord_less_eq_real @ zero_zero_real @ C)) & ((ord_less_eq_real @ (times_times_real @ C @ B) @ (uminus_uminus_real @ A)) <= (ord_less_real @ B @ zero_zero_real))) <= (~ (ord_less_real @ zero_zero_real @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6208_minus__divide__le__eq)). 185.47/93.66 thf(19797,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ A @ B)) @ C) = (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (uminus_uminus_real @ A) @ (times_times_real @ C @ B))) & ((((~ (ord_less_real @ B @ zero_zero_real)) => (ord_less_eq_real @ zero_zero_real @ C)) & ((ord_less_eq_real @ (times_times_real @ C @ B) @ (uminus_uminus_real @ A)) | ~ (ord_less_real @ B @ zero_zero_real))) | (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3676])). 185.47/93.66 thf(3847,axiom,(((semiri5074537144036343181t_real @ zero_zero_nat) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6884_of__nat__0)). 185.47/93.66 thf(20356,plain,(((semiri5074537144036343181t_real @ zero_zero_nat) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3847])). 185.47/93.66 thf(808,axiom,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: ((if_Pro6206227464963214023at_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T)). 185.47/93.66 thf(10480,plain,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: ((if_Pro6206227464963214023at_nat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[808])). 185.47/93.66 thf(1022,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = B) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1518_add__cancel__left__left)). 185.47/93.66 thf(11226,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = B) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022])). 185.47/93.66 thf(4138,axiom,((! [A:int,B:int]: (((modulo_modulo_int @ A @ B) = zero_zero_int) = (? [C:int]: (A = (times_times_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3155_zmod__eq__0__iff)). 185.47/93.66 thf(21255,plain,((! [A:int,B:int]: (((modulo_modulo_int @ A @ B) = zero_zero_int) = (? [C:int]: (A = (times_times_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4138])). 185.47/93.66 thf(4489,axiom,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ (times_times_rat @ A @ B)) = (divide_divide_rat @ one_one_rat @ B)) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1831_nonzero__divide__mult__cancel__left)). 185.47/93.66 thf(22372,plain,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ (times_times_rat @ A @ B)) = (divide_divide_rat @ one_one_rat @ B)) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4489])). 185.47/93.66 thf(5716,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_3907_Orderings_Oorder__eq__iff)). 185.47/93.66 thf(26758,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)],[5716])). 185.47/93.66 thf(7707,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_vebt_member @ A @ B) => ((vEBT_invar_vebt @ A @ C) => (ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_member__bound)). 185.47/93.66 thf(33863,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_vebt_member @ A @ B) => ((vEBT_invar_vebt @ A @ C) => (ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7707])). 185.47/93.66 thf(593,axiom,((! [A:nat,B:int]: ((bit_concat_bit @ A @ (bit_se2923211474154528505it_int @ A @ B)) = (bit_concat_bit @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9274_concat__bit__take__bit__eq)). 185.47/93.66 thf(9706,plain,((! [A:nat,B:int]: ((bit_concat_bit @ A @ (bit_se2923211474154528505it_int @ A @ B)) = (bit_concat_bit @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[593])). 185.47/93.66 thf(5497,axiom,((! [A:nat,B:int]: (((times_times_int @ (power_power_int @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_int @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2967_power__minus__mult)). 185.47/93.66 thf(26038,plain,((! [A:nat,B:int]: (((times_times_int @ (power_power_int @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_int @ B @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5497])). 185.47/93.66 thf(3408,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_eq_real @ (times_times_real @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2844_pos__le__divide__eq)). 185.47/93.66 thf(18953,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_eq_real @ (times_times_real @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3408])). 185.47/93.66 thf(1578,axiom,((! [A:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6362_abs__le__zero__iff)). 185.47/93.66 thf(12958,plain,((! [A:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ zero_zero_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578])). 185.47/93.66 thf(6218,axiom,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2486_power__0)). 185.47/93.66 thf(28657,plain,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6218])). 185.47/93.66 thf(5876,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1499_mult__cancel__left)). 185.47/93.66 thf(27448,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5876])). 185.47/93.66 thf(4460,axiom,((! [A:int,B:int,C:nat]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (ring_1_of_int_real @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7106_of__int__power__less__of__int__cancel__iff)). 185.47/93.66 thf(22277,plain,((! [A:int,B:int,C:nat]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (ring_1_of_int_real @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4460])). 185.47/93.66 thf(2587,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ A @ C) <= (ord_less_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4210_order_Ostrict__trans1)). 185.47/93.66 thf(16323,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ A @ C) | ~ (ord_less_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2587])). 185.47/93.66 thf(4188,axiom,((! [A:num,B:rat,C:rat]: ((ord_less_rat @ (numeral_numeral_rat @ A) @ (divide_divide_rat @ B @ C)) = (((((ord_less_rat @ C @ zero_zero_rat) => (ord_less_rat @ B @ (times_times_rat @ (numeral_numeral_rat @ A) @ C))) & ((ord_less_rat @ (numeral_numeral_rat @ A) @ zero_zero_rat) <= (~ (ord_less_rat @ C @ zero_zero_rat)))) <= (~ (ord_less_rat @ zero_zero_rat @ C))) & ((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ (numeral_numeral_rat @ A) @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2860_less__divide__eq__numeral_I1_J)). 185.47/93.66 thf(21413,plain,((! [A:num,B:rat,C:rat]: ((ord_less_rat @ (numeral_numeral_rat @ A) @ (divide_divide_rat @ B @ C)) = (((((ord_less_rat @ C @ zero_zero_rat) => (ord_less_rat @ B @ (times_times_rat @ (numeral_numeral_rat @ A) @ C))) & ((ord_less_rat @ (numeral_numeral_rat @ A) @ zero_zero_rat) | (ord_less_rat @ C @ zero_zero_rat))) | (ord_less_rat @ zero_zero_rat @ C)) & ((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ (numeral_numeral_rat @ A) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4188])). 185.47/93.66 thf(3720,axiom,((! [A:num,B:num]: (ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (numeral_numeral_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5704_neg__numeral__less__numeral)). 185.47/93.66 thf(19949,plain,((! [A:num,B:num]: (ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (numeral_numeral_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3720])). 185.47/93.66 thf(7115,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_eq_nat @ one_one_nat @ B) => (? [C:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ C) @ B) & (ord_less_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_917_ex__power__ivl1)). 185.47/93.66 thf(31947,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_eq_nat @ one_one_nat @ B) => (? [C:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ C) @ B) & (ord_less_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7115])). 185.47/93.66 thf(518,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ (ln_ln_real @ A)) = (ord_less_eq_real @ (exp_real @ B) @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8207_ln__ge__iff)). 185.47/93.66 thf(9471,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ (ln_ln_real @ A)) = (ord_less_eq_real @ (exp_real @ B) @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[518])). 185.47/93.66 thf(5578,axiom,((! [A:rat,B:rat]: (((times_times_rat @ A @ B) = B) = ((B = zero_zero_rat) | (A = one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1675_mult__cancel__right2)). 185.47/93.66 thf(26296,plain,((! [A:rat,B:rat]: (((times_times_rat @ A @ B) = B) = ((B = zero_zero_rat) | (A = one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5578])). 185.47/93.66 thf(4094,axiom,((finite_finite_nat = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) <= (member_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3394_finite__nat__set__iff__bounded)). 185.47/93.66 thf(21122,plain,(((finite_finite_nat) = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) | ~ (member_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4094])). 185.47/93.66 thf(763,axiom,((! [A:complex]: (ord_less_eq_real @ (abs_abs_real @ (im @ A)) @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9675_abs__Im__le__cmod)). 185.47/93.66 thf(10329,plain,((! [A:complex]: (ord_less_eq_real @ (abs_abs_real @ (im @ A)) @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[763])). 185.47/93.66 thf(153,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (groups6591440286371151544t_real @ B @ A)) @ (groups6591440286371151544t_real @ C @ A)) <= (! [D:nat]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (B @ D)) @ (C @ D)) <= (member_nat @ D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7468_sum__norm__le)). 185.47/93.66 thf(8222,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (groups6591440286371151544t_real @ (B) @ A)) @ (groups6591440286371151544t_real @ (C) @ A)) | ~ (! [D:nat]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (B @ D)) @ (C @ D)) | ~ (member_nat @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 185.47/93.66 thf(1741,axiom,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5948_neg__one__less__numeral)). 185.47/93.66 thf(13569,plain,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741])). 185.47/93.66 thf(540,axiom,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se6526347334894502574or_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ A @ C) != (bit_se1146084159140164899it_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9490_bit__xor__int__iff)). 185.47/93.66 thf(9531,plain,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se6526347334894502574or_int @ A @ B) @ C) = (~ ((bit_se1146084159140164899it_int @ A @ C) = (bit_se1146084159140164899it_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[540])). 185.47/93.66 thf(6317,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (minus_minus_nat @ B @ A) @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2506_diff__less)). 185.47/93.66 thf(28992,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (minus_minus_nat @ B @ A) @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6317])). 185.47/93.66 thf(7521,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6908_of__nat__le__iff)). 185.47/93.66 thf(33350,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7521])). 185.47/93.66 thf(292,axiom,((! [A:set_nat,B:(nat > nat)]: (((groups708209901874060359at_nat @ B @ A) = one_one_nat) <= (! [C:nat]: (((B @ C) = one_one_nat) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8709_prod_Oneutral)). 185.47/93.66 thf(8684,plain,((! [A:set_nat,B:(nat > nat)]: (((groups708209901874060359at_nat @ (B) @ A) = one_one_nat) | ~ (! [C:nat]: (((B @ C) = one_one_nat) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 185.47/93.66 thf(5421,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_add__le__cancel__right)). 185.47/93.66 thf(25658,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5421])). 185.47/93.66 thf(3865,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (times_times_real @ C @ B)) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4606_dvd__mult)). 185.47/93.66 thf(20411,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (times_times_real @ C @ B)) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3865])). 185.47/93.66 thf(2553,axiom,((! [A:int,B:int]: ((ring_1_of_int_rat @ (times_times_int @ A @ B)) = (times_times_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6971_of__int__mult)). 185.47/93.66 thf(16199,plain,((! [A:int,B:int]: ((ring_1_of_int_rat @ (times_times_int @ A @ B)) = (times_times_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2553])). 185.47/93.66 thf(5917,axiom,((! [A:rat,B:rat]: ((power_power_rat @ (minus_minus_rat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_910_power2__diff)). 185.47/93.66 thf(27590,plain,((! [A:rat,B:rat]: ((power_power_rat @ (minus_minus_rat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5917])). 185.47/93.66 thf(3937,axiom,((! [A:nat,B:nat,C:rat]: (((comm_s4028243227959126397er_rat @ C @ B) = (times_times_rat @ (comm_s4028243227959126397er_rat @ C @ A) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ C @ (semiri681578069525770553at_rat @ A)) @ (minus_minus_nat @ B @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8544_pochhammer__product)). 185.47/93.66 thf(20641,plain,((! [A:nat,B:nat,C:rat]: (((comm_s4028243227959126397er_rat @ C @ B) = (times_times_rat @ (comm_s4028243227959126397er_rat @ C @ A) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ C @ (semiri681578069525770553at_rat @ A)) @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3937])). 185.47/93.66 thf(711,axiom,(((arctan @ one_one_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7764_arctan__one)). 185.47/93.66 thf(10100,plain,(((arctan @ one_one_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[711])). 185.47/93.66 thf(5340,axiom,((! [A:nat,B:nat]: (((binomial @ B @ A) = (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8538_binomial__altdef__nat)). 185.47/93.66 thf(25376,plain,((! [A:nat,B:nat]: (((binomial @ B @ A) = (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5340])). 185.47/93.66 thf(2094,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ B) <= (ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6513_abs__le__D2)). 185.47/93.66 thf(14714,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ B) | ~ (ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2094])). 185.47/93.66 thf(2654,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))) = ((B != zero_zero_real) | (A != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2688_sum__squares__gt__zero__iff)). 185.47/93.66 thf(16532,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))) = (~ (B = zero_zero_real) | ~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2654])). 185.47/93.66 thf(91,axiom,((! [A:num,B:num]: ((archim7802044766580827645g_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B))) = (uminus_uminus_int @ (divide_divide_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9065_ceiling__divide__eq__div__numeral)). 185.47/93.66 thf(8027,plain,((! [A:num,B:num]: ((archim7802044766580827645g_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B))) = (uminus_uminus_int @ (divide_divide_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[91])). 185.47/93.66 thf(1549,axiom,((! [A:int,B:int,C:(int > $o)]: ((ord_less_eq_int @ A @ B) => (((! [D:int]: (((C @ (plus_plus_int @ D @ one_one_int)) <= (C @ D)) <= (ord_less_eq_int @ A @ D))) => (C @ B)) <= (C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3179_int__ge__induct)). 185.47/93.66 thf(12862,plain,((! [A:int,B:int,C:(int > $o)]: ((ord_less_eq_int @ A @ B) => (((! [D:int]: ((C @ (plus_plus_int @ D @ one_one_int)) | ~ (C @ D) | ~ (ord_less_eq_int @ A @ D))) => (C @ B)) | ~ (C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549])). 185.47/93.66 thf(4770,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (! [C:real]: ((ord_less_eq_real @ C @ B) <= (ord_less_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4180_dense__le)). 185.47/93.66 thf(23331,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (! [C:real]: ((ord_less_eq_real @ C @ B) | ~ (ord_less_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4770])). 185.47/93.66 thf(1798,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_real @ (times_times_real @ B @ A) @ (uminus_uminus_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6152_pos__less__minus__divide__eq)). 185.47/93.66 thf(13755,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_real @ (times_times_real @ B @ A) @ (uminus_uminus_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1798])). 185.47/93.66 thf(2101,axiom,((! [A:int,B:int,C:nat]: (((ring_1_of_int_real @ A) = (power_power_real @ (ring_1_of_int_real @ B) @ C)) = (A = (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6980_of__int__power__eq__of__int__cancel__iff)). 185.47/93.66 thf(14731,plain,((! [A:int,B:int,C:nat]: (((ring_1_of_int_real @ A) = (power_power_real @ (ring_1_of_int_real @ B) @ C)) = (A = (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2101])). 185.47/93.66 thf(3489,axiom,((! [A:rat,B:rat,C:num]: ((ord_less_rat @ A @ (divide_divide_rat @ B @ (numeral_numeral_rat @ C))) = (ord_less_rat @ (times_times_rat @ A @ (numeral_numeral_rat @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_less__divide__eq__numeral1_I1_J)). 185.47/93.66 thf(19215,plain,((! [A:rat,B:rat,C:num]: ((ord_less_rat @ A @ (divide_divide_rat @ B @ (numeral_numeral_rat @ C))) = (ord_less_rat @ (times_times_rat @ A @ (numeral_numeral_rat @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3489])). 185.47/93.66 thf(6384,axiom,((! [A:num]: ((power_power_rat @ zero_zero_rat @ (numeral_numeral_nat @ A)) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1746_power__zero__numeral)). 185.47/93.66 thf(29225,plain,((! [A:num]: ((power_power_rat @ zero_zero_rat @ (numeral_numeral_nat @ A)) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6384])). 185.47/93.66 thf(1395,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2975_power2__less__imp__less)). 185.47/93.66 thf(12386,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395])). 185.47/93.66 thf(3452,axiom,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ one) @ (numeral_numeral_int @ (bit0 @ A))) != (modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ B)) @ (numeral_numeral_int @ (bit0 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2158_cong__exp__iff__simps_I6_J)). 185.47/93.66 thf(19083,plain,((! [A:num,B:num]: ~ ((modulo_modulo_int @ (numeral_numeral_int @ one) @ (numeral_numeral_int @ (bit0 @ A))) = (modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ B)) @ (numeral_numeral_int @ (bit0 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3452])). 185.47/93.66 thf(6271,axiom,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_776_mult_Ocomm__neutral)). 185.47/93.66 thf(28841,plain,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6271])). 185.47/93.66 thf(1738,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) <= (ord_less_eq_rat @ zero_zero_rat @ B)) <= (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2419_divide__nonpos__nonneg)). 185.47/93.66 thf(13561,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) | ~ (ord_less_eq_rat @ zero_zero_rat @ B) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738])). 185.47/93.66 thf(4090,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_711_diff__strict__right__mono)). 185.47/93.66 thf(21109,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ C)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4090])). 185.47/93.66 thf(5550,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (vEBT_VEBT_less @ (some_nat @ A) @ (some_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_less__shift)). 185.47/93.66 thf(26213,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (vEBT_VEBT_less @ (some_nat @ A) @ (some_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5550])). 185.47/93.66 thf(1359,axiom,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1571_bits__div__by__0)). 185.47/93.66 thf(12259,plain,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359])). 185.47/93.66 thf(4120,axiom,((! [A:int,B:int,C:int,D:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ (plus_plus_int @ (times_times_int @ C @ B) @ D)) = (plus_plus_int @ (times_times_int @ (plus_plus_int @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1146_combine__common__factor)). 185.47/93.66 thf(21201,plain,((! [A:int,B:int,C:int,D:int]: ((plus_plus_int @ (times_times_int @ A @ B) @ (plus_plus_int @ (times_times_int @ C @ B) @ D)) = (plus_plus_int @ (times_times_int @ (plus_plus_int @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4120])). 185.47/93.66 thf(5246,axiom,(((semiri1406184849735516958ct_int @ zero_zero_nat) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7955_fact__0)). 185.47/93.66 thf(25029,plain,(((semiri1406184849735516958ct_int @ zero_zero_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5246])). 185.47/93.66 thf(1187,axiom,((! [A:rat,B:(num > rat),C:num,D:num]: ((((! [E:num,F:num]: ((ord_less_rat @ (B @ E) @ (B @ F)) <= (ord_less_num @ E @ F))) => (ord_less_rat @ A @ (B @ D))) <= (ord_less_num @ C @ D)) <= (ord_less_eq_rat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4328_order__le__less__subst1)). 185.47/93.66 thf(11729,plain,((! [A:rat,B:(num > rat),C:num,D:num]: (((! [E:num,F:num]: ((ord_less_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_num @ E @ F))) => (ord_less_rat @ A @ (B @ D))) | ~ (ord_less_num @ C @ D) | ~ (ord_less_eq_rat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187])). 185.47/93.66 thf(1563,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = ((dvd_dvd_real @ B @ C) | (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4454_dvd__mult__cancel__left)). 185.47/93.66 thf(12909,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = ((dvd_dvd_real @ B @ C) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1563])). 185.47/93.66 thf(3633,axiom,((! [A:rat,B:rat,C:num]: ((times_times_rat @ (plus_plus_rat @ A @ B) @ (numeral_numeral_rat @ C)) = (plus_plus_rat @ (times_times_rat @ A @ (numeral_numeral_rat @ C)) @ (times_times_rat @ B @ (numeral_numeral_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_distrib__right__numeral)). 185.47/93.66 thf(19659,plain,((! [A:rat,B:rat,C:num]: ((times_times_rat @ (plus_plus_rat @ A @ B) @ (numeral_numeral_rat @ C)) = (plus_plus_rat @ (times_times_rat @ A @ (numeral_numeral_rat @ C)) @ (times_times_rat @ B @ (numeral_numeral_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3633])). 185.47/93.66 thf(3791,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ (divide_divide_rat @ A @ C) @ (divide_divide_rat @ B @ C)) <= (ord_less_rat @ zero_zero_rat @ C)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2442_divide__strict__right__mono)). 185.47/93.66 thf(20183,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ C) @ (divide_divide_rat @ B @ C)) | ~ (ord_less_rat @ zero_zero_rat @ C) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3791])). 185.47/93.66 thf(1681,axiom,((ord_less_int = (^ [A:int,B:int]: ? [C:nat]: (B = (plus_plus_int @ A @ (semiri1314217659103216013at_int @ (suc @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7273_zless__iff__Suc__zadd)). 185.47/93.66 thf(13363,plain,(((ord_less_int) = (^ [A:int,B:int]: ? [C:nat]: (B = (plus_plus_int @ A @ (semiri1314217659103216013at_int @ (suc @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681])). 185.47/93.66 thf(6638,axiom,((! [A:(nat > $o),B:$o]: ((A @ (zero_n2687167440665602831ol_nat @ B)) = (~ ((~ (A @ zero_zero_nat) & ~ (B)) | (~ (A @ one_one_nat) & (B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5674_split__of__bool__asm)). 185.47/93.66 thf(30127,plain,((! [A:(nat > $o),B:$o]: ((A @ (zero_n2687167440665602831ol_nat @ B)) = (~ ((~ (A @ zero_zero_nat) & ~ (B)) | (~ (A @ one_one_nat) & (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6638])). 185.47/93.66 thf(4948,axiom,((! [A:num,B:num]: ((A != B) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3978_less__imp__neq)). 185.47/93.66 thf(23934,plain,((! [A:num,B:num]: (~ (A = B) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4948])). 185.47/93.66 thf(7076,axiom,((binomial = (^ [A:nat,B:nat]: (if_nat @ (ord_less_nat @ A @ B) @ zero_zero_nat @ (if_nat @ (ord_less_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (binomial @ A @ (minus_minus_nat @ A @ B)) @ (divide_divide_nat @ (set_fo2584398358068434914at_nat @ times_times_nat @ (plus_plus_nat @ (minus_minus_nat @ A @ B) @ one_one_nat) @ A @ one_one_nat) @ (semiri1408675320244567234ct_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8399_binomial__code)). 185.47/93.66 thf(31823,plain,(((binomial) = (^ [A:nat,B:nat]: (if_nat @ (ord_less_nat @ A @ B) @ zero_zero_nat @ (if_nat @ (ord_less_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (binomial @ A @ (minus_minus_nat @ A @ B)) @ (divide_divide_nat @ (set_fo2584398358068434914at_nat @ times_times_nat @ (plus_plus_nat @ (minus_minus_nat @ A @ B) @ one_one_nat) @ A @ one_one_nat) @ (semiri1408675320244567234ct_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7076])). 185.47/93.66 thf(6778,axiom,((! [A:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one))) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5982_mult__1s__ring__1_I2_J)). 185.47/93.66 thf(30664,plain,((! [A:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one))) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6778])). 185.47/93.66 thf(398,axiom,((! [A:real,B:real]: ((((ord_less_real @ (arccos @ A) @ (arccos @ B)) = (ord_less_real @ B @ A)) <= (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real)) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8367_arccos__less__mono)). 185.47/93.66 thf(9057,plain,((! [A:real,B:real]: (((ord_less_real @ (arccos @ A) @ (arccos @ B)) = (ord_less_real @ B @ A)) | ~ (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[398])). 185.47/93.66 thf(3513,axiom,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5894_neg__numeral__le__zero)). 185.47/93.66 thf(19296,plain,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3513])). 185.47/93.66 thf(5535,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) <= (ord_less_nat @ F @ E))) <= (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ F @ E)))) <= (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) <= (ord_less_nat @ F @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3263_minf_I2_J)). 185.47/93.66 thf(26163,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (? [E:nat]: ! [F:nat]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) | ~ (ord_less_nat @ F @ E)) | ~ (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ F @ E))) | ~ (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) | ~ (ord_less_nat @ F @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5535])). 185.47/93.66 thf(2825,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ A) = (ord_less_eq_real @ B @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1629_add__le__same__cancel1)). 185.47/93.66 thf(17109,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ A) = (ord_less_eq_real @ B @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2825])). 185.47/93.66 thf(2922,axiom,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (times_times_complex @ C @ A)) @ A)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6163_minus__divide__add__eq__iff)). 185.47/93.66 thf(17422,plain,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (times_times_complex @ C @ A)) @ A)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2922])). 185.47/93.66 thf(1947,axiom,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (divide_divide_rat @ (plus_plus_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)) @ A)) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6164_minus__divide__add__eq__iff)). 185.47/93.66 thf(14247,plain,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (divide_divide_rat @ (plus_plus_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)) @ A)) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1947])). 185.47/93.66 thf(4754,axiom,((gbinomial_complex = (^ [A:complex,B:nat]: (divide1717551699836669952omplex @ (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ A) @ B)) @ (semiri5044797733671781792omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8454_gbinomial__pochhammer)). 185.47/93.66 thf(23245,plain,(((gbinomial_complex) = (^ [A:complex,B:nat]: (divide1717551699836669952omplex @ (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ A) @ B)) @ (semiri5044797733671781792omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4754])). 185.47/93.66 thf(801,axiom,((! [A:complex,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (gbinomial_complex @ A @ C) @ (minus_minus_complex @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ (bit0 @ one))) @ (semiri8010041392384452111omplex @ C)))) @ (set_ord_atMost_nat @ B)) = (times_times_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ B) @ one_one_complex) @ (numera6690914467698888265omplex @ (bit0 @ one))) @ (gbinomial_complex @ A @ (plus_plus_nat @ B @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8618_gbinomial__partial__row__sum)). 185.47/93.66 thf(10461,plain,((! [A:complex,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (gbinomial_complex @ A @ C) @ (minus_minus_complex @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ (bit0 @ one))) @ (semiri8010041392384452111omplex @ C)))) @ (set_ord_atMost_nat @ B)) = (times_times_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ B) @ one_one_complex) @ (numera6690914467698888265omplex @ (bit0 @ one))) @ (gbinomial_complex @ A @ (plus_plus_nat @ B @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[801])). 185.47/93.66 thf(2207,axiom,((! [A:int,B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ (ring_1_of_int_rat @ A)) @ B) => ((A = zero_zero_int) | (ord_less_eq_rat @ one_one_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7283_of__int__leD)). 185.47/93.66 thf(15079,plain,((! [A:int,B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ (ring_1_of_int_rat @ A)) @ B) => ((A = zero_zero_int) | (ord_less_eq_rat @ one_one_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2207])). 185.47/93.66 thf(7250,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C))) <= (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1057_lift__Suc__mono__less)). 185.47/93.66 thf(32432,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C))) | ~ (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7250])). 185.47/93.66 thf(4478,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ A @ C)) = ((B = C) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1580_divide__cancel__left)). 185.47/93.66 thf(22340,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ A @ C)) = ((B = C) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4478])). 185.47/93.66 thf(72,axiom,((! [A:int,B:int,C:nat]: ((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (times_times_int @ (power_power_int @ (plus_plus_int @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_int @ A @ D)) @ (power_power_int @ A @ C))) @ (set_ord_lessThan_nat @ C)) = (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (power_power_int @ A @ D) @ (minus_minus_int @ (power_power_int @ (plus_plus_int @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_int @ A @ (minus_minus_nat @ C @ D))))) @ (set_ord_lessThan_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7610_lemma__termdiff1)). 185.47/93.66 thf(7963,plain,((! [A:int,B:int,C:nat]: ((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (times_times_int @ (power_power_int @ (plus_plus_int @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_int @ A @ D)) @ (power_power_int @ A @ C))) @ (set_ord_lessThan_nat @ C)) = (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (power_power_int @ A @ D) @ (minus_minus_int @ (power_power_int @ (plus_plus_int @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_int @ A @ (minus_minus_nat @ C @ D))))) @ (set_ord_lessThan_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 185.47/93.66 thf(5208,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ C)) = (ord_less_nat @ (plus_plus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_810_less__diff__conv)). 185.47/93.66 thf(24897,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ C)) = (ord_less_nat @ (plus_plus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5208])). 185.47/93.66 thf(4579,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_add__diff__cancel__right_H)). 185.47/93.66 thf(22668,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4579])). 185.47/93.66 thf(1971,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ B @ A) @ (times_times_complex @ A @ C)) = (divide1717551699836669952omplex @ B @ C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1696_nonzero__mult__divide__mult__cancel__right2)). 185.47/93.66 thf(14326,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ B @ A) @ (times_times_complex @ A @ C)) = (divide1717551699836669952omplex @ B @ C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1971])). 185.47/93.66 thf(2876,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((((divide_divide_int @ B @ A) = (divide_divide_int @ C @ A)) = (B = C)) <= (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4667_dvd__div__eq__iff)). 185.47/93.66 thf(17273,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((((divide_divide_int @ B @ A) = (divide_divide_int @ C @ A)) = (B = C)) | ~ (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2876])). 185.47/93.66 thf(6110,axiom,((! [A:nat,B:(num > nat),C:num,D:num]: ((((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))) <= (ord_less_eq_num @ C @ D)) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3918_order__subst1)). 185.47/93.66 thf(28251,plain,((! [A:nat,B:(num > nat),C:num,D:num]: (((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) => (ord_less_eq_nat @ A @ (B @ D))) | ~ (ord_less_eq_num @ C @ D) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6110])). 185.47/93.66 thf(110,axiom,((! [A:complex,B:num]: ((im @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B))) = (divide_divide_real @ (im @ A) @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9666_Im__divide__numeral)). 185.47/93.66 thf(8092,plain,((! [A:complex,B:num]: ((im @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B))) = (divide_divide_real @ (im @ A) @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 185.47/93.66 thf(3281,axiom,((! [A:num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2262_zero__less__numeral)). 185.47/93.66 thf(18548,plain,((! [A:num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3281])). 185.47/93.66 thf(5926,axiom,((! [A:nat]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ A) = (minus_minus_nat @ (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9485_Suc__0__xor__eq)). 185.47/93.66 thf(27618,plain,((! [A:nat]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ A) = (minus_minus_nat @ (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5926])). 185.47/93.66 thf(3808,axiom,((! [A:(nat > $o)]: (((collect_nat @ A) = bot_bot_set_nat) = (! [B:nat]: ~ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1272_Collect__empty__eq)). 185.47/93.66 thf(20237,plain,((! [A:(nat > $o)]: (((collect_nat @ (A)) = bot_bot_set_nat) = (! [B:nat]: ~ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3808])). 185.47/93.66 thf(2296,axiom,((! [A:nat,B:num,C:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (numeral_numeral_int @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7130_of__nat__le__numeral__power__cancel__iff)). 185.47/93.66 thf(15348,plain,((! [A:nat,B:num,C:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (numeral_numeral_int @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2296])). 185.47/93.66 thf(6453,axiom,((! [A:int,B:int]: ((times_times_int @ A @ (uminus_uminus_int @ B)) = (uminus_uminus_int @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5080_mult__minus__right)). 185.47/93.66 thf(29492,plain,((! [A:int,B:int]: ((times_times_int @ A @ (uminus_uminus_int @ B)) = (uminus_uminus_int @ (times_times_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6453])). 185.47/93.66 thf(3010,axiom,((! [A:real,B:real]: ((sin_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ (times_times_real @ (sin_real @ A) @ (cos_real @ B)) @ (times_times_real @ (cos_real @ A) @ (sin_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7818_sin__diff)). 185.47/93.66 thf(17705,plain,((! [A:real,B:real]: ((sin_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ (times_times_real @ (sin_real @ A) @ (cos_real @ B)) @ (times_times_real @ (cos_real @ A) @ (sin_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3010])). 185.47/93.66 thf(6206,axiom,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2943_zero__le__power2)). 185.47/93.66 thf(28621,plain,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6206])). 185.47/93.66 thf(2882,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ B @ (plus_plus_int @ A @ C)) <= (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2306_add__increasing)). 185.47/93.66 thf(17292,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ B @ (plus_plus_int @ A @ C)) | ~ (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2882])). 185.47/93.66 thf(7573,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4923_even__even__mod__4__iff)). 185.47/93.66 thf(33498,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7573])). 185.47/93.66 thf(6185,axiom,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ C @ B)) = ((B = zero_zero_complex) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1501_mult__cancel__right)). 185.47/93.66 thf(28543,plain,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ C @ B)) = ((B = zero_zero_complex) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6185])). 185.47/93.66 thf(30,axiom,((! [A:(nat > real),B:real]: ((! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))) => ((! [C:nat]: (ord_less_eq_real @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ C)) @ B)) => (summable_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7721_summableI__nonneg__bounded)). 185.47/93.66 thf(7828,plain,((! [A:(nat > real),B:real]: ((! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))) => ((! [C:nat]: (ord_less_eq_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ C)) @ B)) => (summable_real @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 185.47/93.66 thf(1379,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ B @ A)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4008_dual__order_Oasym)). 185.47/93.66 thf(12322,plain,((! [A:rat,B:rat]: (~ (ord_less_rat @ B @ A) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379])). 185.47/93.66 thf(3428,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (? [D:real]: (! [E:real]: (((ord_less_real @ E @ C) & (ord_less_real @ A @ E)) <= (ord_less_real @ (abs_abs_real @ (minus_minus_real @ B @ E)) @ D)) & (ord_less_real @ zero_zero_real @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6620_lemma__interval__lt)). 185.47/93.66 thf(19015,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (? [D:real]: (! [E:real]: (((ord_less_real @ E @ C) & (ord_less_real @ A @ E)) | ~ (ord_less_real @ (abs_abs_real @ (minus_minus_real @ B @ E)) @ D)) & (ord_less_real @ zero_zero_real @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3428])). 185.47/93.66 thf(478,axiom,((! [A:nat,B:$o,C:$o]: (((A != zero_zero_nat) => (((A = one_one_nat) => ((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ ($true)))) & (((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ C)) <= (A != one_one_nat)))) & ((A = zero_zero_nat) => ((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ ($true) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2016_vebt__insert_Osimps_I1_J)). 185.47/93.66 thf(9339,plain,((! [A:nat,B:$o,C:$o]: (((~ (A = zero_zero_nat)) => (((A = one_one_nat) => ((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ ($true)))) & (((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ C)) | (A = one_one_nat)))) & ((A = zero_zero_nat) => ((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ ($true) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])). 185.47/93.66 thf(3503,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (powr_real @ A @ B) @ (powr_real @ A @ C)) = (ord_less_real @ B @ C)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9072_powr__less__cancel__iff)). 185.47/93.66 thf(19264,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (powr_real @ A @ B) @ (powr_real @ A @ C)) = (ord_less_real @ B @ C)) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3503])). 185.47/93.66 thf(4216,axiom,((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ one_one_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2692_zero__less__two)). 185.47/93.66 thf(21497,plain,((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ one_one_rat @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4216])). 185.47/93.66 thf(7503,axiom,((! [A:rat,B:rat]: (((plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_rat) = ((B = zero_zero_rat) & (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1903_sum__power2__eq__zero__iff)). 185.47/93.66 thf(33296,plain,((! [A:rat,B:rat]: (((plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_rat) = ((B = zero_zero_rat) & (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7503])). 185.47/93.66 thf(5752,axiom,((! [A:rat,B:rat]: (((B = zero_zero_rat) | (A = zero_zero_rat)) <= ((times_times_rat @ A @ B) = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2050_divisors__zero)). 185.47/93.66 thf(26867,plain,((! [A:rat,B:rat]: ((B = zero_zero_rat) | (A = zero_zero_rat) | ~ ((times_times_rat @ A @ B) = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5752])). 185.47/93.66 thf(1481,axiom,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (sin_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7841_sin__ge__minus__one)). 185.47/93.66 thf(12663,plain,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (sin_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481])). 185.47/93.66 thf(2832,axiom,((! [A:nat,B:nat]: ((semiri8010041392384452111omplex @ (power_power_nat @ A @ B)) = (power_power_complex @ (semiri8010041392384452111omplex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6957_of__nat__power)). 185.47/93.66 thf(17130,plain,((! [A:nat,B:nat]: ((semiri8010041392384452111omplex @ (power_power_nat @ A @ B)) = (power_power_complex @ (semiri8010041392384452111omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2832])). 185.47/93.66 thf(4766,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (ord_max_nat @ A @ B) @ C) = (ord_max_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3762_nat__mult__max__left)). 185.47/93.66 thf(23318,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (ord_max_nat @ A @ B) @ C) = (ord_max_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4766])). 185.47/93.66 thf(4082,axiom,((! [A:int,B:(int > $o),C:int]: ((ord_less_int @ zero_zero_int @ A) => ((! [D:int]: ((B @ D) => (B @ (minus_minus_int @ D @ A)))) => ((ord_less_eq_int @ zero_zero_int @ C) => (! [D:int]: ((B @ (minus_minus_int @ D @ (times_times_int @ C @ A))) <= (B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3207_decr__mult__lemma)). 185.47/93.66 thf(21077,plain,((! [A:int,B:(int > $o),C:int]: ((ord_less_int @ zero_zero_int @ A) => ((! [D:int]: ((B @ D) => (B @ (minus_minus_int @ D @ A)))) => ((ord_less_eq_int @ zero_zero_int @ C) => (! [D:int]: ((B @ (minus_minus_int @ D @ (times_times_int @ C @ A))) | ~ (B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4082])). 185.47/93.66 thf(3474,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_diff__right__mono)). 185.47/93.66 thf(19170,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3474])). 185.47/93.66 thf(1778,axiom,((! [A:rat,B:(num > rat),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F)))) => (ord_less_eq_rat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3942_ord__eq__le__subst)). 185.47/93.66 thf(13685,plain,((! [A:rat,B:(num > rat),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F)))) => (ord_less_eq_rat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778])). 185.47/93.66 thf(4145,axiom,((! [A:(nat > nat),B:(nat > nat),C:nat,D:nat]: (((sums_nat @ A @ C) => ((ord_less_eq_nat @ C @ D) <= (sums_nat @ B @ D))) <= (! [E:nat]: (ord_less_eq_nat @ (A @ E) @ (B @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8154_sums__le)). 185.47/93.66 thf(21276,plain,((! [A:(nat > nat),B:(nat > nat),C:nat,D:nat]: (((sums_nat @ (A) @ C) => ((ord_less_eq_nat @ C @ D) | ~ (sums_nat @ (B) @ D))) | ~ (! [E:nat]: (ord_less_eq_nat @ (A @ E) @ (B @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4145])). 185.47/93.66 thf(6269,axiom,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = (suc @ zero_zero_nat)) = ((B = zero_zero_nat) | (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1799_nat__power__eq__Suc__0__iff)). 185.47/93.66 thf(28823,plain,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = (suc @ zero_zero_nat)) = ((B = zero_zero_nat) | (A = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6269])). 185.47/93.66 thf(6455,axiom,((! [A:num,B:nat,C:int]: (((power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ B) = (ring_1_of_int_rat @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7150_neg__numeral__power__eq__of__int__cancel__iff)). 185.47/93.66 thf(29498,plain,((! [A:num,B:nat,C:int]: (((power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ B) = (ring_1_of_int_rat @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6455])). 185.47/93.66 thf(6910,axiom,((! [A:num]: (((numeral_numeral_real @ A) = one_one_real) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_numeral__eq__one__iff)). 185.47/93.66 thf(31163,plain,((! [A:num]: (((numeral_numeral_real @ A) = one_one_real) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6910])). 185.47/93.66 thf(26,axiom,((! [A:complex,B:nat]: ((minus_minus_complex @ (power_power_complex @ A @ B) @ one_one_complex) = (times_times_complex @ (minus_minus_complex @ A @ one_one_complex) @ (groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7596_power__diff__1__eq)). 185.47/93.66 thf(7815,plain,((! [A:complex,B:nat]: ((minus_minus_complex @ (power_power_complex @ A @ B) @ one_one_complex) = (times_times_complex @ (minus_minus_complex @ A @ one_one_complex) @ (groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 185.47/93.66 thf(5291,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5470_neg__one__odd__power)). 185.47/93.66 thf(25223,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5291])). 185.47/93.66 thf(5842,axiom,(((semiri2265585572941072030t_real @ one_one_nat) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7961_fact__1)). 185.47/93.66 thf(27342,plain,(((semiri2265585572941072030t_real @ one_one_nat) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5842])). 185.47/93.66 thf(7256,axiom,(((numeral_numeral_nat @ one) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2775_numeral__1__eq__Suc__0)). 185.47/93.66 thf(32454,plain,(((numeral_numeral_nat @ one) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7256])). 185.47/93.66 thf(6236,axiom,((! [A:set_nat,B:nat]: ((~ (? [C:nat]: (vEBT_is_pred_in_set @ A @ B @ C))) => ((finite_finite_nat @ A) => (~ (? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3377_pred__none__empty)). 185.47/93.66 thf(28716,plain,((! [A:set_nat,B:nat]: ((~ (? [C:nat]: (vEBT_is_pred_in_set @ A @ B @ C))) => ((finite_finite_nat @ A) => (~ (? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6236])). 185.47/93.66 thf(5074,axiom,((! [A:int,B:int]: (((times_times_int @ A @ A) = (times_times_int @ B @ B)) = ((A = (uminus_uminus_int @ B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5541_square__eq__iff)). 185.47/93.66 thf(24415,plain,((! [A:int,B:int]: (((times_times_int @ A @ A) = (times_times_int @ B @ B)) = ((A = (uminus_uminus_int @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5074])). 185.47/93.66 thf(1887,axiom,((! [A:int,B:int,C:int,D:int]: ((A != zero_zero_int) => ((B != zero_zero_int) => ((ord_less_rat @ (fract @ C @ A) @ (fract @ D @ B)) = (ord_less_int @ (times_times_int @ (times_times_int @ C @ B) @ (times_times_int @ A @ B)) @ (times_times_int @ (times_times_int @ D @ A) @ (times_times_int @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9931_less__rat)). 185.47/93.66 thf(14044,plain,((! [A:int,B:int,C:int,D:int]: ((~ (A = zero_zero_int)) => ((~ (B = zero_zero_int)) => ((ord_less_rat @ (fract @ C @ A) @ (fract @ D @ B)) = (ord_less_int @ (times_times_int @ (times_times_int @ C @ B) @ (times_times_int @ A @ B)) @ (times_times_int @ (times_times_int @ D @ A) @ (times_times_int @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1887])). 185.47/93.66 thf(2482,axiom,((! [A:num,B:rat,C:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (plus_plus_rat @ B @ C)) = (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ A) @ B) @ (times_times_rat @ (numeral_numeral_rat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_distrib__left__numeral)). 185.47/93.66 thf(15951,plain,((! [A:num,B:rat,C:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (plus_plus_rat @ B @ C)) = (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ A) @ B) @ (times_times_rat @ (numeral_numeral_rat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2482])). 185.47/93.66 thf(2254,axiom,((! [A:real,B:real]: ((minus_minus_real @ (sin_real @ A) @ (sin_real @ B)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sin_real @ (divide_divide_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))) @ (cos_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7857_sin__diff__sin)). 185.47/93.66 thf(15224,plain,((! [A:real,B:real]: ((minus_minus_real @ (sin_real @ A) @ (sin_real @ B)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sin_real @ (divide_divide_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))) @ (cos_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2254])). 185.47/93.66 thf(5326,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) <= (ord_less_nat @ E @ F))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F))))) <= (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3233_pinf_I2_J)). 185.47/93.66 thf(25330,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) | ~ (ord_less_nat @ E @ F))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F)))) | ~ (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5326])). 185.47/93.66 thf(7179,axiom,((vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ res)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370__092_060open_062both__member__options_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ares_092_060close_062)). 185.47/93.66 thf(32185,plain,((vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ res)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7179])). 185.47/93.66 thf(2795,axiom,((! [A:int,B:int]: (((ord_less_int @ (divide_divide_int @ A @ B) @ A) <= (ord_less_int @ one_one_int @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3061_int__div__less__self)). 185.47/93.66 thf(17009,plain,((! [A:int,B:int]: ((ord_less_int @ (divide_divide_int @ A @ B) @ A) | ~ (ord_less_int @ one_one_int @ B) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2795])). 185.47/93.66 thf(5951,axiom,((! [A:real,B:real]: ((minus_minus_real @ (uminus_uminus_real @ A) @ B) = (minus_minus_real @ (uminus_uminus_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5570_minus__diff__commute)). 185.47/93.66 thf(27694,plain,((! [A:real,B:real]: ((minus_minus_real @ (uminus_uminus_real @ A) @ B) = (minus_minus_real @ (uminus_uminus_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5951])). 185.47/93.66 thf(3189,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ C) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ (times_times_real @ C @ B) @ A) <= (ord_less_real @ B @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ C) <= (~ (ord_less_real @ B @ zero_zero_real))))) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ A @ (times_times_real @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2695_divide__less__eq)). 185.47/93.66 thf(18267,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ C) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ (times_times_real @ C @ B) @ A) | ~ (ord_less_real @ B @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ C) | (ord_less_real @ B @ zero_zero_real)))) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ A @ (times_times_real @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3189])). 185.47/93.66 thf(4887,axiom,((! [A:num,B:num]: ((powr_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (power_power_real @ (numeral_numeral_real @ A) @ (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9077_numeral__powr__numeral__real)). 185.47/93.66 thf(23722,plain,((! [A:num,B:num]: ((powr_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (power_power_real @ (numeral_numeral_real @ A) @ (numeral_numeral_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4887])). 185.47/93.66 thf(2827,axiom,((! [A:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ A @ A) = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1716_div__self)). 185.47/93.66 thf(17115,plain,((! [A:complex]: ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ A @ A) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2827])). 185.47/93.66 thf(6435,axiom,((! [A:nat]: ((semiri5044797733671781792omplex @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (times_times_complex @ (times_times_complex @ (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (comm_s2602460028002588243omplex @ (divide1717551699836669952omplex @ one_one_complex @ (numera6690914467698888265omplex @ (bit0 @ one))) @ A)) @ (semiri5044797733671781792omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8608_fact__double)). 185.47/93.66 thf(29428,plain,((! [A:nat]: ((semiri5044797733671781792omplex @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (times_times_complex @ (times_times_complex @ (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (comm_s2602460028002588243omplex @ (divide1717551699836669952omplex @ one_one_complex @ (numera6690914467698888265omplex @ (bit0 @ one))) @ A)) @ (semiri5044797733671781792omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6435])). 185.47/93.66 thf(7342,axiom,((! [A:complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1546_diff__zero)). 185.47/93.66 thf(32744,plain,((! [A:complex]: ((minus_minus_complex @ A @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7342])). 185.47/93.66 thf(6709,axiom,((! [A:$o]: (ord_less_eq_nat @ zero_zero_nat @ (zero_n2687167440665602831ol_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5663_zero__less__eq__of__bool)). 185.47/93.66 thf(30355,plain,((! [A:$o]: (ord_less_eq_nat @ zero_zero_nat @ (zero_n2687167440665602831ol_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6709])). 185.47/93.66 thf(3296,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2080_comm__monoid__add__class_Oadd__0)). 185.47/93.66 thf(18590,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3296])). 185.47/93.66 thf(5202,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A != B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_le__neq__implies__less)). 185.47/93.66 thf(24880,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (A = B)) => (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5202])). 185.47/93.66 thf(2078,axiom,(((real_V1022390504157884413omplex @ imaginary_unit) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8985_norm__ii)). 185.47/93.66 thf(14667,plain,(((real_V1022390504157884413omplex @ imaginary_unit) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2078])). 185.47/93.66 thf(1643,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ B) = (((ord_less_eq_real @ A @ one_one_real) <= (ord_less_real @ zero_zero_real @ B)) & ((ord_less_eq_real @ one_one_real @ A) <= (ord_less_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2815_mult__le__cancel__right2)). 185.47/93.66 thf(13197,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ B) = (((ord_less_eq_real @ A @ one_one_real) | ~ (ord_less_real @ zero_zero_real @ B)) & ((ord_less_eq_real @ one_one_real @ A) | ~ (ord_less_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643])). 185.47/93.66 thf(1354,axiom,((! [A:real,B:real,C:real]: ((((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = C) <= (A = zero_zero_real)) & (((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (plus_plus_real @ B @ (times_times_real @ C @ A)) @ A)) <= (A != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2748_add__divide__eq__if__simps_I2_J)). 185.47/93.66 thf(12242,plain,((! [A:real,B:real,C:real]: ((((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = C) | ~ (A = zero_zero_real)) & (((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = (divide_divide_real @ (plus_plus_real @ B @ (times_times_real @ C @ A)) @ A)) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354])). 185.47/93.66 thf(6900,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ A)) = ((dvd_dvd_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4808_dvd__minus__self)). 185.47/93.66 thf(31131,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ A)) = ((dvd_dvd_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6900])). 185.47/93.66 thf(1841,axiom,((! [A:nat,B:nat]: (((~ (ord_less_eq_nat @ A @ B)) => ((set_or4665077453230672383an_nat @ A @ (suc @ B)) = bot_bot_set_nat)) & ((ord_less_eq_nat @ A @ B) => ((set_or4665077453230672383an_nat @ A @ (suc @ B)) = (insert_nat @ B @ (set_or4665077453230672383an_nat @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9566_atLeastLessThanSuc)). 185.47/93.66 thf(13908,plain,((! [A:nat,B:nat]: (((~ (ord_less_eq_nat @ A @ B)) => ((set_or4665077453230672383an_nat @ A @ (suc @ B)) = bot_bot_set_nat)) & ((ord_less_eq_nat @ A @ B) => ((set_or4665077453230672383an_nat @ A @ (suc @ B)) = (insert_nat @ B @ (set_or4665077453230672383an_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841])). 185.47/93.66 thf(1855,axiom,((! [A:real]: (((abs_abs_real @ A) = A) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6368_abs__of__nonneg)). 185.47/93.66 thf(13952,plain,((! [A:real]: (((abs_abs_real @ A) = A) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1855])). 185.47/93.66 thf(6660,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3278_minf_I5_J)). 185.47/93.66 thf(30200,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6660])). 185.47/93.66 thf(7428,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8095_fact__ge__self)). 185.47/93.66 thf(33034,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7428])). 185.47/93.66 thf(4523,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ A) <= (ord_less_eq_real @ B @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2669_mult__right__le__one__le)). 185.47/93.66 thf(22491,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ A) | ~ (ord_less_eq_real @ B @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4523])). 185.47/93.66 thf(2027,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ C @ A) => (ord_less_int @ C @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4244_dual__order_Ostrict__trans1)). 185.47/93.66 thf(14508,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ C @ A) => (ord_less_int @ C @ B)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2027])). 185.47/93.66 thf(5224,axiom,((! [A:num]: (ord_less_eq_num @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3810_order__refl)). 185.47/93.66 thf(24948,plain,((! [A:num]: (ord_less_eq_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5224])). 185.47/93.66 thf(6824,axiom,((! [A:(int > $o),B:int,C:(int > $o)]: ((! [D:int,E:int]: ((A @ D) = (A @ (minus_minus_int @ D @ (times_times_int @ E @ B))))) => ((! [D:int,E:int]: (((A @ D) | (C @ D)) = ((C @ (minus_minus_int @ D @ (times_times_int @ E @ B))) | (A @ (minus_minus_int @ D @ (times_times_int @ E @ B)))))) <= (! [D:int,E:int]: ((C @ D) = (C @ (minus_minus_int @ D @ (times_times_int @ E @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3328_inf__period_I2_J)). 185.47/93.66 thf(30819,plain,((! [A:(int > $o),B:int,C:(int > $o)]: ((! [D:int,E:int]: ((A @ D) = (A @ (minus_minus_int @ D @ (times_times_int @ E @ B))))) => (! [D:int,E:int]: (((A @ D) | (C @ D)) = ((C @ (minus_minus_int @ D @ (times_times_int @ E @ B))) | (A @ (minus_minus_int @ D @ (times_times_int @ E @ B))))) | ~ (! [D:int,E:int]: ((C @ D) = (C @ (minus_minus_int @ D @ (times_times_int @ E @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6824])). 185.47/93.66 thf(309,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3569_max_Oabsorb1)). 185.47/93.66 thf(8767,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 185.47/93.66 thf(3476,axiom,((neg_nu5219082963157363817nc_rat = (^ [A:rat]: (plus_plus_rat @ (plus_plus_rat @ A @ A) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7314_dbl__inc__def)). 185.47/93.66 thf(19176,plain,(((neg_nu5219082963157363817nc_rat) = (^ [A:rat]: (plus_plus_rat @ (plus_plus_rat @ A @ A) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3476])). 185.47/93.66 thf(6471,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1795_diff__is__0__eq_H)). 185.47/93.66 thf(29562,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6471])). 185.47/93.66 thf(3046,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ one_one_rat @ (divide_divide_rat @ A @ B)) = (((ord_less_rat @ A @ B) & (ord_less_rat @ B @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ B) & (ord_less_rat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2718_less__divide__eq__1)). 185.47/93.66 thf(17818,plain,((! [A:rat,B:rat]: ((ord_less_rat @ one_one_rat @ (divide_divide_rat @ A @ B)) = (((ord_less_rat @ A @ B) & (ord_less_rat @ B @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ B) & (ord_less_rat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3046])). 185.47/93.66 thf(6905,axiom,((! [A:complex,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((power_power_complex @ A @ (minus_minus_nat @ C @ B)) = (divide1717551699836669952omplex @ (power_power_complex @ A @ C) @ (power_power_complex @ A @ B)))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2904_power__diff)). 185.47/93.66 thf(31146,plain,((! [A:complex,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((power_power_complex @ A @ (minus_minus_nat @ C @ B)) = (divide1717551699836669952omplex @ (power_power_complex @ A @ C) @ (power_power_complex @ A @ B)))) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6905])). 185.47/93.66 thf(7339,axiom,((! [A:rat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((power_power_rat @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ A @ B)))) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2906_power__diff)). 185.47/93.66 thf(32734,plain,((! [A:rat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((power_power_rat @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ A @ B)))) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7339])). 185.47/93.66 thf(3003,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) @ zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2680_sum__squares__le__zero__iff)). 185.47/93.66 thf(17686,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B)) @ zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3003])). 185.47/93.66 thf(1666,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ B)))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9545_or__not__numerals_I8_J)). 185.47/93.66 thf(13319,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ B)))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666])). 185.47/93.66 thf(5547,axiom,((! [A:nat,B:nat,C:nat]: ((((power_power_nat @ A @ B) = (power_power_nat @ A @ C)) = (B = C)) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_power__inject__exp)). 185.47/93.66 thf(26203,plain,((! [A:nat,B:nat,C:nat]: ((((power_power_nat @ A @ B) = (power_power_nat @ A @ C)) = (B = C)) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5547])). 185.47/93.66 thf(6097,axiom,((! [A:num]: ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6662_odd__numeral)). 185.47/93.66 thf(28194,plain,((! [A:num]: ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6097])). 185.47/93.66 thf(1950,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => ((dvd_dvd_rat @ A @ C) => (dvd_dvd_rat @ A @ (plus_plus_rat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4653_dvd__add)). 185.47/93.66 thf(14258,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => ((dvd_dvd_rat @ A @ C) => (dvd_dvd_rat @ A @ (plus_plus_rat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1950])). 185.47/93.66 thf(4635,axiom,((! [A:num,B:num,C:(num > rat),D:rat]: ((ord_less_eq_num @ A @ B) => (((C @ B) = D) => ((! [E:num,F:num]: ((ord_less_eq_rat @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_rat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3952_ord__le__eq__subst)). 185.47/93.66 thf(22848,plain,((! [A:num,B:num,C:(num > rat),D:rat]: ((ord_less_eq_num @ A @ B) => (((C @ B) = D) => ((! [E:num,F:num]: ((ord_less_eq_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_rat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4635])). 185.47/93.66 thf(972,axiom,((set_ord_atMost_nat = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8742_atMost__def)). 185.47/93.66 thf(11070,plain,(((set_ord_atMost_nat) = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[972])). 185.47/93.66 thf(3290,axiom,((! [A:set_nat,B:nat]: ((ord_less_eq_set_nat @ A @ (set_or4665077453230672383an_nat @ zero_zero_nat @ B)) => (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9565_subset__eq__atLeast0__lessThan__finite)). 185.47/93.66 thf(18573,plain,((! [A:set_nat,B:nat]: ((ord_less_eq_set_nat @ A @ (set_or4665077453230672383an_nat @ zero_zero_nat @ B)) => (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3290])). 185.47/93.66 thf(6334,axiom,((! [A:rat]: ((times_times_rat @ A @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5195_mult__minus1__right)). 185.47/93.66 thf(29046,plain,((! [A:rat]: ((times_times_rat @ A @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6334])). 185.47/93.66 thf(1920,axiom,((! [A:rat]: ? [B:nat]: (ord_less_eq_rat @ A @ (semiri681578069525770553at_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7433_real__arch__simple)). 185.47/93.66 thf(14144,plain,((! [A:rat]: ? [B:nat]: (ord_less_eq_rat @ A @ (semiri681578069525770553at_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1920])). 185.47/93.66 thf(574,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (arccos @ A) @ pi)) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8368_arccos__ubound)). 185.47/93.66 thf(9638,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (arccos @ A) @ pi)) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[574])). 185.47/93.66 thf(2472,axiom,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (plus_plus_nat @ A @ B)) = (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6911_of__nat__add)). 185.47/93.66 thf(15919,plain,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (plus_plus_nat @ A @ B)) = (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2472])). 185.47/93.66 thf(1990,axiom,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ (plus_plus_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (comm_s7457072308508201937r_real @ (uminus_uminus_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8588_pochhammer__minus_H)). 185.47/93.66 thf(14384,plain,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ (plus_plus_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (comm_s7457072308508201937r_real @ (uminus_uminus_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1990])). 185.47/93.66 thf(3060,axiom,((! [A:nat,B:nat,C:(nat > nat),D:(nat > nat)]: ((((groups708209901874060359at_nat @ (^ [E:nat]: (if_nat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_nat @ (E = B) @ one_one_nat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups708209901874060359at_nat @ (^ [E:nat]: (if_nat @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8869_prod_Ozero__middle)). 185.47/93.66 thf(17865,plain,((! [A:nat,B:nat,C:(nat > nat),D:(nat > nat)]: (((groups708209901874060359at_nat @ (^ [E:nat]: (if_nat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_nat @ (E = B) @ one_one_nat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups708209901874060359at_nat @ (^ [E:nat]: (if_nat @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3060])). 185.47/93.66 thf(5778,axiom,((! [A:num]: ((plus_plus_num @ (bit1 @ A) @ one) = (bit0 @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6409_semiring__norm_I8_J)). 185.47/93.66 thf(26952,plain,((! [A:num]: ((plus_plus_num @ (bit1 @ A) @ one) = (bit0 @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5778])). 185.47/93.66 thf(4257,axiom,((neg_nu6075765906172075777c_real = (^ [A:real]: (minus_minus_real @ (plus_plus_real @ A @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6834_dbl__dec__def)). 185.47/93.66 thf(21622,plain,(((neg_nu6075765906172075777c_real) = (^ [A:real]: (minus_minus_real @ (plus_plus_real @ A @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4257])). 185.47/93.66 thf(7328,axiom,((! [A:nat]: ((((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = (uminus1482373934393186551omplex @ one_one_complex)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6229_minus__one__power__iff)). 185.47/93.66 thf(32693,plain,((! [A:nat]: ((((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = (uminus1482373934393186551omplex @ one_one_complex)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7328])). 185.47/93.66 thf(6360,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1786_zero__less__Suc)). 185.47/93.66 thf(29148,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6360])). 185.47/93.66 thf(7169,axiom,((! [A:nat,B:nat]: (((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4482_dvd__div__mult__self)). 185.47/93.66 thf(32153,plain,((! [A:nat,B:nat]: (((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7169])). 185.47/93.66 thf(3023,axiom,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2729_divide__add__eq__iff)). 185.47/93.66 thf(17744,plain,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3023])). 185.47/93.66 thf(7270,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_nat @ (power_power_nat @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2966_power__minus__mult)). 185.47/93.66 thf(32496,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_nat @ (power_power_nat @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7270])). 185.47/93.66 thf(5591,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => (((times_times_complex @ A @ B) != zero_zero_complex) <= (B != zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2053_no__zero__divisors)). 185.47/93.66 thf(26335,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => (~ ((times_times_complex @ A @ B) = zero_zero_complex) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5591])). 185.47/93.66 thf(4800,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3159_plus__int__code_I2_J)). 185.47/93.66 thf(23421,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4800])). 185.47/93.66 thf(581,axiom,((! [A:nat,B:nat,C:(nat > real)]: ((((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = zero_zero_real) <= (~ (ord_less_eq_nat @ A @ B))) & ((ord_less_eq_nat @ A @ B) => ((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_real @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6739_sum__natinterval__diff)). 185.47/93.66 thf(9659,plain,((! [A:nat,B:nat,C:(nat > real)]: ((((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = zero_zero_real) | (ord_less_eq_nat @ A @ B)) & ((ord_less_eq_nat @ A @ B) => ((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (C @ D) @ (C @ (plus_plus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_real @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[581])). 185.47/93.66 thf(1226,axiom,((! [A:num,B:num,C:num]: (((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ C)) @ (numeral_numeral_int @ (bit0 @ B)))) = ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (modulo_modulo_int @ (numeral_numeral_int @ C) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6607_cong__exp__iff__simps_I13_J)). 185.47/93.66 thf(11846,plain,((! [A:num,B:num,C:num]: (((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ C)) @ (numeral_numeral_int @ (bit0 @ B)))) = ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (modulo_modulo_int @ (numeral_numeral_int @ C) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226])). 185.47/93.66 thf(2591,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => ((B = (times_times_rat @ C @ A)) => ((divide_divide_rat @ B @ A) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2469_divide__eq__imp)). 185.47/93.66 thf(16334,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => ((B = (times_times_rat @ C @ A)) => ((divide_divide_rat @ B @ A) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2591])). 185.47/93.66 thf(2681,axiom,((! [A:num]: ~ (ord_less_eq_rat @ one_one_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5941_not__one__le__neg__numeral)). 185.47/93.66 thf(16664,plain,((! [A:num]: ~ (ord_less_eq_rat @ one_one_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2681])). 185.47/93.66 thf(4557,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = (divide_divide_real @ C @ B)) => (((A = C) <= (dvd_dvd_real @ B @ C)) <= (dvd_dvd_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4670_dvd__div__eq__cancel)). 185.47/93.66 thf(22597,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = (divide_divide_real @ C @ B)) => ((A = C) | ~ (dvd_dvd_real @ B @ C) | ~ (dvd_dvd_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4557])). 185.47/93.66 thf(141,axiom,((gbinomial_rat = (^ [A:rat,B:nat]: (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (gbinomial_rat @ (minus_minus_rat @ (minus_minus_rat @ (semiri681578069525770553at_rat @ B) @ A) @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8567_gbinomial__negated__upper)). 185.47/93.66 thf(8188,plain,(((gbinomial_rat) = (^ [A:rat,B:nat]: (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (gbinomial_rat @ (minus_minus_rat @ (minus_minus_rat @ (semiri681578069525770553at_rat @ B) @ A) @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 185.47/93.66 thf(2275,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_733_diff__add__eq__diff__diff__swap)). 185.47/93.66 thf(15284,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (plus_plus_real @ B @ C)) = (minus_minus_real @ (minus_minus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2275])). 185.47/93.66 thf(2905,axiom,(((ring_1_of_int_rat @ one_one_int) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6969_of__int__1)). 185.47/93.66 thf(17368,plain,(((ring_1_of_int_rat @ one_one_int) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2905])). 185.47/93.66 thf(5231,axiom,(((size_s170228958280169651at_nat @ none_P5556105721700978146at_nat) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2504_option_Osize_I3_J)). 185.47/93.66 thf(24980,plain,(((size_s170228958280169651at_nat @ none_P5556105721700978146at_nat) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5231])). 185.47/93.66 thf(1300,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_706_diff__strict__left__mono)). 185.47/93.66 thf(12067,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300])). 185.47/93.66 thf(1790,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ C) <= (ord_less_rat @ zero_zero_rat @ A)) <= (ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2604_mult__left__le__imp__le)). 185.47/93.66 thf(13730,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ B @ C) | ~ (ord_less_rat @ zero_zero_rat @ A) | ~ (ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1790])). 185.47/93.66 thf(2617,axiom,((! [A:int,B:nat]: ((ord_less_int @ A @ (bit_se2923211474154528505it_int @ B @ A)) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9281_take__bit__int__greater__self__iff)). 185.47/93.66 thf(16415,plain,((! [A:int,B:nat]: ((ord_less_int @ A @ (bit_se2923211474154528505it_int @ B @ A)) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2617])). 185.47/93.66 thf(173,axiom,((! [A:set_nat,B:(nat > rat)]: ((finite_finite_nat @ A) => (((ord_less_rat @ zero_zero_rat @ (groups2906978787729119204at_rat @ B @ A)) <= (! [C:nat]: ((ord_less_rat @ zero_zero_rat @ (B @ C)) <= (member_nat @ C @ A)))) <= (A != bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6053_sum__pos)). 185.47/93.66 thf(8286,plain,((! [A:set_nat,B:(nat > rat)]: ((finite_finite_nat @ A) => ((ord_less_rat @ zero_zero_rat @ (groups2906978787729119204at_rat @ (B) @ A)) | ~ (! [C:nat]: ((ord_less_rat @ zero_zero_rat @ (B @ C)) | ~ (member_nat @ C @ A))) | (A = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 185.47/93.66 thf(937,axiom,((! [A:real]: (((power_power_real @ (inverse_inverse_real @ (sqrt @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (inverse_inverse_real @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8976_real__inv__sqrt__pow2)). 185.47/93.66 thf(10948,plain,((! [A:real]: (((power_power_real @ (inverse_inverse_real @ (sqrt @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (inverse_inverse_real @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[937])). 185.47/93.66 thf(6329,axiom,((! [A:real,B:real]: ((A = zero_zero_real) <= ((sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8225_real__sqrt__sum__squares__eq__cancel2)). 185.47/93.66 thf(29029,plain,((! [A:real,B:real]: ((A = zero_zero_real) | ~ ((sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6329])). 185.47/93.66 thf(78,axiom,((! [A:real,B:nat,C:(nat > (nat > real))]: ((((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_nat) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_nat)) <= (B != zero_zero_nat)) <= (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8077_Maclaurin__zero)). 185.47/93.66 thf(7983,plain,((! [A:real,B:nat,C:(nat > (nat > real))]: (((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_nat) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_nat)) | (B = zero_zero_nat) | ~ (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 185.47/93.66 thf(6249,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1091_less__eq__Suc__le)). 185.47/93.66 thf(28756,plain,(((ord_less_nat) = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6249])). 185.47/93.66 thf(1499,axiom,((! [A:int,B:int,C:int]: ((((times_times_int @ B @ A) = (times_times_int @ C @ A)) = (B = C)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4731_unit__mult__right__cancel)). 185.47/93.66 thf(12716,plain,((! [A:int,B:int,C:int]: ((((times_times_int @ B @ A) = (times_times_int @ C @ A)) = (B = C)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499])). 185.47/93.66 thf(969,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (ord_max_int @ B @ C)) = ((ord_less_int @ A @ C) | (ord_less_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3723_less__max__iff__disj)). 185.47/93.66 thf(11060,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (ord_max_int @ B @ C)) = ((ord_less_int @ A @ C) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[969])). 185.47/93.66 thf(5783,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ (list_u1324408373059187874T_VEBT @ A @ B @ C)) = (size_s6755466524823107622T_VEBT @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3588_length__list__update)). 185.47/93.66 thf(26967,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ (list_u1324408373059187874T_VEBT @ A @ B @ C)) = (size_s6755466524823107622T_VEBT @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5783])). 185.47/93.66 thf(4237,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_int @ A @ C)) <= (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2589_mult__right__less__imp__less)). 185.47/93.66 thf(21558,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_int @ A @ C)) | ~ (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4237])). 185.47/93.66 thf(4115,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) => ((ord_less_eq_real @ B @ C) <= (ord_less_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2603_mult__left__le__imp__le)). 185.47/93.66 thf(21186,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) => ((ord_less_eq_real @ B @ C) | ~ (ord_less_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4115])). 185.47/93.66 thf(531,axiom,((! [A:(nat > rat),B:nat,C:nat]: ((groups2906978787729119204at_rat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo1949268297981939178at_rat @ (^ [D:nat]: (plus_plus_rat @ (A @ D))) @ B @ C @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8321_sum__atLeastAtMost__code)). 185.47/93.66 thf(9506,plain,((! [A:(nat > rat),B:nat,C:nat]: ((groups2906978787729119204at_rat @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo1949268297981939178at_rat @ (^ [D:nat]: (plus_plus_rat @ (A @ D))) @ B @ C @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[531])). 185.47/93.66 thf(2719,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2927_half__gt__zero__iff)). 185.47/93.66 thf(16779,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2719])). 185.47/93.66 thf(1721,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5139_neg__le__0__iff__le)). 185.47/93.66 thf(13503,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721])). 185.47/93.66 thf(3530,axiom,((! [A:rat,B:nat,C:rat]: (((power_power_rat @ A @ (suc @ B)) = (power_power_rat @ C @ (suc @ B))) => ((ord_less_eq_rat @ zero_zero_rat @ A) => ((A = C) <= (ord_less_eq_rat @ zero_zero_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2751_power__inject__base)). 185.47/93.66 thf(19345,plain,((! [A:rat,B:nat,C:rat]: (((power_power_rat @ A @ (suc @ B)) = (power_power_rat @ C @ (suc @ B))) => ((ord_less_eq_rat @ zero_zero_rat @ A) => ((A = C) | ~ (ord_less_eq_rat @ zero_zero_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3530])). 185.47/93.66 thf(336,axiom,((! [A:nat,B:nat,C:(nat > real)]: (((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (C @ (suc @ D)) @ (C @ D))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_real @ (C @ (suc @ B)) @ (C @ A))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6680_sum__Suc__diff)). 185.47/93.66 thf(8862,plain,((! [A:nat,B:nat,C:(nat > real)]: (((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (C @ (suc @ D)) @ (C @ D))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_real @ (C @ (suc @ B)) @ (C @ A))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 185.47/93.66 thf(4593,axiom,((! [A:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ one_one_rat @ A)) = (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1807_zero__le__divide__1__iff)). 185.47/93.66 thf(22708,plain,((! [A:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ one_one_rat @ A)) = (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4593])). 185.47/93.66 thf(256,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se2159334234014336723it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3125_flip__bit__nonnegative__int__iff)). 185.47/93.66 thf(8566,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se2159334234014336723it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 185.47/93.66 thf(1259,axiom,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1536_add__0)). 185.47/93.66 thf(11951,plain,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259])). 185.47/93.66 thf(3825,axiom,((ord_less_real @ (cos_real @ (numeral_numeral_real @ (bit0 @ one))) @ zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7883_cos__two__less__zero)). 185.47/93.66 thf(20283,plain,((ord_less_real @ (cos_real @ (numeral_numeral_real @ (bit0 @ one))) @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3825])). 185.47/93.66 thf(6986,axiom,((! [A:num,B:num]: ((pow @ A @ (bit1 @ B)) = (times_times_num @ (sqr @ (pow @ A @ B)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9846_pow_Osimps_I3_J)). 185.47/93.66 thf(31502,plain,((! [A:num,B:num]: ((pow @ A @ (bit1 @ B)) = (times_times_num @ (sqr @ (pow @ A @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6986])). 185.47/93.66 thf(6362,axiom,((! [A:num]: ((plus_plus_num @ one @ A) = (plus_plus_num @ A @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_add__One__commute)). 185.47/93.66 thf(29153,plain,((! [A:num]: ((plus_plus_num @ one @ A) = (plus_plus_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6362])). 185.47/93.66 thf(7298,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3306_pinf_I6_J)). 185.47/93.66 thf(32594,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7298])). 185.47/93.66 thf(6979,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4243_dual__order_Ostrict__trans1)). 185.47/93.66 thf(31483,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6979])). 185.47/93.66 thf(3025,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ B @ C) => (ord_less_int @ B @ (plus_plus_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2644_add__strict__increasing2)). 185.47/93.66 thf(17749,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ B @ C) => (ord_less_int @ B @ (plus_plus_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3025])). 185.47/93.66 thf(2413,axiom,((! [A:int]: ((ord_less_rat @ zero_zero_rat @ (ring_1_of_int_rat @ A)) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7040_of__int__0__less__iff)). 185.47/93.66 thf(15718,plain,((! [A:int]: ((ord_less_rat @ zero_zero_rat @ (ring_1_of_int_rat @ A)) = (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2413])). 185.47/93.66 thf(1956,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_3845_nle__le)). 185.47/93.66 thf(14275,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)],[1956])). 185.47/93.66 thf(6594,axiom,(((minus_minus_rat @ one_one_rat @ (uminus_uminus_rat @ one_one_rat)) = (numeral_numeral_rat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5418_diff__numeral__special_I11_J)). 185.47/93.66 thf(29988,plain,(((minus_minus_rat @ one_one_rat @ (uminus_uminus_rat @ one_one_rat)) = (numeral_numeral_rat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6594])). 185.47/93.66 thf(44,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_real @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7553_sum_OlessThan__Suc)). 185.47/93.66 thf(7875,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 185.47/93.66 thf(4802,axiom,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ (minus_minus_real @ B @ D)) @ (times_times_real @ (minus_minus_real @ A @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_mult__diff__mult)). 185.47/93.66 thf(23426,plain,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ D)) = (plus_plus_real @ (times_times_real @ A @ (minus_minus_real @ B @ D)) @ (times_times_real @ (minus_minus_real @ A @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4802])). 185.47/93.66 thf(2351,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (finite_finite_nat @ (vEBT_VEBT_set_vebt @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3376_set__vebt__finite)). 185.47/93.66 thf(15517,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (finite_finite_nat @ (vEBT_VEBT_set_vebt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2351])). 185.47/93.66 thf(2060,axiom,((! [A:set_nat,B:nat]: ((finite_finite_nat @ A) <= (ord_less_eq_set_nat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3435_subset__eq__atLeast0__atMost__finite)). 185.47/93.66 thf(14608,plain,((! [A:set_nat,B:nat]: ((finite_finite_nat @ A) | ~ (ord_less_eq_set_nat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2060])). 185.47/93.66 thf(1538,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C) = (dvd_dvd_Code_integer @ B @ C)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4735_mult__unit__dvd__iff_H)). 185.47/93.66 thf(12830,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C) = (dvd_dvd_Code_integer @ B @ C)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538])). 185.47/93.66 thf(1436,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (ord_max_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3716_max_OcoboundedI2)). 185.47/93.66 thf(12524,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (ord_max_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436])). 185.47/93.66 thf(2932,axiom,((! [A:complex]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (exp_complex @ A)) @ (plus_plus_real @ one_one_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (real_V1022390504157884413omplex @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8273_exp__bound__lemma)). 185.47/93.66 thf(17458,plain,((! [A:complex]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (exp_complex @ A)) @ (plus_plus_real @ one_one_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (real_V1022390504157884413omplex @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2932])). 185.47/93.66 thf(1162,axiom,((! [A:nat]: (((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ (^ [B:nat]: (if_int @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri1314217659103216013at_int @ (binomial @ A @ B)) @ zero_zero_int)) @ (set_ord_atMost_nat @ A))) = (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8626_choose__odd__sum)). 185.47/93.66 thf(11662,plain,((! [A:nat]: (((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ (^ [B:nat]: (if_int @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri1314217659103216013at_int @ (binomial @ A @ B)) @ zero_zero_int)) @ (set_ord_atMost_nat @ A))) = (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162])). 185.47/93.66 thf(2480,axiom,((! [A:num,B:num]: ((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_numeral__le__iff)). 185.47/93.66 thf(15946,plain,((! [A:num,B:num]: ((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2480])). 185.47/93.66 thf(2956,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2228_mult__right__mono)). 185.47/93.66 thf(17525,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2956])). 185.47/93.66 thf(7635,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_906_nat__1__add__1)). 185.47/93.66 thf(33673,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7635])). 185.47/93.66 thf(1756,axiom,((! [A:real]: ((! [B:real]: ? [C:nat]: (ord_less_real @ B @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7266_reals__Archimedean3)). 185.47/93.66 thf(13621,plain,((! [A:real]: (! [B:real]: ? [C:nat]: (ord_less_real @ B @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756])). 185.47/93.66 thf(4109,axiom,((ord_less_real = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4275_order__less__le)). 185.47/93.66 thf(21169,plain,(((ord_less_real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4109])). 185.47/93.66 thf(302,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (powr_real @ A @ C) @ B) = (ord_less_real @ C @ (log @ A @ B)))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9110_powr__less__iff)). 185.47/93.66 thf(8745,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (powr_real @ A @ C) @ B) = (ord_less_real @ C @ (log @ A @ B)))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 185.47/93.67 thf(1044,axiom,((! [A:code_integer]: (ord_le3102999989581377725nteger @ A @ (abs_abs_Code_integer @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6450_abs__ge__self)). 185.47/93.67 thf(11291,plain,((! [A:code_integer]: (ord_le3102999989581377725nteger @ A @ (abs_abs_Code_integer @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044])). 185.47/93.67 thf(7116,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_real @ A @ B) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2933_power2__le__imp__le)). 185.47/93.67 thf(31951,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7116])). 185.47/93.67 thf(4205,axiom,((! [A:int,B:int]: ((plus_plus_int @ (modulo_modulo_int @ A @ B) @ (times_times_int @ B @ (divide_divide_int @ A @ B))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2533_mod__mult__div__eq)). 185.47/93.67 thf(21460,plain,((! [A:int,B:int]: ((plus_plus_int @ (modulo_modulo_int @ A @ B) @ (times_times_int @ B @ (divide_divide_int @ A @ B))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4205])). 185.47/93.67 thf(1250,axiom,((! [A:int,B:int,C:int,D:int]: ((A != zero_zero_int) => ((B != zero_zero_int) => (((((divide_divide_int @ C @ A) = (divide_divide_int @ D @ B)) = ((times_times_int @ C @ B) = (times_times_int @ A @ D))) <= (dvd_dvd_int @ B @ D)) <= (dvd_dvd_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4840_dvd__div__div__eq__mult)). 185.47/93.67 thf(11924,plain,((! [A:int,B:int,C:int,D:int]: ((~ (A = zero_zero_int)) => ((~ (B = zero_zero_int)) => ((((divide_divide_int @ C @ A) = (divide_divide_int @ D @ B)) = ((times_times_int @ C @ B) = (times_times_int @ A @ D))) | ~ (dvd_dvd_int @ B @ D) | ~ (dvd_dvd_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250])). 185.47/93.67 thf(4325,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => (ord_less_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8010_fact__less__mono)). 185.47/93.67 thf(21859,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => (ord_less_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4325])). 185.47/93.67 thf(1265,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ one_one_int @ A) => (ord_less_eq_int @ one_one_int @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_837_one__le__power)). 185.47/93.67 thf(11968,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ one_one_int @ A) => (ord_less_eq_int @ one_one_int @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265])). 185.47/93.67 thf(1115,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_real @ B @ C) <= (ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_real @ C @ B) <= (ord_less_eq_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2583_mult__less__cancel__left)). 185.47/93.67 thf(11515,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_real @ B @ C) | ~ (ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_real @ C @ B) | ~ (ord_less_eq_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115])). 185.47/93.67 thf(1168,axiom,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_rat @ (times_times_rat @ (semiri681578069525770553at_rat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (comm_s4028243227959126397er_rat @ A @ B)) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8402_pochhammer__double)). 185.47/93.67 thf(11678,plain,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_rat @ (times_times_rat @ (semiri681578069525770553at_rat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (comm_s4028243227959126397er_rat @ A @ B)) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168])). 185.47/93.67 thf(4677,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((A = (plus_plus_complex @ B @ C)) => ((minus_minus_complex @ D @ A) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (minus_minus_complex @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5784_group__cancel_Osub2)). 185.47/93.67 thf(22985,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((A = (plus_plus_complex @ B @ C)) => ((minus_minus_complex @ D @ A) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (minus_minus_complex @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4677])). 185.47/93.67 thf(2514,axiom,(((semiri5074537144036343181t_real @ one_one_nat) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6920_of__nat__1)). 185.47/93.67 thf(16065,plain,(((semiri5074537144036343181t_real @ one_one_nat) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2514])). 185.47/93.67 thf(7089,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4135_order__less__imp__not__eq)). 185.47/93.67 thf(31865,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7089])). 185.47/93.67 thf(3570,axiom,((gbinomial_complex = (^ [A:complex,B:nat]: (divide1717551699836669952omplex @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B) @ (semiri5044797733671781792omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8457_gbinomial__pochhammer_H)). 185.47/93.67 thf(19466,plain,(((gbinomial_complex) = (^ [A:complex,B:nat]: (divide1717551699836669952omplex @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B) @ (semiri5044797733671781792omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3570])). 185.47/93.67 thf(877,axiom,((! [A:nat]: ((groups6591440286371151544t_real @ (gbinomial_real @ (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ one_one_real)) @ (set_ord_atMost_nat @ A)) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8631_gbinomial__r__part__sum)). 185.47/93.67 thf(10728,plain,((! [A:nat]: ((groups6591440286371151544t_real @ (gbinomial_real @ (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ one_one_real)) @ (set_ord_atMost_nat @ A)) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[877])). 185.47/93.67 thf(6816,axiom,((! [A:rat,B:rat]: ((times_times_rat @ (uminus_uminus_rat @ A) @ B) = (uminus_uminus_rat @ (times_times_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5072_mult__minus__left)). 185.47/93.67 thf(30797,plain,((! [A:rat,B:rat]: ((times_times_rat @ (uminus_uminus_rat @ A) @ B) = (uminus_uminus_rat @ (times_times_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6816])). 185.47/93.67 thf(1572,axiom,((! [A:num]: ~ (ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5937_not__numeral__le__neg__one)). 185.47/93.67 thf(12936,plain,((! [A:num]: ~ (ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572])). 185.47/93.67 thf(7246,axiom,((! [A:num,B:num]: ((uminus_uminus_rat @ (numeral_numeral_rat @ A)) != (numeral_numeral_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5538_neg__numeral__neq__numeral)). 185.47/93.67 thf(32418,plain,((! [A:num,B:num]: ~ ((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7246])). 185.47/93.67 thf(3247,axiom,((! [A:real,B:int]: (((archim8280529875227126926d_real @ A) = B) <= (ord_less_real @ (abs_abs_real @ (minus_minus_real @ A @ (ring_1_of_int_real @ B))) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7638_round__unique_H)). 185.47/93.67 thf(18444,plain,((! [A:real,B:int]: (((archim8280529875227126926d_real @ A) = B) | ~ (ord_less_real @ (abs_abs_real @ (minus_minus_real @ A @ (ring_1_of_int_real @ B))) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3247])). 185.47/93.67 thf(1934,axiom,((! [A:$o,B:$o]: ((zero_n2684676970156552555ol_int @ ((A) & (B))) = (times_times_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5504_of__bool__conj)). 185.47/93.67 thf(14183,plain,((! [A:$o,B:$o]: ((zero_n2684676970156552555ol_int @ ((A) & (B))) = (times_times_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1934])). 185.47/93.67 thf(6132,axiom,((! [A:nat]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_Code_integer))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5464_power__minus1__even)). 185.47/93.67 thf(28319,plain,((! [A:nat]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6132])). 185.47/93.67 thf(4886,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ (divide_divide_rat @ A @ B)) @ C) = (((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ (times_times_rat @ C @ B)) <= (ord_less_rat @ zero_zero_rat @ B)) & ((((ord_less_eq_rat @ (times_times_rat @ C @ B) @ (uminus_uminus_rat @ A)) <= (ord_less_rat @ B @ zero_zero_rat)) & ((ord_less_eq_rat @ zero_zero_rat @ C) <= (~ (ord_less_rat @ B @ zero_zero_rat)))) <= (~ (ord_less_rat @ zero_zero_rat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6209_minus__divide__le__eq)). 185.47/93.67 thf(23719,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ (divide_divide_rat @ A @ B)) @ C) = (((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ (times_times_rat @ C @ B)) | ~ (ord_less_rat @ zero_zero_rat @ B)) & ((((ord_less_eq_rat @ (times_times_rat @ C @ B) @ (uminus_uminus_rat @ A)) | ~ (ord_less_rat @ B @ zero_zero_rat)) & ((ord_less_eq_rat @ zero_zero_rat @ C) | (ord_less_rat @ B @ zero_zero_rat))) | (ord_less_rat @ zero_zero_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4886])). 185.47/93.67 thf(3985,axiom,((ord_less_int @ (uminus_uminus_int @ one_one_int) @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5749_less__minus__one__simps_I2_J)). 185.47/93.67 thf(20791,plain,((ord_less_int @ (uminus_uminus_int @ one_one_int) @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3985])). 185.47/93.67 thf(528,axiom,((! [A:int,B:int]: ((((sgn_sgn_int @ (modulo_modulo_int @ B @ A)) = (sgn_sgn_int @ A)) <= (~ (dvd_dvd_int @ A @ B))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9223_sgn__mod)). 185.47/93.67 thf(9496,plain,((! [A:int,B:int]: (((sgn_sgn_int @ (modulo_modulo_int @ B @ A)) = (sgn_sgn_int @ A)) | (dvd_dvd_int @ A @ B) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[528])). 185.47/93.67 thf(6691,axiom,((! [A:nat]: ((minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (suc @ zero_zero_nat)) = (groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6754_mask__eq__sum__exp__nat)). 185.47/93.67 thf(30298,plain,((! [A:nat]: ((minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (suc @ zero_zero_nat)) = (groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6691])). 185.47/93.67 thf(4641,axiom,((! [A:num]: ((neg_numeral_dbl_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3828_dbl__simps_I5_J)). 185.47/93.67 thf(22868,plain,((! [A:num]: ((neg_numeral_dbl_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4641])). 185.47/93.67 thf(4173,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((((times_3573771949741848930nteger @ B @ A) = (times_3573771949741848930nteger @ C @ A)) = (B = C)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4729_unit__mult__right__cancel)). 185.47/93.67 thf(21360,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((((times_3573771949741848930nteger @ B @ A) = (times_3573771949741848930nteger @ C @ A)) = (B = C)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4173])). 185.47/93.67 thf(5409,axiom,((! [A:complex]: ((power_power_complex @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1772_power__Suc0__right)). 185.47/93.67 thf(25624,plain,((! [A:complex]: ((power_power_complex @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5409])). 185.47/93.67 thf(6335,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2512_Euclidean__Division_Odiv__eq__0__iff)). 185.47/93.67 thf(29049,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6335])). 185.47/93.67 thf(5672,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B))) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_860_power__gt1__lemma)). 185.47/93.67 thf(26609,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B))) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5672])). 185.47/93.67 thf(4335,axiom,((one_one_Code_integer != (uminus1351360451143612070nteger @ one_one_Code_integer))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5554_one__neq__neg__one)). 185.47/93.67 thf(21886,plain,((~ (one_one_Code_integer = (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4335])). 185.47/93.67 thf(4415,axiom,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (abs_abs_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6477_abs__ge__zero)). 185.47/93.67 thf(22135,plain,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4415])). 185.47/93.67 thf(2052,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ C) <= (dvd_dvd_int @ (times_times_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4599_dvd__mult__left)). 185.47/93.67 thf(14587,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ C) | ~ (dvd_dvd_int @ (times_times_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2052])). 185.47/93.67 thf(1267,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ (divide_divide_int @ B @ A)) <= (ord_less_eq_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2183_div__positive)). 185.47/93.67 thf(11973,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (divide_divide_int @ B @ A)) | ~ (ord_less_eq_int @ A @ B) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267])). 185.47/93.67 thf(5721,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_nat @ zero_zero_nat @ B) => ((divide_divide_nat @ (plus_plus_nat @ one_one_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4424_even__succ__div__exp)). 185.47/93.67 thf(26773,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_nat @ zero_zero_nat @ B) => ((divide_divide_nat @ (plus_plus_nat @ one_one_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5721])). 185.47/93.67 thf(7462,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_add__strict__right__mono)). 185.47/93.67 thf(33152,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7462])). 185.47/93.67 thf(1849,axiom,((! [A:set_nat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (nat_set_encode @ A)) = (~ (member_nat @ zero_zero_nat @ A))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9210_even__set__encode__iff)). 185.47/93.67 thf(13935,plain,((! [A:set_nat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (nat_set_encode @ A)) = (~ (member_nat @ zero_zero_nat @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849])). 185.47/93.67 thf(626,axiom,((! [A:real]: ((cos_real @ (plus_plus_real @ A @ pi)) = (uminus_uminus_real @ (cos_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7785_cos__periodic__pi)). 185.47/93.67 thf(9808,plain,((! [A:real]: ((cos_real @ (plus_plus_real @ A @ pi)) = (uminus_uminus_real @ (cos_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[626])). 185.47/93.67 thf(4443,axiom,((numeral_numeral_rat = (^ [A:num]: (fract @ (numeral_numeral_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9946_rat__number__expand_I3_J)). 185.47/93.67 thf(22227,plain,(((numeral_numeral_rat) = (^ [A:num]: (fract @ (numeral_numeral_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4443])). 185.47/93.67 thf(2462,axiom,((! [A:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ one))) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_numeral__Bit0__div__2)). 185.47/93.67 thf(15887,plain,((! [A:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ one))) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2462])). 185.47/93.67 thf(7244,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4015_dual__order_Oirrefl)). 185.47/93.67 thf(32413,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7244])). 185.47/93.67 thf(6338,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2375_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)). 185.47/93.67 thf(29057,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6338])). 185.47/93.67 thf(2979,axiom,((! [A:real]: (ord_less_real @ A @ (plus_plus_real @ A @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1207_less__add__one)). 185.47/93.67 thf(17611,plain,((! [A:real]: (ord_less_real @ A @ (plus_plus_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2979])). 185.47/93.67 thf(1763,axiom,((! [A:real,B:real]: (ord_less_eq_real @ A @ (sqrt @ (plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8227_real__sqrt__sum__squares__ge2)). 185.47/93.67 thf(13638,plain,((! [A:real,B:real]: (ord_less_eq_real @ A @ (sqrt @ (plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763])). 185.47/93.67 thf(6204,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2345_zero__less__mult__pos2)). 185.47/93.67 thf(28616,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6204])). 185.47/93.67 thf(5605,axiom,((! [A:nat,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4985_even__mask__div__iff_H)). 185.47/93.67 thf(26379,plain,((! [A:nat,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5605])). 185.47/93.67 thf(1193,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7254_zdiv__int)). 185.47/93.67 thf(11750,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193])). 185.47/93.67 thf(3664,axiom,((! [A:real]: ((A != zero_zero_real) => ((divide_divide_real @ A @ A) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1717_div__self)). 185.47/93.67 thf(19762,plain,((! [A:real]: ((~ (A = zero_zero_real)) => ((divide_divide_real @ A @ A) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3664])). 185.47/93.67 thf(3272,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ B @ C) @ (times_times_real @ A @ C))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2232_mult__right__mono__neg)). 185.47/93.67 thf(18519,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ B @ C) @ (times_times_real @ A @ C))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3272])). 185.47/93.67 thf(687,axiom,((! [A:real]: ((sin_real @ (plus_plus_real @ A @ pi)) = (uminus_uminus_real @ (sin_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7787_sin__periodic__pi)). 185.47/93.67 thf(10024,plain,((! [A:real]: ((sin_real @ (plus_plus_real @ A @ pi)) = (uminus_uminus_real @ (sin_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[687])). 185.47/93.67 thf(4553,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_real @ A @ (B @ C)) => (((! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F))) => (ord_less_real @ A @ (B @ D))) <= (ord_less_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4098_order__less__subst1)). 185.47/93.67 thf(22584,plain,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_real @ A @ (B @ C)) => (((! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))) => (ord_less_real @ A @ (B @ D))) | ~ (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4553])). 185.47/93.67 thf(463,axiom,((! [A:set_nat,B:set_nat]: (((minus_minus_set_nat @ A @ B) = bot_bot_set_nat) = (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1257_Diff__eq__empty__iff)). 185.47/93.67 thf(9290,plain,((! [A:set_nat,B:set_nat]: (((minus_minus_set_nat @ A @ B) = bot_bot_set_nat) = (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[463])). 185.47/93.67 thf(2039,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ A @ B) => (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5515_le__imp__neg__le)). 185.47/93.67 thf(14549,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ A @ B) => (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2039])). 185.47/93.67 thf(4626,axiom,((! [A:int,B:nat,C:nat]: (((ord_less_eq_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (ord_less_eq_nat @ B @ C)) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_power__increasing__iff)). 185.47/93.67 thf(22822,plain,((! [A:int,B:nat,C:nat]: (((ord_less_eq_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (ord_less_eq_nat @ B @ C)) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4626])). 185.47/93.67 thf(3665,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_eq_rat @ B @ C) => (ord_less_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4213_order_Ostrict__trans2)). 185.47/93.67 thf(19765,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_eq_rat @ B @ C) => (ord_less_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3665])). 185.47/93.67 thf(7650,axiom,(((divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))) = na)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062)). 185.47/93.67 thf(33710,plain,(((divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))) = na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7650])). 185.47/93.67 thf(6578,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4787_le__imp__power__dvd)). 185.47/93.67 thf(29935,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6578])). 185.47/93.67 thf(6770,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((A = B) | ~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4164_nless__le)). 185.47/93.67 thf(30640,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((A = B) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6770])). 185.47/93.67 thf(5076,axiom,((! [A:num]: (((uminus_uminus_rat @ one_one_rat) = (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5294_neg__one__eq__numeral__iff)). 185.47/93.67 thf(24420,plain,((! [A:num]: (((uminus_uminus_rat @ one_one_rat) = (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5076])). 185.47/93.67 thf(4024,axiom,((! [A:num]: ((ord_max_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3618_max__0__1_I3_J)). 185.47/93.67 thf(20915,plain,((! [A:num]: ((ord_max_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4024])). 185.47/93.67 thf(1923,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4296_order__less__imp__le)). 185.47/93.67 thf(14151,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1923])). 185.47/93.67 thf(7158,axiom,((! [A:num]: ((one_one_rat = (numeral_numeral_rat @ A)) = (one = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_one__eq__numeral__iff)). 185.47/93.67 thf(32113,plain,((! [A:num]: ((one_one_rat = (numeral_numeral_rat @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7158])). 185.47/93.67 thf(2169,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_rat @ C @ B)) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2348_mult__less__cancel__left__neg)). 185.47/93.67 thf(14957,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_rat @ C @ B)) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2169])). 185.47/93.67 thf(945,axiom,((! [A:complex]: ((re @ (exp_complex @ A)) = (times_times_real @ (exp_real @ (re @ A)) @ (cos_real @ (im @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9686_Re__exp)). 185.47/93.67 thf(10974,plain,((! [A:complex]: ((re @ (exp_complex @ A)) = (times_times_real @ (exp_real @ (re @ A)) @ (cos_real @ (im @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[945])). 185.47/93.67 thf(6949,axiom,((! [A:num,B:nat]: ((suc @ (plus_plus_nat @ (numeral_numeral_nat @ A) @ B)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ A @ one)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1118_Suc__nat__number__of__add)). 185.47/93.67 thf(31300,plain,((! [A:num,B:nat]: ((suc @ (plus_plus_nat @ (numeral_numeral_nat @ A) @ B)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ A @ one)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6949])). 185.47/93.67 thf(4965,axiom,(((modulo_modulo_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1877_bits__one__mod__two__eq__one)). 185.47/93.67 thf(23986,plain,(((modulo_modulo_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4965])). 185.47/93.67 thf(2720,axiom,((! [A:rat,B:rat,C:num]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))) = (((~ (ord_less_rat @ zero_zero_rat @ B)) => (((ord_less_eq_rat @ zero_zero_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))) <= (~ (ord_less_rat @ B @ zero_zero_rat))) & ((ord_less_eq_rat @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B) @ A) <= (ord_less_rat @ B @ zero_zero_rat)))) & ((ord_less_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ A @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6261_divide__le__eq__numeral_I2_J)). 185.47/93.67 thf(16782,plain,((! [A:rat,B:rat,C:num]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))) = (((~ (ord_less_rat @ zero_zero_rat @ B)) => (((ord_less_eq_rat @ zero_zero_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))) | (ord_less_rat @ B @ zero_zero_rat)) & ((ord_less_eq_rat @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B) @ A) | ~ (ord_less_rat @ B @ zero_zero_rat)))) & ((ord_less_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ A @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2720])). 185.47/93.67 thf(3870,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4293_order__less__imp__le)). 185.47/93.67 thf(20426,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3870])). 185.47/93.67 thf(4470,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((plus_plus_rat @ A @ C) = (plus_plus_rat @ B @ D)) <= ((C = D) & (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_add__mono__thms__linordered__semiring_I4_J)). 185.47/93.67 thf(22309,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((plus_plus_rat @ A @ C) = (plus_plus_rat @ B @ D)) | ~ ((C = D) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4470])). 185.47/93.67 thf(2569,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4315_order__less__le__trans)). 185.47/93.67 thf(16246,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2569])). 185.47/93.67 thf(6780,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (plus_plus_nat @ (divide_divide_nat @ A @ C) @ (if_nat @ ((modulo_modulo_nat @ B @ C) = zero_zero_nat) @ one_one_nat @ zero_zero_nat)) @ (divide_divide_nat @ B @ C))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3019_verit__le__mono__div)). 185.47/93.67 thf(30669,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (plus_plus_nat @ (divide_divide_nat @ A @ C) @ (if_nat @ ((modulo_modulo_nat @ B @ C) = zero_zero_nat) @ one_one_nat @ zero_zero_nat)) @ (divide_divide_nat @ B @ C))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6780])). 185.47/93.67 thf(2854,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)) <= ((A = B) & (ord_less_rat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_add__mono__thms__linordered__field_I2_J)). 185.47/93.67 thf(17204,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)) | ~ ((A = B) & (ord_less_rat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2854])). 185.47/93.67 thf(1198,axiom,((! [A:num,B:nat,C:nat]: ((ord_less_eq_real @ (power_power_real @ (numeral_numeral_real @ A) @ B) @ (semiri5074537144036343181t_real @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7131_numeral__power__le__of__nat__cancel__iff)). 185.47/93.67 thf(11765,plain,((! [A:num,B:nat,C:nat]: ((ord_less_eq_real @ (power_power_real @ (numeral_numeral_real @ A) @ B) @ (semiri5074537144036343181t_real @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198])). 185.47/93.67 thf(6710,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = (ord_less_eq_nat @ A @ B))) <= (ord_less_eq_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1874_power__mono__iff)). 185.47/93.67 thf(30358,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = (ord_less_eq_nat @ A @ B))) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6710])). 185.47/93.67 thf(2649,axiom,((! [A:num,B:num]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ (numeral_numeral_nat @ B)) = (bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (pred_numeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9417_bit__minus__numeral__int_I1_J)). 185.47/93.67 thf(16518,plain,((! [A:num,B:num]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ (numeral_numeral_nat @ B)) = (bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2649])). 185.47/93.67 thf(202,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (arcsin @ A) @ (arcsin @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8312_arcsin__le__arcsin)). 185.47/93.67 thf(8387,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (arcsin @ A) @ (arcsin @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 185.47/93.67 thf(3635,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ C) => (ord_less_eq_rat @ A @ C)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3876_order__trans)). 185.47/93.67 thf(19666,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ C) => (ord_less_eq_rat @ A @ C)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3635])). 185.47/93.67 thf(1365,axiom,((! [A:int,B:num,C:num]: ((divide_divide_int @ (divide_divide_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ C)) = (divide_divide_int @ A @ (numeral_numeral_int @ (times_times_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_div__mult2__numeral__eq)). 185.47/93.67 thf(12278,plain,((! [A:int,B:num,C:num]: ((divide_divide_int @ (divide_divide_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ C)) = (divide_divide_int @ A @ (numeral_numeral_int @ (times_times_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365])). 185.47/93.67 thf(1431,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (plus_plus_rat @ B @ C)) = (plus_plus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1136_distrib__left)). 185.47/93.67 thf(12509,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ A @ (plus_plus_rat @ B @ C)) = (plus_plus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431])). 185.47/93.67 thf(881,axiom,((! [A:nat,B:real]: ((times_times_real @ (semiri5074537144036343181t_real @ (suc @ A)) @ (gbinomial_real @ B @ (suc @ A))) = (times_times_real @ B @ (gbinomial_real @ (minus_minus_real @ B @ one_one_real) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8536_gbinomial__absorption)). 185.47/93.67 thf(10741,plain,((! [A:nat,B:real]: ((times_times_real @ (semiri5074537144036343181t_real @ (suc @ A)) @ (gbinomial_real @ B @ (suc @ A))) = (times_times_real @ B @ (gbinomial_real @ (minus_minus_real @ B @ one_one_real) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[881])). 185.47/93.67 thf(4149,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1777_mod__mult__self3)). 185.47/93.67 thf(21287,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4149])). 185.47/93.67 thf(4179,axiom,((! [A:nat,B:nat]: (((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B) = zero_zero_real) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8507_pochhammer__of__nat__eq__0__iff)). 185.47/93.67 thf(21381,plain,((! [A:nat,B:nat]: (((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B) = zero_zero_real) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4179])). 185.47/93.67 thf(2432,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ C @ zero_zero_rat) => (ord_less_rat @ (divide_divide_rat @ B @ C) @ (divide_divide_rat @ A @ C))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2444_divide__strict__right__mono__neg)). 185.47/93.67 thf(15789,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ C @ zero_zero_rat) => (ord_less_rat @ (divide_divide_rat @ B @ C) @ (divide_divide_rat @ A @ C))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2432])). 185.47/93.67 thf(408,axiom,((! [A:nat,B:real]: ((root @ A @ (inverse_inverse_real @ B)) = (inverse_inverse_real @ (root @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9181_real__root__inverse)). 185.47/93.67 thf(9089,plain,((! [A:nat,B:real]: ((root @ A @ (inverse_inverse_real @ B)) = (inverse_inverse_real @ (root @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])). 185.47/93.67 thf(469,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A)) & (ord_less_eq_real @ (arcsin @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8328_arcsin__bounded)). 185.47/93.67 thf(9307,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A)) & (ord_less_eq_real @ (arcsin @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])). 185.47/93.67 thf(1160,axiom,((! [A:num]: ((neg_nu6511756317524482435omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu8557863876264182079omplex @ (numera6690914467698888265omplex @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7027_dbl__dec__simps_I1_J)). 185.47/93.67 thf(11657,plain,((! [A:num]: ((neg_nu6511756317524482435omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu8557863876264182079omplex @ (numera6690914467698888265omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160])). 185.47/93.67 thf(3242,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4265_dual__order_Ostrict__implies__order)). 185.47/93.67 thf(18431,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3242])). 185.47/93.67 thf(3522,axiom,((! [A:num,B:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (bit_se2923211474154528505it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9349_take__bit__numeral__minus__bit0)). 185.47/93.67 thf(19321,plain,((! [A:num,B:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (bit_se2923211474154528505it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3522])). 185.47/93.67 thf(460,axiom,((! [A:real]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (tan_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7982_tan__periodic)). 185.47/93.67 thf(9258,plain,((! [A:real]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (tan_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[460])). 185.47/93.67 thf(3963,axiom,((! [A:rat,B:rat]: (ord_less_eq_rat @ zero_zero_rat @ (plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2676_sum__squares__ge__zero)). 185.47/93.67 thf(20724,plain,((! [A:rat,B:rat]: (ord_less_eq_rat @ zero_zero_rat @ (plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3963])). 185.47/93.67 thf(7452,axiom,((! [A:nat]: ((groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A)) = (divide_divide_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6853_gauss__sum__from__Suc__0)). 185.47/93.67 thf(33101,plain,((! [A:nat]: ((groups3542108847815614940at_nat @ (semiri1316708129612266289at_nat) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A)) = (divide_divide_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7452])). 185.47/93.67 thf(1636,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4936_even__two__times__div__two)). 185.47/93.67 thf(13176,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636])). 185.47/93.67 thf(950,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (ord_max_int @ C @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3717_max_OcoboundedI2)). 185.47/93.67 thf(10989,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (ord_max_int @ C @ B)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[950])). 185.47/93.67 thf(6408,axiom,((! [A:(int > (int > $o)),B:int]: ((! [C:int]: ((ord_less_eq_int @ zero_zero_int @ C) => (A @ C @ (power_power_int @ C @ (numeral_numeral_nat @ (bit0 @ one)))))) => (A @ (abs_abs_int @ B) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6709_abs__sqrt__wlog)). 185.47/93.67 thf(29336,plain,((! [A:(int > (int > $o)),B:int]: ((! [C:int]: ((ord_less_eq_int @ zero_zero_int @ C) => (A @ C @ (power_power_int @ C @ (numeral_numeral_nat @ (bit0 @ one)))))) => (A @ (abs_abs_int @ B) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6408])). 185.47/93.67 thf(5663,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1032_Suc__less__eq2)). 185.47/93.67 thf(26583,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5663])). 185.47/93.67 thf(177,axiom,((! [A:real,B:nat,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((log @ (power_power_real @ A @ B) @ C) = (divide_divide_real @ (log @ A @ C) @ (semiri5074537144036343181t_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9048_log__base__pow)). 185.47/93.67 thf(8301,plain,((! [A:real,B:nat,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((log @ (power_power_real @ A @ B) @ C) = (divide_divide_real @ (log @ A @ C) @ (semiri5074537144036343181t_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 185.47/93.67 thf(2912,axiom,((bit_se725231765392027082nd_int = (^ [A:int,B:int]: (plus_plus_int @ (zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) & ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9388_and__int__rec)). 185.47/93.67 thf(17392,plain,(((bit_se725231765392027082nd_int) = (^ [A:int,B:int]: (plus_plus_int @ (zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) & ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2912])). 185.47/93.67 thf(4488,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D))) <= (A = (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_715_group__cancel_Osub1)). 185.47/93.67 thf(22367,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D))) | ~ (A = (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4488])). 185.47/93.67 thf(522,axiom,((gbinomial_complex = (^ [A:complex,B:nat]: (if_complex @ (B = zero_zero_nat) @ one_one_complex @ (divide1717551699836669952omplex @ (set_fo1517530859248394432omplex @ (^ [C:nat]: (times_times_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_complex) @ (semiri5044797733671781792omplex @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8611_gbinomial__code)). 185.47/93.67 thf(9483,plain,(((gbinomial_complex) = (^ [A:complex,B:nat]: (if_complex @ (B = zero_zero_nat) @ one_one_complex @ (divide1717551699836669952omplex @ (set_fo1517530859248394432omplex @ (^ [C:nat]: (times_times_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_complex) @ (semiri5044797733671781792omplex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[522])). 185.47/93.67 thf(7030,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4295_order__less__imp__le)). 185.47/93.67 thf(31678,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7030])). 185.47/93.67 thf(5316,axiom,((! [A:real,B:real]: ((times_times_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5545_minus__mult__commute)). 185.47/93.67 thf(25294,plain,((! [A:real,B:real]: ((times_times_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ A @ (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5316])). 185.47/93.67 thf(3566,axiom,((! [A:num,B:num]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5368_neg__numeral__le__iff)). 185.47/93.67 thf(19453,plain,((! [A:num,B:num]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3566])). 185.47/93.67 thf(4671,axiom,((! [A:complex,B:complex,C:complex]: (((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ B @ (times_times_complex @ C @ A)) @ A)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2762_divide__diff__eq__iff)). 185.47/93.67 thf(22959,plain,((! [A:complex,B:complex,C:complex]: (((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ B @ (times_times_complex @ C @ A)) @ A)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4671])). 185.47/93.67 thf(4085,axiom,((! [A:complex]: (dvd_dvd_complex @ one_one_complex @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4636_one__dvd)). 185.47/93.67 thf(21094,plain,((! [A:complex]: (dvd_dvd_complex @ one_one_complex @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4085])). 185.47/93.67 thf(5855,axiom,((! [A:(int > $o),B:nat,C:nat]: ((A @ (semiri1314217659103216013at_int @ (minus_minus_nat @ B @ C))) = (((A @ (minus_minus_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C))) <= (ord_less_eq_nat @ C @ B)) & ((ord_less_nat @ B @ C) => (A @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7328_zdiff__int__split)). 185.47/93.67 thf(27380,plain,((! [A:(int > $o),B:nat,C:nat]: ((A @ (semiri1314217659103216013at_int @ (minus_minus_nat @ B @ C))) = (((A @ (minus_minus_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C))) | ~ (ord_less_eq_nat @ C @ B)) & ((ord_less_nat @ B @ C) => (A @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5855])). 185.47/93.67 thf(3442,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ (modulo_modulo_int @ B @ A) @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3145_neg__mod__sign)). 185.47/93.67 thf(19057,plain,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ (modulo_modulo_int @ B @ A) @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3442])). 185.47/93.67 thf(1532,axiom,((! [A:num,B:rat,C:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (divide_divide_rat @ B @ C)) = (((((~ (ord_less_rat @ C @ zero_zero_rat)) => (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ zero_zero_rat)) & ((ord_less_eq_rat @ B @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C)) <= (ord_less_rat @ C @ zero_zero_rat))) <= (~ (ord_less_rat @ zero_zero_rat @ C))) & ((ord_less_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6263_le__divide__eq__numeral_I2_J)). 185.47/93.67 thf(12814,plain,((! [A:num,B:rat,C:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (divide_divide_rat @ B @ C)) = (((((~ (ord_less_rat @ C @ zero_zero_rat)) => (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ zero_zero_rat)) & ((ord_less_eq_rat @ B @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C)) | ~ (ord_less_rat @ C @ zero_zero_rat))) | (ord_less_rat @ zero_zero_rat @ C)) & ((ord_less_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1532])). 185.47/93.67 thf(913,axiom,((! [A:real]: (((ord_less_real @ one_one_real @ A) <= (ord_less_real @ zero_zero_real @ A)) <= (ord_less_real @ zero_zero_real @ (ln_ln_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5877_ln__gt__zero__imp__gt__one)). 185.47/93.67 thf(10857,plain,((! [A:real]: ((ord_less_real @ one_one_real @ A) | ~ (ord_less_real @ zero_zero_real @ A) | ~ (ord_less_real @ zero_zero_real @ (ln_ln_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[913])). 185.47/93.67 thf(5736,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4463_dvd__times__left__cancel__iff)). 185.47/93.67 thf(26816,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5736])). 185.47/93.67 thf(1729,axiom,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (times_times_real @ A @ (comm_s7457072308508201937r_real @ (plus_plus_real @ A @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8489_pochhammer__rec)). 185.47/93.67 thf(13531,plain,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (times_times_real @ A @ (comm_s7457072308508201937r_real @ (plus_plus_real @ A @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729])). 185.47/93.67 thf(1719,axiom,((! [A:real,B:(num > real),C:num,D:num]: ((ord_less_real @ A @ (B @ C)) => (((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) <= (ord_less_eq_num @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4346_order__less__le__subst1)). 185.47/93.67 thf(13482,plain,((! [A:real,B:(num > real),C:num,D:num]: ((ord_less_real @ A @ (B @ C)) => (((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) | ~ (ord_less_eq_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719])). 185.47/93.67 thf(5838,axiom,((! [A:nat,B:nat]: ((power_power_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ (plus_plus_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_power2__sum)). 185.47/93.67 thf(27313,plain,((! [A:nat,B:nat]: ((power_power_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ (plus_plus_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5838])). 185.47/93.67 thf(4760,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ zero_zero_rat) = (((ord_less_eq_rat @ A @ zero_zero_rat) & (ord_less_eq_rat @ zero_zero_rat @ B)) | ((ord_less_eq_rat @ zero_zero_rat @ A) & (ord_less_eq_rat @ B @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2226_mult__le__0__iff)). 185.47/93.67 thf(23299,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ zero_zero_rat) = (((ord_less_eq_rat @ A @ zero_zero_rat) & (ord_less_eq_rat @ zero_zero_rat @ B)) | ((ord_less_eq_rat @ zero_zero_rat @ A) & (ord_less_eq_rat @ B @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4760])). 185.47/93.67 thf(7173,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) => ((A = B) <= (~ (ord_less_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1026_less__SucE)). 185.47/93.67 thf(32167,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) => ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7173])). 185.47/93.67 thf(5,axiom,((! [A:complex,B:nat,C:complex]: ((minus_minus_complex @ (power_power_complex @ A @ B) @ (power_power_complex @ C @ B)) = (times_times_complex @ (minus_minus_complex @ A @ C) @ (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (power_power_complex @ C @ (minus_minus_nat @ B @ (suc @ D))) @ (power_power_complex @ A @ D))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7616_power__diff__sumr2)). 185.47/93.67 thf(7741,plain,((! [A:complex,B:nat,C:complex]: ((minus_minus_complex @ (power_power_complex @ A @ B) @ (power_power_complex @ C @ B)) = (times_times_complex @ (minus_minus_complex @ A @ C) @ (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (power_power_complex @ C @ (minus_minus_nat @ B @ (suc @ D))) @ (power_power_complex @ A @ D))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 185.47/93.67 thf(4894,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ A @ B) & (C = D)) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_add__mono__thms__linordered__semiring_I3_J)). 185.47/93.67 thf(23741,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ A @ B) & (C = D)) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4894])). 185.47/93.67 thf(4403,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (plus_plus_nat @ A @ B) @ C) = (groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ (binomial @ C @ D)) @ (power_power_nat @ A @ D)) @ (power_power_nat @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8950_binomial)). 185.47/93.67 thf(22103,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (plus_plus_nat @ A @ B) @ C) = (groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ (binomial @ C @ D)) @ (power_power_nat @ A @ D)) @ (power_power_nat @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4403])). 185.47/93.67 thf(633,axiom,((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7765_minus__pi__half__less__zero)). 185.47/93.67 thf(9835,plain,((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[633])). 185.47/93.67 thf(449,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ B) => ((member_nat @ A @ (minus_minus_set_nat @ B @ C)) <= (~ (member_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1292_DiffI)). 185.47/93.67 thf(9224,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ B) => ((member_nat @ A @ (minus_minus_set_nat @ B @ C)) | (member_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[449])). 185.47/93.67 thf(4314,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (ord_less_eq_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_add__le__cancel__right)). 185.47/93.67 thf(21783,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (ord_less_eq_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4314])). 185.47/93.67 thf(3202,axiom,((! [A:int]: ((! [B:nat]: (A != (semiri1314217659103216013at_int @ B))) => (~ (! [B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => (A != (uminus_uminus_int @ (semiri1314217659103216013at_int @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7268_int__cases4)). 185.47/93.67 thf(18309,plain,((! [A:int]: ((! [B:nat]: ~ (A = (semiri1314217659103216013at_int @ B))) => (~ (! [B:nat]: ((ord_less_nat @ zero_zero_nat @ B) => (~ (A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3202])). 185.47/93.67 thf(5181,axiom,((! [A:num]: ((numeral_numeral_rat @ A) != (uminus_uminus_rat @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5775_numeral__neq__neg__one)). 185.47/93.67 thf(24817,plain,((! [A:num]: ~ ((numeral_numeral_rat @ A) = (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5181])). 185.47/93.67 thf(4454,axiom,((! [A:num,B:num]: ((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5367_neg__numeral__le__iff)). 185.47/93.67 thf(22259,plain,((! [A:num,B:num]: ((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ (numeral_numeral_real @ B))) = (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4454])). 185.47/93.67 thf(6923,axiom,((! [A:nat]: (((A != zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat)) & (((power_power_nat @ zero_zero_nat @ A) = one_one_nat) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1961_power__0__left)). 185.47/93.67 thf(31205,plain,((! [A:nat]: (((~ (A = zero_zero_nat)) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat)) & (((power_power_nat @ zero_zero_nat @ A) = one_one_nat) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6923])). 185.47/93.67 thf(3328,axiom,((! [A:real]: ((~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ A))) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3042_not__real__square__gt__zero)). 185.47/93.67 thf(18695,plain,((! [A:real]: ((~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ A))) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3328])). 185.47/93.67 thf(81,axiom,((! [A:real,B:real,C:nat]: (((((archim7802044766580827645g_real @ (log @ B @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int)) = ((ord_less_real @ (powr_real @ B @ (semiri5074537144036343181t_real @ C)) @ A) & (ord_less_eq_real @ A @ (powr_real @ B @ (semiri5074537144036343181t_real @ (plus_plus_nat @ C @ one_one_nat)))))) <= (ord_less_real @ one_one_real @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9067_ceiling__log__eq__powr__iff)). 185.47/93.67 thf(7995,plain,((! [A:real,B:real,C:nat]: ((((archim7802044766580827645g_real @ (log @ B @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int)) = ((ord_less_real @ (powr_real @ B @ (semiri5074537144036343181t_real @ C)) @ A) & (ord_less_eq_real @ A @ (powr_real @ B @ (semiri5074537144036343181t_real @ (plus_plus_nat @ C @ one_one_nat)))))) | ~ (ord_less_real @ one_one_real @ B) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 185.47/93.67 thf(5300,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((B != A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4237_dual__order_Ostrict__iff__order)). 185.47/93.67 thf(25248,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (B = A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5300])). 185.47/93.67 thf(213,axiom,((! [A:real]: ((cos_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (cos_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7800_cos__periodic)). 185.47/93.67 thf(8419,plain,((! [A:real]: ((cos_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (cos_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 185.47/93.67 thf(4127,axiom,((! [A:real,B:real]: (((ord_less_real @ B @ A) <= (A != B)) <= (~ (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4002_linorder__cases)). 185.47/93.67 thf(21222,plain,((! [A:real,B:real]: ((ord_less_real @ B @ A) | (A = B) | (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4127])). 185.47/93.67 thf(2758,axiom,((! [A:int]: ((ord_less_eq_real @ one_one_real @ (ring_1_of_int_real @ A)) = (ord_less_eq_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7080_of__int__1__le__iff)). 185.47/93.67 thf(16900,plain,((! [A:int]: ((ord_less_eq_real @ one_one_real @ (ring_1_of_int_real @ A)) = (ord_less_eq_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2758])). 185.47/93.67 thf(3271,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sgn_sgn_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9245_zero__le__sgn__iff)). 185.47/93.67 thf(18516,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sgn_sgn_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3271])). 185.47/93.67 thf(218,axiom,((! [A:real]: ((sqrt @ (inverse_inverse_real @ A)) = (inverse_inverse_real @ (sqrt @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8959_real__sqrt__inverse)). 185.47/93.67 thf(8436,plain,((! [A:real]: ((sqrt @ (inverse_inverse_real @ A)) = (inverse_inverse_real @ (sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 185.47/93.67 thf(6148,axiom,((! [A:option_nat]: ((A != none_nat) => (~ (! [B:nat]: (A != (some_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1168_option_Oexhaust)). 185.47/93.67 thf(28379,plain,((! [A:option_nat]: ((~ (A = none_nat)) => (~ (! [B:nat]: ~ (A = (some_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6148])). 185.47/93.67 thf(4590,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1537_add__0)). 185.47/93.67 thf(22700,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4590])). 185.47/93.67 thf(7656,axiom,((! [A:num,B:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) != (modulo_modulo_nat @ (numeral_numeral_nat @ one) @ (numeral_numeral_nat @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2160_cong__exp__iff__simps_I8_J)). 185.47/93.67 thf(33724,plain,((! [A:num,B:num]: ~ ((modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (modulo_modulo_nat @ (numeral_numeral_nat @ one) @ (numeral_numeral_nat @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7656])). 185.47/93.67 thf(947,axiom,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se7879613467334960850it_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) & (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4953_even__set__bit__iff)). 185.47/93.67 thf(10980,plain,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se7879613467334960850it_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) & ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[947])). 185.47/93.67 thf(2930,axiom,((! [A:int,B:(int > $o),C:(int > $o)]: ((ord_less_int @ zero_zero_int @ A) => ((! [D:int,E:int]: ((B @ D) = (B @ (minus_minus_int @ D @ (times_times_int @ E @ A))))) => ((? [D:int]: ! [E:int]: ((ord_less_int @ E @ D) => ((C @ E) = (B @ E)))) => ((? [D:int]: (B @ D)) => (? [D:int]: (C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3337_minusinfinity)). 185.47/93.67 thf(17448,plain,((! [A:int,B:(int > $o),C:(int > $o)]: ((ord_less_int @ zero_zero_int @ A) => ((! [D:int,E:int]: ((B @ D) = (B @ (minus_minus_int @ D @ (times_times_int @ E @ A))))) => ((? [D:int]: ! [E:int]: ((ord_less_int @ E @ D) => ((C @ E) = (B @ E)))) => ((? [D:int]: (B @ D)) => (? [D:int]: (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2930])). 185.47/93.67 thf(7322,axiom,((! [A:rat,B:num]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B))) = (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (A != zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))) | ((numeral_numeral_nat @ B) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4548_zero__less__power__eq__numeral)). 185.47/93.67 thf(32673,plain,((! [A:rat,B:num]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B))) = (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & ~ (A = zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))) | ((numeral_numeral_nat @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7322])). 185.47/93.67 thf(2534,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (times_times_int @ (modulo_modulo_int @ A @ B) @ (modulo_modulo_int @ C @ B)) @ B) = (modulo_modulo_int @ (times_times_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1986_mod__mult__eq)). 185.47/93.67 thf(16133,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (times_times_int @ (modulo_modulo_int @ A @ B) @ (modulo_modulo_int @ C @ B)) @ B) = (modulo_modulo_int @ (times_times_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2534])). 185.47/93.67 thf(6535,axiom,((! [A:int,B:int]: ((uminus_uminus_int @ (minus_minus_int @ A @ B)) = (minus_minus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5100_minus__diff__eq)). 185.47/93.67 thf(29793,plain,((! [A:int,B:int]: ((uminus_uminus_int @ (minus_minus_int @ A @ B)) = (minus_minus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6535])). 185.47/93.67 thf(5945,axiom,((! [A:nat,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) = ((ord_less_eq_nat @ A @ B) | ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4992_even__mask__div__iff)). 185.47/93.67 thf(27677,plain,((! [A:nat,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) = ((ord_less_eq_nat @ A @ B) | ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5945])). 185.47/93.67 thf(4784,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ A @ C) <= (ord_less_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4024_order_Ostrict__trans)). 185.47/93.67 thf(23371,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ A @ C) | ~ (ord_less_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4784])). 185.47/93.67 thf(4991,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (plus_plus_nat @ B @ A)) = (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6236_neg__one__power__add__eq__neg__one__power__diff)). 185.47/93.67 thf(24074,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (plus_plus_nat @ B @ A)) = (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4991])). 185.47/93.67 thf(4737,axiom,((! [A:real]: ((ord_less_eq_real @ (sqrt @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8124_real__sqrt__le__0__iff)). 185.47/93.67 thf(23189,plain,((! [A:real]: ((ord_less_eq_real @ (sqrt @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4737])). 185.47/93.67 thf(5292,axiom,((! [A:rat,B:rat,C:nat]: (((times_times_rat @ A @ B) = one_one_rat) => ((times_times_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C)) = one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_840_left__right__inverse__power)). 185.47/93.67 thf(25226,plain,((! [A:rat,B:rat,C:nat]: (((times_times_rat @ A @ B) = one_one_rat) => ((times_times_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C)) = one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5292])). 185.47/93.67 thf(1961,axiom,((! [A:num,B:num]: (((~ (ord_less_eq_num @ A @ B)) => ((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit1 @ B)) = (unique5026877609467782581ep_nat @ (bit1 @ B) @ (unique5055182867167087721od_nat @ (bit0 @ A) @ (bit0 @ (bit1 @ B)))))) & (((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit1 @ B)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ A)))) <= (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6769_divmod__algorithm__code_I7_J)). 185.47/93.67 thf(14290,plain,((! [A:num,B:num]: (((~ (ord_less_eq_num @ A @ B)) => ((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit1 @ B)) = (unique5026877609467782581ep_nat @ (bit1 @ B) @ (unique5055182867167087721od_nat @ (bit0 @ A) @ (bit0 @ (bit1 @ B)))))) & (((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit1 @ B)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ A)))) | ~ (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1961])). 185.47/93.67 thf(7566,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_real @ (power_power_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_power__even__eq)). 185.47/93.67 thf(33477,plain,((! [A:real,B:nat]: ((power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_real @ (power_power_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7566])). 185.47/93.67 thf(4765,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (ord_less_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6155_pos__minus__divide__less__eq)). 185.47/93.67 thf(23314,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (ord_less_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4765])). 185.47/93.67 thf(4995,axiom,((! [A:num,B:num]: ((numeral_numeral_rat @ A) != (uminus_uminus_rat @ (numeral_numeral_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5533_numeral__neq__neg__numeral)). 185.47/93.67 thf(24085,plain,((! [A:num,B:num]: ~ ((numeral_numeral_rat @ A) = (uminus_uminus_rat @ (numeral_numeral_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4995])). 185.47/93.67 thf(6857,axiom,((! [A:nat]: (((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = one_one_rat) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5468_neg__one__even__power)). 185.47/93.67 thf(30976,plain,((! [A:nat]: (((power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) = one_one_rat) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6857])). 185.47/93.67 thf(5422,axiom,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_mult__numeral__1)). 185.47/93.67 thf(25661,plain,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5422])). 185.47/93.67 thf(3748,axiom,((! [A:num,B:num,C:complex]: ((plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (plus_plus_complex @ (numera6690914467698888265omplex @ B) @ C)) = (plus_plus_complex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add__numeral__left)). 185.47/93.67 thf(20036,plain,((! [A:num,B:num,C:complex]: ((plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (plus_plus_complex @ (numera6690914467698888265omplex @ B) @ C)) = (plus_plus_complex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3748])). 185.47/93.67 thf(5603,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_add__less__mono1)). 185.47/93.67 thf(26373,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5603])). 185.47/93.67 thf(1486,axiom,((! [A:rat,B:int]: (((ord_less_eq_rat @ (ring_1_of_int_rat @ B) @ (plus_plus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one))))) => ((archim7778729529865785530nd_rat @ A) = B)) <= (ord_less_rat @ (minus_minus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ (ring_1_of_int_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7531_round__unique)). 185.47/93.67 thf(12676,plain,((! [A:rat,B:int]: (((ord_less_eq_rat @ (ring_1_of_int_rat @ B) @ (plus_plus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one))))) => ((archim7778729529865785530nd_rat @ A) = B)) | ~ (ord_less_rat @ (minus_minus_rat @ A @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) @ (ring_1_of_int_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486])). 185.47/93.67 thf(1306,axiom,((! [A:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5201_mult__minus1)). 185.47/93.67 thf(12082,plain,((! [A:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306])). 185.47/93.67 thf(3805,axiom,((! [A:num,B:real,C:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (divide_divide_real @ B @ C)) = (((ord_less_eq_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) @ B) <= (ord_less_real @ zero_zero_real @ C)) & ((((ord_less_eq_real @ B @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C)) <= (ord_less_real @ C @ zero_zero_real)) & ((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real) <= (~ (ord_less_real @ C @ zero_zero_real)))) <= (~ (ord_less_real @ zero_zero_real @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6262_le__divide__eq__numeral_I2_J)). 185.47/93.67 thf(20228,plain,((! [A:num,B:real,C:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (divide_divide_real @ B @ C)) = (((ord_less_eq_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) @ B) | ~ (ord_less_real @ zero_zero_real @ C)) & ((((ord_less_eq_real @ B @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C)) | ~ (ord_less_real @ C @ zero_zero_real)) & ((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real) | (ord_less_real @ C @ zero_zero_real))) | (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3805])). 185.47/93.67 thf(7374,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_le__add1)). 185.47/93.67 thf(32842,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7374])). 185.47/93.67 thf(4275,axiom,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o)]: ((! [C:vEBT_VEBT]: ((member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A)) => (B @ C))) = (! [C:nat]: ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)) => (B @ (nth_VEBT_VEBT @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_all__set__conv__all__nth)). 185.47/93.67 thf(21674,plain,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o)]: ((! [C:vEBT_VEBT]: ((member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A)) => (B @ C))) = (! [C:nat]: ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)) => (B @ (nth_VEBT_VEBT @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4275])). 185.47/93.67 thf(2355,axiom,((! [A:real,B:nat,C:nat]: (((comm_s7457072308508201937r_real @ A @ B) = zero_zero_real) => (((comm_s7457072308508201937r_real @ A @ C) = zero_zero_real) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8439_pochhammer__eq__0__mono)). 185.47/93.67 thf(15530,plain,((! [A:real,B:nat,C:nat]: (((comm_s7457072308508201937r_real @ A @ B) = zero_zero_real) => (((comm_s7457072308508201937r_real @ A @ C) = zero_zero_real) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2355])). 185.47/93.67 thf(209,axiom,((! [A:complex]: ((power_power_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9691_cmod__power2)). 185.47/93.67 thf(8408,plain,((! [A:complex]: ((power_power_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 185.47/93.67 thf(5814,axiom,((! [A:vEBT_VEBT,B:nat]: ((((? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))) => (B != (suc @ zero_zero_nat))) => ((! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ G @ C @ E)) => ((((((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (((G = (plus_plus_nat @ D @ F)) => ((~ (! [H:vEBT_VEBT]: ((~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C))))) <= (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ E @ H))))) <= (F = D))) <= (vEBT_invar_vebt @ E @ F)) <= (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ H @ D)))) <= (B = G)))) => ((! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((((! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ D) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))) => ((((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (((G = (plus_plus_nat @ D @ F)) => ((~ (! [H:vEBT_VEBT]: ((~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C))))) <= (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ E @ H))))) <= (F = (suc @ D)))) <= (vEBT_invar_vebt @ E @ F))) <= (B = G)) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ G @ C @ E)))) => ((~ (! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat,H:nat,I:nat]: (((((vEBT_invar_vebt @ E @ F) => (((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (((G = (plus_plus_nat @ D @ F)) => ((((! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K))))) <= (H = I)) => ((ord_less_eq_nat @ H @ I) => ((~ ((H != I) => (! [J:nat]: ((! [K:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ K @ D)) & ((vEBT_VEBT_high @ K @ D) = J)) => ((ord_less_eq_nat @ K @ I) & (ord_less_nat @ H @ K))) & ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ I @ D)) <= ((vEBT_VEBT_high @ I @ D) = J))) <= (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)))))) <= (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ G))))) <= (! [J:nat]: (((? [K:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ K)) = (vEBT_V8194947554948674370ptions @ E @ J)) <= (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)))))) <= (F = (suc @ D))))) <= (! [J:vEBT_VEBT]: ((vEBT_invar_vebt @ J @ D) <= (member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C))))) <= (B = G)) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ H @ I)) @ G @ C @ E))))) <= (! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat,H:nat,I:nat]: ((((! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ J @ D))) => ((vEBT_invar_vebt @ E @ F) => (((F = D) => ((G = (plus_plus_nat @ D @ F)) => ((((H = I) => (! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K)))))) => (((~ ((! [J:nat]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (! [K:nat]: (((ord_less_nat @ H @ K) & (ord_less_eq_nat @ K @ I)) <= ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ K @ D)) & ((vEBT_VEBT_high @ K @ D) = J))) & (((vEBT_VEBT_high @ I @ D) = J) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ I @ D)))))) <= (H != I))) <= (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ G))) <= (ord_less_eq_nat @ H @ I))) <= (! [J:nat]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => ((? [K:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ K)) = (vEBT_V8194947554948674370ptions @ E @ J))))))) <= ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F))))) <= (B = G)) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ H @ I)) @ G @ C @ E)))))))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3017_invar__vebt_Ocases)). 185.47/93.67 thf(27144,plain,((! [A:vEBT_VEBT,B:nat]: ((((? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))) => (~ (B = (suc @ zero_zero_nat)))) => ((! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ G @ C @ E)) => ((((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (((G = (plus_plus_nat @ D @ F)) => (~ (! [H:vEBT_VEBT]: (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))) | ? [H:nat]: (vEBT_V8194947554948674370ptions @ E @ H))) | ~ (F = D))) | ~ (vEBT_invar_vebt @ E @ F) | ~ (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ H @ D))) | ~ (B = G)))) => ((! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: (((! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ D) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))) => ((((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (((G = (plus_plus_nat @ D @ F)) => (~ (! [H:vEBT_VEBT]: (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))) | ? [H:nat]: (vEBT_V8194947554948674370ptions @ E @ H))) | ~ (F = (suc @ D)))) | ~ (vEBT_invar_vebt @ E @ F))) | ~ (B = G) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ G @ C @ E)))) => (~ (! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat,H:nat,I:nat]: (((vEBT_invar_vebt @ E @ F) => (((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (((G = (plus_plus_nat @ D @ F)) => (((! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K)))) | ~ (H = I)) => ((ord_less_eq_nat @ H @ I) => (~ ((~ (H = I)) => (! [J:nat]: ((! [K:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ K @ D)) & ((vEBT_VEBT_high @ K @ D) = J)) => ((ord_less_eq_nat @ K @ I) & (ord_less_nat @ H @ K))) & ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ I @ D)) | ~ ((vEBT_VEBT_high @ I @ D) = J))) | ~ (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F))))) | ~ (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ G))))) | ~ (! [J:nat]: (((? [K:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ K)) = (vEBT_V8194947554948674370ptions @ E @ J)) | ~ (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)))))) | ~ (F = (suc @ D))))) | ~ (! [J:vEBT_VEBT]: ((vEBT_invar_vebt @ J @ D) | ~ (member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)))) | ~ (B = G) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ H @ I)) @ G @ C @ E)))) | ~ (! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat,H:nat,I:nat]: (((! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ J @ D))) => ((vEBT_invar_vebt @ E @ F) => (((F = D) => ((G = (plus_plus_nat @ D @ F)) => ((((H = I) => (! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K)))))) => (~ (! [J:nat]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (! [K:nat]: (((ord_less_nat @ H @ K) & (ord_less_eq_nat @ K @ I)) | ~ ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ K @ D)) & ((vEBT_VEBT_high @ K @ D) = J))) & (((vEBT_VEBT_high @ I @ D) = J) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ I @ D))))) | (H = I)) | ~ (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ G)) | ~ (ord_less_eq_nat @ H @ I))) | ~ (! [J:nat]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => ((? [K:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ K)) = (vEBT_V8194947554948674370ptions @ E @ J))))))) | ~ ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F))))) | ~ (B = G) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ H @ I)) @ G @ C @ E)))))))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5814])). 185.47/93.67 thf(2700,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => ((ord_less_eq_int @ zero_zero_int @ D) => ((ord_less_int @ D @ B) => ((divide_divide_int @ A @ B) = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3067_int__div__pos__eq)). 185.47/93.67 thf(16718,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => ((ord_less_eq_int @ zero_zero_int @ D) => ((ord_less_int @ D @ B) => ((divide_divide_int @ A @ B) = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2700])). 185.47/93.67 thf(7156,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (~ ((! [C:nat]: (B != (times_times_nat @ A @ C))) <= (A != zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4821_unit__dvdE)). 185.47/93.67 thf(32103,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (~ (! [C:nat]: ~ (B = (times_times_nat @ A @ C)) | (A = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7156])). 185.47/93.67 thf(5359,axiom,(((plus_plus_nat @ one_one_nat) = suc)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1106_plus__1__eq__Suc)). 185.47/93.67 thf(25474,plain,(((plus_plus_nat @ one_one_nat) = (suc))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5359])). 185.47/93.67 thf(6053,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) <= (~ (ord_less_nat @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4051_linorder__neqE)). 185.47/93.67 thf(28047,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6053])). 185.47/93.67 thf(1409,axiom,((gbinomial_real = (^ [A:real,B:nat]: (divide_divide_real @ (comm_s7457072308508201937r_real @ (plus_plus_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B) @ (semiri2265585572941072030t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8459_gbinomial__pochhammer_H)). 185.47/93.67 thf(12428,plain,(((gbinomial_real) = (^ [A:real,B:nat]: (divide_divide_real @ (comm_s7457072308508201937r_real @ (plus_plus_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B) @ (semiri2265585572941072030t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409])). 185.47/93.67 thf(7175,axiom,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_power__one__right)). 185.47/93.67 thf(32172,plain,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7175])). 185.47/93.67 thf(2704,axiom,((! [A:real]: (ord_less_eq_real @ (minus_minus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7632_of__int__round__ge)). 185.47/93.67 thf(16735,plain,((! [A:real]: (ord_less_eq_real @ (minus_minus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2704])). 185.47/93.67 thf(3070,axiom,((! [A:int,B:num,C:nat]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7136_of__int__le__numeral__power__cancel__iff)). 185.47/93.67 thf(17892,plain,((! [A:int,B:num,C:nat]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (numeral_numeral_rat @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3070])). 185.47/93.67 thf(2303,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ B) => ((ord_less_eq_real @ (real_V7735802525324610683m_real @ C) @ D) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ C)) @ (plus_plus_real @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7490_norm__triangle__mono)). 185.47/93.67 thf(15367,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ B) => ((ord_less_eq_real @ (real_V7735802525324610683m_real @ C) @ D) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ C)) @ (plus_plus_real @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2303])). 185.47/93.67 thf(6084,axiom,((! [A:vEBT_VEBT,B:nat]: ((? [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ C @ (suc @ (suc @ B)) @ D @ E))) <= (vEBT_invar_vebt @ A @ (suc @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_985_deg__SUcn__Node)). 185.47/93.67 thf(28148,plain,((! [A:vEBT_VEBT,B:nat]: (? [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ C @ (suc @ (suc @ B)) @ D @ E)) | ~ (vEBT_invar_vebt @ A @ (suc @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6084])). 185.47/93.67 thf(5412,axiom,((! [A:num]: ((one_one_complex = (numera6690914467698888265omplex @ A)) = (one = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_one__eq__numeral__iff)). 185.47/93.67 thf(25633,plain,((! [A:num]: ((one_one_complex = (numera6690914467698888265omplex @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5412])). 185.47/93.67 thf(3598,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (minus_minus_real @ A @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A))) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6299_ln__one__plus__pos__lower__bound)). 185.47/93.67 thf(19555,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (minus_minus_real @ A @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A))) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3598])). 185.47/93.67 thf(7577,axiom,((top_top_set_char = (image_nat_char @ unique3096191561947761185of_nat @ (set_or4665077453230672383an_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ one))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9975_UNIV__char__of__nat)). 185.47/93.67 thf(33509,plain,((top_top_set_char = (image_nat_char @ (unique3096191561947761185of_nat) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ one))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7577])). 185.47/93.67 thf(1832,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C)) => ((ord_less_int @ C @ A) => ((ord_less_eq_int @ zero_zero_int @ B) <= (ord_less_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3173_q__pos__lemma)). 185.47/93.67 thf(13871,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C)) => ((ord_less_int @ C @ A) => ((ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1832])). 185.47/93.67 thf(1654,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ B)) @ C) = ((ord_less_rat @ A @ (plus_plus_rat @ B @ C)) & (ord_less_rat @ (minus_minus_rat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6594_abs__diff__less__iff)). 185.47/93.67 thf(13240,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ B)) @ C) = ((ord_less_rat @ A @ (plus_plus_rat @ B @ C)) & (ord_less_rat @ (minus_minus_rat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654])). 185.47/93.67 thf(7607,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (semiri1316708129612266289at_nat @ A)) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7118_even__of__nat)). 185.47/93.67 thf(33592,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (semiri1316708129612266289at_nat @ A)) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7607])). 185.47/93.67 thf(2409,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((divide_divide_rat @ (divide_divide_rat @ A @ B) @ (divide_divide_rat @ C @ D)) = (divide_divide_rat @ (times_times_rat @ A @ D) @ (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_divide__divide__times__eq)). 185.47/93.67 thf(15700,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((divide_divide_rat @ (divide_divide_rat @ A @ B) @ (divide_divide_rat @ C @ D)) = (divide_divide_rat @ (times_times_rat @ A @ D) @ (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2409])). 185.47/93.67 thf(4498,axiom,((! [A:int,B:nat]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ (abs_abs_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6567_zero__le__power__abs)). 185.47/93.67 thf(22399,plain,((! [A:int,B:nat]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ (abs_abs_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4498])). 185.47/93.67 thf(3225,axiom,((! [A:int,B:int]: (((ord_less_eq_rat @ zero_zero_rat @ (fract @ B @ A)) = (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9953_zero__le__Fract__iff)). 185.47/93.67 thf(18382,plain,((! [A:int,B:int]: (((ord_less_eq_rat @ zero_zero_rat @ (fract @ B @ A)) = (ord_less_eq_int @ zero_zero_int @ B)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3225])). 185.47/93.67 thf(5388,axiom,((! [A:num]: (((numeral_numeral_int @ A) = one_one_int) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_numeral__eq__one__iff)). 185.47/93.67 thf(25561,plain,((! [A:num]: (((numeral_numeral_int @ A) = one_one_int) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5388])). 185.47/93.67 thf(3370,axiom,((! [A:set_nat,B:(nat > int),C:(nat > int)]: ((finite_finite_nat @ A) => (((ord_less_int @ (groups3539618377306564664at_int @ B @ A) @ (groups3539618377306564664at_int @ C @ A)) <= (? [D:nat]: ((member_nat @ D @ A) & (ord_less_int @ (B @ D) @ (C @ D))))) <= (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_int @ (B @ D) @ (C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5853_sum__strict__mono__ex1)). 185.47/93.67 thf(18827,plain,((! [A:set_nat,B:(nat > int),C:(nat > int)]: ((finite_finite_nat @ A) => ((ord_less_int @ (groups3539618377306564664at_int @ (B) @ A) @ (groups3539618377306564664at_int @ (C) @ A)) | ~ (? [D:nat]: ((member_nat @ D @ A) & (ord_less_int @ (B @ D) @ (C @ D)))) | ~ (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_int @ (B @ D) @ (C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3370])). 185.47/93.67 thf(6127,axiom,((! [A:nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1209_less__add__one)). 185.47/93.67 thf(28307,plain,((! [A:nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6127])). 185.47/93.67 thf(5210,axiom,((! [A:complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex) = ((A = (uminus1482373934393186551omplex @ one_one_complex)) | (A = one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6224_power2__eq__1__iff)). 185.47/93.67 thf(24904,plain,((! [A:complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex) = ((A = (uminus1482373934393186551omplex @ one_one_complex)) | (A = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5210])). 185.47/93.67 thf(1983,axiom,((! [A:int,B:int]: (ord_less_eq_int @ (minus_minus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) @ (abs_abs_int @ (minus_minus_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6497_abs__triangle__ineq2__sym)). 185.47/93.67 thf(14364,plain,((! [A:int,B:int]: (ord_less_eq_int @ (minus_minus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) @ (abs_abs_int @ (minus_minus_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1983])). 185.47/93.67 thf(6800,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_rat @ zero_zero_rat @ A) = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1965_zero__power)). 185.47/93.67 thf(30737,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_rat @ zero_zero_rat @ A) = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6800])). 185.47/93.67 thf(4209,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ one_one_rat @ A) => ((ord_less_rat @ one_one_rat @ (times_times_rat @ A @ B)) <= (ord_less_rat @ one_one_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1192_less__1__mult)). 185.47/93.67 thf(21469,plain,((! [A:rat,B:rat]: ((ord_less_rat @ one_one_rat @ A) => ((ord_less_rat @ one_one_rat @ (times_times_rat @ A @ B)) | ~ (ord_less_rat @ one_one_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4209])). 185.47/93.67 thf(5815,axiom,((! [A:num]: ((minus_minus_rat @ one_one_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (numeral_numeral_rat @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5447_diff__numeral__special_I3_J)). 185.47/93.67 thf(27242,plain,((! [A:num]: ((minus_minus_rat @ one_one_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (numeral_numeral_rat @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5815])). 185.47/93.67 thf(5835,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2293_add__nonneg__nonneg)). 185.47/93.67 thf(27303,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5835])). 185.47/93.67 thf(4097,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (times_times_rat @ B @ A) @ C) => (ord_less_eq_rat @ B @ (divide_divide_rat @ C @ A))) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2849_mult__imp__le__div__pos)). 185.47/93.67 thf(21129,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (times_times_rat @ B @ A) @ C) => (ord_less_eq_rat @ B @ (divide_divide_rat @ C @ A))) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4097])). 185.47/93.67 thf(1616,axiom,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_rat @ (plus_plus_rat @ (times_times_rat @ A @ B) @ C) @ (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (ord_less_rat @ C @ (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1235_less__add__iff2)). 185.47/93.67 thf(13100,plain,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((ord_less_rat @ (plus_plus_rat @ (times_times_rat @ A @ B) @ C) @ (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = (ord_less_rat @ C @ (plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616])). 185.47/93.67 thf(2331,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1211_linordered__semidom__class_Oadd__diff__inverse)). 185.47/93.67 thf(15460,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2331])). 185.47/93.67 thf(5601,axiom,((! [A:int]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_int @ (times_times_int @ A @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6670_power3__eq__cube)). 185.47/93.67 thf(26367,plain,((! [A:int]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_int @ (times_times_int @ A @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5601])). 185.47/93.67 thf(1724,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => ((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ C @ (times_times_complex @ B @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2735_add__num__frac)). 185.47/93.67 thf(13514,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => ((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ C @ (times_times_complex @ B @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724])). 185.47/93.67 thf(4653,axiom,((! [A:rat]: ((! [B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ B) <= (ord_less_rat @ zero_zero_rat @ B))) => (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6541_dense__eq0__I)). 185.47/93.67 thf(22905,plain,((! [A:rat]: ((! [B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ B) | ~ (ord_less_rat @ zero_zero_rat @ B))) => (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4653])). 185.47/93.67 thf(2562,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ zero_zero_int) => (ord_less_eq_int @ (times_times_int @ B @ C) @ (times_times_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2234_mult__right__mono__neg)). 185.47/93.67 thf(16226,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ zero_zero_int) => (ord_less_eq_int @ (times_times_int @ B @ C) @ (times_times_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2562])). 185.47/93.67 thf(2547,axiom,(((sin_real @ (times_times_real @ (divide_divide_real @ (numeral_numeral_real @ (bit1 @ one)) @ (numeral_numeral_real @ (bit0 @ one))) @ pi)) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7815_sin__3over2__pi)). 185.47/93.67 thf(16182,plain,(((sin_real @ (times_times_real @ (divide_divide_real @ (numeral_numeral_real @ (bit1 @ one)) @ (numeral_numeral_real @ (bit0 @ one))) @ pi)) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2547])). 185.47/93.67 thf(1200,axiom,((! [A:real]: (((sin_real @ A) = zero_zero_real) = (? [B:int]: ((A = (times_times_real @ (ring_1_of_int_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7939_sin__zero__iff__int)). 185.47/93.67 thf(11771,plain,((! [A:real]: (((sin_real @ A) = zero_zero_real) = (? [B:int]: ((A = (times_times_real @ (ring_1_of_int_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200])). 185.47/93.67 thf(1943,axiom,((! [A:int,B:int,C:int]: ((~ (! [D:int,E:int]: (((~ (dvd_dvd_int @ E @ C)) <= (dvd_dvd_int @ D @ B)) <= (A = (times_times_int @ D @ E))))) <= (dvd_dvd_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4628_dvd__productE)). 185.47/93.67 thf(14233,plain,((! [A:int,B:int,C:int]: (~ (! [D:int,E:int]: (~ (dvd_dvd_int @ E @ C) | ~ (dvd_dvd_int @ D @ B) | ~ (A = (times_times_int @ D @ E)))) | ~ (dvd_dvd_int @ A @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1943])). 185.47/93.67 thf(1588,axiom,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7271_int__Suc)). 185.47/93.67 thf(12990,plain,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588])). 185.47/93.67 thf(988,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_727_diff__diff__eq2)). 185.47/93.67 thf(11117,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[988])). 185.47/93.67 thf(2467,axiom,((! [A:int,B:int,C:int]: (((times_times_int @ (divide_divide_int @ B @ A) @ C) = (divide_divide_int @ (times_times_int @ B @ C) @ A)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4752_dvd__div__mult)). 185.47/93.67 thf(15902,plain,((! [A:int,B:int,C:int]: (((times_times_int @ (divide_divide_int @ B @ A) @ C) = (divide_divide_int @ (times_times_int @ B @ C) @ A)) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2467])). 185.47/93.67 thf(3817,axiom,((! [A:rat,B:rat]: ((A != zero_zero_rat) => ((divide_divide_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A)) = (divide_divide_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5763_nonzero__minus__divide__divide)). 185.47/93.67 thf(20260,plain,((! [A:rat,B:rat]: ((~ (A = zero_zero_rat)) => ((divide_divide_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A)) = (divide_divide_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3817])). 185.47/93.67 thf(2800,axiom,((! [A:nat,B:nat]: ((ord_max_nat @ A @ (suc @ B)) = (case_nat_nat @ (suc @ B) @ (^ [C:nat]: (suc @ (ord_max_nat @ C @ B))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9743_max__Suc2)). 185.47/93.67 thf(17031,plain,((! [A:nat,B:nat]: ((ord_max_nat @ A @ (suc @ B)) = (case_nat_nat @ (suc @ B) @ (^ [C:nat]: (suc @ (ord_max_nat @ C @ B))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2800])). 185.47/93.67 thf(5641,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4046_dual__order_Ostrict__implies__not__eq)). 185.47/93.67 thf(26505,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5641])). 185.47/93.67 thf(2630,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_730_diff__add__eq)). 185.47/93.67 thf(16454,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2630])). 185.47/93.67 thf(4242,axiom,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((((ord_less_eq_int @ zero_zero_int @ F) => (((ord_less_eq_int @ E @ B) <= (ord_less_eq_int @ D @ A)) <= (ord_less_int @ zero_zero_int @ D))) <= (ord_less_int @ C @ A)) <= (ord_less_int @ (plus_plus_int @ (times_times_int @ D @ E) @ F) @ zero_zero_int)) <= ((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ E) @ F))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3167_zdiv__mono2__neg__lemma)). 185.47/93.67 thf(21575,plain,((! [A:int,B:int,C:int,D:int,E:int,F:int]: (((ord_less_eq_int @ zero_zero_int @ F) => ((ord_less_eq_int @ E @ B) | ~ (ord_less_eq_int @ D @ A) | ~ (ord_less_int @ zero_zero_int @ D))) | ~ (ord_less_int @ C @ A) | ~ (ord_less_int @ (plus_plus_int @ (times_times_int @ D @ E) @ F) @ zero_zero_int) | ~ ((plus_plus_int @ (times_times_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ D @ E) @ F))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4242])). 185.47/93.67 thf(1345,axiom,((! [A:nat]: ((zero_zero_rat = (semiri681578069525770553at_rat @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6891_of__nat__0__eq__iff)). 185.47/93.67 thf(12214,plain,((! [A:nat]: ((zero_zero_rat = (semiri681578069525770553at_rat @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345])). 185.47/93.67 thf(6195,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ A @ B)) = ((B = zero_zero_nat) | ((ord_less_rat @ zero_zero_rat @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A != zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4980_zero__less__power__eq)). 185.47/93.67 thf(28592,plain,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ A @ B)) = ((B = zero_zero_nat) | ((ord_less_rat @ zero_zero_rat @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & ~ (A = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6195])). 185.47/93.67 thf(3467,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (times_times_rat @ B @ A) @ (times_times_rat @ C @ A)) = (ord_less_eq_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3344_mult__le__cancel__iff1)). 185.47/93.67 thf(19144,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (times_times_rat @ B @ A) @ (times_times_rat @ C @ A)) = (ord_less_eq_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3467])). 185.47/93.67 thf(6702,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_less__not__refl3)). 185.47/93.67 thf(30335,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6702])). 185.47/93.67 thf(5215,axiom,((! [A:rat]: ~ (ord_less_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2945_power2__less__0)). 185.47/93.67 thf(24919,plain,((! [A:rat]: ~ (ord_less_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5215])). 185.47/93.67 thf(5805,axiom,((! [A:real,B:nat,C:real]: (((((A = C) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_eq_real @ zero_zero_real @ A)) <= ((power_power_real @ A @ B) = (power_power_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2142_power__eq__imp__eq__base)). 185.47/93.67 thf(27113,plain,((! [A:real,B:nat,C:real]: ((A = C) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_eq_real @ zero_zero_real @ A) | ~ ((power_power_real @ A @ B) = (power_power_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5805])). 185.47/93.67 thf(3978,axiom,((! [A:real,B:real]: ((minus_minus_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ B) = (divide_divide_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_real__average__minus__second)). 185.47/93.67 thf(20774,plain,((! [A:real,B:real]: ((minus_minus_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))) @ B) = (divide_divide_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3978])). 185.47/93.67 thf(4899,axiom,((! [A:rat,B:rat]: ((A != zero_zero_rat) => ((divide_divide_rat @ (times_times_rat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1682_nonzero__mult__div__cancel__right)). 185.47/93.67 thf(23760,plain,((! [A:rat,B:rat]: ((~ (A = zero_zero_rat)) => ((divide_divide_rat @ (times_times_rat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4899])). 185.47/93.67 thf(7498,axiom,((! [A:real,B:nat]: (((ord_less_eq_real @ A @ (power_power_real @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_eq_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2894_self__le__power)). 185.47/93.67 thf(33279,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ A @ (power_power_real @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7498])). 185.47/93.67 thf(6388,axiom,((! [A:$o]: ((ord_less_nat @ zero_zero_nat @ (zero_n2687167440665602831ol_nat @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5232_zero__less__of__bool__iff)). 185.47/93.67 thf(29238,plain,((! [A:$o]: ((ord_less_nat @ zero_zero_nat @ (zero_n2687167440665602831ol_nat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6388])). 185.47/93.67 thf(1348,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) => ((ord_less_rat @ B @ C) <= (ord_less_eq_rat @ zero_zero_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2576_mult__left__less__imp__less)). 185.47/93.67 thf(12227,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) => ((ord_less_rat @ B @ C) | ~ (ord_less_eq_rat @ zero_zero_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348])). 185.47/93.67 thf(6749,axiom,((! [A:nat,B:real]: ((dvd_dvd_real @ B @ (power_power_real @ B @ A)) <= ((B = one_one_real) | (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4919_dvd__power)). 185.47/93.67 thf(30554,plain,((! [A:nat,B:real]: ((dvd_dvd_real @ B @ (power_power_real @ B @ A)) | ~ ((B = one_one_real) | (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6749])). 185.47/93.67 thf(7248,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = one_one_nat) => ((times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_841_left__right__inverse__power)). 185.47/93.67 thf(32425,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = one_one_nat) => ((times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7248])). 185.47/93.67 thf(3013,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (ord_less_real @ A @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4068_order__less__trans)). 185.47/93.67 thf(17712,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (ord_less_real @ A @ C)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3013])). 185.47/93.67 thf(125,axiom,((! [A:nat,B:real,C:nat]: (((ord_less_real @ one_one_real @ B) => ((semiri5074537144036343181t_real @ C) = (log @ B @ (semiri5074537144036343181t_real @ A)))) <= ((semiri5074537144036343181t_real @ A) = (power_power_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9042_log__of__power__eq)). 185.47/93.67 thf(8135,plain,((! [A:nat,B:real,C:nat]: (((ord_less_real @ one_one_real @ B) => ((semiri5074537144036343181t_real @ C) = (log @ B @ (semiri5074537144036343181t_real @ A)))) | ~ ((semiri5074537144036343181t_real @ A) = (power_power_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 185.47/93.67 thf(5402,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_Nat_Odiff__diff__right)). 185.47/93.67 thf(25601,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5402])). 185.47/93.67 thf(1714,axiom,((! [A:num,B:num,C:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (plus_plus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (plus_plus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ (plus_plus_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5325_semiring__norm_I168_J)). 185.47/93.67 thf(13467,plain,((! [A:num,B:num,C:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (plus_plus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (plus_plus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ (plus_plus_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714])). 185.47/93.67 thf(7022,axiom,((! [A:code_integer,B:nat]: ((abs_abs_Code_integer @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ B)) = (abs_abs_Code_integer @ (power_8256067586552552935nteger @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6386_abs__power__minus)). 185.47/93.67 thf(31627,plain,((! [A:code_integer,B:nat]: ((abs_abs_Code_integer @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ B)) = (abs_abs_Code_integer @ (power_8256067586552552935nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7022])). 185.47/93.67 thf(699,axiom,((! [A:nat,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_concat_bit @ A @ B @ C)) = (ord_less_eq_int @ zero_zero_int @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3825_concat__bit__nonnegative__iff)). 185.47/93.67 thf(10066,plain,((! [A:nat,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_concat_bit @ A @ B @ C)) = (ord_less_eq_int @ zero_zero_int @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[699])). 185.47/93.67 thf(2329,axiom,((! [A:set_nat,B:nat]: (((? [C:nat]: ((member_nat @ C @ A) & ! [D:nat]: (((C = D) <= (ord_less_eq_nat @ D @ C)) <= (member_nat @ D @ A)) & (ord_less_eq_nat @ C @ B))) <= (member_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3476_finite__has__minimal2)). 185.47/93.67 thf(15452,plain,((! [A:set_nat,B:nat]: (? [C:nat]: ((member_nat @ C @ A) & ! [D:nat]: ((C = D) | ~ (ord_less_eq_nat @ D @ C) | ~ (member_nat @ D @ A)) & (ord_less_eq_nat @ C @ B)) | ~ (member_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2329])). 185.47/93.67 thf(2715,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ (times_times_int @ (abs_abs_int @ A) @ (abs_abs_int @ C)) @ (times_times_int @ B @ D)) <= (ord_less_int @ (abs_abs_int @ C) @ D)) <= (ord_less_int @ (abs_abs_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6493_abs__mult__less)). 185.47/93.67 thf(16767,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (times_times_int @ (abs_abs_int @ A) @ (abs_abs_int @ C)) @ (times_times_int @ B @ D)) | ~ (ord_less_int @ (abs_abs_int @ C) @ D) | ~ (ord_less_int @ (abs_abs_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2715])). 185.47/93.67 thf(4187,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ one_one_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_993_div__by__1)). 185.47/93.67 thf(21410,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ one_one_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4187])). 185.47/93.67 thf(3735,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4111_order__less__subst2)). 185.47/93.67 thf(19996,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => ((ord_less_nat @ (C @ B) @ D) => ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3735])). 185.47/93.67 thf(3136,axiom,((ord_less_eq_real @ zero_zero_real @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2271_linordered__nonzero__semiring__class_Ozero__le__one)). 185.47/93.67 thf(18103,plain,((ord_less_eq_real @ zero_zero_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3136])). 185.47/93.67 thf(33,axiom,((! [A:real,B:nat,C:(nat > (complex > real))]: ((A = zero_zero_real) => (((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_complex) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_complex)) <= (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8074_Maclaurin__zero)). 185.47/93.67 thf(7837,plain,((! [A:real,B:nat,C:(nat > (complex > real))]: ((A = zero_zero_real) => (((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_complex) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_complex)) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 185.47/93.67 thf(6451,axiom,((! [A:int,B:int]: ((minus_minus_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (uminus_uminus_int @ (minus_minus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5576_minus__diff__minus)). 185.47/93.67 thf(29486,plain,((! [A:int,B:int]: ((minus_minus_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (uminus_uminus_int @ (minus_minus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6451])). 185.47/93.67 thf(5151,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (suc @ B)) = (minus_minus_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1108_diff__Suc__eq__diff__pred)). 185.47/93.67 thf(24720,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (suc @ B)) = (minus_minus_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5151])). 185.47/93.67 thf(371,axiom,((! [A:real,B:real]: (((cos_real @ A) != zero_zero_real) => (((cos_real @ B) != zero_zero_real) => ((minus_minus_real @ one_one_real @ (times_times_real @ (tan_real @ A) @ (tan_real @ B))) = (divide_divide_real @ (cos_real @ (plus_plus_real @ A @ B)) @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8081_lemma__tan__add1)). 185.47/93.67 thf(8970,plain,((! [A:real,B:real]: ((~ ((cos_real @ A) = zero_zero_real)) => ((~ ((cos_real @ B) = zero_zero_real)) => ((minus_minus_real @ one_one_real @ (times_times_real @ (tan_real @ A) @ (tan_real @ B))) = (divide_divide_real @ (cos_real @ (plus_plus_real @ A @ B)) @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[371])). 185.47/93.67 thf(6855,axiom,((! [A:num,B:num]: ((numeral_numeral_real @ A) != (uminus_uminus_real @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5530_numeral__neq__neg__numeral)). 185.47/93.67 thf(30970,plain,((! [A:num,B:num]: ~ ((numeral_numeral_real @ A) = (uminus_uminus_real @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6855])). 185.47/93.67 thf(7068,axiom,((! [A:num,B:num]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (numeral_numeral_rat @ B)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5345_mult__neg__numeral__simps_I2_J)). 185.47/93.67 thf(31799,plain,((! [A:num,B:num]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (numeral_numeral_rat @ B)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7068])). 185.47/93.67 thf(1745,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) = ((A = B) | ~ (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4162_nless__le)). 185.47/93.67 thf(13582,plain,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) = ((A = B) | ~ (ord_less_eq_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745])). 185.47/93.67 thf(1607,axiom,((! [A:int,B:num,C:nat]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (numeral_numeral_real @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7135_of__int__le__numeral__power__cancel__iff)). 185.47/93.67 thf(13064,plain,((! [A:int,B:num,C:nat]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (numeral_numeral_real @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607])). 185.47/93.67 thf(861,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se4203085406695923979it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3124_unset__bit__nonnegative__int__iff)). 185.47/93.67 thf(10677,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se4203085406695923979it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[861])). 185.47/93.67 thf(7433,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2774_vebt__member_Osimps_I4_J)). 185.47/93.67 thf(33047,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7433])). 185.47/93.67 thf(2066,axiom,((! [A:rat,B:rat,C:(rat > num),D:num]: ((ord_less_eq_rat @ A @ B) => (((ord_less_num @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_rat @ E @ F)))) <= (ord_less_num @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4333_order__le__less__subst2)). 185.47/93.67 thf(14627,plain,((! [A:rat,B:rat,C:(rat > num),D:num]: ((ord_less_eq_rat @ A @ B) => ((ord_less_num @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_rat @ E @ F))) | ~ (ord_less_num @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2066])). 185.47/93.67 thf(1467,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ A @ C) @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9373_AND__upper1_H)). 185.47/93.67 thf(12619,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ A @ C) @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467])). 185.47/93.67 thf(1175,axiom,((! [A:nat,B:nat,C:(nat > complex),D:(nat > complex)]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ A) => ((groups6464643781859351333omplex @ (^ [E:nat]: (if_complex @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_complex @ (E = B) @ one_one_complex @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups6464643781859351333omplex @ (^ [E:nat]: (if_complex @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8866_prod_Ozero__middle)). 185.47/93.67 thf(11697,plain,((! [A:nat,B:nat,C:(nat > complex),D:(nat > complex)]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ A) => ((groups6464643781859351333omplex @ (^ [E:nat]: (if_complex @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_complex @ (E = B) @ one_one_complex @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups6464643781859351333omplex @ (^ [E:nat]: (if_complex @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175])). 185.47/93.67 thf(158,axiom,((! [A:(nat > real),B:real]: (((times_times_real @ (suminf_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C)))) @ B) = (minus_minus_real @ (suminf_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) @ (A @ zero_zero_nat))) <= (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7745_powser__split__head_I2_J)). 185.47/93.67 thf(8237,plain,((! [A:(nat > real),B:real]: (((times_times_real @ (suminf_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C)))) @ B) = (minus_minus_real @ (suminf_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) @ (A @ zero_zero_nat))) | ~ (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 185.47/93.67 thf(4029,axiom,((! [A:rat]: ~ (ord_less_rat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4094_order__less__irrefl)). 185.47/93.67 thf(20928,plain,((! [A:rat]: ~ (ord_less_rat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4029])). 185.47/93.67 thf(3699,axiom,((! [A:int]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (ring_18347121197199848620nteger @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7332_even__of__int__iff)). 185.47/93.67 thf(19870,plain,((! [A:int]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (ring_18347121197199848620nteger @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3699])). 185.47/93.67 thf(3989,axiom,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) = (real_V1022390504157884413omplex @ (minus_minus_complex @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7458_norm__minus__commute)). 185.47/93.67 thf(20801,plain,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) = (real_V1022390504157884413omplex @ (minus_minus_complex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3989])). 185.47/93.67 thf(3252,axiom,((! [A:real]: ((sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sin_real @ A)) @ (cos_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7828_sin__double)). 185.47/93.67 thf(18457,plain,((! [A:real]: ((sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sin_real @ A)) @ (cos_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3252])). 185.47/93.67 thf(6534,axiom,((! [A:nat]: ((power_power_real @ zero_zero_real @ (suc @ A)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1743_power__0__Suc)). 185.47/93.67 thf(29790,plain,((! [A:nat]: ((power_power_real @ zero_zero_real @ (suc @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6534])). 185.47/93.67 thf(2585,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ B @ A)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4054_order__less__asym)). 185.47/93.67 thf(16317,plain,((! [A:rat,B:rat]: (~ (ord_less_rat @ B @ A) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2585])). 185.47/93.67 thf(6091,axiom,((! [A:nat,B:nat]: (((((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (A = B)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1895_power2__eq__iff__nonneg)). 185.47/93.67 thf(28175,plain,((! [A:nat,B:nat]: ((((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (A = B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6091])). 185.47/93.67 thf(5193,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ B) @ B) = (modulo_modulo_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1594_mod__add__self2)). 185.47/93.67 thf(24852,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ B) @ B) = (modulo_modulo_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5193])). 185.47/93.67 thf(2703,axiom,((! [A:real,B:real,C:nat]: (((ord_less_eq_real @ (real_V7735802525324610683m_real @ B) @ one_one_real) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))) @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B))))) <= (ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7520_norm__power__diff)). 185.47/93.67 thf(16732,plain,((! [A:real,B:real,C:nat]: (((ord_less_eq_real @ (real_V7735802525324610683m_real @ B) @ one_one_real) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))) @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B))))) | ~ (ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2703])). 185.47/93.67 thf(7360,axiom,((! [A:nat]: ((modulo_modulo_nat @ A @ (suc @ zero_zero_nat)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1803_mod__by__Suc__0)). 185.47/93.67 thf(32798,plain,((! [A:nat]: ((modulo_modulo_nat @ A @ (suc @ zero_zero_nat)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7360])). 185.47/93.67 thf(327,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((topolo6980174941875973593q_real @ (power_power_real @ A)) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7431_monoseq__realpow)). 185.47/93.67 thf(8831,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((topolo6980174941875973593q_real @ (power_power_real @ A)) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[327])). 185.47/93.67 thf(6967,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ C) => ((divide_divide_nat @ C @ (times_times_nat @ B @ A)) = (divide_divide_nat @ (divide_divide_nat @ C @ B) @ A))) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4862_div__mult__unit2)). 185.47/93.67 thf(31396,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ C) => ((divide_divide_nat @ C @ (times_times_nat @ B @ A)) = (divide_divide_nat @ (divide_divide_nat @ C @ B) @ A))) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6967])). 185.47/93.67 thf(6505,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: (((! [D:nat]: (C @ D @ (suc @ D))) => ((! [D:nat,E:nat,F:nat]: ((((C @ D @ E) => ((C @ D @ F) <= (C @ E @ F))) <= (ord_less_nat @ E @ F)) <= (ord_less_nat @ D @ E))) => (C @ A @ B))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1036_less__Suc__induct)). 185.47/93.67 thf(29683,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: (((! [D:nat]: (C @ D @ (suc @ D))) => ((! [D:nat,E:nat,F:nat]: (((C @ D @ E) => ((C @ D @ F) | ~ (C @ E @ F))) | ~ (ord_less_nat @ E @ F) | ~ (ord_less_nat @ D @ E))) => (C @ A @ B))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6505])). 185.47/93.67 thf(5659,axiom,((! [A:rat]: ((power_power_rat @ A @ zero_zero_nat) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2483_power__0)). 185.47/93.67 thf(26568,plain,((! [A:rat]: ((power_power_rat @ A @ zero_zero_nat) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5659])). 185.47/93.67 thf(6634,axiom,((! [A:rat]: ((minus_minus_rat @ zero_zero_rat @ A) = (uminus_uminus_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5180_diff__0)). 185.47/93.67 thf(30115,plain,((! [A:rat]: ((minus_minus_rat @ zero_zero_rat @ A) = (uminus_uminus_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6634])). 185.47/93.67 thf(2404,axiom,((! [A:set_nat]: ((A = bot_bot_set_nat) <= (! [B:nat]: ~ (member_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1380_equals0I)). 185.47/93.67 thf(15686,plain,((! [A:set_nat]: ((A = bot_bot_set_nat) | ~ (! [B:nat]: ~ (member_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2404])). 185.47/93.67 thf(6719,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1900_zero__less__power2)). 185.47/93.67 thf(30412,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6719])). 185.47/93.67 thf(7362,axiom,((semiri1316708129612266289at_nat = (^ [A:nat]: (semiri8422978514062236437ux_nat @ (^ [B:nat]: (plus_plus_nat @ B @ one_one_nat)) @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8406_of__nat__code)). 185.47/93.67 thf(32804,plain,(((semiri1316708129612266289at_nat) = (^ [A:nat]: (semiri8422978514062236437ux_nat @ (^ [B:nat]: (plus_plus_nat @ B @ one_one_nat)) @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7362])). 185.47/93.67 thf(4420,axiom,((dvd_dvd_rat = (^ [A:rat,B:rat]: ? [C:rat]: (B = (times_times_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4612_dvd__def)). 185.47/93.67 thf(22148,plain,(((dvd_dvd_rat) = (^ [A:rat,B:rat]: ? [C:rat]: (B = (times_times_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4420])). 185.47/93.67 thf(4040,axiom,((! [A:nat]: ((divide_divide_int @ one_one_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (zero_n2684676970156552555ol_int @ (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5478_bits__1__div__exp)). 185.47/93.67 thf(20956,plain,((! [A:nat]: ((divide_divide_int @ one_one_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (zero_n2684676970156552555ol_int @ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4040])). 185.47/93.67 thf(831,axiom,((! [A:set_nat,B:set_nat,C:(nat > real)]: (((finite_finite_nat @ B) => ((groups129246275422532515t_real @ C @ B) = (times_times_real @ (groups129246275422532515t_real @ C @ (minus_minus_set_nat @ B @ A)) @ (groups129246275422532515t_real @ C @ A)))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8892_prod_Osubset__diff)). 185.47/93.67 thf(10564,plain,((! [A:set_nat,B:set_nat,C:(nat > real)]: (((finite_finite_nat @ B) => ((groups129246275422532515t_real @ (C) @ B) = (times_times_real @ (groups129246275422532515t_real @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups129246275422532515t_real @ (C) @ A)))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[831])). 185.47/93.67 thf(228,axiom,((! [A:real]: (((ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((arcsin @ (sin_real @ A)) = A)) <= (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8329_arcsin__sin)). 185.47/93.67 thf(8461,plain,((! [A:real]: (((ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((arcsin @ (sin_real @ A)) = A)) | ~ (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 185.47/93.67 thf(3932,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) <= (ord_less_int @ B @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2327_mult__pos__neg)). 185.47/93.67 thf(20628,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) | ~ (ord_less_int @ B @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3932])). 185.47/93.67 thf(4363,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ A) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5155_neg__less__pos)). 185.47/93.67 thf(21978,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ A) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4363])). 185.47/93.67 thf(2055,axiom,((! [A:nat]: ((ord_max_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3596_max__nat_Oright__neutral)). 185.47/93.67 thf(14595,plain,((! [A:nat]: ((ord_max_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2055])). 185.47/93.67 thf(3507,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ (times_times_rat @ B @ A) @ zero_zero_rat) <= (ord_less_rat @ B @ zero_zero_rat)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2333_mult__pos__neg2)). 185.47/93.67 thf(19276,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (times_times_rat @ B @ A) @ zero_zero_rat) | ~ (ord_less_rat @ B @ zero_zero_rat) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3507])). 185.47/93.67 thf(1188,axiom,((! [A:rat,B:(rat > rat),C:rat,D:rat]: ((ord_less_rat @ A @ (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((ord_less_rat @ A @ (B @ D)) <= (! [E:rat,F:rat]: ((ord_less_eq_rat @ (B @ E) @ (B @ F)) <= (ord_less_eq_rat @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4342_order__less__le__subst1)). 185.47/93.67 thf(11733,plain,((! [A:rat,B:(rat > rat),C:rat,D:rat]: ((ord_less_rat @ A @ (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((ord_less_rat @ A @ (B @ D)) | ~ (! [E:rat,F:rat]: ((ord_less_eq_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_rat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188])). 185.47/93.67 thf(6279,axiom,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ (modulo_modulo_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4803_dvd__minus__mod)). 185.47/93.67 thf(28864,plain,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ (modulo_modulo_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6279])). 185.47/93.67 thf(437,axiom,((! [A:set_nat,B:set_nat,C:(nat > complex)]: (((ord_less_eq_set_nat @ B @ A) => (((groups6464643781859351333omplex @ C @ A) = (groups6464643781859351333omplex @ C @ B)) <= (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_complex))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8936_prod_Omono__neutral__right)). 185.47/93.67 thf(9185,plain,((! [A:set_nat,B:set_nat,C:(nat > complex)]: (((ord_less_eq_set_nat @ B @ A) => (((groups6464643781859351333omplex @ (C) @ A) = (groups6464643781859351333omplex @ (C) @ B)) | ~ (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_complex))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[437])). 185.47/93.67 thf(2077,axiom,((! [A:int,B:int]: (((uminus_uminus_int @ A) = B) = ((plus_plus_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5744_neg__eq__iff__add__eq__0)). 185.47/93.67 thf(14664,plain,((! [A:int,B:int]: (((uminus_uminus_int @ A) = B) = ((plus_plus_int @ A @ B) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2077])). 185.47/93.67 thf(417,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((times_times_real @ (minus_minus_real @ one_one_real @ C) @ (groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ A @ B))) = (minus_minus_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6748_sum__gp__multiplied)). 185.47/93.67 thf(9118,plain,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((times_times_real @ (minus_minus_real @ one_one_real @ C) @ (groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ A @ B))) = (minus_minus_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[417])). 185.47/93.67 thf(2124,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ A @ C) <= (ord_less_eq_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3871_order_Otrans)). 185.47/93.67 thf(14803,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ A @ C) | ~ (ord_less_eq_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2124])). 185.47/93.67 thf(1220,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_3937_linorder__linear)). 185.47/93.67 thf(11829,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)],[1220])). 185.47/93.67 thf(3142,axiom,((! [A:real]: ((times_times_real @ (exp_real @ A) @ A) = (times_times_real @ A @ (exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8145_exp__times__arg__commute)). 185.47/93.67 thf(18118,plain,((! [A:real]: ((times_times_real @ (exp_real @ A) @ A) = (times_times_real @ A @ (exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3142])). 185.47/93.67 thf(6470,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ A @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1073_power__Suc)). 185.47/93.67 thf(29559,plain,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ A @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6470])). 185.47/93.67 thf(222,axiom,((! [A:(nat > real),B:real,C:real]: ((summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D)))) => ((ord_less_real @ (real_V7735802525324610683m_real @ C) @ (real_V7735802525324610683m_real @ B)) => (summable_real @ (^ [D:nat]: (real_V7735802525324610683m_real @ (times_times_real @ (A @ D) @ (power_power_real @ C @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7684_powser__insidea)). 185.47/93.67 thf(8445,plain,((! [A:(nat > real),B:real,C:real]: ((summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D)))) => ((ord_less_real @ (real_V7735802525324610683m_real @ C) @ (real_V7735802525324610683m_real @ B)) => (summable_real @ (^ [D:nat]: (real_V7735802525324610683m_real @ (times_times_real @ (A @ D) @ (power_power_real @ C @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 185.47/93.67 thf(1809,axiom,((! [A:num]: ((neg_numeral_dbl_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_rat @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3829_dbl__simps_I5_J)). 185.47/93.67 thf(13794,plain,((! [A:num]: ((neg_numeral_dbl_rat @ (numeral_numeral_rat @ A)) = (numeral_numeral_rat @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1809])). 185.47/93.67 thf(5853,axiom,((! [A:num,B:num]: ((numeral_numeral_int @ A) != (uminus_uminus_int @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5531_numeral__neq__neg__numeral)). 185.47/93.67 thf(27374,plain,((! [A:num,B:num]: ~ ((numeral_numeral_int @ A) = (uminus_uminus_int @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5853])). 185.47/93.67 thf(1852,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ A @ (bit_ri631733984087533419it_int @ B @ A)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4978_signed__take__bit__int__greater__eq__self__iff)). 185.47/93.67 thf(13945,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ A @ (bit_ri631733984087533419it_int @ B @ A)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1852])). 185.47/93.67 thf(5987,axiom,((! [A:num,B:num,C:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (times_times_rat @ (numeral_numeral_rat @ B) @ C)) = (times_times_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_mult__numeral__left__semiring__numeral)). 185.47/93.67 thf(27851,plain,((! [A:num,B:num,C:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (times_times_rat @ (numeral_numeral_rat @ B) @ C)) = (times_times_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5987])). 185.47/93.67 thf(3724,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ C @ A) => (ord_less_int @ C @ B)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4037_dual__order_Ostrict__trans)). 185.47/93.67 thf(19962,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ C @ A) => (ord_less_int @ C @ B)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3724])). 185.47/93.67 thf(5431,axiom,((! [A:real,B:nat]: ((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3008_odd__power__less__zero)). 185.47/93.67 thf(25690,plain,((! [A:real,B:nat]: ((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5431])). 185.47/93.67 thf(1747,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ B) => (ord_le3102999989581377725nteger @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6454_abs__le__D1)). 185.47/93.67 thf(13588,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ B) => (ord_le3102999989581377725nteger @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747])). 185.47/93.67 thf(1036,axiom,((! [A:int,B:nat]: ((ring_1_of_int_real @ (power_power_int @ A @ B)) = (power_power_real @ (ring_1_of_int_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6988_of__int__power)). 185.47/93.67 thf(11268,plain,((! [A:int,B:nat]: ((ring_1_of_int_real @ (power_power_int @ A @ B)) = (power_power_real @ (ring_1_of_int_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036])). 185.47/93.67 thf(3863,axiom,((! [A:rat]: ? [B:nat]: (ord_less_rat @ A @ (semiri681578069525770553at_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7435_reals__Archimedean2)). 185.47/93.67 thf(20407,plain,((! [A:rat]: ? [B:nat]: (ord_less_rat @ A @ (semiri681578069525770553at_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3863])). 185.47/93.67 thf(3600,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4142_order__less__imp__not__eq2)). 185.47/93.67 thf(19560,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3600])). 185.47/93.67 thf(3752,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7241_nat__int__comparison_I3_J)). 185.47/93.67 thf(20048,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3752])). 185.47/93.67 thf(5176,axiom,((! [A:nat,B:nat,C:nat]: ((((dvd_dvd_nat @ B @ C) => (A = C)) <= (dvd_dvd_nat @ B @ A)) <= ((divide_divide_nat @ A @ B) = (divide_divide_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4672_dvd__div__eq__cancel)). 185.47/93.67 thf(24800,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ C) => (A = C)) | ~ (dvd_dvd_nat @ B @ A) | ~ ((divide_divide_nat @ A @ B) = (divide_divide_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5176])). 185.47/93.67 thf(6392,axiom,((! [A:nat]: ~ (ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7991_fact__not__neg)). 185.47/93.67 thf(29252,plain,((! [A:nat]: ~ (ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6392])). 185.47/93.67 thf(3924,axiom,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ A) => (ord_less_real @ one_one_real @ (times_times_real @ A @ (power_power_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_858_power__gt1__lemma)). 185.47/93.67 thf(20603,plain,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ A) => (ord_less_real @ one_one_real @ (times_times_real @ A @ (power_power_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3924])). 185.47/93.67 thf(5460,axiom,((! [A:rat]: (((ord_less_eq_rat @ A @ one_one_rat) => (ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_rat)) <= (ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6266_square__le__1)). 185.47/93.67 thf(25822,plain,((! [A:rat]: (((ord_less_eq_rat @ A @ one_one_rat) => (ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_rat)) | ~ (ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5460])). 185.47/93.67 thf(7099,axiom,((! [A:nat,B:nat]: (((A = zero_zero_nat) | (B = one_one_nat)) <= (A = (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2518_mult__eq__self__implies__10)). 185.47/93.67 thf(31897,plain,((! [A:nat,B:nat]: ((A = zero_zero_nat) | (B = one_one_nat) | ~ (A = (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7099])). 185.47/93.67 thf(3289,axiom,((! [A:nat]: ((groups3542108847815614940at_nat @ (^ [B:nat]: (power_power_nat @ (binomial @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (set_ord_atMost_nat @ A)) = (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8952_choose__square__sum)). 185.47/93.67 thf(18570,plain,((! [A:nat]: ((groups3542108847815614940at_nat @ (^ [B:nat]: (power_power_nat @ (binomial @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (set_ord_atMost_nat @ A)) = (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3289])). 185.47/93.67 thf(2037,axiom,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((plus_plus_real @ D @ A) = (plus_plus_real @ B @ (plus_plus_real @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_group__cancel_Oadd2)). 185.47/93.67 thf(14540,plain,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((plus_plus_real @ D @ A) = (plus_plus_real @ B @ (plus_plus_real @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2037])). 185.47/93.67 thf(7207,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ A @ B) = (power_power_nat @ C @ B)) => ((ord_less_eq_nat @ zero_zero_nat @ A) => (((A = C) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2144_power__eq__imp__eq__base)). 185.47/93.67 thf(32280,plain,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ A @ B) = (power_power_nat @ C @ B)) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((A = C) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7207])). 185.47/93.67 thf(6289,axiom,((! [A:int,B:int]: ((A = (uminus_uminus_int @ B)) = (B = (uminus_uminus_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5497_equation__minus__iff)). 185.47/93.67 thf(28892,plain,((! [A:int,B:int]: ((A = (uminus_uminus_int @ B)) = (B = (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6289])). 185.47/93.67 thf(1128,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ A @ B)) <= (ord_less_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2626_add__nonneg__pos)). 185.47/93.67 thf(11554,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ A @ B)) | ~ (ord_less_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128])). 185.47/93.67 thf(1440,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) = (((ord_less_eq_rat @ zero_zero_rat @ A) & (ord_less_eq_rat @ zero_zero_rat @ B)) | ((ord_less_eq_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ A @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2413_zero__le__divide__iff)). 185.47/93.67 thf(12537,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) = (((ord_less_eq_rat @ zero_zero_rat @ A) & (ord_less_eq_rat @ zero_zero_rat @ B)) | ((ord_less_eq_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ A @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440])). 185.47/93.67 thf(1591,axiom,((! [A:rat,B:rat,C:rat]: (((! [D:rat]: (((ord_less_eq_rat @ D @ C) <= (ord_less_rat @ D @ B)) <= (ord_less_rat @ A @ D))) => (ord_less_eq_rat @ B @ C)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4226_dense__le__bounded)). 185.47/93.67 thf(13005,plain,((! [A:rat,B:rat,C:rat]: (((! [D:rat]: ((ord_less_eq_rat @ D @ C) | ~ (ord_less_rat @ D @ B) | ~ (ord_less_rat @ A @ D))) => (ord_less_eq_rat @ B @ C)) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591])). 185.47/93.67 thf(2313,axiom,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se725231765392027082nd_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ A @ C) & (bit_se1146084159140164899it_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9420_bit__and__int__iff)). 185.47/93.67 thf(15401,plain,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se725231765392027082nd_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ A @ C) & (bit_se1146084159140164899it_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2313])). 185.47/93.67 thf(599,axiom,((! [A:nat,B:nat,C:(nat > complex)]: ((((groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_complex) <= (ord_less_nat @ (suc @ A) @ B)) & ((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_complex @ (groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8704_prod_Ocl__ivl__Suc)). 185.47/93.67 thf(9723,plain,((! [A:nat,B:nat,C:(nat > complex)]: ((((groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_complex) | ~ (ord_less_nat @ (suc @ A) @ B)) & ((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_complex @ (groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[599])). 185.47/93.67 thf(2821,axiom,((! [A:int,B:int]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6945_of__int__less__iff)). 185.47/93.67 thf(17098,plain,((! [A:int,B:int]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2821])). 185.47/93.67 thf(1383,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (plus_plus_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1624_le__add__same__cancel1)). 185.47/93.67 thf(12337,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (plus_plus_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383])). 185.47/93.67 thf(1796,axiom,((! [A:int]: ((ord_less_int @ A @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5152_less__neg__neg)). 185.47/93.67 thf(13749,plain,((! [A:int]: ((ord_less_int @ A @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796])). 185.47/93.67 thf(592,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (((archim7802044766580827645g_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))) = (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int)) = ((ord_less_eq_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))) & (ord_less_nat @ (power_power_nat @ A @ C) @ B)))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9061_ceiling__log__nat__eq__powr__iff)). 185.47/93.67 thf(9702,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (((archim7802044766580827645g_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))) = (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int)) = ((ord_less_eq_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))) & (ord_less_nat @ (power_power_nat @ A @ C) @ B)))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[592])). 185.47/93.67 thf(7559,axiom,((! [A:real]: ((abs_abs_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6424_abs__power2)). 185.47/93.67 thf(33460,plain,((! [A:real]: ((abs_abs_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7559])). 185.47/93.67 thf(1671,axiom,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (semiri1406184849735516958ct_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7985_fact__ge__zero)). 185.47/93.67 thf(13334,plain,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (semiri1406184849735516958ct_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671])). 185.47/93.67 thf(1071,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ A @ B) = (ord_less_eq_rat @ C @ D)) <= ((minus_minus_rat @ A @ B) = (minus_minus_rat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_diff__eq__diff__less__eq)). 185.47/93.67 thf(11365,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ A @ B) = (ord_less_eq_rat @ C @ D)) | ~ ((minus_minus_rat @ A @ B) = (minus_minus_rat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071])). 185.47/93.67 thf(6021,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_eq_num @ C @ A) <= (ord_less_num @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3315_minf_I6_J)). 185.47/93.67 thf(27957,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_eq_num @ C @ A) | ~ (ord_less_num @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6021])). 185.47/93.67 thf(5100,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_le__refl)). 185.47/93.67 thf(24489,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5100])). 185.47/93.67 thf(425,axiom,(((vEBT_vebt_buildup @ zero_zero_nat) = (vEBT_Leaf @ ($false) @ ($false)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1935_vebt__buildup_Osimps_I1_J)). 185.47/93.67 thf(9146,plain,(((vEBT_vebt_buildup @ zero_zero_nat) = (vEBT_Leaf @ ($false) @ ($false)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])). 185.47/93.67 thf(1650,axiom,((! [A:nat,B:nat]: (((insert_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (set_or1269000886237332187st_nat @ A @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9427_atLeastAtMost__insertL)). 185.47/93.67 thf(13221,plain,((! [A:nat,B:nat]: (((insert_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (set_or1269000886237332187st_nat @ A @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650])). 185.47/93.67 thf(385,axiom,((! [A:(nat > real)]: ((summable_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (A @ B)))) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (suminf_real @ A)) @ (suminf_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7727_summable__norm)). 185.47/93.67 thf(9015,plain,((! [A:(nat > real)]: ((summable_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (A @ B)))) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (suminf_real @ (A))) @ (suminf_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])). 185.47/93.67 thf(7613,axiom,(((vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) = pr)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_True)). 185.47/93.67 thf(33609,plain,(((vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) = pr)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7613])). 185.47/93.67 thf(236,axiom,((! [A:nat,B:(nat > nat),C:set_nat]: ((power_power_nat @ A @ (groups3542108847815614940at_nat @ B @ C)) = (groups708209901874060359at_nat @ (^ [D:nat]: (power_power_nat @ A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8788_power__sum)). 185.47/93.67 thf(8485,plain,((! [A:nat,B:(nat > nat),C:set_nat]: ((power_power_nat @ A @ (groups3542108847815614940at_nat @ (B) @ C)) = (groups708209901874060359at_nat @ (^ [D:nat]: (power_power_nat @ A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 185.47/93.67 thf(5086,axiom,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_one__plus__numeral)). 185.47/93.67 thf(24447,plain,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5086])). 185.47/93.67 thf(886,axiom,((! [A:real]: ((((arctan @ (tan_real @ A)) = A) <= (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8072_arctan__tan)). 185.47/93.67 thf(10766,plain,((! [A:real]: (((arctan @ (tan_real @ A)) = A) | ~ (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[886])). 185.47/93.67 thf(360,axiom,((! [A:num,B:num]: ((numeral_numeral_int @ (bit_or_not_num_neg @ A @ B)) = (uminus_uminus_int @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9530_numeral__or__not__num__eq)). 185.47/93.67 thf(8937,plain,((! [A:num,B:num]: ((numeral_numeral_int @ (bit_or_not_num_neg @ A @ B)) = (uminus_uminus_int @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])). 185.47/93.67 thf(242,axiom,((! [A:int,B:num,C:nat]: (((ring_1_of_int_int @ A) = (power_power_int @ (numeral_numeral_int @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7101_of__int__eq__numeral__power__cancel__iff)). 185.47/93.67 thf(8502,plain,((! [A:int,B:num,C:nat]: (((ring_1_of_int_int @ A) = (power_power_int @ (numeral_numeral_int @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 185.47/93.67 thf(1321,axiom,((! [A:real]: ((plus_plus_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one))) @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_field__sum__of__halves)). 185.47/93.67 thf(12136,plain,((! [A:real]: ((plus_plus_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one))) @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321])). 185.47/93.67 thf(6892,axiom,((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4890_even__zero)). 185.47/93.67 thf(31109,plain,((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6892])). 185.47/93.67 thf(3597,axiom,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (times_times_complex @ A @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ one_one_complex) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8488_pochhammer__rec)). 185.47/93.67 thf(19552,plain,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (times_times_complex @ A @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ one_one_complex) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3597])). 185.47/93.67 thf(3914,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => (((divide_divide_int @ (plus_plus_int @ B @ C) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A))) <= (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4498_div__add)). 185.47/93.67 thf(20568,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => (((divide_divide_int @ (plus_plus_int @ B @ C) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A))) | ~ (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3914])). 185.47/93.67 thf(3068,axiom,((ord_less_rat = (^ [A:rat,B:rat]: ((B != A) & (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4235_dual__order_Ostrict__iff__order)). 185.47/93.67 thf(17886,plain,(((ord_less_rat) = (^ [A:rat,B:rat]: (~ (B = A) & (ord_less_eq_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3068])). 185.47/93.67 thf(6962,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_3887_dual__order_Oeq__iff)). 185.47/93.67 thf(31384,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)],[6962])). 185.47/93.67 thf(4853,axiom,((! [A:num]: (ord_less_rat @ zero_zero_rat @ (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2260_zero__less__numeral)). 185.47/93.67 thf(23584,plain,((! [A:num]: (ord_less_rat @ zero_zero_rat @ (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4853])). 185.47/93.67 thf(2497,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((modulo_modulo_int @ A @ B) = A) <= (ord_less_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1938_unique__euclidean__semiring__numeral__class_Omod__less)). 185.47/93.67 thf(16010,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((modulo_modulo_int @ A @ B) = A) | ~ (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2497])). 185.47/93.67 thf(2234,axiom,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (root @ A @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9193_real__root__pos__pos)). 185.47/93.67 thf(15155,plain,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (root @ A @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2234])). 185.47/93.67 thf(5214,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: (((vEBT_V8194947554948674370ptions @ (vEBT_vebt_insert @ A @ C) @ C) <= (ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_valid__insert__both__member__options__add)). 185.47/93.67 thf(24916,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_V8194947554948674370ptions @ (vEBT_vebt_insert @ A @ C) @ C) | ~ (ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5214])). 185.47/93.67 thf(7251,axiom,((! [A:num,B:num]: ((ord_less_num @ (bit1 @ A) @ (bit1 @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6357_semiring__norm_I80_J)). 185.47/93.67 thf(32435,plain,((! [A:num,B:num]: ((ord_less_num @ (bit1 @ A) @ (bit1 @ B)) = (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7251])). 185.47/93.67 thf(1647,axiom,((ord_less_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2387_zero__less__one)). 185.47/93.67 thf(13210,plain,((ord_less_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647])). 185.47/93.67 thf(4837,axiom,((! [A:int,B:nat]: ((dvd_dvd_int @ (power_power_int @ A @ B) @ one_one_int) = ((B = zero_zero_nat) | (dvd_dvd_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4878_is__unit__power__iff)). 185.47/93.67 thf(23536,plain,((! [A:int,B:nat]: ((dvd_dvd_int @ (power_power_int @ A @ B) @ one_one_int) = ((B = zero_zero_nat) | (dvd_dvd_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4837])). 185.47/93.67 thf(3671,axiom,((! [A:int,B:int,C:int,D:int]: (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ D))) @ (plus_plus_int @ (abs_abs_int @ (minus_minus_int @ A @ C)) @ (abs_abs_int @ (minus_minus_int @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6587_abs__diff__triangle__ineq)). 185.47/93.67 thf(19784,plain,((! [A:int,B:int,C:int,D:int]: (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ D))) @ (plus_plus_int @ (abs_abs_int @ (minus_minus_int @ A @ C)) @ (abs_abs_int @ (minus_minus_int @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3671])). 185.47/93.67 thf(7345,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (modulo_modulo_nat @ B @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1958_mod__le__divisor)). 185.47/93.67 thf(32753,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (modulo_modulo_nat @ B @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7345])). 185.47/93.67 thf(3686,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => ((divide_divide_int @ (plus_plus_int @ A @ B) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2761_div__add__self1)). 185.47/93.67 thf(19824,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (plus_plus_int @ A @ B) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3686])). 185.47/93.67 thf(6612,axiom,((! [A:(nat > real)]: (sums_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B))) @ (A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8204_powser__sums__zero)). 185.47/93.67 thf(30040,plain,((! [A:(nat > real)]: (sums_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B))) @ (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6612])). 185.47/93.67 thf(4398,axiom,((semiri1408675320244567234ct_nat = (comm_s4663373288045622133er_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8448_pochhammer__fact)). 185.47/93.67 thf(22088,plain,(((semiri1408675320244567234ct_nat) = (comm_s4663373288045622133er_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4398])). 185.47/93.67 thf(6428,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_infinite__descent)). 185.47/93.67 thf(29405,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6428])). 185.47/93.67 thf(1888,axiom,((! [A:nat,B:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_vebt_buildup @ A) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1262_buildup__nothing__in__min__max)). 185.47/93.67 thf(14048,plain,((! [A:nat,B:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_vebt_buildup @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1888])). 185.47/93.67 thf(2564,axiom,((! [A:real,B:real,C:real,D:nat]: ((A != zero_zero_real) => ((ord_less_eq_real @ (real_V7735802525324610683m_real @ B) @ C) => ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ B @ A)) @ C) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (divide_divide_real @ (minus_minus_real @ (power_power_real @ (plus_plus_real @ B @ A) @ D) @ (power_power_real @ B @ D)) @ A) @ (times_times_real @ (semiri5074537144036343181t_real @ D) @ (power_power_real @ B @ (minus_minus_nat @ D @ (suc @ zero_zero_nat)))))) @ (times_times_real @ (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ D) @ (semiri5074537144036343181t_real @ (minus_minus_nat @ D @ (suc @ zero_zero_nat)))) @ (power_power_real @ C @ (minus_minus_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (real_V7735802525324610683m_real @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7371_lemma__termdiff3)). 185.47/93.67 thf(16231,plain,((! [A:real,B:real,C:real,D:nat]: ((~ (A = zero_zero_real)) => ((ord_less_eq_real @ (real_V7735802525324610683m_real @ B) @ C) => ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ B @ A)) @ C) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (divide_divide_real @ (minus_minus_real @ (power_power_real @ (plus_plus_real @ B @ A) @ D) @ (power_power_real @ B @ D)) @ A) @ (times_times_real @ (semiri5074537144036343181t_real @ D) @ (power_power_real @ B @ (minus_minus_nat @ D @ (suc @ zero_zero_nat)))))) @ (times_times_real @ (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ D) @ (semiri5074537144036343181t_real @ (minus_minus_nat @ D @ (suc @ zero_zero_nat)))) @ (power_power_real @ C @ (minus_minus_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (real_V7735802525324610683m_real @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2564])). 185.47/93.67 thf(4035,axiom,((! [A:int,B:int]: (((modulo_modulo_int @ A @ B) = A) = ((divide_divide_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1917_mod__eq__self__iff__div__eq__0)). 185.47/93.67 thf(20943,plain,((! [A:int,B:int]: (((modulo_modulo_int @ A @ B) = A) = ((divide_divide_int @ A @ B) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4035])). 185.47/93.67 thf(7165,axiom,((! [A:(real > $o),B:real,C:(real > $o)]: (((! [D:real,E:real]: (((C @ D) & (A @ D)) = ((C @ (minus_minus_real @ D @ (times_times_real @ E @ B))) & (A @ (minus_minus_real @ D @ (times_times_real @ E @ B)))))) <= (! [D:real,E:real]: ((C @ D) = (C @ (minus_minus_real @ D @ (times_times_real @ E @ B)))))) <= (! [D:real,E:real]: ((A @ D) = (A @ (minus_minus_real @ D @ (times_times_real @ E @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3323_inf__period_I1_J)). 185.47/93.67 thf(32140,plain,((! [A:(real > $o),B:real,C:(real > $o)]: (! [D:real,E:real]: (((C @ D) & (A @ D)) = ((C @ (minus_minus_real @ D @ (times_times_real @ E @ B))) & (A @ (minus_minus_real @ D @ (times_times_real @ E @ B))))) | ~ (! [D:real,E:real]: ((C @ D) = (C @ (minus_minus_real @ D @ (times_times_real @ E @ B))))) | ~ (! [D:real,E:real]: ((A @ D) = (A @ (minus_minus_real @ D @ (times_times_real @ E @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7165])). 185.47/93.67 thf(1121,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ A @ C) <= (ord_less_eq_int @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3859_ord__eq__le__trans)). 185.47/93.67 thf(11531,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ C) | ~ (ord_less_eq_int @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121])). 185.47/93.67 thf(3582,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ B) => (ord_less_eq_rat @ (abs_abs_rat @ A) @ B)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6510_abs__leI)). 185.47/93.67 thf(19503,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ B) => (ord_less_eq_rat @ (abs_abs_rat @ A) @ B)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3582])). 185.47/93.67 thf(3763,axiom,((! [A:rat,B:nat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ A @ one_one_rat) => (ord_less_eq_rat @ (power_power_rat @ A @ B) @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2720_power__le__one)). 185.47/93.67 thf(20083,plain,((! [A:rat,B:nat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ A @ one_one_rat) => (ord_less_eq_rat @ (power_power_rat @ A @ B) @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3763])). 185.47/93.67 thf(2624,axiom,((! [A:nat,B:nat]: ((nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))) = (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9296_nat__int__add)). 185.47/93.67 thf(16439,plain,((! [A:nat,B:nat]: ((nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))) = (plus_plus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2624])). 185.47/93.67 thf(715,axiom,((! [A:real]: ((summable_real @ (power_power_real @ A)) = (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7653_summable__geometric__iff)). 185.47/93.67 thf(10115,plain,((! [A:real]: ((summable_real @ (power_power_real @ A)) = (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[715])). 185.47/93.67 thf(2394,axiom,((! [A:real,B:real,C:num]: (((complex2 @ A @ B) = (numera6690914467698888265omplex @ C)) = ((A = (numeral_numeral_real @ C)) & (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8004_Complex__eq__numeral)). 185.47/93.67 thf(15654,plain,((! [A:real,B:real,C:num]: (((complex2 @ A @ B) = (numera6690914467698888265omplex @ C)) = ((A = (numeral_numeral_real @ C)) & (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2394])). 185.47/93.67 thf(3152,axiom,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2675_sum__squares__ge__zero)). 185.47/93.67 thf(18150,plain,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3152])). 185.47/93.67 thf(525,axiom,((ord_less_eq_real @ zero_zero_real @ pi)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7706_pi__ge__zero)). 185.47/93.67 thf(9491,plain,((ord_less_eq_real @ zero_zero_real @ pi)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[525])). 185.47/93.67 thf(1886,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7227_less__imp__of__nat__less)). 185.47/93.67 thf(14042,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1886])). 185.47/93.67 thf(6510,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1902_zero__less__power2)). 185.47/93.67 thf(29702,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (~ (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6510])). 185.47/93.67 thf(1740,axiom,((ord_less_real = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4199_order_Ostrict__iff__order)). 185.47/93.67 thf(13567,plain,(((ord_less_real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1740])). 185.47/93.67 thf(3813,axiom,((! [A:real,B:real]: ~ (ord_less_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2987_not__sum__power2__lt__zero)). 185.47/93.67 thf(20250,plain,((! [A:real,B:real]: ~ (ord_less_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3813])). 185.47/93.67 thf(4409,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4268_dual__order_Ostrict__implies__order)). 185.47/93.67 thf(22120,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4409])). 185.47/93.67 thf(4231,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8240_sqrt__sum__squares__le__sum)). 185.47/93.67 thf(21540,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_real @ A @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4231])). 185.47/93.67 thf(1520,axiom,((! [A:(nat > int),B:nat,C:nat]: ((groups3539618377306564664at_int @ A @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups3539618377306564664at_int @ (^ [D:nat]: (plus_plus_int @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6750_sum_Oin__pairs)). 185.47/93.67 thf(12780,plain,((! [A:(nat > int),B:nat,C:nat]: ((groups3539618377306564664at_int @ (A) @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups3539618377306564664at_int @ (^ [D:nat]: (plus_plus_int @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520])). 185.47/93.67 thf(3194,axiom,((! [A:real,B:real,C:real,D:real]: ((plus_plus_complex @ (complex2 @ A @ B) @ (complex2 @ C @ D)) = (complex2 @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8009_complex__add)). 185.47/93.67 thf(18282,plain,((! [A:real,B:real,C:real,D:real]: ((plus_plus_complex @ (complex2 @ A @ B) @ (complex2 @ C @ D)) = (complex2 @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3194])). 185.47/93.67 thf(2142,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_add_Oright__cancel)). 185.47/93.67 thf(14865,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2142])). 185.47/93.67 thf(1612,axiom,((! [A:rat,B:rat]: ((minus_minus_rat @ A @ (uminus_uminus_rat @ B)) = (plus_plus_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5205_diff__minus__eq__add)). 185.47/93.67 thf(13086,plain,((! [A:rat,B:rat]: ((minus_minus_rat @ A @ (uminus_uminus_rat @ B)) = (plus_plus_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612])). 185.47/93.67 thf(1269,axiom,((ord_less_rat = (^ [A:rat,B:rat]: ((A != B) & (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4277_order__less__le)). 185.47/93.67 thf(11979,plain,(((ord_less_rat) = (^ [A:rat,B:rat]: (~ (A = B) & (ord_less_eq_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269])). 185.47/93.67 thf(5520,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_add__right__cancel)). 185.47/93.67 thf(26114,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5520])). 185.47/93.67 thf(4246,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_real @ C @ (times_times_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2701_neg__less__divide__eq)). 185.47/93.67 thf(21590,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_real @ C @ (times_times_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4246])). 185.47/93.67 thf(7671,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4528_even__Suc__div__two)). 185.47/93.67 thf(33762,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7671])). 185.47/93.67 thf(7575,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((A != B) => ((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ C @ A @ D) @ B) = (nth_VEBT_VEBT @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3604_nth__list__update__neq)). 185.47/93.67 thf(33502,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((~ (A = B)) => ((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ C @ A @ D) @ B) = (nth_VEBT_VEBT @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7575])). 185.47/93.67 thf(2613,axiom,((! [A:num,B:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5696_not__numeral__le__neg__numeral)). 185.47/93.67 thf(16404,plain,((! [A:num,B:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2613])). 185.47/93.67 thf(1595,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (times_times_int @ A @ B)) = (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_int @ B @ one_one_int)) & ((ord_less_int @ one_one_int @ B) <= (ord_less_eq_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2820_mult__less__cancel__left1)). 185.47/93.67 thf(13018,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (times_times_int @ A @ B)) = (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_int @ B @ one_one_int)) & ((ord_less_int @ one_one_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595])). 185.47/93.67 thf(4663,axiom,((! [A:num,B:int]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_eq_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7068_of__int__numeral__le__iff)). 185.47/93.67 thf(22935,plain,((! [A:num,B:int]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_eq_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4663])). 185.47/93.67 thf(7085,axiom,((! [A:real,B:nat]: ((power_power_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5993_power__minus)). 185.47/93.67 thf(31855,plain,((! [A:real,B:nat]: ((power_power_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7085])). 185.47/93.67 thf(4693,axiom,((! [A:num]: ((neg_numeral_dbl_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (uminus_uminus_rat @ (neg_numeral_dbl_rat @ (numeral_numeral_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5269_dbl__simps_I1_J)). 185.47/93.67 thf(23040,plain,((! [A:num]: ((neg_numeral_dbl_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (uminus_uminus_rat @ (neg_numeral_dbl_rat @ (numeral_numeral_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4693])). 185.47/93.67 thf(5235,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => (((times_times_real @ A @ B) = (times_times_real @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2059_mult__left__cancel)). 185.47/93.67 thf(24993,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => (((times_times_real @ A @ B) = (times_times_real @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5235])). 185.47/93.67 thf(7400,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1030_not__less__eq)). 185.47/93.67 thf(32920,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7400])). 185.47/93.67 thf(3017,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((~ (ord_less_int @ A @ C)) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3284_minf_I7_J)). 185.47/93.67 thf(17725,plain,((! [A:int]: ? [B:int]: ! [C:int]: (~ (ord_less_int @ A @ C) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3017])). 185.47/93.67 thf(3807,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ (divide_divide_int @ C @ A)) = (dvd_dvd_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4776_dvd__div__unit__iff)). 185.47/93.67 thf(20233,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ (divide_divide_int @ C @ A)) = (dvd_dvd_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3807])). 185.47/93.67 thf(4781,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ (abs_abs_real @ C) @ D) => (ord_less_real @ (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ C)) @ (times_times_real @ B @ D))) <= (ord_less_real @ (abs_abs_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6491_abs__mult__less)). 185.47/93.67 thf(23362,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ (abs_abs_real @ C) @ D) => (ord_less_real @ (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ C)) @ (times_times_real @ B @ D))) | ~ (ord_less_real @ (abs_abs_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4781])). 185.47/93.67 thf(5343,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1504_mult__cancel__right)). 185.47/93.67 thf(25385,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5343])). 185.47/93.67 thf(4296,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ A @ B) = (divide_divide_int @ C @ B)) => (((A = C) <= (dvd_dvd_int @ B @ C)) <= (dvd_dvd_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4673_dvd__div__eq__cancel)). 185.47/93.67 thf(21731,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ A @ B) = (divide_divide_int @ C @ B)) => ((A = C) | ~ (dvd_dvd_int @ B @ C) | ~ (dvd_dvd_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4296])). 185.47/93.67 thf(7412,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1627_add__le__same__cancel2)). 185.47/93.67 thf(32983,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7412])). 185.47/93.67 thf(6659,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_add__right__imp__eq)). 185.47/93.67 thf(30196,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6659])). 185.47/93.67 thf(5265,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A)))) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9366_and__minus__numerals_I2_J)). 185.47/93.67 thf(25105,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A)))) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5265])). 185.47/93.67 thf(4790,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_diff__eq__diff__less__eq)). 185.47/93.67 thf(23389,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4790])). 185.47/93.67 thf(7043,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_791_diff__add)). 185.47/93.67 thf(31718,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7043])). 185.47/93.67 thf(4012,axiom,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((root @ A @ B) = (powr_real @ B @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ A))))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9207_root__powr__inverse)). 185.47/93.67 thf(20875,plain,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((root @ A @ B) = (powr_real @ B @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ A))))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4012])). 185.47/93.67 thf(2521,axiom,((! [A:nat,B:list_VEBT_VEBT,C:(vEBT_VEBT > $o)]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ B)) => (C @ D))) => (C @ (nth_VEBT_VEBT @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_936_list__ball__nth)). 185.47/93.67 thf(16090,plain,((! [A:nat,B:list_VEBT_VEBT,C:(vEBT_VEBT > $o)]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ B)) => (C @ D))) => (C @ (nth_VEBT_VEBT @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2521])). 185.47/93.67 thf(467,axiom,((real_V1022390504157884413omplex = (^ [A:complex]: (sqrt @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9695_norm__complex__def)). 185.47/93.67 thf(9302,plain,(((real_V1022390504157884413omplex) = (^ [A:complex]: (sqrt @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])). 185.47/93.67 thf(5893,axiom,((! [A:nat]: ((((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4962_mod2__eq__if)). 185.47/93.67 thf(27512,plain,((! [A:nat]: ((((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5893])). 185.47/93.67 thf(3958,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((((ord_less_eq_int @ zero_zero_int @ E) => (((plus_plus_int @ D @ E) = one_one_int) => (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ D @ A) @ (times_times_int @ E @ C)) @ B))) <= (ord_less_eq_int @ zero_zero_int @ D)) <= (ord_less_eq_int @ C @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2858_convex__bound__le)). 185.47/93.67 thf(20709,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_eq_int @ zero_zero_int @ E) => (((plus_plus_int @ D @ E) = one_one_int) => (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ D @ A) @ (times_times_int @ E @ C)) @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ D) | ~ (ord_less_eq_int @ C @ B) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3958])). 185.47/93.67 thf(2103,axiom,((! [A:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ one_one_rat @ A) @ zero_zero_rat) = (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1805_divide__le__0__1__iff)). 185.47/93.67 thf(14736,plain,((! [A:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ one_one_rat @ A) @ zero_zero_rat) = (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2103])). 185.47/93.67 thf(796,axiom,((! [A:$o]: ((A = ($false)) | (A = ($true))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T)). 185.47/93.67 thf(10450,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[796])). 185.47/93.67 thf(2575,axiom,((! [A:rat,B:rat,C:$o]: ((ord_less_rat @ A @ B) => ((C) <= (ord_less_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4124_order__less__imp__triv)). 185.47/93.67 thf(16263,plain,((! [A:rat,B:rat,C:$o]: ((ord_less_rat @ A @ B) => ((C) | ~ (ord_less_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2575])). 185.47/93.67 thf(849,axiom,((! [A:(nat > real),B:(nat > real),C:set_nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (plus_plus_real @ (A @ D) @ (B @ D))) @ C) = (plus_plus_real @ (groups6591440286371151544t_real @ A @ C) @ (groups6591440286371151544t_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5622_sum_Odistrib)). 185.47/93.67 thf(10645,plain,((! [A:(nat > real),B:(nat > real),C:set_nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (plus_plus_real @ (A @ D) @ (B @ D))) @ C) = (plus_plus_real @ (groups6591440286371151544t_real @ (A) @ C) @ (groups6591440286371151544t_real @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[849])). 185.47/93.67 thf(7419,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_left__diff__distrib)). 185.47/93.67 thf(33006,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7419])). 185.47/93.67 thf(1974,axiom,((! [A:rat,B:rat]: ((divide_divide_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (divide_divide_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5587_minus__divide__divide)). 185.47/93.67 thf(14337,plain,((! [A:rat,B:rat]: ((divide_divide_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (divide_divide_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1974])). 185.47/93.67 thf(442,axiom,((! [A:nat,B:int]: ((bit_concat_bit @ A @ B @ zero_zero_int) = (bit_se2923211474154528505it_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9246_concat__bit__of__zero__2)). 185.47/93.67 thf(9206,plain,((! [A:nat,B:int]: ((bit_concat_bit @ A @ B @ zero_zero_int) = (bit_se2923211474154528505it_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[442])). 185.47/93.67 thf(7372,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ B)) = (times_times_real @ A @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_power__Suc)). 185.47/93.67 thf(32836,plain,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ B)) = (times_times_real @ A @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7372])). 185.47/93.67 thf(6399,axiom,((! [A:rat,B:num]: ((ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ zero_zero_rat) = ((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ B)) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_eq_rat @ A @ zero_zero_rat)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (A = zero_zero_rat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4567_power__le__zero__eq__numeral)). 185.47/93.67 thf(29277,plain,((! [A:rat,B:num]: ((ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ zero_zero_rat) = ((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ B)) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_eq_rat @ A @ zero_zero_rat)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (A = zero_zero_rat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6399])). 185.47/93.67 thf(2987,axiom,((! [A:real,B:real,C:(real > rat),D:rat]: ((((! [E:real,F:real]: ((ord_less_rat @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))) => (ord_less_rat @ (C @ A) @ D)) <= (ord_less_eq_rat @ (C @ B) @ D)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4356_order__less__le__subst2)). 185.47/93.67 thf(17637,plain,((! [A:real,B:real,C:(real > rat),D:rat]: (((! [E:real,F:real]: ((ord_less_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))) => (ord_less_rat @ (C @ A) @ D)) | ~ (ord_less_eq_rat @ (C @ B) @ D) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2987])). 185.47/93.67 thf(2991,axiom,((! [A:num]: ((numeral_numeral_int @ (bit0 @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1361_numeral__code_I2_J)). 185.47/93.67 thf(17650,plain,((! [A:num]: ((numeral_numeral_int @ (bit0 @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2991])). 185.47/93.67 thf(1232,axiom,((! [A:int,B:int,C:nat]: ((groups3539618377306564664at_int @ (^ [D:nat]: (plus_plus_int @ A @ (times_times_int @ (semiri1314217659103216013at_int @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C)) = (divide_divide_int @ (times_times_int @ (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int) @ (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7352_arith__series)). 185.47/93.67 thf(11868,plain,((! [A:int,B:int,C:nat]: ((groups3539618377306564664at_int @ (^ [D:nat]: (plus_plus_int @ A @ (times_times_int @ (semiri1314217659103216013at_int @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C)) = (divide_divide_int @ (times_times_int @ (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int) @ (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232])). 185.47/93.67 thf(5171,axiom,((! [A:(int > $o),B:int,C:(int > $o)]: ((! [D:int,E:int]: ((A @ D) = (A @ (minus_minus_int @ D @ (times_times_int @ E @ B))))) => ((! [D:int,E:int]: ((C @ D) = (C @ (minus_minus_int @ D @ (times_times_int @ E @ B))))) => (! [D:int,E:int]: (((A @ D) & (C @ D)) = ((A @ (minus_minus_int @ D @ (times_times_int @ E @ B))) & (C @ (minus_minus_int @ D @ (times_times_int @ E @ B)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3325_inf__period_I1_J)). 185.47/93.67 thf(24785,plain,((! [A:(int > $o),B:int,C:(int > $o)]: ((! [D:int,E:int]: ((A @ D) = (A @ (minus_minus_int @ D @ (times_times_int @ E @ B))))) => ((! [D:int,E:int]: ((C @ D) = (C @ (minus_minus_int @ D @ (times_times_int @ E @ B))))) => (! [D:int,E:int]: (((A @ D) & (C @ D)) = ((A @ (minus_minus_int @ D @ (times_times_int @ E @ B))) & (C @ (minus_minus_int @ D @ (times_times_int @ E @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5171])). 185.47/93.67 thf(4768,axiom,((! [A:rat,B:rat]: ((abs_abs_rat @ (minus_minus_rat @ A @ B)) = (abs_abs_rat @ (minus_minus_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6467_abs__minus__commute)). 185.47/93.67 thf(23324,plain,((! [A:rat,B:rat]: ((abs_abs_rat @ (minus_minus_rat @ A @ B)) = (abs_abs_rat @ (minus_minus_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4768])). 185.47/93.67 thf(3090,axiom,((! [A:int]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (nat2 @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9355_even__nat__iff)). 185.47/93.67 thf(17957,plain,((! [A:int]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (nat2 @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3090])). 185.47/93.67 thf(4383,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => (((times_times_complex @ B @ A) = C) => (B = (divide1717551699836669952omplex @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2464_eq__divide__imp)). 185.47/93.67 thf(22041,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => (((times_times_complex @ B @ A) = C) => (B = (divide1717551699836669952omplex @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4383])). 185.47/93.67 thf(3565,axiom,((! [A:rat,B:(real > rat),C:real,D:real]: ((((ord_less_rat @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_rat @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F)))) <= (ord_less_real @ C @ D)) <= (ord_less_rat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4103_order__less__subst1)). 185.47/93.67 thf(19449,plain,((! [A:rat,B:(real > rat),C:real,D:real]: ((ord_less_rat @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))) | ~ (ord_less_real @ C @ D) | ~ (ord_less_rat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3565])). 185.47/93.67 thf(7658,axiom,(((numeral_numeral_nat @ (bit0 @ one)) = (suc @ (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2902_numeral__2__eq__2)). 185.47/93.67 thf(33730,plain,(((numeral_numeral_nat @ (bit0 @ one)) = (suc @ (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7658])). 185.47/93.67 thf(5679,axiom,((! [A:nat,B:code_integer,C:code_integer]: (((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ B) @ (abs_abs_Code_integer @ C)) => (ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ B @ A) @ (power_8256067586552552935nteger @ C @ A))) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6722_power__mono__even)). 185.47/93.67 thf(26631,plain,((! [A:nat,B:code_integer,C:code_integer]: (((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ B) @ (abs_abs_Code_integer @ C)) => (ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ B @ A) @ (power_8256067586552552935nteger @ C @ A))) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5679])). 185.47/93.67 thf(3500,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))) <= (ord_less_real @ zero_zero_real @ A))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2611_mult__le__less__imp__less)). 185.47/93.67 thf(19256,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))) | ~ (ord_less_real @ zero_zero_real @ A))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3500])). 185.47/93.67 thf(6358,axiom,((! [A:nat]: ~ (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7213_of__nat__less__0__iff)). 185.47/93.67 thf(29142,plain,((! [A:nat]: ~ (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6358])). 185.47/93.67 thf(6620,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_add__less__imp__less__left)). 185.47/93.67 thf(30072,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6620])). 185.47/93.67 thf(3768,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ (times_times_real @ B @ A) @ C)) = (dvd_dvd_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4472_dvd__add__times__triv__left__iff)). 185.47/93.67 thf(20112,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ (times_times_real @ B @ A) @ C)) = (dvd_dvd_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3768])). 185.47/93.67 thf(7640,axiom,((~ (ord_less_nat @ pr @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__092_060open_062pr_A_060_Ahigh_Az_A_Ideg_Adiv_A2_J_A_092_060Longrightarrow_062_AFalse_092_060close_062)). 185.47/93.67 thf(33685,plain,((~ (ord_less_nat @ pr @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7640])). 185.47/93.67 thf(3954,axiom,((! [A:rat,B:rat,C:(rat > int),D:int]: ((ord_less_eq_rat @ A @ B) => (((ord_less_int @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_rat @ E @ F)))) <= (ord_less_int @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4335_order__le__less__subst2)). 185.47/93.67 thf(20696,plain,((! [A:rat,B:rat,C:(rat > int),D:int]: ((ord_less_eq_rat @ A @ B) => ((ord_less_int @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_rat @ E @ F))) | ~ (ord_less_int @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3954])). 185.47/93.67 thf(4269,axiom,(((abs_abs_rat @ one_one_rat) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6343_abs__1)). 185.47/93.67 thf(21657,plain,(((abs_abs_rat @ one_one_rat) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4269])). 185.47/93.67 thf(5490,axiom,((! [A:$o]: (((zero_n2687167440665602831ol_nat @ A) = one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5127_of__bool__eq__1__iff)). 185.47/93.67 thf(26014,plain,((! [A:$o]: (((zero_n2687167440665602831ol_nat @ A) = one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5490])). 185.47/93.67 thf(1603,axiom,((! [A:complex,B:complex,C:complex,D:complex,E:complex]: ((A != zero_zero_complex) => (((plus_plus_complex @ B @ (times_times_complex @ A @ D)) != (plus_plus_complex @ C @ (times_times_complex @ A @ E))) <= ((D != E) & (B = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5010_add__scale__eq__noteq)). 185.47/93.67 thf(13050,plain,((! [A:complex,B:complex,C:complex,D:complex,E:complex]: ((~ (A = zero_zero_complex)) => (~ ((plus_plus_complex @ B @ (times_times_complex @ A @ D)) = (plus_plus_complex @ C @ (times_times_complex @ A @ E))) | ~ (~ (D = E) & (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603])). 185.47/93.67 thf(3061,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ A @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ one_one_real @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_856_less__half__sum)). 185.47/93.67 thf(17869,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ A @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ one_one_real @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3061])). 185.47/93.67 thf(3215,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ (minus_minus_int @ B @ A)) = B) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_le__add__diff__inverse)). 185.47/93.67 thf(18354,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ (minus_minus_int @ B @ A)) = B) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3215])). 185.47/93.67 thf(6026,axiom,((! [A:num,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7125_numeral__power__less__of__nat__cancel__iff)). 185.47/93.67 thf(27971,plain,((! [A:num,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6026])). 185.47/93.67 thf(3554,axiom,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6909_of__nat__le__iff)). 185.47/93.67 thf(19421,plain,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3554])). 185.47/93.67 thf(7243,axiom,((! [A:int]: ((one_one_int = A) = (A = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_one__reorient)). 185.47/93.67 thf(32410,plain,((! [A:int]: ((one_one_int = A) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7243])). 185.47/93.67 thf(3894,axiom,((! [A:int]: ((ord_less_real @ one_one_real @ (ring_1_of_int_real @ A)) = (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7086_of__int__1__less__iff)). 185.47/93.67 thf(20497,plain,((! [A:int]: ((ord_less_real @ one_one_real @ (ring_1_of_int_real @ A)) = (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3894])). 185.47/93.67 thf(2255,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) = (((ord_less_rat @ A @ zero_zero_rat) & (ord_less_rat @ B @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ zero_zero_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2337_zero__less__mult__iff)). 185.47/93.67 thf(15227,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) = (((ord_less_rat @ A @ zero_zero_rat) & (ord_less_rat @ B @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ zero_zero_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2255])). 185.47/93.67 thf(1700,axiom,((! [A:num,B:real,C:real]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (divide_divide_real @ B @ C)) = (((((ord_less_eq_real @ B @ (times_times_real @ (numeral_numeral_real @ A) @ C)) <= (ord_less_real @ C @ zero_zero_real)) & ((ord_less_eq_real @ (numeral_numeral_real @ A) @ zero_zero_real) <= (~ (ord_less_real @ C @ zero_zero_real)))) <= (~ (ord_less_real @ zero_zero_real @ C))) & ((ord_less_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ A) @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2925_le__divide__eq__numeral_I1_J)). 185.47/93.67 thf(13427,plain,((! [A:num,B:real,C:real]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (divide_divide_real @ B @ C)) = (((((ord_less_eq_real @ B @ (times_times_real @ (numeral_numeral_real @ A) @ C)) | ~ (ord_less_real @ C @ zero_zero_real)) & ((ord_less_eq_real @ (numeral_numeral_real @ A) @ zero_zero_real) | (ord_less_real @ C @ zero_zero_real))) | (ord_less_real @ zero_zero_real @ C)) & ((ord_less_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ A) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700])). 185.47/93.67 thf(6129,axiom,(((abs_abs_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6464_abs__one)). 185.47/93.67 thf(28312,plain,(((abs_abs_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6129])). 185.47/93.67 thf(2655,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (powr_real @ A @ B) @ zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9071_powr__nonneg__iff)). 185.47/93.67 thf(16535,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (powr_real @ A @ B) @ zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2655])). 185.47/93.67 thf(7075,axiom,((! [A:nat,B:nat,C:nat]: ((groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ A @ (times_times_nat @ D @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C)) = (divide_divide_nat @ (times_times_nat @ (suc @ C) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (times_times_nat @ C @ B))) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6757_arith__series__nat)). 185.47/93.67 thf(31820,plain,((! [A:nat,B:nat,C:nat]: ((groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ A @ (times_times_nat @ D @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C)) = (divide_divide_nat @ (times_times_nat @ (suc @ C) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (times_times_nat @ C @ B))) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7075])). 185.47/93.67 thf(6116,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ C)) | (B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1028_Ex__less__Suc)). 185.47/93.67 thf(28268,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ C)) | (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6116])). 185.47/93.67 thf(7536,axiom,((! [A:num]: ((divide_divide_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_numeral__Bit0__div__2)). 185.47/93.67 thf(33396,plain,((! [A:num]: ((divide_divide_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7536])). 185.47/93.67 thf(3384,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ A @ C) <= (ord_less_eq_real @ B @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4211_order_Ostrict__trans2)). 185.47/93.67 thf(18876,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ C) | ~ (ord_less_eq_real @ B @ C) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3384])). 185.47/93.67 thf(6592,axiom,((! [A:real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6352_abs__minus__cancel)). 185.47/93.67 thf(29982,plain,((! [A:real]: ((abs_abs_real @ (uminus_uminus_real @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6592])). 185.47/93.67 thf(781,axiom,((! [A:(nat > nat),B:nat,C:nat,D:nat]: ((groups708209901874060359at_nat @ A @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ C) @ (plus_plus_nat @ D @ C))) = (groups708209901874060359at_nat @ (^ [E:nat]: (A @ (plus_plus_nat @ E @ C))) @ (set_or1269000886237332187st_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8791_prod_Oshift__bounds__cl__nat__ivl)). 185.47/93.67 thf(10397,plain,((! [A:(nat > nat),B:nat,C:nat,D:nat]: ((groups708209901874060359at_nat @ (A) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ C) @ (plus_plus_nat @ D @ C))) = (groups708209901874060359at_nat @ (^ [E:nat]: (A @ (plus_plus_nat @ E @ C))) @ (set_or1269000886237332187st_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[781])). 185.47/93.67 thf(7183,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_nat @ zero_zero_nat @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2617_mult__less__le__imp__less)). 185.47/93.67 thf(32195,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_nat @ zero_zero_nat @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7183])). 185.47/93.67 thf(5857,axiom,((! [A:(num > $o),B:num]: (((A @ B) <= (! [C:num]: ((A @ (inc @ C)) <= (A @ C)))) <= (A @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9370_num__induct)). 185.47/93.67 thf(27385,plain,((! [A:(num > $o),B:num]: ((A @ B) | ~ (! [C:num]: ((A @ (inc @ C)) | ~ (A @ C))) | ~ (A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5857])). 185.47/93.67 thf(4404,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D) = (vEBT_Node @ A @ zero_zero_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2521_vebt__insert_Osimps_I2_J)). 185.47/93.67 thf(22106,plain,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D) = (vEBT_Node @ A @ zero_zero_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4404])). 185.47/93.67 thf(7585,axiom,((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__092_060open_0622_A_092_060le_062_Adeg_092_060close_062)). 185.47/93.67 thf(33528,plain,((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7585])). 185.47/93.67 thf(5062,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9452_xor__nat__numerals_I1_J)). 185.47/93.67 thf(24380,plain,((! [A:num]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5062])). 185.47/93.67 thf(5350,axiom,((! [A:(num > (num > $o)),B:num,C:num]: (((! [D:num]: (A @ D @ D)) => ((! [D:num,E:num]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))) <= (! [D:num,E:num]: ((A @ D @ E) <= (ord_less_num @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4020_linorder__less__wlog)). 185.47/93.67 thf(25432,plain,((! [A:(num > (num > $o)),B:num,C:num]: (((! [D:num]: (A @ D @ D)) => ((! [D:num,E:num]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))) | ~ (! [D:num,E:num]: ((A @ D @ E) | ~ (ord_less_num @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5350])). 185.47/93.67 thf(1367,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((((~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G)))) <= (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ B)) @ C @ D) @ E)))) <= (! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ zero_zero_nat) @ C @ D) @ E)))) <= (! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2153_vebt__insert_Ocases)). 185.47/93.67 thf(12284,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))) | ~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ B)) @ C @ D) @ E))) | ~ (! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ zero_zero_nat) @ C @ D) @ E))) | ~ (! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367])). 185.47/93.67 thf(2267,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3235_pinf_I3_J)). 185.47/93.67 thf(15259,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2267])). 185.47/93.67 thf(753,axiom,((! [A:complex]: ((im @ (csqrt @ A)) = (times_times_real @ (if_real @ ((im @ A) = zero_zero_real) @ one_one_real @ (sgn_sgn_real @ (im @ A))) @ (sqrt @ (divide_divide_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9660_csqrt_Osimps_I2_J)). 185.47/93.67 thf(10253,plain,((! [A:complex]: ((im @ (csqrt @ A)) = (times_times_real @ (if_real @ ((im @ A) = zero_zero_real) @ one_one_real @ (sgn_sgn_real @ (im @ A))) @ (sqrt @ (divide_divide_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[753])). 185.47/93.67 thf(6525,axiom,((! [A:nat,B:real]: (((ord_less_eq_real @ zero_zero_real @ (power_power_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4971_zero__le__odd__power)). 185.47/93.67 thf(29761,plain,((! [A:nat,B:real]: (((ord_less_eq_real @ zero_zero_real @ (power_power_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6525])). 185.47/93.67 thf(1421,axiom,((! [A:rat,B:rat]: (((times_times_rat @ (abs_abs_rat @ B) @ A) = (abs_abs_rat @ (times_times_rat @ B @ A))) <= (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6544_abs__mult__pos)). 185.47/93.67 thf(12477,plain,((! [A:rat,B:rat]: (((times_times_rat @ (abs_abs_rat @ B) @ A) = (abs_abs_rat @ (times_times_rat @ B @ A))) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421])). 185.47/93.67 thf(2500,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ zero_zero_complex @ A) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1565_div__0)). 185.47/93.67 thf(16020,plain,((! [A:complex]: ((divide1717551699836669952omplex @ zero_zero_complex @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2500])). 185.47/93.67 thf(1411,axiom,((! [A:(nat > int),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_int @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_int @ (A @ C) @ (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1083_lift__Suc__antimono__le)). 185.47/93.67 thf(12433,plain,((! [A:(nat > int),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_int @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_int @ (A @ C) @ (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411])). 185.47/93.67 thf(4087,axiom,((! [A:rat]: ? [B:rat]: (ord_less_rat @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3968_lt__ex)). 185.47/93.67 thf(21099,plain,((! [A:rat]: ? [B:rat]: (ord_less_rat @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4087])). 185.47/93.67 thf(5961,axiom,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1790_div__by__Suc__0)). 185.47/93.67 thf(27735,plain,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5961])). 185.47/93.67 thf(6585,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_mult__le__mono2)). 185.47/93.67 thf(29956,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6585])). 185.47/93.67 thf(3032,axiom,((! [A:num,B:num]: ((A != B) <= ((size_size_num @ A) != (size_size_num @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_size__neq__size__imp__neq)). 185.47/93.67 thf(17769,plain,((! [A:num,B:num]: (~ (A = B) | ((size_size_num @ A) = (size_size_num @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3032])). 185.47/93.67 thf(7682,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_power2__nat__le__eq__le)). 185.47/93.67 thf(33792,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7682])). 185.47/93.67 thf(2088,axiom,((finite_finite_nat @ bot_bot_set_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3483_finite_OemptyI)). 185.47/93.67 thf(14699,plain,((finite_finite_nat @ bot_bot_set_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2088])). 185.47/93.67 thf(733,axiom,((! [A:real,B:real,C:real]: ((times_times_complex @ (complex2 @ A @ B) @ (real_V4546457046886955230omplex @ C)) = (complex2 @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9141_Complex__mult__complex__of__real)). 185.47/93.67 thf(10179,plain,((! [A:real,B:real,C:real]: ((times_times_complex @ (complex2 @ A @ B) @ (real_V4546457046886955230omplex @ C)) = (complex2 @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[733])). 185.47/93.67 thf(4280,axiom,((! [A:real,B:real]: ((sqrt @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (sqrt @ A) @ (sqrt @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8147_real__sqrt__divide)). 185.47/93.67 thf(21686,plain,((! [A:real,B:real]: ((sqrt @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (sqrt @ A) @ (sqrt @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4280])). 185.47/93.67 thf(1294,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)) <= (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_diff__mono)). 185.47/93.67 thf(12049,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)) | ~ (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294])). 185.47/93.67 thf(7686,axiom,((! [A:nat]: ((divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1018_div2__Suc__Suc)). 185.47/93.67 thf(33801,plain,((! [A:nat]: ((divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7686])). 185.47/93.67 thf(2359,axiom,((! [A:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1614_double__add__le__zero__iff__single__add__le__zero)). 185.47/93.67 thf(15543,plain,((! [A:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2359])). 185.47/93.67 thf(114,axiom,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ A) => ((ord_less_eq_real @ (suminf_real @ A) @ (suminf_real @ B)) <= (summable_real @ B))) <= (! [C:nat]: (ord_less_eq_real @ (A @ C) @ (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7668_suminf__le)). 185.47/93.67 thf(8103,plain,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ (A)) => ((ord_less_eq_real @ (suminf_real @ (A)) @ (suminf_real @ (B))) | ~ (summable_real @ (B)))) | ~ (! [C:nat]: (ord_less_eq_real @ (A @ C) @ (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 185.47/93.67 thf(284,axiom,((! [A:real]: (((log @ (numeral_numeral_real @ (bit0 @ (bit1 @ (bit0 @ one)))) @ A) = (times_times_real @ (divide_divide_real @ (ln_ln_real @ (exp_real @ one_one_real)) @ (ln_ln_real @ (numeral_numeral_real @ (bit0 @ (bit1 @ (bit0 @ one)))))) @ (ln_ln_real @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9019_log__base__10__eq1)). 185.47/93.67 thf(8661,plain,((! [A:real]: (((log @ (numeral_numeral_real @ (bit0 @ (bit1 @ (bit0 @ one)))) @ A) = (times_times_real @ (divide_divide_real @ (ln_ln_real @ (exp_real @ one_one_real)) @ (ln_ln_real @ (numeral_numeral_real @ (bit0 @ (bit1 @ (bit0 @ one)))))) @ (ln_ln_real @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 185.47/93.67 thf(6675,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_diff__right__commute)). 185.47/93.67 thf(30251,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6675])). 185.47/93.67 thf(4794,axiom,((! [A:real]: ((ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1639_double__add__less__zero__iff__single__add__less__zero)). 185.47/93.67 thf(23403,plain,((! [A:real]: ((ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4794])). 185.47/93.67 thf(1792,axiom,((! [A:int,B:int,C:int]: ((A = (times_times_int @ B @ C)) => (dvd_dvd_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4619_dvdI)). 185.47/93.67 thf(13734,plain,((! [A:int,B:int,C:int]: ((A = (times_times_int @ B @ C)) => (dvd_dvd_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792])). 185.47/93.67 thf(5625,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ B)) = (times_times_real @ (power_power_real @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1065_power__Suc2)). 185.47/93.67 thf(26454,plain,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ B)) = (times_times_real @ (power_power_real @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5625])). 185.47/93.67 thf(4452,axiom,((! [A:nat,B:nat,C:nat]: ((member_nat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = ((ord_less_eq_nat @ A @ C) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3218_atLeastAtMost__iff)). 185.47/93.67 thf(22253,plain,((! [A:nat,B:nat,C:nat]: ((member_nat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = ((ord_less_eq_nat @ A @ C) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4452])). 185.47/93.67 thf(4005,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (plus_plus_int @ B @ C)) <= (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4655_dvd__add)). 185.47/93.67 thf(20852,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (plus_plus_int @ B @ C)) | ~ (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4005])). 185.47/93.67 thf(4197,axiom,((! [A:rat]: (ord_less_eq_rat @ (uminus_uminus_rat @ (abs_abs_rat @ A)) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6560_abs__minus__le__zero)). 185.47/93.67 thf(21437,plain,((! [A:rat]: (ord_less_eq_rat @ (uminus_uminus_rat @ (abs_abs_rat @ A)) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4197])). 185.47/93.67 thf(2152,axiom,((! [A:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5929_neg__one__le__numeral)). 185.47/93.67 thf(14907,plain,((! [A:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ one_one_rat) @ (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2152])). 185.47/93.67 thf(590,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) => ((ord_less_eq_real @ (arcsin @ A) @ (arcsin @ B)) = (ord_less_eq_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8313_arcsin__le__mono)). 185.47/93.67 thf(9691,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) => ((ord_less_eq_real @ (arcsin @ A) @ (arcsin @ B)) = (ord_less_eq_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[590])). 185.47/93.67 thf(1292,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ A) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2343_zero__less__mult__pos2)). 185.47/93.67 thf(12044,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292])). 185.47/93.67 thf(7354,axiom,((! [A:int]: ((times_times_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5198_mult__minus1)). 185.47/93.67 thf(32781,plain,((! [A:int]: ((times_times_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7354])). 185.47/93.67 thf(5769,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((A @ (minus_minus_nat @ B @ C)) <= (! [D:nat]: ((A @ (suc @ D)) => (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1052_zero__induct__lemma)). 185.47/93.67 thf(26918,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) | ~ (! [D:nat]: ((A @ (suc @ D)) => (A @ D))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5769])). 185.47/93.67 thf(1080,axiom,(((semiri681578069525770553at_rat @ zero_zero_nat) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6886_of__nat__0)). 185.47/93.67 thf(11392,plain,(((semiri681578069525770553at_rat @ zero_zero_nat) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080])). 185.47/93.67 thf(4252,axiom,((! [A:rat,B:rat,C:rat]: ((A = B) => ((ord_less_rat @ B @ C) => (ord_less_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3987_ord__eq__less__trans)). 185.47/93.67 thf(21607,plain,((! [A:rat,B:rat,C:rat]: ((A = B) => ((ord_less_rat @ B @ C) => (ord_less_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4252])). 185.47/93.67 thf(4065,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((nat2 @ (bit_se2923211474154528505it_int @ B @ A)) = (bit_se2925701944663578781it_nat @ B @ (nat2 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9270_nat__take__bit__eq)). 185.47/93.67 thf(21027,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((nat2 @ (bit_se2923211474154528505it_int @ B @ A)) = (bit_se2925701944663578781it_nat @ B @ (nat2 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4065])). 185.47/93.67 thf(4889,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) <= (ord_less_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2656_divide__nonneg__pos)). 185.47/93.67 thf(23728,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) | ~ (ord_less_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4889])). 185.47/93.67 thf(6756,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ (divide_divide_nat @ B @ A) @ C) = (divide_divide_nat @ (power_power_nat @ B @ C) @ (power_power_nat @ A @ C))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4784_div__power)). 185.47/93.67 thf(30586,plain,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ (divide_divide_nat @ B @ A) @ C) = (divide_divide_nat @ (power_power_nat @ B @ C) @ (power_power_nat @ A @ C))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6756])). 185.47/93.67 thf(1009,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ C) = (((ord_less_eq_rat @ A @ (times_times_rat @ C @ B)) <= (ord_less_rat @ zero_zero_rat @ B)) & ((((ord_less_eq_rat @ (times_times_rat @ C @ B) @ A) <= (ord_less_rat @ B @ zero_zero_rat)) & ((ord_less_eq_rat @ zero_zero_rat @ C) <= (~ (ord_less_rat @ B @ zero_zero_rat)))) <= (~ (ord_less_rat @ zero_zero_rat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2833_divide__le__eq)). 185.47/93.67 thf(11188,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ C) = (((ord_less_eq_rat @ A @ (times_times_rat @ C @ B)) | ~ (ord_less_rat @ zero_zero_rat @ B)) & ((((ord_less_eq_rat @ (times_times_rat @ C @ B) @ A) | ~ (ord_less_rat @ B @ zero_zero_rat)) & ((ord_less_eq_rat @ zero_zero_rat @ C) | (ord_less_rat @ B @ zero_zero_rat))) | (ord_less_rat @ zero_zero_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009])). 185.47/93.67 thf(6342,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_V5719532721284313246member @ A @ B) => ((accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ A @ B)) => ((~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ (suc @ D) @ E @ F)) => ((~ ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ (suc @ D) @ E @ F) @ B)))))) <= (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (~ (((C) <= (B = zero_zero_nat)) & ((B != zero_zero_nat) => ((B = one_one_nat) & ((D) <= (B = one_one_nat)))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3119_VEBT__internal_Onaive__member_Opelims_I2_J)). 185.47/93.67 thf(29069,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_V5719532721284313246member @ A @ B) => ((accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ A @ B)) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ (suc @ D) @ E @ F)) => (~ ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ (suc @ D) @ E @ F) @ B))))) | ~ (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (~ (((C) | ~ (B = zero_zero_nat)) & ((~ (B = zero_zero_nat)) => ((B = one_one_nat) & ((D) | ~ (B = one_one_nat)))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6342])). 185.47/93.67 thf(2091,axiom,((! [A:nat]: ((zero_zero_real = (semiri5074537144036343181t_real @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6889_of__nat__0__eq__iff)). 185.47/93.67 thf(14706,plain,((! [A:nat]: ((zero_zero_real = (semiri5074537144036343181t_real @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2091])). 185.47/93.67 thf(5775,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_power__add)). 185.47/93.67 thf(26944,plain,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5775])). 185.47/93.67 thf(7229,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1152_right__diff__distrib)). 185.47/93.67 thf(32368,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7229])). 185.47/93.67 thf(5689,axiom,((! [A:num]: ((inc @ (bit1 @ A)) = (bit0 @ (inc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9379_inc_Osimps_I3_J)). 185.47/93.67 thf(26663,plain,((! [A:num]: ((inc @ (bit1 @ A)) = (bit0 @ (inc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5689])). 185.47/93.67 thf(5237,axiom,((one_one_rat != (uminus_uminus_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5553_one__neq__neg__one)). 185.47/93.67 thf(25000,plain,((~ (one_one_rat = (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5237])). 185.47/93.67 thf(6372,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (suc @ A) @ B) = (times_times_nat @ (suc @ A) @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1053_Suc__mult__cancel1)). 185.47/93.67 thf(29189,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (suc @ A) @ B) = (times_times_nat @ (suc @ A) @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6372])). 185.47/93.67 thf(6984,axiom,(((modulo_modulo_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5422_bits__minus__1__mod__2__eq)). 185.47/93.67 thf(31498,plain,(((modulo_modulo_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6984])). 185.47/93.67 thf(3691,axiom,((! [A:num]: ~ (ord_less_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5960_not__neg__one__less__neg__numeral)). 185.47/93.67 thf(19848,plain,((! [A:num]: ~ (ord_less_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3691])). 185.47/93.67 thf(6165,axiom,((! [A:rat,B:rat]: (((uminus_uminus_rat @ A) = (uminus_uminus_rat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5023_neg__equal__iff__equal)). 185.47/93.67 thf(28479,plain,((! [A:rat,B:rat]: (((uminus_uminus_rat @ A) = (uminus_uminus_rat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6165])). 185.47/93.67 thf(2279,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (divide_divide_rat @ A @ B) @ C) = (divide_divide_rat @ (times_times_rat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_times__divide__eq__left)). 185.47/93.67 thf(15297,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (divide_divide_rat @ A @ B) @ C) = (divide_divide_rat @ (times_times_rat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2279])). 185.47/93.67 thf(5498,axiom,((! [A:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ one_one_real) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_numeral__le__one__iff)). 185.47/93.67 thf(26042,plain,((! [A:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ one_one_real) = (ord_less_eq_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5498])). 185.47/93.67 thf(3525,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_add_Oleft__cancel)). 185.47/93.67 thf(19330,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3525])). 185.47/93.67 thf(4855,axiom,((! [A:real]: (((cos_real @ A) = zero_zero_real) = (? [B:nat]: ((A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ? [B:nat]: ((A = (uminus_uminus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7944_cos__zero__iff)). 185.47/93.67 thf(23589,plain,((! [A:real]: (((cos_real @ A) = zero_zero_real) = (? [B:nat]: ((A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ? [B:nat]: ((A = (uminus_uminus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4855])). 185.47/93.67 thf(3496,axiom,((ord_less_real = (^ [A:real,B:real]: (ord_less_real @ (minus_minus_real @ A @ B) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2424_less__iff__diff__less__0)). 185.47/93.67 thf(19239,plain,(((ord_less_real) = (^ [A:real,B:real]: (ord_less_real @ (minus_minus_real @ A @ B) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3496])). 185.47/93.67 thf(5745,axiom,((! [A:num]: (ord_less_eq_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2192_zero__le__numeral)). 185.47/93.67 thf(26848,plain,((! [A:num]: (ord_less_eq_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5745])). 185.47/93.67 thf(2620,axiom,((ord_less_eq_int = (^ [A:int,B:int]: (ord_less_real @ (ring_1_of_int_real @ A) @ (plus_plus_real @ (ring_1_of_int_real @ B) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7303_int__le__real__less)). 185.47/93.67 thf(16425,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: (ord_less_real @ (ring_1_of_int_real @ A) @ (plus_plus_real @ (ring_1_of_int_real @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2620])). 185.47/93.67 thf(1512,axiom,((! [A:int,B:nat]: ((bit_se1148574629649215175it_nat @ (nat2 @ A) @ B) = ((bit_se1146084159140164899it_int @ A @ B) & (ord_less_eq_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9473_bit__nat__iff)). 185.47/93.67 thf(12755,plain,((! [A:int,B:nat]: ((bit_se1148574629649215175it_nat @ (nat2 @ A) @ B) = ((bit_se1146084159140164899it_int @ A @ B) & (ord_less_eq_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512])). 185.47/93.67 thf(935,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri7919022796975470100ot_int @ A)) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9522_even__not__iff__int)). 185.47/93.67 thf(10942,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_ri7919022796975470100ot_int @ A)) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[935])). 185.47/93.67 thf(2422,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_3854_order__class_Oorder__eq__iff)). 185.47/93.67 thf(15745,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)],[2422])). 185.47/93.67 thf(4220,axiom,((modulo_modulo_int = (^ [A:int,B:int]: (if_int @ (B = zero_zero_int) @ A @ (if_int @ ((sgn_sgn_int @ A) = (sgn_sgn_int @ B)) @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ (modulo_modulo_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B))))) @ (times_times_int @ (sgn_sgn_int @ B) @ (minus_minus_int @ (times_times_int @ (abs_abs_int @ B) @ (zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ B @ A)))) @ (semiri1314217659103216013at_int @ (modulo_modulo_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9241_modulo__int__def)). 185.47/93.67 thf(21508,plain,(((modulo_modulo_int) = (^ [A:int,B:int]: (if_int @ (B = zero_zero_int) @ A @ (if_int @ ((sgn_sgn_int @ A) = (sgn_sgn_int @ B)) @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ (modulo_modulo_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B))))) @ (times_times_int @ (sgn_sgn_int @ B) @ (minus_minus_int @ (times_times_int @ (abs_abs_int @ B) @ (zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ B @ A)))) @ (semiri1314217659103216013at_int @ (modulo_modulo_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4220])). 185.47/93.67 thf(193,axiom,((ord_less_int = (^ [A:int,B:int]: ((B != A) & (B = (ord_max_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3735_max_Ostrict__order__iff)). 185.47/93.67 thf(8355,plain,(((ord_less_int) = (^ [A:int,B:int]: (~ (B = A) & (B = (ord_max_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 185.47/93.67 thf(6766,axiom,((! [A:nat,B:nat,C:nat]: ((((((~ ((~ (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ C @ A))) <= ((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A)))) <= ((~ (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ C @ B))) <= ((~ (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ C))) <= ((~ (ord_less_eq_nat @ A @ C)) <= (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_3848_le__cases3)). 185.47/93.67 thf(30618,plain,((! [A:nat,B:nat,C:nat]: (~ (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ A)) | ~ ((ord_less_eq_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))) | ~ (~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ C @ B)) | ~ (~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ A @ C)) | ~ (~ (ord_less_eq_nat @ A @ C) | ~ (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)],[6766])). 185.47/93.67 thf(4681,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (! [C:nat]: ((member_nat @ C @ B) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1285_subsetI)). 185.47/93.67 thf(23004,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4681])). 185.47/93.67 thf(3078,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => (((times_times_rat @ B @ A) = C) => (B = (divide_divide_rat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2466_eq__divide__imp)). 185.47/93.67 thf(17914,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => (((times_times_rat @ B @ A) = C) => (B = (divide_divide_rat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3078])). 185.47/93.67 thf(5090,axiom,((! [A:int,B:int]: (((abs_abs_int @ (times_times_int @ A @ B)) = one_one_int) => ((abs_abs_int @ A) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6819_abs__zmult__eq__1)). 185.47/93.67 thf(24457,plain,((! [A:int,B:int]: (((abs_abs_int @ (times_times_int @ A @ B)) = one_one_int) => ((abs_abs_int @ A) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5090])). 185.47/93.67 thf(4622,axiom,((! [A:real,B:real,C:nat]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ (^ [D:nat]: (plus_plus_real @ A @ (times_times_real @ (semiri5074537144036343181t_real @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ C) @ one_one_real) @ (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7343_double__arith__series)). 185.47/93.67 thf(22801,plain,((! [A:real,B:real,C:nat]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ (^ [D:nat]: (plus_plus_real @ A @ (times_times_real @ (semiri5074537144036343181t_real @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ C) @ one_one_real) @ (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4622])). 185.47/93.67 thf(1804,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B)) = (ord_less_real @ (uminus_uminus_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6033_real__0__less__add__iff)). 185.47/93.67 thf(13777,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B)) = (ord_less_real @ (uminus_uminus_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1804])). 185.47/93.67 thf(4055,axiom,((! [A:rat,B:num,C:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ B)) @ C) = (ord_less_rat @ A @ (times_times_rat @ C @ (numeral_numeral_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_divide__less__eq__numeral1_I1_J)). 185.47/93.67 thf(20999,plain,((! [A:rat,B:num,C:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ B)) @ C) = (ord_less_rat @ A @ (times_times_rat @ C @ (numeral_numeral_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4055])). 185.47/93.67 thf(3190,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2628_add__nonneg__pos)). 185.47/93.67 thf(18270,plain,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3190])). 185.47/93.67 thf(3073,axiom,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5951_not__numeral__less__neg__one)). 185.47/93.67 thf(17901,plain,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3073])). 185.47/93.67 thf(6840,axiom,((! [A:nat]: ((modulo_modulo_nat @ (suc @ zero_zero_nat) @ A) = (zero_n2687167440665602831ol_nat @ (A != (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5249_Suc__0__mod__eq)). 185.47/93.67 thf(30868,plain,((! [A:nat]: ((modulo_modulo_nat @ (suc @ zero_zero_nat) @ A) = (zero_n2687167440665602831ol_nat @ (~ (A = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6840])). 185.47/93.67 thf(3625,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B)) = (ord_less_eq_rat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_add__le__cancel__right)). 185.47/93.67 thf(19634,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B)) = (ord_less_eq_rat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3625])). 185.47/93.67 thf(77,axiom,((! [A:real,B:nat,C:(nat > (rat > real))]: (((B != zero_zero_nat) => ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_rat) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_rat))) <= (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8076_Maclaurin__zero)). 185.47/93.67 thf(7978,plain,((! [A:real,B:nat,C:(nat > (rat > real))]: (((~ (B = zero_zero_nat)) => ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_rat) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_rat))) | ~ (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 185.47/93.67 thf(7303,axiom,(((semiri1408675320244567234ct_nat @ zero_zero_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7957_fact__0)). 185.47/93.67 thf(32609,plain,(((semiri1408675320244567234ct_nat @ zero_zero_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7303])). 185.47/93.67 thf(6666,axiom,((! [A:nat]: ((bit_se8570568707652914677it_nat @ A @ (suc @ zero_zero_nat)) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9762_drop__bit__of__Suc__0)). 185.47/93.67 thf(30219,plain,((! [A:nat]: ((bit_se8570568707652914677it_nat @ A @ (suc @ zero_zero_nat)) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6666])). 185.47/93.67 thf(524,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ one_one_real @ (log @ A @ B)) = (ord_less_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9026_one__less__log__cancel__iff)). 185.47/93.67 thf(9487,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ one_one_real @ (log @ A @ B)) = (ord_less_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[524])). 185.47/93.67 thf(6735,axiom,(((((((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (some_nat @ mi)) <= (ord_less_nat @ mi @ xa)) & ((~ (ord_less_nat @ mi @ xa)) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = none_nat))) <= ((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat)) & (((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) != none_nat) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_969__C2_C)). 185.47/93.67 thf(30463,plain,(((((((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (some_nat @ mi)) | ~ (ord_less_nat @ mi @ xa)) & ((~ (ord_less_nat @ mi @ xa)) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = none_nat))) | ~ ((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat)) & ((~ ((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat)) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6735])). 185.47/93.67 thf(5383,axiom,(((neg_nu7009210354673126013omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5457_dbl__simps_I4_J)). 185.47/93.67 thf(25546,plain,(((neg_nu7009210354673126013omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5383])). 185.47/93.67 thf(5832,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2447_power__mono)). 185.47/93.67 thf(27293,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5832])). 185.47/93.67 thf(5279,axiom,((! [A:real]: ((minus_minus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1547_diff__zero)). 185.47/93.67 thf(25184,plain,((! [A:real]: ((minus_minus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5279])). 185.47/93.67 thf(6823,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_add__diff__cancel__right_H)). 185.47/93.67 thf(30816,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6823])). 185.47/93.67 thf(60,axiom,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (set_ord_lessThan_nat @ A) @ (set_ord_lessThan_nat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7542_lessThan__subset__iff)). 185.47/93.67 thf(7928,plain,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (set_ord_lessThan_nat @ A) @ (set_ord_lessThan_nat @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 185.47/93.67 thf(7488,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_748_less__imp__diff__less)). 185.47/93.67 thf(33247,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7488])). 185.47/93.67 thf(6791,axiom,((! [A:nat,B:nat]: ((B = zero_zero_nat) <= ((plus_plus_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2126_add__eq__self__zero)). 185.47/93.67 thf(30705,plain,((! [A:nat,B:nat]: ((B = zero_zero_nat) | ~ ((plus_plus_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6791])). 185.47/93.67 thf(5939,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)) <= (ord_less_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2406_add__neg__neg)). 185.47/93.67 thf(27658,plain,((! [A:nat,B:nat]: (((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)) | ~ (ord_less_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5939])). 185.47/93.67 thf(4980,axiom,((ord_less_nat @ res @ ma)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76__092_060open_062res_A_060_Ama_092_060close_062)). 185.47/93.67 thf(24026,plain,((ord_less_nat @ res @ ma)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4980])). 185.47/93.67 thf(372,axiom,((! [A:set_nat,B:(nat > rat)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_rat @ one_one_rat @ (B @ C)))) => (ord_less_eq_rat @ one_one_rat @ (groups73079841787564623at_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8764_prod__ge__1)). 185.47/93.67 thf(8974,plain,((! [A:set_nat,B:(nat > rat)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_rat @ one_one_rat @ (B @ C)))) => (ord_less_eq_rat @ one_one_rat @ (groups73079841787564623at_rat @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])). 185.47/93.67 thf(2760,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2198_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 185.47/93.67 thf(16905,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2760])). 185.47/93.67 thf(251,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ (sin_real @ A) @ (sin_real @ B))) <= (ord_less_eq_real @ A @ B)) <= (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7901_sin__monotone__2pi__le)). 185.47/93.67 thf(8529,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ (sin_real @ A) @ (sin_real @ B))) | ~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 185.47/93.67 thf(1768,axiom,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ A) @ B) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8594_pochhammer__minus)). 185.47/93.67 thf(13653,plain,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ A) @ B) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768])). 185.47/93.67 thf(3459,axiom,((! [A:(int > $o),B:int,C:int]: ((A @ (divide_divide_int @ B @ C)) = (((! [D:int,E:int]: ((A @ D) <= ((B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_int @ E @ C) & (ord_less_eq_int @ zero_zero_int @ E)))) <= (ord_less_int @ zero_zero_int @ C)) & ((! [D:int,E:int]: (((ord_less_int @ C @ E) & (ord_less_eq_int @ E @ zero_zero_int) & (B = (plus_plus_int @ (times_times_int @ C @ D) @ E))) => (A @ D))) <= (ord_less_int @ C @ zero_zero_int)) & ((C = zero_zero_int) => (A @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3069_split__zdiv)). 185.47/93.67 thf(19103,plain,((! [A:(int > $o),B:int,C:int]: ((A @ (divide_divide_int @ B @ C)) = ((! [D:int,E:int]: ((A @ D) | ~ ((B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_int @ E @ C) & (ord_less_eq_int @ zero_zero_int @ E))) | ~ (ord_less_int @ zero_zero_int @ C)) & (! [D:int,E:int]: (((ord_less_int @ C @ E) & (ord_less_eq_int @ E @ zero_zero_int) & (B = (plus_plus_int @ (times_times_int @ C @ D) @ E))) => (A @ D)) | ~ (ord_less_int @ C @ zero_zero_int)) & ((C = zero_zero_int) => (A @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3459])). 185.47/93.67 thf(7036,axiom,(((('!') @ option4927543243414619207at_nat) = (^ [A:(option4927543243414619207at_nat > $o)]: ((A @ none_P5556105721700978146at_nat) & ! [B:product_prod_nat_nat]: (A @ (some_P7363390416028606310at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1173_split__option__all)). 185.47/93.67 thf(31699,plain,(((('!') @ option4927543243414619207at_nat) = (^ [A:(option4927543243414619207at_nat > $o)]: ((A @ none_P5556105721700978146at_nat) & ! [B:product_prod_nat_nat]: (A @ (some_P7363390416028606310at_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7036])). 185.47/93.67 thf(3347,axiom,((! [A:(nat > int),B:nat,C:nat]: (((ord_less_int @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) <= (! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1063_lift__Suc__mono__less__iff)). 185.47/93.67 thf(18763,plain,((! [A:(nat > int),B:nat,C:nat]: (((ord_less_int @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) | ~ (! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3347])). 185.47/93.67 thf(4213,axiom,((! [A:nat]: ((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ A) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ (semiri5044797733671781792omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8573_pochhammer__same)). 185.47/93.67 thf(21488,plain,((! [A:nat]: ((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ A) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) @ (semiri5044797733671781792omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4213])). 185.47/93.67 thf(5470,axiom,((! [A:vEBT_VEBT,B:nat,C:option_nat]: (((accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ A @ B)) => ((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((B = zero_zero_nat) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ zero_zero_nat))) <= (C = none_nat))))) => ((! [D:$o,E:$o]: ((((((D) => (C = (some_nat @ zero_zero_nat))) & ((C = none_nat) <= (~ (D)))) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ zero_zero_nat))))) <= (B = (suc @ zero_zero_nat))) <= (A = (vEBT_Leaf @ D @ E)))) => ((((! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F) @ B))) <= (C = none_nat)))) => ((~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B))) <= (((ord_less_nat @ E @ B) => (C = (some_nat @ E))) & ((~ (ord_less_nat @ E @ B)) => (C = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) @ (if_option_nat @ ((vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_nat)) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ D @ B) @ (some_nat @ D) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat))))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H))))) <= (! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((C = none_nat) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F) @ B)))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F)))))) <= (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((C = none_nat) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B)))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))))) <= (! [D:$o,E:$o]: ((! [F:nat]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ (suc @ F))))) <= (((E) => (C = (some_nat @ one_one_nat))) & ((((C = none_nat) <= (~ (D))) & ((D) => (C = (some_nat @ zero_zero_nat)))) <= (~ (E))))) <= (B = (suc @ (suc @ F))))) <= (A = (vEBT_Leaf @ D @ E)))))))) <= ((vEBT_vebt_pred @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3023_vebt__pred_Opelims)). 185.47/93.67 thf(25859,plain,((! [A:vEBT_VEBT,B:nat,C:option_nat]: (((accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ A @ B)) => ((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((B = zero_zero_nat) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ zero_zero_nat)) | ~ (C = none_nat))))) => ((! [D:$o,E:$o]: (((((D) => (C = (some_nat @ zero_zero_nat))) & ((C = none_nat) | (D))) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ zero_zero_nat))))) | ~ (B = (suc @ zero_zero_nat)) | ~ (A = (vEBT_Leaf @ D @ E)))) => (((! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F) @ B)) | ~ (C = none_nat)))) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B)) | ~ (((ord_less_nat @ E @ B) => (C = (some_nat @ E))) & ((~ (ord_less_nat @ E @ B)) => (C = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) @ (if_option_nat @ ((vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ~ ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat)) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ D @ B) @ (some_nat @ D) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))) | ~ (! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((C = none_nat) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F) @ B)))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F)))))) | ~ (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((C = none_nat) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B)))) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)))) | ~ (! [D:$o,E:$o]: (! [F:nat]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ (suc @ F)))) | ~ (((E) => (C = (some_nat @ one_one_nat))) & ((((C = none_nat) | (D)) & ((D) => (C = (some_nat @ zero_zero_nat)))) | (E))) | ~ (B = (suc @ (suc @ F)))) | ~ (A = (vEBT_Leaf @ D @ E)))))))) | ~ ((vEBT_vebt_pred @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5470])). 185.47/93.67 thf(5824,axiom,((! [A:num]: ((semiri773545260158071498ct_rat @ (numeral_numeral_nat @ A)) = (times_times_rat @ (numeral_numeral_rat @ A) @ (semiri773545260158071498ct_rat @ (pred_numeral @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8038_fact__numeral)). 185.47/93.67 thf(27271,plain,((! [A:num]: ((semiri773545260158071498ct_rat @ (numeral_numeral_nat @ A)) = (times_times_rat @ (numeral_numeral_rat @ A) @ (semiri773545260158071498ct_rat @ (pred_numeral @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5824])). 185.47/93.67 thf(6569,axiom,((! [A:num]: ((unique5055182867167087721od_nat @ A @ one) = (product_Pair_nat_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6805_divmod__algorithm__code_I2_J)). 185.47/93.67 thf(29899,plain,((! [A:num]: ((unique5055182867167087721od_nat @ A @ one) = (product_Pair_nat_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6569])). 185.47/93.67 thf(2792,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))) => (~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ C) @ D @ E) @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1934_VEBT__internal_Onaive__member_Ocases)). 185.47/93.67 thf(16999,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))) => (~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ C) @ D @ E) @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2792])). 185.47/93.67 thf(16,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (minus_minus_real @ (A @ (suc @ C)) @ (A @ C))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_real @ (A @ B) @ (A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7591_sum__lessThan__telescope)). 185.47/93.67 thf(7778,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (minus_minus_real @ (A @ (suc @ C)) @ (A @ C))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_real @ (A @ B) @ (A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 185.47/93.67 thf(3394,axiom,((! [A:complex,B:complex,C:real]: ((ord_less_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ C) => (ord_less_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7485_norm__triangle__lt)). 185.47/93.67 thf(18912,plain,((! [A:complex,B:complex,C:real]: ((ord_less_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ C) => (ord_less_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3394])). 185.47/93.67 thf(6325,axiom,((! [A:rat]: ((minus_minus_rat @ A @ A) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1543_cancel__comm__monoid__add__class_Odiff__cancel)). 185.47/93.67 thf(29017,plain,((! [A:rat]: ((minus_minus_rat @ A @ A) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6325])). 185.47/93.67 thf(3678,axiom,((! [A:real,B:nat]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (power_power_real @ A @ B)) @ (power_power_real @ (real_V7735802525324610683m_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7488_norm__power__ineq)). 185.47/93.67 thf(19802,plain,((! [A:real,B:nat]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (power_power_real @ A @ B)) @ (power_power_real @ (real_V7735802525324610683m_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3678])). 185.47/93.67 thf(1938,axiom,((! [A:int,B:int]: (((~ (ord_less_int @ A @ B)) = (A = B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4177_antisym__conv2)). 185.47/93.67 thf(14218,plain,((! [A:int,B:int]: (((~ (ord_less_int @ A @ B)) = (A = B)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1938])). 185.47/93.67 thf(2341,axiom,((! [A:real,B:real]: (((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2653_divide__nonneg__neg)). 185.47/93.67 thf(15487,plain,((! [A:real,B:real]: (((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2341])). 185.47/93.67 thf(2196,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ zero_zero_rat @ (comm_s4028243227959126397er_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8466_pochhammer__nonneg)). 185.47/93.67 thf(15049,plain,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ zero_zero_rat @ (comm_s4028243227959126397er_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2196])). 185.47/93.67 thf(3715,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ B)) = (((ord_less_eq_real @ A @ C) <= (ord_less_real @ zero_zero_real @ B)) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2651_divide__le__cancel)). 185.47/93.67 thf(19934,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ B)) = (((ord_less_eq_real @ A @ C) | ~ (ord_less_real @ zero_zero_real @ B)) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3715])). 185.47/93.67 thf(2914,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((times_times_int @ C @ (divide_divide_int @ B @ A)) = (divide_divide_int @ (times_times_int @ C @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4755_div__mult__swap)). 185.47/93.67 thf(17396,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((times_times_int @ C @ (divide_divide_int @ B @ A)) = (divide_divide_int @ (times_times_int @ C @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2914])). 185.47/93.67 thf(4865,axiom,((! [A:rat,B:rat,C:rat]: (((A != zero_zero_rat) => ((minus_minus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ B @ A) @ C) @ A))) & (((minus_minus_rat @ B @ (divide_divide_rat @ C @ A)) = B) <= (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2773_add__divide__eq__if__simps_I4_J)). 185.47/93.67 thf(23620,plain,((! [A:rat,B:rat,C:rat]: (((~ (A = zero_zero_rat)) => ((minus_minus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ B @ A) @ C) @ A))) & (((minus_minus_rat @ B @ (divide_divide_rat @ C @ A)) = B) | ~ (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4865])). 185.47/93.67 thf(4625,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_int @ B @ C)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2352_mult__less__cancel__left__pos)). 185.47/93.67 thf(22818,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_int @ B @ C)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4625])). 185.47/93.67 thf(6624,axiom,((! [A:nat,B:complex]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (power_power_complex @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5441_power__minus__odd)). 185.47/93.67 thf(30083,plain,((! [A:nat,B:complex]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (power_power_complex @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6624])). 185.47/93.67 thf(6934,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_diff__diff__cancel)). 185.47/93.67 thf(31250,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6934])). 185.47/93.67 thf(197,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (ord_max_int @ A @ B) @ C) => (~ ((ord_less_eq_int @ A @ C) => (~ (ord_less_eq_int @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3672_max_OboundedE)). 185.47/93.67 thf(8372,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (ord_max_int @ A @ B) @ C) => (~ ((ord_less_eq_int @ A @ C) => (~ (ord_less_eq_int @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 185.47/93.67 thf(7351,axiom,((! [A:real,B:nat]: ((abs_abs_real @ (power_power_real @ A @ B)) = (power_power_real @ (abs_abs_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6470_power__abs)). 185.47/93.67 thf(32772,plain,((! [A:real,B:nat]: ((abs_abs_real @ (power_power_real @ A @ B)) = (power_power_real @ (abs_abs_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7351])). 185.47/93.67 thf(4732,axiom,((! [A:real,B:real,C:num]: (((divide_divide_real @ A @ B) = (numeral_numeral_real @ C)) = (((B != zero_zero_real) => (A = (times_times_real @ (numeral_numeral_real @ C) @ B))) & ((B = zero_zero_real) => ((numeral_numeral_real @ C) = zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2727_divide__eq__eq__numeral_I1_J)). 185.47/93.67 thf(23174,plain,((! [A:real,B:real,C:num]: (((divide_divide_real @ A @ B) = (numeral_numeral_real @ C)) = (((~ (B = zero_zero_real)) => (A = (times_times_real @ (numeral_numeral_real @ C) @ B))) & ((B = zero_zero_real) => ((numeral_numeral_real @ C) = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4732])). 185.47/93.67 thf(5332,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ (modulo_modulo_nat @ A @ B) @ (modulo_modulo_nat @ C @ B)) @ B) = (modulo_modulo_nat @ (plus_plus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1997_mod__add__eq)). 185.47/93.67 thf(25353,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ (modulo_modulo_nat @ A @ B) @ (modulo_modulo_nat @ C @ B)) @ B) = (modulo_modulo_nat @ (plus_plus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5332])). 185.47/93.67 thf(7493,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2322_mult__neg__pos)). 185.47/93.67 thf(33264,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7493])). 185.47/93.67 thf(4373,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((? [B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) & ((sin_real @ B) = A) & ! [C:real]: (((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ C) & (ord_less_eq_real @ C @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((sin_real @ C) = A)) => (C = B)) & (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7926_sin__total)). 185.47/93.67 thf(22006,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (? [B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) & ((sin_real @ B) = A) & ! [C:real]: (((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ C) & (ord_less_eq_real @ C @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((sin_real @ C) = A)) => (C = B)) & (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4373])). 185.47/93.67 thf(5368,axiom,((! [A:real,B:real]: ((sqrt @ (times_times_real @ A @ B)) = (times_times_real @ (sqrt @ A) @ (sqrt @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8146_real__sqrt__mult)). 185.47/93.67 thf(25501,plain,((! [A:real,B:real]: ((sqrt @ (times_times_real @ A @ B)) = (times_times_real @ (sqrt @ A) @ (sqrt @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5368])). 185.47/93.67 thf(5868,axiom,((! [A:real,B:nat]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2990_zero__le__even__power_H)). 185.47/93.67 thf(27424,plain,((! [A:real,B:nat]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5868])). 185.47/93.67 thf(3785,axiom,((! [A:num,B:nat,C:nat]: ((ord_less_rat @ (power_power_rat @ (numeral_numeral_rat @ A) @ B) @ (semiri681578069525770553at_rat @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7126_numeral__power__less__of__nat__cancel__iff)). 185.47/93.67 thf(20164,plain,((! [A:num,B:nat,C:nat]: ((ord_less_rat @ (power_power_rat @ (numeral_numeral_rat @ A) @ B) @ (semiri681578069525770553at_rat @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3785])). 185.47/93.67 thf(6070,axiom,((! [A:nat,B:num]: ((modulo_modulo_nat @ (suc @ (suc @ (suc @ A))) @ (numeral_numeral_nat @ B)) = (modulo_modulo_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6442_Suc__mod__eq__add3__mod__numeral)). 185.47/93.67 thf(28103,plain,((! [A:nat,B:num]: ((modulo_modulo_nat @ (suc @ (suc @ (suc @ A))) @ (numeral_numeral_nat @ B)) = (modulo_modulo_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ (numeral_numeral_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6070])). 185.47/93.67 thf(4756,axiom,((! [A:(nat > rat),B:nat,C:nat]: ((! [D:nat]: (ord_less_rat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_rat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1055_lift__Suc__mono__less)). 185.47/93.67 thf(23249,plain,((! [A:(nat > rat),B:nat,C:nat]: ((! [D:nat]: (ord_less_rat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_rat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4756])). 185.47/93.67 thf(1725,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_add__right__cancel)). 185.47/93.67 thf(13518,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725])). 185.47/93.67 thf(5628,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3243_pinf_I4_J)). 185.47/93.67 thf(26463,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5628])). 185.47/93.67 thf(4967,axiom,((! [A:nat]: ((order_mono_nat_nat @ (^ [B:nat]: (minus_minus_nat @ (power_power_nat @ A @ B) @ B))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10173_mono__ge2__power__minus__self)). 185.47/93.67 thf(23990,plain,((! [A:nat]: ((order_mono_nat_nat @ (^ [B:nat]: (minus_minus_nat @ (power_power_nat @ A @ B) @ B))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4967])). 185.47/93.67 thf(3229,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (divide_divide_int @ B @ C) @ (divide_divide_int @ A @ C)) <= (ord_less_int @ C @ zero_zero_int)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3050_zdiv__mono1__neg)). 185.47/93.67 thf(18395,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (divide_divide_int @ B @ C) @ (divide_divide_int @ A @ C)) | ~ (ord_less_int @ C @ zero_zero_int) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3229])). 185.47/93.67 thf(4462,axiom,((! [A:int]: ((plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) != zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3161_odd__nonzero)). 185.47/93.67 thf(22283,plain,((! [A:int]: ~ ((plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4462])). 185.47/93.67 thf(5289,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))) <= (ord_less_eq_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2285_add__nonneg__eq__0__iff)). 185.47/93.67 thf(25216,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5289])). 185.47/93.67 thf(1661,axiom,((! [A:nat,B:int]: (ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (bit_ri631733984087533419it_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6239_signed__take__bit__int__greater__eq__minus__exp)). 185.47/93.67 thf(13304,plain,((! [A:nat,B:int]: (ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (bit_ri631733984087533419it_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661])). 185.47/93.67 thf(5962,axiom,((! [A:num]: ((plus_plus_num @ one @ (bit1 @ A)) = (bit0 @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6411_semiring__norm_I4_J)). 185.47/93.67 thf(27738,plain,((! [A:num]: ((plus_plus_num @ one @ (bit1 @ A)) = (bit0 @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5962])). 185.47/93.67 thf(732,axiom,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((member_nat @ B @ A) => ((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (D = B) @ (C @ D) @ one_one_complex)) @ A) = (C @ B))) & ((~ (member_nat @ B @ A)) => ((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (D = B) @ (C @ D) @ one_one_complex)) @ A) = one_one_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8667_prod_Odelta)). 185.47/93.67 thf(10172,plain,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((member_nat @ B @ A) => ((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (D = B) @ (C @ D) @ one_one_complex)) @ A) = (C @ B))) & ((~ (member_nat @ B @ A)) => ((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (D = B) @ (C @ D) @ one_one_complex)) @ A) = one_one_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[732])). 185.47/93.67 thf(2971,axiom,((! [A:$o]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (zero_n2684676970156552555ol_int @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5403_odd__of__bool__self)). 185.47/93.67 thf(17579,plain,((! [A:$o]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (zero_n2684676970156552555ol_int @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2971])). 185.47/93.67 thf(1151,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (ord_less_eq_int @ C @ (plus_plus_int @ (times_times_int @ (minus_minus_int @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1230_ordered__ring__class_Ole__add__iff2)). 185.47/93.67 thf(11630,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (ord_less_eq_int @ C @ (plus_plus_int @ (times_times_int @ (minus_minus_int @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151])). 185.47/93.67 thf(1078,axiom,((! [A:nat,B:int,C:int]: ((bit_ri631733984087533419it_int @ A @ (times_times_int @ (bit_ri631733984087533419it_int @ A @ B) @ (bit_ri631733984087533419it_int @ A @ C))) = (bit_ri631733984087533419it_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4688_signed__take__bit__mult)). 185.47/93.67 thf(11387,plain,((! [A:nat,B:int,C:int]: ((bit_ri631733984087533419it_int @ A @ (times_times_int @ (bit_ri631733984087533419it_int @ A @ B) @ (bit_ri631733984087533419it_int @ A @ C))) = (bit_ri631733984087533419it_int @ A @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078])). 185.47/93.67 thf(3661,axiom,((! [A:nat]: ((semiri5074537144036343181t_real @ (suc @ A)) = (plus_plus_real @ one_one_real @ (semiri5074537144036343181t_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7015_of__nat__Suc)). 185.47/93.67 thf(19753,plain,((! [A:nat]: ((semiri5074537144036343181t_real @ (suc @ A)) = (plus_plus_real @ one_one_real @ (semiri5074537144036343181t_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3661])). 185.47/93.67 thf(539,axiom,((! [A:real,B:(nat > real)]: ((summable_real @ (^ [C:nat]: (times_times_real @ A @ (B @ C)))) = ((A = zero_zero_real) | (summable_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7650_summable__cmult__iff)). 185.47/93.67 thf(9528,plain,((! [A:real,B:(nat > real)]: ((summable_real @ (^ [C:nat]: (times_times_real @ A @ (B @ C)))) = ((A = zero_zero_real) | (summable_real @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[539])). 185.47/93.67 thf(533,axiom,((! [A:real,B:real,C:real]: ((plus_plus_complex @ (complex2 @ A @ B) @ (real_V4546457046886955230omplex @ C)) = (complex2 @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9143_Complex__add__complex__of__real)). 185.47/93.67 thf(9511,plain,((! [A:real,B:real,C:real]: ((plus_plus_complex @ (complex2 @ A @ B) @ (real_V4546457046886955230omplex @ C)) = (complex2 @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[533])). 185.47/93.67 thf(1215,axiom,(((cos_complex @ zero_zero_complex) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7780_cos__zero)). 185.47/93.67 thf(11814,plain,(((cos_complex @ zero_zero_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215])). 185.47/93.67 thf(403,axiom,((! [A:(nat > int),B:int,C:set_nat]: ((modulo_modulo_int @ (groups705719431365010083at_int @ (^ [D:nat]: (modulo_modulo_int @ (A @ D) @ B)) @ C) @ B) = (modulo_modulo_int @ (groups705719431365010083at_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8732_mod__prod__eq)). 185.47/93.67 thf(9074,plain,((! [A:(nat > int),B:int,C:set_nat]: ((modulo_modulo_int @ (groups705719431365010083at_int @ (^ [D:nat]: (modulo_modulo_int @ (A @ D) @ B)) @ C) @ B) = (modulo_modulo_int @ (groups705719431365010083at_int @ (A) @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[403])). 185.47/93.67 thf(585,axiom,((! [A:set_nat,B:(nat > rat)]: ((finite_finite_nat @ A) => ((A != bot_bot_set_nat) => ((ord_less_rat @ one_one_rat @ (groups73079841787564623at_rat @ B @ A)) <= (! [C:nat]: ((member_nat @ C @ A) => (ord_less_rat @ one_one_rat @ (B @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8886_less__1__prod)). 185.47/93.67 thf(9674,plain,((! [A:set_nat,B:(nat > rat)]: ((finite_finite_nat @ A) => ((~ (A = bot_bot_set_nat)) => ((ord_less_rat @ one_one_rat @ (groups73079841787564623at_rat @ (B) @ A)) | ~ (! [C:nat]: ((member_nat @ C @ A) => (ord_less_rat @ one_one_rat @ (B @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[585])). 185.47/93.67 thf(3307,axiom,((! [A:real]: (((sin_real @ (arccos @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8338_sin__arccos__abs)). 185.47/93.67 thf(18631,plain,((! [A:real]: (((sin_real @ (arccos @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3307])). 185.47/93.67 thf(6841,axiom,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1841_power__eq__0__iff)). 185.47/93.67 thf(30871,plain,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6841])). 185.47/93.67 thf(6970,axiom,((! [A:real,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((power_power_real @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_real @ (power_power_real @ A @ C) @ (power_power_real @ A @ B)))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2905_power__diff)). 185.47/93.67 thf(31406,plain,((! [A:real,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((power_power_real @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_real @ (power_power_real @ A @ C) @ (power_power_real @ A @ B)))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6970])). 185.47/93.67 thf(2663,axiom,((! [A:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one)) @ A) = (uminus1351360451143612070nteger @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5979_mult__1s__ring__1_I1_J)). 185.47/93.67 thf(16557,plain,((! [A:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one)) @ A) = (uminus1351360451143612070nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2663])). 185.47/93.67 thf(282,axiom,((! [A:int,B:int]: (((ord_max_int @ B @ A) = B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3587_max_Oabsorb3)). 185.47/93.67 thf(8652,plain,((! [A:int,B:int]: (((ord_max_int @ B @ A) = B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 185.47/93.67 thf(7383,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ A @ (times_times_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ B @ (modulo_modulo_nat @ (divide_divide_nat @ A @ B) @ C)) @ (modulo_modulo_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2566_mod__mult2__eq)). 185.47/93.67 thf(32869,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ A @ (times_times_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ B @ (modulo_modulo_nat @ (divide_divide_nat @ A @ B) @ C)) @ (modulo_modulo_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7383])). 185.47/93.67 thf(1535,axiom,((! [A:complex]: ((power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_complex @ one_one_complex @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7837_sin__squared__eq)). 185.47/93.67 thf(12821,plain,((! [A:complex]: ((power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_complex @ one_one_complex @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535])). 185.47/93.67 thf(3693,axiom,((! [A:int]: ((fract @ A @ one_one_int) = (ring_1_of_int_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9944_Fract__of__int__eq)). 185.47/93.67 thf(19853,plain,((! [A:int]: ((fract @ A @ one_one_int) = (ring_1_of_int_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3693])). 185.47/93.67 thf(5707,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2109_old_Onat_Odistinct_I1_J)). 185.47/93.67 thf(26716,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5707])). 185.47/93.67 thf(6133,axiom,((bit_se6528837805403552850or_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) != (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se6528837805403552850or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9483_xor__nat__rec)). 185.47/93.67 thf(28322,plain,(((bit_se6528837805403552850or_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (~ ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se6528837805403552850or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6133])). 185.47/93.67 thf(1393,axiom,((bit_se7882103937844011126it_nat = (^ [A:nat,B:nat]: (bit_se1412395901928357646or_nat @ B @ (bit_se547839408752420682it_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9509_set__bit__nat__def)). 185.47/93.67 thf(12381,plain,(((bit_se7882103937844011126it_nat) = (^ [A:nat,B:nat]: (bit_se1412395901928357646or_nat @ B @ (bit_se547839408752420682it_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393])). 185.47/93.67 thf(6913,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => (~ (dvd_dvd_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4806_nat__dvd__not__less)). 185.47/93.67 thf(31173,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => (~ (dvd_dvd_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6913])). 185.47/93.67 thf(2776,axiom,((! [A:real]: ((sin_real @ (arctan @ A)) = (divide_divide_real @ A @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8271_sin__arctan)). 185.47/93.67 thf(16952,plain,((! [A:real]: ((sin_real @ (arctan @ A)) = (divide_divide_real @ A @ (sqrt @ (plus_plus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2776])). 185.47/93.67 thf(7226,axiom,((! [A:num]: (ord_less_eq_num @ one @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_semiring__norm_I68_J)). 185.47/93.67 thf(32361,plain,((! [A:num]: (ord_less_eq_num @ one @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7226])). 185.47/93.67 thf(6157,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (divide_divide_nat @ C @ B)) <= (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4763_dvd__mult__imp__div)). 185.47/93.67 thf(28449,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (divide_divide_nat @ C @ B)) | ~ (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6157])). 185.47/93.67 thf(7568,axiom,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ (minus_minus_int @ B @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_894_power2__commute)). 185.47/93.67 thf(33483,plain,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ (minus_minus_int @ B @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7568])). 185.47/93.67 thf(6903,axiom,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_998_lessI)). 185.47/93.67 thf(31141,plain,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6903])). 185.47/93.67 thf(1197,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (~ (! [C:code_integer]: (B != (times_3573771949741848930nteger @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4620_dvdE)). 185.47/93.67 thf(11761,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (~ (! [C:code_integer]: ~ (B = (times_3573771949741848930nteger @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197])). 185.47/93.67 thf(3902,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (real_V7735802525324610683m_real @ A) @ B) => ((ord_less_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ C)) @ (plus_plus_real @ B @ D)) <= (ord_less_real @ (real_V7735802525324610683m_real @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7486_norm__add__less)). 185.47/93.67 thf(20525,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (real_V7735802525324610683m_real @ A) @ B) => ((ord_less_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ C)) @ (plus_plus_real @ B @ D)) | ~ (ord_less_real @ (real_V7735802525324610683m_real @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3902])). 185.47/93.67 thf(5616,axiom,((! [A:num,B:num]: ((B != A) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4140_order__less__imp__not__eq2)). 185.47/93.67 thf(26422,plain,((! [A:num,B:num]: (~ (B = A) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5616])). 185.47/93.67 thf(6602,axiom,((! [A:num,B:(num > num),C:num,D:num]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_num @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3914_order__subst1)). 185.47/93.67 thf(30011,plain,((! [A:num,B:(num > num),C:num,D:num]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_num @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6602])). 185.47/93.67 thf(1720,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_member @ (vEBT_Leaf @ A @ B) @ C) = (((C != zero_zero_nat) => ((C = one_one_nat) & ((C = one_one_nat) => (B)))) & ((A) <= (C = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1951_vebt__member_Osimps_I1_J)). 185.47/93.67 thf(13486,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_member @ (vEBT_Leaf @ A @ B) @ C) = (((~ (C = zero_zero_nat)) => ((C = one_one_nat) & ((C = one_one_nat) => (B)))) & ((A) | ~ (C = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720])). 185.47/93.67 thf(4869,axiom,((! [A:int,B:real]: ((ord_less_eq_real @ (abs_abs_real @ (ring_1_of_int_real @ A)) @ B) => ((ord_less_eq_real @ one_one_real @ B) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7282_of__int__leD)). 185.47/93.67 thf(23638,plain,((! [A:int,B:real]: ((ord_less_eq_real @ (abs_abs_real @ (ring_1_of_int_real @ A)) @ B) => ((ord_less_eq_real @ one_one_real @ B) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4869])). 185.47/93.67 thf(5596,axiom,((! [A:rat,B:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (((ord_less_eq_rat @ zero_zero_rat @ B) => (A = B)) <= (ord_less_eq_rat @ zero_zero_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2938_power2__eq__imp__eq)). 185.47/93.67 thf(26354,plain,((! [A:rat,B:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (((ord_less_eq_rat @ zero_zero_rat @ B) => (A = B)) | ~ (ord_less_eq_rat @ zero_zero_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5596])). 185.47/93.67 thf(3299,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= ((C = D) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_add__mono__thms__linordered__semiring_I3_J)). 185.47/93.67 thf(18599,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ ((C = D) & (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3299])). 185.47/93.67 thf(1363,axiom,((! [A:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5925_neg__numeral__le__one)). 185.47/93.67 thf(12274,plain,((! [A:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363])). 185.47/93.67 thf(4253,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((times_times_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri681578069525770553at_rat @ (binomial @ B @ A))) = (divide_divide_rat @ (semiri773545260158071498ct_rat @ B) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8551_fact__binomial)). 185.47/93.67 thf(21612,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((times_times_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri681578069525770553at_rat @ (binomial @ B @ A))) = (divide_divide_rat @ (semiri773545260158071498ct_rat @ B) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4253])). 185.47/93.67 thf(3441,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (abs_abs_int @ A)) = (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6374_zero__less__abs__iff)). 185.47/93.67 thf(19054,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ (abs_abs_int @ A)) = (~ (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3441])). 185.47/93.67 thf(1452,axiom,((bit_se8568078237143864401it_int = (^ [A:nat,B:int]: (divide_divide_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9759_drop__bit__int__def)). 185.47/93.67 thf(12573,plain,(((bit_se8568078237143864401it_int) = (^ [A:nat,B:int]: (divide_divide_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452])). 185.47/93.67 thf(211,axiom,((! [A:real,B:nat]: ((times_times_real @ (gbinomial_real @ A @ B) @ A) = (plus_plus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (gbinomial_real @ A @ B)) @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (gbinomial_real @ A @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8483_gbinomial__mult__1_H)). 185.47/93.67 thf(8413,plain,((! [A:real,B:nat]: ((times_times_real @ (gbinomial_real @ A @ B) @ A) = (plus_plus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (gbinomial_real @ A @ B)) @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (gbinomial_real @ A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 185.47/93.67 thf(7007,axiom,((! [A:rat,B:rat]: ((minus_minus_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (uminus_uminus_rat @ (minus_minus_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5578_minus__diff__minus)). 185.47/93.67 thf(31575,plain,((! [A:rat,B:rat]: ((minus_minus_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (uminus_uminus_rat @ (minus_minus_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7007])). 185.47/93.67 thf(1117,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4377_bot_Oextremum__unique)). 185.47/93.67 thf(11521,plain,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117])). 185.47/93.67 thf(1074,axiom,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7462_norm__divide)). 185.47/93.67 thf(11375,plain,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074])). 185.47/93.67 thf(6878,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (times_times_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4517_even__mult__iff)). 185.47/93.67 thf(31062,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (times_times_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6878])). 185.47/93.67 thf(4156,axiom,((ord_less_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_4256_dual__order_Ostrict__iff__not)). 185.47/93.67 thf(21314,plain,(((ord_less_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)],[4156])). 185.47/93.67 thf(3340,axiom,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_not__numeral__less__one)). 185.47/93.67 thf(18731,plain,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3340])). 185.47/93.67 thf(2160,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((divide_divide_int @ B @ (times_times_int @ C @ A)) = (divide_divide_int @ (divide_divide_int @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2186_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq)). 185.47/93.67 thf(14930,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((divide_divide_int @ B @ (times_times_int @ C @ A)) = (divide_divide_int @ (divide_divide_int @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2160])). 185.47/93.67 thf(6827,axiom,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ B)) = (times_times_complex @ (power_power_complex @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1064_power__Suc2)). 185.47/93.67 thf(30829,plain,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ B)) = (times_times_complex @ (power_power_complex @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6827])). 185.47/93.67 thf(944,axiom,((! [A:real,B:real,C:real]: (((((plus_plus_real @ (log @ A @ B) @ C) = (log @ A @ (times_times_real @ B @ (powr_real @ A @ C)))) <= (ord_less_real @ zero_zero_real @ B)) <= (A != one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9127_log__add__eq__powr)). 185.47/93.67 thf(10970,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ (log @ A @ B) @ C) = (log @ A @ (times_times_real @ B @ (powr_real @ A @ C)))) | ~ (ord_less_real @ zero_zero_real @ B) | (A = one_one_real) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[944])). 185.47/93.67 thf(4810,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2602_mult__le__cancel__left__pos)). 185.47/93.67 thf(23448,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4810])). 185.47/93.67 thf(7695,axiom,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) = (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_div__exp__eq)). 185.47/93.67 thf(33829,plain,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) = (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7695])). 185.47/93.67 thf(4597,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_nat @ (nat2 @ A) @ B) = (ord_less_int @ A @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9332_nat__less__iff)). 185.47/93.67 thf(22725,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_nat @ (nat2 @ A) @ B) = (ord_less_int @ A @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4597])). 185.47/93.67 thf(5594,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (binomial @ C @ A) @ (binomial @ C @ B)) <= (ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8525_binomial__mono)). 185.47/93.67 thf(26348,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (binomial @ C @ A) @ (binomial @ C @ B)) | ~ (ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5594])). 185.47/93.67 thf(5351,axiom,((! [A:rat]: ((times_times_rat @ zero_zero_rat @ A) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1483_mult__zero__left)). 185.47/93.67 thf(25450,plain,((! [A:rat]: ((times_times_rat @ zero_zero_rat @ A) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5351])). 185.47/93.67 thf(171,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ (ring_1_of_int_int @ A)) @ B) => ((ord_less_eq_int @ one_one_int @ B) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7284_of__int__leD)). 185.47/93.67 thf(8280,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ (ring_1_of_int_int @ A)) @ B) => ((ord_less_eq_int @ one_one_int @ B) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 185.47/93.67 thf(1155,axiom,((! [A:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ zero_zero_real) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7009_of__nat__le__0__iff)). 185.47/93.67 thf(11643,plain,((! [A:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ zero_zero_real) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155])). 185.47/93.67 thf(4222,axiom,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (divide1717551699836669952omplex @ A @ C) @ (divide1717551699836669952omplex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_744_diff__divide__distrib)). 185.47/93.67 thf(21513,plain,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (divide1717551699836669952omplex @ A @ C) @ (divide1717551699836669952omplex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4222])). 185.47/93.67 thf(2778,axiom,((! [A:int,B:int]: ((ord_less_int @ (bit_se1409905431419307370or_int @ A @ B) @ zero_zero_int) = ((ord_less_int @ B @ zero_zero_int) | (ord_less_int @ A @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9409_or__negative__int__iff)). 185.47/93.67 thf(16959,plain,((! [A:int,B:int]: ((ord_less_int @ (bit_se1409905431419307370or_int @ A @ B) @ zero_zero_int) = ((ord_less_int @ B @ zero_zero_int) | (ord_less_int @ A @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2778])). 185.47/93.67 thf(4658,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ (times_times_int @ A @ C)) = (dvd_dvd_int @ B @ C)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4740_dvd__mult__unit__iff_H)). 185.47/93.67 thf(22921,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ (times_times_int @ A @ C)) = (dvd_dvd_int @ B @ C)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4658])). 185.47/93.67 thf(2344,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => (((A = B) <= (dvd_dvd_int @ B @ A)) <= (dvd_dvd_int @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4809_zdvd__antisym__nonneg)). 185.47/93.67 thf(15496,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => ((A = B) | ~ (dvd_dvd_int @ B @ A) | ~ (dvd_dvd_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2344])). 185.47/93.67 thf(1004,axiom,((! [A:real,B:real,C:real,D:real]: ((times_times_complex @ (complex2 @ A @ B) @ (complex2 @ C @ D)) = (complex2 @ (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) @ (plus_plus_real @ (times_times_real @ A @ D) @ (times_times_real @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8027_complex__mult)). 185.47/93.67 thf(11173,plain,((! [A:real,B:real,C:real,D:real]: ((times_times_complex @ (complex2 @ A @ B) @ (complex2 @ C @ D)) = (complex2 @ (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) @ (plus_plus_real @ (times_times_real @ A @ D) @ (times_times_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004])). 185.47/93.67 thf(2962,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (times_times_real @ C @ B) @ (times_times_real @ C @ A)) <= (ord_less_real @ C @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2353_mult__strict__left__mono__neg)). 185.47/93.67 thf(17547,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (times_times_real @ C @ B) @ (times_times_real @ C @ A)) | ~ (ord_less_real @ C @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2962])). 185.47/93.67 thf(5944,axiom,((! [A:num,B:num]: ((numera6620942414471956472nteger @ A) != (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5534_numeral__neq__neg__numeral)). 185.47/93.67 thf(27673,plain,((! [A:num,B:num]: ~ ((numera6620942414471956472nteger @ A) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5944])). 185.47/93.67 thf(2257,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_real @ C @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1234_less__add__iff2)). 185.47/93.67 thf(15233,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_real @ C @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2257])). 185.47/93.67 thf(4736,axiom,((! [A:rat,B:(int > rat),C:int,D:int]: ((ord_less_eq_rat @ A @ (B @ C)) => ((ord_less_int @ C @ D) => ((ord_less_rat @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_rat @ (B @ E) @ (B @ F)) <= (ord_less_int @ E @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4330_order__le__less__subst1)). 185.47/93.67 thf(23185,plain,((! [A:rat,B:(int > rat),C:int,D:int]: ((ord_less_eq_rat @ A @ (B @ C)) => ((ord_less_int @ C @ D) => ((ord_less_rat @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_int @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4736])). 185.47/93.67 thf(1749,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (plus_plus_rat @ B @ A) @ C) <= (ord_less_eq_rat @ B @ C)) <= (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2300_add__decreasing2)). 185.47/93.67 thf(13593,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ B @ A) @ C) | ~ (ord_less_eq_rat @ B @ C) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749])). 185.47/93.67 thf(3238,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ B @ (plus_plus_rat @ A @ C)) <= (ord_less_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2642_add__strict__increasing2)). 185.47/93.67 thf(18419,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_rat @ B @ (plus_plus_rat @ A @ C)) | ~ (ord_less_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3238])). 185.47/93.67 thf(895,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((! [D:nat]: (((ord_less_eq_real @ (B @ D) @ (C @ D)) & (ord_less_eq_real @ zero_zero_real @ (B @ D))) <= (member_nat @ D @ A))) => (ord_less_eq_real @ (groups129246275422532515t_real @ B @ A) @ (groups129246275422532515t_real @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8747_prod__mono)). 185.47/93.67 thf(10793,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((! [D:nat]: (((ord_less_eq_real @ (B @ D) @ (C @ D)) & (ord_less_eq_real @ zero_zero_real @ (B @ D))) | ~ (member_nat @ D @ A))) => (ord_less_eq_real @ (groups129246275422532515t_real @ (B) @ A) @ (groups129246275422532515t_real @ (C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[895])). 185.47/93.67 thf(1786,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => ((B = (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = ((times_times_rat @ B @ A) = (uminus_uminus_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5965_nonzero__neg__divide__eq__eq2)). 185.47/93.67 thf(13717,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => ((B = (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = ((times_times_rat @ B @ A) = (uminus_uminus_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786])). 185.47/93.67 thf(3911,axiom,((! [A:int]: ~ (ord_less_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3095_verit__comp__simplify1_I1_J)). 185.47/93.67 thf(20558,plain,((! [A:int]: ~ (ord_less_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3911])). 185.47/93.67 thf(565,axiom,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C)))) <= (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7703_powser__split__head_I3_J)). 185.47/93.67 thf(9610,plain,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C)))) | ~ (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[565])). 185.47/93.67 thf(855,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (B = (ord_max_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3662_max_OorderE)). 185.47/93.67 thf(10660,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (B = (ord_max_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[855])). 185.47/93.67 thf(2706,axiom,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C) <= (ord_less_eq_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7501_norm__triangle__le__diff)). 185.47/93.67 thf(16742,plain,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C) | ~ (ord_less_eq_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2706])). 185.47/93.67 thf(5770,axiom,((! [A:nat,B:complex]: ((dvd_dvd_complex @ B @ (power_power_complex @ B @ A)) <= ((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4921_dvd__power)). 185.47/93.67 thf(26928,plain,((! [A:nat,B:complex]: ((dvd_dvd_complex @ B @ (power_power_complex @ B @ A)) | ~ ((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5770])). 185.47/93.67 thf(3143,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => (((divide1717551699836669952omplex @ B @ A) = one_one_complex) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2479_right__inverse__eq)). 185.47/93.67 thf(18121,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => (((divide1717551699836669952omplex @ B @ A) = one_one_complex) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3143])). 185.47/93.67 thf(5252,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (uminus1482373934393186551omplex @ (minus_minus_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5577_minus__diff__minus)). 185.47/93.67 thf(25047,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (uminus1482373934393186551omplex @ (minus_minus_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5252])). 185.47/93.67 thf(6187,axiom,((! [A:vEBT_VEBT,B:nat]: ((((! [C:$o,D:$o]: (((accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (~ (((B = zero_zero_nat) => (C)) & ((B != zero_zero_nat) => (((D) <= (B = one_one_nat)) & (B = one_one_nat)))))) <= (A = (vEBT_Leaf @ C @ D)))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G) @ B)) => (~ ((B != C) => ((~ (ord_less_nat @ B @ C) & ((((((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) <= (~ (ord_less_nat @ D @ B))) & ~ (ord_less_nat @ D @ B)) <= (~ (ord_less_nat @ B @ C)))) <= (B != D))))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G)))))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ A @ B))) <= (vEBT_vebt_member @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3121_vebt__member_Opelims_I2_J)). 185.47/93.67 thf(28548,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:$o,D:$o]: (((accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (~ (((B = zero_zero_nat) => (C)) & ((~ (B = zero_zero_nat)) => (((D) | ~ (B = one_one_nat)) & (B = one_one_nat)))))) | ~ (A = (vEBT_Leaf @ C @ D)))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G) @ B)) => (~ ((~ (B = C)) => ((~ (ord_less_nat @ B @ C) & ((((((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) | (ord_less_nat @ D @ B)) & ~ (ord_less_nat @ D @ B)) | (ord_less_nat @ B @ C))) | (B = D))))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G)))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ A @ B)) | ~ (vEBT_vebt_member @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6187])). 185.47/93.67 thf(1592,axiom,((! [A:real,B:nat,C:real]: (((ord_less_real @ A @ C) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2681_power__less__imp__less__base)). 185.47/93.67 thf(13010,plain,((! [A:real,B:nat,C:real]: ((ord_less_real @ A @ C) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592])). 185.47/93.67 thf(3374,axiom,((neg_numeral_dbl_int = (^ [A:int]: (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3841_dbl__def)). 185.47/93.67 thf(18844,plain,(((neg_numeral_dbl_int) = (^ [A:int]: (plus_plus_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3374])). 185.47/93.67 thf(6763,axiom,(((semiri2265585572941072030t_real @ zero_zero_nat) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7956_fact__0)). 185.47/93.67 thf(30609,plain,(((semiri2265585572941072030t_real @ zero_zero_nat) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6763])). 185.47/93.67 thf(4152,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ A @ zero_zero_real) | (ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ zero_zero_real @ B) | (ord_less_eq_real @ B @ zero_zero_real))) => ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6547_abs__eq__mult)). 185.47/93.67 thf(21296,plain,((! [A:real,B:real]: ((((ord_less_eq_real @ A @ zero_zero_real) | (ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ zero_zero_real @ B) | (ord_less_eq_real @ B @ zero_zero_real))) => ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4152])). 185.47/93.67 thf(4786,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ B @ A)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3146_Euclidean__Division_Opos__mod__sign)). 185.47/93.67 thf(23377,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ B @ A)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4786])). 185.47/93.67 thf(5138,axiom,((! [A:nat]: ~ (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3079_not__exp__less__eq__0__int)). 185.47/93.67 thf(24667,plain,((! [A:nat]: ~ (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5138])). 185.47/93.67 thf(6978,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_vebt_maxt @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1447_vebt__maxt_Osimps_I2_J)). 185.47/93.67 thf(31480,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_vebt_maxt @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6978])). 185.47/93.67 thf(6048,axiom,((! [A:(nat > num),B:nat,C:nat]: (((ord_less_num @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) <= (! [D:nat]: (ord_less_num @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1061_lift__Suc__mono__less__iff)). 185.47/93.67 thf(28035,plain,((! [A:(nat > num),B:nat,C:nat]: (((ord_less_num @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) | ~ (! [D:nat]: (ord_less_num @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6048])). 185.47/93.67 thf(3288,axiom,((! [A:int,B:int]: ((A = (abs_abs_int @ B)) = ((ord_less_eq_int @ zero_zero_int @ A) & ((B = A) | (B = (uminus_uminus_int @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6553_eq__abs__iff_H)). 185.47/93.67 thf(18567,plain,((! [A:int,B:int]: ((A = (abs_abs_int @ B)) = ((ord_less_eq_int @ zero_zero_int @ A) & ((B = A) | (B = (uminus_uminus_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3288])). 185.47/93.67 thf(4077,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5567_add_Oinverse__distrib__swap)). 185.47/93.67 thf(21065,plain,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4077])). 185.47/93.67 thf(7657,axiom,(((finite_card_char @ top_top_set_char) = (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ one))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9974_card__UNIV__char)). 185.47/93.67 thf(33728,plain,(((finite_card_char @ top_top_set_char) = (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ one))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7657])). 185.47/93.67 thf(1065,axiom,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5927_neg__one__le__numeral)). 185.47/93.67 thf(11348,plain,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065])). 185.47/93.67 thf(2929,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (ord_less_eq_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6217_pos__minus__divide__le__eq)). 185.47/93.67 thf(17444,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (ord_less_eq_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2929])). 185.47/93.67 thf(3948,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ (bit_se1409905431419307370or_int @ A @ B)) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9423_OR__lower)). 185.47/93.67 thf(20682,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se1409905431419307370or_int @ A @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3948])). 185.47/93.67 thf(7212,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:option4927543243414619207at_nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (((vEBT_Node @ A @ B @ C @ D) = (vEBT_Node @ E @ F @ G @ H)) = ((C = G) & (D = H) & (B = F) & (A = E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_VEBT_Oinject_I1_J)). 185.47/93.67 thf(32300,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:option4927543243414619207at_nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (((vEBT_Node @ A @ B @ C @ D) = (vEBT_Node @ E @ F @ G @ H)) = ((C = G) & (D = H) & (B = F) & (A = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7212])). 185.47/93.67 thf(5633,axiom,(((semiri2265585572941072030t_real @ (suc @ zero_zero_nat)) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7966_fact__Suc__0)). 185.47/93.67 thf(26480,plain,(((semiri2265585572941072030t_real @ (suc @ zero_zero_nat)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5633])). 185.47/93.67 thf(2032,axiom,((! [A:num]: ((numeral_numeral_real @ (bit1 @ A)) = (plus_plus_real @ (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A)) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6601_numeral__Bit1)). 185.47/93.67 thf(14525,plain,((! [A:num]: ((numeral_numeral_real @ (bit1 @ A)) = (plus_plus_real @ (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A)) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2032])). 185.47/93.67 thf(2656,axiom,(((semiri1314217659103216013at_int @ one_one_nat) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6919_of__nat__1)). 185.47/93.67 thf(16538,plain,(((semiri1314217659103216013at_int @ one_one_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2656])). 185.47/93.67 thf(6150,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_add_Oleft__commute)). 185.47/93.67 thf(28386,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6150])). 185.47/93.67 thf(1760,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((((ord_less_int @ C @ A) => ((ord_less_eq_int @ B @ D) <= (ord_less_int @ E @ A))) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ A @ D) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3165_unique__quotient__lemma)). 185.47/93.67 thf(13630,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_int @ C @ A) => ((ord_less_eq_int @ B @ D) | ~ (ord_less_int @ E @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_eq_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ A @ D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760])). 185.47/93.67 thf(2390,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2367_mult__strict__right__mono)). 185.47/93.67 thf(15635,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2390])). 185.47/93.67 thf(1528,axiom,((! [A:real]: ((real_V1022390504157884413omplex @ (complex2 @ (cos_real @ A) @ (sin_real @ A))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7981_norm__cos__sin)). 185.47/93.67 thf(12802,plain,((! [A:real]: ((real_V1022390504157884413omplex @ (complex2 @ (cos_real @ A) @ (sin_real @ A))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528])). 185.47/93.67 thf(5009,axiom,(((neg_nu8557863876264182079omplex @ one_one_complex) = (numera6690914467698888265omplex @ (bit1 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6848_dbl__inc__simps_I3_J)). 185.47/93.67 thf(24132,plain,(((neg_nu8557863876264182079omplex @ one_one_complex) = (numera6690914467698888265omplex @ (bit1 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5009])). 185.47/93.67 thf(4291,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3091_verit__comp__simplify1_I1_J)). 185.47/93.67 thf(21718,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4291])). 185.47/93.67 thf(6574,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit1 @ A) @ (bit0 @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6418_semiring__norm_I74_J)). 185.47/93.67 thf(29921,plain,((! [A:num,B:num]: ((ord_less_eq_num @ (bit1 @ A) @ (bit0 @ B)) = (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6574])). 185.47/93.67 thf(3001,axiom,((! [A:complex,B:complex,C:complex]: ((A = (plus_plus_complex @ B @ C)) => ((uminus1482373934393186551omplex @ A) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5562_group__cancel_Oneg1)). 185.47/93.67 thf(17679,plain,((! [A:complex,B:complex,C:complex]: ((A = (plus_plus_complex @ B @ C)) => ((uminus1482373934393186551omplex @ A) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3001])). 185.47/93.67 thf(5209,axiom,((! [A:nat,B:nat,C:nat]: ((((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_751_Nat_Odiff__diff__eq)). 185.47/93.67 thf(24900,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5209])). 185.47/93.67 thf(5317,axiom,((! [A:num,B:num]: ((ord_less_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_numeral__less__iff)). 185.47/93.67 thf(25297,plain,((! [A:num,B:num]: ((ord_less_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5317])). 185.47/93.67 thf(2251,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4063_order__less__asym_H)). 185.47/93.67 thf(15216,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2251])). 185.47/93.67 thf(5910,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_add__less__imp__less__right)). 185.47/93.67 thf(27571,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5910])). 185.47/93.67 thf(2566,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C)) => (ord_less_eq_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_add__le__imp__le__left)). 185.47/93.67 thf(16238,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C)) => (ord_less_eq_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2566])). 185.47/93.67 thf(6784,axiom,((! [A:num]: ((abs_abs_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6333_abs__numeral)). 185.47/93.67 thf(30682,plain,((! [A:num]: ((abs_abs_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6784])). 185.47/93.67 thf(6842,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (power_power_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8101_fact__div__fact__le__pow)). 185.47/93.67 thf(30874,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (power_power_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6842])). 185.47/93.67 thf(2511,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ C @ A) => (ord_less_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4034_dual__order_Ostrict__trans)). 185.47/93.67 thf(16057,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ C @ A) => (ord_less_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2511])). 185.47/93.67 thf(3551,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ A) @ (sqrt @ (plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8243_real__sqrt__ge__abs2)). 185.47/93.67 thf(19404,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ A) @ (sqrt @ (plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3551])). 185.47/93.67 thf(7416,axiom,((! [A:nat]: ((times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A) @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A)) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5297_minus__one__mult__self)). 185.47/93.67 thf(32996,plain,((! [A:nat]: ((times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A) @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A)) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7416])). 185.47/93.67 thf(7625,axiom,((! [A:nat]: ((bit_se4205575877204974255it_nat @ zero_zero_nat @ A) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3028_unset__bit__0)). 185.47/93.67 thf(33645,plain,((! [A:nat]: ((bit_se4205575877204974255it_nat @ zero_zero_nat @ A) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7625])). 185.47/93.67 thf(5723,axiom,((! [A:rat,B:nat]: ((power_power_rat @ A @ (suc @ B)) = (times_times_rat @ (power_power_rat @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_power__Suc2)). 185.47/93.67 thf(26780,plain,((! [A:rat,B:nat]: ((power_power_rat @ A @ (suc @ B)) = (times_times_rat @ (power_power_rat @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5723])). 185.47/93.67 thf(6876,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => (((times_times_real @ B @ A) = (times_times_real @ C @ A)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2064_mult__right__cancel)). 185.47/93.67 thf(31054,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => (((times_times_real @ B @ A) = (times_times_real @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6876])). 185.47/93.67 thf(3797,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (divide_divide_real @ A @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8265_cos__x__y__le__one)). 185.47/93.67 thf(20201,plain,((! [A:real,B:real]: (ord_less_eq_real @ (abs_abs_real @ (divide_divide_real @ A @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3797])). 185.47/93.67 thf(5546,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (! [D:nat]: ((A @ D) <= (B = (plus_plus_nat @ C @ D))) & ((A @ zero_zero_nat) <= (ord_less_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2794_nat__diff__split)). 185.47/93.67 thf(26200,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (! [D:nat]: ((A @ D) | ~ (B = (plus_plus_nat @ C @ D))) & ((A @ zero_zero_nat) | ~ (ord_less_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5546])). 185.47/93.67 thf(1034,axiom,((! [A:nat,B:int]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7178_of__nat__less__of__int__iff)). 185.47/93.67 thf(11262,plain,((! [A:nat,B:int]: ((ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034])). 185.47/93.67 thf(2374,axiom,((! [A:list_VEBT_VEBT,B:vEBT_VEBT]: ((! [C:vEBT_VEBT]: ((member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A)) => (C = B))) => ((replicate_VEBT_VEBT @ (size_s6755466524823107622T_VEBT @ A) @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5797_replicate__length__same)). 185.47/93.67 thf(15588,plain,((! [A:list_VEBT_VEBT,B:vEBT_VEBT]: ((! [C:vEBT_VEBT]: ((member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A)) => (C = B))) => ((replicate_VEBT_VEBT @ (size_s6755466524823107622T_VEBT @ A) @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2374])). 185.47/93.67 thf(3455,axiom,((! [A:rat]: ((divide_divide_rat @ A @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5216_divide__minus1)). 185.47/93.67 thf(19093,plain,((! [A:rat]: ((divide_divide_rat @ A @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3455])). 185.47/93.67 thf(2146,axiom,((! [A:int]: ((~ ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) != one_one_int))) <= ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4966_parity__cases)). 185.47/93.67 thf(14876,plain,((! [A:int]: (~ ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => (~ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int))) | ~ ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => (~ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2146])). 185.47/93.67 thf(2009,axiom,((gbinomial_rat = (^ [A:rat,B:nat]: (divide_divide_rat @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ B) @ (semiri773545260158071498ct_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8458_gbinomial__pochhammer_H)). 185.47/93.67 thf(14453,plain,(((gbinomial_rat) = (^ [A:rat,B:nat]: (divide_divide_rat @ (comm_s4028243227959126397er_rat @ (plus_plus_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ B) @ (semiri773545260158071498ct_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2009])). 185.47/93.67 thf(4233,axiom,((! [A:real,B:real,C:(real > rat),D:rat]: ((((! [E:real,F:real]: ((ord_less_rat @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))) => (ord_less_rat @ (C @ A) @ D)) <= (ord_less_rat @ (C @ B) @ D)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4109_order__less__subst2)). 185.47/93.67 thf(21545,plain,((! [A:real,B:real,C:(real > rat),D:rat]: (((! [E:real,F:real]: ((ord_less_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))) => (ord_less_rat @ (C @ A) @ D)) | ~ (ord_less_rat @ (C @ B) @ D) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4233])). 185.47/93.67 thf(2747,axiom,((ord_less_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_4182_less__le__not__le)). 185.47/93.67 thf(16863,plain,(((ord_less_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)],[2747])). 185.47/93.67 thf(4241,axiom,((! [A:int,B:nat]: (((bit_se2925701944663578781it_nat @ B @ (nat2 @ A)) = (nat2 @ (bit_se2923211474154528505it_int @ B @ A))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9271_take__bit__nat__eq)). 185.47/93.67 thf(21571,plain,((! [A:int,B:nat]: (((bit_se2925701944663578781it_nat @ B @ (nat2 @ A)) = (nat2 @ (bit_se2923211474154528505it_int @ B @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4241])). 185.47/93.67 thf(301,axiom,((! [A:(real > (real > $o)),B:set_nat,C:(nat > real),D:(nat > real)]: ((A @ one_one_real @ one_one_real) => ((((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups129246275422532515t_real @ C @ B) @ (groups129246275422532515t_real @ D @ B))) <= (finite_finite_nat @ B)) <= (! [E:real,F:real,G:real,H:real]: (((A @ F @ H) & (A @ E @ G)) => (A @ (times_times_real @ E @ F) @ (times_times_real @ G @ H)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8807_prod_Orelated)). 185.47/93.67 thf(8719,plain,((! [A:(real > (real > $o)),B:set_nat,C:(nat > real),D:(nat > real)]: ((A @ one_one_real @ one_one_real) => (((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups129246275422532515t_real @ (C) @ B) @ (groups129246275422532515t_real @ (D) @ B))) | ~ (finite_finite_nat @ B) | ~ (! [E:real,F:real,G:real,H:real]: (((A @ F @ H) & (A @ E @ G)) => (A @ (times_times_real @ E @ F) @ (times_times_real @ G @ H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 185.47/93.67 thf(179,axiom,((! [A:(nat > real),B:real]: (((suminf_real @ (^ [C:nat]: (times_times_real @ B @ (A @ C)))) = (times_times_real @ B @ (suminf_real @ A))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7676_suminf__mult)). 185.47/93.67 thf(8308,plain,((! [A:(nat > real),B:real]: (((suminf_real @ (^ [C:nat]: (times_times_real @ B @ (A @ C)))) = (times_times_real @ B @ (suminf_real @ (A)))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 185.47/93.67 thf(686,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_real @ (log @ A @ B) @ C) = (ord_less_real @ B @ (powr_real @ A @ C))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9108_log__less__iff)). 185.47/93.67 thf(10020,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_real @ (log @ A @ B) @ C) = (ord_less_real @ B @ (powr_real @ A @ C))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[686])). 185.47/93.67 thf(1374,axiom,((! [A:real]: (((ord_less_eq_real @ (sin_real @ A) @ zero_zero_real) <= (ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) <= (ord_less_eq_real @ pi @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7922_sin__le__zero)). 185.47/93.67 thf(12309,plain,((! [A:real]: ((ord_less_eq_real @ (sin_real @ A) @ zero_zero_real) | ~ (ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) | ~ (ord_less_eq_real @ pi @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374])). 185.47/93.67 thf(1176,axiom,((! [A:nat,B:vEBT_VEBT,C:nat,D:vEBT_VEBT]: (((replicate_VEBT_VEBT @ A @ B) = (replicate_VEBT_VEBT @ C @ D)) = ((A = C) & ((B = D) <= (A != zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5130_replicate__eq__replicate)). 185.47/93.67 thf(11701,plain,((! [A:nat,B:vEBT_VEBT,C:nat,D:vEBT_VEBT]: (((replicate_VEBT_VEBT @ A @ B) = (replicate_VEBT_VEBT @ C @ D)) = ((A = C) & ((B = D) | (A = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176])). 185.47/93.67 thf(7376,axiom,((! [A:(nat > num),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_num @ (A @ B) @ (A @ C))) <= (! [D:nat]: (ord_less_eq_num @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1076_lift__Suc__mono__le)). 185.47/93.67 thf(32846,plain,((! [A:(nat > num),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_num @ (A @ B) @ (A @ C))) | ~ (! [D:nat]: (ord_less_eq_num @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7376])). 185.47/93.67 thf(3614,axiom,((bit_se4203085406695923979it_int = (^ [A:nat,B:int]: (minus_minus_int @ B @ (times_times_int @ (zero_n2684676970156552555ol_int @ (bit_se1146084159140164899it_int @ B @ A)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9442_unset__bit__eq)). 185.47/93.67 thf(19602,plain,(((bit_se4203085406695923979it_int) = (^ [A:nat,B:int]: (minus_minus_int @ B @ (times_times_int @ (zero_n2684676970156552555ol_int @ (bit_se1146084159140164899it_int @ B @ A)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3614])). 185.47/93.67 thf(1998,axiom,((! [A:real,B:real]: (((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2429_divide__neg__pos)). 185.47/93.67 thf(14412,plain,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1998])). 185.47/93.67 thf(1484,axiom,((! [A:real,B:real]: ? [C:real]: ! [D:real]: (((dvd_dvd_real @ A @ (plus_plus_real @ D @ B)) = (dvd_dvd_real @ A @ (plus_plus_real @ D @ B))) <= (ord_less_real @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4719_pinf_I9_J)). 185.47/93.67 thf(12672,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1484])). 185.47/93.67 thf(4311,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ C) <= (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4595_dvd__mult__left)). 185.47/93.67 thf(21776,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ C) | ~ (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4311])). 185.47/93.67 thf(5051,axiom,((! [A:nat,B:int]: ((times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A) @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5302_left__minus__one__mult__self)). 185.47/93.67 thf(24332,plain,((! [A:nat,B:int]: ((times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A) @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5051])). 185.47/93.67 thf(3011,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((ord_less_int @ A @ B) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4232_dual__order_Oorder__iff__strict)). 185.47/93.67 thf(17708,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((ord_less_int @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3011])). 185.47/93.67 thf(2716,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ B @ A) | (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4362_linorder__le__less__linear)). 185.47/93.67 thf(16770,plain,((! [A:rat,B:rat]: ((ord_less_rat @ B @ A) | (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2716])). 185.47/93.67 thf(1911,axiom,((! [A:rat,B:rat,C:num]: ((ord_less_rat @ A @ (divide_divide_rat @ B @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)))) = (ord_less_rat @ B @ (times_times_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5394_less__divide__eq__numeral1_I2_J)). 185.47/93.67 thf(14115,plain,((! [A:rat,B:rat,C:num]: ((ord_less_rat @ A @ (divide_divide_rat @ B @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)))) = (ord_less_rat @ B @ (times_times_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911])). 185.47/93.67 thf(3629,axiom,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: (((plus_plus_rat @ (times_times_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = ((plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ A @ D) @ B) @ C) = E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1222_eq__add__iff1)). 185.47/93.67 thf(19648,plain,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: (((plus_plus_rat @ (times_times_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ D @ B) @ E)) = ((plus_plus_rat @ (times_times_rat @ (minus_minus_rat @ A @ D) @ B) @ C) = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3629])). 185.47/93.67 thf(2782,axiom,((! [A:num]: ~ (ord_less_rat @ (numeral_numeral_rat @ A) @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_821_not__numeral__less__one)). 185.47/93.67 thf(16970,plain,((! [A:num]: ~ (ord_less_rat @ (numeral_numeral_rat @ A) @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2782])). 185.47/93.67 thf(4494,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (minus_minus_int @ C @ B)) <= (ord_less_eq_int @ (plus_plus_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1202_add__le__imp__le__diff)). 185.47/93.67 thf(22387,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (minus_minus_int @ C @ B)) | ~ (ord_less_eq_int @ (plus_plus_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4494])). 185.47/93.67 thf(3218,axiom,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ A) @ B)) = (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7475_norm__uminus__minus)). 185.47/93.67 thf(18363,plain,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ A) @ B)) = (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3218])). 185.47/93.67 thf(107,axiom,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7550_sum_OlessThan__Suc)). 185.47/93.67 thf(8084,plain,((! [A:(nat > rat),B:nat]: ((groups2906978787729119204at_rat @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 185.47/93.67 thf(2990,axiom,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (plus_plus_rat @ A @ B)) = (plus_plus_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5558_is__num__normalize_I8_J)). 185.47/93.67 thf(17647,plain,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (plus_plus_rat @ A @ B)) = (plus_plus_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2990])). 185.47/93.67 thf(929,axiom,((! [A:nat,B:nat,C:rat]: ((ord_less_eq_nat @ A @ B) => ((times_times_rat @ (minus_minus_rat @ one_one_rat @ C) @ (groups2906978787729119204at_rat @ (power_power_rat @ C) @ (set_or1269000886237332187st_nat @ A @ B))) = (minus_minus_rat @ (power_power_rat @ C @ A) @ (power_power_rat @ C @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6746_sum__gp__multiplied)). 185.47/93.67 thf(10925,plain,((! [A:nat,B:nat,C:rat]: ((ord_less_eq_nat @ A @ B) => ((times_times_rat @ (minus_minus_rat @ one_one_rat @ C) @ (groups2906978787729119204at_rat @ (power_power_rat @ C) @ (set_or1269000886237332187st_nat @ A @ B))) = (minus_minus_rat @ (power_power_rat @ C @ A) @ (power_power_rat @ C @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[929])). 185.47/93.67 thf(5024,axiom,((! [A:int]: (((uminus_uminus_int @ A) = A) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5038_neg__equal__zero)). 185.47/93.67 thf(24175,plain,((! [A:int]: (((uminus_uminus_int @ A) = A) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5024])). 185.47/93.67 thf(3792,axiom,((bit_se727722235901077358nd_nat = (^ [A:nat,B:nat]: (nat2 @ (bit_se725231765392027082nd_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9399_and__nat__def)). 185.47/93.67 thf(20186,plain,(((bit_se727722235901077358nd_nat) = (^ [A:nat,B:nat]: (nat2 @ (bit_se725231765392027082nd_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3792])). 185.47/93.67 thf(6234,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (modulo_modulo_nat @ A @ B) @ B) = (modulo_modulo_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1475_mod__mod__trivial)). 185.47/93.67 thf(28711,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (modulo_modulo_nat @ A @ B) @ B) = (modulo_modulo_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6234])). 185.47/93.67 thf(3208,axiom,((! [A:code_integer,B:nat]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ B) = (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (power_8256067586552552935nteger @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5997_power__minus)). 185.47/93.67 thf(18335,plain,((! [A:code_integer,B:nat]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ B) = (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (power_8256067586552552935nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3208])). 185.47/93.67 thf(7719,axiom,((! [A:num]: (one != (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_semiring__norm_I83_J)). 185.47/93.67 thf(33894,plain,((! [A:num]: ~ (one = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7719])). 185.47/93.67 thf(6690,axiom,((! [A:nat,B:nat,C:real]: ((root @ (times_times_nat @ A @ B) @ C) = (root @ A @ (root @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9176_real__root__mult__exp)). 185.47/93.67 thf(30295,plain,((! [A:nat,B:nat,C:real]: ((root @ (times_times_nat @ A @ B) @ C) = (root @ A @ (root @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6690])). 185.47/93.67 thf(891,axiom,((! [A:complex]: (A = (plus_plus_complex @ (real_V4546457046886955230omplex @ (re @ A)) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (im @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9688_complex__eq)). 185.47/93.67 thf(10782,plain,((! [A:complex]: (A = (plus_plus_complex @ (real_V4546457046886955230omplex @ (re @ A)) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (im @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[891])). 185.47/93.67 thf(671,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (ord_max_int @ B @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3712_max_OcoboundedI1)). 185.47/93.67 thf(9975,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (ord_max_int @ B @ C)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[671])). 185.47/93.67 thf(702,axiom,((ord_max_int = (^ [A:int,B:int]: (if_int @ (ord_less_eq_int @ A @ B) @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4415_max__def)). 185.47/93.67 thf(10076,plain,(((ord_max_int) = (^ [A:int,B:int]: (if_int @ (ord_less_eq_int @ A @ B) @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[702])). 185.47/93.67 thf(983,axiom,((! [A:int,B:rat]: (((A = zero_zero_int) | (ord_less_rat @ one_one_rat @ B)) <= (ord_less_rat @ (abs_abs_rat @ (ring_1_of_int_rat @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7290_of__int__lessD)). 185.47/93.67 thf(11102,plain,((! [A:int,B:rat]: ((A = zero_zero_int) | (ord_less_rat @ one_one_rat @ B) | ~ (ord_less_rat @ (abs_abs_rat @ (ring_1_of_int_rat @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[983])). 185.47/93.67 thf(1673,axiom,((! [A:complex,B:complex]: ((one_one_complex = (divide1717551699836669952omplex @ A @ B)) = ((A = B) & (B != zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1735_one__eq__divide__iff)). 185.47/93.67 thf(13339,plain,((! [A:complex,B:complex]: ((one_one_complex = (divide1717551699836669952omplex @ A @ B)) = ((A = B) & ~ (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673])). 185.47/93.67 thf(4972,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) = (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4736_mult__unit__dvd__iff_H)). 185.47/93.67 thf(24003,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) = (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4972])). 185.47/93.67 thf(457,axiom,((! [A:nat,B:nat,C:(nat > rat)]: ((ord_less_eq_nat @ A @ B) => ((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (C @ D) @ (C @ (minus_minus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (minus_minus_rat @ (C @ B) @ (C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6740_sum__telescope_H_H)). 185.47/93.67 thf(9249,plain,((! [A:nat,B:nat,C:(nat > rat)]: ((ord_less_eq_nat @ A @ B) => ((groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (C @ D) @ (C @ (minus_minus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (minus_minus_rat @ (C @ B) @ (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])). 185.47/93.67 thf(6850,axiom,((! [A:num]: (ord_less_num @ one @ (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6393_semiring__norm_I77_J)). 185.47/93.67 thf(30935,plain,((! [A:num]: (ord_less_num @ one @ (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6850])). 185.47/93.67 thf(7472,axiom,((! [A:nat]: ((root @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9155_real__root__zero)). 185.47/93.67 thf(33183,plain,((! [A:nat]: ((root @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7472])). 185.47/93.67 thf(526,axiom,(((arccos @ zero_zero_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8361_arccos__0)). 185.47/93.67 thf(9492,plain,(((arccos @ zero_zero_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[526])). 185.47/93.67 thf(5985,axiom,((! [A:nat,B:(nat > $o),C:nat]: ((! [D:nat]: ((ord_less_nat @ A @ D) => (B @ D))) => ((B @ C) <= (! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((! [E:nat]: ((B @ E) <= (ord_less_nat @ D @ E))) => (B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9799_nat__descend__induct)). 185.47/93.67 thf(27841,plain,((! [A:nat,B:(nat > $o),C:nat]: ((! [D:nat]: ((ord_less_nat @ A @ D) => (B @ D))) => ((B @ C) | ~ (! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((! [E:nat]: ((B @ E) | ~ (ord_less_nat @ D @ E))) => (B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5985])). 185.47/93.67 thf(7306,axiom,((! [A:nat]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = one_one_Code_integer) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5469_neg__one__even__power)). 185.47/93.67 thf(32617,plain,((! [A:nat]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = one_one_Code_integer) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7306])). 185.47/93.67 thf(5645,axiom,((! [A:complex]: ((exp_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (power_power_complex @ (exp_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8234_exp__double)). 185.47/93.67 thf(26519,plain,((! [A:complex]: ((exp_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (power_power_complex @ (exp_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5645])). 185.47/93.67 thf(489,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (ln_ln_real @ A)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5879_ln__gt__zero)). 185.47/93.67 thf(9381,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (ln_ln_real @ A)) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[489])). 185.47/93.67 thf(1028,axiom,((! [A:complex,B:nat,C:complex,D:nat]: ((dvd_dvd_complex @ (power_power_complex @ A @ B) @ C) => ((ord_less_eq_nat @ D @ B) => (dvd_dvd_complex @ (power_power_complex @ A @ D) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4795_power__le__dvd)). 185.47/93.67 thf(11245,plain,((! [A:complex,B:nat,C:complex,D:nat]: ((dvd_dvd_complex @ (power_power_complex @ A @ B) @ C) => ((ord_less_eq_nat @ D @ B) => (dvd_dvd_complex @ (power_power_complex @ A @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028])). 185.47/93.67 thf(6191,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_real @ (power_power_real @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2964_power__minus__mult)). 185.47/93.67 thf(28580,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_real @ (power_power_real @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6191])). 185.47/93.67 thf(5669,axiom,(((abs_abs_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6344_abs__1)). 185.47/93.67 thf(26601,plain,(((abs_abs_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5669])). 185.47/93.67 thf(7311,axiom,(((^ [A:int]: (zero_zero_int)) = (times_times_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2150_lambda__zero)). 185.47/93.67 thf(32640,plain,(((^ [A:int]: (zero_zero_int)) = (times_times_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7311])). 185.47/93.67 thf(3966,axiom,((! [A:code_integer]: (((times_3573771949741848930nteger @ A @ A) = one_one_Code_integer) = ((A = (uminus1351360451143612070nteger @ one_one_Code_integer)) | (A = one_one_Code_integer))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5781_square__eq__1__iff)). 185.47/93.67 thf(20731,plain,((! [A:code_integer]: (((times_3573771949741848930nteger @ A @ A) = one_one_Code_integer) = ((A = (uminus1351360451143612070nteger @ one_one_Code_integer)) | (A = one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3966])). 185.47/93.67 thf(4740,axiom,((ord_less_int = (^ [A:int]: (ord_less_eq_int @ (plus_plus_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1461_discrete)). 185.47/93.67 thf(23202,plain,(((ord_less_int) = (^ [A:int]: (ord_less_eq_int @ (plus_plus_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4740])). 185.47/93.67 thf(3736,axiom,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5932_neg__numeral__le__neg__one)). 185.47/93.67 thf(20000,plain,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3736])). 185.47/93.67 thf(3655,axiom,(((code_integer_of_num @ one) = one_one_Code_integer)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9622_integer__of__num__triv_I1_J)). 185.47/93.67 thf(19734,plain,(((code_integer_of_num @ one) = one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3655])). 185.47/93.67 thf(3135,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4044_dual__order_Ostrict__implies__not__eq)). 185.47/93.67 thf(18099,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3135])). 185.47/93.67 thf(5089,axiom,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2277_zero__less__one__class_Ozero__le__one)). 185.47/93.67 thf(24456,plain,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5089])). 185.47/93.67 thf(1234,axiom,((! [A:num]: ((bitM @ (bit1 @ A)) = (bit1 @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8964_semiring__norm_I28_J)). 185.47/93.67 thf(11874,plain,((! [A:num]: ((bitM @ (bit1 @ A)) = (bit1 @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234])). 185.47/93.67 thf(2349,axiom,((! [A:int,B:num,C:nat]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (numeral_numeral_real @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7141_of__int__less__numeral__power__cancel__iff)). 185.47/93.67 thf(15511,plain,((! [A:int,B:num,C:nat]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (numeral_numeral_real @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2349])). 185.47/93.67 thf(1076,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2209_mult__nonpos__nonneg)). 185.47/93.67 thf(11380,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076])). 185.47/93.67 thf(6262,axiom,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ (suc @ B)) = (~ (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9414_bit__minus__numeral__Bit1__Suc__iff)). 185.47/93.67 thf(28802,plain,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ (suc @ B)) = (~ (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6262])). 185.47/93.67 thf(4870,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ A @ C) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2607_mult__right__le__imp__le)). 185.47/93.67 thf(23641,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ C) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4870])). 185.47/93.67 thf(7294,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((divide_divide_nat @ C @ (times_times_nat @ A @ B)) = (divide_divide_nat @ (divide_divide_nat @ C @ A) @ B)) <= (dvd_dvd_nat @ B @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4871_is__unit__div__mult2__eq)). 185.47/93.67 thf(32581,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((divide_divide_nat @ C @ (times_times_nat @ A @ B)) = (divide_divide_nat @ (divide_divide_nat @ C @ A) @ B)) | ~ (dvd_dvd_nat @ B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7294])). 185.47/93.67 thf(23,axiom,((! [A:complex,B:nat,C:complex]: ((minus_minus_complex @ (power_power_complex @ A @ (suc @ B)) @ (power_power_complex @ C @ (suc @ B))) = (times_times_complex @ (minus_minus_complex @ A @ C) @ (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (power_power_complex @ A @ D) @ (power_power_complex @ C @ (minus_minus_nat @ B @ D)))) @ (set_ord_lessThan_nat @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7612_diff__power__eq__sum)). 185.47/93.67 thf(7805,plain,((! [A:complex,B:nat,C:complex]: ((minus_minus_complex @ (power_power_complex @ A @ (suc @ B)) @ (power_power_complex @ C @ (suc @ B))) = (times_times_complex @ (minus_minus_complex @ A @ C) @ (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (power_power_complex @ A @ D) @ (power_power_complex @ C @ (minus_minus_nat @ B @ D)))) @ (set_ord_lessThan_nat @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 185.47/93.67 thf(71,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_real @ (A @ zero_zero_nat) @ (groups6591440286371151544t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7582_sum_OlessThan__Suc__shift)). 185.47/93.67 thf(7960,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_real @ (A @ zero_zero_nat) @ (groups6591440286371151544t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 185.47/93.67 thf(4114,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = (~ (ord_less_eq_int @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4165_nless__le)). 185.47/93.67 thf(21183,plain,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = (~ (ord_less_eq_int @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4114])). 185.47/93.67 thf(3820,axiom,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (numeral_numeral_real @ C)) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ C) @ B) @ A)) & ((ord_less_eq_real @ zero_zero_real @ (numeral_numeral_real @ C)) <= (~ (ord_less_real @ B @ zero_zero_real))))) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ (times_times_real @ (numeral_numeral_real @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2923_divide__le__eq__numeral_I1_J)). 185.47/93.67 thf(20270,plain,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (numeral_numeral_real @ C)) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ C) @ B) @ A)) & ((ord_less_eq_real @ zero_zero_real @ (numeral_numeral_real @ C)) | (ord_less_real @ B @ zero_zero_real)))) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ (times_times_real @ (numeral_numeral_real @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3820])). 185.47/93.67 thf(6484,axiom,((! [A:nat,B:(nat > $o)]: ((ord_less_nat @ zero_zero_nat @ A) => (((B @ A) <= (! [C:nat]: (((B @ C) => (B @ (suc @ C))) <= (ord_less_nat @ zero_zero_nat @ C)))) <= (B @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2788_nat__induct__non__zero)). 185.47/93.67 thf(29606,plain,((! [A:nat,B:(nat > $o)]: ((ord_less_nat @ zero_zero_nat @ A) => ((B @ A) | ~ (! [C:nat]: (((B @ C) => (B @ (suc @ C))) | ~ (ord_less_nat @ zero_zero_nat @ C))) | ~ (B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6484])). 185.47/93.67 thf(5840,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (divide_divide_nat @ B @ A) @ C) = (dvd_dvd_nat @ B @ C)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4772_div__unit__dvd__iff)). 185.47/93.67 thf(27335,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (divide_divide_nat @ B @ A) @ C) = (dvd_dvd_nat @ B @ C)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5840])). 185.47/93.67 thf(7510,axiom,((! [A:nat]: ((ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) => ((A = zero_zero_nat) | (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2956_less__2__cases)). 185.47/93.67 thf(33316,plain,((! [A:nat]: ((ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) => ((A = zero_zero_nat) | (A = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7510])). 185.47/93.67 thf(2847,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((A = zero_zero_real) <= ((sqrt @ A) = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8166_real__sqrt__eq__zero__cancel)). 185.47/93.67 thf(17183,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((A = zero_zero_real) | ~ ((sqrt @ A) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2847])). 185.47/93.67 thf(138,axiom,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) != zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7757_pi__half__neq__zero)). 185.47/93.67 thf(8175,plain,((~ ((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 185.47/93.67 thf(3775,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ A)) = (divide1717551699836669952omplex @ B @ C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1702_nonzero__mult__divide__mult__cancel__left2)). 185.47/93.67 thf(20132,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ A)) = (divide1717551699836669952omplex @ B @ C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3775])). 185.47/93.67 thf(7556,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_mult__numeral__1)). 185.47/93.67 thf(33451,plain,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7556])). 185.47/93.67 thf(3080,axiom,((! [A:real]: ((ord_less_real @ (sqrt @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8122_real__sqrt__lt__0__iff)). 185.47/93.67 thf(17921,plain,((! [A:real]: ((ord_less_real @ (sqrt @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3080])). 185.47/93.67 thf(5269,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_le__eq__less__or__eq)). 185.47/93.67 thf(25142,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5269])). 185.47/93.67 thf(3585,axiom,((! [A:num]: ((ord_max_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3613_max__0__1_I4_J)). 185.47/93.67 thf(19516,plain,((! [A:num]: ((ord_max_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3585])). 185.47/93.67 thf(2440,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4227_dual__order_Oorder__iff__strict)). 185.47/93.67 thf(15814,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2440])). 185.47/93.67 thf(6989,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9272_take__bit__nat__less__eq__self)). 185.47/93.67 thf(31512,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6989])). 185.47/93.67 thf(4575,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_rat @ C @ A) => (ord_less_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4241_dual__order_Ostrict__trans1)). 185.47/93.67 thf(22657,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_rat @ C @ A) => (ord_less_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4575])). 185.47/93.67 thf(4108,axiom,((! [A:int,B:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ B) = (ord_less_int @ (uminus_uminus_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5523_minus__less__iff)). 185.47/93.67 thf(21166,plain,((! [A:int,B:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ B) = (ord_less_int @ (uminus_uminus_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4108])). 185.47/93.67 thf(7151,axiom,((! [A:nat,B:int]: (((ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ B) @ (minus_minus_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9353_take__bit__int__less__eq)). 185.47/93.67 thf(32089,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ B) @ (minus_minus_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7151])). 185.47/93.67 thf(485,axiom,((! [A:complex]: ((re @ (times_times_complex @ imaginary_unit @ A)) = (uminus_uminus_real @ (im @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9665_Re__i__times)). 185.47/93.67 thf(9366,plain,((! [A:complex]: ((re @ (times_times_complex @ imaginary_unit @ A)) = (uminus_uminus_real @ (im @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[485])). 185.47/93.67 thf(1515,axiom,((! [A:real,B:num,C:real]: (((divide_divide_real @ A @ (numeral_numeral_real @ B)) = C) = ((((numeral_numeral_real @ B) != zero_zero_real) => (A = (times_times_real @ C @ (numeral_numeral_real @ B)))) & (((numeral_numeral_real @ B) = zero_zero_real) => (C = zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1824_divide__eq__eq__numeral1_I1_J)). 185.47/93.67 thf(12765,plain,((! [A:real,B:num,C:real]: (((divide_divide_real @ A @ (numeral_numeral_real @ B)) = C) = (((~ ((numeral_numeral_real @ B) = zero_zero_real)) => (A = (times_times_real @ C @ (numeral_numeral_real @ B)))) & (((numeral_numeral_real @ B) = zero_zero_real) => (C = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515])). 185.47/93.67 thf(698,axiom,((! [A:nat,B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (gbinomial_rat @ (semiri681578069525770553at_rat @ C) @ A)) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (gbinomial_rat @ (plus_plus_rat @ (semiri681578069525770553at_rat @ B) @ one_one_rat) @ (plus_plus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8596_gbinomial__sum__up__index)). 185.47/93.67 thf(10063,plain,((! [A:nat,B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (gbinomial_rat @ (semiri681578069525770553at_rat @ C) @ A)) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (gbinomial_rat @ (plus_plus_rat @ (semiri681578069525770553at_rat @ B) @ one_one_rat) @ (plus_plus_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[698])). 185.47/93.67 thf(2850,axiom,(((('!') @ nat) = (^ [A:(nat > $o)]: ! [B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => (A @ (nat2 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9284_all__nat)). 185.47/93.67 thf(17191,plain,(((('!') @ nat) = (^ [A:(nat > $o)]: ! [B:int]: ((ord_less_eq_int @ zero_zero_int @ B) => (A @ (nat2 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2850])). 185.47/93.67 thf(6381,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_diff__commute)). 185.47/93.67 thf(29217,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6381])). 185.47/93.67 thf(1142,axiom,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ A @ B) = (plus_plus_rat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_add_Oleft__cancel)). 185.47/93.67 thf(11605,plain,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ A @ B) = (plus_plus_rat @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142])). 185.47/93.67 thf(5576,axiom,((! [A:rat]: ((times_times_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ one))) = (uminus_uminus_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5983_mult__1s__ring__1_I2_J)). 185.47/93.67 thf(26290,plain,((! [A:rat]: ((times_times_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ one))) = (uminus_uminus_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5576])). 185.47/93.67 thf(1403,axiom,((! [A:int,B:int]: ((A = (uminus_uminus_int @ B)) = ((plus_plus_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5739_eq__neg__iff__add__eq__0)). 185.47/93.67 thf(12409,plain,((! [A:int,B:int]: ((A = (uminus_uminus_int @ B)) = ((plus_plus_int @ A @ B) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403])). 185.47/93.67 thf(3309,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6281_add__0__iff)). 185.47/93.67 thf(18637,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3309])). 185.47/93.67 thf(4849,axiom,((! [A:real]: ((ord_less_eq_real @ (sgn_sgn_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9244_sgn__le__0__iff)). 185.47/93.67 thf(23572,plain,((! [A:real]: ((ord_less_eq_real @ (sgn_sgn_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4849])). 185.47/93.67 thf(5450,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((plus_plus_nat @ (times_times_nat @ B @ C) @ D) = (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = ((plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) = E)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_853_nat__eq__add__iff1)). 185.47/93.67 thf(25793,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((plus_plus_nat @ (times_times_nat @ B @ C) @ D) = (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = ((plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) = E)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5450])). 185.47/93.67 thf(4507,axiom,((! [A:int,B:(int > $o),C:int]: ((ord_less_int @ zero_zero_int @ A) => (((ord_less_eq_int @ zero_zero_int @ C) => (! [D:int]: ((B @ (plus_plus_int @ D @ (times_times_int @ C @ A))) <= (B @ D)))) <= (! [D:int]: ((B @ (plus_plus_int @ D @ A)) <= (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3208_incr__mult__lemma)). 185.47/93.67 thf(22427,plain,((! [A:int,B:(int > $o),C:int]: ((ord_less_int @ zero_zero_int @ A) => (((ord_less_eq_int @ zero_zero_int @ C) => (! [D:int]: ((B @ (plus_plus_int @ D @ (times_times_int @ C @ A))) | ~ (B @ D)))) | ~ (! [D:int]: ((B @ (plus_plus_int @ D @ A)) | ~ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4507])). 185.47/93.67 thf(4519,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5135_neg__0__le__iff__le)). 185.47/93.67 thf(22478,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4519])). 185.47/93.67 thf(2201,axiom,((! [A:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => (~ (! [B:int]: (A != (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ one_one_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4961_oddE)). 185.47/93.67 thf(15063,plain,((! [A:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => (~ (! [B:int]: ~ (A = (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2201])). 185.47/93.67 thf(898,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_real @ A @ B) => ((ord_less_real @ (arccos @ B) @ (arccos @ A)) <= (ord_less_eq_real @ B @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8366_arccos__less__arccos)). 185.47/93.67 thf(10803,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_real @ A @ B) => ((ord_less_real @ (arccos @ B) @ (arccos @ A)) | ~ (ord_less_eq_real @ B @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[898])). 185.47/93.67 thf(2277,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_3903_antisym)). 185.47/93.67 thf(15291,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)],[2277])). 185.47/93.67 thf(6867,axiom,((! [A:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1913_add__self__mod__2)). 185.47/93.67 thf(31028,plain,((! [A:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6867])). 185.47/93.67 thf(6233,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_trans__le__add1)). 185.47/93.67 thf(28708,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6233])). 185.47/93.67 thf(4320,axiom,((! [A:rat,B:rat,C:rat]: ((A = (uminus_uminus_rat @ (divide_divide_rat @ B @ C))) = ((((times_times_rat @ A @ C) = (uminus_uminus_rat @ B)) <= (C != zero_zero_rat)) & ((C = zero_zero_rat) => (A = zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5974_eq__minus__divide__eq)). 185.47/93.67 thf(21842,plain,((! [A:rat,B:rat,C:rat]: ((A = (uminus_uminus_rat @ (divide_divide_rat @ B @ C))) = ((((times_times_rat @ A @ C) = (uminus_uminus_rat @ B)) | (C = zero_zero_rat)) & ((C = zero_zero_rat) => (A = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4320])). 185.47/93.67 thf(5153,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) <= (ord_less_nat @ D @ E))) => ((ord_less_eq_nat @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_less__mono__imp__le__mono)). 185.47/93.67 thf(24725,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) | ~ (ord_less_nat @ D @ E))) => ((ord_less_eq_nat @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5153])). 185.47/93.67 thf(431,axiom,((! [A:nat]: ((tan_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7972_tan__npi)). 185.47/93.67 thf(9165,plain,((! [A:nat]: ((tan_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])). 185.47/93.67 thf(2062,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((ord_less_eq_int @ C @ D) => (((ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) <= (ord_less_int @ zero_zero_int @ C)) <= (ord_less_eq_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2618_mult__less__le__imp__less)). 185.47/93.67 thf(14614,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((ord_less_eq_int @ C @ D) => ((ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) | ~ (ord_less_int @ zero_zero_int @ C) | ~ (ord_less_eq_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2062])). 185.47/93.67 thf(2123,axiom,((! [A:num,B:num]: ((bit_se8568078237143864401it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (bit_se8568078237143864401it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9756_drop__bit__numeral__minus__bit0)). 185.47/93.67 thf(14800,plain,((! [A:num,B:num]: ((bit_se8568078237143864401it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (bit_se8568078237143864401it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2123])). 185.47/93.67 thf(6968,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ B @ A) = (modulo_modulo_nat @ (minus_minus_nat @ B @ A) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2179_le__mod__geq)). 185.47/93.67 thf(31400,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ B @ A) = (modulo_modulo_nat @ (minus_minus_nat @ B @ A) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6968])). 185.47/93.67 thf(289,axiom,((! [A:nat,B:real]: ((ord_less_eq_nat @ A @ (nat2 @ (archim6058952711729229775r_real @ B))) <= (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9323_le__nat__floor)). 185.47/93.67 thf(8676,plain,((! [A:nat,B:real]: ((ord_less_eq_nat @ A @ (nat2 @ (archim6058952711729229775r_real @ B))) | ~ (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 185.47/93.67 thf(7634,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ A)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4511_even__Suc)). 185.47/93.67 thf(33670,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ A)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7634])). 185.47/93.67 thf(3639,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_eq_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3341_mult__le__cancel__iff2)). 185.47/93.67 thf(19680,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (ord_less_eq_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3639])). 185.47/93.67 thf(3000,axiom,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real) = (((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ A @ zero_zero_real)) | ((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2317_mult__less__0__iff)). 185.47/93.67 thf(17676,plain,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real) = (((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ A @ zero_zero_real)) | ((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3000])). 185.47/93.67 thf(3371,axiom,((! [A:nat,B:nat]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ (semiri681578069525770553at_rat @ A) @ B)) = ((B = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7115_of__nat__zero__less__power__iff)). 185.47/93.67 thf(18831,plain,((! [A:nat,B:nat]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ (semiri681578069525770553at_rat @ A) @ B)) = ((B = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3371])). 185.47/93.67 thf(2634,axiom,((((=) @ rat) = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ B @ A) & (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3885_dual__order_Oeq__iff)). 185.47/93.67 thf(16467,plain,((((=) @ rat) = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ B @ A) & (ord_less_eq_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2634])). 185.47/93.67 thf(1697,axiom,((numeral_numeral_nat = (^ [A:num]: (nat2 @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9277_nat__numeral__as__int)). 185.47/93.67 thf(13418,plain,(((numeral_numeral_nat) = (^ [A:num]: (nat2 @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697])). 185.47/93.67 thf(2807,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_add__strict__left__mono)). 185.47/93.67 thf(17051,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2807])). 185.47/93.67 thf(7406,axiom,((! [A:vEBT_VEBT,B:nat]: (((! [C:$o,D:$o]: (A != (vEBT_Leaf @ C @ D))) => (((! [C:nat,D:nat]: ((? [E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F))) => ((B = C) | (B = D)))) => ((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: (((B = C) | (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) | (B = D)) <= (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G))))) => (~ (! [C:nat,D:list_VEBT_VEBT]: ((? [E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E))) => (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)))))))) <= (! [C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ C @ D))))) <= (~ (vEBT_VEBT_membermima @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3014_VEBT__internal_Omembermima_Oelims_I3_J)). 185.47/93.67 thf(32942,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:$o,D:$o]: ~ (A = (vEBT_Leaf @ C @ D))) => (((! [C:nat,D:nat]: ((? [E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F))) => ((B = C) | (B = D)))) => ((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: ((B = C) | (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) | (B = D) | ~ (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G))))) => (~ (! [C:nat,D:list_VEBT_VEBT]: ((? [E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E))) => (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)))))))) | ~ (! [C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ C @ D))))) | (vEBT_VEBT_membermima @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7406])). 185.47/93.67 thf(7588,axiom,((! [A:nat]: ((modulo_modulo_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1882_mod2__Suc__Suc)). 185.47/93.67 thf(33534,plain,((! [A:nat]: ((modulo_modulo_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7588])). 185.47/93.67 thf(7604,axiom,((! [A:num,B:num]: (((numeral_numeral_nat @ A) = (numeral_numeral_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_numeral__eq__iff)). 185.47/93.67 thf(33583,plain,((! [A:num,B:num]: (((numeral_numeral_nat @ A) = (numeral_numeral_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7604])). 185.47/93.67 thf(5570,axiom,((! [A:vEBT_VEBT]: ((! [B:$o,C:$o]: (A != (vEBT_Leaf @ B @ C))) => ((~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A != (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F)))) <= (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2805_vebt__mint_Ocases)). 185.47/93.67 thf(26271,plain,((! [A:vEBT_VEBT]: ((! [B:$o,C:$o]: ~ (A = (vEBT_Leaf @ B @ C))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F))) | ~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5570])). 185.47/93.67 thf(2491,axiom,((! [A:int,B:int]: ((divide_divide_int @ (modulo_modulo_int @ A @ B) @ B) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1764_bits__mod__div__trivial)). 185.47/93.67 thf(15992,plain,((! [A:int,B:int]: ((divide_divide_int @ (modulo_modulo_int @ A @ B) @ B) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2491])). 185.47/93.67 thf(2081,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (comm_s4663373288045622133er_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8436_pochhammer__pos)). 185.47/93.67 thf(14675,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (comm_s4663373288045622133er_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2081])). 185.47/93.67 thf(3624,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) <= (((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ B @ zero_zero_real)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2221_split__mult__neg__le)). 185.47/93.67 thf(19631,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) | ~ (((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ B @ zero_zero_real)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3624])). 185.47/93.67 thf(5954,axiom,((! [A:nat]: ((semiri2265585572941072030t_real @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (times_times_real @ (times_times_real @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (comm_s7457072308508201937r_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ A)) @ (semiri2265585572941072030t_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8610_fact__double)). 185.47/93.67 thf(27702,plain,((! [A:nat]: ((semiri2265585572941072030t_real @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (times_times_real @ (times_times_real @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (comm_s7457072308508201937r_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ A)) @ (semiri2265585572941072030t_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5954])). 185.47/93.67 thf(5585,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6392_semiring__norm_I72_J)). 185.47/93.67 thf(26316,plain,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5585])). 185.47/93.67 thf(2112,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (ord_less_real @ B @ (plus_plus_real @ A @ C))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2395_pos__add__strict)). 185.47/93.67 thf(14763,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (ord_less_real @ B @ (plus_plus_real @ A @ C))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2112])). 185.47/93.67 thf(7166,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ A) = (times_times_complex @ B @ B)) = ((A = (uminus1482373934393186551omplex @ B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5542_square__eq__iff)). 185.47/93.67 thf(32144,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ A) = (times_times_complex @ B @ B)) = ((A = (uminus1482373934393186551omplex @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7166])). 185.47/93.67 thf(1347,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ A) = (ord_less_eq_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1632_add__le__same__cancel1)). 185.47/93.67 thf(12224,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ A) = (ord_less_eq_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347])). 185.47/93.67 thf(7216,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ (divide_divide_nat @ B @ A) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2915_dividend__less__div__times)). 185.47/93.67 thf(32313,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ (divide_divide_nat @ B @ A) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7216])). 185.47/93.67 thf(657,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arctan @ A)) & (ord_less_real @ (arctan @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((tan_real @ (arctan @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8071_arctan)). 185.47/93.67 thf(9921,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arctan @ A)) & (ord_less_real @ (arctan @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((tan_real @ (arctan @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[657])). 185.47/93.67 thf(5533,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2121_less__eq__nat_Osimps_I1_J)). 185.47/93.67 thf(26158,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5533])). 185.47/93.67 thf(5267,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_vebt_mint @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = (some_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1247_vebt__mint_Osimps_I3_J)). 185.47/93.67 thf(25136,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_vebt_mint @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = (some_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5267])). 185.47/93.67 thf(495,axiom,((! [A:complex,B:complex]: ((re @ (minus_minus_complex @ A @ B)) = (minus_minus_real @ (re @ A) @ (re @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9645_minus__complex_Osimps_I1_J)). 185.47/93.67 thf(9398,plain,((! [A:complex,B:complex]: ((re @ (minus_minus_complex @ A @ B)) = (minus_minus_real @ (re @ A) @ (re @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[495])). 185.47/93.67 thf(5667,axiom,((! [A:num]: ((one_one_real = (numeral_numeral_real @ A)) = (one = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_one__eq__numeral__iff)). 185.47/93.67 thf(26596,plain,((! [A:num]: ((one_one_real = (numeral_numeral_real @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5667])). 185.47/93.67 thf(7718,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) = (divide_divide_nat @ (modulo_modulo_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2970_div__exp__mod__exp__eq)). 185.47/93.67 thf(33891,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) = (divide_divide_nat @ (modulo_modulo_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7718])). 185.47/93.67 thf(2048,axiom,((! [A:num,B:num,C:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ B) @ C)) = (times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5356_semiring__norm_I170_J)). 185.47/93.67 thf(14577,plain,((! [A:num,B:num,C:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ B) @ C)) = (times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2048])). 185.47/93.67 thf(6209,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ A) = (ord_less_nat @ B @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1656_add__less__same__cancel1)). 185.47/93.67 thf(28629,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ A) = (ord_less_nat @ B @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6209])). 185.47/93.67 thf(4547,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ B @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9374_AND__upper2)). 185.47/93.67 thf(22566,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ B @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4547])). 185.47/93.67 thf(5044,axiom,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ A @ C) <= (ord_less_eq_num @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3857_ord__eq__le__trans)). 185.47/93.67 thf(24311,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ C) | ~ (ord_less_eq_num @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5044])). 185.47/93.67 thf(2475,axiom,((! [A:int,B:int]: (((ord_less_int @ one_one_int @ B) => (ord_less_int @ one_one_int @ (times_times_int @ A @ B))) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1194_less__1__mult)). 185.47/93.67 thf(15928,plain,((! [A:int,B:int]: (((ord_less_int @ one_one_int @ B) => (ord_less_int @ one_one_int @ (times_times_int @ A @ B))) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2475])). 185.47/93.67 thf(2104,axiom,((! [A:rat,B:nat]: (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ (abs_abs_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6566_zero__le__power__abs)). 185.47/93.67 thf(14739,plain,((! [A:rat,B:nat]: (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ (abs_abs_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104])). 185.47/93.67 thf(6946,axiom,((! [A:int,B:int,C:int,D:int]: (((A = B) = (C = D)) <= ((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_diff__eq__diff__eq)). 185.47/93.67 thf(31291,plain,((! [A:int,B:int,C:int,D:int]: (((A = B) = (C = D)) | ~ ((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6946])). 185.47/93.67 thf(6509,axiom,((! [A:nat,B:nat,C:nat]: (((((modulo_modulo_nat @ A @ C) = zero_zero_nat) => ((ord_less_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) <= ((modulo_modulo_nat @ B @ C) = zero_zero_nat))) <= (ord_less_nat @ zero_zero_nat @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3112_div__less__mono)). 185.47/93.67 thf(29698,plain,((! [A:nat,B:nat,C:nat]: ((((modulo_modulo_nat @ A @ C) = zero_zero_nat) => ((ord_less_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) | ~ ((modulo_modulo_nat @ B @ C) = zero_zero_nat))) | ~ (ord_less_nat @ zero_zero_nat @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6509])). 185.47/93.67 thf(1789,axiom,((! [A:real,B:num]: ((real_V7735802525324610683m_real @ (divide_divide_real @ A @ (numeral_numeral_real @ B))) = (divide_divide_real @ (real_V7735802525324610683m_real @ A) @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7442_norm__divide__numeral)). 185.47/93.67 thf(13727,plain,((! [A:real,B:num]: ((real_V7735802525324610683m_real @ (divide_divide_real @ A @ (numeral_numeral_real @ B))) = (divide_divide_real @ (real_V7735802525324610683m_real @ A) @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789])). 185.47/93.67 thf(2646,axiom,((! [A:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ A) @ A) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5175_ab__left__minus)). 185.47/93.67 thf(16510,plain,((! [A:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ A) @ A) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2646])). 185.47/93.67 thf(1646,axiom,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (cos_real @ A)) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7847_abs__cos__le__one)). 185.47/93.67 thf(13208,plain,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (cos_real @ A)) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646])). 185.47/93.67 thf(2519,axiom,((! [A:rat]: (((divide_divide_rat @ A @ A) = one_one_rat) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1734_divide__self)). 185.47/93.67 thf(16084,plain,((! [A:rat]: (((divide_divide_rat @ A @ A) = one_one_rat) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2519])). 185.47/93.67 thf(7615,axiom,((! [A:int,B:int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = B) | (A = (uminus_uminus_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6180_power2__eq__iff)). 185.47/93.67 thf(33613,plain,((! [A:int,B:int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = B) | (A = (uminus_uminus_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7615])). 185.47/93.67 thf(3607,axiom,((! [A:rat,B:rat,C:rat]: ((A = (divide_divide_rat @ B @ C)) = (((A = zero_zero_rat) <= (C = zero_zero_rat)) & (((times_times_rat @ A @ C) = B) <= (C != zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2472_eq__divide__eq)). 185.47/93.67 thf(19580,plain,((! [A:rat,B:rat,C:rat]: ((A = (divide_divide_rat @ B @ C)) = (((A = zero_zero_rat) | ~ (C = zero_zero_rat)) & (((times_times_rat @ A @ C) = B) | (C = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3607])). 185.47/93.67 thf(6662,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) <= (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_808_diff__less__mono)). 185.47/93.67 thf(30206,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) | ~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6662])). 185.47/93.67 thf(356,axiom,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = zero_zero_complex))) => ((groups2073611262835488442omplex @ C @ B) = (groups2073611262835488442omplex @ C @ A))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6094_sum_Omono__neutral__left)). 185.47/93.67 thf(8922,plain,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = zero_zero_complex))) => ((groups2073611262835488442omplex @ (C) @ B) = (groups2073611262835488442omplex @ (C) @ A))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])). 185.47/93.67 thf(5738,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1801_nat__zero__less__power__iff)). 185.47/93.67 thf(26822,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5738])). 185.47/93.67 thf(47,axiom,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (set_ord_atMost_nat @ A) @ (set_ord_lessThan_nat @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8861_Iic__subset__Iio__iff)). 185.47/93.67 thf(7884,plain,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (set_ord_atMost_nat @ A) @ (set_ord_lessThan_nat @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 185.47/93.67 thf(1069,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ (divide_divide_rat @ B @ C)) = (((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ A @ C) @ B)) & ((~ (ord_less_rat @ zero_zero_rat @ C)) => (((ord_less_rat @ A @ zero_zero_rat) <= (~ (ord_less_rat @ C @ zero_zero_rat))) & ((ord_less_rat @ C @ zero_zero_rat) => (ord_less_rat @ B @ (times_times_rat @ A @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2698_less__divide__eq)). 185.47/93.67 thf(11359,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ (divide_divide_rat @ B @ C)) = (((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ A @ C) @ B)) & ((~ (ord_less_rat @ zero_zero_rat @ C)) => (((ord_less_rat @ A @ zero_zero_rat) | (ord_less_rat @ C @ zero_zero_rat)) & ((ord_less_rat @ C @ zero_zero_rat) => (ord_less_rat @ B @ (times_times_rat @ A @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069])). 185.47/93.67 thf(5438,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((((! [D:nat,E:nat,F:nat]: (((C @ D @ F) <= (C @ E @ F)) <= (C @ D @ E))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))) <= (! [D:nat]: (C @ D @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_transitive__stepwise__le)). 185.47/93.67 thf(25743,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: (((! [D:nat,E:nat,F:nat]: ((C @ D @ F) | ~ (C @ E @ F) | ~ (C @ D @ E))) => ((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B))) | ~ (! [D:nat]: (C @ D @ D)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5438])). 185.47/93.67 thf(255,axiom,((! [A:set_nat,B:(nat > rat),C:nat]: (((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_rat @ zero_zero_rat @ (B @ D)))) => ((((B @ C) = zero_zero_rat) <= (member_nat @ C @ A)) <= ((groups2906978787729119204at_rat @ B @ A) = zero_zero_rat))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6007_sum__nonneg__0)). 185.47/93.67 thf(8560,plain,((! [A:set_nat,B:(nat > rat),C:nat]: (((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_rat @ zero_zero_rat @ (B @ D)))) => (((B @ C) = zero_zero_rat) | ~ (member_nat @ C @ A) | ~ ((groups2906978787729119204at_rat @ (B) @ A) = zero_zero_rat))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 185.47/93.67 thf(6476,axiom,((! [A:complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex) => ((real_V1022390504157884413omplex @ A) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7519_square__norm__one)). 185.47/93.67 thf(29578,plain,((! [A:complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex) => ((real_V1022390504157884413omplex @ A) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6476])). 185.47/93.67 thf(5118,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2051_divisors__zero)). 185.47/93.67 thf(24575,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((B = zero_zero_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5118])). 185.47/93.67 thf(5203,axiom,(((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_fst)). 185.47/93.67 thf(24883,plain,(((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ xa) = (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5203])). 185.47/93.67 thf(611,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((((groups3539618377306564664at_int @ C @ B) = (plus_plus_int @ (groups3539618377306564664at_int @ C @ (minus_minus_set_nat @ B @ A)) @ (groups3539618377306564664at_int @ C @ A))) <= (finite_finite_nat @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6125_sum_Osubset__diff)). 185.47/93.67 thf(9762,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: (((groups3539618377306564664at_int @ (C) @ B) = (plus_plus_int @ (groups3539618377306564664at_int @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups3539618377306564664at_int @ (C) @ A))) | ~ (finite_finite_nat @ B) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[611])). 185.47/93.67 thf(2527,axiom,((! [A:nat,B:nat,C:(nat > rat),D:(nat > rat)]: ((ord_less_eq_nat @ one_one_nat @ A) => (((groups73079841787564623at_rat @ (^ [E:nat]: (if_rat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_rat @ (E = B) @ one_one_rat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups73079841787564623at_rat @ (^ [E:nat]: (if_rat @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))) <= (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8868_prod_Ozero__middle)). 185.47/93.67 thf(16111,plain,((! [A:nat,B:nat,C:(nat > rat),D:(nat > rat)]: ((ord_less_eq_nat @ one_one_nat @ A) => (((groups73079841787564623at_rat @ (^ [E:nat]: (if_rat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_rat @ (E = B) @ one_one_rat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups73079841787564623at_rat @ (^ [E:nat]: (if_rat @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))) | ~ (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2527])). 185.47/93.67 thf(530,axiom,((! [A:num]: ((ord_max_int @ one_one_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3639_max__0__1_I5_J)). 185.47/93.67 thf(9503,plain,((! [A:num]: ((ord_max_int @ one_one_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[530])). 185.47/93.67 thf(5604,axiom,((! [A:rat]: ((times_times_rat @ A @ (numeral_numeral_rat @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_mult__numeral__1__right)). 185.47/93.67 thf(26376,plain,((! [A:rat]: ((times_times_rat @ A @ (numeral_numeral_rat @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5604])). 185.47/93.67 thf(3043,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C)) <= (ord_less_eq_rat @ zero_zero_rat @ C)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2229_mult__right__mono)). 185.47/93.67 thf(17809,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C)) | ~ (ord_less_eq_rat @ zero_zero_rat @ C) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3043])). 185.47/93.67 thf(2924,axiom,((ord_less_eq_int @ zero_zero_int @ zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2023_le__numeral__extra_I3_J)). 185.47/93.67 thf(17430,plain,((ord_less_eq_int @ zero_zero_int @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2924])). 185.47/93.67 thf(3967,axiom,((! [A:nat,B:int]: ((bit_ri631733984087533419it_int @ A @ (uminus_uminus_int @ (bit_ri631733984087533419it_int @ A @ B))) = (bit_ri631733984087533419it_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5490_signed__take__bit__minus)). 185.47/93.67 thf(20734,plain,((! [A:nat,B:int]: ((bit_ri631733984087533419it_int @ A @ (uminus_uminus_int @ (bit_ri631733984087533419it_int @ A @ B))) = (bit_ri631733984087533419it_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3967])). 185.47/93.67 thf(747,axiom,((! [A:nat,B:complex]: (((gbinomial_complex @ B @ A) = (plus_plus_complex @ (gbinomial_complex @ (minus_minus_complex @ B @ one_one_complex) @ (minus_minus_nat @ A @ one_one_nat)) @ (gbinomial_complex @ (minus_minus_complex @ B @ one_one_complex) @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8582_gbinomial__reduce__nat)). 185.47/93.67 thf(10226,plain,((! [A:nat,B:complex]: (((gbinomial_complex @ B @ A) = (plus_plus_complex @ (gbinomial_complex @ (minus_minus_complex @ B @ one_one_complex) @ (minus_minus_nat @ A @ one_one_nat)) @ (gbinomial_complex @ (minus_minus_complex @ B @ one_one_complex) @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[747])). 185.47/93.67 thf(4281,axiom,((! [A:num,B:int]: ((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_eq_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7069_of__int__numeral__le__iff)). 185.47/93.67 thf(21689,plain,((! [A:num,B:int]: ((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_eq_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4281])). 185.47/93.67 thf(7414,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2643_add__strict__increasing2)). 185.47/93.67 thf(32989,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7414])). 185.47/93.67 thf(1837,axiom,((~ (ord_le3102999989581377725nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5715_le__minus__one__simps_I4_J)). 185.47/93.67 thf(13889,plain,((~ (ord_le3102999989581377725nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1837])). 185.47/93.67 thf(3998,axiom,((! [A:set_nat,B:set_nat]: (((finite_finite_nat @ B) <= (ord_less_eq_set_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3492_rev__finite__subset)). 185.47/93.67 thf(20828,plain,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ B) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3998])). 185.47/93.67 thf(2356,axiom,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ B) = (uminus_uminus_rat @ one_one_rat)) = ((B != zero_zero_rat) & (A = (uminus_uminus_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5987_divide__eq__minus__1__iff)). 185.47/93.67 thf(15534,plain,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ B) = (uminus_uminus_rat @ one_one_rat)) = (~ (B = zero_zero_rat) & (A = (uminus_uminus_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2356])). 185.47/93.67 thf(3115,axiom,((! [A:set_nat,B:(nat > int),C:(nat > int)]: ((ord_less_eq_int @ (groups3539618377306564664at_int @ B @ A) @ (groups3539618377306564664at_int @ C @ A)) <= (! [D:nat]: ((ord_less_eq_int @ (B @ D) @ (C @ D)) <= (member_nat @ D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5604_sum__mono)). 185.47/93.67 thf(18041,plain,((! [A:set_nat,B:(nat > int),C:(nat > int)]: ((ord_less_eq_int @ (groups3539618377306564664at_int @ (B) @ A) @ (groups3539618377306564664at_int @ (C) @ A)) | ~ (! [D:nat]: ((ord_less_eq_int @ (B @ D) @ (C @ D)) | ~ (member_nat @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3115])). 185.47/93.67 thf(5251,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2122_bot__nat__0_Oextremum__unique)). 185.47/93.67 thf(25044,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5251])). 185.47/93.67 thf(3845,axiom,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4579_dvd__triv__right)). 185.47/93.67 thf(20351,plain,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3845])). 185.47/93.67 thf(6568,axiom,((! [A:real,B:num]: ((ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ B))) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_eq_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4531_zero__le__power__eq__numeral)). 185.47/93.67 thf(29896,plain,((! [A:real,B:num]: ((ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ B))) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_eq_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6568])). 185.47/93.67 thf(7205,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((((minus_minus_nat @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ B) = (modulo_modulo_nat @ A @ B)) <= (ord_less_eq_nat @ B @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2527_divmod__digit__1_I2_J)). 185.47/93.67 thf(32268,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (((minus_minus_nat @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ B) = (modulo_modulo_nat @ A @ B)) | ~ (ord_less_eq_nat @ B @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7205])). 185.47/93.67 thf(1814,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((((modulo_modulo_int @ D @ B) = (modulo_modulo_int @ E @ B)) => ((modulo_modulo_int @ (plus_plus_int @ A @ D) @ B) = (modulo_modulo_int @ (plus_plus_int @ C @ E) @ B))) <= ((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1995_mod__add__cong)). 185.47/93.67 thf(13806,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((((modulo_modulo_int @ D @ B) = (modulo_modulo_int @ E @ B)) => ((modulo_modulo_int @ (plus_plus_int @ A @ D) @ B) = (modulo_modulo_int @ (plus_plus_int @ C @ E) @ B))) | ~ ((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1814])). 185.47/93.67 thf(293,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((tanh_real @ (ln_ln_real @ A)) = (divide_divide_real @ (minus_minus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6307_tanh__ln__real)). 185.47/93.67 thf(8689,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((tanh_real @ (ln_ln_real @ A)) = (divide_divide_real @ (minus_minus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 185.47/93.67 thf(3132,axiom,((! [A:int,B:int]: ((A = B) => (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3933_order__eq__refl)). 185.47/93.67 thf(18089,plain,((! [A:int,B:int]: ((A = B) => (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3132])). 185.47/93.67 thf(4345,axiom,((! [A:real,B:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ B) = (minus_minus_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5207_uminus__add__conv__diff)). 185.47/93.67 thf(21918,plain,((! [A:real,B:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ B) = (minus_minus_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4345])). 185.47/93.67 thf(1728,axiom,((! [A:real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1561_div__by__0)). 185.47/93.67 thf(13528,plain,((! [A:real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728])). 185.47/93.67 thf(5896,axiom,((ord_less_num = (^ [A:num,B:num]: (~ (ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4185_less__le__not__le)). 185.47/93.67 thf(27526,plain,(((ord_less_num) = (^ [A:num,B:num]: (~ (ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5896])). 185.47/93.67 thf(2522,axiom,((! [A:real,B:real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5094_minus__add__distrib)). 185.47/93.67 thf(16094,plain,((! [A:real,B:real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2522])). 185.47/93.67 thf(1554,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (plus_plus_real @ C @ A)) <= (ord_less_eq_real @ B @ C)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2295_add__increasing2)). 185.47/93.67 thf(12886,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ (plus_plus_real @ C @ A)) | ~ (ord_less_eq_real @ B @ C) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554])). 185.47/93.67 thf(6180,axiom,((! [A:rat]: (((times_times_rat @ A @ A) = one_one_rat) = ((A = one_one_rat) | (A = (uminus_uminus_rat @ one_one_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5780_square__eq__1__iff)). 185.47/93.67 thf(28528,plain,((! [A:rat]: (((times_times_rat @ A @ A) = one_one_rat) = ((A = one_one_rat) | (A = (uminus_uminus_rat @ one_one_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6180])). 185.47/93.67 thf(5221,axiom,((! [A:num,B:num]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5066_neg__numeral__eq__iff)). 185.47/93.67 thf(24937,plain,((! [A:num,B:num]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5221])). 185.47/93.67 thf(3544,axiom,((! [A:int,B:int]: ((divide_divide_int @ A @ (uminus_uminus_int @ B)) = (divide_divide_int @ (uminus_uminus_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5580_div__minus__right)). 185.47/93.67 thf(19384,plain,((! [A:int,B:int]: ((divide_divide_int @ A @ (uminus_uminus_int @ B)) = (divide_divide_int @ (uminus_uminus_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3544])). 185.47/93.67 thf(2919,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ (divide_divide_int @ B @ A) @ C) = (divide_divide_int @ (times_times_int @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4866_unit__div__commute)). 185.47/93.67 thf(17413,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ (divide_divide_int @ B @ A) @ C) = (divide_divide_int @ (times_times_int @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2919])). 185.47/93.67 thf(1771,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6910_of__nat__add)). 185.47/93.67 thf(13662,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771])). 185.47/93.67 thf(4901,axiom,((! [A:real,B:real]: (((~ (ord_less_real @ B @ A)) = (B = A)) <= (~ (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3997_antisym__conv3)). 185.47/93.67 thf(23766,plain,((! [A:real,B:real]: (((~ (ord_less_real @ B @ A)) = (B = A)) | (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4901])). 185.47/93.67 thf(5763,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1020_n__not__Suc__n)). 185.47/93.67 thf(26899,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5763])). 185.47/93.67 thf(7586,axiom,((! [A:nat,B:nat]: ((vEBT_VEBT_bit_concat @ (vEBT_VEBT_high @ A @ B) @ (vEBT_VEBT_low @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_bit__split__inv)). 185.47/93.67 thf(33529,plain,((! [A:nat,B:nat]: ((vEBT_VEBT_bit_concat @ (vEBT_VEBT_high @ A @ B) @ (vEBT_VEBT_low @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7586])). 185.47/93.67 thf(7326,axiom,((! [A:num]: (zero_zero_nat != (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2038_zero__neq__numeral)). 185.47/93.67 thf(32685,plain,((! [A:num]: ~ (zero_zero_nat = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7326])). 185.47/93.67 thf(2022,axiom,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (times_times_complex @ A @ B)) = (times_times_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7461_norm__mult)). 185.47/93.67 thf(14493,plain,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (times_times_complex @ A @ B)) = (times_times_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022])). 185.47/93.67 thf(5685,axiom,((! [A:real,B:real]: ((times_times_real @ A @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (times_times_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5079_mult__minus__right)). 185.47/93.67 thf(26651,plain,((! [A:real,B:real]: ((times_times_real @ A @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (times_times_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5685])). 185.47/93.67 thf(4161,axiom,((! [A:nat]: (((semiri681578069525770553at_rat @ A) = zero_zero_rat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6896_of__nat__eq__0__iff)). 185.47/93.67 thf(21329,plain,((! [A:nat]: (((semiri681578069525770553at_rat @ A) = zero_zero_rat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4161])). 185.47/93.67 thf(3424,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1231_ordered__ring__class_Ole__add__iff1)). 185.47/93.67 thf(19003,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3424])). 185.47/93.67 thf(411,axiom,((bit_ri7919022796975470100ot_int = (^ [A:int]: (minus_minus_int @ (uminus_uminus_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9511_not__int__def)). 185.47/93.67 thf(9097,plain,(((bit_ri7919022796975470100ot_int) = (^ [A:int]: (minus_minus_int @ (uminus_uminus_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[411])). 185.47/93.67 thf(2299,axiom,((! [A:real]: ((A != zero_zero_real) => ((divide_divide_real @ A @ A) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1733_divide__self)). 185.47/93.67 thf(15355,plain,((! [A:real]: ((~ (A = zero_zero_real)) => ((divide_divide_real @ A @ A) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2299])). 185.47/93.67 thf(4961,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_nat__less__le)). 185.47/93.67 thf(23975,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4961])). 185.47/93.67 thf(5378,axiom,((! [A:nat]: ((bit_se2161824704523386999it_nat @ zero_zero_nat @ A) = (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5006_flip__bit__0)). 185.47/93.67 thf(25533,plain,((! [A:nat]: ((bit_se2161824704523386999it_nat @ zero_zero_nat @ A) = (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5378])). 185.47/93.67 thf(6008,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ B @ A) | (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3935_linorder__linear)). 185.47/93.67 thf(27921,plain,((! [A:num,B:num]: ((ord_less_eq_num @ B @ A) | (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6008])). 185.47/93.67 thf(7411,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (plus_plus_nat @ B @ A) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2758_div__add__self2)). 185.47/93.67 thf(32979,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (plus_plus_nat @ B @ A) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7411])). 185.47/93.67 thf(3396,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = C) = (((B != zero_zero_real) => (A = (times_times_real @ C @ B))) & ((C = zero_zero_real) <= (B = zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2474_divide__eq__eq)). 185.47/93.67 thf(18918,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = C) = (((~ (B = zero_zero_real)) => (A = (times_times_real @ C @ B))) & ((C = zero_zero_real) | ~ (B = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3396])). 185.47/93.67 thf(4714,axiom,((! [A:real,B:real,C:(real > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4351_order__less__le__subst2)). 185.47/93.67 thf(23119,plain,((! [A:real,B:real,C:(real > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4714])). 185.47/93.67 thf(4243,axiom,((! [A:int,B:int]: (((ord_less_int @ A @ zero_zero_int) => ((minus_minus_nat @ (nat2 @ B) @ (nat2 @ A)) = (nat2 @ B))) & (((minus_minus_nat @ (nat2 @ B) @ (nat2 @ A)) = (if_nat @ (ord_less_int @ (minus_minus_int @ B @ A) @ zero_zero_int) @ zero_zero_nat @ (nat2 @ (minus_minus_int @ B @ A)))) <= (~ (ord_less_int @ A @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9337_diff__nat__eq__if)). 185.47/93.67 thf(21578,plain,((! [A:int,B:int]: (((ord_less_int @ A @ zero_zero_int) => ((minus_minus_nat @ (nat2 @ B) @ (nat2 @ A)) = (nat2 @ B))) & (((minus_minus_nat @ (nat2 @ B) @ (nat2 @ A)) = (if_nat @ (ord_less_int @ (minus_minus_int @ B @ A) @ zero_zero_int) @ zero_zero_nat @ (nat2 @ (minus_minus_int @ B @ A)))) | (ord_less_int @ A @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4243])). 185.47/93.67 thf(7490,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_add__leE)). 185.47/93.67 thf(33253,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7490])). 185.47/93.67 thf(3828,axiom,((! [A:rat]: ((abs_abs_rat @ (uminus_uminus_rat @ A)) = (abs_abs_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6354_abs__minus__cancel)). 185.47/93.67 thf(20291,plain,((! [A:rat]: ((abs_abs_rat @ (uminus_uminus_rat @ A)) = (abs_abs_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3828])). 185.47/93.67 thf(4013,axiom,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5891_neg__numeral__le__zero)). 185.47/93.67 thf(20879,plain,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4013])). 185.47/93.67 thf(7082,axiom,((! [A:real,B:real]: ((((times_times_real @ A @ B) != zero_zero_real) <= (B != zero_zero_real)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2054_no__zero__divisors)). 185.47/93.67 thf(31841,plain,((! [A:real,B:real]: (~ ((times_times_real @ A @ B) = zero_zero_real) | (B = zero_zero_real) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7082])). 185.47/93.67 thf(7364,axiom,((! [A:num,B:nat,C:int]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ B) = (ring_18347121197199848620nteger @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7151_neg__numeral__power__eq__of__int__cancel__iff)). 185.47/93.67 thf(32809,plain,((! [A:num,B:nat,C:int]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ B) = (ring_18347121197199848620nteger @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7364])). 185.47/93.67 thf(2537,axiom,((ord_less_rat = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) & ~ (ord_less_eq_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4184_less__le__not__le)). 185.47/93.67 thf(16143,plain,(((ord_less_rat) = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) & ~ (ord_less_eq_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2537])). 185.47/93.67 thf(4831,axiom,((semiri773545260158071498ct_rat = (comm_s4028243227959126397er_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8445_pochhammer__fact)). 185.47/93.67 thf(23517,plain,(((semiri773545260158071498ct_rat) = (comm_s4028243227959126397er_rat @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4831])). 185.47/93.67 thf(3883,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ B @ (plus_plus_rat @ A @ C)) <= (ord_less_eq_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2304_add__increasing)). 185.47/93.67 thf(20467,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ B @ (plus_plus_rat @ A @ C)) | ~ (ord_less_eq_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3883])). 185.47/93.67 thf(3451,axiom,((! [A:rat,B:rat]: ((((ord_less_eq_rat @ A @ zero_zero_rat) & (ord_less_eq_rat @ B @ zero_zero_rat)) | ((ord_less_eq_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ zero_zero_rat @ A))) => (ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2246_split__mult__pos__le)). 185.47/93.67 thf(19080,plain,((! [A:rat,B:rat]: ((((ord_less_eq_rat @ A @ zero_zero_rat) & (ord_less_eq_rat @ B @ zero_zero_rat)) | ((ord_less_eq_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ zero_zero_rat @ A))) => (ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3451])). 185.47/93.67 thf(5930,axiom,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = B) => (((sqrt @ B) = A) <= (ord_less_eq_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8222_real__sqrt__unique)). 185.47/93.67 thf(27630,plain,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = B) => (((sqrt @ B) = A) | ~ (ord_less_eq_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5930])). 185.47/93.67 thf(1381,axiom,((! [A:rat,B:rat,C:rat]: ((((plus_plus_rat @ B @ (divide_divide_rat @ C @ A)) = B) <= (A = zero_zero_rat)) & (((plus_plus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (plus_plus_rat @ (times_times_rat @ B @ A) @ C) @ A)) <= (A != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2746_add__divide__eq__if__simps_I1_J)). 185.47/93.67 thf(12326,plain,((! [A:rat,B:rat,C:rat]: ((((plus_plus_rat @ B @ (divide_divide_rat @ C @ A)) = B) | ~ (A = zero_zero_rat)) & (((plus_plus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (plus_plus_rat @ (times_times_rat @ B @ A) @ C) @ A)) | (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381])). 185.47/93.67 thf(3952,axiom,((! [A:real,B:real]: ((ord_less_real @ (sqrt @ A) @ (sqrt @ B)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8151_real__sqrt__less__mono)). 185.47/93.67 thf(20692,plain,((! [A:real,B:real]: ((ord_less_real @ (sqrt @ A) @ (sqrt @ B)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3952])). 185.47/93.67 thf(366,axiom,((! [A:int,B:num,C:nat]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (ord_less_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7169_of__int__less__neg__numeral__power__cancel__iff)). 185.47/93.67 thf(8954,plain,((! [A:int,B:num,C:nat]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (ord_less_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])). 185.47/93.67 thf(3273,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_set_vebt @ A) = (vEBT_VEBT_set_vebt @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_set__vebt__set__vebt_H__valid)). 185.47/93.67 thf(18522,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_set_vebt @ A) = (vEBT_VEBT_set_vebt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3273])). 185.47/93.67 thf(5278,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ (suc @ C))) | (B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2491_Ex__less__Suc2)). 185.47/93.67 thf(25181,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((B @ C) & (ord_less_nat @ C @ (suc @ A)))) = (? [C:nat]: ((ord_less_nat @ C @ A) & (B @ (suc @ C))) | (B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5278])). 185.47/93.67 thf(4372,axiom,((order_mono_nat_nat @ suc)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10170_mono__Suc)). 185.47/93.67 thf(22005,plain,((order_mono_nat_nat @ (suc))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4372])). 185.47/93.67 thf(2789,axiom,((! [A:nat]: (ord_less_int @ zero_zero_int @ (semiri1406184849735516958ct_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7993_fact__gt__zero)). 185.47/93.67 thf(16991,plain,((! [A:nat]: (ord_less_int @ zero_zero_int @ (semiri1406184849735516958ct_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2789])). 185.47/93.67 thf(7728,axiom,((? [A:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ pr) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79__092_060open_062_092_060exists_062maxy_O_Aboth__member__options_A_ItreeList_A_B_Apr_J_Amaxy_092_060close_062)). 185.47/93.67 thf(33919,plain,((? [A:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ pr) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7728])). 185.47/93.67 thf(4560,axiom,((! [A:num,B:num,C:(num > int),D:int]: ((ord_less_eq_num @ A @ B) => ((ord_less_int @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_int @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4340_order__le__less__subst2)). 185.47/93.67 thf(22606,plain,((! [A:num,B:num,C:(num > int),D:int]: ((ord_less_eq_num @ A @ B) => ((ord_less_int @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_int @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4560])). 185.47/93.67 thf(6480,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8526_binomial__maximum_H)). 185.47/93.67 thf(29591,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6480])). 185.47/93.67 thf(1684,axiom,((! [A:real]: ((plus_plus_real @ (times_times_real @ (cos_real @ A) @ (cos_real @ A)) @ (times_times_real @ (sin_real @ A) @ (sin_real @ A))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7792_sin__cos__squared__add3)). 185.47/93.67 thf(13371,plain,((! [A:real]: ((plus_plus_real @ (times_times_real @ (cos_real @ A) @ (cos_real @ A)) @ (times_times_real @ (sin_real @ A) @ (sin_real @ A))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684])). 185.47/93.67 thf(3627,axiom,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ B @ A) = bot_bot_set_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3186_atLeastatMost__empty)). 185.47/93.67 thf(19641,plain,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ B @ A) = bot_bot_set_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3627])). 185.47/93.67 thf(1624,axiom,((semiri681578069525770553at_rat = (^ [A:nat]: (if_rat @ (A = zero_zero_nat) @ zero_zero_rat @ (produc6207742614233964070at_rat @ (^ [B:nat,C:nat]: (if_rat @ (C = zero_zero_nat) @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (semiri681578069525770553at_rat @ B)) @ (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (semiri681578069525770553at_rat @ B)) @ one_one_rat))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7527_of__nat__code__if)). 185.47/93.67 thf(13144,plain,(((semiri681578069525770553at_rat) = (^ [A:nat]: (if_rat @ (A = zero_zero_nat) @ zero_zero_rat @ (produc6207742614233964070at_rat @ (^ [B:nat,C:nat]: (if_rat @ (C = zero_zero_nat) @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (semiri681578069525770553at_rat @ B)) @ (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (semiri681578069525770553at_rat @ B)) @ one_one_rat))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624])). 185.47/93.67 thf(3499,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ A @ C)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1837_div__mult__self2)). 185.47/93.67 thf(19252,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ A @ C)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3499])). 185.47/93.67 thf(2148,axiom,((! [A:num,B:num]: ((((ord_max_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ A)) <= (~ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))) & ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) => ((ord_max_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3608_max__number__of_I1_J)). 185.47/93.67 thf(14887,plain,((! [A:num,B:num]: ((((ord_max_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ A)) | (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))) & ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) => ((ord_max_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2148])). 185.47/93.67 thf(3512,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (times_times_rat @ B @ C) @ (times_times_rat @ A @ C)) <= (ord_less_rat @ C @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2364_mult__strict__right__mono__neg)). 185.47/93.67 thf(19293,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (times_times_rat @ B @ C) @ (times_times_rat @ A @ C)) | ~ (ord_less_rat @ C @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3512])). 185.47/93.67 thf(19,axiom,((! [A:int,B:nat,C:int]: ((minus_minus_int @ (power_power_int @ A @ B) @ (power_power_int @ C @ B)) = (times_times_int @ (minus_minus_int @ A @ C) @ (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (power_power_int @ C @ (minus_minus_nat @ B @ (suc @ D))) @ (power_power_int @ A @ D))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7618_power__diff__sumr2)). 185.47/93.67 thf(7788,plain,((! [A:int,B:nat,C:int]: ((minus_minus_int @ (power_power_int @ A @ B) @ (power_power_int @ C @ B)) = (times_times_int @ (minus_minus_int @ A @ C) @ (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (power_power_int @ C @ (minus_minus_nat @ B @ (suc @ D))) @ (power_power_int @ A @ D))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 185.47/93.67 thf(1163,axiom,((! [A:num,B:num]: (((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = zero_zero_int) = ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1943_cong__exp__iff__simps_I2_J)). 185.47/93.67 thf(11665,plain,((! [A:num,B:num]: (((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = zero_zero_int) = ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163])). 185.47/93.67 thf(5441,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3316_minf_I6_J)). 185.47/93.67 thf(25764,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5441])). 185.47/93.67 thf(2395,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ B @ A)) = (divide_divide_real @ (real_V1022390504157884413omplex @ B) @ (real_V1022390504157884413omplex @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7477_nonzero__norm__divide)). 185.47/93.67 thf(15657,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => ((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ B @ A)) = (divide_divide_real @ (real_V1022390504157884413omplex @ B) @ (real_V1022390504157884413omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2395])). 185.47/93.67 thf(5757,axiom,((! [A:rat,B:nat]: ((times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ A) @ B) @ (power_power_rat @ (uminus_uminus_rat @ A) @ B)) = (power_power_rat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6271_minus__power__mult__self)). 185.47/93.67 thf(26882,plain,((! [A:rat,B:nat]: ((times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ A) @ B) @ (power_power_rat @ (uminus_uminus_rat @ A) @ B)) = (power_power_rat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5757])). 185.47/93.67 thf(4125,axiom,((! [A:num]: (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4844_even__numeral)). 185.47/93.67 thf(21215,plain,((! [A:num]: (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4125])). 185.47/93.67 thf(5890,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (divide_divide_nat @ A @ B)) = (divide_divide_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7235_unique__euclidean__semiring__with__nat__class_Oof__nat__div)). 185.47/93.67 thf(27498,plain,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (divide_divide_nat @ A @ B)) = (divide_divide_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5890])). 185.47/93.67 thf(4192,axiom,((minus_minus_complex = (^ [A:complex,B:complex]: (plus_plus_complex @ A @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5794_ab__group__add__class_Oab__diff__conv__add__uminus)). 185.47/93.67 thf(21425,plain,(((minus_minus_complex) = (^ [A:complex,B:complex]: (plus_plus_complex @ A @ (uminus1482373934393186551omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4192])). 185.47/93.67 thf(4805,axiom,((! [A:code_integer,B:code_integer]: (((dvd_dvd_Code_integer @ B @ one_one_Code_integer) => (dvd_dvd_Code_integer @ A @ one_one_Code_integer)) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4629_dvd__unit__imp__unit)). 185.47/93.67 thf(23434,plain,((! [A:code_integer,B:code_integer]: (((dvd_dvd_Code_integer @ B @ one_one_Code_integer) => (dvd_dvd_Code_integer @ A @ one_one_Code_integer)) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4805])). 185.47/93.67 thf(2309,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4938_even__iff__mod__2__eq__zero)). 185.47/93.67 thf(15390,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2309])). 185.47/93.67 thf(1496,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => (ord_less_eq_int @ (archim7778729529865785530nd_rat @ A) @ (archim7778729529865785530nd_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7573_round__mono)). 185.47/93.67 thf(12708,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => (ord_less_eq_int @ (archim7778729529865785530nd_rat @ A) @ (archim7778729529865785530nd_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496])). 185.47/93.67 thf(4411,axiom,((unique5055182867167087721od_nat = (^ [A:num,B:num]: (if_Pro6206227464963214023at_nat @ (ord_less_num @ A @ B) @ (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)) @ (unique5026877609467782581ep_nat @ B @ (unique5055182867167087721od_nat @ A @ (bit0 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6842_divmod__divmod__step)). 185.47/93.67 thf(22125,plain,(((unique5055182867167087721od_nat) = (^ [A:num,B:num]: (if_Pro6206227464963214023at_nat @ (ord_less_num @ A @ B) @ (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)) @ (unique5026877609467782581ep_nat @ B @ (unique5055182867167087721od_nat @ A @ (bit0 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4411])). 185.47/93.67 thf(5111,axiom,(((modulo_modulo_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1880_one__mod__two__eq__one)). 185.47/93.67 thf(24553,plain,(((modulo_modulo_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5111])). 185.47/93.67 thf(1159,axiom,((! [A:rat,B:rat]: (((plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B)) = zero_zero_rat) = ((B = zero_zero_rat) & (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1678_sum__squares__eq__zero__iff)). 185.47/93.67 thf(11654,plain,((! [A:rat,B:rat]: (((plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B)) = zero_zero_rat) = ((B = zero_zero_rat) & (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159])). 185.47/93.67 thf(7389,axiom,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2022_le__numeral__extra_I3_J)). 185.47/93.67 thf(32889,plain,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7389])). 185.47/93.67 thf(7314,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7228_less__imp__of__nat__less)). 185.47/93.67 thf(32653,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7314])). 185.47/93.67 thf(6625,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ A) @ B) = (uminus1482373934393186551omplex @ (times_times_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5071_mult__minus__left)). 185.47/93.67 thf(30087,plain,((! [A:complex,B:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ A) @ B) = (uminus1482373934393186551omplex @ (times_times_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6625])). 185.47/93.67 thf(1426,axiom,((! [A:int,B:int]: ((divide_divide_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (divide_divide_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5104_div__minus__minus)). 185.47/93.67 thf(12492,plain,((! [A:int,B:int]: ((divide_divide_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (divide_divide_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1426])). 185.47/93.67 thf(5532,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_V5719532721284313246member @ A @ C) | (vEBT_VEBT_membermima @ A @ C)) <= (vEBT_vebt_member @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1248_member__valid__both__member__options)). 185.47/93.67 thf(26155,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_V5719532721284313246member @ A @ C) | (vEBT_VEBT_membermima @ A @ C) | ~ (vEBT_vebt_member @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5532])). 185.47/93.67 thf(1574,axiom,((! [A:real,B:real,C:real]: (((A = zero_zero_real) => ((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = B)) & ((A != zero_zero_real) => ((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ B @ A) @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2772_add__divide__eq__if__simps_I4_J)). 185.47/93.67 thf(12941,plain,((! [A:real,B:real,C:real]: (((A = zero_zero_real) => ((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = B)) & ((~ (A = zero_zero_real)) => ((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ B @ A) @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1574])). 185.47/93.67 thf(450,axiom,((! [A:complex,B:complex]: ((re @ (divide1717551699836669952omplex @ A @ B)) = (divide_divide_real @ (plus_plus_real @ (times_times_real @ (re @ A) @ (re @ B)) @ (times_times_real @ (im @ A) @ (im @ B))) @ (plus_plus_real @ (power_power_real @ (re @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9698_Re__divide)). 185.47/93.67 thf(9227,plain,((! [A:complex,B:complex]: ((re @ (divide1717551699836669952omplex @ A @ B)) = (divide_divide_real @ (plus_plus_real @ (times_times_real @ (re @ A) @ (re @ B)) @ (times_times_real @ (im @ A) @ (im @ B))) @ (plus_plus_real @ (power_power_real @ (re @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[450])). 185.47/93.67 thf(7161,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_769_diff__mult__distrib2)). 185.47/93.67 thf(32121,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7161])). 185.47/93.67 thf(6566,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ B)) = (((ord_less_eq_int @ zero_zero_int @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4970_zero__le__power__eq)). 185.47/93.67 thf(29889,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ B)) = (((ord_less_eq_int @ zero_zero_int @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6566])). 185.47/93.67 thf(2090,axiom,((! [A:(nat > nat),B:nat,C:(nat > nat),D:nat]: (((sums_nat @ (^ [E:nat]: (plus_plus_nat @ (A @ E) @ (C @ E))) @ (plus_plus_nat @ B @ D)) <= (sums_nat @ C @ D)) <= (sums_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8159_sums__add)). 185.47/93.67 thf(14703,plain,((! [A:(nat > nat),B:nat,C:(nat > nat),D:nat]: ((sums_nat @ (^ [E:nat]: (plus_plus_nat @ (A @ E) @ (C @ E))) @ (plus_plus_nat @ B @ D)) | ~ (sums_nat @ (C) @ D) | ~ (sums_nat @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2090])). 185.47/93.67 thf(6781,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_787_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc)). 185.47/93.67 thf(30672,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6781])). 185.47/93.67 thf(4712,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (times_times_int @ A @ B) @ B) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1752_mod__mult__self2__is__0)). 185.47/93.67 thf(23113,plain,((! [A:int,B:int]: ((modulo_modulo_int @ (times_times_int @ A @ B) @ B) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4712])). 185.47/93.67 thf(407,axiom,((! [A:complex,B:complex]: ((re @ (times_times_complex @ A @ B)) = (minus_minus_real @ (times_times_real @ (re @ A) @ (re @ B)) @ (times_times_real @ (im @ A) @ (im @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9679_times__complex_Osimps_I1_J)). 185.47/93.67 thf(9086,plain,((! [A:complex,B:complex]: ((re @ (times_times_complex @ A @ B)) = (minus_minus_real @ (times_times_real @ (re @ A) @ (re @ B)) @ (times_times_real @ (im @ A) @ (im @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])). 185.47/93.67 thf(7019,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4209_order_Ostrict__trans1)). 185.47/93.67 thf(31618,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7019])). 185.47/93.67 thf(2127,axiom,((! [A:rat,B:rat]: ((A != B) => ((~ (ord_less_rat @ A @ B)) => (ord_less_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1114_linorder__neqE__linordered__idom)). 185.47/93.67 thf(14813,plain,((! [A:rat,B:rat]: ((~ (A = B)) => ((~ (ord_less_rat @ A @ B)) => (ord_less_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2127])). 185.47/93.67 thf(1830,axiom,((! [A:$o]: (((zero_n2684676970156552555ol_int @ A) = one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5128_of__bool__eq__1__iff)). 185.47/93.67 thf(13861,plain,((! [A:$o]: (((zero_n2684676970156552555ol_int @ A) = one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1830])). 185.47/93.67 thf(3643,axiom,((! [A:rat,B:rat,C:rat]: (((minus_minus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ B @ A) @ C) @ A)) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2767_diff__divide__eq__iff)). 185.47/93.67 thf(19695,plain,((! [A:rat,B:rat,C:rat]: (((minus_minus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (minus_minus_rat @ (times_times_rat @ B @ A) @ C) @ A)) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3643])). 185.47/93.67 thf(3329,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1633_diff__ge__0__iff__ge)). 185.47/93.67 thf(18698,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3329])). 185.47/93.67 thf(4066,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2303_add__increasing)). 185.47/93.67 thf(21031,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4066])). 185.47/93.67 thf(5081,axiom,(((semiri773545260158071498ct_rat @ (suc @ zero_zero_nat)) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7964_fact__Suc__0)). 185.47/93.67 thf(24435,plain,(((semiri773545260158071498ct_rat @ (suc @ zero_zero_nat)) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5081])). 185.47/93.67 thf(1368,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = ((dvd_dvd_complex @ B @ C) | (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4453_dvd__mult__cancel__left)). 185.47/93.67 thf(12288,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = ((dvd_dvd_complex @ B @ C) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368])). 185.47/93.67 thf(5511,axiom,((! [A:real,B:real]: ((A = (times_times_real @ B @ A)) = ((B = one_one_real) | (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1670_mult__cancel__right1)). 185.47/93.67 thf(26083,plain,((! [A:real,B:real]: ((A = (times_times_real @ B @ A)) = ((B = one_one_real) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5511])). 185.47/93.67 thf(6678,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ (suc @ A)) = (B = A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1089_le__less__Suc__eq)). 185.47/93.67 thf(30260,plain,((! [A:nat,B:nat]: (((ord_less_nat @ B @ (suc @ A)) = (B = A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6678])). 185.47/93.67 thf(5906,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1928_zero__reorient)). 185.47/93.67 thf(27558,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5906])). 185.47/93.67 thf(3869,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ zero_zero_real @ A)) | ((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2202_zero__le__mult__iff)). 185.47/93.67 thf(20423,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ zero_zero_real @ A)) | ((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3869])). 185.47/93.67 thf(5079,axiom,((! [A:int,B:nat,C:int]: (((ord_less_eq_int @ zero_zero_int @ A) => (((A = C) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_eq_int @ zero_zero_int @ C))) <= ((power_power_int @ A @ B) = (power_power_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2145_power__eq__imp__eq__base)). 185.47/93.67 thf(24429,plain,((! [A:int,B:nat,C:int]: (((ord_less_eq_int @ zero_zero_int @ A) => ((A = C) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_int @ zero_zero_int @ C))) | ~ ((power_power_int @ A @ B) = (power_power_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5079])). 185.47/93.67 thf(5172,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (suc @ A) @ C) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1035_less__trans__Suc)). 185.47/93.67 thf(24789,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (suc @ A) @ C) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5172])). 185.47/93.67 thf(6109,axiom,((! [A:nat,B:num,C:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7129_of__nat__le__numeral__power__cancel__iff)). 185.47/93.67 thf(28248,plain,((! [A:nat,B:num,C:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6109])). 185.47/93.67 thf(3549,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((~ (ord_less_real @ C @ A)) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3245_pinf_I5_J)). 185.47/93.67 thf(19399,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (ord_less_real @ C @ A) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3549])). 185.47/93.67 thf(737,axiom,((! [A:num,B:nat,C:int]: (((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = (ring_1_of_int_int @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7148_neg__numeral__power__eq__of__int__cancel__iff)). 185.47/93.67 thf(10191,plain,((! [A:num,B:nat,C:int]: (((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = (ring_1_of_int_int @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[737])). 185.47/93.67 thf(76,axiom,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ A @ (set_ord_atMost_nat @ B)) = (times_times_real @ (A @ zero_zero_nat) @ (groups129246275422532515t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8770_prod_OatMost__shift)). 185.47/93.67 thf(7975,plain,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ (A) @ (set_ord_atMost_nat @ B)) = (times_times_real @ (A @ zero_zero_nat) @ (groups129246275422532515t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 185.47/93.67 thf(5565,axiom,((! [A:nat,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_real @ zero_zero_real @ (power_power_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4974_zero__le__even__power)). 185.47/93.67 thf(26256,plain,((! [A:nat,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_real @ zero_zero_real @ (power_power_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5565])). 185.47/93.67 thf(1978,axiom,((! [A:int,B:int]: (((((nat2 @ A) = (nat2 @ B)) = (A = B)) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9285_eq__nat__nat__iff)). 185.47/93.67 thf(14349,plain,((! [A:int,B:int]: ((((nat2 @ A) = (nat2 @ B)) = (A = B)) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1978])). 185.47/93.67 thf(2669,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (divide_divide_int @ B @ A) @ C) = (dvd_dvd_int @ B @ C)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4773_div__unit__dvd__iff)). 185.47/93.67 thf(16574,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (divide_divide_int @ B @ A) @ C) = (dvd_dvd_int @ B @ C)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2669])). 185.47/93.67 thf(1314,axiom,((ord_less_eq_real @ (cos_real @ (numeral_numeral_real @ (bit0 @ one))) @ zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7885_cos__two__le__zero)). 185.47/93.67 thf(12118,plain,((ord_less_eq_real @ (cos_real @ (numeral_numeral_real @ (bit0 @ one))) @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314])). 185.47/93.67 thf(534,axiom,((! [A:nat,B:nat,C:real]: (((times_times_real @ (gbinomial_real @ C @ B) @ (gbinomial_real @ (semiri5074537144036343181t_real @ B) @ A)) = (times_times_real @ (gbinomial_real @ C @ A) @ (gbinomial_real @ (minus_minus_real @ C @ (semiri5074537144036343181t_real @ A)) @ (minus_minus_nat @ B @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8539_gbinomial__trinomial__revision)). 185.47/93.67 thf(9514,plain,((! [A:nat,B:nat,C:real]: (((times_times_real @ (gbinomial_real @ C @ B) @ (gbinomial_real @ (semiri5074537144036343181t_real @ B) @ A)) = (times_times_real @ (gbinomial_real @ C @ A) @ (gbinomial_real @ (minus_minus_real @ C @ (semiri5074537144036343181t_real @ A)) @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[534])). 185.47/93.67 thf(578,axiom,((! [A:set_nat,B:set_nat]: (((minus_minus_set_nat @ A @ B) = bot_bot_set_nat) = (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5008_diff__shunt__var)). 185.47/93.67 thf(9651,plain,((! [A:set_nat,B:set_nat]: (((minus_minus_set_nat @ A @ B) = bot_bot_set_nat) = (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[578])). 185.47/93.67 thf(2685,axiom,((! [A:real]: (((ord_less_real @ (cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) @ one_one_real) <= (ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7898_cos__double__less__one)). 185.47/93.67 thf(16674,plain,((! [A:real]: ((ord_less_real @ (cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) @ one_one_real) | ~ (ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2685])). 185.47/93.67 thf(591,axiom,((! [A:num,B:num]: ((((ord_max_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ B)) <= (ord_less_eq_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))) & (((ord_max_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ A)) <= (~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3609_max__number__of_I1_J)). 185.47/93.67 thf(9695,plain,((! [A:num,B:num]: ((((ord_max_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ B)) | ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))) & (((ord_max_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ A)) | (ord_less_eq_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[591])). 185.47/93.67 thf(6641,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) <= (~ (ord_less_nat @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_linorder__neqE__nat)). 185.47/93.67 thf(30136,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6641])). 185.47/93.67 thf(4002,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3963_order__antisym__conv)). 185.47/93.67 thf(20843,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4002])). 185.47/93.67 thf(5123,axiom,((! [A:nat]: ((divide_divide_nat @ one_one_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5477_bits__1__div__exp)). 185.47/93.67 thf(24594,plain,((! [A:nat]: ((divide_divide_nat @ one_one_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5123])). 185.47/93.67 thf(746,axiom,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (divide_divide_real @ (A @ C) @ B))) = ((summable_real @ A) | (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7652_summable__divide__iff)). 185.47/93.67 thf(10223,plain,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (divide_divide_real @ (A @ C) @ B))) = ((summable_real @ (A)) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[746])). 185.47/93.67 thf(2217,axiom,((! [A:rat]: (ord_less_eq_rat @ A @ (abs_abs_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6451_abs__ge__self)). 185.47/93.67 thf(15112,plain,((! [A:rat]: (ord_less_eq_rat @ A @ (abs_abs_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2217])). 185.47/93.67 thf(133,axiom,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: (((ord_le6747313008572928689nteger @ (times_3573771949741848930nteger @ (abs_abs_Code_integer @ A) @ (abs_abs_Code_integer @ C)) @ (times_3573771949741848930nteger @ B @ D)) <= (ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ C) @ D)) <= (ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6490_abs__mult__less)). 185.47/93.67 thf(8160,plain,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: ((ord_le6747313008572928689nteger @ (times_3573771949741848930nteger @ (abs_abs_Code_integer @ A) @ (abs_abs_Code_integer @ C)) @ (times_3573771949741848930nteger @ B @ D)) | ~ (ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ C) @ D) | ~ (ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 185.47/93.67 thf(2131,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ zero_zero_rat) = (((ord_less_rat @ A @ zero_zero_rat) & (ord_less_rat @ zero_zero_rat @ B)) | ((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ B @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2318_mult__less__0__iff)). 185.47/93.67 thf(14827,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ zero_zero_rat) = (((ord_less_rat @ A @ zero_zero_rat) & (ord_less_rat @ zero_zero_rat @ B)) | ((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ B @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2131])). 185.47/93.67 thf(916,axiom,((! [A:(nat > rat),B:set_nat]: ((~ (! [C:nat]: (((A @ C) = one_one_rat) <= (member_nat @ C @ B)))) <= ((groups73079841787564623at_rat @ A @ B) != one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8720_prod_Onot__neutral__contains__not__neutral)). 185.47/93.67 thf(10867,plain,((! [A:(nat > rat),B:set_nat]: (~ (! [C:nat]: (((A @ C) = one_one_rat) | ~ (member_nat @ C @ B))) | ((groups73079841787564623at_rat @ (A) @ B) = one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[916])). 185.47/93.67 thf(1460,axiom,((! [A:num]: ~ (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5959_not__neg__one__less__neg__numeral)). 185.47/93.67 thf(12599,plain,((! [A:num]: ~ (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460])). 185.47/93.67 thf(2593,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (modulo_modulo_nat @ A @ B)) = (modulo_modulo_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7246_of__nat__mod)). 185.47/93.67 thf(16342,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (modulo_modulo_nat @ A @ B)) = (modulo_modulo_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2593])). 185.47/93.67 thf(648,axiom,(((zero_n2687167440665602831ol_nat @ ($true)) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5121_of__bool__eq_I2_J)). 185.47/93.67 thf(9884,plain,(((zero_n2687167440665602831ol_nat @ ($true)) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[648])). 185.47/93.67 thf(2625,axiom,((! [A:nat]: (((semiri5074537144036343181t_real @ A) = zero_zero_real) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6894_of__nat__eq__0__iff)). 185.47/93.67 thf(16442,plain,((! [A:nat]: (((semiri5074537144036343181t_real @ A) = zero_zero_real) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2625])). 185.47/93.67 thf(630,axiom,((! [A:complex]: ((A != zero_zero_complex) => ((plus_plus_real @ (power_power_real @ (divide_divide_real @ (re @ A) @ (real_V1022390504157884413omplex @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (divide_divide_real @ (im @ A) @ (real_V1022390504157884413omplex @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9704_complex__unit__circle)). 185.47/93.67 thf(9826,plain,((! [A:complex]: ((~ (A = zero_zero_complex)) => ((plus_plus_real @ (power_power_real @ (divide_divide_real @ (re @ A) @ (real_V1022390504157884413omplex @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (divide_divide_real @ (im @ A) @ (real_V1022390504157884413omplex @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[630])). 185.47/93.67 thf(4815,axiom,((! [A:set_nat,B:set_nat,C:nat]: (((member_nat @ C @ B) <= (member_nat @ C @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1435_in__mono)). 185.47/93.67 thf(23466,plain,((! [A:set_nat,B:set_nat,C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4815])). 185.47/93.67 thf(6754,axiom,((one_one_complex != (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5552_one__neq__neg__one)). 185.47/93.67 thf(30569,plain,((~ (one_one_complex = (uminus1482373934393186551omplex @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6754])). 185.47/93.67 thf(3139,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5583_minus__divide__left)). 185.47/93.67 thf(18109,plain,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3139])). 185.47/93.67 thf(7086,axiom,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_775_mult_Ocomm__neutral)). 185.47/93.67 thf(31858,plain,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7086])). 185.47/93.67 thf(4451,axiom,((minus_minus_int = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5793_ab__group__add__class_Oab__diff__conv__add__uminus)). 185.47/93.67 thf(22251,plain,(((minus_minus_int) = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4451])). 185.47/93.67 thf(3898,axiom,((! [A:nat,B:nat,C:nat]: ((comm_s4663373288045622133er_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (comm_s4663373288045622133er_nat @ A @ B) @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8521_pochhammer__product_H)). 185.47/93.67 thf(20509,plain,((! [A:nat,B:nat,C:nat]: ((comm_s4663373288045622133er_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (comm_s4663373288045622133er_nat @ A @ B) @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3898])). 185.47/93.67 thf(2942,axiom,((ord_less_eq_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2278_zero__less__one__class_Ozero__le__one)). 185.47/93.67 thf(17487,plain,((ord_less_eq_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2942])). 185.47/93.67 thf(975,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((divide1717551699836669952omplex @ (divide1717551699836669952omplex @ A @ B) @ (divide1717551699836669952omplex @ C @ D)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ D) @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_divide__divide__times__eq)). 185.47/93.67 thf(11077,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((divide1717551699836669952omplex @ (divide1717551699836669952omplex @ A @ B) @ (divide1717551699836669952omplex @ C @ D)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ D) @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[975])). 185.47/93.67 thf(6298,axiom,((! [A:num]: (zero_zero_rat != (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2037_zero__neq__numeral)). 185.47/93.67 thf(28919,plain,((! [A:num]: ~ (zero_zero_rat = (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6298])). 185.47/93.67 thf(3186,axiom,((! [A:(nat > nat),B:(nat > nat),C:set_nat]: ((groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ (A @ D) @ (B @ D))) @ C) = (plus_plus_nat @ (groups3542108847815614940at_nat @ A @ C) @ (groups3542108847815614940at_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5621_sum_Odistrib)). 185.47/93.67 thf(18258,plain,((! [A:(nat > nat),B:(nat > nat),C:set_nat]: ((groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ (A @ D) @ (B @ D))) @ C) = (plus_plus_nat @ (groups3542108847815614940at_nat @ (A) @ C) @ (groups3542108847815614940at_nat @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3186])). 185.47/93.67 thf(5676,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_add__lessD1)). 185.47/93.67 thf(26623,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5676])). 185.47/93.67 thf(2937,axiom,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_numeral__Bit0)). 185.47/93.67 thf(17472,plain,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2937])). 185.47/93.67 thf(3432,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ B @ A) <= (~ (ord_less_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4156_leI)). 185.47/93.67 thf(19029,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ B @ A) | (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3432])). 185.47/93.67 thf(616,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (log @ A @ B) @ zero_zero_real) = (ord_less_eq_real @ B @ one_one_real))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9033_log__le__zero__cancel__iff)). 185.47/93.67 thf(9777,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (log @ A @ B) @ zero_zero_real) = (ord_less_eq_real @ B @ one_one_real))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[616])). 185.47/93.67 thf(5943,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (semiri1316708129612266289at_nat @ C)) = ((power_power_nat @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6955_of__nat__eq__of__nat__power__cancel__iff)). 185.47/93.67 thf(27670,plain,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (semiri1316708129612266289at_nat @ C)) = ((power_power_nat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5943])). 185.47/93.67 thf(1908,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) = (((ord_less_eq_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ A @ zero_zero_rat)) | ((ord_less_eq_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ zero_zero_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2203_zero__le__mult__iff)). 185.47/93.67 thf(14106,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) = (((ord_less_eq_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ A @ zero_zero_rat)) | ((ord_less_eq_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ zero_zero_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908])). 185.47/93.67 thf(6767,axiom,((zero_zero_int != one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2075_zero__neq__one)). 185.47/93.67 thf(30632,plain,((~ (zero_zero_int = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6767])). 185.47/93.67 thf(7487,axiom,((! [A:nat]: ((! [B:nat]: (A != (plus_plus_nat @ B @ B))) => (~ (! [B:nat]: (A != (plus_plus_nat @ B @ (suc @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_984_even__odd__cases)). 185.47/93.67 thf(33243,plain,((! [A:nat]: ((! [B:nat]: ~ (A = (plus_plus_nat @ B @ B))) => (~ (! [B:nat]: ~ (A = (plus_plus_nat @ B @ (suc @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7487])). 185.47/93.67 thf(4644,axiom,((! [A:complex,B:num]: ((divide1717551699836669952omplex @ A @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ imaginary_unit)) = (divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ (times_times_complex @ imaginary_unit @ A)) @ (numera6690914467698888265omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8989_divide__numeral__i)). 185.47/93.67 thf(22876,plain,((! [A:complex,B:num]: ((divide1717551699836669952omplex @ A @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ imaginary_unit)) = (divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ (times_times_complex @ imaginary_unit @ A)) @ (numera6690914467698888265omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4644])). 185.47/93.67 thf(2426,axiom,((! [A:real,B:real]: (((complex2 @ A @ B) = imaginary_unit) = ((B = one_one_real) & (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9007_Complex__eq__i)). 185.47/93.67 thf(15757,plain,((! [A:real,B:real]: (((complex2 @ A @ B) = imaginary_unit) = ((B = one_one_real) & (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2426])). 185.47/93.67 thf(4537,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ C @ D)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_add__mono__thms__linordered__semiring_I1_J)). 185.47/93.67 thf(22534,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) & (ord_less_eq_real @ C @ D)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4537])). 185.47/93.67 thf(1594,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_add_Oleft__cancel)). 185.47/93.67 thf(13015,plain,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594])). 185.47/93.67 thf(6902,axiom,((! [A:nat,B:real,C:real]: ((((root @ A @ B) = (root @ A @ C)) = (B = C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9159_real__root__eq__iff)). 185.47/93.67 thf(31137,plain,((! [A:nat,B:real,C:real]: ((((root @ A @ B) = (root @ A @ C)) = (B = C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6902])). 185.47/93.67 thf(2182,axiom,((! [A:complex,B:complex,C:nat]: ((power_power_complex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_power__divide)). 185.47/93.67 thf(15006,plain,((! [A:complex,B:complex,C:nat]: ((power_power_complex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2182])). 185.47/93.67 thf(961,axiom,((! [A:(nat > int),B:(nat > int),C:set_nat]: ((groups705719431365010083at_int @ (^ [D:nat]: (times_times_int @ (A @ D) @ (B @ D))) @ C) = (times_times_int @ (groups705719431365010083at_int @ A @ C) @ (groups705719431365010083at_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8726_prod_Odistrib)). 185.47/93.67 thf(11030,plain,((! [A:(nat > int),B:(nat > int),C:set_nat]: ((groups705719431365010083at_int @ (^ [D:nat]: (times_times_int @ (A @ D) @ (B @ D))) @ C) = (times_times_int @ (groups705719431365010083at_int @ (A) @ C) @ (groups705719431365010083at_int @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[961])). 185.47/93.67 thf(3009,axiom,((sums_real @ (^ [A:nat]: (power_power_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (suc @ A))) @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8239_power__half__series)). 185.47/93.67 thf(17704,plain,((sums_real @ (^ [A:nat]: (power_power_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (suc @ A))) @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3009])). 185.47/93.67 thf(50,axiom,((! [A:int,B:nat]: ((minus_minus_int @ one_one_int @ (power_power_int @ A @ B)) = (times_times_int @ (minus_minus_int @ one_one_int @ A) @ (groups3539618377306564664at_int @ (power_power_int @ A) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7594_one__diff__power__eq)). 185.47/93.67 thf(7897,plain,((! [A:int,B:nat]: ((minus_minus_int @ one_one_int @ (power_power_int @ A @ B)) = (times_times_int @ (minus_minus_int @ one_one_int @ A) @ (groups3539618377306564664at_int @ (power_power_int @ A) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 185.47/93.67 thf(7125,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_maxt @ A) = (some_nat @ C)) => (vEBT_vebt_member @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_955_maxt__member)). 185.47/93.67 thf(31976,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_maxt @ A) = (some_nat @ C)) => (vEBT_vebt_member @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7125])). 185.47/93.67 thf(2506,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ C)) & ((ord_less_real @ C @ A) <= (ord_less_eq_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2594_mult__less__cancel__right)). 185.47/93.67 thf(16042,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ C)) & ((ord_less_real @ C @ A) | ~ (ord_less_eq_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2506])). 185.47/93.67 thf(4675,axiom,((! [A:real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1721_zero__eq__1__divide__iff)). 185.47/93.67 thf(22977,plain,((! [A:real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4675])). 185.47/93.67 thf(4809,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ B @ (plus_plus_rat @ A @ C)) <= (ord_less_rat @ B @ C)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2396_pos__add__strict)). 185.47/93.67 thf(23445,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ B @ (plus_plus_rat @ A @ C)) | ~ (ord_less_rat @ B @ C) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4809])). 185.47/93.67 thf(364,axiom,((nat_set_encode = (groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9238_set__encode__def)). 185.47/93.67 thf(8949,plain,(((nat_set_encode) = (groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])). 185.47/93.67 thf(243,axiom,((! [A:nat,B:nat,C:(nat > rat)]: (((plus_plus_rat @ (groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_rat @ (C @ A) @ (groups2906978787729119204at_rat @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6674_sum_OSuc__reindex__ivl)). 185.47/93.67 thf(8505,plain,((! [A:nat,B:nat,C:(nat > rat)]: (((plus_plus_rat @ (groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_rat @ (C @ A) @ (groups2906978787729119204at_rat @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 185.47/93.67 thf(7571,axiom,((! [A:nat,B:nat]: ((member_nat @ (suc @ A) @ (nat_set_decode @ B)) = (member_nat @ A @ (nat_set_decode @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4428_set__decode__Suc)). 185.47/93.67 thf(33492,plain,((! [A:nat,B:nat]: ((member_nat @ (suc @ A) @ (nat_set_decode @ B)) = (member_nat @ A @ (nat_set_decode @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7571])). 185.47/93.67 thf(6518,axiom,((! [A:nat]: ((semiri1408675320244567234ct_nat @ (suc @ A)) = (times_times_nat @ (semiri1316708129612266289at_nat @ (suc @ A)) @ (semiri1408675320244567234ct_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7971_fact__Suc)). 185.47/93.67 thf(29730,plain,((! [A:nat]: ((semiri1408675320244567234ct_nat @ (suc @ A)) = (times_times_nat @ (semiri1316708129612266289at_nat @ (suc @ A)) @ (semiri1408675320244567234ct_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6518])). 185.47/93.67 thf(5271,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2507_mult__less__mono1)). 185.47/93.67 thf(25148,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5271])). 185.47/93.67 thf(498,axiom,((! [A:complex]: (((csqrt @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = A) <= (((ord_less_eq_real @ zero_zero_real @ (im @ A)) & ((re @ A) = zero_zero_real)) | (ord_less_real @ zero_zero_real @ (re @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9700_csqrt__square)). 185.47/93.67 thf(9408,plain,((! [A:complex]: (((csqrt @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = A) | ~ (((ord_less_eq_real @ zero_zero_real @ (im @ A)) & ((re @ A) = zero_zero_real)) | (ord_less_real @ zero_zero_real @ (re @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])). 185.47/93.67 thf(1996,axiom,((! [A:nat,B:nat]: (((ord_max_nat @ B @ A) = B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3586_max_Oabsorb3)). 185.47/93.67 thf(14406,plain,((! [A:nat,B:nat]: (((ord_max_nat @ B @ A) = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996])). 185.47/93.67 thf(3538,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7229_less__imp__of__nat__less)). 185.47/93.67 thf(19367,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3538])). 185.47/93.67 thf(1353,axiom,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (divide_divide_rat @ A @ C) @ (divide_divide_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_746_diff__divide__distrib)). 185.47/93.67 thf(12239,plain,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ (divide_divide_rat @ A @ C) @ (divide_divide_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353])). 185.47/93.67 thf(720,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (ord_max_int @ B @ C)) = (ord_max_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3751_max__add__distrib__right)). 185.47/93.67 thf(10132,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (ord_max_int @ B @ C)) = (ord_max_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[720])). 185.47/93.67 thf(6359,axiom,((! [A:nat,B:nat]: ((bit_se4205575877204974255it_nat @ (suc @ A) @ B) = (plus_plus_nat @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se4205575877204974255it_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3032_unset__bit__Suc)). 185.47/93.67 thf(29145,plain,((! [A:nat,B:nat]: ((bit_se4205575877204974255it_nat @ (suc @ A) @ B) = (plus_plus_nat @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se4205575877204974255it_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6359])). 185.47/93.67 thf(2233,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (ord_less_eq_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5035_neg__le__iff__le)). 185.47/93.67 thf(15152,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (ord_less_eq_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2233])). 185.47/93.67 thf(4731,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => (((modulo_modulo_int @ A @ B) = (plus_plus_int @ A @ B)) <= (ord_less_eq_int @ (plus_plus_int @ A @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3163_mod__pos__neg__trivial)). 185.47/93.67 thf(23170,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => (((modulo_modulo_int @ A @ B) = (plus_plus_int @ A @ B)) | ~ (ord_less_eq_int @ (plus_plus_int @ A @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4731])). 185.47/93.67 thf(1310,axiom,((! [A:nat,B:nat]: (ord_less_eq_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ (semiri1314217659103216013at_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6876_negative__zle)). 185.47/93.67 thf(12107,plain,((! [A:nat,B:nat]: (ord_less_eq_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ (semiri1314217659103216013at_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310])). 185.47/93.67 thf(2874,axiom,(((semiri1314217659103216013at_int @ one_one_nat) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7251_int__ops_I2_J)). 185.47/93.67 thf(17268,plain,(((semiri1314217659103216013at_int @ one_one_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2874])). 185.47/93.67 thf(580,axiom,((! [A:int,B:int]: ((ring_1_of_int_int @ (times_times_int @ A @ B)) = (times_times_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6972_of__int__mult)). 185.47/93.67 thf(9656,plain,((! [A:int,B:int]: ((ring_1_of_int_int @ (times_times_int @ A @ B)) = (times_times_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[580])). 185.47/93.67 thf(4169,axiom,((! [A:complex]: ((plus_plus_complex @ A @ (uminus1482373934393186551omplex @ A)) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5169_add_Oright__inverse)). 185.47/93.67 thf(21350,plain,((! [A:complex]: ((plus_plus_complex @ A @ (uminus1482373934393186551omplex @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4169])). 185.47/93.67 thf(4371,axiom,((! [A:num,B:nat]: ((ord_less_real @ (numeral_numeral_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_nat @ (numeral_numeral_nat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7019_numeral__less__real__of__nat__iff)). 185.47/93.67 thf(22002,plain,((! [A:num,B:nat]: ((ord_less_real @ (numeral_numeral_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_nat @ (numeral_numeral_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4371])). 185.47/93.67 thf(7500,axiom,((! [A:num]: ((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ A)) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1750_power__zero__numeral)). 185.47/93.67 thf(33285,plain,((! [A:num]: ((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7500])). 185.47/93.67 thf(4268,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ C) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ C @ B) @ A)) & ((~ (ord_less_real @ B @ zero_zero_real)) => (ord_less_eq_real @ zero_zero_real @ C)))) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ (times_times_real @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2832_divide__le__eq)). 185.47/93.67 thf(21654,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ C) = (((~ (ord_less_real @ zero_zero_real @ B)) => (((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ C @ B) @ A)) & ((~ (ord_less_real @ B @ zero_zero_real)) => (ord_less_eq_real @ zero_zero_real @ C)))) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ (times_times_real @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4268])). 185.47/93.67 thf(3630,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_eq_int @ (plus_plus_int @ B @ A) @ C) <= (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2302_add__decreasing2)). 185.47/93.67 thf(19651,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_eq_int @ (plus_plus_int @ B @ A) @ C) | ~ (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3630])). 185.47/93.67 thf(7098,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ A @ one_one_rat) => (ord_less_rat @ (times_times_rat @ A @ (power_power_rat @ A @ B)) @ (power_power_rat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2868_power__Suc__less)). 185.47/93.67 thf(31894,plain,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ A @ one_one_rat) => (ord_less_rat @ (times_times_rat @ A @ (power_power_rat @ A @ B)) @ (power_power_rat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7098])). 185.47/93.67 thf(2915,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ imaginary_unit) = (times_times_complex @ (uminus1482373934393186551omplex @ imaginary_unit) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8987_divide__i)). 185.47/93.67 thf(17400,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ imaginary_unit) = (times_times_complex @ (uminus1482373934393186551omplex @ imaginary_unit) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2915])). 185.47/93.67 thf(903,axiom,((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7761_pi__half__ge__zero)). 185.47/93.67 thf(10829,plain,((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[903])). 185.47/93.67 thf(545,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (ord_max_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3692_max_Ocobounded2)). 185.47/93.67 thf(9546,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (ord_max_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[545])). 185.47/93.67 thf(2908,axiom,((! [A:rat,B:rat,C:(rat > nat),D:nat]: ((((ord_less_nat @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F))))) <= ((C @ B) = D)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4091_ord__less__eq__subst)). 185.47/93.67 thf(17376,plain,((! [A:rat,B:rat,C:(rat > nat),D:nat]: ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_nat @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2908])). 185.47/93.67 thf(3884,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_eq_real @ (uminus_uminus_real @ C) @ (times_times_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6210_neg__le__minus__divide__eq)). 185.47/93.67 thf(20470,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_eq_real @ (uminus_uminus_real @ C) @ (times_times_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3884])). 185.47/93.67 thf(2034,axiom,((! [A:int,B:int]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6944_of__int__less__iff)). 185.47/93.67 thf(14530,plain,((! [A:int,B:int]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2034])). 185.47/93.67 thf(4646,axiom,((! [A:int,B:int,C:num]: ((times_times_int @ (plus_plus_int @ A @ B) @ (numeral_numeral_int @ C)) = (plus_plus_int @ (times_times_int @ A @ (numeral_numeral_int @ C)) @ (times_times_int @ B @ (numeral_numeral_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_distrib__right__numeral)). 185.47/93.67 thf(22881,plain,((! [A:int,B:int,C:num]: ((times_times_int @ (plus_plus_int @ A @ B) @ (numeral_numeral_int @ C)) = (plus_plus_int @ (times_times_int @ A @ (numeral_numeral_int @ C)) @ (times_times_int @ B @ (numeral_numeral_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4646])). 185.47/93.67 thf(5744,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (power_power_nat @ A @ C) @ B) = (times_times_nat @ B @ (power_power_nat @ A @ C))) <= ((times_times_nat @ A @ B) = (times_times_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_power__commuting__commutes)). 185.47/93.67 thf(26844,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (power_power_nat @ A @ C) @ B) = (times_times_nat @ B @ (power_power_nat @ A @ C))) | ~ ((times_times_nat @ A @ B) = (times_times_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5744])). 185.47/93.67 thf(6650,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (suc @ (modulo_modulo_nat @ A @ B))) @ B) = (modulo_modulo_nat @ (suc @ (suc @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2014_mod__Suc__Suc__eq)). 185.47/93.67 thf(30169,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (suc @ (modulo_modulo_nat @ A @ B))) @ B) = (modulo_modulo_nat @ (suc @ (suc @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6650])). 185.47/93.67 thf(2866,axiom,((ord_less_int = (^ [A:int,B:int]: (ord_less_eq_real @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real) @ (ring_1_of_int_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7304_int__less__real__le)). 185.47/93.67 thf(17244,plain,(((ord_less_int) = (^ [A:int,B:int]: (ord_less_eq_real @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real) @ (ring_1_of_int_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2866])). 185.47/93.67 thf(4882,axiom,((semiri2265585572941072030t_real = (comm_s7457072308508201937r_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8447_pochhammer__fact)). 185.47/93.67 thf(23696,plain,(((semiri2265585572941072030t_real) = (comm_s7457072308508201937r_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4882])). 185.47/93.67 thf(4982,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2114_bot__nat__0_Oextremum__strict)). 185.47/93.67 thf(24030,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4982])). 185.47/93.67 thf(4767,axiom,((! [A:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ zero_zero_rat) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6361_abs__le__zero__iff)). 185.47/93.67 thf(23321,plain,((! [A:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ zero_zero_rat) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4767])). 185.47/93.67 thf(4582,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ A @ B)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1855_divide__le__eq__1__neg)). 185.47/93.67 thf(22676,plain,((! [A:real,B:real]: (((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ A @ B)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4582])). 185.47/93.67 thf(5178,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ one_one_nat @ B) => (ord_less_nat @ one_one_nat @ (times_times_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1193_less__1__mult)). 185.47/93.67 thf(24806,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ one_one_nat @ B) => (ord_less_nat @ one_one_nat @ (times_times_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5178])). 185.47/93.67 thf(6528,axiom,(((sqrt @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8132_real__sqrt__four)). 185.47/93.67 thf(29771,plain,(((sqrt @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6528])). 185.47/93.67 thf(7554,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_V5719532721284313246member @ (vEBT_Node @ A @ (suc @ B) @ C @ D) @ E) = (((ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ (suc @ B) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ (suc @ B) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ E @ (divide_divide_nat @ (suc @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ (suc @ B) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1441_VEBT__internal_Onaive__member_Osimps_I3_J)). 185.47/93.67 thf(33445,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_V5719532721284313246member @ (vEBT_Node @ A @ (suc @ B) @ C @ D) @ E) = (((ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ (suc @ B) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ (suc @ B) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ E @ (divide_divide_nat @ (suc @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ (suc @ B) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7554])). 185.47/93.67 thf(5066,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039_Suc__leD)). 185.47/93.67 thf(24392,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5066])). 185.47/93.67 thf(2826,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4523_even__add)). 185.47/93.67 thf(17112,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2826])). 185.47/93.67 thf(2581,axiom,((! [A:int,B:int,C:int]: ((((ord_less_eq_int @ B @ A) => (~ (ord_less_eq_int @ A @ C))) => ((((~ (ord_less_eq_int @ B @ A)) <= (ord_less_eq_int @ C @ B)) => (((ord_less_eq_int @ B @ C) => (~ (ord_less_eq_int @ C @ A))) => (~ ((ord_less_eq_int @ C @ A) => (~ (ord_less_eq_int @ A @ B)))))) <= ((~ (ord_less_eq_int @ C @ B)) <= (ord_less_eq_int @ A @ C)))) <= ((ord_less_eq_int @ A @ B) => (~ (ord_less_eq_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3849_le__cases3)). 185.47/93.67 thf(16290,plain,((! [A:int,B:int,C:int]: ((((ord_less_eq_int @ B @ A) => (~ (ord_less_eq_int @ A @ C))) => (((~ (ord_less_eq_int @ B @ A) | ~ (ord_less_eq_int @ C @ B)) => (((ord_less_eq_int @ B @ C) => (~ (ord_less_eq_int @ C @ A))) => (~ ((ord_less_eq_int @ C @ A) => (~ (ord_less_eq_int @ A @ B)))))) | ~ (~ (ord_less_eq_int @ C @ B) | ~ (ord_less_eq_int @ A @ C)))) | ~ ((ord_less_eq_int @ A @ B) => (~ (ord_less_eq_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2581])). 185.47/93.67 thf(2523,axiom,((! [A:rat,B:rat]: ~ (ord_less_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2988_not__sum__power2__lt__zero)). 185.47/93.67 thf(16097,plain,((! [A:rat,B:rat]: ~ (ord_less_rat @ (plus_plus_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2523])). 185.47/93.67 thf(3021,axiom,((! [A:set_nat,B:nat]: (((member_nat @ B @ A) => (? [C:nat]: ((member_nat @ C @ A) & ! [D:nat]: (((C = D) <= (ord_less_eq_nat @ C @ D)) <= (member_nat @ D @ A)) & (ord_less_eq_nat @ B @ C)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3470_finite__has__maximal2)). 185.47/93.67 thf(17736,plain,((! [A:set_nat,B:nat]: (((member_nat @ B @ A) => (? [C:nat]: ((member_nat @ C @ A) & ! [D:nat]: ((C = D) | ~ (ord_less_eq_nat @ C @ D) | ~ (member_nat @ D @ A)) & (ord_less_eq_nat @ B @ C)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3021])). 185.47/93.67 thf(6030,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4313_order__le__less__trans)). 185.47/93.67 thf(27983,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6030])). 185.47/93.67 thf(5395,axiom,((ord_less_eq_num = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4272_order__le__less)). 185.47/93.67 thf(25582,plain,(((ord_less_eq_num) = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5395])). 185.47/93.67 thf(5921,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6899_of__nat__less__iff)). 185.47/93.67 thf(27603,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5921])). 185.47/93.67 thf(1178,axiom,((! [A:real,B:real,C:real,D:real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ D)) = (divide_divide_real @ (times_times_real @ A @ D) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_divide__divide__times__eq)). 185.47/93.67 thf(11706,plain,((! [A:real,B:real,C:real,D:real]: ((divide_divide_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ D)) = (divide_divide_real @ (times_times_real @ A @ D) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178])). 185.47/93.67 thf(6214,axiom,((! [A:code_integer,B:code_integer]: (((uminus1351360451143612070nteger @ A) = B) = ((uminus1351360451143612070nteger @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5495_minus__equation__iff)). 185.47/93.67 thf(28644,plain,((! [A:code_integer,B:code_integer]: (((uminus1351360451143612070nteger @ A) = B) = ((uminus1351360451143612070nteger @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6214])). 185.47/93.67 thf(7530,axiom,((! [A:int]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_int @ (times_times_int @ (times_times_int @ A @ A) @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_power4__eq__xxxx)). 185.47/93.67 thf(33381,plain,((! [A:int]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_int @ (times_times_int @ (times_times_int @ A @ A) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7530])). 185.47/93.67 thf(1709,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ (times_times_rat @ A @ B) @ C) => (dvd_dvd_rat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4597_dvd__mult__left)). 185.47/93.67 thf(13454,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ (times_times_rat @ A @ B) @ C) => (dvd_dvd_rat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709])). 185.47/93.67 thf(6997,axiom,((! [A:int,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (power_power_int @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4561_even__power)). 185.47/93.67 thf(31544,plain,((! [A:int,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (power_power_int @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6997])). 185.47/93.67 thf(2738,axiom,((! [A:int,B:nat,C:set_nat]: ((groups3539618377306564664at_int @ (^ [D:nat]: (power_power_int @ A @ (plus_plus_nat @ B @ D))) @ C) = (times_times_int @ (power_power_int @ A @ B) @ (groups3539618377306564664at_int @ (power_power_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6623_sum__power__add)). 185.47/93.67 thf(16838,plain,((! [A:int,B:nat,C:set_nat]: ((groups3539618377306564664at_int @ (^ [D:nat]: (power_power_int @ A @ (plus_plus_nat @ B @ D))) @ C) = (times_times_int @ (power_power_int @ A @ B) @ (groups3539618377306564664at_int @ (power_power_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2738])). 185.47/93.67 thf(2126,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (times_times_real @ B @ A)) = (((ord_less_eq_real @ one_one_real @ B) <= (ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ one_one_real) <= (ord_less_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2812_mult__le__cancel__right1)). 185.47/93.67 thf(14810,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (times_times_real @ B @ A)) = (((ord_less_eq_real @ one_one_real @ B) | ~ (ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ one_one_real) | ~ (ord_less_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2126])). 185.47/93.67 thf(4199,axiom,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ A @ A)) = (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1637_zero__less__double__add__iff__zero__less__single__add)). 185.47/93.67 thf(21442,plain,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ A @ A)) = (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4199])). 185.47/93.67 thf(1466,axiom,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1529_add__cancel__right__right)). 185.47/93.67 thf(12616,plain,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466])). 185.47/93.67 thf(2353,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1818_zero__less__divide__1__iff)). 185.47/93.67 thf(15524,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2353])). 185.47/93.67 thf(2264,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ C @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1228_ordered__ring__class_Ole__add__iff2)). 185.47/93.67 thf(15252,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ B) @ C) @ (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (ord_less_eq_real @ C @ (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2264])). 185.47/93.67 thf(3177,axiom,((! [A:complex,B:nat,C:nat]: ((((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (plus_plus_complex @ (semiri8010041392384452111omplex @ C) @ one_one_complex)) <= (A = one_one_complex)) & ((A != one_one_complex) => ((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (divide1717551699836669952omplex @ (times_times_complex @ (power_power_complex @ A @ B) @ (minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ (suc @ C)))) @ (minus_minus_complex @ one_one_complex @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7361_sum__gp__offset)). 185.47/93.67 thf(18226,plain,((! [A:complex,B:nat,C:nat]: ((((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (plus_plus_complex @ (semiri8010041392384452111omplex @ C) @ one_one_complex)) | ~ (A = one_one_complex)) & ((~ (A = one_one_complex)) => ((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (divide1717551699836669952omplex @ (times_times_complex @ (power_power_complex @ A @ B) @ (minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ (suc @ C)))) @ (minus_minus_complex @ one_one_complex @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3177])). 185.47/93.67 thf(1657,axiom,((! [A:rat]: ((plus_plus_rat @ A @ zero_zero_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2083_add_Ocomm__neutral)). 185.47/93.67 thf(13292,plain,((! [A:rat]: ((plus_plus_rat @ A @ zero_zero_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657])). 185.47/93.67 thf(1895,axiom,((! [A:rat,B:rat]: ? [C:rat]: ! [D:rat]: (((dvd_dvd_rat @ A @ (plus_plus_rat @ D @ B)) = (dvd_dvd_rat @ A @ (plus_plus_rat @ D @ B))) <= (ord_less_rat @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4720_pinf_I9_J)). 185.47/93.67 thf(14068,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1895])). 185.47/93.67 thf(6012,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A)))) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9368_and__minus__numerals_I1_J)). 185.47/93.67 thf(27933,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A)))) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6012])). 185.47/93.67 thf(1208,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ (^ [B:nat]: (if_complex @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri8010041392384452111omplex @ (binomial @ A @ B)) @ zero_zero_complex)) @ (set_ord_atMost_nat @ A))) = (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8621_choose__even__sum)). 185.47/93.67 thf(11795,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (groups2073611262835488442omplex @ (^ [B:nat]: (if_complex @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri8010041392384452111omplex @ (binomial @ A @ B)) @ zero_zero_complex)) @ (set_ord_atMost_nat @ A))) = (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208])). 185.47/93.67 thf(234,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ pi) => (((((cos_real @ A) = (cos_real @ B)) => (A = B)) <= (ord_less_eq_real @ B @ pi)) <= (ord_less_eq_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7842_cos__inj__pi)). 185.47/93.67 thf(8477,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ pi) => ((((cos_real @ A) = (cos_real @ B)) => (A = B)) | ~ (ord_less_eq_real @ B @ pi) | ~ (ord_less_eq_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 185.47/93.67 thf(2631,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ (times_times_int @ B @ C)) @ C) = (modulo_modulo_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1783_mod__mult__self1)). 185.47/93.67 thf(16457,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ (times_times_int @ B @ C)) @ C) = (modulo_modulo_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2631])). 185.47/93.67 thf(143,axiom,((! [A:(nat > real),B:(nat > real)]: ((summable_real @ A) => ((summable_real @ B) => (summable_real @ (^ [C:nat]: (plus_plus_real @ (A @ C) @ (B @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7664_summable__add)). 185.47/93.67 thf(8194,plain,((! [A:(nat > real),B:(nat > real)]: ((summable_real @ (A)) => ((summable_real @ (B)) => (summable_real @ (^ [C:nat]: (plus_plus_real @ (A @ C) @ (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 185.47/93.67 thf(2722,axiom,((! [A:real,B:real,C:real,D:real]: (((A = B) & (ord_less_eq_real @ C @ D)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_add__mono__thms__linordered__semiring_I2_J)). 185.47/93.67 thf(16787,plain,((! [A:real,B:real,C:real,D:real]: (((A = B) & (ord_less_eq_real @ C @ D)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2722])). 185.47/93.67 thf(1196,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ B @ A)) = (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1645_less__add__same__cancel2)). 185.47/93.67 thf(11758,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ B @ A)) = (ord_less_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196])). 185.47/93.67 thf(5341,axiom,((! [A:complex,B:complex]: ((A = (times_times_complex @ A @ B)) = ((A = zero_zero_complex) | (B = one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1661_mult__cancel__left1)). 185.47/93.67 thf(25379,plain,((! [A:complex,B:complex]: ((A = (times_times_complex @ A @ B)) = ((A = zero_zero_complex) | (B = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5341])). 185.47/93.67 thf(1351,axiom,((! [A:int]: ((zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) = (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6204_of__bool__odd__eq__mod__2)). 185.47/93.67 thf(12234,plain,((! [A:int]: ((zero_n2684676970156552555ol_int @ (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) = (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351])). 185.47/93.67 thf(5241,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_976_le__add__diff__inverse)). 185.47/93.67 thf(25015,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5241])). 185.47/93.67 thf(1492,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ (times_times_int @ B @ A) @ C) @ A) = (plus_plus_int @ B @ (divide_divide_int @ C @ A))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1835_div__mult__self3)). 185.47/93.67 thf(12695,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ (times_times_int @ B @ A) @ C) @ A) = (plus_plus_int @ B @ (divide_divide_int @ C @ A))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492])). 185.47/93.67 thf(3325,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5159_neg__0__less__iff__less)). 185.47/93.67 thf(18686,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3325])). 185.47/93.67 thf(5261,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_le__add2)). 185.47/93.67 thf(25088,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5261])). 185.47/93.67 thf(4586,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B)) = ((dvd_dvd_rat @ A @ C) | (B = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4460_dvd__mult__cancel__right)). 185.47/93.67 thf(22689,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B)) = ((dvd_dvd_rat @ A @ C) | (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4586])). 185.47/93.67 thf(4299,axiom,((! [A:int]: ~ (! [B:nat,C:nat]: (A != (minus_minus_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7191_int__diff__cases)). 185.47/93.67 thf(21740,plain,((! [A:int]: ~ (! [B:nat,C:nat]: ~ (A = (minus_minus_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4299])). 185.47/93.67 thf(4951,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1592_bot__nat__0_Oextremum)). 185.47/93.67 thf(23943,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4951])). 185.47/93.67 thf(2837,axiom,((! [A:real,B:real]: (((times_times_real @ A @ (powr_real @ A @ B)) = (powr_real @ A @ (plus_plus_real @ one_one_real @ B))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9117_powr__mult__base)). 185.47/93.67 thf(17151,plain,((! [A:real,B:real]: (((times_times_real @ A @ (powr_real @ A @ B)) = (powr_real @ A @ (plus_plus_real @ one_one_real @ B))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2837])). 185.47/93.67 thf(1533,axiom,((~ (ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5714_le__minus__one__simps_I4_J)). 185.47/93.67 thf(12817,plain,((~ (ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533])). 185.47/93.67 thf(2554,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_add__right__mono)). 185.47/93.67 thf(16202,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2554])). 185.47/93.67 thf(2163,axiom,((! [A:real,B:real]: (((ord_less_real @ one_one_real @ (times_times_real @ A @ B)) <= (ord_less_real @ one_one_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1191_less__1__mult)). 185.47/93.67 thf(14940,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ (times_times_real @ A @ B)) | ~ (ord_less_real @ one_one_real @ B) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2163])). 185.47/93.67 thf(6550,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ (times_times_nat @ C @ A)) @ A) = (plus_plus_nat @ C @ (divide_divide_nat @ B @ A))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1838_div__mult__self1)). 185.47/93.67 thf(29839,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ (times_times_nat @ C @ A)) @ A) = (plus_plus_nat @ C @ (divide_divide_nat @ B @ A))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6550])). 185.47/93.67 thf(5986,axiom,((! [A:num,B:num]: (((ord_less_num @ A @ B) <= (ord_less_eq_num @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4306_order__neq__le__trans)). 185.47/93.67 thf(27848,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) | ~ (ord_less_eq_num @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5986])). 185.47/93.67 thf(5984,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2289_add__nonpos__nonpos)). 185.47/93.67 thf(27838,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5984])). 185.47/93.67 thf(7228,axiom,((! [A:num]: ((plus_plus_int @ (numeral_numeral_int @ A) @ one_one_int) = (numeral_numeral_int @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_numeral__plus__one)). 185.47/93.67 thf(32365,plain,((! [A:num]: ((plus_plus_int @ (numeral_numeral_int @ A) @ one_one_int) = (numeral_numeral_int @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7228])). 185.47/93.67 thf(4669,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_nat @ A @ B) => ((ord_less_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) <= (ord_less_real @ one_one_real @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_power__strict__increasing)). 185.47/93.67 thf(22953,plain,((! [A:nat,B:nat,C:real]: ((ord_less_nat @ A @ B) => ((ord_less_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) | ~ (ord_less_real @ one_one_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4669])). 185.47/93.67 thf(7187,axiom,((! [A:nat,B:int]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_int @ (abs_abs_int @ B) @ A) = (power_power_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6693_power__even__abs)). 185.47/93.67 thf(32207,plain,((! [A:nat,B:int]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_int @ (abs_abs_int @ B) @ A) = (power_power_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7187])). 185.47/93.67 thf(5579,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4450_nat__mult__dvd__cancel__disj)). 185.47/93.67 thf(26299,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5579])). 185.47/93.67 thf(472,axiom,((! [A:real]: (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (tanh_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6539_tanh__real__gt__neg1)). 185.47/93.67 thf(9317,plain,((! [A:real]: (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (tanh_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])). 185.47/93.67 thf(6972,axiom,((! [A:vEBT_VEBT,B:nat]: (((((! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ zero_zero_nat @ D @ E))) => ((! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ (suc @ zero_zero_nat) @ D @ E))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: ((((((~ (ord_less_nat @ D @ B) & (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))))) <= (~ (ord_less_nat @ D @ B)))) <= (~ (ord_less_nat @ B @ C))) & ~ (ord_less_nat @ B @ C)) <= (B != D)) <= (B != C)) <= (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G)))))))) <= (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) <= (! [C:$o,D:$o]: (((((B = one_one_nat) & ((B = one_one_nat) => (D))) <= (B != zero_zero_nat)) & ((C) <= (B = zero_zero_nat))) <= (A = (vEBT_Leaf @ C @ D))))) <= (~ (vEBT_vebt_member @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3004_vebt__member_Oelims_I3_J)). 185.47/93.67 thf(31413,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ zero_zero_nat @ D @ E))) => ((! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ (suc @ zero_zero_nat) @ D @ E))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: ((((~ (ord_less_nat @ D @ B) & (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))))) | (ord_less_nat @ D @ B))) | (ord_less_nat @ B @ C)) & ~ (ord_less_nat @ B @ C)) | (B = D) | (B = C) | ~ (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G)))))))) | ~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) | ~ (! [C:$o,D:$o]: (((((B = one_one_nat) & ((B = one_one_nat) => (D))) | (B = zero_zero_nat)) & ((C) | ~ (B = zero_zero_nat))) | ~ (A = (vEBT_Leaf @ C @ D)))) | (vEBT_vebt_member @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6972])). 185.47/93.67 thf(2959,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_real @ (uminus_uminus_real @ C) @ (times_times_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6148_neg__less__minus__divide__eq)). 185.47/93.67 thf(17532,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_real @ (uminus_uminus_real @ C) @ (times_times_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2959])). 185.47/93.67 thf(5167,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1469_deg__not__0)). 185.47/93.67 thf(24774,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5167])). 185.47/93.67 thf(5020,axiom,((! [A:nat]: ((bit_se547839408752420682it_nat @ A @ (suc @ zero_zero_nat)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9502_push__bit__of__Suc__0)). 185.47/93.67 thf(24164,plain,((! [A:nat]: ((bit_se547839408752420682it_nat @ A @ (suc @ zero_zero_nat)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5020])). 185.47/93.67 thf(5958,axiom,((! [A:(nat > $o),B:nat]: ((((A @ B) <= (! [C:nat]: ((A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) <= (A @ C)))) <= (! [C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) <= (A @ C)))) <= (A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2993_nat__bit__induct)). 185.47/93.67 thf(27716,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) | ~ (A @ C))) | ~ (! [C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) | ~ (A @ C))) | ~ (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5958])). 185.47/93.67 thf(1507,axiom,((! [A:real,B:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ (plus_plus_real @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5089_minus__add__cancel)). 185.47/93.67 thf(12740,plain,((! [A:real,B:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ (plus_plus_real @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507])). 185.47/93.67 thf(2543,axiom,((! [A:num]: ((real_V7735802525324610683m_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7448_norm__neg__numeral)). 185.47/93.67 thf(16166,plain,((! [A:num]: ((real_V7735802525324610683m_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2543])). 185.47/93.67 thf(2161,axiom,((! [A:nat,B:nat]: ((ord_max_nat @ (suc @ A) @ B) = (case_nat_nat @ (suc @ A) @ (^ [C:nat]: (suc @ (ord_max_nat @ A @ C))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9742_max__Suc1)). 185.47/93.67 thf(14934,plain,((! [A:nat,B:nat]: ((ord_max_nat @ (suc @ A) @ B) = (case_nat_nat @ (suc @ A) @ (^ [C:nat]: (suc @ (ord_max_nat @ A @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2161])). 185.47/93.67 thf(2694,axiom,((! [A:int,B:int]: (((plus_plus_int @ (minus_minus_int @ B @ A) @ A) = B) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_981_le__add__diff__inverse2)). 185.47/93.67 thf(16699,plain,((! [A:int,B:int]: (((plus_plus_int @ (minus_minus_int @ B @ A) @ A) = B) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2694])). 185.47/93.67 thf(5790,axiom,((! [A:int]: ((zero_zero_int = A) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1929_zero__reorient)). 185.47/93.67 thf(26989,plain,((! [A:int]: ((zero_zero_int = A) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5790])). 185.47/93.67 thf(3838,axiom,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5943_neg__numeral__less__one)). 185.47/93.67 thf(20319,plain,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3838])). 185.47/93.67 thf(4164,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ C @ A) @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9372_AND__upper2_H)). 185.47/93.67 thf(21337,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ C @ A) @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4164])). 185.47/93.67 thf(4080,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (sqrt @ A) @ (sqrt @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8115_real__sqrt__le__iff)). 185.47/93.67 thf(21071,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (sqrt @ A) @ (sqrt @ B)) = (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4080])). 185.47/93.67 thf(3122,axiom,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (divide1717551699836669952omplex @ A @ C) @ (divide1717551699836669952omplex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_add__divide__distrib)). 185.47/93.67 thf(18060,plain,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (divide1717551699836669952omplex @ A @ C) @ (divide1717551699836669952omplex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3122])). 185.47/93.67 thf(2283,axiom,((! [A:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ one_one_real) = (times_times_real @ (plus_plus_real @ A @ one_one_real) @ (minus_minus_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1241_square__diff__one__factored)). 185.47/93.67 thf(15308,plain,((! [A:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ one_one_real) = (times_times_real @ (plus_plus_real @ A @ one_one_real) @ (minus_minus_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2283])). 185.47/93.67 thf(5608,axiom,((! [A:nat,B:nat]: (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) != zero_zero_int) <= ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2950_exp__add__not__zero__imp__left)). 185.47/93.67 thf(26391,plain,((! [A:nat,B:nat]: (~ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = zero_zero_int) | ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5608])). 185.47/93.67 thf(4400,axiom,((! [A:nat,B:nat]: (((semiri1314217659103216013at_int @ A) = (semiri1314217659103216013at_int @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6867_of__nat__eq__iff)). 185.47/93.67 thf(22093,plain,((! [A:nat,B:nat]: (((semiri1314217659103216013at_int @ A) = (semiri1314217659103216013at_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4400])). 185.47/93.67 thf(5070,axiom,((! [A:num,B:num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5342_mult__neg__numeral__simps_I2_J)). 185.47/93.67 thf(24403,plain,((! [A:num,B:num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5070])). 185.47/93.67 thf(2650,axiom,((! [A:int,B:int]: (((~ (ord_less_int @ B @ A)) = (B = A)) <= (~ (ord_less_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4001_antisym__conv3)). 185.47/93.67 thf(16521,plain,((! [A:int,B:int]: (((~ (ord_less_int @ B @ A)) = (B = A)) | (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2650])). 185.47/93.67 thf(571,axiom,(((exp_complex @ (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (real_V4546457046886955230omplex @ pi)) @ imaginary_unit)) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9138_exp__two__pi__i)). 185.47/93.67 thf(9631,plain,(((exp_complex @ (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (real_V4546457046886955230omplex @ pi)) @ imaginary_unit)) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[571])). 185.47/93.67 thf(2188,axiom,((! [A:num,B:int]: ((ord_less_real @ (numeral_numeral_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7074_of__int__numeral__less__iff)). 185.47/93.67 thf(15021,plain,((! [A:num,B:int]: ((ord_less_real @ (numeral_numeral_real @ A) @ (ring_1_of_int_real @ B)) = (ord_less_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2188])). 185.47/93.67 thf(6297,axiom,((! [A:nat]: ((divide_divide_nat @ one_one_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5480_one__div__2__pow__eq)). 185.47/93.67 thf(28916,plain,((! [A:nat]: ((divide_divide_nat @ one_one_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6297])). 185.47/93.67 thf(7715,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((binomial @ A @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = (binomial @ A @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8548_central__binomial__odd)). 185.47/93.67 thf(33883,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((binomial @ A @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = (binomial @ A @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7715])). 185.47/93.67 thf(350,axiom,((! [A:(nat > complex)]: ((groups6464643781859351333omplex @ A @ bot_bot_set_nat) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8641_prod_Oempty)). 185.47/93.67 thf(8905,plain,((! [A:(nat > complex)]: ((groups6464643781859351333omplex @ (A) @ bot_bot_set_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])). 185.47/93.67 thf(3558,axiom,((ord_less_eq_int @ one_one_int @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_763_le__numeral__extra_I4_J)). 185.47/93.67 thf(19431,plain,((ord_less_eq_int @ one_one_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3558])). 185.47/93.67 thf(3149,axiom,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (minus_minus_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))) = (bit_se2923211474154528505it_int @ A @ (minus_minus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9269_take__bit__diff)). 185.47/93.67 thf(18141,plain,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (minus_minus_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))) = (bit_se2923211474154528505it_int @ A @ (minus_minus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3149])). 185.47/93.67 thf(6579,axiom,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ (times_times_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ C)) @ (divide_divide_nat @ (times_times_nat @ A @ (modulo_modulo_nat @ B @ C)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2550_div__mult1__eq)). 185.47/93.67 thf(29938,plain,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ (times_times_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ C)) @ (divide_divide_nat @ (times_times_nat @ A @ (modulo_modulo_nat @ B @ C)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6579])). 185.47/93.67 thf(6589,axiom,((! [A:real,B:real]: (((sqrt @ A) = (sqrt @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8111_real__sqrt__eq__iff)). 185.47/93.67 thf(29973,plain,((! [A:real,B:real]: (((sqrt @ A) = (sqrt @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6589])). 185.47/93.67 thf(3439,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_max_nat @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3701_max_Oabsorb__iff1)). 185.47/93.67 thf(19050,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_max_nat @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3439])). 185.47/93.67 thf(7449,axiom,((! [A:num,B:num]: (((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5067_neg__numeral__eq__iff)). 185.47/93.67 thf(33093,plain,((! [A:num,B:num]: (((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7449])). 185.47/93.67 thf(3669,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (((ord_less_eq_int @ C @ A) <= (ord_less_int @ B @ zero_zero_int)) & ((ord_less_eq_int @ A @ C) <= (ord_less_int @ zero_zero_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2574_mult__le__cancel__right)). 185.47/93.67 thf(19778,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (((ord_less_eq_int @ C @ A) | ~ (ord_less_int @ B @ zero_zero_int)) & ((ord_less_eq_int @ A @ C) | ~ (ord_less_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3669])). 185.47/93.67 thf(6066,axiom,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_complex @ A @ (power_power_complex @ (power_power_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1120_power__odd__eq)). 185.47/93.67 thf(28091,plain,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_complex @ A @ (power_power_complex @ (power_power_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6066])). 185.47/93.67 thf(1254,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ B @ A) => (A = B)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3900_antisym)). 185.47/93.67 thf(11937,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ B @ A) => (A = B)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254])). 185.47/93.67 thf(2494,axiom,((! [A:num,B:nat,C:int]: ((ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ (nat2 @ C)) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9264_numeral__power__le__nat__cancel__iff)). 185.47/93.67 thf(16001,plain,((! [A:num,B:nat,C:int]: ((ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ (nat2 @ C)) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2494])). 185.47/93.67 thf(5306,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2219_mult__nonneg__nonneg)). 185.47/93.67 thf(25262,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5306])). 185.47/93.67 thf(6049,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1050_add__Suc)). 185.47/93.67 thf(28039,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6049])). 185.47/93.67 thf(3557,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8007_fact__dvd)). 185.47/93.67 thf(19429,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3557])). 185.47/93.67 thf(1910,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ A @ (times_times_complex @ B @ A)) = (divide1717551699836669952omplex @ one_one_complex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1826_nonzero__divide__mult__cancel__right)). 185.47/93.67 thf(14111,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ A @ (times_times_complex @ B @ A)) = (divide1717551699836669952omplex @ one_one_complex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1910])). 185.47/93.67 thf(4867,axiom,((! [A:num,B:num]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ (numeral_numeral_nat @ B)) = (~ (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ (pred_numeral @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9418_bit__minus__numeral__int_I2_J)). 185.47/93.67 thf(23630,plain,((! [A:num,B:num]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ (numeral_numeral_nat @ B)) = (~ (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ (pred_numeral @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4867])). 185.47/93.67 thf(6849,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (semiri1316708129612266289at_nat @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7062_of__nat__power__le__of__nat__cancel__iff)). 185.47/93.67 thf(30932,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (semiri1316708129612266289at_nat @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6849])). 185.47/93.67 thf(4997,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => ((ord_less_eq_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A)) <= (ord_less_eq_nat @ C @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2885_power__decreasing)). 185.47/93.67 thf(24093,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => ((ord_less_eq_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A)) | ~ (ord_less_eq_nat @ C @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4997])). 185.47/93.67 thf(262,axiom,((! [A:complex]: ? [B:real,C:real]: (A = (times_times_complex @ (real_V4546457046886955230omplex @ B) @ (plus_plus_complex @ (real_V4546457046886955230omplex @ (cos_real @ C)) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sin_real @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9148_complex__split__polar)). 185.47/93.67 thf(8592,plain,((! [A:complex]: ? [B:real,C:real]: (A = (times_times_complex @ (real_V4546457046886955230omplex @ B) @ (plus_plus_complex @ (real_V4546457046886955230omplex @ (cos_real @ C)) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sin_real @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 185.47/93.67 thf(7242,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_eq_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1623_le__add__same__cancel1)). 185.47/93.67 thf(32407,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_eq_nat @ zero_zero_nat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7242])). 185.47/93.67 thf(4102,axiom,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1564_div__by__0)). 185.47/93.67 thf(21147,plain,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4102])). 185.47/93.67 thf(5858,axiom,((! [A:num,B:nat,C:nat]: (((power_power_nat @ (numeral_numeral_nat @ A) @ B) = (semiri1316708129612266289at_nat @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7053_numeral__power__eq__of__nat__cancel__iff)). 185.47/93.67 thf(27395,plain,((! [A:num,B:nat,C:nat]: (((power_power_nat @ (numeral_numeral_nat @ A) @ B) = (semiri1316708129612266289at_nat @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5858])). 185.47/93.67 thf(6111,axiom,((one_one_int = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9603_one__integer_Orsp)). 185.47/93.67 thf(28255,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6111])). 185.47/93.67 thf(2855,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ (minus_minus_rat @ B @ C)) = (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_793_le__diff__eq)). 185.47/93.67 thf(17208,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ (minus_minus_rat @ B @ C)) = (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2855])). 185.47/93.67 thf(7026,axiom,((! [A:num,B:num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5327_diff__numeral__simps_I3_J)). 185.47/93.67 thf(31667,plain,((! [A:num,B:num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7026])). 185.47/93.67 thf(257,axiom,((! [A:set_nat,B:(nat > rat)]: ((((groups2906978787729119204at_rat @ (^ [C:nat]: (times_times_rat @ (B @ C) @ (power_power_rat @ zero_zero_rat @ C))) @ A) = (B @ zero_zero_nat)) <= ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))) & ((~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))) => ((groups2906978787729119204at_rat @ (^ [C:nat]: (times_times_rat @ (B @ C) @ (power_power_rat @ zero_zero_rat @ C))) @ A) = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6435_sum__zero__power)). 185.47/93.67 thf(8569,plain,((! [A:set_nat,B:(nat > rat)]: ((((groups2906978787729119204at_rat @ (^ [C:nat]: (times_times_rat @ (B @ C) @ (power_power_rat @ zero_zero_rat @ C))) @ A) = (B @ zero_zero_nat)) | ~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))) & ((~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))) => ((groups2906978787729119204at_rat @ (^ [C:nat]: (times_times_rat @ (B @ C) @ (power_power_rat @ zero_zero_rat @ C))) @ A) = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 185.47/93.67 thf(964,axiom,((! [A:real]: ((cos_real @ (minus_minus_real @ pi @ A)) = (uminus_uminus_real @ (cos_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7788_cos__pi__minus)). 185.47/93.67 thf(11045,plain,((! [A:real]: ((cos_real @ (minus_minus_real @ pi @ A)) = (uminus_uminus_real @ (cos_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[964])). 185.47/93.67 thf(83,axiom,((! [A:complex,B:complex,C:nat]: ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (times_times_complex @ (power_power_complex @ (plus_plus_complex @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_complex @ A @ D)) @ (power_power_complex @ A @ C))) @ (set_ord_lessThan_nat @ C)) = (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (power_power_complex @ A @ D) @ (minus_minus_complex @ (power_power_complex @ (plus_plus_complex @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_complex @ A @ (minus_minus_nat @ C @ D))))) @ (set_ord_lessThan_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7608_lemma__termdiff1)). 185.47/93.67 thf(8003,plain,((! [A:complex,B:complex,C:nat]: ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (times_times_complex @ (power_power_complex @ (plus_plus_complex @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_complex @ A @ D)) @ (power_power_complex @ A @ C))) @ (set_ord_lessThan_nat @ C)) = (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (power_power_complex @ A @ D) @ (minus_minus_complex @ (power_power_complex @ (plus_plus_complex @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_complex @ A @ (minus_minus_nat @ C @ D))))) @ (set_ord_lessThan_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 185.47/93.67 thf(2362,axiom,((! [A:rat,B:rat]: ((A = (plus_plus_rat @ A @ B)) = (B = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1531_add__cancel__right__right)). 185.47/93.67 thf(15551,plain,((! [A:rat,B:rat]: ((A = (plus_plus_rat @ A @ B)) = (B = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2362])). 185.47/93.67 thf(6983,axiom,((! [A:int,B:int]: ((A = (times_times_int @ A @ B)) = ((B = one_one_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1664_mult__cancel__left1)). 185.47/93.67 thf(31495,plain,((! [A:int,B:int]: ((A = (times_times_int @ A @ B)) = ((B = one_one_int) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6983])). 185.47/93.67 thf(1540,axiom,((! [A:int,B:int]: (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2677_sum__squares__ge__zero)). 185.47/93.67 thf(12839,plain,((! [A:int,B:int]: (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540])). 185.47/93.67 thf(6126,axiom,((zero_zero_real != (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5718_zero__neq__neg__one)). 185.47/93.67 thf(28304,plain,((~ (zero_zero_real = (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6126])). 185.47/93.67 thf(2712,axiom,((! [A:nat]: (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7319_of__nat__less__two__power)). 185.47/93.67 thf(16759,plain,((! [A:nat]: (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2712])). 185.47/93.67 thf(311,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A)) & (ord_less_real @ (arcsin @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8325_arcsin__lt__bounded)). 185.47/93.67 thf(8772,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A)) & (ord_less_real @ (arcsin @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) | ~ (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 185.47/93.67 thf(7100,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_maxt @ A) = (some_nat @ C)) => ((ord_less_eq_nat @ D @ C) <= (vEBT_vebt_member @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_957_maxt__corr__help)). 185.47/93.67 thf(31900,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_maxt @ A) = (some_nat @ C)) => ((ord_less_eq_nat @ D @ C) | ~ (vEBT_vebt_member @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7100])). 185.47/93.67 thf(1057,axiom,((! [A:num]: ((pred_numeral @ (inc @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9365_pred__numeral__inc)). 185.47/93.67 thf(11327,plain,((! [A:num]: ((pred_numeral @ (inc @ A)) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057])). 185.47/93.67 thf(2338,axiom,(((exp_complex @ zero_zero_complex) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8119_exp__zero)). 185.47/93.67 thf(15479,plain,(((exp_complex @ zero_zero_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2338])). 185.47/93.67 thf(6039,axiom,(((abs_abs_real @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6325_abs__zero)). 185.47/93.67 thf(28011,plain,(((abs_abs_real @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6039])). 185.47/93.67 thf(2270,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B)) = (ord_less_rat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_add__less__cancel__right)). 185.47/93.67 thf(15269,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B)) = (ord_less_rat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2270])). 185.47/93.67 thf(621,axiom,((ord_less_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7758_pi__half__less__two)). 185.47/93.67 thf(9794,plain,((ord_less_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[621])). 185.47/93.67 thf(6023,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1791_zero__less__diff)). 185.47/93.67 thf(27962,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6023])). 185.47/93.67 thf(822,axiom,((! [A:real,B:nat,C:real]: (((ord_less_real @ (semiri5074537144036343181t_real @ B) @ (log @ A @ C)) <= (ord_less_real @ one_one_real @ A)) <= (ord_less_real @ (power_power_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9043_less__log__of__power)). 185.47/93.67 thf(10540,plain,((! [A:real,B:nat,C:real]: ((ord_less_real @ (semiri5074537144036343181t_real @ B) @ (log @ A @ C)) | ~ (ord_less_real @ one_one_real @ A) | ~ (ord_less_real @ (power_power_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[822])). 185.47/93.67 thf(7711,axiom,((! [A:int]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_power2__eq__square)). 185.47/93.67 thf(33872,plain,((! [A:int]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7711])). 185.47/93.67 thf(5802,axiom,((! [A:nat]: (((? [B:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ B)) = (vEBT_V8194947554948674370ptions @ summary @ A)) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103__C4_Ohyps_C_I7_J)). 185.47/93.67 thf(27104,plain,((! [A:nat]: (((? [B:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ B)) = (vEBT_V8194947554948674370ptions @ summary @ A)) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5802])). 185.47/93.67 thf(6192,axiom,((! [A:num]: (ord_less_eq_num @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3088_verit__comp__simplify1_I2_J)). 185.47/93.67 thf(28584,plain,((! [A:num]: (ord_less_eq_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6192])). 185.47/93.67 thf(6011,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (uminus_uminus_int @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6177_even__minus)). 185.47/93.67 thf(27930,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (uminus_uminus_int @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6011])). 185.47/93.67 thf(191,axiom,((! [A:set_nat,B:nat,C:(nat > real)]: (((((groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (B = D) @ (C @ D) @ one_one_real)) @ A) = one_one_real) <= (~ (member_nat @ B @ A))) & (((groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (B = D) @ (C @ D) @ one_one_real)) @ A) = (C @ B)) <= (member_nat @ B @ A))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8681_prod_Odelta_H)). 185.47/93.67 thf(8345,plain,((! [A:set_nat,B:nat,C:(nat > real)]: (((((groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (B = D) @ (C @ D) @ one_one_real)) @ A) = one_one_real) | (member_nat @ B @ A)) & (((groups129246275422532515t_real @ (^ [D:nat]: (if_real @ (B = D) @ (C @ D) @ one_one_real)) @ A) = (C @ B)) | ~ (member_nat @ B @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 185.47/93.67 thf(2069,axiom,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ B))) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7270_int__zle__neg)). 185.47/93.67 thf(14635,plain,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ B))) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2069])). 185.47/93.67 thf(6426,axiom,((! [A:(nat > real)]: ((suminf_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B)))) = (A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7557_powser__zero)). 185.47/93.67 thf(29400,plain,((! [A:(nat > real)]: ((suminf_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B)))) = (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6426])). 185.47/93.67 thf(679,axiom,((! [A:(nat > real)]: ((summable_real @ (^ [B:nat]: (abs_abs_real @ (A @ B)))) => (ord_less_eq_real @ (abs_abs_real @ (suminf_real @ A)) @ (suminf_real @ (^ [B:nat]: (abs_abs_real @ (A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7709_summable__rabs)). 185.47/93.67 thf(10001,plain,((! [A:(nat > real)]: ((summable_real @ (^ [B:nat]: (abs_abs_real @ (A @ B)))) => (ord_less_eq_real @ (abs_abs_real @ (suminf_real @ (A))) @ (suminf_real @ (^ [B:nat]: (abs_abs_real @ (A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[679])). 185.47/93.67 thf(7546,axiom,((! [A:nat]: (((plus_plus_nat @ A @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_nat) <= ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2514_bits__stable__imp__add__self)). 185.47/93.67 thf(33423,plain,((! [A:nat]: (((plus_plus_nat @ A @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_nat) | ~ ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7546])). 185.47/93.67 thf(458,axiom,((! [A:nat,B:nat]: ((times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ (gbinomial_real @ (minus_minus_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ A)) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (gbinomial_real @ (minus_minus_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8563_gbinomial__index__swap)). 185.47/93.67 thf(9253,plain,((! [A:nat,B:nat]: ((times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ (gbinomial_real @ (minus_minus_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ A)) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (gbinomial_real @ (minus_minus_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[458])). 185.47/93.67 thf(5643,axiom,((! [A:int]: ((power_power_int @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1771_power__Suc0__right)). 185.47/93.67 thf(26513,plain,((! [A:int]: ((power_power_int @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5643])). 185.47/93.67 thf(3696,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (minus_minus_int @ C @ B) @ (minus_minus_int @ C @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_708_diff__strict__left__mono)). 185.47/93.67 thf(19862,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (minus_minus_int @ C @ B) @ (minus_minus_int @ C @ A)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3696])). 185.47/93.67 thf(1861,axiom,((! [A:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ zero_zero_real) = (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7033_of__int__le__0__iff)). 185.47/93.67 thf(13967,plain,((! [A:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ zero_zero_real) = (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1861])). 185.47/93.67 thf(3972,axiom,((! [A:real,B:nat]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ (abs_abs_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6565_zero__le__power__abs)). 185.47/93.67 thf(20750,plain,((! [A:real,B:nat]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ (abs_abs_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3972])). 185.47/93.67 thf(6814,axiom,((times_times_rat = (^ [A:rat,B:rat]: (times_times_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_mult_Ocommute)). 185.47/93.67 thf(30791,plain,(((times_times_rat) = (^ [A:rat,B:rat]: (times_times_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6814])). 185.47/93.67 thf(1133,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => (((ord_less_real @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_real @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F)))) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4083_ord__less__eq__subst)). 185.47/93.67 thf(11573,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_real @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133])). 185.47/93.67 thf(3376,axiom,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ A) @ B) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8590_pochhammer__minus)). 185.47/93.67 thf(18848,plain,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ A) @ B) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3376])). 185.47/93.67 thf(6723,axiom,((! [A:real,B:nat]: ((A != zero_zero_real) => ((power_power_real @ A @ B) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2096_power__not__zero)). 185.47/93.67 thf(30422,plain,((! [A:real,B:nat]: ((~ (A = zero_zero_real)) => (~ ((power_power_real @ A @ B) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6723])). 185.47/93.67 thf(1308,axiom,((ord_less_real @ zero_zero_real @ (plus_plus_real @ one_one_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2691_zero__less__two)). 185.47/93.67 thf(12088,plain,((ord_less_real @ zero_zero_real @ (plus_plus_real @ one_one_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308])). 185.47/93.67 thf(180,axiom,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((ord_less_eq_set_nat @ A @ B) => (((groups73079841787564623at_rat @ C @ B) = (times_times_rat @ (groups73079841787564623at_rat @ C @ (minus_minus_set_nat @ B @ A)) @ (groups73079841787564623at_rat @ C @ A))) <= (finite_finite_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8894_prod_Osubset__diff)). 185.47/93.67 thf(8312,plain,((! [A:set_nat,B:set_nat,C:(nat > rat)]: ((ord_less_eq_set_nat @ A @ B) => (((groups73079841787564623at_rat @ (C) @ B) = (times_times_rat @ (groups73079841787564623at_rat @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups73079841787564623at_rat @ (C) @ A))) | ~ (finite_finite_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 185.47/93.67 thf(6688,axiom,(((semiri1316708129612266289at_nat @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6885_of__nat__0)). 185.47/93.67 thf(30291,plain,(((semiri1316708129612266289at_nat @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6688])). 185.47/93.67 thf(4902,axiom,((neg_numeral_dbl_rat = (^ [A:rat]: (plus_plus_rat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3840_dbl__def)). 185.47/93.67 thf(23769,plain,(((neg_numeral_dbl_rat) = (^ [A:rat]: (plus_plus_rat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4902])). 185.47/93.67 thf(1124,axiom,((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5914_le__minus__one__simps_I1_J)). 185.47/93.67 thf(11540,plain,((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124])). 185.47/93.67 thf(4386,axiom,((! [A:int,B:int,C:int,D:int]: ((times_times_rat @ (fract @ A @ B) @ (fract @ C @ D)) = (fract @ (times_times_int @ A @ C) @ (times_times_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9929_mult__rat)). 185.47/93.67 thf(22053,plain,((! [A:int,B:int,C:int,D:int]: ((times_times_rat @ (fract @ A @ B) @ (fract @ C @ D)) = (fract @ (times_times_int @ A @ C) @ (times_times_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4386])). 185.47/93.67 thf(7213,axiom,((! [A:complex,B:nat]: (((power_power_complex @ A @ B) != zero_zero_complex) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2098_power__not__zero)). 185.47/93.67 thf(32303,plain,((! [A:complex,B:nat]: (~ ((power_power_complex @ A @ B) = zero_zero_complex) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7213])). 185.47/93.67 thf(3055,axiom,((! [A:complex,B:complex,C:num]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ C)) = (plus_plus_complex @ (times_times_complex @ A @ (numera6690914467698888265omplex @ C)) @ (times_times_complex @ B @ (numera6690914467698888265omplex @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_distrib__right__numeral)). 185.47/93.67 thf(17850,plain,((! [A:complex,B:complex,C:num]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ C)) = (plus_plus_complex @ (times_times_complex @ A @ (numera6690914467698888265omplex @ C)) @ (times_times_complex @ B @ (numera6690914467698888265omplex @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3055])). 185.47/93.67 thf(714,axiom,((! [A:int,B:nat,C:int]: (((ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => ((ord_less_int @ (bit_se6526347334894502574or_int @ A @ C) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) <= (ord_less_int @ C @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9493_XOR__upper)). 185.47/93.67 thf(10112,plain,((! [A:int,B:nat,C:int]: (((ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => ((ord_less_int @ (bit_se6526347334894502574or_int @ A @ C) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) | ~ (ord_less_int @ C @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[714])). 185.47/93.67 thf(3646,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (ord_less_int @ C @ (plus_plus_int @ (times_times_int @ (minus_minus_int @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1236_less__add__iff2)). 185.47/93.67 thf(19705,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (ord_less_int @ C @ (plus_plus_int @ (times_times_int @ (minus_minus_int @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3646])). 185.47/93.67 thf(2953,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ B @ A)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4119_order__less__not__sym)). 185.47/93.67 thf(17519,plain,((! [A:rat,B:rat]: (~ (ord_less_rat @ B @ A) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2953])). 185.47/93.67 thf(3039,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ (divide_divide_rat @ C @ A)) = (ord_less_eq_rat @ (times_times_rat @ B @ A) @ C)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2845_pos__le__divide__eq)). 185.47/93.67 thf(17796,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ (divide_divide_rat @ C @ A)) = (ord_less_eq_rat @ (times_times_rat @ B @ A) @ C)) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3039])). 185.47/93.67 thf(6352,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3104_verit__comp__simplify1_I3_J)). 185.47/93.67 thf(29120,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6352])). 185.47/93.67 thf(4264,axiom,((! [A:rat]: (((abs_abs_rat @ A) = (uminus_uminus_rat @ A)) <= (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6405_abs__of__nonpos)). 185.47/93.67 thf(21643,plain,((! [A:rat]: (((abs_abs_rat @ A) = (uminus_uminus_rat @ A)) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4264])). 185.47/93.67 thf(3502,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_rat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4368_order__le__imp__less__or__eq)). 185.47/93.67 thf(19261,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_rat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3502])). 185.47/93.67 thf(1194,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((modulo_modulo_int @ (semiri1406184849735516958ct_int @ B) @ (semiri1406184849735516958ct_int @ A)) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8015_fact__mod)). 185.47/93.67 thf(11753,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((modulo_modulo_int @ (semiri1406184849735516958ct_int @ B) @ (semiri1406184849735516958ct_int @ A)) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194])). 185.47/93.67 thf(6259,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((root @ A @ (power_power_real @ B @ A)) = B) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9197_real__root__power__cancel)). 185.47/93.67 thf(28792,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((root @ A @ (power_power_real @ B @ A)) = B) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6259])). 185.47/93.67 thf(5705,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ C @ (divide_divide_nat @ B @ A)) = (dvd_dvd_nat @ (times_times_nat @ C @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4836_dvd__div__iff__mult)). 185.47/93.67 thf(26709,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ C @ (divide_divide_nat @ B @ A)) = (dvd_dvd_nat @ (times_times_nat @ C @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5705])). 185.47/93.67 thf(2640,axiom,((! [A:real,B:real,C:real]: (((A != zero_zero_real) => ((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (divide_divide_real @ B @ C))) & (((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = zero_zero_real) <= (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1709_mult__divide__mult__cancel__left__if)). 185.47/93.67 thf(16489,plain,((! [A:real,B:real,C:real]: (((~ (A = zero_zero_real)) => ((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (divide_divide_real @ B @ C))) & (((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = zero_zero_real) | ~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2640])). 185.47/93.67 thf(1174,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (ord_max_nat @ A @ C) @ (ord_max_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3656_max_Omono)). 185.47/93.67 thf(11694,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (ord_max_nat @ A @ C) @ (ord_max_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174])). 185.47/93.67 thf(7517,axiom,((! [A:nat]: ((groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) = (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9571_sum__power2)). 185.47/93.67 thf(33336,plain,((! [A:nat]: ((groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) = (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7517])). 185.47/93.67 thf(7141,axiom,(((minus_minus_rat @ (uminus_uminus_rat @ one_one_rat) @ (uminus_uminus_rat @ one_one_rat)) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5284_diff__numeral__special_I12_J)). 185.47/93.67 thf(32040,plain,(((minus_minus_rat @ (uminus_uminus_rat @ one_one_rat) @ (uminus_uminus_rat @ one_one_rat)) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7141])). 185.47/93.67 thf(6347,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ A))) = (! [C:nat]: ((member_nat @ C @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) => (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9563_all__nat__less__eq)). 185.47/93.67 thf(29106,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ A))) = (! [C:nat]: ((member_nat @ C @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6347])). 185.47/93.67 thf(1322,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (ord_less_eq_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ one_one_real) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7308_nat__less__real__le)). 185.47/93.67 thf(12139,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (ord_less_eq_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ one_one_real) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322])). 185.47/93.67 thf(5146,axiom,((! [A:(real > $o),B:nat,C:real]: ((A @ (root @ B @ C)) = (((B = zero_zero_nat) => (A @ zero_zero_real)) & ((ord_less_nat @ zero_zero_nat @ B) => (! [D:real]: (((times_times_real @ (sgn_sgn_real @ D) @ (power_power_real @ (abs_abs_real @ D) @ B)) = C) => (A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9346_split__root)). 185.47/93.67 thf(24706,plain,((! [A:(real > $o),B:nat,C:real]: ((A @ (root @ B @ C)) = (((B = zero_zero_nat) => (A @ zero_zero_real)) & ((ord_less_nat @ zero_zero_nat @ B) => (! [D:real]: (((times_times_real @ (sgn_sgn_real @ D) @ (power_power_real @ (abs_abs_real @ D) @ B)) = C) => (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5146])). 185.47/93.67 thf(2504,axiom,((! [A:num,B:(rat > num),C:rat,D:rat]: ((A = (B @ C)) => (((ord_less_eq_num @ A @ (B @ D)) <= (! [E:rat,F:rat]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_rat @ E @ F)))) <= (ord_less_eq_rat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3939_ord__eq__le__subst)). 185.47/93.67 thf(16032,plain,((! [A:num,B:(rat > num),C:rat,D:rat]: ((A = (B @ C)) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:rat,F:rat]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_rat @ E @ F))) | ~ (ord_less_eq_rat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2504])). 185.47/93.67 thf(7048,axiom,((vEBT_vebt_member @ summary @ pr)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22__092_060open_062vebt__member_Asummary_Apr_092_060close_062)). 185.47/93.67 thf(31740,plain,((vEBT_vebt_member @ summary @ pr)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7048])). 185.47/93.67 thf(4038,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) <= (ord_less_eq_int @ B @ C)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2310_add__decreasing)). 185.47/93.67 thf(20951,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) | ~ (ord_less_eq_int @ B @ C) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4038])). 185.47/93.67 thf(6467,axiom,((! [A:rat,B:rat]: ((times_times_rat @ A @ (uminus_uminus_rat @ B)) = (uminus_uminus_rat @ (times_times_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5082_mult__minus__right)). 185.47/93.67 thf(29551,plain,((! [A:rat,B:rat]: ((times_times_rat @ A @ (uminus_uminus_rat @ B)) = (uminus_uminus_rat @ (times_times_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6467])). 185.47/93.67 thf(2796,axiom,((! [A:rat,B:nat,C:nat]: (((A = one_one_rat) => ((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (plus_plus_rat @ (semiri681578069525770553at_rat @ C) @ one_one_rat))) & (((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (divide_divide_rat @ (times_times_rat @ (power_power_rat @ A @ B) @ (minus_minus_rat @ one_one_rat @ (power_power_rat @ A @ (suc @ C)))) @ (minus_minus_rat @ one_one_rat @ A))) <= (A != one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7362_sum__gp__offset)). 185.47/93.67 thf(17012,plain,((! [A:rat,B:nat,C:nat]: (((A = one_one_rat) => ((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (plus_plus_rat @ (semiri681578069525770553at_rat @ C) @ one_one_rat))) & (((groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (divide_divide_rat @ (times_times_rat @ (power_power_rat @ A @ B) @ (minus_minus_rat @ one_one_rat @ (power_power_rat @ A @ (suc @ C)))) @ (minus_minus_rat @ one_one_rat @ A))) | (A = one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2796])). 185.47/93.67 thf(3222,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ A @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8694_sum_OatMost__Suc)). 185.47/93.67 thf(18373,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3222])). 185.47/93.67 thf(5728,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ (divide_divide_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1103_Suc__div__le__mono)). 185.47/93.67 thf(26793,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ (divide_divide_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5728])). 185.47/93.67 thf(2179,axiom,((! [A:rat,B:rat]: ((! [C:rat]: ((ord_less_eq_rat @ B @ C) <= (ord_less_rat @ A @ C))) => (ord_less_eq_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4179_dense__ge)). 185.47/93.67 thf(14998,plain,((! [A:rat,B:rat]: ((! [C:rat]: ((ord_less_eq_rat @ B @ C) | ~ (ord_less_rat @ A @ C))) => (ord_less_eq_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2179])). 185.47/93.67 thf(1602,axiom,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ A) => (ord_less_real @ one_one_real @ (power_power_real @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1109_power__gt1)). 185.47/93.67 thf(13047,plain,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ A) => (ord_less_real @ one_one_real @ (power_power_real @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1602])). 185.47/93.67 thf(1580,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (divide_divide_rat @ B @ A) @ one_one_rat) = (ord_less_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1813_divide__less__eq__1__pos)). 185.47/93.67 thf(12963,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (divide_divide_rat @ B @ A) @ one_one_rat) = (ord_less_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1580])). 185.47/93.67 thf(6067,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_nat__neq__iff)). 185.47/93.67 thf(28094,plain,((! [A:nat,B:nat]: ((~ (A = B)) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6067])). 185.47/93.67 thf(2380,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ C) => (ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ C)) <= (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2308_add__decreasing)). 185.47/93.67 thf(15608,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ C) => (ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ C)) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2380])). 185.47/93.67 thf(7478,axiom,((! [A:num]: ((fract @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int) = (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9957_rat__number__collapse_I4_J)). 185.47/93.67 thf(33204,plain,((! [A:num]: ((fract @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int) = (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7478])). 185.47/93.67 thf(7323,axiom,((! [A:nat]: ((bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9462_bit__Suc__0__iff)). 185.47/93.67 thf(32676,plain,((! [A:nat]: ((bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7323])). 185.47/93.67 thf(5755,axiom,((! [A:rat]: ((times_times_rat @ one_one_rat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_772_comm__monoid__mult__class_Omult__1)). 185.47/93.67 thf(26876,plain,((! [A:rat]: ((times_times_rat @ one_one_rat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5755])). 185.47/93.67 thf(2777,axiom,((! [A:nat,B:real]: (((sgn_sgn_real @ (root @ A @ B)) = (sgn_sgn_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9288_sgn__root)). 185.47/93.67 thf(16955,plain,((! [A:nat,B:real]: (((sgn_sgn_real @ (root @ A @ B)) = (sgn_sgn_real @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2777])). 185.47/93.67 thf(2406,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => ((nat2 @ (plus_plus_int @ A @ B)) = (plus_plus_nat @ (nat2 @ A) @ (nat2 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9310_nat__add__distrib)). 185.47/93.67 thf(15693,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ B) => ((nat2 @ (plus_plus_int @ A @ B)) = (plus_plus_nat @ (nat2 @ A) @ (nat2 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2406])). 185.47/93.67 thf(1332,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) = (((ord_less_eq_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ zero_zero_rat @ A)) | ((ord_less_eq_rat @ A @ zero_zero_rat) & (ord_less_eq_rat @ zero_zero_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2409_divide__le__0__iff)). 185.47/93.67 thf(12174,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) = (((ord_less_eq_rat @ B @ zero_zero_rat) & (ord_less_eq_rat @ zero_zero_rat @ A)) | ((ord_less_eq_rat @ A @ zero_zero_rat) & (ord_less_eq_rat @ zero_zero_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332])). 185.47/93.67 thf(345,axiom,((sgn_sgn_int = (^ [A:int]: (if_int @ (A = zero_zero_int) @ zero_zero_int @ (if_int @ (ord_less_int @ zero_zero_int @ A) @ one_one_int @ (uminus_uminus_int @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9225_zsgn__def)). 185.47/93.67 thf(8890,plain,(((sgn_sgn_int) = (^ [A:int]: (if_int @ (A = zero_zero_int) @ zero_zero_int @ (if_int @ (ord_less_int @ zero_zero_int @ A) @ one_one_int @ (uminus_uminus_int @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])). 185.47/93.67 thf(151,axiom,((summable_real @ (power_power_real @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7673_summable__zero__power)). 185.47/93.67 thf(8218,plain,((summable_real @ (power_power_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 185.47/93.67 thf(5179,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2635_add__pos__nonneg)). 185.47/93.67 thf(24809,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5179])). 185.47/93.67 thf(4941,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3109_verit__sum__simplify)). 185.47/93.67 thf(23911,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4941])). 185.47/93.67 thf(7336,axiom,((! [A:num,B:complex,C:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ B) @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_right__diff__distrib__numeral)). 185.47/93.67 thf(32725,plain,((! [A:num,B:complex,C:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ B) @ (times_times_complex @ (numera6690914467698888265omplex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7336])). 185.47/93.67 thf(392,axiom,((! [A:complex,B:(nat > nat),C:set_nat]: ((power_power_complex @ A @ (groups3542108847815614940at_nat @ B @ C)) = (groups6464643781859351333omplex @ (^ [D:nat]: (power_power_complex @ A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8787_power__sum)). 185.47/93.67 thf(9037,plain,((! [A:complex,B:(nat > nat),C:set_nat]: ((power_power_complex @ A @ (groups3542108847815614940at_nat @ (B) @ C)) = (groups6464643781859351333omplex @ (^ [D:nat]: (power_power_complex @ A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[392])). 185.47/93.67 thf(3257,axiom,((! [A:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ zero_zero_int) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5142_neg__le__0__iff__le)). 185.47/93.67 thf(18473,plain,((! [A:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ zero_zero_int) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3257])). 185.47/93.67 thf(3767,axiom,((! [A:nat]: ((ord_less_rat @ zero_zero_rat @ (semiri681578069525770553at_rat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7024_of__nat__0__less__iff)). 185.47/93.67 thf(20109,plain,((! [A:nat]: ((ord_less_rat @ zero_zero_rat @ (semiri681578069525770553at_rat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3767])). 185.47/93.67 thf(2042,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ A @ C) <= (ord_less_eq_rat @ B @ C)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4317_order__less__le__trans)). 185.47/93.67 thf(14557,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ C) | ~ (ord_less_eq_rat @ B @ C) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2042])). 185.47/93.67 thf(1799,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (exp_real @ A) @ (plus_plus_real @ (plus_plus_real @ one_one_real @ A) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8254_exp__bound)). 185.47/93.67 thf(13759,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (exp_real @ A) @ (plus_plus_real @ (plus_plus_real @ one_one_real @ A) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1799])). 185.47/93.67 thf(3409,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_5513_minus__le__iff)). 185.47/93.67 thf(18957,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)],[3409])). 185.47/93.67 thf(2576,axiom,((! [A:real,B:real]: (((ord_less_real @ B @ A) <= (~ (ord_less_real @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4048_linorder__neqE)). 185.47/93.67 thf(16266,plain,((! [A:real,B:real]: ((ord_less_real @ B @ A) | (ord_less_real @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2576])). 185.47/93.67 thf(3542,axiom,((! [A:real]: ((comm_s7457072308508201937r_real @ A @ zero_zero_nat) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8421_pochhammer__0)). 185.47/93.67 thf(19377,plain,((! [A:real]: ((comm_s7457072308508201937r_real @ A @ zero_zero_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3542])). 185.47/93.67 thf(4434,axiom,((! [A:$o,B:$o]: ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2018_vebt__pred_Osimps_I1_J)). 185.47/93.67 thf(22192,plain,((! [A:$o,B:$o]: ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4434])). 185.47/93.67 thf(4750,axiom,((! [A:num]: ((real_V1022390504157884413omplex @ (numera6690914467698888265omplex @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7453_norm__numeral)). 185.47/93.67 thf(23228,plain,((! [A:num]: ((real_V1022390504157884413omplex @ (numera6690914467698888265omplex @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4750])). 185.47/93.67 thf(7103,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_div__times__less__eq__dividend)). 185.47/93.67 thf(31909,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7103])). 185.47/93.67 thf(4833,axiom,((! [A:real,B:real]: ((plus_plus_real @ (sin_real @ A) @ (sin_real @ B)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sin_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))) @ (cos_real @ (divide_divide_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7855_sin__plus__sin)). 185.47/93.67 thf(23522,plain,((! [A:real,B:real]: ((plus_plus_real @ (sin_real @ A) @ (sin_real @ B)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sin_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one))))) @ (cos_real @ (divide_divide_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4833])). 185.47/93.67 thf(6223,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4319_order__less__le__trans)). 185.47/93.67 thf(28671,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6223])). 185.47/93.67 thf(2889,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ B) @ A) = (ord_less_rat @ B @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1655_add__less__same__cancel1)). 185.47/93.67 thf(17319,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ B) @ A) = (ord_less_rat @ B @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2889])). 185.47/93.67 thf(3403,axiom,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1507_add_Oright__neutral)). 185.47/93.67 thf(18940,plain,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3403])). 185.47/93.67 thf(3938,axiom,((! [A:nat,B:num]: ((ord_max_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (suc @ (ord_max_nat @ A @ (pred_numeral @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6792_max__Suc__numeral)). 185.47/93.67 thf(20645,plain,((! [A:nat,B:num]: ((ord_max_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (suc @ (ord_max_nat @ A @ (pred_numeral @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3938])). 185.47/93.67 thf(1693,axiom,((! [A:int,B:int]: (((modulo_modulo_int @ A @ B) = zero_zero_int) => (? [C:int]: (A = (times_times_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3156_zmod__eq__0D)). 185.47/93.67 thf(13399,plain,((! [A:int,B:int]: (((modulo_modulo_int @ A @ B) = zero_zero_int) => (? [C:int]: (A = (times_times_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693])). 185.47/93.67 thf(1273,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (times_times_real @ C @ A)) => (ord_less_real @ (divide_divide_real @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2707_mult__imp__div__pos__less)). 185.47/93.67 thf(11989,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (times_times_real @ C @ A)) => (ord_less_real @ (divide_divide_real @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273])). 185.47/93.67 thf(7062,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_V8194947554948674370ptions @ A @ B) <= ((vEBT_vebt_maxt @ A) = (some_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_951_maxbmo)). 185.47/93.67 thf(31782,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_V8194947554948674370ptions @ A @ B) | ~ ((vEBT_vebt_maxt @ A) = (some_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7062])). 185.47/93.67 thf(7446,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_set_nat @ (vEBT_VEBT_set_vebt @ A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3020_inrange)). 185.47/93.67 thf(33085,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_set_nat @ (vEBT_VEBT_set_vebt @ A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7446])). 185.47/93.67 thf(5240,axiom,((! [A:real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5037_neg__equal__zero)). 185.47/93.67 thf(25012,plain,((! [A:real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5240])). 185.47/93.67 thf(863,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((ord_max_int @ B @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3702_max_Oabsorb__iff1)). 185.47/93.67 thf(10684,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((ord_max_int @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[863])). 185.47/93.67 thf(2167,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_real @ zero_zero_real @ (ring_1_of_int_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7285_of__int__pos)). 185.47/93.67 thf(14951,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_real @ zero_zero_real @ (ring_1_of_int_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2167])). 185.47/93.67 thf(6526,axiom,((! [A:num,B:nat,C:int]: (((power_power_real @ (numeral_numeral_real @ A) @ B) = (ring_1_of_int_real @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7103_numeral__power__eq__of__int__cancel__iff)). 185.47/93.67 thf(29765,plain,((! [A:num,B:nat,C:int]: (((power_power_real @ (numeral_numeral_real @ A) @ B) = (ring_1_of_int_real @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6526])). 185.47/93.67 thf(134,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ D) @ (minus_minus_set_nat @ B @ C)) <= (ord_less_eq_set_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1429_Diff__mono)). 185.47/93.67 thf(8163,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ D) @ (minus_minus_set_nat @ B @ C)) | ~ (ord_less_eq_set_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 185.47/93.67 thf(4490,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ (^ [B:nat]: (if_real @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri5074537144036343181t_real @ (binomial @ A @ B)) @ zero_zero_real)) @ (set_ord_atMost_nat @ A))) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8628_choose__odd__sum)). 185.47/93.67 thf(22376,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ (^ [B:nat]: (if_real @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri5074537144036343181t_real @ (binomial @ A @ B)) @ zero_zero_real)) @ (set_ord_atMost_nat @ A))) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4490])). 185.47/93.67 thf(1844,axiom,((! [A:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5173_ab__left__minus)). 185.47/93.67 thf(13921,plain,((! [A:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1844])). 185.47/93.67 thf(5709,axiom,((sin_coeff = (^ [A:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ zero_zero_real @ (divide_divide_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ (divide_divide_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri2265585572941072030t_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8094_sin__coeff__def)). 185.47/93.67 thf(26722,plain,(((sin_coeff) = (^ [A:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ zero_zero_real @ (divide_divide_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ (divide_divide_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri2265585572941072030t_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5709])). 185.47/93.67 thf(6951,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) <= (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3007_odd__0__le__power__imp__0__le)). 185.47/93.67 thf(31306,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) | ~ (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6951])). 185.47/93.67 thf(6672,axiom,((unique5055182867167087721od_nat = (^ [A:num,B:num]: (product_Pair_nat_nat @ (divide_divide_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) @ (modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6829_divmod__def)). 185.47/93.67 thf(30243,plain,(((unique5055182867167087721od_nat) = (^ [A:num,B:num]: (product_Pair_nat_nat @ (divide_divide_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) @ (modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6672])). 185.47/93.67 thf(6920,axiom,((! [A:num]: ((~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ A)))) = (A != one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5375_not__neg__one__le__neg__numeral__iff)). 185.47/93.67 thf(31195,plain,((! [A:num]: ((~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ A)))) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6920])). 185.47/93.67 thf(5255,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (~ ((A != zero_zero_nat) => (! [C:nat]: ((C != zero_zero_nat) => ((((divide_divide_nat @ one_one_nat @ A) = C) => (((divide_divide_nat @ one_one_nat @ C) = A) => (((divide_divide_nat @ B @ A) != (times_times_nat @ B @ C)) <= ((times_times_nat @ A @ C) = one_one_nat)))) <= (dvd_dvd_nat @ C @ one_one_nat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4892_is__unitE)). 185.47/93.67 thf(25056,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (~ ((~ (A = zero_zero_nat)) => (! [C:nat]: ((~ (C = zero_zero_nat)) => ((((divide_divide_nat @ one_one_nat @ A) = C) => (((divide_divide_nat @ one_one_nat @ C) = A) => (~ ((divide_divide_nat @ B @ A) = (times_times_nat @ B @ C)) | ~ ((times_times_nat @ A @ C) = one_one_nat)))) | ~ (dvd_dvd_nat @ C @ one_one_nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5255])). 185.47/93.67 thf(4709,axiom,((! [A:num,B:rat,C:rat]: (((numeral_numeral_rat @ A) = (divide_divide_rat @ B @ C)) = ((((numeral_numeral_rat @ A) = zero_zero_rat) <= (C = zero_zero_rat)) & (((times_times_rat @ (numeral_numeral_rat @ A) @ C) = B) <= (C != zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2725_eq__divide__eq__numeral_I1_J)). 185.47/93.67 thf(23104,plain,((! [A:num,B:rat,C:rat]: (((numeral_numeral_rat @ A) = (divide_divide_rat @ B @ C)) = ((((numeral_numeral_rat @ A) = zero_zero_rat) | ~ (C = zero_zero_rat)) & (((times_times_rat @ (numeral_numeral_rat @ A) @ C) = B) | (C = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4709])). 185.47/93.67 thf(7321,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2519_vebt__member_Osimps_I3_J)). 185.47/93.67 thf(32670,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7321])). 185.47/93.67 thf(2414,axiom,((! [A:complex]: ((plus_plus_complex @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ A)) @ (times_times_complex @ (sin_complex @ A) @ (sin_complex @ A))) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7791_sin__cos__squared__add3)). 185.47/93.67 thf(15721,plain,((! [A:complex]: ((plus_plus_complex @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ A)) @ (times_times_complex @ (sin_complex @ A) @ (sin_complex @ A))) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2414])). 185.47/93.67 thf(3378,axiom,((! [A:int,B:(int > $o),C:(int > $o)]: (((! [D:int,E:int]: ((B @ D) = (B @ (minus_minus_int @ D @ (times_times_int @ E @ A))))) => ((? [D:int]: ! [E:int]: (((C @ E) = (B @ E)) <= (ord_less_int @ D @ E))) => ((? [D:int]: (C @ D)) <= (? [D:int]: (B @ D))))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3338_plusinfinity)). 185.47/93.67 thf(18854,plain,((! [A:int,B:(int > $o),C:(int > $o)]: (((! [D:int,E:int]: ((B @ D) = (B @ (minus_minus_int @ D @ (times_times_int @ E @ A))))) => ((? [D:int]: ! [E:int]: (((C @ E) = (B @ E)) | ~ (ord_less_int @ D @ E))) => (? [D:int]: (C @ D) | ~ (? [D:int]: (B @ D))))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3378])). 185.47/93.67 thf(6580,axiom,((! [A:num,B:num]: ((A = B) | ~ (ord_less_eq_num @ A @ B) | ~ (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3083_verit__la__disequality)). 185.47/93.67 thf(29941,plain,((! [A:num,B:num]: ((A = B) | ~ (ord_less_eq_num @ A @ B) | ~ (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6580])). 185.47/93.67 thf(1703,axiom,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((((B = C) & (D != E)) => ((plus_plus_rat @ B @ (times_times_rat @ A @ D)) != (plus_plus_rat @ C @ (times_times_rat @ A @ E)))) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5012_add__scale__eq__noteq)). 185.47/93.67 thf(13435,plain,((! [A:rat,B:rat,C:rat,D:rat,E:rat]: ((((B = C) & ~ (D = E)) => (~ ((plus_plus_rat @ B @ (times_times_rat @ A @ D)) = (plus_plus_rat @ C @ (times_times_rat @ A @ E))))) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703])). 185.47/93.67 thf(5829,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_add__leD2)). 185.47/93.67 thf(27285,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5829])). 185.47/93.67 thf(6376,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2358_mult__strict__left__mono)). 185.47/93.67 thf(29202,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6376])). 185.47/93.67 thf(6415,axiom,((! [A:num,B:num]: ((ord_less_num @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6417_semiring__norm_I79_J)). 185.47/93.67 thf(29354,plain,((! [A:num,B:num]: ((ord_less_num @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6415])). 185.47/93.67 thf(1186,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (divide1717551699836669952omplex @ B @ C)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_times__divide__eq__right)). 185.47/93.67 thf(11726,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (divide1717551699836669952omplex @ B @ C)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186])). 185.47/93.67 thf(5280,axiom,((! [A:nat]: ((minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int) = (groups3539618377306564664at_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one))) @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6743_mask__eq__sum__exp)). 185.47/93.67 thf(25187,plain,((! [A:nat]: ((minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int) = (groups3539618377306564664at_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one))) @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5280])). 185.47/93.67 thf(399,axiom,((! [A:real]: ((cos_real @ (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ A)) = (cos_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7802_cos__2pi__minus)). 185.47/93.67 thf(9061,plain,((! [A:real]: ((cos_real @ (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ A)) = (cos_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])). 185.47/93.67 thf(827,axiom,((! [A:real,B:nat]: ((gbinomial_real @ (plus_plus_real @ A @ one_one_real) @ (suc @ B)) = (times_times_real @ (gbinomial_real @ A @ B) @ (divide_divide_real @ (plus_plus_real @ A @ one_one_real) @ (semiri5074537144036343181t_real @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8560_gbinomial__rec)). 185.47/93.67 thf(10553,plain,((! [A:real,B:nat]: ((gbinomial_real @ (plus_plus_real @ A @ one_one_real) @ (suc @ B)) = (times_times_real @ (gbinomial_real @ A @ B) @ (divide_divide_real @ (plus_plus_real @ A @ one_one_real) @ (semiri5074537144036343181t_real @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[827])). 185.47/93.67 thf(516,axiom,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ B)))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9538_and__not__numerals_I6_J)). 185.47/93.67 thf(9467,plain,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ B)))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[516])). 185.47/93.67 thf(3239,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (ord_less_int @ (plus_plus_int @ (times_times_int @ (minus_minus_int @ A @ D) @ B) @ C) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1239_less__add__iff1)). 185.47/93.67 thf(18422,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_int @ (plus_plus_int @ (times_times_int @ A @ B) @ C) @ (plus_plus_int @ (times_times_int @ D @ B) @ E)) = (ord_less_int @ (plus_plus_int @ (times_times_int @ (minus_minus_int @ A @ D) @ B) @ C) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3239])). 185.47/93.67 thf(2610,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B) @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_sum__squares__bound)). 185.47/93.67 thf(16396,plain,((! [A:real,B:real]: (ord_less_eq_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B) @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2610])). 185.47/93.67 thf(1138,axiom,((! [A:complex]: ((plus_plus_complex @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7808_sin__cos__squared__add2)). 185.47/93.67 thf(11594,plain,((! [A:complex]: ((plus_plus_complex @ (power_power_complex @ (cos_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138])). 185.47/93.67 thf(7295,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_750_le__diff__iff)). 185.47/93.67 thf(32585,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7295])). 185.47/93.67 thf(1517,axiom,((ord_less_int = (^ [A:int,B:int]: ((A != B) & (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4204_order_Ostrict__iff__order)). 185.47/93.67 thf(12772,plain,(((ord_less_int) = (^ [A:int,B:int]: (~ (A = B) & (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517])). 185.47/93.67 thf(4733,axiom,((! [A:real]: (ord_less_real @ zero_zero_real @ (plus_plus_real @ one_one_real @ (abs_abs_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6640_abs__add__one__gt__zero)). 185.47/93.67 thf(23177,plain,((! [A:real]: (ord_less_real @ zero_zero_real @ (plus_plus_real @ one_one_real @ (abs_abs_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4733])). 185.47/93.67 thf(6118,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) => ((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2588_mult__right__less__imp__less)). 185.47/93.67 thf(28274,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) => ((ord_less_nat @ A @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6118])). 185.47/93.67 thf(1229,axiom,((! [A:real,B:real]: (((divide_divide_real @ (times_times_real @ A @ B) @ A) = B) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1686_nonzero__mult__div__cancel__left)). 185.47/93.67 thf(11855,plain,((! [A:real,B:real]: (((divide_divide_real @ (times_times_real @ A @ B) @ A) = B) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229])). 185.47/93.67 thf(3681,axiom,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B)) = (divide_divide_real @ (minus_minus_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ (modulo_modulo_nat @ A @ B))) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7301_field__char__0__class_Oof__nat__div)). 185.47/93.68 thf(19810,plain,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B)) = (divide_divide_real @ (minus_minus_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ (modulo_modulo_nat @ A @ B))) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3681])). 185.47/93.68 thf(4619,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (plus_plus_int @ B @ C)) = (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4645_dvd__add__right__iff)). 185.47/93.68 thf(22793,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (plus_plus_int @ B @ C)) = (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4619])). 185.47/93.68 thf(612,axiom,((! [A:complex,B:complex]: (((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) = (ord_less_eq_real @ (abs_abs_real @ (im @ A)) @ (abs_abs_real @ (im @ B)))) <= ((re @ A) = (re @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9677_cmod__Im__le__iff)). 185.47/93.68 thf(9766,plain,((! [A:complex,B:complex]: (((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) = (ord_less_eq_real @ (abs_abs_real @ (im @ A)) @ (abs_abs_real @ (im @ B)))) | ~ ((re @ A) = (re @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[612])). 185.47/93.68 thf(818,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & (ord_less_eq_real @ C @ A) & ((sin_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (sin_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (sin_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8091_Maclaurin__sin__expansion4)). 185.47/93.68 thf(10521,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & (ord_less_eq_real @ C @ A) & ((sin_real @ A) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (sin_coeff @ D) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) @ (times_times_real @ (divide_divide_real @ (sin_real @ (plus_plus_real @ C @ (times_times_real @ (times_times_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ B)) @ pi))) @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[818])). 185.47/93.68 thf(3688,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1625_add__le__same__cancel2)). 185.47/93.68 thf(19838,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3688])). 185.47/93.68 thf(3104,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri5074537144036343181t_real @ (minus_minus_nat @ B @ A)) = (minus_minus_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7263_of__nat__diff)). 185.47/93.68 thf(18009,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri5074537144036343181t_real @ (minus_minus_nat @ B @ A)) = (minus_minus_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3104])). 185.47/93.68 thf(6314,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (times_times_nat @ (modulo_modulo_nat @ A @ B) @ C) @ B) = (modulo_modulo_nat @ (times_times_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1973_mod__mult__left__eq)). 185.47/93.68 thf(28969,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (times_times_nat @ (modulo_modulo_nat @ A @ B) @ C) @ B) = (modulo_modulo_nat @ (times_times_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6314])). 185.47/93.68 thf(2877,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => (((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) <= (ord_less_eq_int @ zero_zero_int @ C))) <= (ord_less_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2614_mult__le__less__imp__less)). 185.47/93.68 thf(17277,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => (((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) | ~ (ord_less_eq_int @ zero_zero_int @ C))) | ~ (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2877])). 185.47/93.68 thf(2214,axiom,((! [A:int,B:nat]: ((ring_17405671764205052669omplex @ (power_power_int @ A @ B)) = (power_power_complex @ (ring_17405671764205052669omplex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6990_of__int__power)). 185.47/93.68 thf(15102,plain,((! [A:int,B:nat]: ((ring_17405671764205052669omplex @ (power_power_int @ A @ B)) = (power_power_complex @ (ring_17405671764205052669omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2214])). 185.47/93.68 thf(991,axiom,((~ (ord_less_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5919_less__minus__one__simps_I3_J)). 185.47/93.68 thf(11126,plain,((~ (ord_less_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[991])). 185.47/93.68 thf(7703,axiom,(((semiri2265585572941072030t_real @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7979_fact__2)). 185.47/93.68 thf(33852,plain,(((semiri2265585572941072030t_real @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7703])). 185.47/93.68 thf(3590,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ (divide_divide_rat @ B @ C)) = (((~ (ord_less_rat @ zero_zero_rat @ C)) => (((ord_less_rat @ C @ zero_zero_rat) => (ord_less_eq_rat @ B @ (times_times_rat @ A @ C))) & ((~ (ord_less_rat @ C @ zero_zero_rat)) => (ord_less_eq_rat @ A @ zero_zero_rat)))) & ((ord_less_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ (times_times_rat @ A @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2835_le__divide__eq)). 185.47/93.68 thf(19531,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ (divide_divide_rat @ B @ C)) = (((~ (ord_less_rat @ zero_zero_rat @ C)) => (((ord_less_rat @ C @ zero_zero_rat) => (ord_less_eq_rat @ B @ (times_times_rat @ A @ C))) & ((~ (ord_less_rat @ C @ zero_zero_rat)) => (ord_less_eq_rat @ A @ zero_zero_rat)))) & ((ord_less_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ (times_times_rat @ A @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3590])). 185.47/93.68 thf(3920,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7230_of__nat__mono)). 185.47/93.68 thf(20590,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3920])). 185.47/93.68 thf(5362,axiom,((! [A:num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5449_diff__numeral__special_I4_J)). 185.47/93.68 thf(25482,plain,((! [A:num]: ((minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ (plus_plus_num @ A @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5362])). 185.47/93.68 thf(3487,axiom,((tanh_complex = (^ [A:complex]: (divide1717551699836669952omplex @ (minus_minus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) @ (plus_plus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8220_tanh__altdef)). 185.47/93.68 thf(19211,plain,(((tanh_complex) = (^ [A:complex]: (divide1717551699836669952omplex @ (minus_minus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) @ (plus_plus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3487])). 185.47/93.68 thf(3734,axiom,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ B) = A) = (B = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1521_add__cancel__left__right)). 185.47/93.68 thf(19993,plain,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ B) = A) = (B = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3734])). 185.47/93.68 thf(6493,axiom,((one_one_nat = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9604_one__natural_Orsp)). 185.47/93.68 thf(29643,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6493])). 185.47/93.68 thf(3269,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((modulo_modulo_int @ (modulo_modulo_int @ C @ B) @ A) = (modulo_modulo_int @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4686_mod__mod__cancel)). 185.47/93.68 thf(18509,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((modulo_modulo_int @ (modulo_modulo_int @ C @ B) @ A) = (modulo_modulo_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3269])). 185.47/93.68 thf(4069,axiom,((! [A:int,B:int]: ((((divide_divide_int @ A @ (times_times_int @ B @ A)) = (divide_divide_int @ one_one_int @ B)) <= (dvd_dvd_int @ B @ one_one_int)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4899_is__unit__div__mult__cancel__right)). 185.47/93.68 thf(21039,plain,((! [A:int,B:int]: (((divide_divide_int @ A @ (times_times_int @ B @ A)) = (divide_divide_int @ one_one_int @ B)) | ~ (dvd_dvd_int @ B @ one_one_int) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4069])). 185.47/93.68 thf(6797,axiom,((! [A:rat]: ((one_one_rat = A) = (A = one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_one__reorient)). 185.47/93.68 thf(30724,plain,((! [A:rat]: ((one_one_rat = A) = (A = one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6797])). 185.47/93.68 thf(4570,axiom,((! [A:rat,B:(rat > rat),C:rat,D:rat]: (((ord_less_rat @ C @ D) => ((ord_less_rat @ A @ (B @ D)) <= (! [E:rat,F:rat]: ((ord_less_rat @ (B @ E) @ (B @ F)) <= (ord_less_rat @ E @ F))))) <= (ord_less_eq_rat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4327_order__le__less__subst1)). 185.47/93.68 thf(22644,plain,((! [A:rat,B:(rat > rat),C:rat,D:rat]: (((ord_less_rat @ C @ D) => ((ord_less_rat @ A @ (B @ D)) | ~ (! [E:rat,F:rat]: ((ord_less_rat @ (B @ E) @ (B @ F)) | ~ (ord_less_rat @ E @ F))))) | ~ (ord_less_eq_rat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4570])). 185.47/93.68 thf(2484,axiom,((! [A:real,B:real,C:num]: ((ord_less_real @ A @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ C)))) = (ord_less_real @ B @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5393_less__divide__eq__numeral1_I2_J)). 185.47/93.68 thf(15956,plain,((! [A:real,B:real,C:num]: ((ord_less_real @ A @ (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ C)))) = (ord_less_real @ B @ (times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2484])). 185.47/93.68 thf(663,axiom,((! [A:complex]: (((im @ A) = zero_zero_real) => (((csqrt @ A) = (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sqrt @ (abs_abs_real @ (re @ A)))))) <= (ord_less_eq_real @ (re @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9669_csqrt__of__real__nonpos)). 185.47/93.68 thf(9948,plain,((! [A:complex]: (((im @ A) = zero_zero_real) => (((csqrt @ A) = (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sqrt @ (abs_abs_real @ (re @ A)))))) | ~ (ord_less_eq_real @ (re @ A) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[663])). 185.47/93.68 thf(3446,axiom,((! [A:int]: (ord_less_int @ A @ (plus_plus_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1210_less__add__one)). 185.47/93.68 thf(19067,plain,((! [A:int]: (ord_less_int @ A @ (plus_plus_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3446])). 185.47/93.68 thf(4037,axiom,((! [A:real,B:real,C:real]: ((((ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B)) <= (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))) <= (ord_less_real @ C @ zero_zero_real)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2713_divide__strict__left__mono__neg)). 185.47/93.68 thf(20948,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B)) | ~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) | ~ (ord_less_real @ C @ zero_zero_real) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4037])). 185.47/93.68 thf(2378,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ (divide_divide_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ one_one_rat @ one_one_rat)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_855_gt__half__sum)). 185.47/93.68 thf(15603,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (ord_less_rat @ (divide_divide_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ one_one_rat @ one_one_rat)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2378])). 185.47/93.68 thf(6745,axiom,((! [A:(int > $o),B:int]: ((((! [C:int]: ((A @ C) => ((C != zero_zero_int) => (A @ (times_times_int @ C @ (numeral_numeral_int @ (bit0 @ one))))))) => ((A @ B) <= (! [C:int]: ((A @ C) => ((A @ (plus_plus_int @ one_one_int @ (times_times_int @ C @ (numeral_numeral_int @ (bit0 @ one))))) <= (C != (uminus_uminus_int @ one_one_int))))))) <= (A @ (uminus_uminus_int @ one_one_int))) <= (A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6298_int__bit__induct)). 185.47/93.68 thf(30501,plain,((! [A:(int > $o),B:int]: (((! [C:int]: ((A @ C) => ((~ (C = zero_zero_int)) => (A @ (times_times_int @ C @ (numeral_numeral_int @ (bit0 @ one))))))) => ((A @ B) | ~ (! [C:int]: ((A @ C) => ((A @ (plus_plus_int @ one_one_int @ (times_times_int @ C @ (numeral_numeral_int @ (bit0 @ one))))) | (C = (uminus_uminus_int @ one_one_int))))))) | ~ (A @ (uminus_uminus_int @ one_one_int)) | ~ (A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6745])). 185.47/93.68 thf(4316,axiom,((! [A:int,B:num,C:nat]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (ord_less_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7170_of__int__less__neg__numeral__power__cancel__iff)). 185.47/93.68 thf(21789,plain,((! [A:int,B:num,C:nat]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)) @ C)) = (ord_less_int @ A @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4316])). 185.47/93.68 thf(5796,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_vebt_member @ A @ B) => ((! [C:$o,D:$o]: ((~ ((((B = one_one_nat) & ((B = one_one_nat) => (D))) <= (B != zero_zero_nat)) & ((C) <= (B = zero_zero_nat)))) <= (A = (vEBT_Leaf @ C @ D)))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: ((? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G))) => (~ (((((((((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) <= (~ (ord_less_nat @ D @ B))) & ~ (ord_less_nat @ D @ B)) <= (~ (ord_less_nat @ B @ C))) & ~ (ord_less_nat @ B @ C)) <= (B != D)) <= (B != C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2999_vebt__member_Oelims_I2_J)). 185.47/93.68 thf(27008,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_vebt_member @ A @ B) => ((! [C:$o,D:$o]: (~ ((((B = one_one_nat) & ((B = one_one_nat) => (D))) | (B = zero_zero_nat)) & ((C) | ~ (B = zero_zero_nat))) | ~ (A = (vEBT_Leaf @ C @ D)))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: ((? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G))) => (~ ((((((((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) | (ord_less_nat @ D @ B)) & ~ (ord_less_nat @ D @ B)) | (ord_less_nat @ B @ C)) & ~ (ord_less_nat @ B @ C)) | (B = D) | (B = C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5796])). 185.47/93.68 thf(10,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_int @ (A @ zero_zero_nat) @ (groups3539618377306564664at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7580_sum_OlessThan__Suc__shift)). 185.47/93.68 thf(7756,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_int @ (A @ zero_zero_nat) @ (groups3539618377306564664at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[10])). 185.47/93.68 thf(4107,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (times_times_int @ A @ (modulo_modulo_int @ B @ C)) @ C) = (modulo_modulo_int @ (times_times_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1971_mod__mult__right__eq)). 185.47/93.68 thf(21163,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (times_times_int @ A @ (modulo_modulo_int @ B @ C)) @ C) = (modulo_modulo_int @ (times_times_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4107])). 185.47/93.68 thf(7181,axiom,((! [A:num]: ((minus_minus_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (numeral_numeral_real @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5444_diff__numeral__special_I3_J)). 185.47/93.68 thf(32189,plain,((! [A:num]: ((minus_minus_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (numeral_numeral_real @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7181])). 185.47/93.68 thf(7502,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2111_nat_Odistinct_I1_J)). 185.47/93.68 thf(33292,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7502])). 185.47/93.68 thf(25,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ A) => ((suminf_real @ A) = (plus_plus_real @ (suminf_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B)))) @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7732_suminf__split__initial__segment)). 185.47/93.68 thf(7811,plain,((! [A:(nat > real),B:nat]: ((summable_real @ (A)) => ((suminf_real @ (A)) = (plus_plus_real @ (suminf_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B)))) @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 185.47/93.68 thf(3980,axiom,((! [A:nat]: ((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ A)) @ A) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ (semiri773545260158071498ct_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8576_pochhammer__same)). 185.47/93.68 thf(20779,plain,((! [A:nat]: ((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ A)) @ A) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ (semiri773545260158071498ct_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3980])). 185.47/93.68 thf(4877,axiom,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_real @ B @ C) => (ord_less_real @ (root @ A @ B) @ (root @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9183_real__root__less__mono)). 185.47/93.68 thf(23662,plain,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_real @ B @ C) => (ord_less_real @ (root @ A @ B) @ (root @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4877])). 185.47/93.68 thf(5331,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5101_minus__diff__eq)). 185.47/93.68 thf(25350,plain,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5331])). 185.47/93.68 thf(779,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (ring_1_of_int_int @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7280_of__int__nonneg)). 185.47/93.68 thf(10392,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (ring_1_of_int_int @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[779])). 185.47/93.68 thf(2156,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((ord_less_int @ A @ B) & (ord_less_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_add__mono__thms__linordered__field_I5_J)). 185.47/93.68 thf(14919,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ ((ord_less_int @ A @ B) & (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2156])). 185.47/93.68 thf(5481,axiom,((! [A:num]: ((modulo_modulo_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)) = (product_snd_nat_nat @ (unique5055182867167087721od_nat @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9751_Suc__0__mod__numeral)). 185.47/93.68 thf(25978,plain,((! [A:num]: ((modulo_modulo_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)) = (product_snd_nat_nat @ (unique5055182867167087721od_nat @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5481])). 185.47/93.68 thf(6825,axiom,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2128_minus__nat_Odiff__0)). 185.47/93.68 thf(30823,plain,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6825])). 185.47/93.68 thf(6323,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ (power_power_nat @ A @ (suc @ B)) @ A) <= (ord_less_eq_nat @ A @ one_one_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2873_power__Suc__le__self)). 185.47/93.68 thf(29010,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (suc @ B)) @ A) | ~ (ord_less_eq_nat @ A @ one_one_nat) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6323])). 185.47/93.68 thf(2884,axiom,((! [A:int,B:int,C:nat]: ((modulo_modulo_int @ (power_power_int @ (modulo_modulo_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ (power_power_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2009_power__mod)). 185.47/93.68 thf(17304,plain,((! [A:int,B:int,C:nat]: ((modulo_modulo_int @ (power_power_int @ (modulo_modulo_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ (power_power_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2884])). 185.47/93.68 thf(6355,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ A @ one_one_int) => (ord_less_eq_int @ (power_power_int @ A @ (suc @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2874_power__Suc__le__self)). 185.47/93.68 thf(29133,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ A @ one_one_int) => (ord_less_eq_int @ (power_power_int @ A @ (suc @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6355])). 185.47/93.68 thf(3051,axiom,((! [A:nat,B:nat,C:nat]: (((semiri8010041392384452111omplex @ A) = (power_power_complex @ (semiri8010041392384452111omplex @ B) @ C)) = (A = (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6947_of__nat__power__eq__of__nat__cancel__iff)). 185.47/93.68 thf(17833,plain,((! [A:nat,B:nat,C:nat]: (((semiri8010041392384452111omplex @ A) = (power_power_complex @ (semiri8010041392384452111omplex @ B) @ C)) = (A = (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3051])). 185.47/93.68 thf(2594,axiom,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) = (((ord_less_int @ zero_zero_int @ A) & (ord_less_int @ B @ zero_zero_int)) | ((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ zero_zero_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2319_mult__less__0__iff)). 185.47/93.68 thf(16345,plain,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) = (((ord_less_int @ zero_zero_int @ A) & (ord_less_int @ B @ zero_zero_int)) | ((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2594])). 185.47/93.68 thf(2960,axiom,((! [A:num,B:(real > num),C:real,D:real]: ((((ord_less_num @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_num @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F)))) <= (ord_less_real @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4075_ord__eq__less__subst)). 185.47/93.68 thf(17536,plain,((! [A:num,B:(real > num),C:real,D:real]: ((ord_less_num @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_num @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))) | ~ (ord_less_real @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2960])). 185.47/93.68 thf(7426,axiom,((! [A:num]: ((bit_or_not_num_neg @ one @ (bit1 @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9466_or__not__num__neg_Osimps_I3_J)). 185.47/93.68 thf(33028,plain,((! [A:num]: ((bit_or_not_num_neg @ one @ (bit1 @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7426])). 185.47/93.68 thf(688,axiom,((! [A:complex,B:nat]: ((gbinomial_complex @ A @ (suc @ B)) = (plus_plus_complex @ (gbinomial_complex @ (minus_minus_complex @ A @ one_one_complex) @ (suc @ B)) @ (gbinomial_complex @ (minus_minus_complex @ A @ one_one_complex) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8475_gbinomial__addition__formula)). 185.47/93.68 thf(10027,plain,((! [A:complex,B:nat]: ((gbinomial_complex @ A @ (suc @ B)) = (plus_plus_complex @ (gbinomial_complex @ (minus_minus_complex @ A @ one_one_complex) @ (suc @ B)) @ (gbinomial_complex @ (minus_minus_complex @ A @ one_one_complex) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[688])). 185.47/93.68 thf(6194,axiom,((! [A:num]: (((numeral_numeral_rat @ A) = one_one_rat) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_numeral__eq__one__iff)). 185.47/93.68 thf(28589,plain,((! [A:num]: (((numeral_numeral_rat @ A) = one_one_rat) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6194])). 185.47/93.68 thf(7731,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4907_odd__even__add)). 185.47/93.68 thf(33926,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7731])). 185.47/93.68 thf(4764,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ A) = (((ord_less_rat @ one_one_rat @ B) <= (ord_less_eq_rat @ A @ zero_zero_rat)) & ((ord_less_rat @ B @ one_one_rat) <= (ord_less_eq_rat @ zero_zero_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2822_mult__less__cancel__left2)). 185.47/93.68 thf(23311,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ A) = (((ord_less_rat @ one_one_rat @ B) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)) & ((ord_less_rat @ B @ one_one_rat) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4764])). 185.47/93.68 thf(1937,axiom,((! [A:rat,B:rat]: ((A = (uminus_uminus_rat @ B)) = ((plus_plus_rat @ A @ B) = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5741_eq__neg__iff__add__eq__0)). 185.47/93.68 thf(14215,plain,((! [A:rat,B:rat]: ((A = (uminus_uminus_rat @ B)) = ((plus_plus_rat @ A @ B) = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937])). 185.47/93.68 thf(3004,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2414_divide__nonneg__nonneg)). 185.47/93.68 thf(17689,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3004])). 185.47/93.68 thf(5448,axiom,((! [A:real,B:num]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ B))) = (((numeral_numeral_nat @ B) = zero_zero_nat) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (A != zero_zero_real)) | ((ord_less_real @ zero_zero_real @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4547_zero__less__power__eq__numeral)). 185.47/93.68 thf(25786,plain,((! [A:real,B:num]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ B))) = (((numeral_numeral_nat @ B) = zero_zero_nat) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & ~ (A = zero_zero_real)) | ((ord_less_real @ zero_zero_real @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5448])). 185.47/93.68 thf(6906,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat) <= (dvd_dvd_nat @ B @ one_one_nat)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4469_unit__prod)). 185.47/93.68 thf(31150,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat) | ~ (dvd_dvd_nat @ B @ one_one_nat) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6906])). 185.47/93.68 thf(5477,axiom,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ C @ A) => (ord_less_num @ C @ B)) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4248_dual__order_Ostrict__trans2)). 185.47/93.68 thf(25963,plain,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ C @ A) => (ord_less_num @ C @ B)) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5477])). 185.47/93.68 thf(6229,axiom,(((fract @ (uminus_uminus_int @ one_one_int) @ one_one_int) = (uminus_uminus_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9951_rat__number__collapse_I5_J)). 185.47/93.68 thf(28689,plain,(((fract @ (uminus_uminus_int @ one_one_int) @ one_one_int) = (uminus_uminus_rat @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6229])). 185.47/93.68 thf(4910,axiom,((! [A:num,B:num]: ((numera6690914467698888265omplex @ A) != (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5532_numeral__neq__neg__numeral)). 185.47/93.68 thf(23791,plain,((! [A:num,B:num]: ~ ((numera6690914467698888265omplex @ A) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4910])). 185.47/93.68 thf(5556,axiom,((semiri1408675320244567234ct_nat = (^ [A:nat]: (semiri1316708129612266289at_nat @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8333_fact__code)). 185.47/93.68 thf(26232,plain,(((semiri1408675320244567234ct_nat) = (^ [A:nat]: (semiri1316708129612266289at_nat @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5556])). 185.47/93.68 thf(4814,axiom,((! [A:rat,B:(int > rat),C:int,D:int]: ((ord_less_rat @ A @ (B @ C)) => (((! [E:int,F:int]: ((ord_less_int @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F)))) => (ord_less_rat @ A @ (B @ D))) <= (ord_less_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4107_order__less__subst1)). 185.47/93.68 thf(23462,plain,((! [A:rat,B:(int > rat),C:int,D:int]: ((ord_less_rat @ A @ (B @ C)) => (((! [E:int,F:int]: ((ord_less_int @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F)))) => (ord_less_rat @ A @ (B @ D))) | ~ (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4814])). 185.47/93.68 thf(7486,axiom,((! [A:code_integer,B:num]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6619_power__minus__Bit1)). 185.47/93.68 thf(33240,plain,((! [A:code_integer,B:num]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7486])). 185.47/93.68 thf(4539,axiom,((! [A:rat]: (((divide_divide_rat @ one_one_rat @ A) = zero_zero_rat) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1724_one__divide__eq__0__iff)). 185.47/93.68 thf(22539,plain,((! [A:rat]: (((divide_divide_rat @ one_one_rat @ A) = zero_zero_rat) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4539])). 185.47/93.68 thf(7637,axiom,(((semiri773545260158071498ct_rat @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_rat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7977_fact__2)). 185.47/93.68 thf(33677,plain,(((semiri773545260158071498ct_rat @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_rat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7637])). 185.47/93.68 thf(1087,axiom,((! [A:num,B:num,C:code_integer]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ A) @ (times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5361_semiring__norm_I171_J)). 185.47/93.68 thf(11428,plain,((! [A:num,B:num,C:code_integer]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ A) @ (times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087])). 185.47/93.68 thf(6333,axiom,((! [A:nat,B:(num > nat),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_nat @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) <= (ord_less_nat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4349_order__less__le__subst1)). 185.47/93.68 thf(29042,plain,((! [A:nat,B:(num > nat),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) | ~ (ord_less_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6333])). 185.47/93.68 thf(2570,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ (abs_abs_int @ B))) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6826_even__add__abs__iff)). 185.47/93.68 thf(16249,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ (abs_abs_int @ B))) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2570])). 185.47/93.68 thf(6987,axiom,((! [A:num,B:code_integer]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) => ((power_8256067586552552935nteger @ (abs_abs_Code_integer @ B) @ (numeral_numeral_nat @ A)) = (power_8256067586552552935nteger @ B @ (numeral_numeral_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6437_power__even__abs__numeral)). 185.47/93.68 thf(31505,plain,((! [A:num,B:code_integer]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) => ((power_8256067586552552935nteger @ (abs_abs_Code_integer @ B) @ (numeral_numeral_nat @ A)) = (power_8256067586552552935nteger @ B @ (numeral_numeral_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6987])). 185.47/93.68 thf(6517,axiom,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & ((power_power_real @ C @ A) = B)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3099_realpow__pos__nth)). 185.47/93.68 thf(29725,plain,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & ((power_power_real @ C @ A) = B)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6517])). 185.47/93.68 thf(927,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (ln_ln_real @ A) @ (divide_divide_real @ (powr_real @ A @ B) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9124_ln__powr__bound)). 185.47/93.68 thf(10915,plain,((! [A:real,B:real]: ((ord_less_eq_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ (ln_ln_real @ A) @ (divide_divide_real @ (powr_real @ A @ B) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[927])). 185.47/93.68 thf(5227,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((divide_divide_nat @ B @ A) = C) = (B = (times_times_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4856_unit__eq__div1)). 185.47/93.68 thf(24960,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((divide_divide_nat @ B @ A) = C) = (B = (times_times_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5227])). 185.47/93.68 thf(1541,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2323_mult__neg__pos)). 185.47/93.68 thf(12841,plain,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541])). 185.47/93.68 thf(2801,axiom,((! [A:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ A) = (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6365_abs__le__self__iff)). 185.47/93.68 thf(17034,plain,((! [A:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ A) = (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2801])). 185.47/93.68 thf(5028,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2034_zero__less__iff__neq__zero)). 185.47/93.68 thf(24186,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5028])). 185.47/93.68 thf(3245,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_add__strict__left__mono)). 185.47/93.68 thf(18439,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3245])). 185.47/93.68 thf(1857,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4053_order__less__asym)). 185.47/93.68 thf(13957,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1857])). 185.47/93.68 thf(1955,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ C @ D) => (((ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)) <= (ord_less_eq_rat @ zero_zero_rat @ C)) <= (ord_less_rat @ zero_zero_rat @ A))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2612_mult__le__less__imp__less)). 185.47/93.68 thf(14272,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ C @ D) => ((ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)) | ~ (ord_less_eq_rat @ zero_zero_rat @ C) | ~ (ord_less_rat @ zero_zero_rat @ A))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1955])). 185.47/93.68 thf(3718,axiom,((ord_less_rat = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) & ~ (ord_less_eq_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4219_order_Ostrict__iff__not)). 185.47/93.68 thf(19944,plain,(((ord_less_rat) = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) & ~ (ord_less_eq_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3718])). 185.47/93.68 thf(268,axiom,((topolo6980174941875973593q_real = (^ [A:(nat > real)]: (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_real @ (A @ C) @ (A @ B))) | ! [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_8340_monoseq__def)). 185.47/93.68 thf(8612,plain,(((topolo6980174941875973593q_real) = (^ [A:(nat > real)]: (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_real @ (A @ C) @ (A @ B))) | ! [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)],[268])). 185.47/93.68 thf(1678,axiom,((! [A:complex,B:complex]: (((times_times_complex @ imaginary_unit @ A) = B) = (A = (uminus1482373934393186551omplex @ (times_times_complex @ imaginary_unit @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9001_i__times__eq__iff)). 185.47/93.68 thf(13354,plain,((! [A:complex,B:complex]: (((times_times_complex @ imaginary_unit @ A) = B) = (A = (uminus1482373934393186551omplex @ (times_times_complex @ imaginary_unit @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678])). 185.47/93.68 thf(5978,axiom,((! [A:nat]: ((dvd_dvd_nat @ (divide_divide_nat @ one_one_nat @ A) @ one_one_nat) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4491_unit__div__1__unit)). 185.47/93.68 thf(27823,plain,((! [A:nat]: ((dvd_dvd_nat @ (divide_divide_nat @ one_one_nat @ A) @ one_one_nat) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5978])). 185.47/93.68 thf(3562,axiom,((! [A:rat,B:rat,C:rat]: ((A = (minus_minus_rat @ C @ B)) <= ((plus_plus_rat @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_add__implies__diff)). 185.47/93.68 thf(19441,plain,((! [A:rat,B:rat,C:rat]: ((A = (minus_minus_rat @ C @ B)) | ~ ((plus_plus_rat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3562])). 185.47/93.68 thf(7083,axiom,((! [A:int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_int) = ((abs_abs_int @ A) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6689_abs__square__eq__1)). 185.47/93.68 thf(31845,plain,((! [A:int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_int) = ((abs_abs_int @ A) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7083])). 185.47/93.68 thf(7609,axiom,((! [A:complex]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_complex @ (times_times_complex @ (times_times_complex @ A @ A) @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_power4__eq__xxxx)). 185.47/93.68 thf(33598,plain,((! [A:complex]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_complex @ (times_times_complex @ (times_times_complex @ A @ A) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7609])). 185.47/93.68 thf(6486,axiom,((! [A:nat,B:num,C:num]: ((power_power_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (power_power_nat @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_power__mult__numeral)). 185.47/93.68 thf(29623,plain,((! [A:nat,B:num,C:num]: ((power_power_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (power_power_nat @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6486])). 185.47/93.68 thf(5420,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ (times_times_nat @ B @ A) @ C)) = (dvd_dvd_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4474_dvd__add__times__triv__left__iff)). 185.47/93.68 thf(25655,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ (times_times_nat @ B @ A) @ C)) = (dvd_dvd_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5420])). 185.47/93.68 thf(1900,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (exp_real @ A) @ (plus_plus_real @ one_one_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A))) <= (ord_less_eq_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8264_real__exp__bound__lemma)). 185.47/93.68 thf(14081,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (exp_real @ A) @ (plus_plus_real @ one_one_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A))) | ~ (ord_less_eq_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1900])). 185.47/93.68 thf(7722,axiom,((za != ma)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66__092_060open_062z_A_092_060noteq_062_Ama_092_060close_062)). 185.47/93.68 thf(33904,plain,((~ (za = ma))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7722])). 185.47/93.68 thf(2868,axiom,((! [A:int]: ~ (ord_less_int @ (abs_abs_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6485_abs__not__less__zero)). 185.47/93.68 thf(17249,plain,((! [A:int]: ~ (ord_less_int @ (abs_abs_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2868])). 185.47/93.68 thf(5895,axiom,((! [A:nat,B:nat]: (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) != zero_zero_nat) <= ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2949_exp__add__not__zero__imp__left)). 185.47/93.68 thf(27522,plain,((! [A:nat,B:nat]: (~ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = zero_zero_nat) | ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5895])). 185.47/93.68 thf(205,axiom,((divide_divide_real = (^ [A:real,B:real]: (times_times_real @ A @ (inverse_inverse_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8962_divide__real__def)). 185.47/93.68 thf(8396,plain,(((divide_divide_real) = (^ [A:real,B:real]: (times_times_real @ A @ (inverse_inverse_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 185.47/93.68 thf(7612,axiom,((za != mi)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_False)). 185.47/93.68 thf(33606,plain,((~ (za = mi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7612])). 185.47/93.68 thf(1218,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_rat @ (fract @ B @ A) @ one_one_rat) = (ord_less_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9948_Fract__less__one__iff)). 185.47/93.68 thf(11823,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_rat @ (fract @ B @ A) @ one_one_rat) = (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218])). 185.47/93.68 thf(1801,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7222_of__nat__less__imp__less)). 185.47/93.68 thf(13769,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801])). 185.47/93.68 thf(4892,axiom,((! [A:real]: (((ord_less_real @ zero_zero_real @ (sin_real @ A)) <= (ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7882_sin__gt__zero__02)). 185.47/93.68 thf(23737,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (sin_real @ A)) | ~ (ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4892])). 185.47/93.68 thf(4484,axiom,((! [A:rat]: ((divide_divide_rat @ A @ (numeral_numeral_rat @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_divide__numeral__1)). 185.47/93.68 thf(22355,plain,((! [A:rat]: ((divide_divide_rat @ A @ (numeral_numeral_rat @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4484])). 185.47/93.68 thf(6961,axiom,((! [A:int,B:num,C:nat]: (((ring_17405671764205052669omplex @ A) = (power_power_complex @ (numera6690914467698888265omplex @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7098_of__int__eq__numeral__power__cancel__iff)). 185.47/93.68 thf(31381,plain,((! [A:int,B:num,C:nat]: (((ring_17405671764205052669omplex @ A) = (power_power_complex @ (numera6690914467698888265omplex @ B) @ C)) = (A = (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6961])). 185.47/93.68 thf(5970,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9450_or__nat__numerals_I1_J)). 185.47/93.68 thf(27798,plain,((! [A:num]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5970])). 185.47/93.68 thf(2058,axiom,((~ (ord_less_real @ one_one_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_764_less__numeral__extra_I4_J)). 185.47/93.68 thf(14604,plain,((~ (ord_less_real @ one_one_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2058])). 185.47/93.68 thf(4807,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat)) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2430_divide__neg__pos)). 185.47/93.68 thf(23440,plain,((! [A:rat,B:rat]: (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat)) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4807])). 185.47/93.68 thf(4453,axiom,((! [A:rat,B:rat,C:num]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ (numeral_numeral_rat @ C)) = (((ord_less_rat @ A @ (times_times_rat @ (numeral_numeral_rat @ C) @ B)) <= (ord_less_rat @ zero_zero_rat @ B)) & ((~ (ord_less_rat @ zero_zero_rat @ B)) => (((ord_less_rat @ zero_zero_rat @ (numeral_numeral_rat @ C)) <= (~ (ord_less_rat @ B @ zero_zero_rat))) & ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (times_times_rat @ (numeral_numeral_rat @ C) @ B) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2862_divide__less__eq__numeral_I1_J)). 185.47/93.68 thf(22256,plain,((! [A:rat,B:rat,C:num]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ (numeral_numeral_rat @ C)) = (((ord_less_rat @ A @ (times_times_rat @ (numeral_numeral_rat @ C) @ B)) | ~ (ord_less_rat @ zero_zero_rat @ B)) & ((~ (ord_less_rat @ zero_zero_rat @ B)) => (((ord_less_rat @ zero_zero_rat @ (numeral_numeral_rat @ C)) | (ord_less_rat @ B @ zero_zero_rat)) & ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (times_times_rat @ (numeral_numeral_rat @ C) @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4453])). 185.47/93.68 thf(1853,axiom,((ord_less_real @ zero_zero_real @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2384_zero__less__one)). 185.47/93.68 thf(13948,plain,((ord_less_real @ zero_zero_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853])). 185.47/93.68 thf(7582,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ A))) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4512_even__Suc__Suc__iff)). 185.47/93.68 thf(33519,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ A))) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7582])). 185.47/93.68 thf(6557,axiom,((! [A:nat,B:num]: ((bit_ri631733984087533419it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ (times_times_int @ (bit_ri631733984087533419it_int @ A @ (minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ one_one_int)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6309_signed__take__bit__Suc__minus__bit1)). 185.47/93.68 thf(29860,plain,((! [A:nat,B:num]: ((bit_ri631733984087533419it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ (times_times_int @ (bit_ri631733984087533419it_int @ A @ (minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ one_one_int)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6557])). 185.47/93.68 thf(6465,axiom,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: (((? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F))))) <= (? [E:num]: ! [F:num]: (((C @ F) = (D @ F)) <= (ord_less_num @ E @ F)))) <= (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3232_pinf_I2_J)). 185.47/93.68 thf(29538,plain,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F)))) | ~ (? [E:num]: ! [F:num]: (((C @ F) = (D @ F)) | ~ (ord_less_num @ E @ F))) | ~ (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6465])). 185.47/93.68 thf(3922,axiom,((! [A:rat,B:rat]: ((plus_plus_rat @ (minus_minus_rat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_diff__add__cancel)). 185.47/93.68 thf(20596,plain,((! [A:rat,B:rat]: ((plus_plus_rat @ (minus_minus_rat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3922])). 185.47/93.68 thf(952,axiom,((! [A:real,B:real,C:real]: ((((ord_less_eq_real @ (log @ A @ B) @ C) = (ord_less_eq_real @ B @ (powr_real @ A @ C))) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9120_log__le__iff)). 185.47/93.68 thf(10994,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (log @ A @ B) @ C) = (ord_less_eq_real @ B @ (powr_real @ A @ C))) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[952])). 185.47/93.68 thf(6732,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ zero_zero_nat @ (binomial @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8449_zero__less__binomial)). 185.47/93.68 thf(30454,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ zero_zero_nat @ (binomial @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6732])). 185.47/93.68 thf(240,axiom,((! [A:nat,B:real,C:nat]: (((ord_less_real @ one_one_real @ B) => ((ord_less_eq_real @ (log @ B @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ C)) <= (ord_less_nat @ zero_zero_nat @ A))) <= (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9055_log__of__power__le)). 185.47/93.68 thf(8498,plain,((! [A:nat,B:real,C:nat]: (((ord_less_real @ one_one_real @ B) => ((ord_less_eq_real @ (log @ B @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A))) | ~ (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 185.47/93.68 thf(4842,axiom,((! [A:nat,B:nat,C:rat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_rat @ one_one_rat @ C) => (ord_less_eq_rat @ (power_power_rat @ C @ A) @ (power_power_rat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_875_power__increasing)). 185.47/93.68 thf(23553,plain,((! [A:nat,B:nat,C:rat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_rat @ one_one_rat @ C) => (ord_less_eq_rat @ (power_power_rat @ C @ A) @ (power_power_rat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4842])). 185.47/93.68 thf(6868,axiom,((! [A:rat,B:rat]: ((((times_times_rat @ A @ B) != zero_zero_rat) <= (B != zero_zero_rat)) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2055_no__zero__divisors)). 185.47/93.68 thf(31031,plain,((! [A:rat,B:rat]: (~ ((times_times_rat @ A @ B) = zero_zero_rat) | (B = zero_zero_rat) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6868])). 185.47/93.68 thf(5825,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ A @ (times_times_nat @ (semiri1316708129612266289at_nat @ B) @ (semiri1316708129612266289at_nat @ C))) = (plus_plus_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ B) @ (modulo_modulo_nat @ (divide_divide_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ (semiri1316708129612266289at_nat @ C))) @ (modulo_modulo_nat @ A @ (semiri1316708129612266289at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7294_mod__mult2__eq_H)). 185.47/93.68 thf(27274,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ A @ (times_times_nat @ (semiri1316708129612266289at_nat @ B) @ (semiri1316708129612266289at_nat @ C))) = (plus_plus_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ B) @ (modulo_modulo_nat @ (divide_divide_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ (semiri1316708129612266289at_nat @ C))) @ (modulo_modulo_nat @ A @ (semiri1316708129612266289at_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5825])). 185.47/93.68 thf(4153,axiom,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) = (real_V7735802525324610683m_real @ (minus_minus_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7457_norm__minus__commute)). 185.47/93.68 thf(21305,plain,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) = (real_V7735802525324610683m_real @ (minus_minus_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4153])). 185.47/93.68 thf(7561,axiom,((vEBT_VEBT_max_in_set @ (vEBT_VEBT_set_vebt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ maxy)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540__092_060open_062max__in__set_A_Iset__vebt_H_A_ItreeList_A_B_Athe_A_Ivebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_J_Amaxy_092_060close_062)). 185.47/93.68 thf(33466,plain,((vEBT_VEBT_max_in_set @ (vEBT_VEBT_set_vebt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ maxy)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7561])). 185.47/93.68 thf(7532,axiom,((vEBT_invar_vebt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ na)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644__092_060open_062invar__vebt_A_ItreeList_A_B_Athe_A_Ivebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_An_092_060close_062)). 185.47/93.68 thf(33387,plain,((vEBT_invar_vebt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7532])). 185.47/93.68 thf(676,axiom,((! [A:real,B:real]: (((((powr_real @ A @ (log @ A @ B)) = B) <= (ord_less_real @ zero_zero_real @ B)) <= (A != one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9079_powr__log__cancel)). 185.47/93.68 thf(9991,plain,((! [A:real,B:real]: (((powr_real @ A @ (log @ A @ B)) = B) | ~ (ord_less_real @ zero_zero_real @ B) | (A = one_one_real) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[676])). 185.47/93.68 thf(4850,axiom,((! [A:num,B:num]: ((plus_plus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (uminus_uminus_rat @ (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5190_add__neg__numeral__simps_I3_J)). 185.47/93.68 thf(23575,plain,((! [A:num,B:num]: ((plus_plus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (uminus_uminus_rat @ (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4850])). 185.47/93.68 thf(3034,axiom,((! [A:real,B:real,C:$o]: ((ord_less_real @ A @ B) => ((C) <= (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4123_order__less__imp__triv)). 185.47/93.68 thf(17777,plain,((! [A:real,B:real,C:$o]: ((ord_less_real @ A @ B) => ((C) | ~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3034])). 185.47/93.68 thf(2842,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8001_fact__mono)). 185.47/93.68 thf(17166,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2842])). 185.47/93.68 thf(4075,axiom,((! [A:int]: (((nat2 @ A) = zero_zero_nat) = (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9249_nat__0__iff)). 185.47/93.68 thf(21058,plain,((! [A:int]: (((nat2 @ A) = zero_zero_nat) = (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4075])). 185.47/93.68 thf(2311,axiom,((semiri1406184849735516958ct_int = (^ [A:nat]: (if_int @ (A = zero_zero_nat) @ one_one_int @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1406184849735516958ct_int @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8046_fact__num__eq__if)). 185.47/93.68 thf(15396,plain,(((semiri1406184849735516958ct_int) = (^ [A:nat]: (if_int @ (A = zero_zero_nat) @ one_one_int @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1406184849735516958ct_int @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2311])). 185.47/93.68 thf(4556,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4134_order__less__imp__not__eq)). 185.47/93.68 thf(22593,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4556])). 185.47/93.68 thf(5548,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2627_add__nonneg__pos)). 185.47/93.68 thf(26207,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5548])). 185.47/93.68 thf(1623,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((((! [E:real,F:real]: ((ord_less_real @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))) => (ord_less_real @ (C @ A) @ D)) <= (ord_less_real @ (C @ B) @ D)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4108_order__less__subst2)). 185.47/93.68 thf(13140,plain,((! [A:real,B:real,C:(real > real),D:real]: (((! [E:real,F:real]: ((ord_less_real @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))) => (ord_less_real @ (C @ A) @ D)) | ~ (ord_less_real @ (C @ B) @ D) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623])). 185.47/93.68 thf(3274,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ one_one_real) = (((ord_less_real @ B @ zero_zero_real) & (ord_less_eq_real @ B @ A)) | (B = zero_zero_real) | ((ord_less_eq_real @ A @ B) & (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2852_divide__le__eq__1)). 185.47/93.68 thf(18526,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ one_one_real) = (((ord_less_real @ B @ zero_zero_real) & (ord_less_eq_real @ B @ A)) | (B = zero_zero_real) | ((ord_less_eq_real @ A @ B) & (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3274])). 185.47/93.68 thf(3076,axiom,((! [A:nat]: (ord_less_eq_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri681578069525770553at_rat @ (power_power_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8023_fact__le__power)). 185.47/93.68 thf(17909,plain,((! [A:nat]: (ord_less_eq_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri681578069525770553at_rat @ (power_power_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3076])). 185.47/93.68 thf(6760,axiom,((! [A:real]: (((sqrt @ A) = one_one_real) = (A = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8117_real__sqrt__eq__1__iff)). 185.47/93.68 thf(30600,plain,((! [A:real]: (((sqrt @ A) = one_one_real) = (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6760])). 185.47/93.68 thf(7123,axiom,((semiri1408675320244567234ct_nat = (^ [A:nat]: (if_nat @ (A = zero_zero_nat) @ one_one_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8049_fact__num__eq__if)). 185.47/93.68 thf(31969,plain,(((semiri1408675320244567234ct_nat) = (^ [A:nat]: (if_nat @ (A = zero_zero_nat) @ one_one_nat @ (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7123])). 185.47/93.68 thf(5537,axiom,((! [A:nat]: ((power_power_nat @ one_one_nat @ A) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_power__one)). 185.47/93.68 thf(26177,plain,((! [A:nat]: ((power_power_nat @ one_one_nat @ A) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5537])). 185.47/93.68 thf(6643,axiom,((! [A:$o]: (ord_less_eq_nat @ (zero_n2687167440665602831ol_nat @ A) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5668_of__bool__less__eq__one)). 185.47/93.68 thf(30142,plain,((! [A:$o]: (ord_less_eq_nat @ (zero_n2687167440665602831ol_nat @ A) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6643])). 185.47/93.68 thf(1500,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ C) <= (ord_less_eq_int @ zero_zero_int @ A)) <= (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2578_mult__left__less__imp__less)). 185.47/93.68 thf(12720,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ C) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ (ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1500])). 185.47/93.68 thf(6488,axiom,((! [A:num,B:num]: ((ord_less_num @ B @ A) <= (~ (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4190_not__le__imp__less)). 185.47/93.68 thf(29629,plain,((! [A:num,B:num]: ((ord_less_num @ B @ A) | (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6488])). 185.47/93.68 thf(5622,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_add__diff__cancel__right)). 185.47/93.68 thf(26444,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5622])). 185.47/93.68 thf(2396,axiom,((! [A:int,B:num]: (((ring_17405671764205052669omplex @ A) = (numera6690914467698888265omplex @ B)) = (A = (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6940_of__int__eq__numeral__iff)). 185.47/93.68 thf(15661,plain,((! [A:int,B:num]: (((ring_17405671764205052669omplex @ A) = (numera6690914467698888265omplex @ B)) = (A = (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2396])). 185.47/93.68 thf(2965,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4324_order__le__less__subst1)). 185.47/93.68 thf(17558,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2965])). 185.47/93.68 thf(5515,axiom,((zero_zero_real != one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2072_zero__neq__one)). 185.47/93.68 thf(26095,plain,((~ (zero_zero_real = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5515])). 185.47/93.68 thf(960,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (ring_1_of_int_int @ A)) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7032_of__int__0__le__iff)). 185.47/93.68 thf(11027,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (ring_1_of_int_int @ A)) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[960])). 185.47/93.68 thf(7200,axiom,((! [A:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_numeral__plus__one)). 185.47/93.68 thf(32249,plain,((! [A:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7200])). 185.47/93.68 thf(772,axiom,((! [A:nat,B:rat]: ((times_times_rat @ (semiri681578069525770553at_rat @ (suc @ A)) @ (gbinomial_rat @ (plus_plus_rat @ B @ one_one_rat) @ (suc @ A))) = (times_times_rat @ (plus_plus_rat @ B @ one_one_rat) @ (gbinomial_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8534_Suc__times__gbinomial)). 185.47/93.68 thf(10360,plain,((! [A:nat,B:rat]: ((times_times_rat @ (semiri681578069525770553at_rat @ (suc @ A)) @ (gbinomial_rat @ (plus_plus_rat @ B @ one_one_rat) @ (suc @ A))) = (times_times_rat @ (plus_plus_rat @ B @ one_one_rat) @ (gbinomial_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[772])). 185.47/93.68 thf(6077,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7066_of__nat__le__of__nat__power__cancel__iff)). 185.47/93.68 thf(28126,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6077])). 185.47/93.68 thf(5218,axiom,((! [A:num]: ((archim8280529875227126926d_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7554_round__neg__numeral)). 185.47/93.68 thf(24928,plain,((! [A:num]: ((archim8280529875227126926d_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5218])). 185.47/93.68 thf(2087,axiom,((! [A:real,B:int]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_eq_int @ zero_zero_int @ B) => ((powr_real @ A @ (ring_1_of_int_real @ B)) = (power_power_real @ A @ (nat2 @ B)))) & (((powr_real @ A @ (ring_1_of_int_real @ B)) = (inverse_inverse_real @ (power_power_real @ A @ (nat2 @ (uminus_uminus_int @ B))))) <= (~ (ord_less_eq_int @ zero_zero_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9358_powr__real__of__int)). 185.47/93.68 thf(14692,plain,((! [A:real,B:int]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_eq_int @ zero_zero_int @ B) => ((powr_real @ A @ (ring_1_of_int_real @ B)) = (power_power_real @ A @ (nat2 @ B)))) & (((powr_real @ A @ (ring_1_of_int_real @ B)) = (inverse_inverse_real @ (power_power_real @ A @ (nat2 @ (uminus_uminus_int @ B))))) | (ord_less_eq_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2087])). 185.47/93.68 thf(6871,axiom,((! [A:product_prod_nat_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (vEBT_VEBT_minNull @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1464_VEBT__internal_OminNull_Osimps_I5_J)). 185.47/93.68 thf(31041,plain,((! [A:product_prod_nat_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (vEBT_VEBT_minNull @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ B @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6871])). 185.47/93.68 thf(6260,axiom,((! [A:int]: ((minus_minus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1555_diff__0__right)). 185.47/93.68 thf(28796,plain,((! [A:int]: ((minus_minus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6260])). 185.47/93.68 thf(7646,axiom,((! [A:nat]: ((divide_divide_nat @ (plus_plus_nat @ A @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add__self__div__2)). 185.47/93.68 thf(33698,plain,((! [A:nat]: ((divide_divide_nat @ (plus_plus_nat @ A @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7646])). 185.47/93.68 thf(3651,axiom,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2030_less__numeral__extra_I3_J)). 185.47/93.68 thf(19724,plain,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3651])). 185.47/93.68 thf(838,axiom,((gbinomial_real = (^ [A:real,B:nat]: (if_real @ (B = zero_zero_nat) @ one_one_real @ (divide_divide_real @ (set_fo3111899725591712190t_real @ (^ [C:nat]: (times_times_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_real) @ (semiri2265585572941072030t_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8613_gbinomial__code)). 185.47/93.68 thf(10585,plain,(((gbinomial_real) = (^ [A:real,B:nat]: (if_real @ (B = zero_zero_nat) @ one_one_real @ (divide_divide_real @ (set_fo3111899725591712190t_real @ (^ [C:nat]: (times_times_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_real) @ (semiri2265585572941072030t_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[838])). 185.47/93.68 thf(6147,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_mult__1)). 185.47/93.68 thf(28376,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6147])). 185.47/93.68 thf(7235,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_power__mult__distrib)). 185.47/93.68 thf(32386,plain,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7235])). 185.47/93.68 thf(2894,axiom,((nat_prod_decode_aux = (^ [A:nat,B:nat]: (if_Pro6206227464963214023at_nat @ (ord_less_eq_nat @ B @ A) @ (product_Pair_nat_nat @ B @ (minus_minus_nat @ A @ B)) @ (nat_prod_decode_aux @ (suc @ A) @ (minus_minus_nat @ B @ (suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9747_prod__decode__aux_Osimps)). 185.47/93.68 thf(17337,plain,(((nat_prod_decode_aux) = (^ [A:nat,B:nat]: (if_Pro6206227464963214023at_nat @ (ord_less_eq_nat @ B @ A) @ (product_Pair_nat_nat @ B @ (minus_minus_nat @ A @ B)) @ (nat_prod_decode_aux @ (suc @ A) @ (minus_minus_nat @ B @ (suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2894])). 185.47/93.68 thf(3802,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ A)) = (divide_divide_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1703_nonzero__mult__divide__mult__cancel__left2)). 185.47/93.68 thf(20218,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ A)) = (divide_divide_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3802])). 185.47/93.68 thf(6238,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (modulo_modulo_nat @ B @ C)) = (modulo_modulo_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1976_mult__mod__right)). 185.47/93.68 thf(28721,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (modulo_modulo_nat @ B @ C)) = (modulo_modulo_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6238])). 185.47/93.68 thf(1613,axiom,((! [A:nat,B:nat,C:nat]: (((semiri1314217659103216013at_int @ A) = (power_power_int @ (semiri1314217659103216013at_int @ B) @ C)) = (A = (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6948_of__nat__power__eq__of__nat__cancel__iff)). 185.47/93.68 thf(13089,plain,((! [A:nat,B:nat,C:nat]: (((semiri1314217659103216013at_int @ A) = (power_power_int @ (semiri1314217659103216013at_int @ B) @ C)) = (A = (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613])). 185.47/93.68 thf(3769,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ A @ (divide_divide_real @ (minus_minus_real @ (exp_real @ A) @ (inverse_inverse_real @ (exp_real @ A))) @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8978_real__le__x__sinh)). 185.47/93.68 thf(20115,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ A @ (divide_divide_real @ (minus_minus_real @ (exp_real @ A) @ (inverse_inverse_real @ (exp_real @ A))) @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3769])). 185.47/93.68 thf(5990,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_ab__semigroup__add__class_Oadd__ac_I1_J)). 185.47/93.68 thf(27861,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5990])). 185.47/93.68 thf(4292,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ B @ (plus_plus_int @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2298_add__increasing2)). 185.47/93.68 thf(21721,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ B @ (plus_plus_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4292])). 185.47/93.68 thf(7302,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3901_antisym)). 185.47/93.68 thf(32606,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7302])). 185.47/93.68 thf(4385,axiom,((! [A:int,B:int,C:int]: ((A = B) => ((ord_less_int @ B @ C) => (ord_less_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3990_ord__eq__less__trans)). 185.47/93.68 thf(22048,plain,((! [A:int,B:int,C:int]: ((A = B) => ((ord_less_int @ B @ C) => (ord_less_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4385])). 185.47/93.68 thf(3874,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ (times_times_real @ B @ A) @ (times_times_real @ A @ C)) = (divide_divide_real @ B @ C)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1697_nonzero__mult__divide__mult__cancel__right2)). 185.47/93.68 thf(20438,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ (times_times_real @ B @ A) @ (times_times_real @ A @ C)) = (divide_divide_real @ B @ C)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3874])). 185.47/93.68 thf(1916,axiom,((! [A:int,B:int]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ (divide_divide_int @ A @ B)) @ (fract @ A @ B)) & (ord_less_rat @ (fract @ A @ B) @ (ring_1_of_int_rat @ (plus_plus_int @ (divide_divide_int @ A @ B) @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9927_rat__floor__lemma)). 185.47/93.68 thf(14130,plain,((! [A:int,B:int]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ (divide_divide_int @ A @ B)) @ (fract @ A @ B)) & (ord_less_rat @ (fract @ A @ B) @ (ring_1_of_int_rat @ (plus_plus_int @ (divide_divide_int @ A @ B) @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916])). 185.47/93.68 thf(3927,axiom,((! [A:nat,B:num]: ((minus_minus_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (minus_minus_nat @ A @ (pred_numeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6791_diff__Suc__numeral)). 185.47/93.68 thf(20613,plain,((! [A:nat,B:num]: ((minus_minus_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (minus_minus_nat @ A @ (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3927])). 185.47/93.68 thf(6583,axiom,((! [A:int,B:int]: (((uminus_uminus_int @ A) = (uminus_uminus_int @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5021_neg__equal__iff__equal)). 185.47/93.68 thf(29950,plain,((! [A:int,B:int]: (((uminus_uminus_int @ A) = (uminus_uminus_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6583])). 185.47/93.68 thf(7230,axiom,((! [A:num,B:num,C:$o]: ((ord_less_num @ A @ B) => ((C) <= (ord_less_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4125_order__less__imp__triv)). 185.47/93.68 thf(32371,plain,((! [A:num,B:num,C:$o]: ((ord_less_num @ A @ B) => ((C) | ~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7230])). 185.47/93.68 thf(4248,axiom,((! [A:int,B:nat,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((ord_less_int @ C @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => (ord_less_int @ (bit_se1409905431419307370or_int @ A @ C) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) <= (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9439_OR__upper)). 185.47/93.68 thf(21597,plain,((! [A:int,B:nat,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((ord_less_int @ C @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => (ord_less_int @ (bit_se1409905431419307370or_int @ A @ C) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) | ~ (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4248])). 185.47/93.68 thf(396,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1416_Diff__subset)). 185.47/93.68 thf(9050,plain,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])). 185.47/93.68 thf(2977,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2077_comm__monoid__add__class_Oadd__0)). 185.47/93.68 thf(17600,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2977])). 185.47/93.68 thf(4817,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ one_one_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ one_one_real @ (powr_real @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9098_ge__one__powr__ge__zero)). 185.47/93.68 thf(23472,plain,((! [A:real,B:real]: ((ord_less_eq_real @ one_one_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ one_one_real @ (powr_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4817])). 185.47/93.68 thf(5185,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_3902_antisym)). 185.47/93.68 thf(24828,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)],[5185])). 185.47/93.68 thf(5929,axiom,((! [A:int]: ((zero_zero_int = (uminus_uminus_int @ A)) = (zero_zero_int = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5051_neg__0__equal__iff__equal)). 185.47/93.68 thf(27627,plain,((! [A:int]: ((zero_zero_int = (uminus_uminus_int @ A)) = (zero_zero_int = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5929])). 185.47/93.68 thf(958,axiom,((plus_plus_complex = (^ [A:complex,B:complex]: (complex2 @ (plus_plus_real @ (re @ A) @ (re @ B)) @ (plus_plus_real @ (im @ A) @ (im @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9680_plus__complex_Ocode)). 185.47/93.68 thf(11022,plain,(((plus_plus_complex) = (^ [A:complex,B:complex]: (complex2 @ (plus_plus_real @ (re @ A) @ (re @ B)) @ (plus_plus_real @ (im @ A) @ (im @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[958])). 185.47/93.68 thf(6524,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((C @ (suc @ D)) <= (C @ D)))) => (C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1047_nat__induct__at__least)). 185.47/93.68 thf(29747,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((C @ (suc @ D)) | ~ (C @ D)))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6524])). 185.47/93.68 thf(1599,axiom,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ A @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (plus_plus_rat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_728_diff__diff__eq2)). 185.47/93.68 thf(13032,plain,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ A @ (minus_minus_rat @ B @ C)) = (minus_minus_rat @ (plus_plus_rat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599])). 185.47/93.68 thf(7550,axiom,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_mult__2__right)). 185.47/93.68 thf(33434,plain,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7550])). 185.47/93.68 thf(287,axiom,((! [A:real]: ~ (! [B:int]: ((arccos @ (cos_real @ A)) != (abs_abs_real @ (minus_minus_real @ A @ (times_times_real @ (ring_1_of_int_real @ B) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8380_arccos__cos__eq__abs__2pi)). 185.47/93.68 thf(8669,plain,((! [A:real]: ~ (! [B:int]: ~ ((arccos @ (cos_real @ A)) = (abs_abs_real @ (minus_minus_real @ A @ (times_times_real @ (ring_1_of_int_real @ B) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 185.47/93.68 thf(5732,axiom,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4593_dvd__triv__left)). 185.47/93.68 thf(26805,plain,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5732])). 185.47/93.68 thf(1433,axiom,((! [A:int]: (((ring_1_of_int_real @ A) = one_one_real) = (A = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6964_of__int__eq__1__iff)). 185.47/93.68 thf(12514,plain,((! [A:int]: (((ring_1_of_int_real @ A) = one_one_real) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1433])). 185.47/93.68 thf(674,axiom,((! [A:nat,B:int]: ((ord_less_int @ (bit_se2159334234014336723it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3128_flip__bit__negative__int__iff)). 185.47/93.68 thf(9986,plain,((! [A:nat,B:int]: ((ord_less_int @ (bit_se2159334234014336723it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[674])). 185.47/93.68 thf(4970,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4260_order_Ostrict__implies__order)). 185.47/93.68 thf(23998,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4970])). 185.47/93.68 thf(2642,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ (abs_abs_int @ A) @ B)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6825_even__abs__add__iff)). 185.47/93.68 thf(16499,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ (abs_abs_int @ A) @ B)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2642])). 185.47/93.68 thf(436,axiom,((! [A:nat,B:real]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ B) => (((nat2 @ (archim6058952711729229775r_real @ B)) = A) <= (ord_less_real @ B @ (semiri5074537144036343181t_real @ (suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9322_floor__eq3)). 185.47/93.68 thf(9182,plain,((! [A:nat,B:real]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ B) => (((nat2 @ (archim6058952711729229775r_real @ B)) = A) | ~ (ord_less_real @ B @ (semiri5074537144036343181t_real @ (suc @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[436])). 185.47/93.68 thf(5188,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_diff__eq__diff__eq)). 185.47/93.68 thf(24837,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5188])). 185.47/93.68 thf(3391,axiom,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ (uminus_uminus_int @ A) @ B) = (modulo_modulo_int @ (uminus_uminus_int @ C) @ B)) <= ((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5593_mod__minus__cong)). 185.47/93.68 thf(18903,plain,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ (uminus_uminus_int @ A) @ B) = (modulo_modulo_int @ (uminus_uminus_int @ C) @ B)) | ~ ((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3391])). 185.47/93.68 thf(4564,axiom,((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5711_le__minus__one__simps_I2_J)). 185.47/93.68 thf(22623,plain,((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4564])). 185.47/93.68 thf(1046,axiom,((! [A:int,B:int]: ((ord_less_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5527_verit__negate__coefficient_I2_J)). 185.47/93.68 thf(11295,plain,((! [A:int,B:int]: ((ord_less_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046])). 185.47/93.68 thf(5408,axiom,((! [A:int,B:int]: (((A = one_one_int) | (A = (uminus_uminus_int @ one_one_int))) <= ((times_times_int @ A @ B) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5822_pos__zmult__eq__1__iff__lemma)). 185.47/93.68 thf(25620,plain,((! [A:int,B:int]: ((A = one_one_int) | (A = (uminus_uminus_int @ one_one_int)) | ~ ((times_times_int @ A @ B) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5408])). 185.47/93.68 thf(156,axiom,((! [A:set_nat,B:(nat > rat)]: (((groups73079841787564623at_rat @ B @ A) = one_one_rat) <= (~ (finite_finite_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8657_prod_Oinfinite)). 185.47/93.68 thf(8231,plain,((! [A:set_nat,B:(nat > rat)]: (((groups73079841787564623at_rat @ (B) @ A) = one_one_rat) | (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 185.47/93.68 thf(6403,axiom,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3872_order_Otrans)). 185.47/93.68 thf(29290,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6403])). 185.47/93.68 thf(6506,axiom,((! [A:nat,B:nat]: ((divide_divide_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (times_times_int @ (zero_n2684676970156552555ol_int @ ((ord_less_eq_nat @ B @ A) & ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) != zero_zero_int))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6302_exp__div__exp__eq)). 185.47/93.68 thf(29690,plain,((! [A:nat,B:nat]: ((divide_divide_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (times_times_int @ (zero_n2684676970156552555ol_int @ ((ord_less_eq_nat @ B @ A) & ~ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = zero_zero_int))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6506])). 185.47/93.68 thf(1047,axiom,((ord_less_int = (^ [A:int,B:int]: ((B != A) & (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4238_dual__order_Ostrict__iff__order)). 185.47/93.68 thf(11297,plain,(((ord_less_int) = (^ [A:int,B:int]: (~ (B = A) & (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047])). 185.47/93.68 thf(4056,axiom,((! [A:int,B:int]: ((minus_minus_int @ A @ (times_times_int @ (divide_divide_int @ A @ B) @ B)) = (modulo_modulo_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2563_minus__div__mult__eq__mod)). 185.47/93.68 thf(21002,plain,((! [A:int,B:int]: ((minus_minus_int @ A @ (times_times_int @ (divide_divide_int @ A @ B) @ B)) = (modulo_modulo_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4056])). 185.47/93.68 thf(2100,axiom,((! [A:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((abs_abs_rat @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6369_abs__of__nonneg)). 185.47/93.68 thf(14728,plain,((! [A:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((abs_abs_rat @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2100])). 185.47/93.68 thf(3460,axiom,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ A) = (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1657_add__less__same__cancel1)). 185.47/93.68 thf(19106,plain,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ A) = (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3460])). 185.47/93.68 thf(4128,axiom,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (comm_s7457072308508201937r_real @ A @ B)) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8401_pochhammer__double)). 185.47/93.68 thf(21225,plain,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (comm_s7457072308508201937r_real @ A @ B)) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4128])). 185.47/93.68 thf(535,axiom,((tanh_real = (^ [A:real]: (divide_divide_real @ (minus_minus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))) @ (plus_plus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8219_tanh__altdef)). 185.47/93.68 thf(9518,plain,(((tanh_real) = (^ [A:real]: (divide_divide_real @ (minus_minus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))) @ (plus_plus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[535])). 185.47/93.68 thf(874,axiom,((! [A:real,B:real]: (((ln_ln_real @ (powr_real @ A @ B)) = (times_times_real @ B @ (ln_ln_real @ A))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9103_ln__powr)). 185.47/93.68 thf(10717,plain,((! [A:real,B:real]: (((ln_ln_real @ (powr_real @ A @ B)) = (times_times_real @ B @ (ln_ln_real @ A))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[874])). 185.47/93.68 thf(1511,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) | (ord_less_real @ B @ A) | (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4128_linorder__less__linear)). 185.47/93.68 thf(12752,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) | (ord_less_real @ B @ A) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511])). 185.47/93.68 thf(803,axiom,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_nat @ (groups708209901874060359at_nat @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8702_prod_OatMost__Suc)). 185.47/93.68 thf(10466,plain,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_nat @ (groups708209901874060359at_nat @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[803])). 185.47/93.68 thf(876,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ B @ (powr_real @ A @ C)) = (ord_less_eq_real @ (log @ A @ B) @ C))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9119_le__powr__iff)). 185.47/93.68 thf(10724,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ B @ (powr_real @ A @ C)) = (ord_less_eq_real @ (log @ A @ B) @ C))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[876])). 185.47/93.68 thf(6231,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3283_minf_I7_J)). 185.47/93.68 thf(28696,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6231])). 185.47/93.68 thf(2225,axiom,((! [A:int,B:int]: (ord_less_eq_int @ (abs_abs_int @ (plus_plus_int @ A @ B)) @ (plus_plus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6489_abs__triangle__ineq)). 185.47/93.68 thf(15132,plain,((! [A:int,B:int]: (ord_less_eq_int @ (abs_abs_int @ (plus_plus_int @ A @ B)) @ (plus_plus_int @ (abs_abs_int @ A) @ (abs_abs_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2225])). 185.47/93.68 thf(4977,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2297_add__increasing2)). 185.47/93.68 thf(24018,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4977])). 185.47/93.68 thf(2478,axiom,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ zero_zero_real @ (sqrt @ (times_times_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (plus_plus_real @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8256_real__sqrt__sum__squares__mult__ge__zero)). 185.47/93.68 thf(15937,plain,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ zero_zero_real @ (sqrt @ (times_times_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (plus_plus_real @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2478])). 185.47/93.68 thf(5839,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_V5719532721284313246member @ A @ B) = C) => ((! [D:$o,E:$o]: ((C = (~ (((B != zero_zero_nat) => ((B = one_one_nat) & ((B = one_one_nat) => (E)))) & ((D) <= (B = zero_zero_nat))))) <= (A = (vEBT_Leaf @ D @ E)))) => (((C) <= (? [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ D @ zero_zero_nat @ E @ F)))) => (~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT]: ((? [G:vEBT_VEBT]: (A = (vEBT_Node @ D @ (suc @ E) @ F @ G))) => (C = (~ ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3000_VEBT__internal_Onaive__member_Oelims_I1_J)). 185.47/93.68 thf(27316,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_V5719532721284313246member @ A @ B) = C) => ((! [D:$o,E:$o]: ((C = (~ (((~ (B = zero_zero_nat)) => ((B = one_one_nat) & ((B = one_one_nat) => (E)))) & ((D) | ~ (B = zero_zero_nat))))) | ~ (A = (vEBT_Leaf @ D @ E)))) => (((C) | ~ (? [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ D @ zero_zero_nat @ E @ F)))) => (~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT]: ((? [G:vEBT_VEBT]: (A = (vEBT_Node @ D @ (suc @ E) @ F @ G))) => (C = (~ ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5839])). 185.47/93.68 thf(915,axiom,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((finite_finite_nat @ A) => ((((groups6464643781859351333omplex @ C @ B) = (groups6464643781859351333omplex @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_complex)))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8926_prod_Omono__neutral__left)). 185.47/93.68 thf(10861,plain,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((groups6464643781859351333omplex @ (C) @ B) = (groups6464643781859351333omplex @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_complex))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[915])). 185.47/93.68 thf(6434,axiom,((! [A:num]: ((abs_abs_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (numera6620942414471956472nteger @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6378_abs__neg__numeral)). 185.47/93.68 thf(29425,plain,((! [A:num]: ((abs_abs_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (numera6620942414471956472nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6434])). 185.47/93.68 thf(79,axiom,((! [A:real,B:nat,C:(nat > (real > real))]: ((A = zero_zero_real) => ((B != zero_zero_nat) => ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_real) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8075_Maclaurin__zero)). 185.47/93.68 thf(7988,plain,((! [A:real,B:nat,C:(nat > (real > real))]: ((A = zero_zero_real) => ((~ (B = zero_zero_nat)) => ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_zero_real) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 185.47/93.68 thf(3155,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ B @ C)) & ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2571_mult__le__cancel__left)). 185.47/93.68 thf(18163,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ B @ C)) & ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3155])). 185.47/93.68 thf(4277,axiom,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ C)) @ (abs_abs_real @ (minus_minus_real @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6585_abs__diff__triangle__ineq)). 185.47/93.68 thf(21679,plain,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (abs_abs_real @ (minus_minus_real @ A @ C)) @ (abs_abs_real @ (minus_minus_real @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4277])). 185.47/93.68 thf(3804,axiom,((! [A:num]: ((plus_plus_int @ one_one_int @ (numeral_numeral_int @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_828_one__plus__numeral__commute)). 185.47/93.68 thf(20225,plain,((! [A:num]: ((plus_plus_int @ one_one_int @ (numeral_numeral_int @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3804])). 185.47/93.68 thf(6999,axiom,((! [A:num]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ one_one_int) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_numeral__le__one__iff)). 185.47/93.68 thf(31550,plain,((! [A:num]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ one_one_int) = (ord_less_eq_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6999])). 185.47/93.68 thf(6292,axiom,((bit_se727722235901077358nd_nat = (^ [A:nat,B:nat]: (if_nat @ ((A = zero_zero_nat) | (B = zero_zero_nat)) @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9403_and__nat__unfold)). 185.47/93.68 thf(28902,plain,(((bit_se727722235901077358nd_nat) = (^ [A:nat,B:nat]: (if_nat @ ((A = zero_zero_nat) | (B = zero_zero_nat)) @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6292])). 185.47/93.68 thf(1327,axiom,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_mem__Collect__eq)). 185.47/93.68 thf(12160,plain,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327])). 185.47/93.68 thf(5739,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2074_zero__neq__one)). 185.47/93.68 thf(26825,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5739])). 185.47/93.68 thf(1277,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_add__less__cancel__left)). 185.47/93.68 thf(12001,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277])). 185.47/93.68 thf(1406,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ C @ A) => (ord_less_eq_rat @ C @ B)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3895_dual__order_Otrans)). 185.47/93.68 thf(12419,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ C @ A) => (ord_less_eq_rat @ C @ B)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406])). 185.47/93.68 thf(7247,axiom,((! [A:complex,B:nat]: (((B = zero_zero_nat) | ((real_V1022390504157884413omplex @ A) = one_one_real)) <= ((power_power_complex @ A @ B) = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7513_power__eq__1__iff)). 185.47/93.68 thf(32422,plain,((! [A:complex,B:nat]: ((B = zero_zero_nat) | ((real_V1022390504157884413omplex @ A) = one_one_real) | ~ ((power_power_complex @ A @ B) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7247])). 185.47/93.68 thf(5959,axiom,((! [A:num,B:num]: ((ord_less_num @ B @ A) | (A = B) | (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4130_linorder__less__linear)). 185.47/93.68 thf(27729,plain,((! [A:num,B:num]: ((ord_less_num @ B @ A) | (A = B) | (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5959])). 185.47/93.68 thf(6940,axiom,((! [A:vEBT_VEBT]: (((vEBT_invar_vebt @ A @ na) & ! [B:nat,C:nat]: (((vEBT_vebt_pred @ A @ B) = (some_nat @ C)) = (vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ A) @ B @ C))) <= (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561__C4_Ohyps_C_I1_J)). 185.47/93.68 thf(31269,plain,((! [A:vEBT_VEBT]: (((vEBT_invar_vebt @ A @ na) & ! [B:nat,C:nat]: (((vEBT_vebt_pred @ A @ B) = (some_nat @ C)) = (vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ A) @ B @ C))) | ~ (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6940])). 185.47/93.68 thf(5527,axiom,((! [A:num]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ one_one_complex)) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5288_numeral__eq__neg__one__iff)). 185.47/93.68 thf(26138,plain,((! [A:num]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ one_one_complex)) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5527])). 185.47/93.68 thf(1626,axiom,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_Code_integer) = (ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6714_abs__square__le__1)). 185.47/93.68 thf(13149,plain,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_Code_integer) = (ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626])). 185.47/93.68 thf(3075,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (plus_plus_int @ B @ A)) = (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1620_le__add__same__cancel2)). 185.47/93.68 thf(17906,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (plus_plus_int @ B @ A)) = (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3075])). 185.47/93.68 thf(1808,axiom,((! [A:complex,B:complex,C:num]: ((A = (divide1717551699836669952omplex @ B @ (numera6690914467698888265omplex @ C))) = ((((numera6690914467698888265omplex @ C) != zero_zero_complex) => ((times_times_complex @ A @ (numera6690914467698888265omplex @ C)) = B)) & (((numera6690914467698888265omplex @ C) = zero_zero_complex) => (A = zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1820_eq__divide__eq__numeral1_I1_J)). 185.47/93.68 thf(13791,plain,((! [A:complex,B:complex,C:num]: ((A = (divide1717551699836669952omplex @ B @ (numera6690914467698888265omplex @ C))) = (((~ ((numera6690914467698888265omplex @ C) = zero_zero_complex)) => ((times_times_complex @ A @ (numera6690914467698888265omplex @ C)) = B)) & (((numera6690914467698888265omplex @ C) = zero_zero_complex) => (A = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808])). 185.47/93.68 thf(5373,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_add__left__mono)). 185.47/93.68 thf(25514,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5373])). 185.47/93.68 thf(2011,axiom,((! [A:int]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ zero_zero_rat) = (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7034_of__int__le__0__iff)). 185.47/93.68 thf(14459,plain,((! [A:int]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ zero_zero_rat) = (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011])). 185.47/93.68 thf(244,axiom,(((bit_se1409905431419307370or_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (bit_ri7919022796975470100ot_int @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9513_or__not__numerals_I1_J)). 185.47/93.68 thf(8509,plain,(((bit_se1409905431419307370or_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (bit_ri7919022796975470100ot_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 185.47/93.68 thf(5996,axiom,((((=) @ list_VEBT_VEBT) = (^ [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: (! [C:nat]: (((nth_VEBT_VEBT @ A @ C) = (nth_VEBT_VEBT @ B @ C)) <= (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A))) & ((size_s6755466524823107622T_VEBT @ A) = (size_s6755466524823107622T_VEBT @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_926_list__eq__iff__nth__eq)). 185.47/93.68 thf(27880,plain,((((=) @ list_VEBT_VEBT) = (^ [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: (! [C:nat]: (((nth_VEBT_VEBT @ A @ C) = (nth_VEBT_VEBT @ B @ C)) | ~ (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A))) & ((size_s6755466524823107622T_VEBT @ A) = (size_s6755466524823107622T_VEBT @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5996])). 185.47/93.68 thf(2981,axiom,((! [A:rat,B:rat,C:(rat > rat),D:rat]: ((((C @ B) = D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ (C @ E) @ (C @ F)) <= (ord_less_eq_rat @ E @ F))) => (ord_less_eq_rat @ (C @ A) @ D))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3948_ord__le__eq__subst)). 185.47/93.68 thf(17615,plain,((! [A:rat,B:rat,C:(rat > rat),D:rat]: ((((C @ B) = D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_rat @ E @ F))) => (ord_less_eq_rat @ (C @ A) @ D))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2981])). 185.47/93.68 thf(6815,axiom,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) != zero_zero_nat) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2095_power__not__zero)). 185.47/93.68 thf(30793,plain,((! [A:nat,B:nat]: (~ ((power_power_nat @ A @ B) = zero_zero_nat) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6815])). 185.47/93.68 thf(1224,axiom,((! [A:(int > $o),B:int]: ((? [C:int]: (A @ (times_times_int @ B @ C))) = (? [C:int]: ((A @ C) & (dvd_dvd_int @ B @ (plus_plus_int @ C @ zero_zero_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4828_unity__coeff__ex)). 185.47/93.68 thf(11840,plain,((! [A:(int > $o),B:int]: ((? [C:int]: (A @ (times_times_int @ B @ C))) = (? [C:int]: ((A @ C) & (dvd_dvd_int @ B @ (plus_plus_int @ C @ zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224])). 185.47/93.68 thf(6806,axiom,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1572_bits__div__0)). 185.47/93.68 thf(30756,plain,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6806])). 185.47/93.68 thf(5127,axiom,((! [A:rat]: ((^ [B:rat]: (times_times_rat @ B @ A)) = (times_times_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1335_mult__commute__abs)). 185.47/93.68 thf(24606,plain,((! [A:rat]: ((^ [B:rat]: (times_times_rat @ B @ A)) = (times_times_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5127])). 185.47/93.68 thf(3101,axiom,((! [A:num]: ((bitM @ (bit0 @ A)) = (bit1 @ (bitM @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8965_semiring__norm_I27_J)). 185.47/93.68 thf(17996,plain,((! [A:num]: ((bitM @ (bit0 @ A)) = (bit1 @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3101])). 185.47/93.68 thf(5342,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1029_less__Suc__eq)). 185.47/93.68 thf(25382,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5342])). 185.47/93.68 thf(7371,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_le__trans)). 185.47/93.68 thf(32833,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7371])). 185.47/93.68 thf(6168,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9454_xor__nat__numerals_I3_J)). 185.47/93.68 thf(28488,plain,((! [A:num]: ((bit_se6528837805403552850or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6168])). 185.47/93.68 thf(3204,axiom,((! [A:nat,B:int]: ((ord_less_int @ (bit_se8568078237143864401it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9753_drop__bit__negative__int__iff)). 185.47/93.68 thf(18318,plain,((! [A:nat,B:int]: ((ord_less_int @ (bit_se8568078237143864401it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3204])). 185.47/93.68 thf(1148,axiom,((ord_less_eq_real = (^ [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ A @ B) @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2377_le__iff__diff__le__0)). 185.47/93.68 thf(11622,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ A @ B) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148])). 185.47/93.68 thf(7649,axiom,((! [A:$o]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (zero_n2687167440665602831ol_nat @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5402_odd__of__bool__self)). 185.47/93.68 thf(33705,plain,((! [A:$o]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (zero_n2687167440665602831ol_nat @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7649])). 185.47/93.68 thf(4010,axiom,((! [A:(nat > real),B:real,C:(nat > real),D:real]: ((sums_real @ A @ B) => ((sums_real @ (^ [E:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E) @ (C @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))) @ (A @ (divide_divide_nat @ (minus_minus_nat @ E @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_real @ B @ D)) <= (sums_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8252_sums__if)). 185.47/93.68 thf(20868,plain,((! [A:(nat > real),B:real,C:(nat > real),D:real]: ((sums_real @ (A) @ B) => ((sums_real @ (^ [E:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E) @ (C @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))) @ (A @ (divide_divide_nat @ (minus_minus_nat @ E @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_real @ B @ D)) | ~ (sums_real @ (C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4010])). 185.47/93.68 thf(587,axiom,((bit_se2159334234014336723it_int = (^ [A:nat,B:int]: (bit_se6526347334894502574or_int @ B @ (bit_se545348938243370406it_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9520_flip__bit__int__def)). 185.47/93.68 thf(9683,plain,(((bit_se2159334234014336723it_int) = (^ [A:nat,B:int]: (bit_se6526347334894502574or_int @ B @ (bit_se545348938243370406it_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[587])). 185.47/93.68 thf(3733,axiom,((! [A:real,B:real]: ? [C:real,D:real]: ((B = (times_times_real @ C @ (sin_real @ D))) & (A = (times_times_real @ C @ (cos_real @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7819_polar__Ex)). 185.47/93.68 thf(19988,plain,((! [A:real,B:real]: ? [C:real,D:real]: ((B = (times_times_real @ C @ (sin_real @ D))) & (A = (times_times_real @ C @ (cos_real @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3733])). 185.47/93.68 thf(2819,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ A @ (uminus1351360451143612070nteger @ B)) = (ord_le3102999989581377725nteger @ B @ (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5507_le__minus__iff)). 185.47/93.68 thf(17092,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ A @ (uminus1351360451143612070nteger @ B)) = (ord_le3102999989581377725nteger @ B @ (uminus1351360451143612070nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2819])). 185.47/93.68 thf(4007,axiom,((! [A:product_prod_nat_nat]: ((uminus_uminus_int @ (abs_Integ @ A)) = (abs_Integ @ (produc2626176000494625587at_nat @ (^ [B:nat,C:nat]: (product_Pair_nat_nat @ C @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9818_uminus__int_Oabs__eq)). 185.47/93.68 thf(20860,plain,((! [A:product_prod_nat_nat]: ((uminus_uminus_int @ (abs_Integ @ A)) = (abs_Integ @ (produc2626176000494625587at_nat @ (^ [B:nat,C:nat]: (product_Pair_nat_nat @ C @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4007])). 185.47/93.68 thf(4583,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ A @ zero_zero_real)) | ((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2408_divide__le__0__iff)). 185.47/93.68 thf(22680,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ A @ zero_zero_real)) | ((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4583])). 185.47/93.68 thf(1803,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se725231765392027082nd_int @ A @ B)) = ((ord_less_eq_int @ zero_zero_int @ A) | (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9363_and__nonnegative__int__iff)). 185.47/93.68 thf(13774,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se725231765392027082nd_int @ A @ B)) = ((ord_less_eq_int @ zero_zero_int @ A) | (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1803])). 185.47/93.68 thf(2304,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => ((ord_less_eq_int @ zero_zero_int @ D) => (((modulo_modulo_int @ A @ B) = D) <= (ord_less_int @ D @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3171_int__mod__pos__eq)). 185.47/93.68 thf(15370,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ (times_times_int @ B @ C) @ D)) => ((ord_less_eq_int @ zero_zero_int @ D) => (((modulo_modulo_int @ A @ B) = D) | ~ (ord_less_int @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2304])). 185.47/93.68 thf(6103,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2494_gr0__implies__Suc)). 185.47/93.68 thf(28215,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6103])). 185.47/93.68 thf(7097,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((((vEBT_vebt_mint @ A) = (some_nat @ C)) => (vEBT_VEBT_min_in_set @ (vEBT_VEBT_set_vebt @ A) @ C)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_949_mint__corr)). 185.47/93.68 thf(31890,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((((vEBT_vebt_mint @ A) = (some_nat @ C)) => (vEBT_VEBT_min_in_set @ (vEBT_VEBT_set_vebt @ A) @ C)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7097])). 185.47/93.68 thf(331,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (bit_se6526347334894502574or_int @ A @ B))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9491_XOR__lower)). 185.47/93.68 thf(8840,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ zero_zero_int @ (bit_se6526347334894502574or_int @ A @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 185.47/93.68 thf(129,axiom,((gbinomial_real = (^ [A:real,B:nat]: (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (gbinomial_real @ (minus_minus_real @ (minus_minus_real @ (semiri5074537144036343181t_real @ B) @ A) @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8566_gbinomial__negated__upper)). 185.47/93.68 thf(8148,plain,(((gbinomial_real) = (^ [A:real,B:nat]: (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (gbinomial_real @ (minus_minus_real @ (minus_minus_real @ (semiri5074537144036343181t_real @ B) @ A) @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 185.47/93.68 thf(6684,axiom,((! [A:num,B:num,C:num]: ((A = B) => ((ord_less_num @ A @ C) <= (ord_less_num @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3988_ord__eq__less__trans)). 185.47/93.68 thf(30278,plain,((! [A:num,B:num,C:num]: ((A = B) => ((ord_less_num @ A @ C) | ~ (ord_less_num @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6684])). 185.47/93.68 thf(7148,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1591_less__nat__zero__code)). 185.47/93.68 thf(32076,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7148])). 185.47/93.68 thf(2451,axiom,((! [A:int,B:int,C:(int > $o)]: ((ord_less_eq_int @ A @ B) => ((C @ B) => ((C @ A) <= (! [D:int]: ((ord_less_eq_int @ D @ B) => ((C @ D) => (C @ (minus_minus_int @ D @ one_one_int)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3138_int__le__induct)). 185.47/93.68 thf(15846,plain,((! [A:int,B:int,C:(int > $o)]: ((ord_less_eq_int @ A @ B) => ((C @ B) => ((C @ A) | ~ (! [D:int]: ((ord_less_eq_int @ D @ B) => ((C @ D) => (C @ (minus_minus_int @ D @ one_one_int)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2451])). 185.47/93.68 thf(582,axiom,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5946_neg__numeral__less__one)). 185.47/93.68 thf(9666,plain,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[582])). 185.47/93.68 thf(4374,axiom,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ (divide_divide_nat @ B @ A)) = (divide_divide_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7276_real__of__nat__div)). 185.47/93.68 thf(22014,plain,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ (divide_divide_nat @ B @ A)) = (divide_divide_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4374])). 185.47/93.68 thf(3305,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2085_add_Ocomm__neutral)). 185.47/93.68 thf(18625,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3305])). 185.47/93.68 thf(499,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => (ord_less_real @ (ln_ln_real @ A) @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5878_ln__less__zero)). 185.47/93.68 thf(9413,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => (ord_less_real @ (ln_ln_real @ A) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])). 185.47/93.68 thf(7595,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) | (F = C) | (F = B)) <= (vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ A @ D @ E) @ F)) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_both__member__options__from__complete__tree__to__child)). 185.47/93.68 thf(33561,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) | (F = C) | (F = B) | ~ (vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ A @ D @ E) @ F) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7595])). 185.47/93.68 thf(7524,axiom,((! [A:real,B:real]: (((A != zero_zero_real) & (B != zero_zero_real)) <= ((times_times_real @ A @ B) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2044_mult__not__zero)). 185.47/93.68 thf(33359,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real) & ~ (B = zero_zero_real)) | ((times_times_real @ A @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7524])). 185.47/93.68 thf(4912,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (vEBT_VEBT_low @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3012_VEBT__internal_Oexp__split__high__low_I2_J)). 185.47/93.68 thf(23798,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (vEBT_VEBT_low @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4912])). 185.47/93.68 thf(147,axiom,((! [A:num]: ((re @ (numera6690914467698888265omplex @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9637_complex__Re__numeral)). 185.47/93.68 thf(8206,plain,((! [A:num]: ((re @ (numera6690914467698888265omplex @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 185.47/93.68 thf(279,axiom,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9531_and__not__numerals_I5_J)). 185.47/93.68 thf(8644,plain,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 185.47/93.68 thf(7396,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_773_comm__monoid__mult__class_Omult__1)). 185.47/93.68 thf(32906,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7396])). 185.47/93.68 thf(2018,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat))) => ((! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ zero_zero_nat)))) => ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ (suc @ D))))) => (((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E))) => ((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G)))))) <= (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2152_vebt__pred_Ocases)). 185.47/93.68 thf(14480,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat))) => ((! [B:$o,C:$o]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ zero_zero_nat)))) => ((! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ (suc @ D))))) => (((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E))) => ((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G)))))) | ~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2018])). 185.47/93.68 thf(4497,axiom,((! [A:rat,B:rat]: ((A != zero_zero_rat) => ((divide_divide_rat @ (times_times_rat @ A @ B) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1687_nonzero__mult__div__cancel__left)). 185.47/93.68 thf(22395,plain,((! [A:rat,B:rat]: ((~ (A = zero_zero_rat)) => ((divide_divide_rat @ (times_times_rat @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4497])). 185.47/93.68 thf(1882,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1611_zero__le__double__add__iff__zero__le__single__add)). 185.47/93.68 thf(14031,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1882])). 185.47/93.68 thf(1980,axiom,(((plus_plus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5277_add__neg__numeral__special_I7_J)). 185.47/93.68 thf(14356,plain,(((plus_plus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1980])). 185.47/93.68 thf(3897,axiom,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5060_neg__less__iff__less)). 185.47/93.68 thf(20506,plain,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3897])). 185.47/93.68 thf(683,axiom,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit1 @ one)))) = (divide_divide_real @ (sqrt @ (numeral_numeral_real @ (bit1 @ one))) @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8247_sin__60)). 185.47/93.68 thf(10012,plain,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit1 @ one)))) = (divide_divide_real @ (sqrt @ (numeral_numeral_real @ (bit1 @ one))) @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[683])). 185.47/93.68 thf(2024,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => (! [D:int,E:int]: ((~ (dvd_dvd_int @ A @ (plus_plus_int @ D @ C))) = (~ (dvd_dvd_int @ A @ (plus_plus_int @ (minus_minus_int @ D @ (times_times_int @ E @ B)) @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4850_inf__period_I4_J)). 185.47/93.68 thf(14498,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => (! [D:int,E:int]: ((~ (dvd_dvd_int @ A @ (plus_plus_int @ D @ C))) = (~ (dvd_dvd_int @ A @ (plus_plus_int @ (minus_minus_int @ D @ (times_times_int @ E @ B)) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2024])). 185.47/93.68 thf(5391,axiom,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1551_zero__diff)). 185.47/93.68 thf(25570,plain,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5391])). 185.47/93.68 thf(4195,axiom,((! [A:int,B:int,C:nat]: ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ (^ [D:nat]: (plus_plus_int @ A @ (times_times_int @ (semiri1314217659103216013at_int @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_int @ (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int) @ (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7340_double__arith__series)). 185.47/93.68 thf(21432,plain,((! [A:int,B:int,C:nat]: ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups3539618377306564664at_int @ (^ [D:nat]: (plus_plus_int @ A @ (times_times_int @ (semiri1314217659103216013at_int @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_int @ (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int) @ (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4195])). 185.47/93.68 thf(5190,axiom,((! [A:complex,B:complex]: (((A = zero_zero_complex) | (B = zero_zero_complex)) <= ((times_times_complex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2048_divisors__zero)). 185.47/93.68 thf(24844,plain,((! [A:complex,B:complex]: ((A = zero_zero_complex) | (B = zero_zero_complex) | ~ ((times_times_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5190])). 185.47/93.68 thf(5182,axiom,((! [A:nat,B:nat]: ? [C:nat]: ! [D:nat]: (((dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B)) = (dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B))) <= (ord_less_nat @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4721_pinf_I9_J)). 185.47/93.68 thf(24821,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5182])). 185.47/93.68 thf(6795,axiom,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ (abs_abs_int @ A) @ B)) = ((B = zero_zero_nat) | (A != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6422_zero__less__power__abs__iff)). 185.47/93.68 thf(30719,plain,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ (abs_abs_int @ A) @ B)) = ((B = zero_zero_nat) | ~ (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6795])). 185.47/93.68 thf(2879,axiom,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6449_abs__ge__self)). 185.47/93.68 thf(17283,plain,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2879])). 185.47/93.68 thf(4423,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ C @ A)) <= (ord_less_rat @ C @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2354_mult__strict__left__mono__neg)). 185.47/93.68 thf(22156,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ (times_times_rat @ C @ B) @ (times_times_rat @ C @ A)) | ~ (ord_less_rat @ C @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4423])). 185.47/93.68 thf(6099,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se547839408752420682it_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ (minus_minus_nat @ C @ A)) & (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9515_bit__push__bit__iff__nat)). 185.47/93.68 thf(28198,plain,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se547839408752420682it_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ (minus_minus_nat @ C @ A)) & (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6099])). 185.47/93.68 thf(4885,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = (ord_less_eq_rat @ (times_times_rat @ B @ A) @ (uminus_uminus_rat @ C))) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6215_pos__le__minus__divide__eq)). 185.47/93.68 thf(23715,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ B @ (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = (ord_less_eq_rat @ (times_times_rat @ B @ A) @ (uminus_uminus_rat @ C))) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4885])). 185.47/93.68 thf(1454,axiom,((! [A:int,B:int,C:nat]: (((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)))) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2174_power__strict__mono)). 185.47/93.68 thf(12580,plain,((! [A:int,B:int,C:nat]: (((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)))) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454])). 185.47/93.68 thf(2053,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_int @ (power_power_int @ (semiri1314217659103216013at_int @ A) @ B) @ (semiri1314217659103216013at_int @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7046_of__nat__less__of__nat__power__cancel__iff)). 185.47/93.68 thf(14589,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_int @ (power_power_int @ (semiri1314217659103216013at_int @ A) @ B) @ (semiri1314217659103216013at_int @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2053])). 185.47/93.68 thf(2038,axiom,((! [A:real,B:(nat > real),C:real]: ((A != zero_zero_real) => ((sums_real @ (^ [D:nat]: (times_times_real @ (B @ D) @ A)) @ (times_times_real @ C @ A)) = (sums_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8177_sums__mult2__iff)). 185.47/93.68 thf(14545,plain,((! [A:real,B:(nat > real),C:real]: ((~ (A = zero_zero_real)) => ((sums_real @ (^ [D:nat]: (times_times_real @ (B @ D) @ A)) @ (times_times_real @ C @ A)) = (sums_real @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2038])). 185.47/93.68 thf(6600,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1606_mult__is__0)). 185.47/93.68 thf(30005,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6600])). 185.47/93.68 thf(3019,axiom,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ A @ A) = (times_3573771949741848930nteger @ B @ B)) = ((A = (uminus1351360451143612070nteger @ B)) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5544_square__eq__iff)). 185.47/93.68 thf(17730,plain,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ A @ A) = (times_3573771949741848930nteger @ B @ B)) = ((A = (uminus1351360451143612070nteger @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3019])). 185.47/93.68 thf(1328,axiom,((! [A:num,B:real,C:real]: (((numeral_numeral_real @ A) = (divide_divide_real @ B @ C)) = ((((times_times_real @ (numeral_numeral_real @ A) @ C) = B) <= (C != zero_zero_real)) & (((numeral_numeral_real @ A) = zero_zero_real) <= (C = zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2724_eq__divide__eq__numeral_I1_J)). 185.47/93.68 thf(12163,plain,((! [A:num,B:real,C:real]: (((numeral_numeral_real @ A) = (divide_divide_real @ B @ C)) = ((((times_times_real @ (numeral_numeral_real @ A) @ C) = B) | (C = zero_zero_real)) & (((numeral_numeral_real @ A) = zero_zero_real) | ~ (C = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328])). 185.47/93.68 thf(5937,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: (((A @ E @ (modulo_modulo_nat @ D @ E)) => (A @ D @ E)) <= (ord_less_nat @ zero_zero_nat @ E))) => (A @ B @ C)) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3802_gcd__nat__induct)). 185.47/93.68 thf(27650,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: (((A @ E @ (modulo_modulo_nat @ D @ E)) => (A @ D @ E)) | ~ (ord_less_nat @ zero_zero_nat @ E))) => (A @ B @ C)) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5937])). 185.47/93.68 thf(1418,axiom,((ord_less_rat = (^ [A:rat,B:rat]: (~ (ord_less_eq_rat @ B @ A) & (ord_less_eq_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4253_dual__order_Ostrict__iff__not)). 185.47/93.68 thf(12470,plain,(((ord_less_rat) = (^ [A:rat,B:rat]: (~ (ord_less_eq_rat @ B @ A) & (ord_less_eq_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418])). 185.47/93.68 thf(3531,axiom,((divide_divide_int = (^ [A:int,B:int]: (if_int @ (B = zero_zero_int) @ zero_zero_int @ (if_int @ ((sgn_sgn_int @ A) = (sgn_sgn_int @ B)) @ (semiri1314217659103216013at_int @ (divide_divide_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B)))) @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (plus_plus_nat @ (divide_divide_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B))) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_int @ B @ A))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9242_divide__int__def)). 185.47/93.68 thf(19348,plain,(((divide_divide_int) = (^ [A:int,B:int]: (if_int @ (B = zero_zero_int) @ zero_zero_int @ (if_int @ ((sgn_sgn_int @ A) = (sgn_sgn_int @ B)) @ (semiri1314217659103216013at_int @ (divide_divide_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B)))) @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (plus_plus_nat @ (divide_divide_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B))) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_int @ B @ A))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3531])). 185.47/93.68 thf(3949,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) => (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9056_less__log2__of__power)). 185.47/93.68 thf(20685,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) => (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3949])). 185.47/93.68 thf(491,axiom,((! [A:complex]: ((re @ (invers8013647133539491842omplex @ A)) = (divide_divide_real @ (re @ A) @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9696_inverse__complex_Osimps_I1_J)). 185.47/93.68 thf(9386,plain,((! [A:complex]: ((re @ (invers8013647133539491842omplex @ A)) = (divide_divide_real @ (re @ A) @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[491])). 185.47/93.68 thf(5639,axiom,((! [A:nat,B:rat,C:rat]: ((((ord_less_eq_rat @ zero_zero_rat @ C) => (((power_power_rat @ B @ A) = (power_power_rat @ C @ A)) = (B = C))) <= (ord_less_eq_rat @ zero_zero_rat @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2139_power__eq__iff__eq__base)). 185.47/93.68 thf(26495,plain,((! [A:nat,B:rat,C:rat]: (((ord_less_eq_rat @ zero_zero_rat @ C) => (((power_power_rat @ B @ A) = (power_power_rat @ C @ A)) = (B = C))) | ~ (ord_less_eq_rat @ zero_zero_rat @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5639])). 185.47/93.68 thf(90,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_nat @ (A @ zero_zero_nat) @ (groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7581_sum_OlessThan__Suc__shift)). 185.47/93.68 thf(8024,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_nat @ (A @ zero_zero_nat) @ (groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 185.47/93.68 thf(4856,axiom,((! [A:complex]: ((re @ (csqrt @ A)) = (sqrt @ (divide_divide_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9632_csqrt_Osimps_I1_J)). 185.47/93.68 thf(23592,plain,((! [A:complex]: ((re @ (csqrt @ A)) = (sqrt @ (divide_divide_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (re @ A)) @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4856])). 185.47/93.68 thf(6373,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: (B != (plus_plus_nat @ A @ C)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_less__eqE)). 185.47/93.68 thf(29192,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ~ (B = (plus_plus_nat @ A @ C))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6373])). 185.47/93.68 thf(7518,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1150_right__diff__distrib)). 185.47/93.68 thf(33339,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7518])). 185.47/93.68 thf(4611,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (times_times_int @ B @ A) @ C) = (dvd_dvd_int @ B @ C)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4743_mult__unit__dvd__iff)). 185.47/93.68 thf(22764,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (times_times_int @ B @ A) @ C) = (dvd_dvd_int @ B @ C)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4611])). 185.47/93.68 thf(5836,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_771_comm__monoid__mult__class_Omult__1)). 185.47/93.68 thf(27306,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5836])). 185.47/93.68 thf(5697,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((binomial @ B @ A) = (binomial @ B @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8431_binomial__symmetric)). 185.47/93.68 thf(26688,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((binomial @ B @ A) = (binomial @ B @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5697])). 185.47/93.68 thf(7430,axiom,((! [A:rat,B:num,C:num,D:rat]: ((times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ (times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_power__add__numeral2)). 185.47/93.68 thf(33038,plain,((! [A:rat,B:num,C:num,D:rat]: ((times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ B)) @ (times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7430])). 185.47/93.68 thf(4204,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: (((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((times_times_complex @ (B @ D) @ (C @ D)) != one_one_complex))))) <= (finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((C @ D) != one_one_complex) & (member_nat @ D @ A)))))) <= (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((B @ D) != one_one_complex)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3533_prod_Ofinite__Collect__op)). 185.47/93.68 thf(21457,plain,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((times_times_complex @ (B @ D) @ (C @ D)) = one_one_complex))))) | ~ (finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((C @ D) = one_one_complex) & (member_nat @ D @ A))))) | ~ (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((B @ D) = one_one_complex)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4204])). 185.47/93.68 thf(1206,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (minus_minus_nat @ A @ B)) = (semiri1314217659103216013at_int @ (nat2 @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9297_int__minus)). 185.47/93.68 thf(11788,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (minus_minus_nat @ A @ B)) = (semiri1314217659103216013at_int @ (nat2 @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206])). 185.47/93.68 thf(5048,axiom,((vEBT_V8194947554948674370ptions @ summary @ pr)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75__092_060open_062both__member__options_Asummary_Apr_092_060close_062)). 185.47/93.68 thf(24325,plain,((vEBT_V8194947554948674370ptions @ summary @ pr)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5048])). 185.47/93.68 thf(1962,axiom,((! [A:rat]: ((plus_plus_rat @ zero_zero_rat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1538_add__0)). 185.47/93.68 thf(14297,plain,((! [A:rat]: ((plus_plus_rat @ zero_zero_rat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1962])). 185.47/93.68 thf(4680,axiom,((! [A:int,B:int,C:$o,D:$o]: ((((C = D) <= (ord_less_eq_int @ zero_zero_int @ B)) => (((ord_less_eq_int @ zero_zero_int @ A) => (C)) = ((ord_less_eq_int @ zero_zero_int @ B) => (D)))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3329_imp__le__cong)). 185.47/93.68 thf(22996,plain,((! [A:int,B:int,C:$o,D:$o]: ((((C = D) | ~ (ord_less_eq_int @ zero_zero_int @ B)) => (((ord_less_eq_int @ zero_zero_int @ A) => (C)) = ((ord_less_eq_int @ zero_zero_int @ B) => (D)))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4680])). 185.47/93.68 thf(2723,axiom,((! [A:num,B:int]: ((ord_less_rat @ (numeral_numeral_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7075_of__int__numeral__less__iff)). 185.47/93.68 thf(16791,plain,((! [A:num,B:int]: ((ord_less_rat @ (numeral_numeral_rat @ A) @ (ring_1_of_int_rat @ B)) = (ord_less_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2723])). 185.47/93.68 thf(3605,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2320_mult__neg__pos)). 185.47/93.68 thf(19574,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3605])). 185.47/93.68 thf(3891,axiom,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (sin_real @ A)) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7846_abs__sin__le__one)). 185.47/93.68 thf(20489,plain,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (sin_real @ A)) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3891])). 185.47/93.68 thf(3297,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (plus_plus_rat @ A @ B)) = (ord_less_rat @ zero_zero_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1647_less__add__same__cancel1)). 185.47/93.68 thf(18593,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (plus_plus_rat @ A @ B)) = (ord_less_rat @ zero_zero_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3297])). 185.47/93.68 thf(3618,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => (((divide_divide_rat @ B @ A) = C) = (B = (times_times_rat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2463_nonzero__divide__eq__eq)). 185.47/93.68 thf(19613,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => (((divide_divide_rat @ B @ A) = C) = (B = (times_times_rat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3618])). 185.47/93.68 thf(4720,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_is__num__normalize_I1_J)). 185.47/93.68 thf(23138,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ A @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4720])). 185.47/93.68 thf(4827,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((~ (finite_finite_nat @ B)) <= (~ (finite_finite_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3489_infinite__super)). 185.47/93.68 thf(23505,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (~ (finite_finite_nat @ B) | (finite_finite_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4827])). 185.47/93.68 thf(1102,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = one_one_complex) = ((A = B) & (B != zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1738_divide__eq__1__iff)). 185.47/93.68 thf(11475,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = one_one_complex) = ((A = B) & ~ (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102])). 185.47/93.68 thf(2209,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_5509_le__minus__iff)). 185.47/93.68 thf(15085,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)],[2209])). 185.47/93.68 thf(6283,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7232_of__nat__mono)). 185.47/93.68 thf(28874,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6283])). 185.47/93.68 thf(229,axiom,((! [A:real,B:real]: ((((arccos @ A) = (arccos @ B)) = (A = B)) <= ((ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) & (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8363_arccos__eq__iff)). 185.47/93.68 thf(8464,plain,((! [A:real,B:real]: ((((arccos @ A) = (arccos @ B)) = (A = B)) | ~ ((ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) & (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 185.47/93.68 thf(1988,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) @ zero_zero_real) = ((B = zero_zero_real) & (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2678_sum__squares__le__zero__iff)). 185.47/93.68 thf(14378,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) @ zero_zero_real) = ((B = zero_zero_real) & (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1988])). 185.47/93.68 thf(1116,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (minus_minus_rat @ A @ C) @ (minus_minus_rat @ B @ C)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_diff__strict__right__mono)). 185.47/93.68 thf(11518,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (minus_minus_rat @ A @ C) @ (minus_minus_rat @ B @ C)) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116])). 185.47/93.68 thf(3766,axiom,((! [A:int,B:int]: (((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ (divide_divide_int @ A @ B) @ one_one_int)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4489_unit__div)). 185.47/93.68 thf(20106,plain,((! [A:int,B:int]: (((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ (divide_divide_int @ A @ B) @ one_one_int)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3766])). 185.47/93.68 thf(4330,axiom,((! [A:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ A) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5150_neg__less__eq__nonneg)). 185.47/93.68 thf(21872,plain,((! [A:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ A) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4330])). 185.47/93.68 thf(3673,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ one_one_rat) = ((B = zero_zero_rat) | ((ord_less_eq_rat @ B @ A) & (ord_less_rat @ B @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2853_divide__le__eq__1)). 185.47/93.68 thf(19788,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ one_one_rat) = ((B = zero_zero_rat) | ((ord_less_eq_rat @ B @ A) & (ord_less_rat @ B @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ B) & (ord_less_eq_rat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3673])). 185.47/93.68 thf(719,axiom,((! [A:nat,B:int]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7176_of__nat__less__of__int__iff)). 185.47/93.68 thf(10129,plain,((! [A:nat,B:int]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[719])). 185.47/93.68 thf(7061,axiom,((! [A:rat,B:nat,C:rat]: (((power_power_rat @ A @ B) = (power_power_rat @ C @ B)) => ((ord_less_eq_rat @ zero_zero_rat @ A) => (((A = C) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_eq_rat @ zero_zero_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2143_power__eq__imp__eq__base)). 185.47/93.68 thf(31779,plain,((! [A:rat,B:nat,C:rat]: (((power_power_rat @ A @ B) = (power_power_rat @ C @ B)) => ((ord_less_eq_rat @ zero_zero_rat @ A) => ((A = C) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_rat @ zero_zero_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7061])). 185.47/93.68 thf(4708,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (minus_minus_real @ B @ C)) = (ord_less_real @ (plus_plus_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_798_less__diff__eq)). 185.47/93.68 thf(23101,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (minus_minus_real @ B @ C)) = (ord_less_real @ (plus_plus_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4708])). 185.47/93.68 thf(2678,axiom,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((((! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ D @ zero_zero_nat @ E @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ zero_zero_nat @ E @ F) @ B))) <= (C = (vEBT_Node @ D @ zero_zero_nat @ E @ F))))) => ((! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)) => ((C = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F) @ B)))))) => ((~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B))) <= (C = (if_VEBT_VEBT @ ((ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ~ ((B = E) | (B = D))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (ord_less_nat @ B @ D) @ B @ D) @ (ord_max_nat @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ H @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ H)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H))))) <= (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F) @ B))) <= (C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ (suc @ (suc @ D)) @ E @ F)))))))) <= (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B))) <= (((((C = (vEBT_Leaf @ D @ ($true))) <= (B = one_one_nat)) & ((C = (vEBT_Leaf @ D @ E)) <= (B != one_one_nat))) <= (B != zero_zero_nat)) & ((C = (vEBT_Leaf @ ($true) @ E)) <= (B = zero_zero_nat))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ A @ B))) <= ((vEBT_vebt_insert @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3791_vebt__insert_Opelims)). 185.47/93.68 thf(16607,plain,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ D @ zero_zero_nat @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ zero_zero_nat @ E @ F) @ B)) | ~ (C = (vEBT_Node @ D @ zero_zero_nat @ E @ F))))) => ((! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)) => ((C = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F) @ B)))))) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B)) | ~ (C = (if_VEBT_VEBT @ ((ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ~ ((B = E) | (B = D))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (ord_less_nat @ B @ D) @ B @ D) @ (ord_max_nat @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_insert @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_insert @ H @ (vEBT_VEBT_high @ (if_nat @ (ord_less_nat @ B @ D) @ D @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ H)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))) | ~ (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F) @ B)) | ~ (C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ (suc @ (suc @ D)) @ E @ F)))))))) | ~ (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)) | ~ (((((C = (vEBT_Leaf @ D @ ($true))) | ~ (B = one_one_nat)) & ((C = (vEBT_Leaf @ D @ E)) | (B = one_one_nat))) | (B = zero_zero_nat)) & ((C = (vEBT_Leaf @ ($true) @ E)) | ~ (B = zero_zero_nat)))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ A @ B)) | ~ ((vEBT_vebt_insert @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2678])). 185.47/93.68 thf(7317,axiom,((! [A:num,B:num]: (((A = B) <= (ord_less_eq_num @ B @ A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3867_order__antisym)). 185.47/93.68 thf(32659,plain,((! [A:num,B:num]: ((A = B) | ~ (ord_less_eq_num @ B @ A) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7317])). 185.47/93.68 thf(1441,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ C @ zero_zero_rat) => ((ord_less_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ C @ B)) <= (ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B)))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2714_divide__strict__left__mono__neg)). 185.47/93.68 thf(12540,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ C @ zero_zero_rat) => ((ord_less_rat @ (divide_divide_rat @ C @ A) @ (divide_divide_rat @ C @ B)) | ~ (ord_less_rat @ zero_zero_rat @ (times_times_rat @ A @ B)))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1441])). 185.47/93.68 thf(9,axiom,((! [A:(nat > nat),B:(nat > nat),C:nat]: (((minus_minus_nat @ (groups3542108847815614940at_nat @ B @ (set_ord_lessThan_nat @ C)) @ (groups3542108847815614940at_nat @ A @ (set_ord_lessThan_nat @ C))) = (groups3542108847815614940at_nat @ (^ [D:nat]: (minus_minus_nat @ (B @ D) @ (A @ D))) @ (set_ord_lessThan_nat @ C))) <= (! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7578_sum__diff__distrib)). 185.47/93.68 thf(7752,plain,((! [A:(nat > nat),B:(nat > nat),C:nat]: (((minus_minus_nat @ (groups3542108847815614940at_nat @ (B) @ (set_ord_lessThan_nat @ C)) @ (groups3542108847815614940at_nat @ (A) @ (set_ord_lessThan_nat @ C))) = (groups3542108847815614940at_nat @ (^ [D:nat]: (minus_minus_nat @ (B @ D) @ (A @ D))) @ (set_ord_lessThan_nat @ C))) | ~ (! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[9])). 185.47/93.68 thf(5682,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ (times_times_nat @ A @ C)) @ A) = (plus_plus_nat @ C @ (divide_divide_nat @ B @ A))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1836_div__mult__self2)). 185.47/93.68 thf(26641,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ (times_times_nat @ A @ C)) @ A) = (plus_plus_nat @ C @ (divide_divide_nat @ B @ A))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5682])). 185.47/93.68 thf(1476,axiom,((! [A:real,B:nat]: ((times_times_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ (comm_s7457072308508201937r_real @ (uminus_uminus_real @ A) @ B)) = (times_times_real @ A @ (comm_s7457072308508201937r_real @ (plus_plus_real @ (uminus_uminus_real @ A) @ one_one_real) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8571_pochhammer__absorb__comp)). 185.47/93.68 thf(12647,plain,((! [A:real,B:nat]: ((times_times_real @ (minus_minus_real @ A @ (semiri5074537144036343181t_real @ B)) @ (comm_s7457072308508201937r_real @ (uminus_uminus_real @ A) @ B)) = (times_times_real @ A @ (comm_s7457072308508201937r_real @ (plus_plus_real @ (uminus_uminus_real @ A) @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1476])). 185.47/93.68 thf(4749,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ C @ A) @ (plus_plus_rat @ C @ B)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_add__left__mono)). 185.47/93.68 thf(23225,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ C @ A) @ (plus_plus_rat @ C @ B)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4749])). 185.47/93.68 thf(4046,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = ((dvd_dvd_int @ B @ C) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4456_dvd__mult__cancel__left)). 185.47/93.68 thf(20974,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = ((dvd_dvd_int @ B @ C) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4046])). 185.47/93.68 thf(7570,axiom,((! [A:complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex) = (A = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1871_zero__eq__power2)). 185.47/93.68 thf(33489,plain,((! [A:complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex) = (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7570])). 185.47/93.68 thf(2445,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => ((dvd_dvd_Code_integer @ B @ one_one_Code_integer) => (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ one_one_Code_integer))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4468_unit__prod)). 185.47/93.68 thf(15828,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => ((dvd_dvd_Code_integer @ B @ one_one_Code_integer) => (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2445])). 185.47/93.68 thf(5244,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((A = zero_zero_nat) | ? [C:nat]: ((ord_less_nat @ C @ B) & (A = (suc @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2495_less__Suc__eq__0__disj)). 185.47/93.68 thf(25023,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((A = zero_zero_nat) | ? [C:nat]: ((ord_less_nat @ C @ B) & (A = (suc @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5244])). 185.47/93.68 thf(7664,axiom,((! [A:complex,B:complex]: ((power_power_complex @ (minus_minus_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_complex @ (minus_minus_complex @ B @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_891_power2__commute)). 185.47/93.68 thf(33748,plain,((! [A:complex,B:complex]: ((power_power_complex @ (minus_minus_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_complex @ (minus_minus_complex @ B @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7664])). 185.47/93.68 thf(2639,axiom,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_less_real @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F))))) <= (ord_less_eq_real @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4321_order__le__less__subst1)). 185.47/93.68 thf(16485,plain,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))))) | ~ (ord_less_eq_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2639])). 185.47/93.68 thf(3438,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => ((divide_divide_rat @ (times_times_rat @ B @ A) @ (times_times_rat @ A @ C)) = (divide_divide_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1698_nonzero__mult__divide__mult__cancel__right2)). 185.47/93.68 thf(19046,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => ((divide_divide_rat @ (times_times_rat @ B @ A) @ (times_times_rat @ A @ C)) = (divide_divide_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3438])). 185.47/93.68 thf(3888,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_3888_dual__order_Oeq__iff)). 185.47/93.68 thf(20483,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)],[3888])). 185.47/93.68 thf(6980,axiom,((! [A:complex]: ((times_times_complex @ A @ (numera6690914467698888265omplex @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_mult__numeral__1__right)). 185.47/93.68 thf(31486,plain,((! [A:complex]: ((times_times_complex @ A @ (numera6690914467698888265omplex @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6980])). 185.47/93.68 thf(4623,axiom,((! [A:nat,B:nat,C:real]: ((((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = zero_zero_real) <= (ord_less_nat @ A @ B)) & ((~ (ord_less_nat @ A @ B)) => (((C = one_one_real) => ((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (semiri5074537144036343181t_real @ (minus_minus_nat @ (plus_plus_nat @ A @ one_one_nat) @ B)))) & (((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (divide_divide_real @ (minus_minus_real @ (power_power_real @ C @ B) @ (power_power_real @ C @ (suc @ A))) @ (minus_minus_real @ one_one_real @ C))) <= (C != one_one_real))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6847_sum__gp)). 185.47/93.68 thf(22804,plain,((! [A:nat,B:nat,C:real]: ((((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = zero_zero_real) | ~ (ord_less_nat @ A @ B)) & ((~ (ord_less_nat @ A @ B)) => (((C = one_one_real) => ((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (semiri5074537144036343181t_real @ (minus_minus_nat @ (plus_plus_nat @ A @ one_one_nat) @ B)))) & (((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (divide_divide_real @ (minus_minus_real @ (power_power_real @ C @ B) @ (power_power_real @ C @ (suc @ A))) @ (minus_minus_real @ one_one_real @ C))) | (C = one_one_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4623])). 185.47/93.68 thf(2699,axiom,((! [A:complex,B:complex,C:complex]: (((((divide1717551699836669952omplex @ B @ A) = (divide1717551699836669952omplex @ C @ A)) = (B = C)) <= (dvd_dvd_complex @ A @ C)) <= (dvd_dvd_complex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4663_dvd__div__eq__iff)). 185.47/93.68 thf(16714,plain,((! [A:complex,B:complex,C:complex]: ((((divide1717551699836669952omplex @ B @ A) = (divide1717551699836669952omplex @ C @ A)) = (B = C)) | ~ (dvd_dvd_complex @ A @ C) | ~ (dvd_dvd_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2699])). 185.47/93.68 thf(181,axiom,((! [A:nat,B:nat]: (((semiri1408675320244567234ct_nat @ B) = (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (groups708209901874060359at_nat @ (^ [C:nat]: (C)) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8945_fact__eq__fact__times)). 185.47/93.68 thf(8316,plain,((! [A:nat,B:nat]: (((semiri1408675320244567234ct_nat @ B) = (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (groups708209901874060359at_nat @ (^ [C:nat]: (C)) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 185.47/93.68 thf(1866,axiom,((! [A:rat]: ((plus_plus_rat @ zero_zero_rat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2078_comm__monoid__add__class_Oadd__0)). 185.47/93.68 thf(13983,plain,((! [A:rat]: ((plus_plus_rat @ zero_zero_rat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1866])). 185.47/93.68 thf(1502,axiom,((! [A:num]: ((plus_plus_num @ (bitM @ A) @ one) = (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8967_BitM__plus__one)). 185.47/93.68 thf(12726,plain,((! [A:num]: ((plus_plus_num @ (bitM @ A) @ one) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502])). 185.47/93.68 thf(1432,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7223_of__nat__less__imp__less)). 185.47/93.68 thf(12512,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432])). 185.47/93.68 thf(6652,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4880_nat__mult__dvd__cancel1)). 185.47/93.68 thf(30174,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6652])). 185.47/93.68 thf(710,axiom,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) => ((suminf_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) = (plus_plus_real @ (A @ zero_zero_nat) @ (times_times_real @ (suminf_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C)))) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7743_powser__split__head_I1_J)). 185.47/93.68 thf(10097,plain,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) => ((suminf_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) = (plus_plus_real @ (A @ zero_zero_nat) @ (times_times_real @ (suminf_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C)))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[710])). 185.47/93.68 thf(223,axiom,((! [A:(nat > real)]: (((ord_less_real @ zero_zero_real @ (suminf_real @ A)) <= (! [B:nat]: (ord_less_real @ zero_zero_real @ (A @ B)))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7692_suminf__pos)). 185.47/93.68 thf(8448,plain,((! [A:(nat > real)]: ((ord_less_real @ zero_zero_real @ (suminf_real @ (A))) | ~ (! [B:nat]: (ord_less_real @ zero_zero_real @ (A @ B))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 185.47/93.68 thf(2232,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ B) = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8509_pochhammer__of__nat__eq__0__lemma)). 185.47/93.68 thf(15149,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2232])). 185.47/93.68 thf(1413,axiom,((! [A:int,B:int,C:(int > $o)]: ((ord_less_int @ A @ B) => ((C @ (plus_plus_int @ A @ one_one_int)) => ((C @ B) <= (! [D:int]: (((C @ (plus_plus_int @ D @ one_one_int)) <= (C @ D)) <= (ord_less_int @ A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3178_int__gr__induct)). 185.47/93.68 thf(12439,plain,((! [A:int,B:int,C:(int > $o)]: ((ord_less_int @ A @ B) => ((C @ (plus_plus_int @ A @ one_one_int)) => ((C @ B) | ~ (! [D:int]: ((C @ (plus_plus_int @ D @ one_one_int)) | ~ (C @ D) | ~ (ord_less_int @ A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413])). 185.47/93.68 thf(4033,axiom,((! [A:real]: (((abs_abs_real @ A) = (uminus_uminus_real @ A)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6576_abs__of__neg)). 185.47/93.68 thf(20938,plain,((! [A:real]: (((abs_abs_real @ A) = (uminus_uminus_real @ A)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4033])). 185.47/93.68 thf(7675,axiom,((! [A:num]: ~ (ord_less_eq_num @ (bit0 @ A) @ one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_semiring__norm_I69_J)). 185.47/93.68 thf(33774,plain,((! [A:num]: ~ (ord_less_eq_num @ (bit0 @ A) @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7675])). 185.47/93.68 thf(7143,axiom,((! [A:num]: (zero_zero_real != (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5697_zero__neq__neg__numeral)). 185.47/93.68 thf(32044,plain,((! [A:num]: ~ (zero_zero_real = (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7143])). 185.47/93.68 thf(6227,axiom,((! [A:code_integer,B:nat]: ((abs_abs_Code_integer @ (power_8256067586552552935nteger @ A @ B)) = (power_8256067586552552935nteger @ (abs_abs_Code_integer @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6469_power__abs)). 185.47/93.68 thf(28683,plain,((! [A:code_integer,B:nat]: ((abs_abs_Code_integer @ (power_8256067586552552935nteger @ A @ B)) = (power_8256067586552552935nteger @ (abs_abs_Code_integer @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6227])). 185.47/93.68 thf(6573,axiom,(((neg_numeral_dbl_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3807_dbl__simps_I3_J)). 185.47/93.68 thf(29919,plain,(((neg_numeral_dbl_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6573])). 185.47/93.68 thf(7469,axiom,((! [A:real,B:num]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ zero_zero_real) = ((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ B)) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_eq_real @ A @ zero_zero_real)) | ((A = zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4566_power__le__zero__eq__numeral)). 185.47/93.68 thf(33175,plain,((! [A:real,B:num]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ zero_zero_real) = ((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ B)) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_eq_real @ A @ zero_zero_real)) | ((A = zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7469])). 185.47/93.68 thf(4518,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ B @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9381_and__less__eq)). 185.47/93.68 thf(22475,plain,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ B @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4518])). 185.47/93.68 thf(3198,axiom,((! [A:real,B:nat]: (((power_power_real @ A @ B) = one_one_real) => (((real_V7735802525324610683m_real @ A) = one_one_real) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7512_power__eq__1__iff)). 185.47/93.68 thf(18295,plain,((! [A:real,B:nat]: (((power_power_real @ A @ B) = one_one_real) => (((real_V7735802525324610683m_real @ A) = one_one_real) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3198])). 185.47/93.68 thf(1471,axiom,((! [A:real,B:real,C:nat]: ((dvd_dvd_real @ A @ B) => (dvd_dvd_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4679_dvd__power__same)). 185.47/93.68 thf(12630,plain,((! [A:real,B:real,C:nat]: ((dvd_dvd_real @ A @ B) => (dvd_dvd_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471])). 185.47/93.68 thf(4008,axiom,((bit_se1412395901928357646or_nat = (^ [A:nat,B:nat]: (nat2 @ (bit_se1409905431419307370or_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9470_or__nat__def)). 185.47/93.68 thf(20863,plain,(((bit_se1412395901928357646or_nat) = (^ [A:nat,B:nat]: (nat2 @ (bit_se1409905431419307370or_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4008])). 185.47/93.68 thf(4219,axiom,((! [A:int]: ((ord_less_eq_int @ A @ (uminus_uminus_int @ A)) = (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5146_less__eq__neg__nonpos)). 185.47/93.68 thf(21505,plain,((! [A:int]: ((ord_less_eq_int @ A @ (uminus_uminus_int @ A)) = (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4219])). 185.47/93.68 thf(1879,axiom,((! [A:int]: ((ord_less_int @ (plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3174_odd__less__0__iff)). 185.47/93.68 thf(14022,plain,((! [A:int]: ((ord_less_int @ (plus_plus_int @ (plus_plus_int @ one_one_int @ A) @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1879])). 185.47/93.68 thf(3757,axiom,((dvd_dvd_rat = (^ [A:rat,B:rat]: ((B = zero_zero_rat) <= (A = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4574_dvd__field__iff)). 185.47/93.68 thf(20062,plain,(((dvd_dvd_rat) = (^ [A:rat,B:rat]: ((B = zero_zero_rat) | ~ (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3757])). 185.47/93.68 thf(1360,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => (? [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ B @ (minus_minus_real @ A @ one_one_real)) & ((exp_real @ B) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8206_lemma__exp__total)). 185.47/93.68 thf(12262,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => (? [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ B @ (minus_minus_real @ A @ one_one_real)) & ((exp_real @ B) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360])). 185.47/93.68 thf(7272,axiom,(((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5412_diff__numeral__special_I10_J)). 185.47/93.68 thf(32502,plain,(((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7272])). 185.47/93.68 thf(4819,axiom,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ C)) @ (real_V7735802525324610683m_real @ (minus_minus_real @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7514_norm__diff__triangle__ineq)). 185.47/93.68 thf(23478,plain,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D))) @ (plus_plus_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ C)) @ (real_V7735802525324610683m_real @ (minus_minus_real @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4819])). 185.47/93.68 thf(755,axiom,((! [A:complex]: ((re @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (minus_minus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9693_Re__power2)). 185.47/93.68 thf(10260,plain,((! [A:complex]: ((re @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (minus_minus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[755])). 185.47/93.68 thf(1746,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ A) @ (collect_nat @ B)) <= (! [C:nat]: ((B @ C) <= (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1411_Collect__mono)). 185.47/93.68 thf(13585,plain,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) | ~ (! [C:nat]: ((B @ C) | ~ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746])). 185.47/93.68 thf(1706,axiom,(((abs_abs_rat @ (uminus_uminus_rat @ one_one_rat)) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6381_abs__neg__one)). 185.47/93.68 thf(13446,plain,(((abs_abs_rat @ (uminus_uminus_rat @ one_one_rat)) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706])). 185.47/93.68 thf(2637,axiom,((! [A:int]: (((ord_less_eq_int @ zero_zero_int @ A) => ((semiri1314217659103216013at_int @ (nat2 @ A)) = A)) & (((semiri1314217659103216013at_int @ (nat2 @ A)) = zero_zero_int) <= (~ (ord_less_eq_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9253_int__nat__eq)). 185.47/93.68 thf(16475,plain,((! [A:int]: (((ord_less_eq_int @ zero_zero_int @ A) => ((semiri1314217659103216013at_int @ (nat2 @ A)) = A)) & (((semiri1314217659103216013at_int @ (nat2 @ A)) = zero_zero_int) | (ord_less_eq_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2637])). 185.47/93.68 thf(2692,axiom,((! [A:rat,B:rat]: ((A != zero_zero_rat) => ((uminus_uminus_rat @ (divide_divide_rat @ B @ A)) = (divide_divide_rat @ B @ (uminus_uminus_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5766_nonzero__minus__divide__right)). 185.47/93.68 thf(16692,plain,((! [A:rat,B:rat]: ((~ (A = zero_zero_rat)) => ((uminus_uminus_rat @ (divide_divide_rat @ B @ A)) = (divide_divide_rat @ B @ (uminus_uminus_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2692])). 185.47/93.68 thf(4859,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4118_order__less__not__sym)). 185.47/93.68 thf(23602,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4859])). 185.47/93.68 thf(3868,axiom,((neg_nu3179335615603231917ec_rat = (^ [A:rat]: (minus_minus_rat @ (plus_plus_rat @ A @ A) @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6835_dbl__dec__def)). 185.47/93.68 thf(20421,plain,(((neg_nu3179335615603231917ec_rat) = (^ [A:rat]: (minus_minus_rat @ (plus_plus_rat @ A @ A) @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3868])). 185.47/93.68 thf(5164,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ (suc @ zero_zero_nat)) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9398_and__Suc__0__eq)). 185.47/93.68 thf(24765,plain,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ (suc @ zero_zero_nat)) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5164])). 185.47/93.68 thf(2857,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ B @ C)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4604_dvd__mult2)). 185.47/93.68 thf(17215,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ B @ C)) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2857])). 185.47/93.68 thf(2741,axiom,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ (plus_plus_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ B) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8589_pochhammer__minus_H)). 185.47/93.68 thf(16846,plain,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ (plus_plus_rat @ (minus_minus_rat @ A @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ B) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2741])). 185.47/93.68 thf(2972,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ A)) = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A))) <= (dvd_dvd_complex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5809_dvd__div__neg)). 185.47/93.68 thf(17584,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ A)) = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A))) | ~ (dvd_dvd_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2972])). 185.47/93.68 thf(1106,axiom,((! [A:num,B:(rat > num),C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => ((ord_less_num @ A @ (B @ D)) <= (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))))) <= (ord_less_num @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4343_order__less__le__subst1)). 185.47/93.68 thf(11486,plain,((! [A:num,B:(rat > num),C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => ((ord_less_num @ A @ (B @ D)) | ~ (! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))))) | ~ (ord_less_num @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106])). 185.47/93.68 thf(2597,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ C @ D) => ((ord_less_rat @ zero_zero_rat @ B) => ((ord_less_eq_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2580_mult__strict__mono)). 185.47/93.68 thf(16354,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ C @ D) => ((ord_less_rat @ zero_zero_rat @ B) => ((ord_less_eq_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2597])). 185.47/93.68 thf(4578,axiom,((! [A:nat,B:num]: ((ord_less_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (ord_less_nat @ A @ (pred_numeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6785_less__Suc__numeral)). 185.47/93.68 thf(22665,plain,((! [A:nat,B:num]: ((ord_less_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (ord_less_nat @ A @ (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4578])). 185.47/93.68 thf(5798,axiom,(((semiri773545260158071498ct_rat @ one_one_nat) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7959_fact__1)). 185.47/93.68 thf(27093,plain,(((semiri773545260158071498ct_rat @ one_one_nat) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5798])). 185.47/93.68 thf(7249,axiom,((! [A:nat]: (((root @ A @ one_one_real) = one_one_real) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9165_real__root__one)). 185.47/93.68 thf(32429,plain,((! [A:nat]: (((root @ A @ one_one_real) = one_one_real) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7249])). 185.47/93.68 thf(6477,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))) <= (ord_less_eq_nat @ B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2281_add__nonpos__eq__0__iff)). 185.47/93.68 thf(29581,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))) | ~ (ord_less_eq_nat @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6477])). 185.47/93.68 thf(3596,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (minus_minus_int @ B @ C)) = (dvd_dvd_int @ A @ (minus_minus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4657_dvd__diff__commute)). 185.47/93.68 thf(19549,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (minus_minus_int @ B @ C)) = (dvd_dvd_int @ A @ (minus_minus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3596])). 185.47/93.68 thf(3207,axiom,((! [A:int,B:(rat > int),C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))) => (ord_less_eq_int @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3941_ord__eq__le__subst)). 185.47/93.68 thf(18327,plain,((! [A:int,B:(rat > int),C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))) => (ord_less_eq_int @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3207])). 185.47/93.68 thf(4235,axiom,((! [A:nat]: ~ (member_nat @ A @ bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1388_emptyE)). 185.47/93.68 thf(21552,plain,((! [A:nat]: ~ (member_nat @ A @ bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4235])). 185.47/93.68 thf(529,axiom,((! [A:int,B:int,C:nat]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (ring_1_of_int_int @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7108_of__int__power__less__of__int__cancel__iff)). 185.47/93.68 thf(9500,plain,((! [A:int,B:int,C:nat]: ((ord_less_int @ (ring_1_of_int_int @ A) @ (power_power_int @ (ring_1_of_int_int @ B) @ C)) = (ord_less_int @ A @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[529])). 185.47/93.68 thf(6748,axiom,((! [A:product_prod_nat_nat]: ~ (! [B:nat,C:nat]: (A != (product_Pair_nat_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4148_prod__decode__aux_Ocases)). 185.47/93.68 thf(30550,plain,((! [A:product_prod_nat_nat]: ~ (! [B:nat,C:nat]: ~ (A = (product_Pair_nat_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6748])). 185.47/93.68 thf(2474,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real) <= (ord_less_eq_real @ B @ zero_zero_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2416_divide__nonneg__nonpos)). 185.47/93.68 thf(15925,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real) | ~ (ord_less_eq_real @ B @ zero_zero_real) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2474])). 185.47/93.68 thf(5387,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9455_xor__nat__numerals_I4_J)). 185.47/93.68 thf(25558,plain,((! [A:num]: ((bit_se6528837805403552850or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5387])). 185.47/93.68 thf(427,axiom,((! [A:set_nat,B:(nat > int)]: (((groups705719431365010083at_int @ B @ A) = one_one_int) <= (! [C:nat]: ((member_nat @ C @ A) => ((B @ C) = one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8710_prod_Oneutral)). 185.47/93.68 thf(9151,plain,((! [A:set_nat,B:(nat > int)]: (((groups705719431365010083at_int @ (B) @ A) = one_one_int) | ~ (! [C:nat]: ((member_nat @ C @ A) => ((B @ C) = one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])). 185.47/93.68 thf(6398,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: ((ord_less_nat @ A @ C) => (B != (suc @ C))))) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1024_Suc__lessE)). 185.47/93.68 thf(29273,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (~ (B = (suc @ C))))) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6398])). 185.47/93.68 thf(7494,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2200_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 185.47/93.68 thf(33267,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7494])). 185.47/93.68 thf(7164,axiom,((! [A:nat,B:int]: (((ord_less_eq_int @ zero_zero_int @ (power_power_int @ B @ A)) = (ord_less_eq_int @ zero_zero_int @ B)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4973_zero__le__odd__power)). 185.47/93.68 thf(32136,plain,((! [A:nat,B:int]: (((ord_less_eq_int @ zero_zero_int @ (power_power_int @ B @ A)) = (ord_less_eq_int @ zero_zero_int @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7164])). 185.47/93.68 thf(5065,axiom,((! [A:int]: ((minus_minus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1550_diff__zero)). 185.47/93.68 thf(24389,plain,((! [A:int]: ((minus_minus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5065])). 185.47/93.68 thf(4704,axiom,((! [A:complex,B:complex]: ((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (divide1717551699836669952omplex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5586_minus__divide__divide)). 185.47/93.68 thf(23083,plain,((! [A:complex,B:complex]: ((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (divide1717551699836669952omplex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4704])). 185.47/93.68 thf(3100,axiom,((! [A:num,B:num,C:(num > rat),D:rat]: ((ord_less_eq_num @ A @ B) => (((ord_less_rat @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_rat @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_less_rat @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4337_order__le__less__subst2)). 185.47/93.68 thf(17992,plain,((! [A:num,B:num,C:(num > rat),D:rat]: ((ord_less_eq_num @ A @ B) => ((ord_less_rat @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_less_rat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3100])). 185.47/93.68 thf(5609,axiom,((! [A:nat,B:nat,C:nat]: (((vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ A) @ B) = A) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_low__inv)). 185.47/93.68 thf(26395,plain,((! [A:nat,B:nat,C:nat]: (((vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ A) @ B) = A) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5609])). 185.47/93.68 thf(6051,axiom,((! [A:nat]: (ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1316708129612266289at_nat @ (power_power_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8026_fact__le__power)). 185.47/93.68 thf(28043,plain,((! [A:nat]: (ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1316708129612266289at_nat @ (power_power_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6051])). 185.47/93.68 thf(6327,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2129_mult__0)). 185.47/93.68 thf(29023,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6327])). 185.47/93.68 thf(5706,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) <= (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2517_nat__power__less__imp__less)). 185.47/93.68 thf(26713,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) | ~ (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5706])). 185.47/93.68 thf(639,axiom,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit1 @ one))))) = (divide_divide_real @ (sqrt @ (numeral_numeral_real @ (bit1 @ one))) @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8246_cos__30)). 185.47/93.68 thf(9851,plain,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit1 @ one))))) = (divide_divide_real @ (sqrt @ (numeral_numeral_real @ (bit1 @ one))) @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[639])). 185.47/93.68 thf(2799,axiom,((! [A:real,B:real,C:(real > int),D:int]: ((((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_int @ (C @ E) @ (C @ F)))) => (ord_less_int @ (C @ A) @ D)) <= (ord_less_int @ (C @ B) @ D)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4112_order__less__subst2)). 185.47/93.68 thf(17027,plain,((! [A:real,B:real,C:(real > int),D:int]: (((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_int @ (C @ E) @ (C @ F)))) => (ord_less_int @ (C @ A) @ D)) | ~ (ord_less_int @ (C @ B) @ D) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2799])). 185.47/93.68 thf(5624,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ B) => (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (A = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1894_power2__eq__iff__nonneg)). 185.47/93.68 thf(26450,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ B) => (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (A = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5624])). 185.47/93.68 thf(5834,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ B @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4745_dvd__mult__unit__iff)). 185.47/93.68 thf(27299,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ B @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5834])). 185.47/93.68 thf(3632,axiom,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ B) = zero_zero_rat) = (B = (uminus_uminus_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5726_add__eq__0__iff)). 185.47/93.68 thf(19656,plain,((! [A:rat,B:rat]: (((plus_plus_rat @ A @ B) = zero_zero_rat) = (B = (uminus_uminus_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3632])). 185.47/93.68 thf(1585,axiom,((! [A:int]: ((~ (! [B:nat]: (A != (semiri1314217659103216013at_int @ B)))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7243_nonneg__int__cases)). 185.47/93.68 thf(12980,plain,((! [A:int]: (~ (! [B:nat]: ~ (A = (semiri1314217659103216013at_int @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585])). 185.47/93.68 thf(967,axiom,((! [A:complex]: (((ord_less_eq_real @ zero_zero_real @ (re @ A)) => ((csqrt @ A) = (real_V4546457046886955230omplex @ (sqrt @ (re @ A))))) <= ((im @ A) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9667_csqrt__of__real__nonneg)). 185.47/93.68 thf(11054,plain,((! [A:complex]: (((ord_less_eq_real @ zero_zero_real @ (re @ A)) => ((csqrt @ A) = (real_V4546457046886955230omplex @ (sqrt @ (re @ A))))) | ~ ((im @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[967])). 185.47/93.68 thf(2836,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ C) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2299_add__decreasing2)). 185.47/93.68 thf(17148,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ C) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2836])). 185.47/93.68 thf(5277,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (B = (plus_plus_nat @ A @ C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_le__Suc__ex)). 185.47/93.68 thf(25178,plain,((! [A:nat,B:nat]: (? [C:nat]: (B = (plus_plus_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5277])). 185.47/93.68 thf(5293,axiom,((! [A:real]: ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (minus_minus_real @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7861_cos__double)). 185.47/93.68 thf(25230,plain,((! [A:real]: ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (minus_minus_real @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5293])). 185.47/93.68 thf(1751,axiom,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ A) => (~ (! [B:nat]: ~ (ord_less_rat @ (divide_divide_rat @ one_one_rat @ (semiri681578069525770553at_rat @ (suc @ B))) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7365_nat__approx__posE)). 185.47/93.68 thf(13605,plain,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ A) => (~ (! [B:nat]: ~ (ord_less_rat @ (divide_divide_rat @ one_one_rat @ (semiri681578069525770553at_rat @ (suc @ B))) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751])). 185.47/93.68 thf(5666,axiom,((! [A:num,B:num]: (((numera6690914467698888265omplex @ A) = (numera6690914467698888265omplex @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_numeral__eq__iff)). 185.47/93.68 thf(26593,plain,((! [A:num,B:num]: (((numera6690914467698888265omplex @ A) = (numera6690914467698888265omplex @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5666])). 185.47/93.68 thf(480,axiom,((! [A:real]: (ord_less_eq_real @ A @ (plus_plus_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9113_real__of__int__floor__add__one__ge)). 185.47/93.68 thf(9353,plain,((! [A:real]: (ord_less_eq_real @ A @ (plus_plus_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[480])). 185.47/93.68 thf(1788,axiom,((! [A:real,B:real]: (((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) <= (ord_less_real @ B @ zero_zero_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2431_divide__pos__neg)). 185.47/93.68 thf(13724,plain,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) | ~ (ord_less_real @ B @ zero_zero_real) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1788])). 185.47/93.68 thf(3423,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4584_dvd__mult__right)). 185.47/93.68 thf(19001,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3423])). 185.47/93.68 thf(5518,axiom,((! [A:num,B:num,C:(num > num),D:num]: ((((! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3953_ord__le__eq__subst)). 185.47/93.68 thf(26103,plain,((! [A:num,B:num,C:(num > num),D:num]: (((! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5518])). 185.47/93.68 thf(1237,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ (^ [B:nat]: (if_rat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri681578069525770553at_rat @ (binomial @ A @ B)) @ zero_zero_rat)) @ (set_ord_atMost_nat @ A))) = (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8623_choose__even__sum)). 185.47/93.68 thf(11882,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ (^ [B:nat]: (if_rat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri681578069525770553at_rat @ (binomial @ A @ B)) @ zero_zero_rat)) @ (set_ord_atMost_nat @ A))) = (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237])). 185.47/93.68 thf(6511,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5474_neg__one__odd__power)). 185.47/93.68 thf(29705,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6511])). 185.47/93.68 thf(2849,axiom,((! [A:rat]: (((divide_divide_rat @ A @ A) = one_one_rat) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1718_div__self)). 185.47/93.68 thf(17188,plain,((! [A:rat]: (((divide_divide_rat @ A @ A) = one_one_rat) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2849])). 185.47/93.68 thf(484,axiom,((! [A:rat,B:nat]: ((gbinomial_rat @ (plus_plus_rat @ A @ one_one_rat) @ (suc @ B)) = (plus_plus_rat @ (gbinomial_rat @ A @ B) @ (gbinomial_rat @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8462_gbinomial__Suc__Suc)). 185.47/93.68 thf(9363,plain,((! [A:rat,B:nat]: ((gbinomial_rat @ (plus_plus_rat @ A @ one_one_rat) @ (suc @ B)) = (plus_plus_rat @ (gbinomial_rat @ A @ B) @ (gbinomial_rat @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])). 185.47/93.68 thf(3617,axiom,((! [A:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ A) = (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5149_neg__less__eq__nonneg)). 185.47/93.68 thf(19610,plain,((! [A:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ A) = (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3617])). 185.47/93.68 thf(2463,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5557_is__num__normalize_I8_J)). 185.47/93.68 thf(15890,plain,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2463])). 185.47/93.68 thf(4133,axiom,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5208_uminus__add__conv__diff)). 185.47/93.68 thf(21240,plain,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4133])). 185.47/93.68 thf(6543,axiom,((! [A:num,B:num]: ((pow @ A @ (bit0 @ B)) = (sqr @ (pow @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9850_pow_Osimps_I2_J)). 185.47/93.68 thf(29818,plain,((! [A:num,B:num]: ((pow @ A @ (bit0 @ B)) = (sqr @ (pow @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6543])). 185.47/93.68 thf(6894,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((times_times_nat @ B @ (divide_divide_nat @ C @ A)) = (divide_divide_nat @ (times_times_nat @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4868_unit__div__mult__swap)). 185.47/93.68 thf(31113,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((times_times_nat @ B @ (divide_divide_nat @ C @ A)) = (divide_divide_nat @ (times_times_nat @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6894])). 185.47/93.68 thf(728,axiom,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo3111899725591712190t_real @ (^ [D:nat]: (plus_plus_real @ (A @ D))) @ B @ C @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8324_sum__atLeastAtMost__code)). 185.47/93.68 thf(10160,plain,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo3111899725591712190t_real @ (^ [D:nat]: (plus_plus_real @ (A @ D))) @ B @ C @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[728])). 185.47/93.68 thf(951,axiom,((bit_ri631733984087533419it_int = (^ [A:nat,B:int]: (bit_concat_bit @ A @ B @ (uminus_uminus_int @ (zero_n2684676970156552555ol_int @ (bit_se1146084159140164899it_int @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9434_signed__take__bit__eq__concat__bit)). 185.47/93.68 thf(10992,plain,(((bit_ri631733984087533419it_int) = (^ [A:nat,B:int]: (bit_concat_bit @ A @ B @ (uminus_uminus_int @ (zero_n2684676970156552555ol_int @ (bit_se1146084159140164899it_int @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[951])). 185.47/93.68 thf(1531,axiom,((! [A:real]: ((divide_divide_real @ A @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5214_divide__minus1)). 185.47/93.68 thf(12811,plain,((! [A:real]: ((divide_divide_real @ A @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531])). 185.47/93.68 thf(3725,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ one_one_real) @ (plus_plus_real @ B @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1203_add__mono1)). 185.47/93.68 thf(19965,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ one_one_real) @ (plus_plus_real @ B @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3725])). 185.47/93.68 thf(7107,axiom,(((semiri1406184849735516958ct_int @ one_one_nat) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7960_fact__1)). 185.47/93.68 thf(31921,plain,(((semiri1406184849735516958ct_int @ one_one_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7107])). 185.47/93.68 thf(4455,axiom,((! [A:set_nat,B:nat]: ((~ (member_nat @ B @ A)) <= (A = bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1384_equals0D)). 185.47/93.68 thf(22262,plain,((! [A:set_nat,B:nat]: (~ (member_nat @ B @ A) | ~ (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4455])). 185.47/93.68 thf(7002,axiom,(((minus_minus_complex @ one_one_complex @ one_one_complex) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1711_diff__numeral__special_I9_J)). 185.47/93.68 thf(31559,plain,(((minus_minus_complex @ one_one_complex @ one_one_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7002])). 185.47/93.68 thf(4876,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2087_add_Ogroup__left__neutral)). 185.47/93.68 thf(23659,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4876])). 185.47/93.68 thf(2601,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_5517_le__imp__neg__le)). 185.47/93.68 thf(16367,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)],[2601])). 185.47/93.68 thf(5480,axiom,((! [A:nat]: ((((power_power_int @ (uminus_uminus_int @ one_one_int) @ A) = one_one_int) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & (((power_power_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ one_one_int)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6228_minus__one__power__iff)). 185.47/93.68 thf(25971,plain,((! [A:nat]: ((((power_power_int @ (uminus_uminus_int @ one_one_int) @ A) = one_one_int) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & (((power_power_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ one_one_int)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5480])). 185.47/93.68 thf(456,axiom,((! [A:real]: (((ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => (ord_less_real @ (sin_real @ A) @ zero_zero_real)) <= (ord_less_real @ pi @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7897_sin__lt__zero)). 185.47/93.68 thf(9247,plain,((! [A:real]: (((ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => (ord_less_real @ (sin_real @ A) @ zero_zero_real)) | ~ (ord_less_real @ pi @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[456])). 185.47/93.68 thf(5112,axiom,((! [A:complex,B:nat]: (((power_power_complex @ A @ B) = zero_zero_complex) = ((ord_less_nat @ zero_zero_nat @ B) & (A = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1844_power__eq__0__iff)). 185.47/93.68 thf(24555,plain,((! [A:complex,B:nat]: (((power_power_complex @ A @ B) = zero_zero_complex) = ((ord_less_nat @ zero_zero_nat @ B) & (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5112])). 185.47/93.68 thf(3645,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) = (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3343_mult__le__cancel__iff1)). 185.47/93.68 thf(19701,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) = (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3645])). 185.47/93.68 thf(100,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((! [E:nat]: ((ord_less_eq_nat @ (B @ E) @ C) <= (ord_less_nat @ E @ A))) => ((ord_less_eq_nat @ (groups3542108847815614940at_nat @ B @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7622_real__sum__nat__ivl__bounded2)). 185.47/93.68 thf(8061,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((! [E:nat]: ((ord_less_eq_nat @ (B @ E) @ C) | ~ (ord_less_nat @ E @ A))) => ((ord_less_eq_nat @ (groups3542108847815614940at_nat @ (B) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ C)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 185.47/93.68 thf(4465,axiom,((! [A:int]: ? [B:int]: (ord_less_int @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3973_gt__ex)). 185.47/93.68 thf(22295,plain,((! [A:int]: ? [B:int]: (ord_less_int @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4465])). 185.47/93.68 thf(2143,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_eq_real @ A @ (plus_plus_real @ B @ C)) & (ord_less_eq_real @ (minus_minus_real @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6589_abs__diff__le__iff)). 185.47/93.68 thf(14868,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_eq_real @ A @ (plus_plus_real @ B @ C)) & (ord_less_eq_real @ (minus_minus_real @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2143])). 185.47/93.68 thf(2419,axiom,((! [A:nat,B:num]: ((ord_less_eq_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (ord_less_eq_nat @ A @ (pred_numeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6788_le__Suc__numeral)). 185.47/93.68 thf(15736,plain,((! [A:nat,B:num]: ((ord_less_eq_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (ord_less_eq_nat @ A @ (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2419])). 185.47/93.68 thf(3259,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_rat @ zero_zero_rat @ (ring_1_of_int_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7279_of__int__nonneg)). 185.47/93.68 thf(18478,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_rat @ zero_zero_rat @ (ring_1_of_int_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3259])). 185.47/93.68 thf(4230,axiom,((! [A:complex,B:nat,C:complex]: ((((real_V1022390504157884413omplex @ A) = (real_V1022390504157884413omplex @ C)) <= (ord_less_nat @ zero_zero_nat @ B)) <= ((power_power_complex @ A @ B) = (power_power_complex @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7479_power__eq__imp__eq__norm)). 185.47/93.68 thf(21537,plain,((! [A:complex,B:nat,C:complex]: (((real_V1022390504157884413omplex @ A) = (real_V1022390504157884413omplex @ C)) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ ((power_power_complex @ A @ B) = (power_power_complex @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4230])). 185.47/93.68 thf(6501,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((C != D) & (A != B)) = ((plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) != (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6291_crossproduct__noteq)). 185.47/93.68 thf(29671,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((~ (C = D) & ~ (A = B)) = (~ ((plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) = (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6501])). 185.47/93.68 thf(2067,axiom,((gbinomial_rat = (^ [A:rat,B:nat]: (divide_divide_rat @ (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ A) @ B)) @ (semiri773545260158071498ct_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8455_gbinomial__pochhammer)). 185.47/93.68 thf(14631,plain,(((gbinomial_rat) = (^ [A:rat,B:nat]: (divide_divide_rat @ (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ A) @ B)) @ (semiri773545260158071498ct_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2067])). 185.47/93.68 thf(5505,axiom,((! [A:int]: ~ (ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2946_power2__less__0)). 185.47/93.68 thf(26065,plain,((! [A:int]: ~ (ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5505])). 185.47/93.68 thf(3560,axiom,((! [A:real,B:real,C:real,D:real]: ((((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)))) <= (ord_less_eq_real @ C @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2251_mult__mono_H)). 185.47/93.68 thf(19435,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)))) | ~ (ord_less_eq_real @ C @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3560])). 185.47/93.68 thf(3729,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1127_ring__class_Oring__distribs_I2_J)). 185.47/93.68 thf(19976,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3729])). 185.47/93.68 thf(5914,axiom,((! [A:real,B:nat]: ((ord_less_real @ (power_power_real @ A @ B) @ zero_zero_real) = ((ord_less_real @ A @ zero_zero_real) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4534_power__less__zero__eq)). 185.47/93.68 thf(27581,plain,((! [A:real,B:nat]: ((ord_less_real @ (power_power_real @ A @ B) @ zero_zero_real) = ((ord_less_real @ A @ zero_zero_real) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5914])). 185.47/93.68 thf(3916,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((minus_minus_int @ A @ D) = (plus_plus_int @ B @ (minus_minus_int @ C @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_717_group__cancel_Osub1)). 185.47/93.68 thf(20575,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((minus_minus_int @ A @ D) = (plus_plus_int @ B @ (minus_minus_int @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3916])). 185.47/93.68 thf(4990,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ B) @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1754_mod__mult__self1__is__0)). 185.47/93.68 thf(24071,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ B) @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4990])). 185.47/93.68 thf(3855,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) <= (((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ zero_zero_int @ A)) | ((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ A @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2247_split__mult__pos__le)). 185.47/93.68 thf(20385,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) | ~ (((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_eq_int @ zero_zero_int @ A)) | ((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ A @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3855])). 185.47/93.68 thf(6447,axiom,((! [A:complex,B:nat,C:nat]: ((power_power_complex @ A @ (plus_plus_nat @ B @ C)) = (times_times_complex @ (power_power_complex @ A @ B) @ (power_power_complex @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_power__add)). 185.47/93.68 thf(29474,plain,((! [A:complex,B:nat,C:nat]: ((power_power_complex @ A @ (plus_plus_nat @ B @ C)) = (times_times_complex @ (power_power_complex @ A @ B) @ (power_power_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6447])). 185.47/93.68 thf(5321,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((C != A) <= (ord_less_num @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3237_pinf_I3_J)). 185.47/93.68 thf(25310,plain,((! [A:num]: ? [B:num]: ! [C:num]: (~ (C = A) | ~ (ord_less_num @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5321])). 185.47/93.68 thf(3746,axiom,((! [A:rat,B:int]: ((ord_less_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ (ring_1_of_int_rat @ B))) @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) => ((archim7778729529865785530nd_rat @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7639_round__unique_H)). 185.47/93.68 thf(20030,plain,((! [A:rat,B:int]: ((ord_less_rat @ (abs_abs_rat @ (minus_minus_rat @ A @ (ring_1_of_int_rat @ B))) @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))) => ((archim7778729529865785530nd_rat @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3746])). 185.47/93.68 thf(7096,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (~ (ord_less_eq_num @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3305_pinf_I6_J)). 185.47/93.68 thf(31888,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (~ (ord_less_eq_num @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7096])). 185.47/93.68 thf(454,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBT]: ((if_VEBT_VEBT @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T)). 185.47/93.68 thf(9242,plain,((! [A:vEBT_VEBT,B:vEBT_VEBT]: ((if_VEBT_VEBT @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])). 185.47/93.68 thf(3923,axiom,((! [A:int,B:int,C:int]: ((((divide_divide_int @ C @ (times_times_int @ A @ B)) = (divide_divide_int @ (divide_divide_int @ C @ A) @ B)) <= (dvd_dvd_int @ B @ one_one_int)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4872_is__unit__div__mult2__eq)). 185.47/93.68 thf(20599,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ C @ (times_times_int @ A @ B)) = (divide_divide_int @ (divide_divide_int @ C @ A) @ B)) | ~ (dvd_dvd_int @ B @ one_one_int) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3923])). 185.47/93.68 thf(3323,axiom,((! [A:int,B:int]: (((ord_less_eq_rat @ (fract @ B @ A) @ zero_zero_rat) = (ord_less_eq_int @ B @ zero_zero_int)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9954_Fract__le__zero__iff)). 185.47/93.68 thf(18679,plain,((! [A:int,B:int]: (((ord_less_eq_rat @ (fract @ B @ A) @ zero_zero_rat) = (ord_less_eq_int @ B @ zero_zero_int)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3323])). 185.47/93.68 thf(3327,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) = ((A = B) | (ord_less_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4029_not__less__iff__gr__or__eq)). 185.47/93.68 thf(18692,plain,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) = ((A = B) | (ord_less_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3327])). 185.47/93.68 thf(5122,axiom,((! [A:nat,B:(nat > int),C:int]: (((ord_less_eq_int @ (B @ zero_zero_nat) @ C) => ((ord_less_eq_int @ C @ (B @ A)) => (? [D:nat]: (((B @ D) = C) & (ord_less_eq_nat @ D @ A))))) <= (! [D:nat]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (B @ (suc @ D)) @ (B @ D))) @ one_one_int) <= (ord_less_nat @ D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6839_nat__ivt__aux)). 185.47/93.68 thf(24586,plain,((! [A:nat,B:(nat > int),C:int]: (((ord_less_eq_int @ (B @ zero_zero_nat) @ C) => ((ord_less_eq_int @ C @ (B @ A)) => (? [D:nat]: (((B @ D) = C) & (ord_less_eq_nat @ D @ A))))) | ~ (! [D:nat]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (B @ (suc @ D)) @ (B @ D))) @ one_one_int) | ~ (ord_less_nat @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5122])). 185.47/93.68 thf(5891,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: (((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ C) @ A) = C) <= (ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3644_nth__list__update__eq)). 185.47/93.68 thf(27501,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: (((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ C) @ A) = C) | ~ (ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5891])). 185.47/93.68 thf(832,axiom,((! [A:(nat > nat),B:nat,C:set_nat]: ((modulo_modulo_nat @ (groups708209901874060359at_nat @ (^ [D:nat]: (modulo_modulo_nat @ (A @ D) @ B)) @ C) @ B) = (modulo_modulo_nat @ (groups708209901874060359at_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8731_mod__prod__eq)). 185.47/93.68 thf(10568,plain,((! [A:(nat > nat),B:nat,C:set_nat]: ((modulo_modulo_nat @ (groups708209901874060359at_nat @ (^ [D:nat]: (modulo_modulo_nat @ (A @ D) @ B)) @ C) @ B) = (modulo_modulo_nat @ (groups708209901874060359at_nat @ (A) @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[832])). 185.47/93.68 thf(856,axiom,((! [A:real]: (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arctan @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7767_arctan__lbound)). 185.47/93.68 thf(10663,plain,((! [A:real]: (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arctan @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[856])). 185.47/93.68 thf(5021,axiom,((! [A:int]: (((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) != one_one_int) = ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1907_not__mod__2__eq__1__eq__0)). 185.47/93.68 thf(24167,plain,((! [A:int]: ((~ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)) = ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5021])). 185.47/93.68 thf(6558,axiom,((! [A:complex,B:num,C:complex]: (((divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = C) = (((C = zero_zero_complex) <= ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) = zero_zero_complex)) & (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) != zero_zero_complex) => (A = (times_times_complex @ C @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5387_divide__eq__eq__numeral1_I2_J)). 185.47/93.68 thf(29863,plain,((! [A:complex,B:num,C:complex]: (((divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = C) = (((C = zero_zero_complex) | ~ ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) = zero_zero_complex)) & ((~ ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) = zero_zero_complex)) => (A = (times_times_complex @ C @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6558])). 185.47/93.68 thf(3641,axiom,((! [A:int,B:int]: (((times_times_int @ (abs_abs_int @ B) @ A) = (abs_abs_int @ (times_times_int @ B @ A))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6545_abs__mult__pos)). 185.47/93.68 thf(19688,plain,((! [A:int,B:int]: (((times_times_int @ (abs_abs_int @ B) @ A) = (abs_abs_int @ (times_times_int @ B @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3641])). 185.47/93.68 thf(6619,axiom,((! [A:real]: ((minus_minus_real @ A @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1542_cancel__comm__monoid__add__class_Odiff__cancel)). 185.47/93.68 thf(30069,plain,((! [A:real]: ((minus_minus_real @ A @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6619])). 185.47/93.68 thf(673,axiom,((! [A:nat,B:int,C:int]: ((ord_less_int @ (bit_concat_bit @ A @ B @ C) @ zero_zero_int) = (ord_less_int @ C @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3826_concat__bit__negative__iff)). 185.47/93.68 thf(9983,plain,((! [A:nat,B:int,C:int]: ((ord_less_int @ (bit_concat_bit @ A @ B @ C) @ zero_zero_int) = (ord_less_int @ C @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[673])). 185.47/93.68 thf(4499,axiom,((! [A:int,B:int]: ? [C:int]: ! [D:int]: (((~ (dvd_dvd_int @ A @ (plus_plus_int @ D @ B))) = (~ (dvd_dvd_int @ A @ (plus_plus_int @ D @ B)))) <= (ord_less_int @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4717_pinf_I10_J)). 185.47/93.68 thf(22401,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4499])). 185.47/93.68 thf(6536,axiom,((! [A:nat,B:complex]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (power_power_complex @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5436_Parity_Oring__1__class_Opower__minus__even)). 185.47/93.68 thf(29796,plain,((! [A:nat,B:complex]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (power_power_complex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6536])). 185.47/93.68 thf(7592,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ A @ B @ C @ D) @ E) => ((ord_less_nat @ F @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_V8194947554948674370ptions @ (vEBT_Node @ A @ B @ C @ D) @ F) <= (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_both__member__options__ding)). 185.47/93.68 thf(33546,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ A @ B @ C @ D) @ E) => ((ord_less_nat @ F @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_V8194947554948674370ptions @ (vEBT_Node @ A @ B @ C @ D) @ F) | ~ (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ F @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7592])). 185.47/93.68 thf(5712,axiom,((! [A:rat,B:rat]: (((times_times_rat @ A @ A) = (times_times_rat @ B @ B)) = ((A = B) | (A = (uminus_uminus_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5543_square__eq__iff)). 185.47/93.68 thf(26745,plain,((! [A:rat,B:rat]: (((times_times_rat @ A @ A) = (times_times_rat @ B @ B)) = ((A = B) | (A = (uminus_uminus_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5712])). 185.47/93.68 thf(2770,axiom,((! [A:(nat > $o),B:(nat > nat)]: ((finite_finite_nat @ (collect_nat @ (^ [C:nat]: ? [D:nat]: ((C = (B @ D)) & (A @ D))))) <= (finite_finite_nat @ (collect_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3513_finite__image__set)). 185.47/93.68 thf(16934,plain,((! [A:(nat > $o),B:(nat > nat)]: ((finite_finite_nat @ (collect_nat @ (^ [C:nat]: ? [D:nat]: ((C = (B @ D)) & (A @ D))))) | ~ (finite_finite_nat @ (collect_nat @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2770])). 185.47/93.68 thf(6004,axiom,((! [A:num,B:num]: ((times_times_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5338_mult__neg__numeral__simps_I3_J)). 185.47/93.68 thf(27911,plain,((! [A:num,B:num]: ((times_times_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (uminus_uminus_int @ (numeral_numeral_int @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6004])). 185.47/93.68 thf(3385,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (modulo_modulo_int @ B @ C)) = (modulo_modulo_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1977_mult__mod__right)). 185.47/93.68 thf(18879,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (modulo_modulo_int @ B @ C)) = (modulo_modulo_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3385])). 185.47/93.68 thf(3875,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (semiri1314217659103216013at_int @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7042_of__nat__power__less__of__nat__cancel__iff)). 185.47/93.68 thf(20442,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (semiri1314217659103216013at_int @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3875])). 185.47/93.68 thf(7655,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4522_even__add)). 185.47/93.68 thf(33721,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7655])). 185.47/93.68 thf(7716,axiom,((! [A:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => (ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2995_div__2__gt__zero)). 185.47/93.68 thf(33886,plain,((! [A:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => (ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7716])). 185.47/93.68 thf(7356,axiom,(((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera6690914467698888265omplex @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_one__add__one)). 185.47/93.68 thf(32786,plain,(((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera6690914467698888265omplex @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7356])). 185.47/93.68 thf(4144,axiom,((! [A:num]: ((set_ord_atMost_nat @ (numeral_numeral_nat @ A)) = (insert_nat @ (numeral_numeral_nat @ A) @ (set_ord_atMost_nat @ (pred_numeral @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9431_atMost__nat__numeral)). 185.47/93.68 thf(21273,plain,((! [A:num]: ((set_ord_atMost_nat @ (numeral_numeral_nat @ A)) = (insert_nat @ (numeral_numeral_nat @ A) @ (set_ord_atMost_nat @ (pred_numeral @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4144])). 185.47/93.68 thf(5946,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1147_left__diff__distrib)). 185.47/93.68 thf(27680,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5946])). 185.47/93.68 thf(7606,axiom,((! [A:rat]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_rat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_power2__eq__square)). 185.47/93.68 thf(33589,plain,((! [A:rat]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_rat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7606])). 185.47/93.68 thf(7624,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((divide_divide_nat @ (plus_plus_nat @ A @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4554_even__succ__div__two)). 185.47/93.68 thf(33642,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((divide_divide_nat @ (plus_plus_nat @ A @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7624])). 185.47/93.68 thf(7666,axiom,((vEBT_vebt_member @ summary @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_abh)). 185.47/93.68 thf(33753,plain,((vEBT_vebt_member @ summary @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7666])). 185.47/93.68 thf(2452,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((divide_divide_int @ (plus_plus_int @ one_one_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4558_even__succ__div__2)). 185.47/93.68 thf(15860,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((divide_divide_int @ (plus_plus_int @ one_one_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2452])). 185.47/93.68 thf(1576,axiom,((! [A:rat]: ((divide_divide_rat @ A @ one_one_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_995_div__by__1)). 185.47/93.68 thf(12952,plain,((! [A:rat]: ((divide_divide_rat @ A @ one_one_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576])). 185.47/93.68 thf(5084,axiom,(((neg_nu6511756317524482435omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit1 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6763_dbl__dec__simps_I4_J)). 185.47/93.68 thf(24443,plain,(((neg_nu6511756317524482435omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit1 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5084])). 185.47/93.68 thf(920,axiom,((! [A:complex]: ((A = zero_zero_complex) = ((plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9694_complex__eq__0)). 185.47/93.68 thf(10884,plain,((! [A:complex]: ((A = zero_zero_complex) = ((plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[920])). 185.47/93.68 thf(1685,axiom,((! [A:rat]: ~ (ord_less_rat @ (abs_abs_rat @ A) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6484_abs__not__less__zero)). 185.47/93.68 thf(13374,plain,((! [A:rat]: ~ (ord_less_rat @ (abs_abs_rat @ A) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685])). 185.47/93.68 thf(1712,axiom,((! [A:rat]: ((divide_divide_rat @ A @ zero_zero_rat) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1562_div__by__0)). 185.47/93.68 thf(13460,plain,((! [A:rat]: ((divide_divide_rat @ A @ zero_zero_rat) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712])). 185.47/93.68 thf(3674,axiom,((! [A:rat]: ((plus_plus_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))) @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one)))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_field__sum__of__halves)). 185.47/93.68 thf(19791,plain,((! [A:rat]: ((plus_plus_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))) @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one)))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3674])). 185.47/93.68 thf(1655,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) = (divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5765_nonzero__minus__divide__right)). 185.47/93.68 thf(13243,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) = (divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655])). 185.47/93.68 thf(2135,axiom,((neg_nu8295874005876285629c_real = (^ [A:real]: (plus_plus_real @ (plus_plus_real @ A @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7313_dbl__inc__def)). 185.47/93.68 thf(14838,plain,(((neg_nu8295874005876285629c_real) = (^ [A:real]: (plus_plus_real @ (plus_plus_real @ A @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2135])). 185.47/93.68 thf(5621,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => (((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2058_mult__left__cancel)). 185.47/93.68 thf(26440,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => (((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5621])). 185.47/93.68 thf(4801,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ A @ B) => ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ B) <= (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6509_abs__leI)). 185.47/93.68 thf(23424,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ A @ B) => ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ A) @ B) | ~ (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4801])). 185.47/93.68 thf(5197,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3136_int__distrib_I4_J)). 185.47/93.68 thf(24864,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (minus_minus_int @ B @ C)) = (minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5197])). 185.47/93.68 thf(2117,axiom,((! [A:num]: ((semiri681578069525770553at_rat @ (numeral_numeral_nat @ A)) = (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6905_of__nat__numeral)). 185.47/93.68 thf(14781,plain,((! [A:num]: ((semiri681578069525770553at_rat @ (numeral_numeral_nat @ A)) = (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2117])). 185.47/93.68 thf(5968,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4197_order_Oorder__iff__strict)). 185.47/93.68 thf(27793,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5968])). 185.47/93.68 thf(1774,axiom,(((times_times_complex @ imaginary_unit @ imaginary_unit) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8988_i__squared)). 185.47/93.68 thf(13674,plain,(((times_times_complex @ imaginary_unit @ imaginary_unit) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774])). 185.47/93.68 thf(7055,axiom,((suc = (^ [A:nat]: (plus_plus_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1107_Suc__eq__plus1)). 185.47/93.68 thf(31764,plain,(((suc) = (^ [A:nat]: (plus_plus_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7055])). 185.47/93.68 thf(793,axiom,((! [A:set_nat,B:nat,C:(nat > rat)]: (((member_nat @ B @ A) => ((ord_less_rat @ zero_zero_rat @ (C @ B)) => ((ord_less_rat @ zero_zero_rat @ (groups2906978787729119204at_rat @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_rat @ zero_zero_rat @ (C @ D))))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6043_sum__pos2)). 185.47/93.68 thf(10436,plain,((! [A:set_nat,B:nat,C:(nat > rat)]: (((member_nat @ B @ A) => ((ord_less_rat @ zero_zero_rat @ (C @ B)) => ((ord_less_rat @ zero_zero_rat @ (groups2906978787729119204at_rat @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_rat @ zero_zero_rat @ (C @ D))))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[793])). 185.47/93.68 thf(3433,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (((ord_less_int @ B @ zero_zero_int) & (ord_less_int @ C @ A)) | ((ord_less_int @ zero_zero_int @ B) & (ord_less_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2372_mult__less__cancel__right__disj)). 185.47/93.68 thf(19031,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (((ord_less_int @ B @ zero_zero_int) & (ord_less_int @ C @ A)) | ((ord_less_int @ zero_zero_int @ B) & (ord_less_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3433])). 185.47/93.68 thf(1153,axiom,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = B) = (A = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1514_add__cancel__left__left)). 185.47/93.68 thf(11636,plain,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = B) = (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153])). 185.47/93.68 thf(6414,axiom,((! [A:int,B:int,C:int,D:int]: ((A != zero_zero_int) => ((B != zero_zero_int) => ((minus_minus_rat @ (fract @ C @ A) @ (fract @ D @ B)) = (fract @ (minus_minus_int @ (times_times_int @ C @ B) @ (times_times_int @ D @ A)) @ (times_times_int @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9934_diff__rat)). 185.47/93.68 thf(29350,plain,((! [A:int,B:int,C:int,D:int]: ((~ (A = zero_zero_int)) => ((~ (B = zero_zero_int)) => ((minus_minus_rat @ (fract @ C @ A) @ (fract @ D @ B)) = (fract @ (minus_minus_int @ (times_times_int @ C @ B) @ (times_times_int @ D @ A)) @ (times_times_int @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6414])). 185.47/93.68 thf(6912,axiom,((! [A:num,B:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ B)) = (times_times_rat @ B @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5759_numeral__times__minus__swap)). 185.47/93.68 thf(31170,plain,((! [A:num,B:rat]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ B)) = (times_times_rat @ B @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6912])). 185.47/93.68 thf(6818,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ A @ B)) = ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ A) & (ord_less_eq_nat @ (suc @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1846_one__le__mult__iff)). 185.47/93.68 thf(30803,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ A @ B)) = ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ A) & (ord_less_eq_nat @ (suc @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6818])). 185.47/93.68 thf(555,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (tanh_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6396_tanh__real__nonneg__iff)). 185.47/93.68 thf(9574,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (tanh_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[555])). 185.47/93.68 thf(3536,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) & (ord_less_eq_int @ A @ B)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_add__mono__thms__linordered__field_I4_J)). 185.47/93.68 thf(19363,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) & (ord_less_eq_int @ A @ B)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3536])). 185.47/93.68 thf(108,axiom,((! [A:complex]: ((gbinomial_complex @ A @ zero_zero_nat) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8414_gbinomial__0_I1_J)). 185.47/93.68 thf(8087,plain,((! [A:complex]: ((gbinomial_complex @ A @ zero_zero_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 185.47/93.68 thf(5430,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => (((times_times_int @ B @ A) = (times_times_int @ C @ A)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2067_mult__right__cancel)). 185.47/93.68 thf(25686,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => (((times_times_int @ B @ A) = (times_times_int @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5430])). 185.47/93.68 thf(4278,axiom,((! [A:complex,B:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7493_norm__triangle__ineq)). 185.47/93.68 thf(21681,plain,((! [A:complex,B:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4278])). 185.47/93.68 thf(2177,axiom,((! [A:nat]: ~ (member_nat @ A @ bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1280_empty__iff)). 185.47/93.68 thf(14992,plain,((! [A:nat]: ~ (member_nat @ A @ bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2177])). 185.47/93.68 thf(1261,axiom,((~ (ord_less_rat @ one_one_rat @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2381_not__one__less__zero)). 185.47/93.68 thf(11957,plain,((~ (ord_less_rat @ one_one_rat @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261])). 185.47/93.68 thf(6545,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => (((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D) <= (ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B))) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C))) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1197_add__le__add__imp__diff__le)). 185.47/93.68 thf(29823,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D) | ~ (ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C))) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6545])). 185.47/93.68 thf(5924,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => ((ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_mi__ma__2__deg)). 185.47/93.68 thf(27612,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => ((ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5924])). 185.47/93.68 thf(7349,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_mint @ A) = none_nat) => ((vEBT_VEBT_set_vebt @ A) = bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_958_mint__corr__help__empty)). 185.47/93.68 thf(32765,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_mint @ A) = none_nat) => ((vEBT_VEBT_set_vebt @ A) = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7349])). 185.47/93.68 thf(7439,axiom,((! [A:nat,B:nat,C:real]: (((ord_less_nat @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ C @ one_one_real) => (ord_less_real @ (root @ A @ C) @ (root @ B @ C))))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9194_real__root__strict__increasing)). 185.47/93.68 thf(33065,plain,((! [A:nat,B:nat,C:real]: (((ord_less_nat @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ C @ one_one_real) => (ord_less_real @ (root @ A @ C) @ (root @ B @ C))))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7439])). 185.47/93.68 thf(4294,axiom,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_distrib__left__numeral)). 185.47/93.68 thf(21726,plain,((! [A:num,B:real,C:real]: ((times_times_real @ (numeral_numeral_real @ A) @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ A) @ B) @ (times_times_real @ (numeral_numeral_real @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4294])). 185.47/93.68 thf(1401,axiom,((! [A:nat,B:nat,C:(nat > int)]: (((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (C @ (suc @ D)) @ (C @ D))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_int @ (C @ (suc @ B)) @ (C @ A))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6679_sum__Suc__diff)). 185.47/93.68 thf(12402,plain,((! [A:nat,B:nat,C:(nat > int)]: (((groups3539618377306564664at_int @ (^ [D:nat]: (minus_minus_int @ (C @ (suc @ D)) @ (C @ D))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_int @ (C @ (suc @ B)) @ (C @ A))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401])). 185.47/93.68 thf(7679,axiom,((! [A:char]: (ord_less_nat @ (comm_s629917340098488124ar_nat @ A) @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ one)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9977_nat__of__char__less__256)). 185.47/93.68 thf(33785,plain,((! [A:char]: (ord_less_nat @ (comm_s629917340098488124ar_nat @ A) @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ one)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7679])). 185.47/93.68 thf(7293,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) => (ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8013_fact__less__mono)). 185.47/93.68 thf(32578,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) => (ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7293])). 185.47/93.68 thf(6433,axiom,((bit_se545348938243370406it_int = (^ [A:nat,B:int]: (times_times_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9536_push__bit__int__def)). 185.47/93.68 thf(29423,plain,(((bit_se545348938243370406it_int) = (^ [A:nat,B:int]: (times_times_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6433])). 185.47/93.68 thf(7471,axiom,((! [A:nat,B:nat,C:real]: ((((ord_less_real @ C @ one_one_real) => (ord_less_real @ (power_power_real @ C @ B) @ (power_power_real @ C @ A))) <= (ord_less_real @ zero_zero_real @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2879_power__strict__decreasing)). 185.47/93.68 thf(33180,plain,((! [A:nat,B:nat,C:real]: (((ord_less_real @ C @ one_one_real) => (ord_less_real @ (power_power_real @ C @ B) @ (power_power_real @ C @ A))) | ~ (ord_less_real @ zero_zero_real @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7471])). 185.47/93.68 thf(1236,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ (times_times_int @ B @ A) @ C)) = (dvd_dvd_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4475_dvd__add__times__triv__left__iff)). 185.47/93.68 thf(11879,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ (times_times_int @ B @ A) @ C)) = (dvd_dvd_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236])). 185.47/93.68 thf(5236,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (modulo_modulo_nat @ A @ B)) = (~ (dvd_dvd_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4884_mod__greater__zero__iff__not__dvd)). 185.47/93.68 thf(24997,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (modulo_modulo_nat @ A @ B)) = (~ (dvd_dvd_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5236])). 185.47/93.68 thf(985,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3342_mult__le__cancel__iff2)). 185.47/93.68 thf(11108,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[985])). 185.47/93.68 thf(319,axiom,((! [A:real]: ((ord_less_eq_real @ (tanh_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6395_tanh__real__nonpos__iff)). 185.47/93.68 thf(8798,plain,((! [A:real]: ((ord_less_eq_real @ (tanh_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 185.47/93.68 thf(2107,axiom,((! [A:num]: ((neg_nu3179335615603231917ec_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (uminus_uminus_rat @ (neg_nu5219082963157363817nc_rat @ (numeral_numeral_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7028_dbl__dec__simps_I1_J)). 185.47/93.68 thf(14747,plain,((! [A:num]: ((neg_nu3179335615603231917ec_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (uminus_uminus_rat @ (neg_nu5219082963157363817nc_rat @ (numeral_numeral_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107])). 185.47/93.68 thf(2498,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ B @ (divide_divide_rat @ C @ A)) <= (ord_less_rat @ (times_times_rat @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2710_mult__imp__less__div__pos)). 185.47/93.68 thf(16014,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ B @ (divide_divide_rat @ C @ A)) | ~ (ord_less_rat @ (times_times_rat @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2498])). 185.47/93.68 thf(579,axiom,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5950_neg__one__less__numeral)). 185.47/93.68 thf(9654,plain,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[579])). 185.47/93.68 thf(7285,axiom,((! [A:real,B:real]: ((plus_plus_real @ A @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_left__add__twice)). 185.47/93.68 thf(32542,plain,((! [A:real,B:real]: ((plus_plus_real @ A @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7285])). 185.47/93.68 thf(1912,axiom,((! [A:code_integer,B:nat]: ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ B) @ one_one_Code_integer) = ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4876_is__unit__power__iff)). 185.47/93.68 thf(14118,plain,((! [A:code_integer,B:nat]: ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ B) @ one_one_Code_integer) = ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1912])). 185.47/93.68 thf(6873,axiom,((! [A:num,B:num,C:real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5362_semiring__norm_I172_J)). 185.47/93.68 thf(31046,plain,((! [A:num,B:num,C:real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ C)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6873])). 185.47/93.68 thf(6326,axiom,((! [A:nat,B:num]: ((bit_ri631733984087533419it_int @ (suc @ A) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (bit_ri631733984087533419it_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4529_signed__take__bit__Suc__bit0)). 185.47/93.68 thf(29020,plain,((! [A:nat,B:num]: ((bit_ri631733984087533419it_int @ (suc @ A) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (bit_ri631733984087533419it_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6326])). 185.47/93.68 thf(2743,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((modulo_modulo_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3071_pos__zmod__mult__2)). 185.47/93.68 thf(16852,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((modulo_modulo_int @ (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2743])). 185.47/93.68 thf(1252,axiom,((! [A:real]: ((divide_divide_real @ A @ (numeral_numeral_real @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_divide__numeral__1)). 185.47/93.68 thf(11931,plain,((! [A:real]: ((divide_divide_real @ A @ (numeral_numeral_real @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252])). 185.47/93.68 thf(3695,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ D @ B))) <= (ord_less_eq_real @ one_one_real @ C)) <= (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9097_powr__mono__both)). 185.47/93.68 thf(19859,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ D @ B))) | ~ (ord_less_eq_real @ one_one_real @ C) | ~ (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3695])). 185.47/93.68 thf(4934,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4733_unit__mult__left__cancel)). 185.47/93.68 thf(23888,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4934])). 185.47/93.68 thf(1482,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ one_one_rat) = (ord_less_eq_rat @ B @ A)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1858_divide__le__eq__1__pos)). 185.47/93.68 thf(12665,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ B @ A) @ one_one_rat) = (ord_less_eq_rat @ B @ A)) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482])). 185.47/93.68 thf(6739,axiom,(((numeral_numeral_rat @ one) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_831_numeral__One)). 185.47/93.68 thf(30477,plain,(((numeral_numeral_rat @ one) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6739])). 185.47/93.68 thf(887,axiom,((! [A:complex,B:nat]: ((gbinomial_complex @ (plus_plus_complex @ A @ one_one_complex) @ (suc @ B)) = (times_times_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ one_one_complex) @ (semiri8010041392384452111omplex @ (suc @ B))) @ (gbinomial_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8556_gbinomial__factors)). 185.47/93.68 thf(10769,plain,((! [A:complex,B:nat]: ((gbinomial_complex @ (plus_plus_complex @ A @ one_one_complex) @ (suc @ B)) = (times_times_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ one_one_complex) @ (semiri8010041392384452111omplex @ (suc @ B))) @ (gbinomial_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[887])). 185.47/93.68 thf(7366,axiom,((! [A:nat]: (((power_power_complex @ zero_zero_complex @ A) = zero_zero_complex) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1969_zero__power)). 185.47/93.68 thf(32816,plain,((! [A:nat]: (((power_power_complex @ zero_zero_complex @ A) = zero_zero_complex) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7366])). 185.47/93.68 thf(5206,axiom,((! [A:real]: (((power_power_real @ (sqrt @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8140_real__sqrt__pow2)). 185.47/93.68 thf(24891,plain,((! [A:real]: (((power_power_real @ (sqrt @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5206])). 185.47/93.68 thf(1674,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (~ (ord_less_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3280_minf_I7_J)). 185.47/93.68 thf(13342,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (~ (ord_less_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674])). 185.47/93.68 thf(7481,axiom,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = (ord_less_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3103_verit__comp__simplify1_I3_J)). 185.47/93.68 thf(33213,plain,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = (ord_less_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7481])). 185.47/93.68 thf(6385,axiom,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_827_one__plus__numeral__commute)). 185.47/93.68 thf(29228,plain,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6385])). 185.47/93.68 thf(7525,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((binomial @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8428_binomial__eq__0)). 185.47/93.68 thf(33366,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((binomial @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7525])). 185.47/93.68 thf(2287,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2621_add__neg__nonpos)). 185.47/93.68 thf(15319,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2287])). 185.47/93.68 thf(3016,axiom,((! [A:nat,B:complex]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_complex @ (exp_complex @ (divide1717551699836669952omplex @ B @ (semiri8010041392384452111omplex @ A))) @ A) = (exp_complex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8217_exp__divide__power__eq)). 185.47/93.68 thf(17721,plain,((! [A:nat,B:complex]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_complex @ (exp_complex @ (divide1717551699836669952omplex @ B @ (semiri8010041392384452111omplex @ A))) @ A) = (exp_complex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3016])). 185.47/93.68 thf(860,axiom,((! [A:real,B:nat]: ((times_times_real @ A @ (gbinomial_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (gbinomial_real @ A @ B)) @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (gbinomial_real @ A @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8485_gbinomial__mult__1)). 185.47/93.68 thf(10674,plain,((! [A:real,B:nat]: ((times_times_real @ A @ (gbinomial_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (gbinomial_real @ A @ B)) @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (gbinomial_real @ A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[860])). 185.47/93.68 thf(1099,axiom,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ A) = (((ord_less_real @ one_one_real @ B) <= (ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ one_one_real) <= (ord_less_eq_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2821_mult__less__cancel__left2)). 185.47/93.68 thf(11465,plain,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ A) = (((ord_less_real @ one_one_real @ B) | ~ (ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ one_one_real) | ~ (ord_less_eq_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099])). 185.47/93.68 thf(5913,axiom,((ord_less_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8202_sqrt2__less__2)). 185.47/93.68 thf(27580,plain,((ord_less_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5913])). 185.47/93.68 thf(2375,axiom,((! [A:rat]: ((divide_divide_rat @ A @ zero_zero_rat) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1576_division__ring__divide__zero)). 185.47/93.68 thf(15593,plain,((! [A:rat]: ((divide_divide_rat @ A @ zero_zero_rat) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2375])). 185.47/93.68 thf(4348,axiom,((! [A:int,B:num]: (((ring_1_of_int_rat @ A) = (numeral_numeral_rat @ B)) = (A = (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6942_of__int__eq__numeral__iff)). 185.47/93.68 thf(21927,plain,((! [A:int,B:num]: (((ring_1_of_int_rat @ A) = (numeral_numeral_rat @ B)) = (A = (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4348])). 185.47/93.68 thf(862,axiom,((! [A:nat,B:nat,C:(nat > rat)]: (((groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_rat @ (C @ (suc @ B)) @ (groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6650_sum_Onat__ivl__Suc_H)). 185.47/93.68 thf(10680,plain,((! [A:nat,B:nat,C:(nat > rat)]: (((groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_rat @ (C @ (suc @ B)) @ (groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[862])). 185.47/93.68 thf(3986,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((A != B) => (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4297_order__le__neq__trans)). 185.47/93.68 thf(20792,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((~ (A = B)) => (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3986])). 185.47/93.68 thf(6582,axiom,((! [A:num]: ((times_times_num @ A @ one) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_semiring__norm_I11_J)). 185.47/93.68 thf(29947,plain,((! [A:num]: ((times_times_num @ A @ one) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6582])). 185.47/93.68 thf(1870,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (minus_minus_rat @ C @ B) @ (minus_minus_rat @ C @ A)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_707_diff__strict__left__mono)). 185.47/93.68 thf(13994,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (minus_minus_rat @ C @ B) @ (minus_minus_rat @ C @ A)) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1870])). 185.47/93.68 thf(6846,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_754_le__diff__iff_H)). 185.47/93.68 thf(30922,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ B) => ((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6846])). 185.47/93.68 thf(797,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) = (? [B:nat]: ((B != zero_zero_nat) & (ord_less_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B)) @ A) & (ord_less_real @ zero_zero_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8971_real__arch__inverse)). 185.47/93.68 thf(10451,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) = (? [B:nat]: (~ (B = zero_zero_nat) & (ord_less_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B)) @ A) & (ord_less_real @ zero_zero_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[797])). 185.47/93.68 thf(2023,axiom,((! [A:int]: ((dvd_dvd_int @ A @ one_one_int) => (dvd_dvd_int @ (divide_divide_int @ one_one_int @ A) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4492_unit__div__1__unit)). 185.47/93.68 thf(14496,plain,((! [A:int]: ((dvd_dvd_int @ A @ one_one_int) => (dvd_dvd_int @ (divide_divide_int @ one_one_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2023])). 185.47/93.68 thf(6944,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => ((modulo_modulo_nat @ (suc @ (times_times_nat @ A @ B)) @ A) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2168_Suc__times__mod__eq)). 185.47/93.68 thf(31283,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => ((modulo_modulo_nat @ (suc @ (times_times_nat @ A @ B)) @ A) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6944])). 185.47/93.68 thf(5678,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ B @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_mult_Oleft__commute)). 185.47/93.68 thf(26628,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ B @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5678])). 185.47/93.68 thf(563,axiom,((! [A:(nat > rat),B:set_nat,C:(nat > rat),D:nat]: (((! [E:nat]: ((member_nat @ E @ B) => (ord_less_eq_rat @ (A @ E) @ (C @ E)))) => ((member_nat @ D @ B) => (((A @ D) = (C @ D)) <= (finite_finite_nat @ B)))) <= ((groups2906978787729119204at_rat @ A @ B) = (groups2906978787729119204at_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5652_sum__mono__inv)). 185.47/93.68 thf(9601,plain,((! [A:(nat > rat),B:set_nat,C:(nat > rat),D:nat]: (((! [E:nat]: ((member_nat @ E @ B) => (ord_less_eq_rat @ (A @ E) @ (C @ E)))) => ((member_nat @ D @ B) => (((A @ D) = (C @ D)) | ~ (finite_finite_nat @ B)))) | ~ ((groups2906978787729119204at_rat @ (A) @ B) = (groups2906978787729119204at_rat @ (C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[563])). 185.47/93.68 thf(5170,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (modulo_modulo_nat @ A @ B)) = (times_times_nat @ B @ (divide_divide_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2556_minus__mod__eq__mult__div)). 185.47/93.68 thf(24782,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (modulo_modulo_nat @ A @ B)) = (times_times_nat @ B @ (divide_divide_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5170])). 185.47/93.68 thf(3413,axiom,((! [A:num,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (ord_less_eq_nat @ (pred_numeral @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6789_le__numeral__Suc)). 185.47/93.68 thf(18969,plain,((! [A:num,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (ord_less_eq_nat @ (pred_numeral @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3413])). 185.47/93.68 thf(3332,axiom,((! [A:complex,B:nat]: ((real_V1022390504157884413omplex @ (power_power_complex @ A @ B)) = (power_power_real @ (real_V1022390504157884413omplex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7470_norm__power)). 185.47/93.68 thf(18707,plain,((! [A:complex,B:nat]: ((real_V1022390504157884413omplex @ (power_power_complex @ A @ B)) = (power_power_real @ (real_V1022390504157884413omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3332])). 185.47/93.68 thf(2643,axiom,((! [A:num,B:nat,C:int]: ((ord_less_eq_real @ (power_power_real @ (numeral_numeral_real @ A) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7138_numeral__power__le__of__int__cancel__iff)). 185.47/93.68 thf(16502,plain,((! [A:num,B:nat,C:int]: ((ord_less_eq_real @ (power_power_real @ (numeral_numeral_real @ A) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2643])). 185.47/93.68 thf(6829,axiom,((! [A:complex,B:complex]: ((power_power_complex @ (plus_plus_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_complex @ (plus_plus_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_power2__sum)). 185.47/93.68 thf(30835,plain,((! [A:complex,B:complex]: ((power_power_complex @ (plus_plus_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_complex @ (plus_plus_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6829])). 185.47/93.68 thf(4354,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) <= (ord_less_int @ zero_zero_int @ A)) <= (ord_less_int @ zero_zero_int @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2342_zero__less__mult__pos)). 185.47/93.68 thf(21945,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ B) | ~ (ord_less_int @ zero_zero_int @ A) | ~ (ord_less_int @ zero_zero_int @ (times_times_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4354])). 185.47/93.68 thf(353,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) => ((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (((sin_real @ A) = (sin_real @ B)) => (A = B))))) <= (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7903_sin__inj__pi)). 185.47/93.68 thf(8914,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) => ((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (((sin_real @ A) = (sin_real @ B)) => (A = B))))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])). 185.47/93.68 thf(677,axiom,((! [A:nat,B:nat,C:(nat > real)]: (((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (C @ D) @ (C @ (minus_minus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (minus_minus_real @ (C @ B) @ (C @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6742_sum__telescope_H_H)). 185.47/93.68 thf(9995,plain,((! [A:nat,B:nat,C:(nat > real)]: (((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (C @ D) @ (C @ (minus_minus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (minus_minus_real @ (C @ B) @ (C @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[677])). 185.47/93.68 thf(2812,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_3908_Orderings_Oorder__eq__iff)). 185.47/93.68 thf(17067,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)],[2812])). 185.47/93.68 thf(1049,axiom,((! [A:num,B:complex,C:complex]: (((numera6690914467698888265omplex @ A) = (divide1717551699836669952omplex @ B @ C)) = (((C = zero_zero_complex) => ((numera6690914467698888265omplex @ A) = zero_zero_complex)) & (((times_times_complex @ (numera6690914467698888265omplex @ A) @ C) = B) <= (C != zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2723_eq__divide__eq__numeral_I1_J)). 185.47/93.68 thf(11302,plain,((! [A:num,B:complex,C:complex]: (((numera6690914467698888265omplex @ A) = (divide1717551699836669952omplex @ B @ C)) = (((C = zero_zero_complex) => ((numera6690914467698888265omplex @ A) = zero_zero_complex)) & (((times_times_complex @ (numera6690914467698888265omplex @ A) @ C) = B) | (C = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049])). 185.47/93.68 thf(3088,axiom,((! [A:real,B:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = (times_times_real @ (plus_plus_real @ A @ B) @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1215_square__diff__square__factored)). 185.47/93.68 thf(17947,plain,((! [A:real,B:real]: ((minus_minus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)) = (times_times_real @ (plus_plus_real @ A @ B) @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3088])). 185.47/93.68 thf(6755,axiom,((! [A:(nat > $o),B:nat,C:nat,D:nat]: ((((ord_less_nat @ D @ C) => ((! [E:nat]: (((A @ E) => (A @ (modulo_modulo_nat @ (suc @ E) @ C))) <= (ord_less_nat @ E @ C))) => (A @ D))) <= (ord_less_nat @ B @ C)) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2169_mod__induct)). 185.47/93.68 thf(30572,plain,((! [A:(nat > $o),B:nat,C:nat,D:nat]: (((ord_less_nat @ D @ C) => ((! [E:nat]: (((A @ E) => (A @ (modulo_modulo_nat @ (suc @ E) @ C))) | ~ (ord_less_nat @ E @ C))) => (A @ D))) | ~ (ord_less_nat @ B @ C) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6755])). 185.47/93.68 thf(216,axiom,((! [A:int,B:int]: ((if_int @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Int__Oint_T)). 185.47/93.68 thf(8431,plain,((! [A:int,B:int]: ((if_int @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 185.47/93.68 thf(1249,axiom,((! [A:int]: ((modulo_modulo_int @ A @ one_one_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1761_bits__mod__by__1)). 185.47/93.68 thf(11921,plain,((! [A:int]: ((modulo_modulo_int @ A @ one_one_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249])). 185.47/93.68 thf(3915,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ (times_times_int @ A @ C))) = (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4818_zdvd__reduce)). 185.47/93.68 thf(20572,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ (times_times_int @ A @ C))) = (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3915])). 185.47/93.68 thf(6313,axiom,((! [A:int,B:int,C:nat]: (((ord_less_eq_int @ zero_zero_int @ B) => (((ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = (ord_less_eq_int @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ C))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1875_power__mono__iff)). 185.47/93.68 thf(28965,plain,((! [A:int,B:int,C:nat]: (((ord_less_eq_int @ zero_zero_int @ B) => (((ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = (ord_less_eq_int @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6313])). 185.47/93.68 thf(5701,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((numeral_numeral_nat @ (num_of_nat @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9842_numeral__num__of__nat)). 185.47/93.68 thf(26698,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((numeral_numeral_nat @ (num_of_nat @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5701])). 185.47/93.68 thf(7399,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_nat @ (modulo_modulo_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ A))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2996_mult__exp__mod__exp__eq)). 185.47/93.68 thf(32916,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_nat @ (modulo_modulo_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ A))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7399])). 185.47/93.68 thf(3056,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = ((A != zero_zero_real) | (B != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2984_sum__power2__gt__zero__iff)). 185.47/93.68 thf(17853,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = (~ (A = zero_zero_real) | ~ (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3056])). 185.47/93.68 thf(3212,axiom,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ A @ (plus_plus_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_ab__semigroup__add__class_Oadd__ac_I1_J)). 185.47/93.68 thf(18345,plain,((! [A:rat,B:rat,C:rat]: ((plus_plus_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ A @ (plus_plus_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3212])). 185.47/93.68 thf(2334,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (powr_real @ B @ A) @ one_one_real))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9096_powr__le1)). 185.47/93.68 thf(15469,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ B @ one_one_real) => (ord_less_eq_real @ (powr_real @ B @ A) @ one_one_real))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2334])). 185.47/93.68 thf(6423,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7023_of__nat__0__less__iff)). 185.47/93.68 thf(29391,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6423])). 185.47/93.68 thf(4492,axiom,((! [A:real,B:real]: (((abs_abs_real @ A) = B) = (((A = (uminus_uminus_real @ B)) | (A = B)) & (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6554_abs__eq__iff_H)). 185.47/93.68 thf(22381,plain,((! [A:real,B:real]: (((abs_abs_real @ A) = B) = (((A = (uminus_uminus_real @ B)) | (A = B)) & (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4492])). 185.47/93.68 thf(5993,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_756_Nat_Odiff__cancel)). 185.47/93.68 thf(27871,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5993])). 185.47/93.68 thf(3103,axiom,((! [A:(nat > (nat > nat)),B:nat,C:nat,D:nat,E:nat]: ((((E = (set_fo2584398358068434914at_nat @ A @ (plus_plus_nat @ B @ one_one_nat) @ C @ (A @ B @ D))) <= (~ (ord_less_nat @ C @ B))) & ((ord_less_nat @ C @ B) => (E = D))) <= ((set_fo2584398358068434914at_nat @ A @ B @ C @ D) = E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8317_fold__atLeastAtMost__nat_Oelims)). 185.47/93.68 thf(18002,plain,((! [A:(nat > (nat > nat)),B:nat,C:nat,D:nat,E:nat]: ((((E = (set_fo2584398358068434914at_nat @ (A) @ (plus_plus_nat @ B @ one_one_nat) @ C @ (A @ B @ D))) | (ord_less_nat @ C @ B)) & ((ord_less_nat @ C @ B) => (E = D))) | ~ ((set_fo2584398358068434914at_nat @ (A) @ B @ C @ D) = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3103])). 185.47/93.68 thf(6442,axiom,((! [A:real,B:real]: ((A = (times_times_real @ A @ B)) = ((B = one_one_real) | (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1662_mult__cancel__left1)). 185.47/93.68 thf(29459,plain,((! [A:real,B:real]: ((A = (times_times_real @ A @ B)) = ((B = one_one_real) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6442])). 185.47/93.68 thf(195,axiom,((! [A:nat,B:nat]: ((times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ (gbinomial_rat @ (minus_minus_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ A)) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (gbinomial_rat @ (minus_minus_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ A)) @ one_one_rat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8564_gbinomial__index__swap)). 185.47/93.68 thf(8360,plain,((! [A:nat,B:nat]: ((times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ A) @ (gbinomial_rat @ (minus_minus_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ B)) @ one_one_rat) @ A)) = (times_times_rat @ (power_power_rat @ (uminus_uminus_rat @ one_one_rat) @ B) @ (gbinomial_rat @ (minus_minus_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ A)) @ one_one_rat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 185.47/93.68 thf(1692,axiom,((! [A:nat,B:nat]: (((semiri1314217659103216013at_int @ (minus_minus_nat @ B @ A)) = (minus_minus_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7262_of__nat__diff)). 185.47/93.68 thf(13396,plain,((! [A:nat,B:nat]: (((semiri1314217659103216013at_int @ (minus_minus_nat @ B @ A)) = (minus_minus_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692])). 185.47/93.68 thf(5175,axiom,((! [A:int,B:int,C:nat]: ((power_power_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_power__mult__distrib)). 185.47/93.68 thf(24797,plain,((! [A:int,B:int,C:nat]: ((power_power_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5175])). 185.47/93.68 thf(1630,axiom,((comm_s7457072308508201937r_real = (^ [A:real,B:nat]: (if_real @ (B = zero_zero_nat) @ one_one_real @ (set_fo3111899725591712190t_real @ (^ [C:nat]: (times_times_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8603_pochhammer__code)). 185.47/93.68 thf(13160,plain,(((comm_s7457072308508201937r_real) = (^ [A:real,B:nat]: (if_real @ (B = zero_zero_nat) @ one_one_real @ (set_fo3111899725591712190t_real @ (^ [C:nat]: (times_times_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630])). 185.47/93.68 thf(5036,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_not__add__less1)). 185.47/93.68 thf(24211,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5036])). 185.47/93.68 thf(7307,axiom,((! [A:num]: (((uminus_uminus_real @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ A))) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5291_neg__one__eq__numeral__iff)). 185.47/93.68 thf(32620,plain,((! [A:num]: (((uminus_uminus_real @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ A))) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7307])). 185.47/93.68 thf(7662,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_nat @ (power_power_nat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_power__even__eq)). 185.47/93.68 thf(33742,plain,((! [A:nat,B:nat]: ((power_power_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_nat @ (power_power_nat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7662])). 185.47/93.68 thf(4017,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) <= (ord_less_real @ B @ zero_zero_real)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2311_mult__neg__neg)). 185.47/93.68 thf(20888,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) | ~ (ord_less_real @ B @ zero_zero_real) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4017])). 185.47/93.68 thf(2516,axiom,((! [A:int]: (((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((cos_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = (uminus_uminus_real @ one_one_real))) & (((cos_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = one_one_real) <= (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7816_cos__npi__int)). 185.47/93.68 thf(16070,plain,((! [A:int]: (((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((cos_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = (uminus_uminus_real @ one_one_real))) & (((cos_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = one_one_real) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2516])). 185.47/93.68 thf(6869,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_238_le__antisym)). 185.47/93.68 thf(31035,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)],[6869])). 185.47/93.68 thf(2728,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2453_zero__less__power)). 185.47/93.68 thf(16807,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2728])). 185.47/93.68 thf(2041,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2422_divide__right__mono__neg)). 185.47/93.68 thf(14554,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2041])). 185.47/93.68 thf(7081,axiom,((! [A:int,B:nat]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2992_zero__le__even__power_H)). 185.47/93.68 thf(31839,plain,((! [A:int,B:nat]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7081])). 185.47/93.68 thf(1625,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_add_Oleft__commute)). 185.47/93.68 thf(13146,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ A @ (plus_plus_int @ B @ C)) = (plus_plus_int @ B @ (plus_plus_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625])). 185.47/93.68 thf(2278,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => (((ord_less_eq_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D))) <= (ord_less_eq_rat @ zero_zero_rat @ B))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2256_mult__mono)). 185.47/93.68 thf(15294,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) => (((ord_less_eq_rat @ zero_zero_rat @ C) => (ord_less_eq_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D))) | ~ (ord_less_eq_rat @ zero_zero_rat @ B))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2278])). 185.47/93.68 thf(4054,axiom,((! [A:num,B:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (bit_ri631733984087533419it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6816_signed__take__bit__numeral__minus__bit0)). 185.47/93.68 thf(20996,plain,((! [A:num,B:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (bit_ri631733984087533419it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4054])). 185.47/93.68 thf(2265,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_eq_rat @ C @ A) <= (ord_less_rat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3314_minf_I6_J)). 185.47/93.68 thf(15255,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_eq_rat @ C @ A) | ~ (ord_less_rat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2265])). 185.47/93.68 thf(3074,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (plus_plus_real @ one_one_real @ A) @ (exp_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8205_exp__ge__add__one__self__aux)). 185.47/93.68 thf(17904,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (plus_plus_real @ one_one_real @ A) @ (exp_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3074])). 185.47/93.68 thf(3276,axiom,((! [A:nat,B:nat]: ((semiri681578069525770553at_rat @ (plus_plus_nat @ A @ B)) = (plus_plus_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6913_of__nat__add)). 185.47/93.68 thf(18533,plain,((! [A:nat,B:nat]: ((semiri681578069525770553at_rat @ (plus_plus_nat @ A @ B)) = (plus_plus_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3276])). 185.47/93.68 thf(2539,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ B @ C) => (ord_less_rat @ A @ C)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4207_order_Ostrict__trans1)). 185.47/93.68 thf(16153,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ B @ C) => (ord_less_rat @ A @ C)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2539])). 185.47/93.68 thf(2155,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => ((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6190_div__eq__minus1)). 185.47/93.68 thf(14916,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => ((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2155])). 185.47/93.68 thf(3879,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) <= (ord_less_eq_rat @ B @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2421_divide__nonpos__nonpos)). 185.47/93.68 thf(20453,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) | ~ (ord_less_eq_rat @ B @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3879])). 185.47/93.68 thf(2425,axiom,((! [A:(nat > int),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_int @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_eq_int @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_lift__Suc__mono__le)). 185.47/93.68 thf(15754,plain,((! [A:(nat > int),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_int @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_eq_int @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2425])). 185.47/93.68 thf(4461,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (groups3542108847815614940at_nat @ (^ [D:nat]: (A @ (minus_minus_nat @ (plus_plus_nat @ C @ B) @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6625_sum_OatLeastAtMost__rev)). 185.47/93.68 thf(22280,plain,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (groups3542108847815614940at_nat @ (^ [D:nat]: (A @ (minus_minus_nat @ (plus_plus_nat @ C @ B) @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4461])). 185.47/93.68 thf(7730,axiom,((! [A:rat]: ((power_power_rat @ (uminus_uminus_rat @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5400_power2__minus)). 185.47/93.68 thf(33923,plain,((! [A:rat]: ((power_power_rat @ (uminus_uminus_rat @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7730])). 185.47/93.68 thf(4727,axiom,((! [A:int]: (((divide_divide_int @ (plus_plus_int @ A @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (plus_plus_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)) <= (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4552_odd__succ__div__two)). 185.47/93.68 thf(23160,plain,((! [A:int]: (((divide_divide_int @ (plus_plus_int @ A @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (plus_plus_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4727])). 185.47/93.68 thf(2602,axiom,((! [A:nat]: (((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ (^ [B:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri5074537144036343181t_real @ (binomial @ A @ B)) @ zero_zero_real)) @ (set_ord_atMost_nat @ A))) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8624_choose__even__sum)). 185.47/93.68 thf(16369,plain,((! [A:nat]: (((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (groups6591440286371151544t_real @ (^ [B:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri5074537144036343181t_real @ (binomial @ A @ B)) @ zero_zero_real)) @ (set_ord_atMost_nat @ A))) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2602])). 185.47/93.68 thf(1593,axiom,((! [A:int,B:num,C:nat]: ((ord_less_eq_nat @ (nat2 @ A) @ (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9265_nat__le__numeral__power__cancel__iff)). 185.47/93.68 thf(13012,plain,((! [A:int,B:num,C:nat]: ((ord_less_eq_nat @ (nat2 @ A) @ (power_power_nat @ (numeral_numeral_nat @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1593])). 185.47/93.68 thf(7693,axiom,((~ (! [A:nat]: ((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) != (some_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062pr_O_Avebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_A_061_ASome_Apr_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 185.47/93.68 thf(33821,plain,((~ (! [A:nat]: ~ ((vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) = (some_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7693])). 185.47/93.68 thf(2899,axiom,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ B) => (((divide1717551699836669952omplex @ B @ A) = zero_zero_complex) = (B = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4724_dvd__div__eq__0__iff)). 185.47/93.68 thf(17352,plain,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ B) => (((divide1717551699836669952omplex @ B @ A) = zero_zero_complex) = (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2899])). 185.47/93.68 thf(395,axiom,((! [A:(nat > real),B:nat,C:(nat > real)]: ((summable_real @ A) => ((! [D:nat]: ((ord_less_eq_nat @ B @ D) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (C @ D)) @ (A @ D)))) => (summable_real @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7655_summable__comparison__test_H)). 185.47/93.68 thf(9046,plain,((! [A:(nat > real),B:nat,C:(nat > real)]: ((summable_real @ (A)) => ((! [D:nat]: ((ord_less_eq_nat @ B @ D) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (C @ D)) @ (A @ D)))) => (summable_real @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])). 185.47/93.68 thf(6374,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ A @ (times_times_nat @ (semiri1316708129612266289at_nat @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_nat @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ C) @ one_one_nat) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (times_times_nat @ (semiri1316708129612266289at_nat @ C) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7342_double__arith__series)). 185.47/93.68 thf(29196,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (groups3542108847815614940at_nat @ (^ [D:nat]: (plus_plus_nat @ A @ (times_times_nat @ (semiri1316708129612266289at_nat @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_times_nat @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ C) @ one_one_nat) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (times_times_nat @ (semiri1316708129612266289at_nat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6374])). 185.47/93.68 thf(4360,axiom,((! [A:int,B:int,C:int]: ((A = (minus_minus_int @ B @ C)) = ((plus_plus_int @ A @ C) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_723_eq__diff__eq)). 185.47/93.68 thf(21968,plain,((! [A:int,B:int,C:int]: ((A = (minus_minus_int @ B @ C)) = ((plus_plus_int @ A @ C) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4360])). 185.47/93.68 thf(6632,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_add__le__mono)). 185.47/93.68 thf(30109,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6632])). 185.47/93.68 thf(4771,axiom,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A)) @ A)) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7636_of__int__round__abs__le)). 185.47/93.68 thf(23334,plain,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (ring_1_of_int_real @ (archim8280529875227126926d_real @ A)) @ A)) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4771])). 185.47/93.68 thf(7038,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_3853_order__class_Oorder__eq__iff)). 185.47/93.68 thf(31704,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)],[7038])). 185.47/93.68 thf(4338,axiom,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (powr_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9088_powr__ge__pzero)). 185.47/93.68 thf(21895,plain,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (powr_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4338])). 185.47/93.68 thf(749,axiom,((! [A:real,B:real,C:real]: ((((ord_less_eq_real @ C @ (log @ A @ B)) = (ord_less_eq_real @ (powr_real @ A @ C) @ B)) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9121_le__log__iff)). 185.47/93.68 thf(10241,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ C @ (log @ A @ B)) = (ord_less_eq_real @ (powr_real @ A @ C) @ B)) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[749])). 185.47/93.68 thf(494,axiom,((! [A:num,B:nat,C:int]: (((power_power_int @ (numeral_numeral_int @ A) @ B) = (ring_1_of_int_int @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7105_numeral__power__eq__of__int__cancel__iff)). 185.47/93.68 thf(9395,plain,((! [A:num,B:nat,C:int]: (((power_power_int @ (numeral_numeral_int @ A) @ B) = (ring_1_of_int_int @ C)) = ((power_power_int @ (numeral_numeral_int @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[494])). 185.47/93.68 thf(4315,axiom,((! [A:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7450_norm__le__zero__iff)). 185.47/93.68 thf(21786,plain,((! [A:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4315])). 185.47/93.68 thf(882,axiom,((! [A:num,B:num]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (ord_less_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5374_neg__numeral__less__iff)). 185.47/93.68 thf(10744,plain,((! [A:num,B:num]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (ord_less_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[882])). 185.47/93.68 thf(5860,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1041_le__SucI)). 185.47/93.68 thf(27402,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5860])). 185.47/93.68 thf(7492,axiom,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ (suc @ B)) = (bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9413_bit__minus__numeral__Bit0__Suc__iff)). 185.47/93.68 thf(33261,plain,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ (suc @ B)) = (bit_se1146084159140164899it_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7492])). 185.47/93.68 thf(4638,axiom,((! [A:nat,B:int]: (ord_less_eq_int @ zero_zero_int @ (bit_se2923211474154528505it_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9278_take__bit__nonnegative)). 185.47/93.68 thf(22862,plain,((! [A:nat,B:int]: (ord_less_eq_int @ zero_zero_int @ (bit_se2923211474154528505it_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4638])). 185.47/93.68 thf(2618,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4012_dual__order_Oirrefl)). 185.47/93.68 thf(16418,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2618])). 185.47/93.68 thf(1965,axiom,((! [A:complex]: (((A != zero_zero_complex) => ((divide1717551699836669952omplex @ A @ A) = one_one_complex)) & ((A = zero_zero_complex) => ((divide1717551699836669952omplex @ A @ A) = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1729_divide__self__if)). 185.47/93.68 thf(14306,plain,((! [A:complex]: (((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ A @ A) = one_one_complex)) & ((A = zero_zero_complex) => ((divide1717551699836669952omplex @ A @ A) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1965])). 185.47/93.68 thf(6499,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ one_one_nat @ C) => (ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_power__strict__increasing)). 185.47/93.68 thf(29660,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ one_one_nat @ C) => (ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6499])). 185.47/93.68 thf(363,axiom,((! [A:rat,B:rat]: ((if_rat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Rat__Orat_T)). 185.47/93.68 thf(8946,plain,((! [A:rat,B:rat]: ((if_rat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[363])). 185.47/93.68 thf(2199,axiom,((! [A:int]: (((divide_divide_int @ A @ A) = one_one_int) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1720_div__self)). 185.47/93.68 thf(15056,plain,((! [A:int]: (((divide_divide_int @ A @ A) = one_one_int) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2199])). 185.47/93.68 thf(5584,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) @ (plus_plus_nat @ A @ C)) @ (binomial @ (plus_plus_nat @ A @ C) @ C)) = (times_times_nat @ (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) @ C) @ (binomial @ (plus_plus_nat @ A @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8432_choose__mult__lemma)). 185.47/93.68 thf(26313,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) @ (plus_plus_nat @ A @ C)) @ (binomial @ (plus_plus_nat @ A @ C) @ C)) = (times_times_nat @ (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) @ C) @ (binomial @ (plus_plus_nat @ A @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5584])). 185.47/93.68 thf(4682,axiom,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1506_add_Oright__neutral)). 185.47/93.68 thf(23007,plain,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4682])). 185.47/93.68 thf(990,axiom,((! [A:rat,B:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ A) @ B) = (minus_minus_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5210_uminus__add__conv__diff)). 185.47/93.68 thf(11123,plain,((! [A:rat,B:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ A) @ B) = (minus_minus_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[990])). 185.47/93.68 thf(7476,axiom,((! [A:num,B:num]: (((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (modulo_modulo_int @ (numeral_numeral_int @ one) @ (numeral_numeral_int @ (bit0 @ B)))) = ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6699_cong__exp__iff__simps_I11_J)). 185.47/93.68 thf(33198,plain,((! [A:num,B:num]: (((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (modulo_modulo_int @ (numeral_numeral_int @ one) @ (numeral_numeral_int @ (bit0 @ B)))) = ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7476])). 185.47/93.68 thf(5339,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1589_bot__nat__0_Onot__eq__extremum)). 185.47/93.68 thf(25373,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5339])). 185.47/93.68 thf(1564,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ C @ B) <= (ord_less_eq_rat @ C @ A)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4247_dual__order_Ostrict__trans2)). 185.47/93.68 thf(12912,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ C @ B) | ~ (ord_less_eq_rat @ C @ A) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564])). 185.47/93.68 thf(7245,axiom,((times_times_int = (^ [A:int,B:int]: (times_times_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_mult_Ocommute)). 185.47/93.68 thf(32416,plain,(((times_times_int) = (^ [A:int,B:int]: (times_times_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7245])). 185.47/93.68 thf(2082,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7492_norm__triangle__ineq)). 185.47/93.68 thf(14678,plain,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2082])). 185.47/93.68 thf(5904,axiom,((! [A:nat,B:num,C:num,D:nat]: ((times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ B)) @ (times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_power__add__numeral2)). 185.47/93.68 thf(27552,plain,((! [A:nat,B:num,C:num,D:nat]: ((times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ B)) @ (times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ C)) @ D)) = (times_times_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C))) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5904])). 185.47/93.68 thf(2580,axiom,((! [A:real,B:real,C:(real > (real > $o))]: ((ord_less_eq_real @ A @ B) => ((! [D:real,E:real,F:real]: (((C @ E @ F) => ((ord_less_eq_real @ D @ E) => ((ord_less_eq_real @ E @ F) => (C @ D @ F)))) <= (C @ D @ E))) => ((C @ A @ B) <= (! [D:real]: ((ord_less_eq_real @ A @ D) => ((ord_less_eq_real @ D @ B) => (? [E:real]: (! [F:real,G:real]: ((C @ F @ G) <= ((ord_less_eq_real @ D @ G) & (ord_less_real @ (minus_minus_real @ G @ F) @ E) & (ord_less_eq_real @ F @ D))) & (ord_less_real @ zero_zero_real @ E))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3339_Bolzano)). 185.47/93.68 thf(16277,plain,((! [A:real,B:real,C:(real > (real > $o))]: ((ord_less_eq_real @ A @ B) => ((! [D:real,E:real,F:real]: (((C @ E @ F) => ((ord_less_eq_real @ D @ E) => ((ord_less_eq_real @ E @ F) => (C @ D @ F)))) | ~ (C @ D @ E))) => ((C @ A @ B) | ~ (! [D:real]: ((ord_less_eq_real @ A @ D) => ((ord_less_eq_real @ D @ B) => (? [E:real]: (! [F:real,G:real]: ((C @ F @ G) | ~ ((ord_less_eq_real @ D @ G) & (ord_less_real @ (minus_minus_real @ G @ F) @ E) & (ord_less_eq_real @ F @ D))) & (ord_less_real @ zero_zero_real @ E))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2580])). 185.47/93.68 thf(2788,axiom,((! [A:num,B:num,C:int]: ((plus_plus_int @ (numeral_numeral_int @ A) @ (plus_plus_int @ (numeral_numeral_int @ B) @ C)) = (plus_plus_int @ (numeral_numeral_int @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add__numeral__left)). 185.47/93.68 thf(16988,plain,((! [A:num,B:num,C:int]: ((plus_plus_int @ (numeral_numeral_int @ A) @ (plus_plus_int @ (numeral_numeral_int @ B) @ C)) = (plus_plus_int @ (numeral_numeral_int @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2788])). 185.47/93.68 thf(4904,axiom,((! [A:complex]: ((times_times_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) = one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8194_exp__minus__inverse)). 185.47/93.68 thf(23774,plain,((! [A:complex]: ((times_times_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4904])). 185.47/93.68 thf(7350,axiom,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) != zero_zero_nat) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1909_not__mod__2__eq__0__eq__1)). 185.47/93.68 thf(32769,plain,((! [A:nat]: ((~ ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7350])). 185.47/93.68 thf(6954,axiom,((! [A:num,B:nat]: (((modulo_modulo_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ A) @ B)) @ (numeral_numeral_nat @ A)) = one_one_nat) <= ((numeral_numeral_nat @ A) != one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1884_Suc__times__numeral__mod__eq)). 185.47/93.68 thf(31316,plain,((! [A:num,B:nat]: (((modulo_modulo_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ A) @ B)) @ (numeral_numeral_nat @ A)) = one_one_nat) | ((numeral_numeral_nat @ A) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6954])). 185.47/93.68 thf(7602,axiom,(((numeral_numeral_nat @ one) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_846_numerals_I1_J)). 185.47/93.68 thf(33578,plain,(((numeral_numeral_nat @ one) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7602])). 185.47/93.68 thf(5311,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_789_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2)). 185.47/93.68 thf(25278,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5311])). 185.47/93.68 thf(3020,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ one_one_real @ A) => (ord_less_eq_real @ one_one_real @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_one__le__power)). 185.47/93.68 thf(17733,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ one_one_real @ A) => (ord_less_eq_real @ one_one_real @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3020])). 185.47/93.68 thf(3839,axiom,((! [A:nat,B:real]: ((ord_less_eq_real @ (plus_plus_real @ one_one_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ B)) @ (power_power_real @ (plus_plus_real @ one_one_real @ B) @ A)) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7338_Bernoulli__inequality__even)). 185.47/93.68 thf(20321,plain,((! [A:nat,B:real]: ((ord_less_eq_real @ (plus_plus_real @ one_one_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ B)) @ (power_power_real @ (plus_plus_real @ one_one_real @ B) @ A)) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3839])). 185.47/93.68 thf(3659,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ (times_times_int @ C @ A)) = (dvd_dvd_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4746_dvd__mult__unit__iff)). 185.47/93.68 thf(19746,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ (times_times_int @ C @ A)) = (dvd_dvd_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3659])). 185.47/93.68 thf(2129,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3977_less__imp__neq)). 185.47/93.68 thf(14819,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2129])). 185.47/93.68 thf(3443,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ A @ B) => (((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) <= (ord_less_eq_real @ zero_zero_real @ C))) <= (ord_less_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2590_mult__strict__mono_H)). 185.47/93.68 thf(19060,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ A @ B) => (((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) | ~ (ord_less_eq_real @ zero_zero_real @ C))) | ~ (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3443])). 185.47/93.68 thf(2530,axiom,((! [A:(int > $o),B:int,C:int]: ((A @ (modulo_modulo_int @ B @ C)) = (((C = zero_zero_int) => (A @ B)) & ((! [D:int,E:int]: ((A @ E) <= ((ord_less_eq_int @ E @ zero_zero_int) & (B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_int @ C @ E)))) <= (ord_less_int @ C @ zero_zero_int)) & ((ord_less_int @ zero_zero_int @ C) => (! [D:int,E:int]: ((A @ E) <= ((B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_int @ E @ C) & (ord_less_eq_int @ zero_zero_int @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3175_split__zmod)). 185.47/93.68 thf(16121,plain,((! [A:(int > $o),B:int,C:int]: ((A @ (modulo_modulo_int @ B @ C)) = (((C = zero_zero_int) => (A @ B)) & (! [D:int,E:int]: ((A @ E) | ~ ((ord_less_eq_int @ E @ zero_zero_int) & (B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_int @ C @ E))) | ~ (ord_less_int @ C @ zero_zero_int)) & ((ord_less_int @ zero_zero_int @ C) => (! [D:int,E:int]: ((A @ E) | ~ ((B = (plus_plus_int @ (times_times_int @ C @ D) @ E)) & (ord_less_int @ E @ C) & (ord_less_eq_int @ zero_zero_int @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2530])). 185.47/93.68 thf(5922,axiom,((! [A:num]: (zero_zero_int != (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5698_zero__neq__neg__numeral)). 185.47/93.68 thf(27606,plain,((! [A:num]: ~ (zero_zero_int = (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5922])). 185.47/93.68 thf(1810,axiom,((! [A:complex,B:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (plus_plus_real @ (real_V1022390504157884413omplex @ B) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7507_norm__triangle__sub)). 185.47/93.68 thf(13797,plain,((! [A:complex,B:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (plus_plus_real @ (real_V1022390504157884413omplex @ B) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1810])). 185.47/93.68 thf(4124,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ B) @ B) = (modulo_modulo_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1595_mod__add__self2)). 185.47/93.68 thf(21212,plain,((! [A:int,B:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ B) @ B) = (modulo_modulo_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4124])). 185.47/93.68 thf(6834,axiom,((! [A:num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ one_one_real)) = (A != one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5389_neg__numeral__less__neg__one__iff)). 185.47/93.68 thf(30850,plain,((! [A:num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ one_one_real)) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6834])). 185.47/93.68 thf(3066,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = one_one_real) = ((B != zero_zero_real) & (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1739_divide__eq__1__iff)). 185.47/93.68 thf(17881,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = one_one_real) = (~ (B = zero_zero_real) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3066])). 185.47/93.68 thf(6390,axiom,((! [A:int,B:nat]: (((ord_less_eq_int @ A @ (power_power_int @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_eq_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2897_self__le__power)). 185.47/93.68 thf(29246,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ A @ (power_power_int @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6390])). 185.47/93.68 thf(3759,axiom,((! [A:int,B:int]: ((plus_plus_int @ (times_times_int @ (divide_divide_int @ A @ B) @ B) @ (modulo_modulo_int @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2539_div__mult__mod__eq)). 185.47/93.68 thf(20067,plain,((! [A:int,B:int]: ((plus_plus_int @ (times_times_int @ (divide_divide_int @ A @ B) @ B) @ (modulo_modulo_int @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3759])). 185.47/93.68 thf(2071,axiom,((! [A:int,B:code_integer]: ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ (ring_18347121197199848620nteger @ A)) @ B) => ((ord_le3102999989581377725nteger @ one_one_Code_integer @ B) | (A = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7281_of__int__leD)). 185.47/93.68 thf(14641,plain,((! [A:int,B:code_integer]: ((ord_le3102999989581377725nteger @ (abs_abs_Code_integer @ (ring_18347121197199848620nteger @ A)) @ B) => ((ord_le3102999989581377725nteger @ one_one_Code_integer @ B) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2071])). 185.47/93.68 thf(899,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B)))) = (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7647_summable__iff__shift)). 185.47/93.68 thf(10806,plain,((! [A:(nat > real),B:nat]: ((summable_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B)))) = (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[899])). 185.47/93.68 thf(669,axiom,((! [A:nat,B:nat,C:(nat > rat)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups73079841787564623at_rat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_rat @ (groups73079841787564623at_rat @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & (((groups73079841787564623at_rat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_rat) <= (ord_less_nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8706_prod_Ocl__ivl__Suc)). 185.47/93.68 thf(9966,plain,((! [A:nat,B:nat,C:(nat > rat)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups73079841787564623at_rat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_rat @ (groups73079841787564623at_rat @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & (((groups73079841787564623at_rat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_rat) | ~ (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[669])). 185.47/93.68 thf(2213,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ (divide_divide_rat @ C @ B)) = (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ A @ C)) & ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2652_divide__le__cancel)). 185.47/93.68 thf(15099,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ (divide_divide_rat @ C @ B)) = (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ A @ C)) & ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2213])). 185.47/93.68 thf(1648,axiom,((! [A:real,B:int]: ((((~ (ord_less_eq_int @ zero_zero_int @ B)) => ((powr_real @ A @ (ring_1_of_int_real @ B)) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ (nat2 @ (uminus_uminus_int @ B)))))) & (((powr_real @ A @ (ring_1_of_int_real @ B)) = (power_power_real @ A @ (nat2 @ B))) <= (ord_less_eq_int @ zero_zero_int @ B))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9243_powr__int)). 185.47/93.68 thf(13211,plain,((! [A:real,B:int]: ((((~ (ord_less_eq_int @ zero_zero_int @ B)) => ((powr_real @ A @ (ring_1_of_int_real @ B)) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ (nat2 @ (uminus_uminus_int @ B)))))) & (((powr_real @ A @ (ring_1_of_int_real @ B)) = (power_power_real @ A @ (nat2 @ B))) | ~ (ord_less_eq_int @ zero_zero_int @ B))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648])). 185.47/93.68 thf(6074,axiom,((! [A:nat,B:nat]: (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A) | (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3084_verit__la__disequality)). 185.47/93.68 thf(28119,plain,((! [A:nat,B:nat]: (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6074])). 185.47/93.68 thf(4866,axiom,((! [A:real]: ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1804_divide__le__0__1__iff)). 185.47/93.68 thf(23627,plain,((! [A:real]: ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4866])). 185.47/93.68 thf(4516,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ (plus_plus_int @ C @ B)) = (dvd_dvd_int @ A @ C)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4650_dvd__add__left__iff)). 185.47/93.68 thf(22469,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ (plus_plus_int @ C @ B)) = (dvd_dvd_int @ A @ C)) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4516])). 185.47/93.68 thf(7677,axiom,((! [A:num]: ((times_times_num @ (bit0 @ one) @ A) = (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_num__double)). 185.47/93.68 thf(33780,plain,((! [A:num]: ((times_times_num @ (bit0 @ one) @ A) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7677])). 185.47/93.68 thf(802,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ (ln_ln_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5876_ln__bound)). 185.47/93.68 thf(10464,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ (ln_ln_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[802])). 185.47/93.68 thf(2831,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = zero_zero_complex) = ((A = zero_zero_complex) | (B = zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1583_divide__eq__0__iff)). 185.47/93.68 thf(17127,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = zero_zero_complex) = ((A = zero_zero_complex) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2831])). 185.47/93.68 thf(3527,axiom,((! [A:$o]: (ord_less_eq_int @ (zero_n2684676970156552555ol_int @ A) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5669_of__bool__less__eq__one)). 185.47/93.68 thf(19336,plain,((! [A:$o]: (ord_less_eq_int @ (zero_n2684676970156552555ol_int @ A) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3527])). 185.47/93.68 thf(6861,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (suc @ B) @ A) = (suc @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1101_Suc__diff__le)). 185.47/93.68 thf(30990,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (suc @ B) @ A) = (suc @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6861])). 185.47/93.68 thf(3358,axiom,((! [A:num,B:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5707_not__numeral__less__neg__numeral)). 185.47/93.68 thf(18797,plain,((! [A:num,B:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3358])). 185.47/93.68 thf(409,axiom,((! [A:real]: ((sin_real @ (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ A)) = (uminus_uminus_real @ (sin_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7811_sin__2pi__minus)). 185.47/93.68 thf(9092,plain,((! [A:real]: ((sin_real @ (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ A)) = (uminus_uminus_real @ (sin_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[409])). 185.47/93.68 thf(3975,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => (((plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) @ one_one_int) = (divide_divide_int @ A @ B)) <= (ord_less_eq_int @ B @ (modulo_modulo_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2802_divmod__digit__1_I1_J)). 185.47/93.68 thf(20764,plain,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => (((plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) @ one_one_int) = (divide_divide_int @ A @ B)) | ~ (ord_less_eq_int @ B @ (modulo_modulo_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3975])). 185.47/93.68 thf(5635,axiom,(((neg_numeral_dbl_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5456_dbl__simps_I4_J)). 185.47/93.68 thf(26484,plain,(((neg_numeral_dbl_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5635])). 185.47/93.68 thf(3919,axiom,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (minus_minus_real @ (uminus_uminus_real @ A) @ B)) = (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7474_norm__uminus__minus)). 185.47/93.68 thf(20587,plain,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (minus_minus_real @ (uminus_uminus_real @ A) @ B)) = (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3919])). 185.47/93.68 thf(4302,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_real @ A @ B) = (ord_less_real @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_703_diff__eq__diff__less)). 185.47/93.68 thf(21749,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_real @ A @ B) = (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4302])). 185.47/93.68 thf(2084,axiom,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1569_div__0)). 185.47/93.68 thf(14683,plain,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2084])). 185.47/93.68 thf(7119,axiom,((! [A:nat]: ((binomial @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8427_choose__one)). 185.47/93.68 thf(31957,plain,((! [A:nat]: ((binomial @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7119])). 185.47/93.68 thf(1490,axiom,((! [A:int,B:int,C:int]: (((B = (divide_divide_int @ C @ A)) = ((times_times_int @ B @ A) = C)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4860_unit__eq__div2)). 185.47/93.68 thf(12690,plain,((! [A:int,B:int,C:int]: (((B = (divide_divide_int @ C @ A)) = ((times_times_int @ B @ A) = C)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490])). 185.47/93.68 thf(4021,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6914_of__nat__mult)). 185.47/93.68 thf(20906,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4021])). 185.47/93.68 thf(5634,axiom,((one_one_int = (abs_Integ @ (product_Pair_nat_nat @ one_one_nat @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9819_one__int__def)). 185.47/93.68 thf(26482,plain,((one_one_int = (abs_Integ @ (product_Pair_nat_nat @ one_one_nat @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5634])). 185.47/93.68 thf(6927,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ (modulo_modulo_nat @ A @ B)) @ C) = (plus_plus_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2544_cancel__div__mod__rules_I1_J)). 185.47/93.68 thf(31223,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ (modulo_modulo_nat @ A @ B)) @ C) = (plus_plus_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6927])). 185.47/93.68 thf(3622,axiom,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = (bit_se2000444600071755411sk_int @ A)) = ((bit_se2923211474154528505it_int @ A @ (plus_plus_int @ B @ one_one_int)) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9290_take__bit__eq__mask__iff)). 185.47/93.68 thf(19624,plain,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = (bit_se2000444600071755411sk_int @ A)) = ((bit_se2923211474154528505it_int @ A @ (plus_plus_int @ B @ one_one_int)) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3622])). 185.47/93.68 thf(610,axiom,((! [A:real]: (ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ (plus_plus_real @ (exp_real @ A) @ (inverse_inverse_real @ (exp_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8974_exp__plus__inverse__exp)). 185.47/93.68 thf(9760,plain,((! [A:real]: (ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ (plus_plus_real @ (exp_real @ A) @ (inverse_inverse_real @ (exp_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[610])). 185.47/93.68 thf(4509,axiom,((! [A:nat,B:nat]: (ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7329_real__of__nat__div2)). 185.47/93.68 thf(22440,plain,((! [A:nat,B:nat]: (ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4509])). 185.47/93.68 thf(4343,axiom,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ B @ (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_add_Oleft__commute)). 185.47/93.68 thf(21910,plain,((! [A:real,B:real,C:real]: ((plus_plus_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ B @ (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4343])). 185.47/93.68 thf(3523,axiom,((! [A:int,B:int]: ((ring_1_of_int_real @ (times_times_int @ A @ B)) = (times_times_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6970_of__int__mult)). 185.47/93.68 thf(19324,plain,((! [A:int,B:int]: ((ring_1_of_int_real @ (times_times_int @ A @ B)) = (times_times_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3523])). 185.47/93.68 thf(4761,axiom,((! [A:num,B:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (divide_divide_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1474_zdiv__numeral__Bit0)). 185.47/93.68 thf(23302,plain,((! [A:num,B:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (divide_divide_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4761])). 185.47/93.68 thf(3493,axiom,((! [A:int,B:int,C:int,D:int]: ((A != zero_zero_int) => ((B != zero_zero_int) => ((ord_less_eq_rat @ (fract @ C @ A) @ (fract @ D @ B)) = (ord_less_eq_int @ (times_times_int @ (times_times_int @ C @ B) @ (times_times_int @ A @ B)) @ (times_times_int @ (times_times_int @ D @ A) @ (times_times_int @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9933_le__rat)). 185.47/93.68 thf(19229,plain,((! [A:int,B:int,C:int,D:int]: ((~ (A = zero_zero_int)) => ((~ (B = zero_zero_int)) => ((ord_less_eq_rat @ (fract @ C @ A) @ (fract @ D @ B)) = (ord_less_eq_int @ (times_times_int @ (times_times_int @ C @ B) @ (times_times_int @ A @ B)) @ (times_times_int @ (times_times_int @ D @ A) @ (times_times_int @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3493])). 185.47/93.68 thf(3236,axiom,((! [A:num]: ~ (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5904_not__zero__less__neg__numeral)). 185.47/93.68 thf(18413,plain,((! [A:num]: ~ (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3236])). 185.47/93.68 thf(3662,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2307_add__decreasing)). 185.47/93.68 thf(19756,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3662])). 185.47/93.68 thf(6208,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ C) @ (A @ B))) <= (! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1082_lift__Suc__antimono__le)). 185.47/93.68 thf(28626,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ C) @ (A @ B))) | ~ (! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6208])). 185.47/93.68 thf(1275,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ one_one_rat @ (divide_divide_rat @ B @ A)) = (ord_less_eq_rat @ B @ A)) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1860_le__divide__eq__1__neg)). 185.47/93.68 thf(11995,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ one_one_rat @ (divide_divide_rat @ B @ A)) = (ord_less_eq_rat @ B @ A)) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275])). 185.47/93.68 thf(2829,axiom,((! [A:nat,B:int]: (ord_less_int @ (bit_se2923211474154528505it_int @ A @ B) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9330_take__bit__int__less__exp)). 185.47/93.68 thf(17121,plain,((! [A:nat,B:int]: (ord_less_int @ (bit_se2923211474154528505it_int @ A @ B) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2829])). 185.47/93.68 thf(3567,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ B)) & ((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ B @ (times_times_real @ A @ C))) & ((ord_less_real @ A @ zero_zero_real) <= (~ (ord_less_real @ C @ zero_zero_real))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2697_less__divide__eq)). 185.47/93.68 thf(19456,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ B)) & ((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ B @ (times_times_real @ A @ C))) & ((ord_less_real @ A @ zero_zero_real) | (ord_less_real @ C @ zero_zero_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3567])). 185.47/93.68 thf(492,axiom,((! [A:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (uminus_uminus_real @ pi) @ A) => ((arccos @ (cos_real @ A)) = (uminus_uminus_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8375_arccos__cos2)). 185.47/93.68 thf(9389,plain,((! [A:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (uminus_uminus_real @ pi) @ A) => ((arccos @ (cos_real @ A)) = (uminus_uminus_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[492])). 185.47/93.68 thf(4743,axiom,((! [A:nat,B:nat]: ((ord_less_eq_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8002_fact__mono)). 185.47/93.68 thf(23210,plain,((! [A:nat,B:nat]: ((ord_less_eq_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4743])). 185.47/93.68 thf(6256,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A)) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6630_numeral__code_I3_J)). 185.47/93.68 thf(28782,plain,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (plus_plus_nat @ (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A)) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6256])). 185.47/93.68 thf(5476,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_749_eq__diff__iff)). 185.47/93.68 thf(25959,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5476])). 185.47/93.68 thf(3404,axiom,((! [A:num]: ~ (ord_less_eq_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5942_not__one__le__neg__numeral)). 185.47/93.68 thf(18943,plain,((! [A:num]: ~ (ord_less_eq_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3404])). 185.47/93.68 thf(6515,axiom,((! [A:int,B:nat]: ((abs_abs_int @ (power_power_int @ (uminus_uminus_int @ A) @ B)) = (abs_abs_int @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6384_abs__power__minus)). 185.47/93.68 thf(29720,plain,((! [A:int,B:nat]: ((abs_abs_int @ (power_power_int @ (uminus_uminus_int @ A) @ B)) = (abs_abs_int @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6515])). 185.47/93.68 thf(690,axiom,((! [A:complex,B:complex]: ((im @ (minus_minus_complex @ A @ B)) = (minus_minus_real @ (im @ A) @ (im @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9674_minus__complex_Osimps_I2_J)). 185.47/93.68 thf(10033,plain,((! [A:complex,B:complex]: ((im @ (minus_minus_complex @ A @ B)) = (minus_minus_real @ (im @ A) @ (im @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[690])). 185.47/93.68 thf(1553,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => (ord_less_eq_rat @ (minus_minus_rat @ A @ C) @ (minus_minus_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_diff__right__mono)). 185.47/93.68 thf(12883,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => (ord_less_eq_rat @ (minus_minus_rat @ A @ C) @ (minus_minus_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553])). 185.47/93.68 thf(4603,axiom,((! [A:real,B:real,C:num]: ((times_times_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ C)) = (plus_plus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_distrib__right__numeral)). 185.47/93.68 thf(22743,plain,((! [A:real,B:real,C:num]: ((times_times_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ C)) = (plus_plus_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ (times_times_real @ B @ (numeral_numeral_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4603])). 185.47/93.68 thf(1005,axiom,((semiri5044797733671781792omplex = (^ [A:nat]: (if_complex @ (A = zero_zero_nat) @ one_one_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8045_fact__num__eq__if)). 185.47/93.68 thf(11176,plain,(((semiri5044797733671781792omplex) = (^ [A:nat]: (if_complex @ (A = zero_zero_nat) @ one_one_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005])). 185.47/93.68 thf(4775,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (ord_max_nat @ A @ B)) = (ord_max_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7258_of__nat__max)). 185.47/93.68 thf(23343,plain,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (ord_max_nat @ A @ B)) = (ord_max_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4775])). 185.47/93.68 thf(6083,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ (times_times_nat @ C @ A))) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4479_dvd__add__times__triv__right__iff)). 185.47/93.68 thf(28145,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ (times_times_nat @ C @ A))) = (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6083])). 185.47/93.68 thf(7423,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ one_one_nat)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4541_even__plus__one__iff)). 185.47/93.68 thf(33020,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ one_one_nat)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7423])). 185.47/93.68 thf(4113,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1140_distrib__right)). 185.47/93.68 thf(21180,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4113])). 185.47/93.68 thf(2002,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ (modulo_modulo_int @ B @ A) @ zero_zero_int) & (ord_less_int @ A @ (modulo_modulo_int @ B @ A))) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3141_neg__mod__conj)). 185.47/93.68 thf(14425,plain,((! [A:int,B:int]: (((ord_less_eq_int @ (modulo_modulo_int @ B @ A) @ zero_zero_int) & (ord_less_int @ A @ (modulo_modulo_int @ B @ A))) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002])). 185.47/93.68 thf(6715,axiom,((! [A:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ one)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1945_cong__exp__iff__simps_I1_J)). 185.47/93.68 thf(30376,plain,((! [A:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ one)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6715])). 185.47/93.68 thf(4863,axiom,((minus_minus_nat = (^ [A:nat,B:nat]: (nat2 @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9302_nat__minus__as__int)). 185.47/93.68 thf(23614,plain,(((minus_minus_nat) = (^ [A:nat,B:nat]: (nat2 @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4863])). 185.47/93.68 thf(3701,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((comm_s4028243227959126397er_rat @ zero_zero_rat @ A) = one_one_rat)) & (((comm_s4028243227959126397er_rat @ zero_zero_rat @ A) = zero_zero_rat) <= (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8471_pochhammer__0__left)). 185.47/93.68 thf(19876,plain,((! [A:nat]: (((A = zero_zero_nat) => ((comm_s4028243227959126397er_rat @ zero_zero_rat @ A) = one_one_rat)) & (((comm_s4028243227959126397er_rat @ zero_zero_rat @ A) = zero_zero_rat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3701])). 185.47/93.68 thf(7225,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => ((minus_minus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (divide_divide_rat @ (minus_minus_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6170_minus__divide__diff__eq__iff)). 185.47/93.68 thf(32357,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => ((minus_minus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (divide_divide_rat @ (minus_minus_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7225])). 185.47/93.68 thf(6085,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (ord_less_eq_num @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3310_pinf_I8_J)). 185.47/93.68 thf(28151,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (ord_less_eq_num @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6085])). 185.47/93.68 thf(1679,axiom,((! [A:int,B:nat]: ((ord_less_int @ one_one_int @ (times_times_int @ A @ (power_power_int @ A @ B))) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_861_power__gt1__lemma)). 185.47/93.68 thf(13357,plain,((! [A:int,B:nat]: ((ord_less_int @ one_one_int @ (times_times_int @ A @ (power_power_int @ A @ B))) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679])). 185.47/93.68 thf(4337,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2443_divide__strict__right__mono__neg)). 185.47/93.68 thf(21892,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4337])). 185.47/93.68 thf(3981,axiom,((semiri1314217659103216013at_int = (^ [A:nat]: (if_int @ (A = zero_zero_nat) @ zero_zero_int @ (produc6840382203811409530at_int @ (^ [B:nat,C:nat]: (if_int @ (C = zero_zero_nat) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (semiri1314217659103216013at_int @ B)) @ (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (semiri1314217659103216013at_int @ B)) @ one_one_int))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7524_of__nat__code__if)). 185.47/93.68 thf(20782,plain,(((semiri1314217659103216013at_int) = (^ [A:nat]: (if_int @ (A = zero_zero_nat) @ zero_zero_int @ (produc6840382203811409530at_int @ (^ [B:nat,C:nat]: (if_int @ (C = zero_zero_nat) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (semiri1314217659103216013at_int @ B)) @ (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (semiri1314217659103216013at_int @ B)) @ one_one_int))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3981])). 185.47/93.68 thf(1472,axiom,((! [A:nat,B:nat,C:(nat > int)]: ((((groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_int) <= (ord_less_nat @ (suc @ A) @ B)) & (((groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_int @ (groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) <= (~ (ord_less_nat @ (suc @ A) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6431_sum_Ocl__ivl__Suc)). 185.47/93.68 thf(12633,plain,((! [A:nat,B:nat,C:(nat > int)]: ((((groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_int) | ~ (ord_less_nat @ (suc @ A) @ B)) & (((groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_int @ (groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) | (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472])). 185.47/93.68 thf(5379,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1484_mult__zero__left)). 185.47/93.68 thf(25536,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5379])). 185.47/93.68 thf(7194,axiom,((! [A:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_numeral__plus__one)). 185.47/93.68 thf(32232,plain,((! [A:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7194])). 185.47/93.68 thf(5149,axiom,((! [A:int,B:int]: ((power_power_int @ (plus_plus_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_power2__sum)). 185.47/93.68 thf(24714,plain,((! [A:int,B:int]: ((power_power_int @ (plus_plus_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5149])). 185.47/93.68 thf(5352,axiom,((! [A:nat,B:(real > real),C:filter_real]: ((ord_less_nat @ zero_zero_nat @ A) => ((filterlim_real_real @ B @ at_bot_real @ C) => ((filterlim_real_real @ (^ [D:real]: (power_power_real @ (B @ D) @ A)) @ at_bot_real @ C) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10139_filterlim__pow__at__bot__odd)). 185.47/93.68 thf(25453,plain,((! [A:nat,B:(real > real),C:filter_real]: ((ord_less_nat @ zero_zero_nat @ A) => ((filterlim_real_real @ (B) @ at_bot_real @ C) => ((filterlim_real_real @ (^ [D:real]: (power_power_real @ (B @ D) @ A)) @ at_bot_real @ C) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5352])). 185.47/93.68 thf(5848,axiom,((! [A:num]: (zero_zero_real != (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2036_zero__neq__numeral)). 185.47/93.68 thf(27358,plain,((! [A:num]: ~ (zero_zero_real = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5848])). 185.47/93.68 thf(1596,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ B @ (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = (ord_less_eq_rat @ (uminus_uminus_rat @ C) @ (times_times_rat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6211_neg__le__minus__divide__eq)). 185.47/93.68 thf(13021,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_eq_rat @ B @ (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = (ord_less_eq_rat @ (uminus_uminus_rat @ C) @ (times_times_rat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596])). 185.47/93.68 thf(5095,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((times_times_nat @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (binomial @ B @ A)) = (semiri1408675320244567234ct_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8487_binomial__fact__lemma)). 185.47/93.68 thf(24475,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((times_times_nat @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (binomial @ B @ A)) = (semiri1408675320244567234ct_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5095])). 185.47/93.68 thf(6959,axiom,((! [A:nat,B:nat]: (((bit_se2925701944663578781it_nat @ B @ A) = A) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9324_take__bit__nat__eq__self)). 185.47/93.68 thf(31375,plain,((! [A:nat,B:nat]: (((bit_se2925701944663578781it_nat @ B @ A) = A) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6959])). 185.47/93.68 thf(1169,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (power_power_nat @ A @ B)) = (power_power_int @ (semiri1314217659103216013at_int @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6958_of__nat__power)). 185.47/93.68 thf(11681,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (power_power_nat @ A @ B)) = (power_power_int @ (semiri1314217659103216013at_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169])). 185.47/93.68 thf(896,axiom,((! [A:vEBT_VEBT]: (((! [B:$o]: (A != (vEBT_Leaf @ ($true) @ B))) => ((! [B:$o]: (A != (vEBT_Leaf @ B @ ($true)))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E)))))) <= (~ (vEBT_VEBT_minNull @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2457_VEBT__internal_OminNull_Oelims_I3_J)). 185.47/93.68 thf(10796,plain,((! [A:vEBT_VEBT]: (((! [B:$o]: ~ (A = (vEBT_Leaf @ ($true) @ B))) => ((! [B:$o]: ~ (A = (vEBT_Leaf @ B @ ($true)))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E)))))) | (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[896])). 185.47/93.68 thf(2361,axiom,((! [A:int,B:int,C:int,D:int]: (((C != D) & (A != B)) = ((plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) != (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6292_crossproduct__noteq)). 185.47/93.68 thf(15548,plain,((! [A:int,B:int,C:int,D:int]: ((~ (C = D) & ~ (A = B)) = (~ ((plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) = (plus_plus_int @ (times_times_int @ A @ D) @ (times_times_int @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2361])). 185.47/93.68 thf(7127,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((modulo_modulo_nat @ B @ (times_times_nat @ C @ A)) = (plus_plus_nat @ (times_times_nat @ C @ (modulo_modulo_nat @ (divide_divide_nat @ B @ C) @ A)) @ (modulo_modulo_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2135_unique__euclidean__semiring__numeral__class_Omod__mult2__eq)). 185.47/93.68 thf(31984,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((modulo_modulo_nat @ B @ (times_times_nat @ C @ A)) = (plus_plus_nat @ (times_times_nat @ C @ (modulo_modulo_nat @ (divide_divide_nat @ B @ C) @ A)) @ (modulo_modulo_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7127])). 185.47/93.68 thf(7074,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) <= (ord_less_nat @ A @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_747_diff__less__mono2)). 185.47/93.68 thf(31817,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) | ~ (ord_less_nat @ A @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7074])). 185.47/93.68 thf(5213,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9453_xor__nat__numerals_I2_J)). 185.47/93.68 thf(24913,plain,((! [A:num]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5213])). 185.47/93.68 thf(5708,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ C) <= (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4598_dvd__mult__left)). 185.47/93.68 thf(26720,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ C) | ~ (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5708])). 185.47/93.68 thf(367,axiom,((! [A:complex]: ((A != zero_zero_complex) = (ord_less_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9697_complex__neq__0)). 185.47/93.68 thf(8957,plain,((! [A:complex]: ((~ (A = zero_zero_complex)) = (ord_less_real @ zero_zero_real @ (plus_plus_real @ (power_power_real @ (re @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (im @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])). 185.47/93.68 thf(2150,axiom,((! [A:int,B:int,C:int,D:int]: ((((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)))) <= (ord_less_int @ C @ D)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2582_mult__strict__mono)). 185.47/93.68 thf(14896,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)))) | ~ (ord_less_int @ C @ D) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2150])). 185.47/93.68 thf(2619,axiom,((! [A:rat,B:rat,C:rat]: ((A = C) <= ((plus_plus_rat @ A @ B) = (plus_plus_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_add__right__imp__eq)). 185.47/93.68 thf(16421,plain,((! [A:rat,B:rat,C:rat]: ((A = C) | ~ ((plus_plus_rat @ A @ B) = (plus_plus_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2619])). 185.47/93.68 thf(6957,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_VEBT_membermima @ A @ B) = C) => (((((! [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((C = ((B = E) | (B = D))) => (~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G) @ B)))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G)))) => ((~ (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ D) @ E @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ D) @ E @ F) @ B))) <= (C = (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)))))))) <= (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H) @ B))) <= (C = (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one))))))) | (B = E) | (B = D)))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H)))))) <= (! [D:list_VEBT_VEBT,E:vEBT_VEBT]: (((~ (C)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E) @ B)))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E))))) <= (! [D:$o,E:$o]: (((~ (C)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)))) <= (A = (vEBT_Leaf @ D @ E))))) <= (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3122_VEBT__internal_Omembermima_Opelims_I1_J)). 185.47/93.68 thf(31326,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_VEBT_membermima @ A @ B) = C) => (((! [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((C = ((B = E) | (B = D))) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G) @ B)))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G)))) => (~ (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ D) @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ D) @ E @ F) @ B)) | ~ (C = (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))))))) | ~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H) @ B)) | ~ (C = (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ F) @ (numeral_numeral_nat @ (bit0 @ one))))))) | (B = E) | (B = D))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H)))))) | ~ (! [D:list_VEBT_VEBT,E:vEBT_VEBT]: (((~ (C)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E) @ B)))) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E)))) | ~ (! [D:$o,E:$o]: (((~ (C)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)))) | ~ (A = (vEBT_Leaf @ D @ E)))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6957])). 185.47/93.68 thf(6198,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1787_add__gr__0)). 185.47/93.68 thf(28600,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6198])). 185.47/93.68 thf(3230,axiom,((! [A:int,B:nat,C:int]: ((ord_less_eq_real @ (power_power_real @ (ring_1_of_int_real @ A) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_eq_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7095_of__int__le__of__int__power__cancel__iff)). 185.47/93.68 thf(18398,plain,((! [A:int,B:nat,C:int]: ((ord_less_eq_real @ (power_power_real @ (ring_1_of_int_real @ A) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_eq_int @ (power_power_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3230])). 185.47/93.68 thf(7642,axiom,(((power_power_rat @ zero_zero_rat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2888_zero__power2)). 185.47/93.68 thf(33688,plain,(((power_power_rat @ zero_zero_rat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7642])). 185.47/93.68 thf(7265,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1527_add__cancel__right__left)). 185.47/93.68 thf(32481,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7265])). 185.47/93.68 thf(7698,axiom,((! [A:nat,B:nat]: ((((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => (A = B)) <= ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4922_div2__even__ext__nat)). 185.47/93.68 thf(33838,plain,((! [A:nat,B:nat]: ((((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => (A = B)) | ~ ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7698])). 185.47/93.68 thf(4177,axiom,((! [A:real,B:real]: (ord_less_eq_real @ A @ (sqrt @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8186_le__real__sqrt__sumsq)). 185.47/93.68 thf(21376,plain,((! [A:real,B:real]: (ord_less_eq_real @ A @ (sqrt @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4177])). 185.47/93.68 thf(2387,axiom,((! [A:nat,B:nat]: ((member_nat @ A @ (set_ord_atMost_nat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8636_atMost__iff)). 185.47/93.68 thf(15625,plain,((! [A:nat,B:nat]: ((member_nat @ A @ (set_ord_atMost_nat @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2387])). 185.47/93.68 thf(2838,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ zero_zero_int) => (ord_less_int @ (times_times_int @ C @ B) @ (times_times_int @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2355_mult__strict__left__mono__neg)). 185.47/93.68 thf(17155,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ zero_zero_int) => (ord_less_int @ (times_times_int @ C @ B) @ (times_times_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2838])). 185.47/93.68 thf(6151,axiom,(((numeral_numeral_nat @ (bit1 @ one)) = (suc @ (suc @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6671_numeral__3__eq__3)). 185.47/93.68 thf(28389,plain,(((numeral_numeral_nat @ (bit1 @ one)) = (suc @ (suc @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6151])). 185.47/93.68 thf(1423,axiom,((! [A:nat]: (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3437_finite__Collect__less__nat)). 185.47/93.68 thf(12484,plain,((! [A:nat]: (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1423])). 185.47/93.68 thf(4954,axiom,((! [A:num,B:(nat > num),C:nat,D:nat]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_num @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3915_order__subst1)). 185.47/93.68 thf(23952,plain,((! [A:num,B:(nat > num),C:nat,D:nat]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_num @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4954])). 185.47/93.68 thf(2786,axiom,((! [A:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5172_ab__left__minus)). 185.47/93.68 thf(16983,plain,((! [A:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2786])). 185.47/93.68 thf(1427,axiom,((! [A:real,B:real,C:real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3986_ord__eq__less__trans)). 185.47/93.68 thf(12495,plain,((! [A:real,B:real,C:real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427])). 185.47/93.68 thf(3971,axiom,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B)) = (minus_minus_rat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_add__diff__cancel__right)). 185.47/93.68 thf(20747,plain,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B)) = (minus_minus_rat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3971])). 185.47/93.68 thf(1041,axiom,((! [A:int,B:int,C:int]: ((divide_divide_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (plus_plus_int @ (divide_divide_int @ A @ C) @ (divide_divide_int @ B @ C)) @ (divide_divide_int @ (plus_plus_int @ (modulo_modulo_int @ A @ C) @ (modulo_modulo_int @ B @ C)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2166_div__add1__eq)). 185.47/93.68 thf(11282,plain,((! [A:int,B:int,C:int]: ((divide_divide_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (plus_plus_int @ (divide_divide_int @ A @ C) @ (divide_divide_int @ B @ C)) @ (divide_divide_int @ (plus_plus_int @ (modulo_modulo_int @ A @ C) @ (modulo_modulo_int @ B @ C)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041])). 185.47/93.68 thf(847,axiom,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ B) = (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A))) <= (A = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9051_log2__of__power__eq)). 185.47/93.68 thf(10637,plain,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ B) = (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A))) | ~ (A = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[847])). 185.47/93.68 thf(1761,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5215_divide__minus1)). 185.47/93.68 thf(13632,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761])). 185.47/93.68 thf(155,axiom,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (ord_le6747313008572928689nteger @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5063_neg__less__iff__less)). 185.47/93.68 thf(8228,plain,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (ord_le6747313008572928689nteger @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 185.47/93.68 thf(3846,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_set_nat @ (set_or1269000886237332187st_nat @ A @ B) @ (set_ord_atMost_nat @ C)) = (~ (ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8689_Icc__subset__Iic__iff)). 185.47/93.68 thf(20353,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_set_nat @ (set_or1269000886237332187st_nat @ A @ B) @ (set_ord_atMost_nat @ C)) = (~ (ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3846])). 185.47/93.68 thf(1754,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ C) => ((divide_divide_int @ C @ (times_times_int @ B @ A)) = (divide_divide_int @ (divide_divide_int @ C @ B) @ A))) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4863_div__mult__unit2)). 185.47/93.68 thf(13615,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ C) => ((divide_divide_int @ C @ (times_times_int @ B @ A)) = (divide_divide_int @ (divide_divide_int @ C @ B) @ A))) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754])). 185.47/93.68 thf(736,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ A)) = (groups708209901874060359at_nat @ (^ [C:nat]: (C)) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ A @ one_one_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8948_fact__div__fact)). 185.47/93.68 thf(10188,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ A)) = (groups708209901874060359at_nat @ (^ [C:nat]: (C)) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ A @ one_one_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[736])). 185.47/93.68 thf(3390,axiom,((! [A:(nat > $o),B:(nat > $o)]: (((collect_nat @ A) = (collect_nat @ B)) <= (! [C:nat]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_Collect__cong)). 185.47/93.68 thf(18900,plain,((! [A:(nat > $o),B:(nat > $o)]: (((collect_nat @ (A)) = (collect_nat @ (B))) | ~ (! [C:nat]: ((A @ C) = (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3390])). 185.47/93.68 thf(776,axiom,((! [A:nat,B:int]: ((ord_less_int @ (bit_se4203085406695923979it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3127_unset__bit__negative__int__iff)). 185.47/93.68 thf(10376,plain,((! [A:nat,B:int]: ((ord_less_int @ (bit_se4203085406695923979it_int @ A @ B) @ zero_zero_int) = (ord_less_int @ B @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[776])). 185.47/93.68 thf(7479,axiom,((! [A:code_integer,B:nat]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_8256067586552552935nteger @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5430_Power_Oring__1__class_Opower__minus__even)). 185.47/93.68 thf(33207,plain,((! [A:code_integer,B:nat]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_8256067586552552935nteger @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7479])). 185.47/93.68 thf(1125,axiom,((ord_less_eq_real @ (exp_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8229_exp__half__le2)). 185.47/93.68 thf(11541,plain,((ord_less_eq_real @ (exp_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125])). 185.47/93.68 thf(925,axiom,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((finite_finite_nat @ A) => (((! [D:nat]: ((ord_less_rat @ (B @ D) @ (C @ D)) <= (member_nat @ D @ A))) => (ord_less_rat @ (groups2906978787729119204at_rat @ B @ A) @ (groups2906978787729119204at_rat @ C @ A))) <= (A != bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5870_sum__strict__mono)). 185.47/93.68 thf(10905,plain,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((finite_finite_nat @ A) => (((! [D:nat]: ((ord_less_rat @ (B @ D) @ (C @ D)) | ~ (member_nat @ D @ A))) => (ord_less_rat @ (groups2906978787729119204at_rat @ (B) @ A) @ (groups2906978787729119204at_rat @ (C) @ A))) | (A = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[925])). 185.47/93.68 thf(3253,axiom,((! [A:real,B:real]: (((times_times_real @ (abs_abs_real @ B) @ A) = (abs_abs_real @ (times_times_real @ B @ A))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6543_abs__mult__pos)). 185.47/93.68 thf(18460,plain,((! [A:real,B:real]: (((times_times_real @ (abs_abs_real @ B) @ A) = (abs_abs_real @ (times_times_real @ B @ A))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3253])). 185.47/93.68 thf(6189,axiom,((! [A:nat,B:num]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9339_take__bit__Suc__minus__bit0)). 185.47/93.68 thf(28574,plain,((! [A:nat,B:num]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6189])). 185.47/93.68 thf(5462,axiom,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))) => (ord_less_eq_num @ (C @ A) @ D)) <= (ord_less_eq_num @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3928_order__subst2)). 185.47/93.68 thf(25827,plain,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ (ord_less_eq_num @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5462])). 185.47/93.68 thf(567,axiom,((! [A:set_nat]: ((minus_minus_set_nat @ bot_bot_set_nat @ A) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1303_empty__Diff)). 185.47/93.68 thf(9615,plain,((! [A:set_nat]: ((minus_minus_set_nat @ bot_bot_set_nat @ A) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[567])). 185.47/93.68 thf(3786,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (((times_3573771949741848930nteger @ A @ B) = (times_3573771949741848930nteger @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4732_unit__mult__left__cancel)). 185.47/93.68 thf(20167,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (((times_3573771949741848930nteger @ A @ B) = (times_3573771949741848930nteger @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3786])). 185.47/93.68 thf(6610,axiom,((! [A:real,B:num,C:num]: ((times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ (power_power_real @ A @ (numeral_numeral_nat @ C))) = (power_power_real @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_power__add__numeral)). 185.47/93.68 thf(30034,plain,((! [A:real,B:num,C:num]: ((times_times_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ (power_power_real @ A @ (numeral_numeral_nat @ C))) = (power_power_real @ A @ (numeral_numeral_nat @ (plus_plus_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6610])). 185.47/93.68 thf(7313,axiom,((! [A:num,B:num,C:(num > nat),D:nat]: ((((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F)))) <= ((C @ B) = D)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3954_ord__le__eq__subst)). 185.47/93.68 thf(32645,plain,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7313])). 185.47/93.68 thf(3357,axiom,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ B)))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9543_and__not__numerals_I8_J)). 185.47/93.68 thf(18794,plain,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ B)))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3357])). 185.47/93.68 thf(3094,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_real @ A @ zero_zero_real) & (ord_less_real @ C @ B)) | ((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2360_mult__less__cancel__left__disj)). 185.47/93.68 thf(17970,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_real @ A @ zero_zero_real) & (ord_less_real @ C @ B)) | ((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3094])). 185.47/93.68 thf(4392,axiom,((! [A:rat,B:nat]: (((comm_s4028243227959126397er_rat @ A @ B) = zero_zero_rat) = (? [C:nat]: ((A = (uminus_uminus_rat @ (semiri681578069525770553at_rat @ C))) & (ord_less_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8503_pochhammer__eq__0__iff)). 185.47/93.68 thf(22070,plain,((! [A:rat,B:nat]: (((comm_s4028243227959126397er_rat @ A @ B) = zero_zero_rat) = (? [C:nat]: ((A = (uminus_uminus_rat @ (semiri681578069525770553at_rat @ C))) & (ord_less_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4392])). 185.47/93.68 thf(5688,axiom,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ (semiri1316708129612266289at_nat @ B) @ (semiri1316708129612266289at_nat @ C))) = (divide_divide_nat @ (divide_divide_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ (semiri1316708129612266289at_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7221_div__mult2__eq_H)). 185.47/93.68 thf(26660,plain,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ (semiri1316708129612266289at_nat @ B) @ (semiri1316708129612266289at_nat @ C))) = (divide_divide_nat @ (divide_divide_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ (semiri1316708129612266289at_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5688])). 185.47/93.68 thf(5806,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_nat @ A @ B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_add__mono__thms__linordered__field_I1_J)). 185.47/93.68 thf(27116,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_nat @ A @ B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5806])). 185.47/93.68 thf(5131,axiom,((! [A:num]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9468_not__bit__Suc__0__numeral)). 185.47/93.68 thf(24618,plain,((! [A:num]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5131])). 185.47/93.68 thf(3412,axiom,((! [A:rat]: (ord_less_rat @ A @ (plus_plus_rat @ A @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1208_less__add__one)). 185.47/93.68 thf(18967,plain,((! [A:rat]: (ord_less_rat @ A @ (plus_plus_rat @ A @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3412])). 185.47/93.68 thf(5644,axiom,((! [A:int,B:int]: ((times_times_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (times_times_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5075_minus__mult__minus)). 185.47/93.68 thf(26516,plain,((! [A:int,B:int]: ((times_times_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (times_times_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5644])). 185.47/93.68 thf(307,axiom,((! [A:set_nat,B:(nat > rat)]: ((ord_less_eq_rat @ zero_zero_rat @ (groups2906978787729119204at_rat @ B @ A)) <= (! [C:nat]: ((ord_less_eq_rat @ zero_zero_rat @ (B @ C)) <= (member_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5643_sum__nonneg)). 185.47/93.68 thf(8761,plain,((! [A:set_nat,B:(nat > rat)]: ((ord_less_eq_rat @ zero_zero_rat @ (groups2906978787729119204at_rat @ (B) @ A)) | ~ (! [C:nat]: ((ord_less_eq_rat @ zero_zero_rat @ (B @ C)) | ~ (member_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 185.47/93.68 thf(2767,axiom,((! [A:int,B:num]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_int @ A @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7077_of__int__less__numeral__iff)). 185.47/93.68 thf(16925,plain,((! [A:int,B:num]: ((ord_less_real @ (ring_1_of_int_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_int @ A @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2767])). 185.47/93.68 thf(1501,axiom,((! [A:int,B:nat,C:nat]: ((ord_less_int @ one_one_int @ A) => (((power_power_int @ A @ B) = (power_power_int @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_power__inject__exp)). 185.47/93.68 thf(12722,plain,((! [A:int,B:nat,C:nat]: ((ord_less_int @ one_one_int @ A) => (((power_power_int @ A @ B) = (power_power_int @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501])). 185.47/93.68 thf(643,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ln_ln_real @ (divide_divide_real @ A @ B)) = (minus_minus_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6143_ln__div)). 185.47/93.68 thf(9866,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ln_ln_real @ (divide_divide_real @ A @ B)) = (minus_minus_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[643])). 185.47/93.68 thf(2400,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((divide_divide_real @ A @ (sqrt @ A)) = (sqrt @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8181_real__div__sqrt)). 185.47/93.68 thf(15672,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((divide_divide_real @ A @ (sqrt @ A)) = (sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2400])). 185.47/93.68 thf(5414,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ A @ B)) <= (ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2936_power2__le__imp__le)). 185.47/93.68 thf(25638,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ A @ B)) | ~ (ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5414])). 185.47/93.68 thf(112,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (minus_minus_set_nat @ B @ C)) => (member_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1319_DiffD1)). 185.47/93.68 thf(8098,plain,((! [A:nat,B:set_nat,C:set_nat]: ((member_nat @ A @ (minus_minus_set_nat @ B @ C)) => (member_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[112])). 185.47/93.68 thf(5150,axiom,((! [A:rat,B:num,C:rat]: (((divide_divide_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = C) = (((A = (times_times_rat @ C @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)))) <= ((uminus_uminus_rat @ (numeral_numeral_rat @ B)) != zero_zero_rat)) & (((uminus_uminus_rat @ (numeral_numeral_rat @ B)) = zero_zero_rat) => (C = zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5388_divide__eq__eq__numeral1_I2_J)). 185.47/93.68 thf(24717,plain,((! [A:rat,B:num,C:rat]: (((divide_divide_rat @ A @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = C) = (((A = (times_times_rat @ C @ (uminus_uminus_rat @ (numeral_numeral_rat @ B)))) | ((uminus_uminus_rat @ (numeral_numeral_rat @ B)) = zero_zero_rat)) & (((uminus_uminus_rat @ (numeral_numeral_rat @ B)) = zero_zero_rat) => (C = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5150])). 185.47/93.68 thf(1993,axiom,((! [A:int]: ((dvd_dvd_int @ A @ one_one_int) = ((abs_abs_int @ A) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6774_zdvd1__eq)). 185.47/93.68 thf(14393,plain,((! [A:int]: ((dvd_dvd_int @ A @ one_one_int) = ((abs_abs_int @ A) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993])). 185.47/93.68 thf(7395,axiom,((! [A:nat,B:nat]: ((((binomial @ A @ B) = (plus_plus_nat @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ (minus_minus_nat @ B @ one_one_nat)) @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ B))) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8530_choose__reduce__nat)). 185.47/93.68 thf(32902,plain,((! [A:nat,B:nat]: (((binomial @ A @ B) = (plus_plus_nat @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ (minus_minus_nat @ B @ one_one_nat)) @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ B))) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7395])). 185.47/93.68 thf(3178,axiom,((! [A:nat]: ((abs_abs_real @ (semiri5074537144036343181t_real @ A)) = (semiri5074537144036343181t_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6874_abs__of__nat)). 185.47/93.68 thf(18234,plain,((! [A:nat]: ((abs_abs_real @ (semiri5074537144036343181t_real @ A)) = (semiri5074537144036343181t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3178])). 185.47/93.68 thf(258,axiom,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ A @ ($true))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1948_VEBT__internal_OminNull_Osimps_I3_J)). 185.47/93.68 thf(8579,plain,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ A @ ($true))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 185.47/93.68 thf(1668,axiom,((! [A:num,B:(rat > num),C:rat,D:rat]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3913_order__subst1)). 185.47/93.68 thf(13324,plain,((! [A:num,B:(rat > num),C:rat,D:rat]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668])). 185.47/93.68 thf(6024,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)) @ (modulo_modulo_nat @ B @ A)) @ C) = (plus_plus_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2547_cancel__div__mod__rules_I2_J)). 185.47/93.68 thf(27965,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)) @ (modulo_modulo_nat @ B @ A)) @ C) = (plus_plus_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6024])). 185.47/93.68 thf(3462,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ B) = (((ord_less_eq_int @ one_one_int @ A) <= (ord_less_int @ B @ zero_zero_int)) & ((ord_less_eq_int @ A @ one_one_int) <= (ord_less_int @ zero_zero_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2817_mult__le__cancel__right2)). 185.47/93.68 thf(19111,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ B) = (((ord_less_eq_int @ one_one_int @ A) | ~ (ord_less_int @ B @ zero_zero_int)) & ((ord_less_eq_int @ A @ one_one_int) | ~ (ord_less_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3462])). 185.47/93.68 thf(1077,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ B @ A) @ C) = (dvd_dvd_Code_integer @ B @ C)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4741_mult__unit__dvd__iff)). 185.47/93.68 thf(11383,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ B @ A) @ C) = (dvd_dvd_Code_integer @ B @ C)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077])). 185.47/93.68 thf(4816,axiom,((! [A:complex,B:complex]: ((exp_complex @ (minus_minus_complex @ A @ B)) = (divide1717551699836669952omplex @ (exp_complex @ A) @ (exp_complex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8174_exp__diff)). 185.47/93.68 thf(23469,plain,((! [A:complex,B:complex]: ((exp_complex @ (minus_minus_complex @ A @ B)) = (divide1717551699836669952omplex @ (exp_complex @ A) @ (exp_complex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4816])). 185.47/93.68 thf(4369,axiom,((! [A:complex,B:nat]: ((times_times_complex @ (comm_s2602460028002588243omplex @ A @ (suc @ B)) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ (divide1717551699836669952omplex @ one_one_complex @ (numera6690914467698888265omplex @ (bit0 @ one)))) @ (suc @ B))) = (groups6464643781859351333omplex @ (^ [C:nat]: (plus_plus_complex @ A @ (divide1717551699836669952omplex @ (semiri8010041392384452111omplex @ C) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8615_pochhammer__times__pochhammer__half)). 185.47/93.68 thf(21996,plain,((! [A:complex,B:nat]: ((times_times_complex @ (comm_s2602460028002588243omplex @ A @ (suc @ B)) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ (divide1717551699836669952omplex @ one_one_complex @ (numera6690914467698888265omplex @ (bit0 @ one)))) @ (suc @ B))) = (groups6464643781859351333omplex @ (^ [C:nat]: (plus_plus_complex @ A @ (divide1717551699836669952omplex @ (semiri8010041392384452111omplex @ C) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4369])). 185.47/93.68 thf(7162,axiom,((! [A:complex,B:complex,C:complex]: ((((minus_minus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (uminus1482373934393186551omplex @ C)) <= (A = zero_zero_complex)) & (((minus_minus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ B) @ (times_times_complex @ C @ A)) @ A)) <= (A != zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6175_add__divide__eq__if__simps_I6_J)). 185.47/93.68 thf(32124,plain,((! [A:complex,B:complex,C:complex]: ((((minus_minus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (uminus1482373934393186551omplex @ C)) | ~ (A = zero_zero_complex)) & (((minus_minus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ B) @ (times_times_complex @ C @ A)) @ A)) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7162])). 185.47/93.68 thf(231,axiom,(((arccos @ one_one_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8358_arccos__1)). 185.47/93.68 thf(8469,plain,(((arccos @ one_one_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 185.47/93.68 thf(4004,axiom,((! [A:nat,B:nat,C:int]: ((bit_se8568078237143864401it_int @ A @ (bit_se545348938243370406it_int @ B @ C)) = (bit_se8568078237143864401it_int @ (minus_minus_nat @ A @ B) @ (bit_se545348938243370406it_int @ (minus_minus_nat @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9758_drop__bit__push__bit__int)). 185.47/93.68 thf(20849,plain,((! [A:nat,B:nat,C:int]: ((bit_se8568078237143864401it_int @ A @ (bit_se545348938243370406it_int @ B @ C)) = (bit_se8568078237143864401it_int @ (minus_minus_nat @ A @ B) @ (bit_se545348938243370406it_int @ (minus_minus_nat @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4004])). 185.47/93.68 thf(6319,axiom,((! [A:rat,B:nat]: ((power_power_rat @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_rat @ A @ (power_power_rat @ (power_power_rat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1122_power__odd__eq)). 185.47/93.68 thf(28998,plain,((! [A:rat,B:nat]: ((power_power_rat @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = (times_times_rat @ A @ (power_power_rat @ (power_power_rat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6319])). 185.47/93.68 thf(7355,axiom,(((uminus_uminus_real @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5055_add_Oinverse__neutral)). 185.47/93.68 thf(32784,plain,(((uminus_uminus_real @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7355])). 185.47/93.68 thf(1793,axiom,((! [A:rat,B:rat,C:rat]: (((minus_minus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (minus_minus_rat @ B @ (times_times_rat @ C @ A)) @ A)) <= (A != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2764_divide__diff__eq__iff)). 185.47/93.68 thf(13739,plain,((! [A:rat,B:rat,C:rat]: (((minus_minus_rat @ (divide_divide_rat @ B @ A) @ C) = (divide_divide_rat @ (minus_minus_rat @ B @ (times_times_rat @ C @ A)) @ A)) | (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1793])). 185.47/93.68 thf(7361,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)) @ (modulo_modulo_nat @ B @ A)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2529_mult__div__mod__eq)). 185.47/93.68 thf(32801,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)) @ (modulo_modulo_nat @ B @ A)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7361])). 185.47/93.68 thf(4513,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [C:real]: (((power_power_real @ C @ (suc @ B)) = A) & (ord_less_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3096_realpow__pos__nth2)). 185.47/93.68 thf(22458,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [C:real]: (((power_power_real @ C @ (suc @ B)) = A) & (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4513])). 185.47/93.68 thf(1213,axiom,((! [A:nat,B:nat]: (((ord_less_eq_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9059_log2__of__power__le)). 185.47/93.68 thf(11810,plain,((! [A:nat,B:nat]: ((ord_less_eq_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213])). 185.47/93.68 thf(3773,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (minus_minus_int @ A @ B) @ A) = (modulo_modulo_int @ (uminus_uminus_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5227_minus__mod__self1)). 185.47/93.68 thf(20126,plain,((! [A:int,B:int]: ((modulo_modulo_int @ (minus_minus_int @ A @ B) @ A) = (modulo_modulo_int @ (uminus_uminus_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3773])). 185.47/93.68 thf(7466,axiom,((! [A:num,B:num]: ((uminus_uminus_int @ (numeral_numeral_int @ A)) != (numeral_numeral_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5536_neg__numeral__neq__numeral)). 185.47/93.68 thf(33166,plain,((! [A:num,B:num]: ~ ((uminus_uminus_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7466])). 185.47/93.68 thf(3576,axiom,((! [A:real]: ((divide_divide_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_994_div__by__1)). 185.47/93.68 thf(19482,plain,((! [A:real]: ((divide_divide_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3576])). 185.47/93.68 thf(4342,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ (times_times_rat @ B @ A) @ zero_zero_rat)) <= (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2206_mult__nonneg__nonpos2)). 185.47/93.68 thf(21907,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ (times_times_rat @ B @ A) @ zero_zero_rat)) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4342])). 185.47/93.68 thf(207,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (((ord_less_real @ (log @ A @ B) @ (log @ A @ C)) = (ord_less_real @ B @ C)) <= (ord_less_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9024_log__less__cancel__iff)). 185.47/93.68 thf(8401,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (((ord_less_real @ (log @ A @ B) @ (log @ A @ C)) = (ord_less_real @ B @ C)) | ~ (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 185.47/93.68 thf(2046,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ B) => ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ A) <= (ord_less_eq_rat @ B @ one_one_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2670_mult__right__le__one__le)). 185.47/93.68 thf(14571,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ zero_zero_rat @ B) => ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ A) | ~ (ord_less_eq_rat @ B @ one_one_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2046])). 185.47/93.68 thf(7067,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (power_power_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4560_even__power)). 185.47/93.68 thf(31796,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (power_power_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7067])). 185.47/93.68 thf(2434,axiom,((! [A:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ A @ A) = one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1732_divide__self)). 185.47/93.68 thf(15796,plain,((! [A:complex]: ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ A @ A) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2434])). 185.47/93.68 thf(4594,axiom,((! [A:real,B:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ B @ A)) = (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4436_dvd__add__triv__right__iff)). 185.47/93.68 thf(22711,plain,((! [A:real,B:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ B @ A)) = (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4594])). 185.47/93.68 thf(6665,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4968_zero__le__power__eq)). 185.47/93.68 thf(30216,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6665])). 185.47/93.68 thf(104,axiom,((! [A:int,B:nat,C:int]: ((minus_minus_int @ (power_power_int @ A @ (suc @ B)) @ (power_power_int @ C @ (suc @ B))) = (times_times_int @ (minus_minus_int @ A @ C) @ (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (power_power_int @ A @ D) @ (power_power_int @ C @ (minus_minus_nat @ B @ D)))) @ (set_ord_lessThan_nat @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7614_diff__power__eq__sum)). 185.47/93.68 thf(8075,plain,((! [A:int,B:nat,C:int]: ((minus_minus_int @ (power_power_int @ A @ (suc @ B)) @ (power_power_int @ C @ (suc @ B))) = (times_times_int @ (minus_minus_int @ A @ C) @ (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (power_power_int @ A @ D) @ (power_power_int @ C @ (minus_minus_nat @ B @ D)))) @ (set_ord_lessThan_nat @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 185.47/93.68 thf(4589,axiom,((! [A:int]: (((abs_abs_int @ A) = (uminus_uminus_int @ A)) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6577_abs__of__neg)). 185.47/93.68 thf(22697,plain,((! [A:int]: (((abs_abs_int @ A) = (uminus_uminus_int @ A)) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4589])). 185.47/93.68 thf(3219,axiom,((! [A:nat,B:nat]: ((B = (ord_max_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3661_max_OorderE)). 185.47/93.68 thf(18366,plain,((! [A:nat,B:nat]: ((B = (ord_max_nat @ B @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3219])). 185.47/93.68 thf(7647,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_one__add__one)). 185.47/93.68 thf(33701,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7647])). 185.47/93.68 thf(7408,axiom,((! [A:num,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7133_numeral__power__le__of__nat__cancel__iff)). 185.47/93.68 thf(32969,plain,((! [A:num,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7408])). 185.47/93.68 thf(2864,axiom,((! [A:real,B:real]: ((A != zero_zero_real) => ((uminus_uminus_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ B @ (uminus_uminus_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5764_nonzero__minus__divide__right)). 185.47/93.68 thf(17237,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real)) => ((uminus_uminus_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ B @ (uminus_uminus_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2864])). 185.47/93.68 thf(1372,axiom,((! [A:complex,B:(nat > complex),C:complex]: ((A != zero_zero_complex) => ((sums_complex @ (^ [D:nat]: (times_times_complex @ A @ (B @ D))) @ (times_times_complex @ A @ C)) = (sums_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8178_sums__mult__iff)). 185.47/93.68 thf(12302,plain,((! [A:complex,B:(nat > complex),C:complex]: ((~ (A = zero_zero_complex)) => ((sums_complex @ (^ [D:nat]: (times_times_complex @ A @ (B @ D))) @ (times_times_complex @ A @ C)) = (sums_complex @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372])). 185.47/93.68 thf(6123,axiom,((! [A:int]: ((minus_minus_int @ A @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1559_diff__self)). 185.47/93.68 thf(28296,plain,((! [A:int]: ((minus_minus_int @ A @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6123])). 185.47/93.68 thf(5427,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (suc @ (minus_minus_nat @ B @ A)) @ C) = (minus_minus_nat @ (suc @ B) @ (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1013_diff__Suc__diff__eq2)). 185.47/93.68 thf(25676,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (suc @ (minus_minus_nat @ B @ A)) @ C) = (minus_minus_nat @ (suc @ B) @ (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5427])). 185.47/93.68 thf(1437,axiom,((! [A:int]: (((suc @ (nat2 @ A)) = (nat2 @ (plus_plus_int @ one_one_int @ A))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9331_Suc__nat__eq__nat__zadd1)). 185.47/93.68 thf(12527,plain,((! [A:int]: (((suc @ (nat2 @ A)) = (nat2 @ (plus_plus_int @ one_one_int @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437])). 185.47/93.68 thf(2733,axiom,((! [A:rat]: ((((divide_divide_rat @ A @ A) = one_one_rat) <= (A != zero_zero_rat)) & ((A = zero_zero_rat) => ((divide_divide_rat @ A @ A) = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1731_divide__self__if)). 185.47/93.68 thf(16820,plain,((! [A:rat]: ((((divide_divide_rat @ A @ A) = one_one_rat) | (A = zero_zero_rat)) & ((A = zero_zero_rat) => ((divide_divide_rat @ A @ A) = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2733])). 185.47/93.68 thf(4757,axiom,((! [A:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (exp_real @ A)) @ (exp_real @ (real_V7735802525324610683m_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8149_norm__exp)). 185.47/93.68 thf(23252,plain,((! [A:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (exp_real @ A)) @ (exp_real @ (real_V7735802525324610683m_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4757])). 185.47/93.68 thf(2438,axiom,((! [A:real]: ((ord_less_eq_real @ (exp_real @ A) @ one_one_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8135_exp__le__one__iff)). 185.47/93.68 thf(15809,plain,((! [A:real]: ((ord_less_eq_real @ (exp_real @ A) @ one_one_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2438])). 185.47/93.68 thf(3890,axiom,((! [A:code_integer,B:code_integer]: (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4575_dvd__triv__right)). 185.47/93.68 thf(20487,plain,((! [A:code_integer,B:code_integer]: (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3890])). 185.47/93.68 thf(608,axiom,((! [A:real,B:nat]: ((gbinomial_real @ (plus_plus_real @ A @ one_one_real) @ (suc @ B)) = (times_times_real @ (divide_divide_real @ (plus_plus_real @ A @ one_one_real) @ (semiri5074537144036343181t_real @ (suc @ B))) @ (gbinomial_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8557_gbinomial__factors)). 185.47/93.68 thf(9755,plain,((! [A:real,B:nat]: ((gbinomial_real @ (plus_plus_real @ A @ one_one_real) @ (suc @ B)) = (times_times_real @ (divide_divide_real @ (plus_plus_real @ A @ one_one_real) @ (semiri5074537144036343181t_real @ (suc @ B))) @ (gbinomial_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[608])). 185.47/93.68 thf(5502,axiom,((! [A:nat,B:real]: ((((root @ A @ B) = one_one_real) = (B = one_one_real)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9164_real__root__eq__1__iff)). 185.47/93.68 thf(26056,plain,((! [A:nat,B:real]: ((((root @ A @ B) = one_one_real) = (B = one_one_real)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5502])). 185.47/93.68 thf(5942,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2182_div__positive)). 185.47/93.68 thf(27667,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5942])). 185.47/93.68 thf(6220,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = ((ord_less_eq_nat @ A @ B) | ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4991_even__mask__div__iff)). 185.47/93.68 thf(28662,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) = ((ord_less_eq_nat @ A @ B) | ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6220])). 185.47/93.68 thf(3892,axiom,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ one_one_rat @ A)) = (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1819_zero__less__divide__1__iff)). 185.47/93.68 thf(20491,plain,((! [A:rat]: ((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ one_one_rat @ A)) = (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3892])). 185.47/93.68 thf(7638,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4527_odd__Suc__div__two)). 185.47/93.68 thf(33679,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7638])). 185.47/93.68 thf(6884,axiom,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (minus_minus_rat @ A @ B)) = (minus_minus_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5102_minus__diff__eq)). 185.47/93.68 thf(31081,plain,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (minus_minus_rat @ A @ B)) = (minus_minus_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6884])). 185.47/93.68 thf(1312,axiom,((! [A:(nat > nat),B:set_nat,C:(nat > nat),D:set_nat]: ((times_times_nat @ (groups3542108847815614940at_nat @ A @ B) @ (groups3542108847815614940at_nat @ C @ D)) = (groups3542108847815614940at_nat @ (^ [E:nat]: (groups3542108847815614940at_nat @ (^ [F:nat]: (times_times_nat @ (A @ E) @ (C @ F))) @ D)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5609_sum__product)). 185.47/93.68 thf(12112,plain,((! [A:(nat > nat),B:set_nat,C:(nat > nat),D:set_nat]: ((times_times_nat @ (groups3542108847815614940at_nat @ (A) @ B) @ (groups3542108847815614940at_nat @ (C) @ D)) = (groups3542108847815614940at_nat @ (^ [E:nat]: (groups3542108847815614940at_nat @ (^ [F:nat]: (times_times_nat @ (A @ E) @ (C @ F))) @ D)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312])). 185.47/93.68 thf(6278,axiom,((! [A:num]: (((uminus1482373934393186551omplex @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5293_neg__one__eq__numeral__iff)). 185.47/93.68 thf(28861,plain,((! [A:num]: (((uminus1482373934393186551omplex @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6278])). 185.47/93.68 thf(5015,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((A = B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4031_not__less__iff__gr__or__eq)). 185.47/93.68 thf(24150,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((A = B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5015])). 185.47/93.68 thf(7144,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ (times_times_nat @ A @ B)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2781_n__less__n__mult__m)). 185.47/93.68 thf(32048,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (times_times_nat @ A @ B)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7144])). 185.47/93.68 thf(6473,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3979_less__imp__neq)). 185.47/93.68 thf(29568,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6473])). 185.47/93.68 thf(5793,axiom,((vEBT_invar_vebt = (^ [A:vEBT_VEBT,B:nat]: (((B = (suc @ zero_zero_nat)) & ? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT]: (! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ F @ D)) & (B = (plus_plus_nat @ D @ (suc @ D))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F)) & ! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C)) => (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)))) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))) & (vEBT_invar_vebt @ E @ (suc @ D)) & (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ E))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ B @ C @ E)) & ! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ D) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C))) & (ord_less_eq_nat @ F @ G) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & ((! [H:nat]: ((! [I:nat]: (((ord_less_eq_nat @ I @ G) & (ord_less_nat @ F @ I)) <= (((vEBT_VEBT_high @ I @ D) = H) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ I @ D)))) & (((vEBT_VEBT_high @ G @ D) = H) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ G @ D)))) <= (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))))) <= (F != G)) & ((! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))))) <= (F = G)) & ! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))) => ((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ I)) = (vEBT_V8194947554948674370ptions @ E @ H))) & (B = (plus_plus_nat @ D @ (suc @ D))) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))) & (vEBT_invar_vebt @ E @ (suc @ D))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ B @ C @ E)) & (vEBT_invar_vebt @ E @ D) & (B = (plus_plus_nat @ D @ D)) & ! [H:nat]: (((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ I)) = (vEBT_V8194947554948674370ptions @ E @ H)) <= (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) & ((F != G) => (! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => (! [I:nat]: (((ord_less_nat @ F @ I) & (ord_less_eq_nat @ I @ G)) <= (((vEBT_VEBT_high @ I @ D) = H) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ I @ D)))) & (((vEBT_VEBT_high @ G @ D) = H) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ G @ D))))))) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & (ord_less_eq_nat @ F @ G) & ((! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))))) <= (F = G)) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ D) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT]: ((vEBT_invar_vebt @ E @ D) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F)) & ! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C)) => (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)))) & (B = (plus_plus_nat @ D @ D)) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [F:vEBT_VEBT]: ((vEBT_invar_vebt @ F @ D) <= (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3018_invar__vebt_Osimps)). 185.47/93.68 thf(27000,plain,(((vEBT_invar_vebt) = (^ [A:vEBT_VEBT,B:nat]: (((B = (suc @ zero_zero_nat)) & ? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT]: (! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ F @ D)) & (B = (plus_plus_nat @ D @ (suc @ D))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F)) & ! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C)) => (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)))) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))) & (vEBT_invar_vebt @ E @ (suc @ D)) & (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ E))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ B @ C @ E)) & ! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ D) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C))) & (ord_less_eq_nat @ F @ G) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & (! [H:nat]: ((! [I:nat]: (((ord_less_eq_nat @ I @ G) & (ord_less_nat @ F @ I)) | ~ (((vEBT_VEBT_high @ I @ D) = H) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ I @ D)))) & (((vEBT_VEBT_high @ G @ D) = H) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ G @ D)))) | ~ (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D)))) | (F = G)) & (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)))) | ~ (F = G)) & ! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))) => ((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ I)) = (vEBT_V8194947554948674370ptions @ E @ H))) & (B = (plus_plus_nat @ D @ (suc @ D))) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))) & (vEBT_invar_vebt @ E @ (suc @ D))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ B @ C @ E)) & (vEBT_invar_vebt @ E @ D) & (B = (plus_plus_nat @ D @ D)) & ! [H:nat]: (((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ I)) = (vEBT_V8194947554948674370ptions @ E @ H)) | ~ (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) & ((~ (F = G)) => (! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => (! [I:nat]: (((ord_less_nat @ F @ I) & (ord_less_eq_nat @ I @ G)) | ~ (((vEBT_VEBT_high @ I @ D) = H) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ I @ D)))) & (((vEBT_VEBT_high @ G @ D) = H) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ G @ D))))))) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & (ord_less_eq_nat @ F @ G) & (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)))) | ~ (F = G)) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ D) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT]: ((vEBT_invar_vebt @ E @ D) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F)) & ! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C)) => (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)))) & (B = (plus_plus_nat @ D @ D)) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [F:vEBT_VEBT]: ((vEBT_invar_vebt @ F @ D) | ~ (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5793])). 185.47/93.68 thf(1901,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6216_pos__minus__divide__le__eq)). 185.47/93.68 thf(14083,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1901])). 185.47/93.68 thf(3083,axiom,((! [A:real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1575_division__ring__divide__zero)). 185.47/93.68 thf(17930,plain,((! [A:real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3083])). 185.47/93.68 thf(1358,axiom,((ord_less_real @ zero_zero_real @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2388_less__numeral__extra_I1_J)). 185.47/93.68 thf(12258,plain,((ord_less_real @ zero_zero_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358])). 185.47/93.68 thf(2487,axiom,((! [A:real]: (((powr_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) = (sqrt @ A)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9130_powr__half__sqrt)). 185.47/93.68 thf(15964,plain,((! [A:real]: (((powr_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) = (sqrt @ A)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2487])). 185.47/93.68 thf(2456,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (ord_less_eq_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_add__le__cancel__left)). 185.47/93.68 thf(15869,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (ord_less_eq_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2456])). 185.47/93.68 thf(5916,axiom,((! [A:real,B:real,C:real]: (((times_times_real @ A @ B) = (times_times_real @ C @ B)) = ((B = zero_zero_real) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1502_mult__cancel__right)). 185.47/93.68 thf(27587,plain,((! [A:real,B:real,C:real]: (((times_times_real @ A @ B) = (times_times_real @ C @ B)) = ((B = zero_zero_real) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5916])). 185.47/93.68 thf(4003,axiom,((! [A:num]: (((uminus1351360451143612070nteger @ one_one_Code_integer) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5295_neg__one__eq__numeral__iff)). 185.47/93.68 thf(20846,plain,((! [A:num]: (((uminus1351360451143612070nteger @ one_one_Code_integer) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4003])). 185.47/93.68 thf(2573,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (times_times_int @ A @ B)) = (((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ one_one_int @ B)) & ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ B @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2808_mult__le__cancel__left1)). 185.47/93.68 thf(16257,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (times_times_int @ A @ B)) = (((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ one_one_int @ B)) & ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ B @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2573])). 185.47/93.68 thf(2846,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B))) = ((A != zero_zero_int) | (B != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2690_sum__squares__gt__zero__iff)). 185.47/93.68 thf(17180,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ (times_times_int @ A @ A) @ (times_times_int @ B @ B))) = (~ (A = zero_zero_int) | ~ (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2846])). 185.47/93.68 thf(3264,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B)) = (((ord_less_rat @ zero_zero_rat @ B) & (ord_less_rat @ A @ C)) | ((ord_less_rat @ C @ A) & (ord_less_rat @ B @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2371_mult__less__cancel__right__disj)). 185.47/93.68 thf(18495,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ B)) = (((ord_less_rat @ zero_zero_rat @ B) & (ord_less_rat @ A @ C)) | ((ord_less_rat @ C @ A) & (ord_less_rat @ B @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3264])). 185.47/93.68 thf(5357,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ A @ B) <= (ord_less_eq_rat @ zero_zero_rat @ B)) <= (ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2934_power2__le__imp__le)). 185.47/93.68 thf(25468,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) | ~ (ord_less_eq_rat @ zero_zero_rat @ B) | ~ (ord_less_eq_rat @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5357])). 185.47/93.68 thf(4884,axiom,((! [A:int,B:int,C:(int > $o)]: ((((! [D:int]: ((ord_less_int @ D @ B) => ((C @ (minus_minus_int @ D @ one_one_int)) <= (C @ D)))) => (C @ A)) <= (C @ (minus_minus_int @ B @ one_one_int))) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3139_int__less__induct)). 185.47/93.68 thf(23701,plain,((! [A:int,B:int,C:(int > $o)]: (((! [D:int]: ((ord_less_int @ D @ B) => ((C @ (minus_minus_int @ D @ one_one_int)) | ~ (C @ D)))) => (C @ A)) | ~ (C @ (minus_minus_int @ B @ one_one_int)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4884])). 185.47/93.68 thf(4717,axiom,((! [A:complex,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => ((comm_s2602460028002588243omplex @ A @ C) != zero_zero_complex)) <= ((comm_s2602460028002588243omplex @ A @ B) != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8441_pochhammer__neq__0__mono)). 185.47/93.68 thf(23128,plain,((! [A:complex,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => (~ ((comm_s2602460028002588243omplex @ A @ C) = zero_zero_complex))) | ((comm_s2602460028002588243omplex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4717])). 185.47/93.68 thf(721,axiom,((ord_max_int = (^ [A:int,B:int]: (if_int @ (ord_less_eq_int @ A @ B) @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3768_max__def__raw)). 185.47/93.68 thf(10135,plain,(((ord_max_int) = (^ [A:int,B:int]: (if_int @ (ord_less_eq_int @ A @ B) @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[721])). 185.47/93.68 thf(7393,axiom,(((neg_nu6511756317524482435omplex @ zero_zero_complex) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6796_dbl__dec__simps_I2_J)). 185.47/93.68 thf(32897,plain,(((neg_nu6511756317524482435omplex @ zero_zero_complex) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7393])). 185.47/93.68 thf(5325,axiom,((! [A:num,B:nat,C:nat]: (((power_power_rat @ (numeral_numeral_rat @ A) @ B) = (semiri681578069525770553at_rat @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7054_numeral__power__eq__of__nat__cancel__iff)). 185.47/93.68 thf(25327,plain,((! [A:num,B:nat,C:nat]: (((power_power_rat @ (numeral_numeral_rat @ A) @ B) = (semiri681578069525770553at_rat @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5325])). 185.47/93.68 thf(3128,axiom,((! [A:rat,B:rat]: ((A = B) | ~ (ord_less_eq_rat @ B @ A) | ~ (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3082_verit__la__disequality)). 185.47/93.68 thf(18078,plain,((! [A:rat,B:rat]: ((A = B) | ~ (ord_less_eq_rat @ B @ A) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3128])). 185.47/93.68 thf(1280,axiom,((! [A:rat]: (ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ one_one_rat @ (abs_abs_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6641_abs__add__one__gt__zero)). 185.47/93.68 thf(12010,plain,((! [A:rat]: (ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ one_one_rat @ (abs_abs_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280])). 185.47/93.68 thf(1797,axiom,((! [A:real,B:real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5565_add_Oinverse__distrib__swap)). 185.47/93.68 thf(13752,plain,((! [A:real,B:real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1797])). 185.47/93.68 thf(5841,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2973_vebt__pred_Osimps_I6_J)). 185.47/93.68 thf(27339,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5841])). 185.47/93.68 thf(1061,axiom,((((=) @ rat) = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) & (ord_less_eq_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3851_order__class_Oorder__eq__iff)). 185.47/93.68 thf(11337,plain,((((=) @ rat) = (^ [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) & (ord_less_eq_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061])). 185.47/93.68 thf(1326,axiom,((! [A:real]: (((exp_real @ A) = one_one_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8129_exp__eq__one__iff)). 185.47/93.68 thf(12157,plain,((! [A:real]: (((exp_real @ A) = one_one_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326])). 185.47/93.68 thf(2820,axiom,((! [A:complex,B:num]: ((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B))) = (divide_divide_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7443_norm__divide__numeral)). 185.47/93.68 thf(17095,plain,((! [A:complex,B:num]: ((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B))) = (divide_divide_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2820])). 185.47/93.68 thf(7504,axiom,((! [A:num,B:num,C:num]: (((ord_less_num @ B @ C) => (ord_less_num @ A @ C)) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4025_order_Ostrict__trans)). 185.47/93.68 thf(33299,plain,((! [A:num,B:num,C:num]: (((ord_less_num @ B @ C) => (ord_less_num @ A @ C)) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7504])). 185.47/93.68 thf(2769,axiom,((! [A:nat,B:(real > real),C:filter_real]: ((((filterlim_real_real @ (^ [D:real]: (power_power_real @ (B @ D) @ A)) @ at_top_real @ C) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) <= (filterlim_real_real @ B @ at_bot_real @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10135_filterlim__pow__at__bot__even)). 185.47/93.68 thf(16931,plain,((! [A:nat,B:(real > real),C:filter_real]: ((filterlim_real_real @ (^ [D:real]: (power_power_real @ (B @ D) @ A)) @ at_top_real @ C) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) | ~ (filterlim_real_real @ (B) @ at_bot_real @ C) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2769])). 185.47/93.68 thf(2888,axiom,((! [A:nat,B:nat]: (((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ A)) @ B) = zero_zero_rat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8513_pochhammer__of__nat__eq__0__lemma)). 185.47/93.68 thf(17316,plain,((! [A:nat,B:nat]: (((comm_s4028243227959126397er_rat @ (uminus_uminus_rat @ (semiri681578069525770553at_rat @ A)) @ B) = zero_zero_rat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2888])). 185.47/93.68 thf(7444,axiom,((! [A:nat,B:nat,C:num]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ C)) = (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ C)) @ (times_times_nat @ B @ (numeral_numeral_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_distrib__right__numeral)). 185.47/93.68 thf(33080,plain,((! [A:nat,B:nat,C:num]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ (numeral_numeral_nat @ C)) = (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ C)) @ (times_times_nat @ B @ (numeral_numeral_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7444])). 185.47/93.68 thf(3753,axiom,((! [A:int,B:int]: ((A != B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4137_order__less__imp__not__eq)). 185.47/93.68 thf(20050,plain,((! [A:int,B:int]: (~ (A = B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3753])). 185.47/93.68 thf(3732,axiom,((! [A:real,B:num,C:real]: ((ord_less_real @ (divide_divide_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B))) @ C) = (ord_less_real @ (times_times_real @ C @ (uminus_uminus_real @ (numeral_numeral_real @ B))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5395_divide__less__eq__numeral1_I2_J)). 185.47/93.68 thf(19985,plain,((! [A:real,B:num,C:real]: ((ord_less_real @ (divide_divide_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B))) @ C) = (ord_less_real @ (times_times_real @ C @ (uminus_uminus_real @ (numeral_numeral_real @ B))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3732])). 185.47/93.68 thf(4185,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ zero_zero_rat @ C) => ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ B @ A)) => (ord_less_eq_rat @ (divide_divide_rat @ C @ B) @ (divide_divide_rat @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2837_divide__left__mono)). 185.47/93.68 thf(21404,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ zero_zero_rat @ C) => ((ord_less_rat @ zero_zero_rat @ (times_times_rat @ B @ A)) => (ord_less_eq_rat @ (divide_divide_rat @ C @ B) @ (divide_divide_rat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4185])). 185.47/93.68 thf(6530,axiom,((one_one_int != (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5551_one__neq__neg__one)). 185.47/93.68 thf(29776,plain,((~ (one_one_int = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6530])). 185.47/93.68 thf(4824,axiom,((! [A:set_nat]: ((~ (finite_finite_nat @ A)) => (A != bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3479_infinite__imp__nonempty)). 185.47/93.68 thf(23495,plain,((! [A:set_nat]: ((~ (finite_finite_nat @ A)) => (~ (A = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4824])). 185.47/93.68 thf(3054,axiom,((! [A:real,B:nat,C:nat]: (((A = one_one_real) => ((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (plus_plus_real @ (semiri5074537144036343181t_real @ C) @ one_one_real))) & ((A != one_one_real) => ((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (divide_divide_real @ (times_times_real @ (power_power_real @ A @ B) @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (suc @ C)))) @ (minus_minus_real @ one_one_real @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7363_sum__gp__offset)). 185.47/93.68 thf(17842,plain,((! [A:real,B:nat,C:nat]: (((A = one_one_real) => ((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (plus_plus_real @ (semiri5074537144036343181t_real @ C) @ one_one_real))) & ((~ (A = one_one_real)) => ((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_or1269000886237332187st_nat @ B @ (plus_plus_nat @ B @ C))) = (divide_divide_real @ (times_times_real @ (power_power_real @ A @ B) @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (suc @ C)))) @ (minus_minus_real @ one_one_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3054])). 185.47/93.68 thf(3292,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ C @ A) @ (times_times_rat @ C @ B))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2374_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)). 185.47/93.68 thf(18579,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ zero_zero_rat @ C) => (ord_less_rat @ (times_times_rat @ C @ A) @ (times_times_rat @ C @ B))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3292])). 185.47/93.68 thf(1154,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((divide_divide_int @ (plus_plus_int @ B @ C) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4782_div__plus__div__distrib__dvd__left)). 185.47/93.68 thf(11639,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((divide_divide_int @ (plus_plus_int @ B @ C) @ A) = (plus_plus_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154])). 185.47/93.68 thf(5569,axiom,((! [A:num]: ((minus_minus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (numera6690914467698888265omplex @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5446_diff__numeral__special_I3_J)). 185.47/93.68 thf(26268,plain,((! [A:num]: ((minus_minus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (numera6690914467698888265omplex @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5569])). 185.47/93.68 thf(135,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (ord_max_int @ B @ C)) = ((ord_less_eq_int @ A @ C) | (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3697_le__max__iff__disj)). 185.47/93.68 thf(8166,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (ord_max_int @ B @ C)) = ((ord_less_eq_int @ A @ C) | (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 185.47/93.68 thf(3592,axiom,((! [A:set_nat,B:nat]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_nat @ C @ B))) => (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3395_bounded__nat__set__is__finite)). 185.47/93.68 thf(19536,plain,((! [A:set_nat,B:nat]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_nat @ C @ B))) => (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3592])). 185.47/93.68 thf(2370,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_real @ A @ zero_zero_real) => (ord_less_eq_real @ C @ B)) & ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2569_mult__le__cancel__left)). 185.47/93.68 thf(15576,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_real @ A @ zero_zero_real) => (ord_less_eq_real @ C @ B)) & ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2370])). 185.47/93.68 thf(6142,axiom,(((neg_nu3179335615603231917ec_rat @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (bit1 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6764_dbl__dec__simps_I4_J)). 185.47/93.68 thf(28361,plain,(((neg_nu3179335615603231917ec_rat @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (bit1 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6142])). 185.47/93.68 thf(4947,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => (((dvd_dvd_nat @ (divide_divide_nat @ B @ A) @ (divide_divide_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)) <= (dvd_dvd_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4448_div__dvd__div)). 185.47/93.68 thf(23930,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => (((dvd_dvd_nat @ (divide_divide_nat @ B @ A) @ (divide_divide_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)) | ~ (dvd_dvd_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4947])). 185.47/93.68 thf(7178,axiom,((! [A:num]: (zero_zero_int != (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2039_zero__neq__numeral)). 185.47/93.68 thf(32181,plain,((! [A:num]: ~ (zero_zero_int = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7178])). 185.47/93.68 thf(5410,axiom,((! [A:real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5025_add_Oinverse__inverse)). 185.47/93.68 thf(25627,plain,((! [A:real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5410])). 185.47/93.68 thf(6812,axiom,((! [A:nat,B:nat,C:nat]: ((((~ (ord_less_eq_nat @ B @ C)) => ((divide_divide_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B)) = (divide_divide_nat @ one_one_nat @ (power_power_nat @ A @ (minus_minus_nat @ B @ C))))) & ((ord_less_eq_nat @ B @ C) => ((divide_divide_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B)) = (power_power_nat @ A @ (minus_minus_nat @ C @ B))))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2953_power__diff__power__eq)). 185.47/93.68 thf(30780,plain,((! [A:nat,B:nat,C:nat]: ((((~ (ord_less_eq_nat @ B @ C)) => ((divide_divide_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B)) = (divide_divide_nat @ one_one_nat @ (power_power_nat @ A @ (minus_minus_nat @ B @ C))))) & ((ord_less_eq_nat @ B @ C) => ((divide_divide_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B)) = (power_power_nat @ A @ (minus_minus_nat @ C @ B))))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6812])). 185.47/93.68 thf(2470,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B)) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2636_add__pos__nonneg)). 185.47/93.68 thf(15913,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2470])). 185.47/93.68 thf(4974,axiom,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_power__one__right)). 185.47/93.68 thf(24010,plain,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4974])). 185.47/93.68 thf(6571,axiom,(((^ [A:complex]: (zero_zero_complex)) = (times_times_complex @ zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2146_lambda__zero)). 185.47/93.68 thf(29915,plain,(((^ [A:complex]: (zero_zero_complex)) = (times_times_complex @ zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6571])). 185.47/93.68 thf(5750,axiom,(((^ [A:rat]: (A)) = (times_times_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1354_lambda__one)). 185.47/93.68 thf(26862,plain,(((^ [A:rat]: (A)) = (times_times_rat @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5750])). 185.47/93.68 thf(4778,axiom,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ A) @ B) = (uminus1351360451143612070nteger @ (times_3573771949741848930nteger @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5073_mult__minus__left)). 185.47/93.68 thf(23353,plain,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ A) @ B) = (uminus1351360451143612070nteger @ (times_3573771949741848930nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4778])). 185.47/93.68 thf(3141,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_eq_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_add__le__cancel__left)). 185.47/93.68 thf(18115,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ A @ C)) = (ord_less_eq_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3141])). 185.47/93.68 thf(4202,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ B)) @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ A))) <= (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7322_inverse__of__nat__le)). 185.47/93.68 thf(21451,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ B)) @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ A))) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4202])). 185.47/93.68 thf(4041,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (uminus_uminus_int @ (modulo_modulo_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5106_mod__minus__minus)). 185.47/93.68 thf(20959,plain,((! [A:int,B:int]: ((modulo_modulo_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (uminus_uminus_int @ (modulo_modulo_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4041])). 185.47/93.68 thf(5610,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = A) = ((A = zero_zero_real) | (B = one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1666_mult__cancel__left2)). 185.47/93.68 thf(26399,plain,((! [A:real,B:real]: (((times_times_real @ A @ B) = A) = ((A = zero_zero_real) | (B = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5610])). 185.47/93.68 thf(7310,axiom,((! [A:(nat > $o),B:nat]: (((! [C:nat]: ((A @ C) <= (A @ (suc @ C)))) => (A @ zero_zero_nat)) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2104_zero__induct)). 185.47/93.68 thf(32630,plain,((! [A:(nat > $o),B:nat]: (((! [C:nat]: ((A @ C) | ~ (A @ (suc @ C)))) => (A @ zero_zero_nat)) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7310])). 185.47/93.68 thf(1858,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ B @ A) @ zero_zero_int) <= (ord_less_int @ B @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2335_mult__pos__neg2)). 185.47/93.68 thf(13959,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ B @ A) @ zero_zero_int) | ~ (ord_less_int @ B @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1858])). 185.47/93.68 thf(4176,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ C) => ((A = B) => (! [F:vEBT_VEBT]: ((~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) <= (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ D))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_mi__eq__ma__no__ch)). 185.47/93.68 thf(21369,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ C) => ((A = B) => (! [F:vEBT_VEBT]: (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)) | ~ (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ D))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4176])). 185.47/93.68 thf(1565,axiom,((! [A:vEBT_VEBT,B:list_VEBT_VEBT]: ((ord_less_nat @ zero_zero_nat @ (size_s6755466524823107622T_VEBT @ B)) <= (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2784_length__pos__if__in__set)). 185.47/93.68 thf(12915,plain,((! [A:vEBT_VEBT,B:list_VEBT_VEBT]: ((ord_less_nat @ zero_zero_nat @ (size_s6755466524823107622T_VEBT @ B)) | ~ (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565])). 185.47/93.68 thf(6773,axiom,((! [A:nat,B:real,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((root @ A @ (power_power_real @ B @ C)) = (power_power_real @ (root @ A @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9185_real__root__power)). 185.47/93.68 thf(30649,plain,((! [A:nat,B:real,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((root @ A @ (power_power_real @ B @ C)) = (power_power_real @ (root @ A @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6773])). 185.47/93.68 thf(7474,axiom,(((semiri1408675320244567234ct_nat @ (suc @ zero_zero_nat)) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7967_fact__Suc__0)). 185.47/93.68 thf(33193,plain,(((semiri1408675320244567234ct_nat @ (suc @ zero_zero_nat)) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7474])). 185.47/93.68 thf(731,axiom,((! [A:int,B:int]: ((A = (ord_max_int @ A @ B)) => (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3667_max_OorderI)). 185.47/93.68 thf(10169,plain,((! [A:int,B:int]: ((A = (ord_max_int @ A @ B)) => (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[731])). 185.47/93.68 thf(3199,axiom,((! [A:int]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ zero_zero_rat) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7037_of__int__less__0__iff)). 185.47/93.68 thf(18298,plain,((! [A:int]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ zero_zero_rat) = (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3199])). 185.47/93.68 thf(233,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (ord_max_int @ A @ B) @ C) = (ord_max_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3755_max__add__distrib__left)). 185.47/93.68 thf(8474,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (ord_max_int @ A @ B) @ C) = (ord_max_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 185.47/93.68 thf(5692,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_add__strict__left__mono)). 185.47/93.68 thf(26673,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5692])). 185.47/93.68 thf(6498,axiom,((! [A:real,B:real,C:nat]: (((times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) = one_one_real) <= ((times_times_real @ A @ B) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_839_left__right__inverse__power)). 185.47/93.68 thf(29656,plain,((! [A:real,B:real,C:nat]: (((times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) = one_one_real) | ~ ((times_times_real @ A @ B) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6498])). 185.47/93.68 thf(1522,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri681578069525770553at_rat @ (binomial @ B @ A)) = (divide_divide_rat @ (semiri773545260158071498ct_rat @ B) @ (times_times_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ B @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8554_binomial__fact)). 185.47/93.68 thf(12786,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri681578069525770553at_rat @ (binomial @ B @ A)) = (divide_divide_rat @ (semiri773545260158071498ct_rat @ B) @ (times_times_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1522])). 185.47/93.68 thf(1651,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => ((abs_abs_int @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6481_abs__of__pos)). 185.47/93.68 thf(13224,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => ((abs_abs_int @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651])). 185.47/93.68 thf(4076,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_real @ B @ C)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2350_mult__less__cancel__left__pos)). 185.47/93.68 thf(21061,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_real @ B @ C)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4076])). 185.47/93.68 thf(6947,axiom,((! [A:rat,B:nat]: ((A != zero_zero_rat) => ((power_power_rat @ A @ B) != zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2094_power__not__zero)). 185.47/93.68 thf(31294,plain,((! [A:rat,B:nat]: ((~ (A = zero_zero_rat)) => (~ ((power_power_rat @ A @ B) = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6947])). 185.47/93.68 thf(664,axiom,((! [A:(nat > nat),B:set_nat,C:nat]: ((power_power_nat @ (groups708209901874060359at_nat @ A @ B) @ C) = (groups708209901874060359at_nat @ (^ [D:nat]: (power_power_nat @ (A @ D) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8728_prod__power__distrib)). 185.47/93.68 thf(9951,plain,((! [A:(nat > nat),B:set_nat,C:nat]: ((power_power_nat @ (groups708209901874060359at_nat @ (A) @ B) @ C) = (groups708209901874060359at_nat @ (^ [D:nat]: (power_power_nat @ (A @ D) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[664])). 185.47/93.68 thf(6102,axiom,((! [A:num,B:num]: ((minus_minus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (numeral_numeral_rat @ B)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (plus_plus_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5330_diff__numeral__simps_I3_J)). 185.47/93.68 thf(28212,plain,((! [A:num,B:num]: ((minus_minus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (numeral_numeral_rat @ B)) = (uminus_uminus_rat @ (numeral_numeral_rat @ (plus_plus_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6102])). 185.47/93.68 thf(3338,axiom,((! [A:real,B:nat,C:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_power__increasing__iff)). 185.47/93.68 thf(18724,plain,((! [A:real,B:nat,C:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3338])). 185.47/93.68 thf(1329,axiom,((ord_less_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_4251_dual__order_Ostrict__iff__not)). 185.47/93.68 thf(12166,plain,(((ord_less_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)],[1329])). 185.47/93.68 thf(342,axiom,(((ord_max_int @ zero_zero_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3629_max__0__1_I1_J)). 185.47/93.68 thf(8882,plain,(((ord_max_int @ zero_zero_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 185.47/93.68 thf(4533,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_add__diff__cancel)). 185.47/93.68 thf(22522,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4533])). 185.47/93.68 thf(4020,axiom,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_less_real @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4073_ord__eq__less__subst)). 185.47/93.68 thf(20898,plain,((! [A:real,B:(real > real),C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4020])). 185.47/93.68 thf(6611,axiom,((! [A:num,B:num,C:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ C)) @ (numeral_numeral_nat @ (bit0 @ B)))) = ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (modulo_modulo_nat @ (numeral_numeral_nat @ C) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6606_cong__exp__iff__simps_I13_J)). 185.47/93.68 thf(30037,plain,((! [A:num,B:num,C:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ C)) @ (numeral_numeral_nat @ (bit0 @ B)))) = ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (modulo_modulo_nat @ (numeral_numeral_nat @ C) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6611])). 185.47/93.68 thf(5057,axiom,(((semiri1406184849735516958ct_int @ (suc @ zero_zero_nat)) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7965_fact__Suc__0)). 185.47/93.68 thf(24360,plain,(((semiri1406184849735516958ct_int @ (suc @ zero_zero_nat)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5057])). 185.47/93.68 thf(5983,axiom,((! [A:nat]: ((dvd_dvd_nat @ A @ (suc @ zero_zero_nat)) = (A = (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4446_dvd__1__iff__1)). 185.47/93.68 thf(27835,plain,((! [A:nat]: ((dvd_dvd_nat @ A @ (suc @ zero_zero_nat)) = (A = (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5983])). 185.47/93.68 thf(1054,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => (~ (! [B:code_integer]: (A != (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4900_evenE)). 185.47/93.68 thf(11317,plain,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => (~ (! [B:code_integer]: ~ (A = (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054])). 185.47/93.68 thf(4141,axiom,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ (root @ A @ B) @ (root @ A @ C)) = (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9163_real__root__le__iff)). 185.47/93.68 thf(21264,plain,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ (root @ A @ B) @ (root @ A @ C)) = (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4141])). 185.47/93.68 thf(3517,axiom,((! [A:num]: ((ring_1_of_int_rat @ (numeral_numeral_int @ A)) = (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6938_of__int__numeral)). 185.47/93.68 thf(19307,plain,((! [A:num]: ((ring_1_of_int_rat @ (numeral_numeral_int @ A)) = (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3517])). 185.47/93.68 thf(4960,axiom,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (root @ A @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9188_real__root__gt__zero)). 185.47/93.68 thf(23972,plain,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (root @ A @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4960])). 185.47/93.68 thf(4615,axiom,((! [A:nat]: ((bit_se8568078237143864401it_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9754_drop__bit__minus__one)). 185.47/93.68 thf(22775,plain,((! [A:nat]: ((bit_se8568078237143864401it_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4615])). 185.47/93.68 thf(86,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7575_sum_Onat__diff__reindex)). 185.47/93.68 thf(8011,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 185.47/93.68 thf(3631,axiom,((semiri2265585572941072030t_real = (^ [A:nat]: (semiri5074537144036343181t_real @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8332_fact__code)). 185.47/93.68 thf(19654,plain,(((semiri2265585572941072030t_real) = (^ [A:nat]: (semiri5074537144036343181t_real @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3631])). 185.47/93.68 thf(1445,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) <= (ord_less_eq_real @ one_one_real @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_874_power__increasing)). 185.47/93.68 thf(12552,plain,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) | ~ (ord_less_eq_real @ one_one_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445])). 185.47/93.68 thf(5714,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (suc @ (numeral_numeral_nat @ (bit0 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6605_eval__nat__numeral_I3_J)). 185.47/93.68 thf(26752,plain,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (suc @ (numeral_numeral_nat @ (bit0 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5714])). 185.47/93.68 thf(4068,axiom,((! [A:code_integer,B:code_integer]: ((abs_abs_Code_integer @ (times_3573771949741848930nteger @ A @ B)) = (times_3573771949741848930nteger @ (abs_abs_Code_integer @ A) @ (abs_abs_Code_integer @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6457_abs__mult)). 185.47/93.68 thf(21036,plain,((! [A:code_integer,B:code_integer]: ((abs_abs_Code_integer @ (times_3573771949741848930nteger @ A @ B)) = (times_3573771949741848930nteger @ (abs_abs_Code_integer @ A) @ (abs_abs_Code_integer @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4068])). 185.47/93.68 thf(6316,axiom,((! [A:nat,B:rat]: (((power_power_rat @ (uminus_uminus_rat @ B) @ A) = (power_power_rat @ B @ A)) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5437_Parity_Oring__1__class_Opower__minus__even)). 185.47/93.68 thf(28988,plain,((! [A:nat,B:rat]: (((power_power_rat @ (uminus_uminus_rat @ B) @ A) = (power_power_rat @ B @ A)) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6316])). 185.47/93.68 thf(7620,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (vEBT_VEBT_high @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_high__bound__aux)). 185.47/93.68 thf(33625,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (vEBT_VEBT_high @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7620])). 185.47/93.68 thf(6046,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ one_one_nat) = ((dvd_dvd_nat @ A @ one_one_nat) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4877_is__unit__power__iff)). 185.47/93.68 thf(28029,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ one_one_nat) = ((dvd_dvd_nat @ A @ one_one_nat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6046])). 185.47/93.68 thf(3176,axiom,(((semiri681578069525770553at_rat @ one_one_nat) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6922_of__nat__1)). 185.47/93.68 thf(18224,plain,(((semiri681578069525770553at_rat @ one_one_nat) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3176])). 185.47/93.68 thf(2202,axiom,((! [A:real,B:real]: ((times_times_complex @ (complex2 @ A @ B) @ imaginary_unit) = (complex2 @ (uminus_uminus_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9009_Complex__mult__i)). 185.47/93.68 thf(15067,plain,((! [A:real,B:real]: ((times_times_complex @ (complex2 @ A @ B) @ imaginary_unit) = (complex2 @ (uminus_uminus_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2202])). 185.47/93.68 thf(4568,axiom,((! [A:int,B:(num > int),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_eq_int @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F))))) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3945_ord__eq__le__subst)). 185.47/93.68 thf(22633,plain,((! [A:int,B:(num > int),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_eq_int @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4568])). 185.47/93.68 thf(174,axiom,((! [A:real]: (((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A)) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8326_arcsin__lbound)). 185.47/93.68 thf(8292,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A)) | ~ (ord_less_eq_real @ A @ one_one_real) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 185.47/93.68 thf(1896,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ B @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4122_order__less__not__sym)). 185.47/93.68 thf(14069,plain,((! [A:int,B:int]: (~ (ord_less_int @ B @ A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1896])). 185.47/93.68 thf(7668,axiom,((vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ maxy)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_scmem)). 185.47/93.68 thf(33757,plain,((vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) @ maxy)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7668])). 185.47/93.68 thf(1508,axiom,((! [A:nat,B:nat,C:code_integer]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ C @ A) @ (power_8256067586552552935nteger @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4786_le__imp__power__dvd)). 185.47/93.68 thf(12743,plain,((! [A:nat,B:nat,C:code_integer]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ C @ A) @ (power_8256067586552552935nteger @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508])). 185.47/93.68 thf(4950,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1509_add_Oright__neutral)). 185.47/93.68 thf(23940,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4950])). 185.47/93.68 thf(1135,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (exp_real @ A) @ (exp_real @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8118_exp__le__cancel__iff)). 185.47/93.68 thf(11585,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (exp_real @ A) @ (exp_real @ B)) = (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135])). 185.47/93.68 thf(4835,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) <= (! [C:real]: ((ord_less_real @ A @ C) => (ord_less_eq_real @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4178_dense__ge)). 185.47/93.68 thf(23529,plain,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) | ~ (! [C:real]: ((ord_less_real @ A @ C) => (ord_less_eq_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4835])). 185.47/93.68 thf(1645,axiom,((! [A:$o]: ((ord_less_int @ (zero_n2684676970156552555ol_int @ A) @ one_one_int) = (~ (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5241_of__bool__less__one__iff)). 185.47/93.68 thf(13203,plain,((! [A:$o]: ((ord_less_int @ (zero_n2684676970156552555ol_int @ A) @ one_one_int) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645])). 185.47/93.68 thf(2737,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2220_mult__nonneg__nonneg)). 185.47/93.68 thf(16835,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2737])). 185.47/93.68 thf(7029,axiom,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = (ord_less_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4283_linorder__not__le)). 185.47/93.68 thf(31675,plain,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = (ord_less_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7029])). 185.47/93.68 thf(259,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (divide_divide_real @ (ln_ln_real @ B) @ B) @ (divide_divide_real @ (ln_ln_real @ A) @ A)) <= (ord_less_eq_real @ A @ B)) <= (ord_less_eq_real @ (exp_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8208_ln__x__over__x__mono)). 185.47/93.68 thf(8584,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (divide_divide_real @ (ln_ln_real @ B) @ B) @ (divide_divide_real @ (ln_ln_real @ A) @ A)) | ~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ (exp_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 185.47/93.68 thf(2324,axiom,((! [A:nat,B:nat]: ((semiri681578069525770553at_rat @ (times_times_nat @ A @ B)) = (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6917_of__nat__mult)). 185.47/93.68 thf(15436,plain,((! [A:nat,B:nat]: ((semiri681578069525770553at_rat @ (times_times_nat @ A @ B)) = (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2324])). 185.47/93.68 thf(144,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (ln_ln_real @ A)) = (ord_less_real @ one_one_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5236_ln__gt__zero__iff)). 185.47/93.68 thf(8197,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (ln_ln_real @ A)) = (ord_less_real @ one_one_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 185.47/93.68 thf(2210,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_add__less__le__mono)). 185.47/93.68 thf(15088,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2210])). 185.47/93.68 thf(5979,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ A @ C) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3311_pinf_I8_J)). 185.47/93.68 thf(27825,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5979])). 185.47/93.68 thf(2293,axiom,((ord_less_eq_rat = (^ [A:rat,B:rat]: ((B = A) | (ord_less_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4229_dual__order_Oorder__iff__strict)). 185.47/93.68 thf(15341,plain,(((ord_less_eq_rat) = (^ [A:rat,B:rat]: ((B = A) | (ord_less_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2293])). 185.47/93.68 thf(6094,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2237_mult__left__mono)). 185.47/93.68 thf(28185,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6094])). 185.47/93.68 thf(3367,axiom,((! [A:int,B:real]: ((times_times_real @ (ring_1_of_int_real @ A) @ B) = (times_times_real @ B @ (ring_1_of_int_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7179_mult__of__int__commute)). 185.47/93.68 thf(18818,plain,((! [A:int,B:real]: ((times_times_real @ (ring_1_of_int_real @ A) @ B) = (times_times_real @ B @ (ring_1_of_int_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3367])). 185.47/93.68 thf(1182,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A)) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_eq_real @ (abs_abs_real @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6310_abs__ln__one__plus__x__minus__x__bound)). 185.47/93.68 thf(11717,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A)) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182])). 185.47/93.68 thf(2025,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7260_nat__less__as__int)). 185.47/93.68 thf(14503,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2025])). 185.47/93.68 thf(3407,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ B @ A) @ C) => (ord_less_real @ B @ (divide_divide_real @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2709_mult__imp__less__div__pos)). 185.47/93.68 thf(18950,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ B @ A) @ C) => (ord_less_real @ B @ (divide_divide_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3407])). 185.47/93.68 thf(2797,axiom,((! [A:(nat > real),B:nat,C:nat]: ((! [D:nat]: (ord_less_real @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_real @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1059_lift__Suc__mono__less__iff)). 185.47/93.68 thf(17020,plain,((! [A:(nat > real),B:nat,C:nat]: ((! [D:nat]: (ord_less_real @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_real @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2797])). 185.47/93.68 thf(3156,axiom,((! [A:real,B:real,C:real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_718_diff__eq__eq)). 185.47/93.68 thf(18166,plain,((! [A:real,B:real,C:real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3156])). 185.47/93.68 thf(390,axiom,((! [A:int,B:int]: (((ord_max_int @ B @ A) = B) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4409_max__absorb1)). 185.47/93.68 thf(9029,plain,((! [A:int,B:int]: (((ord_max_int @ B @ A) = B) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])). 185.47/93.68 thf(2242,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3101_verit__comp__simplify1_I3_J)). 185.47/93.68 thf(15191,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2242])). 185.47/93.68 thf(5475,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_int @ (uminus_uminus_int @ one_one_int) @ A) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5466_neg__one__even__power)). 185.47/93.68 thf(25956,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_int @ (uminus_uminus_int @ one_one_int) @ A) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5475])). 185.47/93.68 thf(6838,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2451_zero__le__power)). 185.47/93.68 thf(30862,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6838])). 185.47/93.68 thf(4883,axiom,((! [A:nat,B:real,C:real]: ((root @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (root @ A @ B) @ (root @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9180_real__root__divide)). 185.47/93.68 thf(23698,plain,((! [A:nat,B:real,C:real]: ((root @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (root @ A @ B) @ (root @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4883])). 185.47/93.68 thf(2139,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) => ((dvd_dvd_int @ B @ C) <= (A != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4814_zdvd__mult__cancel)). 185.47/93.68 thf(14849,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) => ((dvd_dvd_int @ B @ C) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2139])). 185.47/93.68 thf(3453,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (C = (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1218_eq__add__iff2)). 185.47/93.68 thf(19087,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((plus_plus_real @ (times_times_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ D @ B) @ E)) = (C = (plus_plus_real @ (times_times_real @ (minus_minus_real @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3453])). 185.47/93.68 thf(7057,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ (power_power_nat @ A @ B))) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2896_self__le__power)). 185.47/93.68 thf(31768,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ (power_power_nat @ A @ B))) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7057])). 185.47/93.68 thf(2891,axiom,((! [A:nat,B:int]: ((ord_less_int @ (bit_ri631733984087533419it_int @ A @ B) @ B) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4977_signed__take__bit__int__less__self__iff)). 185.47/93.68 thf(17327,plain,((! [A:nat,B:int]: ((ord_less_int @ (bit_ri631733984087533419it_int @ A @ B) @ B) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2891])). 185.47/93.68 thf(3426,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1560_div__by__0)). 185.47/93.68 thf(19009,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3426])). 185.47/93.68 thf(4721,axiom,((! [A:nat]: ((bit_ri631733984087533419it_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5251_signed__take__bit__of__minus__1)). 185.47/93.68 thf(23141,plain,((! [A:nat]: ((bit_ri631733984087533419it_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4721])). 185.47/93.68 thf(4791,axiom,((! [A:real,B:real,C:real]: (((((powr_real @ A @ B) = (powr_real @ A @ C)) = (B = C)) <= (A != one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9094_powr__inj)). 185.47/93.68 thf(23392,plain,((! [A:real,B:real,C:real]: ((((powr_real @ A @ B) = (powr_real @ A @ C)) = (B = C)) | (A = one_one_real) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4791])). 185.47/93.68 thf(2558,axiom,((! [A:complex,B:real,C:complex,D:real]: (((ord_less_eq_real @ (real_V1022390504157884413omplex @ C) @ D) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ C)) @ (plus_plus_real @ B @ D))) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7491_norm__triangle__mono)). 185.47/93.68 thf(16213,plain,((! [A:complex,B:real,C:complex,D:real]: (((ord_less_eq_real @ (real_V1022390504157884413omplex @ C) @ D) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ C)) @ (plus_plus_real @ B @ D))) | ~ (ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2558])). 185.47/93.68 thf(5014,axiom,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1468_valid__tree__deg__neq__0)). 185.47/93.68 thf(24147,plain,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5014])). 185.47/93.68 thf(7563,axiom,(((numeral_numeral_nat @ one) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_832_numeral__One)). 185.47/93.68 thf(33469,plain,(((numeral_numeral_nat @ one) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7563])). 185.47/93.68 thf(6883,axiom,((! [A:num,B:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_numeral__le__iff)). 185.47/93.68 thf(31078,plain,((! [A:num,B:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6883])). 185.47/93.68 thf(2300,axiom,((! [A:nat]: ((comm_s4663373288045622133er_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8423_pochhammer__0)). 185.47/93.68 thf(15358,plain,((! [A:nat]: ((comm_s4663373288045622133er_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2300])). 185.47/93.68 thf(3091,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se1409905431419307370or_int @ A @ B)) = ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9408_or__nonnegative__int__iff)). 185.47/93.68 thf(17960,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se1409905431419307370or_int @ A @ B)) = ((ord_less_eq_int @ zero_zero_int @ A) & (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3091])). 185.47/93.68 thf(2967,axiom,((! [A:real,B:real,C:real,D:real]: (((((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) <= (ord_less_real @ zero_zero_real @ C)) <= (ord_less_eq_real @ zero_zero_real @ A)) <= (ord_less_eq_real @ C @ D)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2615_mult__less__le__imp__less)). 185.47/93.68 thf(17565,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) | ~ (ord_less_real @ zero_zero_real @ C) | ~ (ord_less_eq_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ C @ D) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2967])). 185.47/93.68 thf(1640,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (times_times_int @ A @ B) @ C) = (dvd_dvd_int @ B @ C)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4737_mult__unit__dvd__iff_H)). 185.47/93.68 thf(13188,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (times_times_int @ A @ B) @ C) = (dvd_dvd_int @ B @ C)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640])). 185.47/93.68 thf(6926,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => (((times_times_rat @ A @ B) = (times_times_rat @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2060_mult__left__cancel)). 185.47/93.68 thf(31219,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => (((times_times_rat @ A @ B) = (times_times_rat @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6926])). 185.47/93.68 thf(3910,axiom,((! [A:num,B:nat,C:int]: ((ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ (nat2 @ C)) = (ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9262_numeral__power__less__nat__cancel__iff)). 185.47/93.68 thf(20555,plain,((! [A:num,B:nat,C:int]: ((ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ (nat2 @ C)) = (ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3910])). 185.47/93.68 thf(3587,axiom,((! [A:real,B:real]: (((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1812_divide__less__eq__1__pos)). 185.47/93.68 thf(19522,plain,((! [A:real,B:real]: (((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3587])). 185.47/93.68 thf(3702,axiom,((comm_s4028243227959126397er_rat = (^ [A:rat,B:nat]: (if_rat @ (B = zero_zero_nat) @ one_one_rat @ (set_fo1949268297981939178at_rat @ (^ [C:nat]: (times_times_rat @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8604_pochhammer__code)). 185.47/93.68 thf(19884,plain,(((comm_s4028243227959126397er_rat) = (^ [A:rat,B:nat]: (if_rat @ (B = zero_zero_nat) @ one_one_rat @ (set_fo1949268297981939178at_rat @ (^ [C:nat]: (times_times_rat @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3702])). 185.47/93.68 thf(6108,axiom,((! [A:nat,B:real]: ((root @ A @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (root @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9178_real__root__minus)). 185.47/93.68 thf(28245,plain,((! [A:nat,B:real]: ((root @ A @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (root @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6108])). 185.47/93.68 thf(7543,axiom,((! [A:nat]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_nat @ (times_times_nat @ (times_times_nat @ A @ A) @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_power4__eq__xxxx)). 185.47/93.68 thf(33415,plain,((! [A:nat]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_nat @ (times_times_nat @ (times_times_nat @ A @ A) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7543])). 185.47/93.68 thf(5205,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ (suc @ (plus_plus_nat @ A @ B)) @ (suc @ A))) = (times_times_nat @ (suc @ B) @ (binomial @ (suc @ (plus_plus_nat @ A @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8450_Suc__times__binomial__add)). 185.47/93.68 thf(24888,plain,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ (suc @ (plus_plus_nat @ A @ B)) @ (suc @ A))) = (times_times_nat @ (suc @ B) @ (binomial @ (suc @ (plus_plus_nat @ A @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5205])). 185.47/93.68 thf(7512,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ A) <= (ord_less_num @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3277_minf_I5_J)). 185.47/93.68 thf(33321,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ A) | ~ (ord_less_num @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7512])). 185.47/93.68 thf(3475,axiom,((! [A:real,B:real]: ((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ A)) = (divide_divide_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_real__divide__square__eq)). 185.47/93.68 thf(19173,plain,((! [A:real,B:real]: ((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ A)) = (divide_divide_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3475])). 185.47/93.68 thf(5758,axiom,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = one_one_nat) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6931_of__nat__eq__1__iff)). 185.47/93.68 thf(26885,plain,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = one_one_nat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5758])). 185.47/93.68 thf(4100,axiom,((! [A:nat]: ~ (ord_less_int @ (bit_se2000444600071755411sk_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9222_not__mask__negative__int)). 185.47/93.68 thf(21140,plain,((! [A:nat]: ~ (ord_less_int @ (bit_se2000444600071755411sk_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4100])). 185.47/93.68 thf(5201,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4937_even__iff__mod__2__eq__zero)). 185.47/93.68 thf(24877,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5201])). 185.47/93.68 thf(2638,axiom,((! [A:complex,B:complex,C:nat]: ((dvd_dvd_complex @ A @ B) => (dvd_dvd_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4681_dvd__power__same)). 185.47/93.68 thf(16482,plain,((! [A:complex,B:complex,C:nat]: ((dvd_dvd_complex @ A @ B) => (dvd_dvd_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2638])). 185.47/93.68 thf(1715,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4600_dvd__mult2)). 185.47/93.68 thf(13470,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715])). 185.47/93.68 thf(2337,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_complex @ (semiri8010041392384452111omplex @ A) @ B) = (semiri8010041392384452111omplex @ C)) = ((power_power_nat @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6952_of__nat__eq__of__nat__power__cancel__iff)). 185.47/93.68 thf(15476,plain,((! [A:nat,B:nat,C:nat]: (((power_power_complex @ (semiri8010041392384452111omplex @ A) @ B) = (semiri8010041392384452111omplex @ C)) = ((power_power_nat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2337])). 185.47/93.68 thf(5686,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ one_one_nat @ (power_power_nat @ A @ B)) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_836_one__le__power)). 185.47/93.68 thf(26654,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ one_one_nat @ (power_power_nat @ A @ B)) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5686])). 185.47/93.68 thf(6752,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4146_order__less__imp__not__less)). 185.47/93.68 thf(30565,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6752])). 185.47/93.68 thf(3450,axiom,((! [A:num]: ((fract @ (numeral_numeral_int @ A) @ one_one_int) = (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9947_rat__number__collapse_I3_J)). 185.47/93.68 thf(19077,plain,((! [A:num]: ((fract @ (numeral_numeral_int @ A) @ one_one_int) = (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3450])). 185.47/93.68 thf(2031,axiom,((! [A:rat,B:rat,C:num]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ (numeral_numeral_rat @ C)) = (((ord_less_eq_rat @ A @ (times_times_rat @ (numeral_numeral_rat @ C) @ B)) <= (ord_less_rat @ zero_zero_rat @ B)) & ((~ (ord_less_rat @ zero_zero_rat @ B)) => (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ (times_times_rat @ (numeral_numeral_rat @ C) @ B) @ A)) & ((ord_less_eq_rat @ zero_zero_rat @ (numeral_numeral_rat @ C)) <= (~ (ord_less_rat @ B @ zero_zero_rat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2924_divide__le__eq__numeral_I1_J)). 185.47/93.68 thf(14522,plain,((! [A:rat,B:rat,C:num]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ (numeral_numeral_rat @ C)) = (((ord_less_eq_rat @ A @ (times_times_rat @ (numeral_numeral_rat @ C) @ B)) | ~ (ord_less_rat @ zero_zero_rat @ B)) & ((~ (ord_less_rat @ zero_zero_rat @ B)) => (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ (times_times_rat @ (numeral_numeral_rat @ C) @ B) @ A)) & ((ord_less_eq_rat @ zero_zero_rat @ (numeral_numeral_rat @ C)) | (ord_less_rat @ B @ zero_zero_rat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2031])). 185.47/93.68 thf(187,axiom,((! [A:complex]: ((im @ (exp_complex @ A)) = (times_times_real @ (exp_real @ (re @ A)) @ (sin_real @ (im @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9687_Im__exp)). 185.47/93.68 thf(8336,plain,((! [A:complex]: ((im @ (exp_complex @ A)) = (times_times_real @ (exp_real @ (re @ A)) @ (sin_real @ (im @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 185.47/93.68 thf(7579,axiom,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_mult__numeral__1__right)). 185.47/93.68 thf(33514,plain,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7579])). 185.47/93.68 thf(4813,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1658_diff__gt__0__iff__gt)). 185.47/93.68 thf(23459,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4813])). 185.47/93.68 thf(2886,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) <= (ord_less_eq_rat @ B @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2417_divide__nonneg__nonpos)). 185.47/93.68 thf(17311,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) | ~ (ord_less_eq_rat @ B @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2886])). 185.47/93.68 thf(850,axiom,((! [A:num]: ~ (ord_le6747313008572928689nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5958_not__one__less__neg__numeral)). 185.47/93.68 thf(10648,plain,((! [A:num]: ~ (ord_le6747313008572928689nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[850])). 185.47/93.68 thf(4089,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ B @ (divide_divide_int @ C @ A)) = (divide_divide_int @ (times_times_int @ B @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4869_unit__div__mult__swap)). 185.47/93.68 thf(21105,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ B @ (divide_divide_int @ C @ A)) = (divide_divide_int @ (times_times_int @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4089])). 185.47/93.68 thf(5143,axiom,((! [A:real]: ~ (ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2944_power2__less__0)). 185.47/93.68 thf(24685,plain,((! [A:real]: ~ (ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5143])). 185.47/93.68 thf(7177,axiom,((! [A:nat,B:nat]: (((some_nat @ A) = (some_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_option_Oinject)). 185.47/93.68 thf(32178,plain,((! [A:nat,B:nat]: (((some_nat @ A) = (some_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7177])). 185.47/93.68 thf(1033,axiom,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ B @ C) | (bit_se1146084159140164899it_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9421_bit__or__int__iff)). 185.47/93.68 thf(11259,plain,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ B @ C) | (bit_se1146084159140164899it_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033])). 185.47/93.68 thf(5154,axiom,((! [A:real,B:real,C:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) = (ord_less_eq_real @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1872_power__mono__iff)). 185.47/93.68 thf(24729,plain,((! [A:real,B:real,C:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) = (ord_less_eq_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5154])). 185.47/93.68 thf(7170,axiom,((! [A:real,B:nat,C:real,D:real]: (((times_times_real @ (sgn_sgn_real @ A) @ (power_power_real @ (abs_abs_real @ A) @ B)) = C) => (((A = D) <= (ord_less_nat @ zero_zero_nat @ B)) <= (C = (times_times_real @ (sgn_sgn_real @ D) @ (power_power_real @ (abs_abs_real @ D) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9329_sgn__power__injE)). 185.47/93.68 thf(32156,plain,((! [A:real,B:nat,C:real,D:real]: (((times_times_real @ (sgn_sgn_real @ A) @ (power_power_real @ (abs_abs_real @ A) @ B)) = C) => ((A = D) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (C = (times_times_real @ (sgn_sgn_real @ D) @ (power_power_real @ (abs_abs_real @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7170])). 185.47/93.68 thf(1847,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_eq_nat @ C @ A) & (B @ C))) = (? [C:nat]: ((B @ C) & (member_nat @ C @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3077_ex__nat__less)). 185.47/93.68 thf(13929,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_eq_nat @ C @ A) & (B @ C))) = (? [C:nat]: ((B @ C) & (member_nat @ C @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1847])). 185.47/93.68 thf(3836,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_add__left__mono)). 185.47/93.68 thf(20314,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3836])). 185.47/93.68 thf(3555,axiom,((! [A:real,B:nat]: ((times_times_real @ (comm_s7457072308508201937r_real @ A @ (suc @ B)) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (suc @ B))) = (groups129246275422532515t_real @ (^ [C:nat]: (plus_plus_real @ A @ (divide_divide_real @ (semiri5074537144036343181t_real @ C) @ (numeral_numeral_real @ (bit0 @ one))))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8616_pochhammer__times__pochhammer__half)). 185.47/93.68 thf(19424,plain,((! [A:real,B:nat]: ((times_times_real @ (comm_s7457072308508201937r_real @ A @ (suc @ B)) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (suc @ B))) = (groups129246275422532515t_real @ (^ [C:nat]: (plus_plus_real @ A @ (divide_divide_real @ (semiri5074537144036343181t_real @ C) @ (numeral_numeral_real @ (bit0 @ one))))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3555])). 185.47/93.68 thf(6737,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_add__mono__thms__linordered__field_I5_J)). 185.47/93.68 thf(30472,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6737])). 185.47/93.68 thf(734,axiom,((! [A:int]: ((ord_less_int @ one_one_int @ (ring_1_of_int_int @ A)) = (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7088_of__int__1__less__iff)). 185.47/93.68 thf(10182,plain,((! [A:int]: ((ord_less_int @ one_one_int @ (ring_1_of_int_int @ A)) = (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[734])). 185.47/93.68 thf(3201,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_eq_real @ (times_times_real @ C @ A) @ (uminus_uminus_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6212_neg__minus__divide__le__eq)). 185.47/93.68 thf(18305,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_eq_real @ (times_times_real @ C @ A) @ (uminus_uminus_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3201])). 185.47/93.68 thf(5230,axiom,((! [A:real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1487_mult__zero__right)). 185.47/93.68 thf(24977,plain,((! [A:real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5230])). 185.47/93.68 thf(3709,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B)) => (ord_less_eq_rat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_add__le__imp__le__right)). 185.47/93.68 thf(19916,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B)) => (ord_less_eq_rat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3709])). 185.47/93.68 thf(3642,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (times_times_rat @ B @ A)) = (((ord_less_rat @ B @ one_one_rat) <= (ord_less_eq_rat @ A @ zero_zero_rat)) & ((ord_less_rat @ one_one_rat @ B) <= (ord_less_eq_rat @ zero_zero_rat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2825_mult__less__cancel__right1)). 185.47/93.68 thf(19692,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (times_times_rat @ B @ A)) = (((ord_less_rat @ B @ one_one_rat) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)) & ((ord_less_rat @ one_one_rat @ B) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3642])). 185.47/93.68 thf(5283,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ (abs_abs_real @ A) @ B)) = ((B = zero_zero_nat) | (A != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6420_zero__less__power__abs__iff)). 185.47/93.68 thf(25195,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ (abs_abs_real @ A) @ B)) = ((B = zero_zero_nat) | ~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5283])). 185.47/93.68 thf(4986,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1000_Suc__less__eq)). 185.47/93.68 thf(24042,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4986])). 185.47/93.68 thf(7138,axiom,((! [A:complex,B:nat]: ((times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ A) @ B) @ (power_power_complex @ (uminus1482373934393186551omplex @ A) @ B)) = (power_power_complex @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6270_minus__power__mult__self)). 185.47/93.68 thf(32031,plain,((! [A:complex,B:nat]: ((times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ A) @ B) @ (power_power_complex @ (uminus1482373934393186551omplex @ A) @ B)) = (power_power_complex @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7138])). 185.47/93.68 thf(560,axiom,((! [A:nat]: ((groups2073611262835488442omplex @ (gbinomial_complex @ (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (semiri8010041392384452111omplex @ A)) @ one_one_complex)) @ (set_ord_atMost_nat @ A)) = (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8629_gbinomial__r__part__sum)). 185.47/93.68 thf(9591,plain,((! [A:nat]: ((groups2073611262835488442omplex @ (gbinomial_complex @ (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (semiri8010041392384452111omplex @ A)) @ one_one_complex)) @ (set_ord_atMost_nat @ A)) = (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[560])). 185.47/93.68 thf(6320,axiom,((! [A:complex,B:num]: ((real_V1022390504157884413omplex @ (times_times_complex @ A @ (numera6690914467698888265omplex @ B))) = (times_times_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7445_norm__mult__numeral2)). 185.47/93.68 thf(29001,plain,((! [A:complex,B:num]: ((real_V1022390504157884413omplex @ (times_times_complex @ A @ (numera6690914467698888265omplex @ B))) = (times_times_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6320])). 185.47/93.68 thf(1787,axiom,((! [A:real]: ((((ln_ln_real @ A) = (suminf_real @ (^ [B:nat]: (times_times_real @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ B @ one_one_nat)))) @ (power_power_real @ (minus_minus_real @ A @ one_one_real) @ (suc @ B)))))) <= (ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7522_ln__series)). 185.47/93.68 thf(13721,plain,((! [A:real]: (((ln_ln_real @ A) = (suminf_real @ (^ [B:nat]: (times_times_real @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ B @ one_one_nat)))) @ (power_power_real @ (minus_minus_real @ A @ one_one_real) @ (suc @ B)))))) | ~ (ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787])). 185.47/93.68 thf(6759,axiom,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1785_less__Suc0)). 185.47/93.68 thf(30597,plain,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6759])). 185.47/93.68 thf(314,axiom,((! [A:complex]: ((ord_less_real @ zero_zero_real @ (re @ (csqrt @ A))) | (((re @ (csqrt @ A)) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ (im @ (csqrt @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9683_csqrt__principal)). 185.47/93.68 thf(8781,plain,((! [A:complex]: ((ord_less_real @ zero_zero_real @ (re @ (csqrt @ A))) | (((re @ (csqrt @ A)) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ (im @ (csqrt @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 185.47/93.68 thf(7435,axiom,((! [A:nat]: ((times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A)) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5296_minus__one__mult__self)). 185.47/93.68 thf(33052,plain,((! [A:nat]: ((times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A)) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7435])). 185.47/93.68 thf(7591,axiom,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B))) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) != (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4519_odd__add)). 185.47/93.68 thf(33542,plain,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B))) = (~ ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7591])). 185.47/93.68 thf(7681,axiom,((! [A:nat,B:nat]: (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ A)) = (divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_power__minus__is__div)). 185.47/93.68 thf(33789,plain,((! [A:nat,B:nat]: (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ A)) = (divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7681])). 185.47/93.68 thf(5374,axiom,((! [A:num,B:nat,C:nat]: ((((unique5026877609467782581ep_nat @ A @ (product_Pair_nat_nat @ C @ B)) = (product_Pair_nat_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ B)) <= (~ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ B))) & ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ B) => ((unique5026877609467782581ep_nat @ A @ (product_Pair_nat_nat @ C @ B)) = (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ one_one_nat) @ (minus_minus_nat @ B @ (numeral_numeral_nat @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1456_divmod__step__eq)). 185.47/93.68 thf(25517,plain,((! [A:num,B:nat,C:nat]: ((((unique5026877609467782581ep_nat @ A @ (product_Pair_nat_nat @ C @ B)) = (product_Pair_nat_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ B)) | (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ B)) & ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ B) => ((unique5026877609467782581ep_nat @ A @ (product_Pair_nat_nat @ C @ B)) = (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ one_one_nat) @ (minus_minus_nat @ B @ (numeral_numeral_nat @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5374])). 185.47/93.68 thf(6747,axiom,((! [A:complex,B:complex,C:num]: ((A = (divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)))) = ((((times_times_complex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = B) <= ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) != zero_zero_complex)) & ((A = zero_zero_complex) <= ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5384_eq__divide__eq__numeral1_I2_J)). 185.47/93.68 thf(30547,plain,((! [A:complex,B:complex,C:num]: ((A = (divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)))) = ((((times_times_complex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = B) | ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex)) & ((A = zero_zero_complex) | ~ ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6747])). 185.47/93.68 thf(5349,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => ((num_of_nat @ A) = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9843_num__of__nat__One)). 185.47/93.68 thf(25429,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => ((num_of_nat @ A) = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5349])). 185.47/93.68 thf(300,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ A @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_real @ (groups6591440286371151544t_real @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8695_sum_OatMost__Suc)). 185.47/93.68 thf(8716,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 185.47/93.68 thf(3174,axiom,((! [A:int,B:int,C:int,D:int]: (((dvd_dvd_int @ C @ D) => ((times_times_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ D @ C)) = (divide_divide_int @ (times_times_int @ B @ D) @ (times_times_int @ A @ C)))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4767_div__mult__div__if__dvd)). 185.47/93.68 thf(18217,plain,((! [A:int,B:int,C:int,D:int]: (((dvd_dvd_int @ C @ D) => ((times_times_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ D @ C)) = (divide_divide_int @ (times_times_int @ B @ D) @ (times_times_int @ A @ C)))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3174])). 185.47/93.68 thf(1829,axiom,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1524_add__cancel__right__left)). 185.47/93.68 thf(13858,plain,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1829])). 185.47/93.68 thf(4331,axiom,((! [A:$o]: ((semiri1314217659103216013at_int @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n2684676970156552555ol_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6998_of__nat__of__bool)). 185.47/93.68 thf(21875,plain,((! [A:$o]: ((semiri1314217659103216013at_int @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n2684676970156552555ol_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4331])). 185.47/93.68 thf(5455,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (power_power_nat @ A @ B) @ A) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_power__commutes)). 185.47/93.68 thf(25808,plain,((! [A:nat,B:nat]: ((times_times_nat @ (power_power_nat @ A @ B) @ A) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5455])). 185.47/93.68 thf(5623,axiom,((! [A:num,B:num]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)) = (numeral_numeral_rat @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_numeral__times__numeral)). 185.47/93.68 thf(26447,plain,((! [A:num,B:num]: ((times_times_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)) = (numeral_numeral_rat @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5623])). 185.47/93.68 thf(6847,axiom,((! [A:num,B:num]: ((bit_or_not_num_neg @ (bit0 @ A) @ (bit1 @ B)) = (bit0 @ (bit_or_not_num_neg @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9464_or__not__num__neg_Osimps_I6_J)). 185.47/93.68 thf(30926,plain,((! [A:num,B:num]: ((bit_or_not_num_neg @ (bit0 @ A) @ (bit1 @ B)) = (bit0 @ (bit_or_not_num_neg @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6847])). 185.47/93.68 thf(7700,axiom,(((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2891_zero__power2)). 185.47/93.68 thf(33844,plain,(((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7700])). 185.47/93.68 thf(6507,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6342_abs__1)). 185.47/93.68 thf(29693,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6507])). 185.47/93.68 thf(3866,axiom,((! [A:int,B:int,C:nat]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (ring_1_of_int_rat @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7093_of__int__power__le__of__int__cancel__iff)). 185.47/93.68 thf(20414,plain,((! [A:int,B:int,C:nat]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ (power_power_rat @ (ring_1_of_int_rat @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3866])). 185.47/93.68 thf(5804,axiom,((! [A:nat]: (((power_power_int @ zero_zero_int @ A) = zero_zero_int) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1968_zero__power)). 185.47/93.68 thf(27110,plain,((! [A:nat]: (((power_power_int @ zero_zero_int @ A) = zero_zero_int) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5804])). 185.47/93.68 thf(1932,axiom,((! [A:real]: ((plus_plus_real @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7807_sin__cos__squared__add2)). 185.47/93.68 thf(14177,plain,((! [A:real]: ((plus_plus_real @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (sin_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932])). 185.47/93.68 thf(6055,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => ((divide_divide_nat @ B @ A) = (suc @ (divide_divide_nat @ (minus_minus_nat @ B @ A) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2968_le__div__geq)). 185.47/93.68 thf(28053,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => ((divide_divide_nat @ B @ A) = (suc @ (divide_divide_nat @ (minus_minus_nat @ B @ A) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6055])). 185.47/93.68 thf(997,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = (B = (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6753_eq__diff__eq_H)). 185.47/93.68 thf(11145,plain,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = (B = (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[997])). 185.47/93.68 thf(5754,axiom,((! [A:num]: ((ord_less_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (ord_less_num @ one @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_one__less__numeral__iff)). 185.47/93.68 thf(26873,plain,((! [A:num]: ((ord_less_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (ord_less_num @ one @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5754])). 185.47/93.68 thf(660,axiom,((! [A:(nat > real)]: (summable_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7699_summable__0__powser)). 185.47/93.68 thf(9940,plain,((! [A:(nat > real)]: (summable_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[660])). 185.47/93.68 thf(602,axiom,((! [A:nat]: ((sin_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7793_sin__npi)). 185.47/93.68 thf(9736,plain,((! [A:nat]: ((sin_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[602])). 185.47/93.68 thf(1999,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ B) = (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ one_one_rat @ A)) & ((ord_less_eq_rat @ A @ one_one_rat) <= (ord_less_rat @ zero_zero_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2816_mult__le__cancel__right2)). 185.47/93.68 thf(14415,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ B) = (((ord_less_rat @ B @ zero_zero_rat) => (ord_less_eq_rat @ one_one_rat @ A)) & ((ord_less_eq_rat @ A @ one_one_rat) | ~ (ord_less_rat @ zero_zero_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1999])). 185.47/93.68 thf(6485,axiom,((! [A:nat]: ((binomial @ A @ A) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8412_binomial__n__n)). 185.47/93.68 thf(29620,plain,((! [A:nat]: ((binomial @ A @ A) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6485])). 185.47/93.68 thf(1513,axiom,((! [A:real,B:real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1525_add__cancel__right__left)). 185.47/93.68 thf(12758,plain,((! [A:real,B:real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513])). 185.47/93.68 thf(321,axiom,((! [A:(nat > complex),B:set_nat]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (groups2073611262835488442omplex @ A @ B)) @ (groups6591440286371151544t_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7471_norm__sum)). 185.47/93.68 thf(8805,plain,((! [A:(nat > complex),B:set_nat]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (groups2073611262835488442omplex @ (A) @ B)) @ (groups6591440286371151544t_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 185.47/93.68 thf(758,axiom,((! [A:option_nat,B:option_nat]: ((if_option_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T)). 185.47/93.68 thf(10268,plain,((! [A:option_nat,B:option_nat]: ((if_option_nat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[758])). 185.47/93.68 thf(6945,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => (((times_times_int @ A @ B) != zero_zero_int) <= (B != zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2057_no__zero__divisors)). 185.47/93.68 thf(31287,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => (~ ((times_times_int @ A @ B) = zero_zero_int) | (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6945])). 185.47/93.68 thf(3835,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ (times_times_rat @ C @ A) @ (times_times_rat @ C @ B)) <= (ord_less_eq_rat @ zero_zero_rat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2236_mult__left__mono)). 185.47/93.68 thf(20311,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ B) => ((ord_less_eq_rat @ (times_times_rat @ C @ A) @ (times_times_rat @ C @ B)) | ~ (ord_less_eq_rat @ zero_zero_rat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3835])). 185.47/93.68 thf(159,axiom,((! [A:int,B:int]: ((ring_1_of_int_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6973_of__int__add)). 185.47/93.68 thf(8240,plain,((! [A:int,B:int]: ((ring_1_of_int_int @ (plus_plus_int @ A @ B)) = (plus_plus_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 185.47/93.68 thf(5492,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2368_mult__strict__right__mono)). 185.47/93.68 thf(26023,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5492])). 185.47/93.68 thf(55,axiom,((! [A:rat,B:nat]: ((minus_minus_rat @ one_one_rat @ (power_power_rat @ A @ B)) = (times_times_rat @ (minus_minus_rat @ one_one_rat @ A) @ (groups2906978787729119204at_rat @ (^ [C:nat]: (power_power_rat @ A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7626_one__diff__power__eq_H)). 185.47/93.68 thf(7912,plain,((! [A:rat,B:nat]: ((minus_minus_rat @ one_one_rat @ (power_power_rat @ A @ B)) = (times_times_rat @ (minus_minus_rat @ one_one_rat @ A) @ (groups2906978787729119204at_rat @ (^ [C:nat]: (power_power_rat @ A @ (minus_minus_nat @ B @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 185.47/93.68 thf(6606,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4266_dual__order_Ostrict__implies__order)). 185.47/93.68 thf(30024,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6606])). 185.47/93.68 thf(4045,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ B @ A)) = (ord_less_eq_int @ B @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3057_neg__imp__zdiv__nonneg__iff)). 185.47/93.68 thf(20970,plain,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ B @ A)) = (ord_less_eq_int @ B @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4045])). 185.47/93.68 thf(119,axiom,((! [A:int,B:real]: ((ord_less_eq_int @ zero_zero_int @ A) => ((archim6058952711729229775r_real @ (divide_divide_real @ B @ (ring_1_of_int_real @ A))) = (divide_divide_int @ (archim6058952711729229775r_real @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9123_floor__divide__real__eq__div)). 185.47/93.68 thf(8119,plain,((! [A:int,B:real]: ((ord_less_eq_int @ zero_zero_int @ A) => ((archim6058952711729229775r_real @ (divide_divide_real @ B @ (ring_1_of_int_real @ A))) = (divide_divide_int @ (archim6058952711729229775r_real @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 185.47/93.68 thf(7134,axiom,((! [A:vEBT_VEBT]: ((? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B)) <= (~ (vEBT_VEBT_minNull @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_not__min__Null__member)). 185.47/93.68 thf(32021,plain,((! [A:vEBT_VEBT]: (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B) | (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7134])). 185.47/93.68 thf(7318,axiom,((! [A:nat,B:num,C:nat]: (((semiri1314217659103216013at_int @ A) = (power_power_int @ (numeral_numeral_int @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7056_real__of__nat__eq__numeral__power__cancel__iff)). 185.47/93.68 thf(32662,plain,((! [A:nat,B:num,C:nat]: (((semiri1314217659103216013at_int @ A) = (power_power_int @ (numeral_numeral_int @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7318])). 185.47/93.68 thf(429,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((groups708209901874060359at_nat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (groups708209901874060359at_nat @ (^ [D:nat]: (A @ (minus_minus_nat @ (plus_plus_nat @ C @ B) @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8864_prod_OatLeastAtMost__rev)). 185.47/93.68 thf(9160,plain,((! [A:(nat > nat),B:nat,C:nat]: ((groups708209901874060359at_nat @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (groups708209901874060359at_nat @ (^ [D:nat]: (A @ (minus_minus_nat @ (plus_plus_nat @ C @ B) @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])). 185.47/93.68 thf(782,axiom,((! [A:nat,B:int,C:int,D:int,E:int]: (((bit_concat_bit @ A @ B @ C) = (bit_concat_bit @ A @ D @ E)) = (((bit_se2923211474154528505it_int @ A @ B) = (bit_se2923211474154528505it_int @ A @ D)) & (C = E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9275_concat__bit__eq__iff)). 185.47/93.68 thf(10400,plain,((! [A:nat,B:int,C:int,D:int,E:int]: (((bit_concat_bit @ A @ B @ C) = (bit_concat_bit @ A @ D @ E)) = (((bit_se2923211474154528505it_int @ A @ B) = (bit_se2923211474154528505it_int @ A @ D)) & (C = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[782])). 185.47/93.68 thf(6922,axiom,((! [A:int]: ((minus_minus_int @ zero_zero_int @ A) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5183_verit__minus__simplify_I3_J)). 185.47/93.68 thf(31202,plain,((! [A:int]: ((minus_minus_int @ zero_zero_int @ A) = (uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6922])). 185.47/93.68 thf(5382,axiom,((! [A:real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6321_abs__eq__0)). 185.47/93.68 thf(25543,plain,((! [A:real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5382])). 185.47/93.68 thf(5096,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) <= (ord_less_nat @ B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2334_mult__pos__neg2)). 185.47/93.68 thf(24478,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) | ~ (ord_less_nat @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5096])). 185.47/93.68 thf(6718,axiom,((! [A:num,B:num,C:rat]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (times_times_rat @ (numeral_numeral_rat @ B) @ C)) = (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5355_semiring__norm_I170_J)). 185.47/93.68 thf(30409,plain,((! [A:num,B:num,C:rat]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (times_times_rat @ (numeral_numeral_rat @ B) @ C)) = (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ (times_times_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6718])). 185.47/93.68 thf(2314,axiom,((! [A:real,B:real]: (((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2324_mult__pos__neg)). 185.47/93.68 thf(15404,plain,((! [A:real,B:real]: (((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2314])). 185.47/93.68 thf(4305,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ B @ C) @ (times_times_int @ A @ C)) <= (ord_less_int @ C @ zero_zero_int)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2365_mult__strict__right__mono__neg)). 185.47/93.68 thf(21758,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ B @ C) @ (times_times_int @ A @ C)) | ~ (ord_less_int @ C @ zero_zero_int) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4305])). 185.47/93.68 thf(3109,axiom,((! [A:num,B:nat,C:int]: ((ord_less_eq_rat @ (power_power_rat @ (numeral_numeral_rat @ A) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7139_numeral__power__le__of__int__cancel__iff)). 185.47/93.68 thf(18024,plain,((! [A:num,B:nat,C:int]: ((ord_less_eq_rat @ (power_power_rat @ (numeral_numeral_rat @ A) @ B) @ (ring_1_of_int_rat @ C)) = (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3109])). 185.47/93.68 thf(303,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (ord_max_int @ C @ B)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3747_max_Ostrict__coboundedI2)). 185.47/93.68 thf(8749,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (ord_max_int @ C @ B)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 185.47/93.68 thf(7541,axiom,((vEBT_VEBT_low = (^ [A:nat,B:nat]: (modulo_modulo_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1462_low__def)). 185.47/93.68 thf(33410,plain,(((vEBT_VEBT_low) = (^ [A:nat,B:nat]: (modulo_modulo_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7541])). 185.47/93.68 thf(4979,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_add__right__mono)). 185.47/93.68 thf(24023,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4979])). 185.47/93.68 thf(416,axiom,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) != (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7741_pi__half__neq__two)). 185.47/93.68 thf(9115,plain,((~ ((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) = (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])). 185.47/93.68 thf(1140,axiom,((! [A:int,B:int,C:nat]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (ring_1_of_int_real @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7092_of__int__power__le__of__int__cancel__iff)). 185.47/93.68 thf(11599,plain,((! [A:int,B:int,C:nat]: ((ord_less_eq_real @ (ring_1_of_int_real @ A) @ (power_power_real @ (ring_1_of_int_real @ B) @ C)) = (ord_less_eq_int @ A @ (power_power_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140])). 185.47/93.68 thf(5658,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ (power_power_int @ A @ B) @ zero_zero_int) = ((ord_less_nat @ zero_zero_nat @ B) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_int @ A @ zero_zero_int)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = zero_zero_int))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4988_power__le__zero__eq)). 185.47/93.68 thf(26565,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ (power_power_int @ A @ B) @ zero_zero_int) = ((ord_less_nat @ zero_zero_nat @ B) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_int @ A @ zero_zero_int)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5658])). 185.47/93.68 thf(5992,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_Nat_Oadd__diff__assoc2)). 185.47/93.68 thf(27867,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5992])). 185.47/93.68 thf(4678,axiom,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (set_ord_atMost_nat @ A) @ (set_ord_atMost_nat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8664_atMost__subset__iff)). 185.47/93.68 thf(22990,plain,((! [A:nat,B:nat]: ((ord_less_eq_set_nat @ (set_ord_atMost_nat @ A) @ (set_ord_atMost_nat @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4678])). 185.47/93.68 thf(3800,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ B @ C) => (ord_less_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4069_order__less__trans)). 185.47/93.68 thf(20210,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ B @ C) => (ord_less_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3800])). 185.47/93.68 thf(2043,axiom,((! [A:int,B:int]: ((((times_times_int @ A @ B) = one_one_int) = ((A = one_one_int) & (B = one_one_int))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3170_pos__zmult__eq__1__iff)). 185.47/93.68 thf(14560,plain,((! [A:int,B:int]: ((((times_times_int @ A @ B) = one_one_int) = ((A = one_one_int) & (B = one_one_int))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2043])). 185.47/93.68 thf(6939,axiom,((! [A:complex]: ((minus_minus_complex @ zero_zero_complex @ A) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5184_verit__minus__simplify_I3_J)). 185.47/93.68 thf(31266,plain,((! [A:complex]: ((minus_minus_complex @ zero_zero_complex @ A) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6939])). 185.47/93.68 thf(1805,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ A) <= (A = (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4616_dvdI)). 185.47/93.68 thf(13780,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ A) | ~ (A = (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805])). 185.47/93.68 thf(2920,axiom,((neg_numeral_dbl_real = (^ [A:real]: (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3839_dbl__def)). 185.47/93.68 thf(17417,plain,(((neg_numeral_dbl_real) = (^ [A:real]: (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2920])). 185.47/93.68 thf(6336,axiom,((! [A:nat,B:nat]: (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) != zero_zero_nat) <= ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2947_exp__add__not__zero__imp__right)). 185.47/93.68 thf(29052,plain,((! [A:nat,B:nat]: (~ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) = zero_zero_nat) | ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6336])). 185.47/93.68 thf(6565,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_add__mono__thms__linordered__semiring_I1_J)). 185.47/93.68 thf(29887,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6565])). 185.47/93.68 thf(933,axiom,((! [A:nat,B:rat]: ((ord_less_eq_rat @ (power_power_rat @ (divide_divide_rat @ B @ (semiri681578069525770553at_rat @ A)) @ A) @ (gbinomial_rat @ B @ A)) <= (ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8482_gbinomial__ge__n__over__k__pow__k)). 185.47/93.68 thf(10937,plain,((! [A:nat,B:rat]: ((ord_less_eq_rat @ (power_power_rat @ (divide_divide_rat @ B @ (semiri681578069525770553at_rat @ A)) @ A) @ (gbinomial_rat @ B @ A)) | ~ (ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[933])). 185.47/93.68 thf(137,axiom,((! [A:set_nat,B:(nat > real)]: ((! [C:nat]: (((ord_less_eq_real @ (B @ C) @ one_one_real) & (ord_less_eq_real @ zero_zero_real @ (B @ C))) <= (member_nat @ C @ A))) => (ord_less_eq_real @ (groups129246275422532515t_real @ B @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8794_prod__le__1)). 185.47/93.68 thf(8172,plain,((! [A:set_nat,B:(nat > real)]: ((! [C:nat]: (((ord_less_eq_real @ (B @ C) @ one_one_real) & (ord_less_eq_real @ zero_zero_real @ (B @ C))) | ~ (member_nat @ C @ A))) => (ord_less_eq_real @ (groups129246275422532515t_real @ (B) @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 185.47/93.68 thf(6171,axiom,((! [A:(real > (real > $o)),B:real]: ((! [C:real]: ((A @ C @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one)))) <= (ord_less_eq_real @ zero_zero_real @ C))) => (A @ (abs_abs_real @ B) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6707_abs__sqrt__wlog)). 185.47/93.68 thf(28498,plain,((! [A:(real > (real > $o)),B:real]: ((! [C:real]: ((A @ C @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (ord_less_eq_real @ zero_zero_real @ C))) => (A @ (abs_abs_real @ B) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6171])). 185.47/93.68 thf(1109,axiom,((~ (ord_less_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5752_less__minus__one__simps_I4_J)). 185.47/93.68 thf(11497,plain,((~ (ord_less_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109])). 185.47/93.68 thf(678,axiom,(((ln_ln_real @ one_one_real) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5243_ln__one)). 185.47/93.68 thf(9999,plain,(((ln_ln_real @ one_one_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[678])). 185.47/93.68 thf(6069,axiom,((! [A:nat,B:nat]: ((bit_se7882103937844011126it_nat @ (suc @ A) @ B) = (plus_plus_nat @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se7882103937844011126it_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3115_set__bit__Suc)). 185.47/93.68 thf(28100,plain,((! [A:nat,B:nat]: ((bit_se7882103937844011126it_nat @ (suc @ A) @ B) = (plus_plus_nat @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se7882103937844011126it_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6069])). 185.47/93.68 thf(163,axiom,((! [A:(nat > real)]: (((! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B))) => (((suminf_real @ A) = zero_zero_real) = (! [B:nat]: ((A @ B) = zero_zero_real)))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7689_suminf__eq__zero__iff)). 185.47/93.68 thf(8253,plain,((! [A:(nat > real)]: (((! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B))) => (((suminf_real @ (A)) = zero_zero_real) = (! [B:nat]: ((A @ B) = zero_zero_real)))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 185.47/93.68 thf(1769,axiom,((! [A:num,B:num]: ((bit_or_not_num_neg @ (bit0 @ A) @ (bit0 @ B)) = (bitM @ (bit_or_not_num_neg @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9467_or__not__num__neg_Osimps_I5_J)). 185.47/93.68 thf(13656,plain,((! [A:num,B:num]: ((bit_or_not_num_neg @ (bit0 @ A) @ (bit0 @ B)) = (bitM @ (bit_or_not_num_neg @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769])). 185.47/93.68 thf(2237,axiom,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((ord_less_int @ A @ B) = (ord_less_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_705_diff__eq__diff__less)). 185.47/93.68 thf(15176,plain,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D)) => ((ord_less_int @ A @ B) = (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2237])). 185.47/93.68 thf(6874,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((semiri1408675320244567234ct_nat @ A) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8053_fact__reduce)). 185.47/93.68 thf(31049,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((semiri1408675320244567234ct_nat @ A) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6874])). 185.47/93.68 thf(237,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => (ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5880_ln__ge__zero)). 185.47/93.68 thf(8488,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => (ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 185.47/93.68 thf(2171,axiom,((! [A:int,B:int,C:nat,D:nat]: ((((C = zero_zero_nat) | ((sgn_sgn_int @ B) = zero_zero_int) | ((sgn_sgn_int @ A) = zero_zero_int)) => ((divide_divide_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = zero_zero_int)) & (((((sgn_sgn_int @ B) = (sgn_sgn_int @ A)) => ((divide_divide_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (semiri1314217659103216013at_int @ (divide_divide_nat @ D @ C)))) & (((sgn_sgn_int @ B) != (sgn_sgn_int @ A)) => ((divide_divide_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (uminus_uminus_int @ (semiri1314217659103216013at_int @ (plus_plus_nat @ (divide_divide_nat @ D @ C) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ C @ D))))))))) <= (~ (((sgn_sgn_int @ A) = zero_zero_int) | ((sgn_sgn_int @ B) = zero_zero_int) | (C = zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9240_divide__int__unfold)). 185.47/93.68 thf(14963,plain,((! [A:int,B:int,C:nat,D:nat]: ((((C = zero_zero_nat) | ((sgn_sgn_int @ B) = zero_zero_int) | ((sgn_sgn_int @ A) = zero_zero_int)) => ((divide_divide_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = zero_zero_int)) & (((((sgn_sgn_int @ B) = (sgn_sgn_int @ A)) => ((divide_divide_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (semiri1314217659103216013at_int @ (divide_divide_nat @ D @ C)))) & ((~ ((sgn_sgn_int @ B) = (sgn_sgn_int @ A))) => ((divide_divide_int @ (times_times_int @ (sgn_sgn_int @ B) @ (semiri1314217659103216013at_int @ D)) @ (times_times_int @ (sgn_sgn_int @ A) @ (semiri1314217659103216013at_int @ C))) = (uminus_uminus_int @ (semiri1314217659103216013at_int @ (plus_plus_nat @ (divide_divide_nat @ D @ C) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ C @ D))))))))) | ((sgn_sgn_int @ A) = zero_zero_int) | ((sgn_sgn_int @ B) = zero_zero_int) | (C = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2171])). 185.47/93.68 thf(1203,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7510_norm__triangle__ineq2)). 185.47/93.68 thf(11780,plain,((! [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203])). 185.47/93.68 thf(3430,axiom,((! [A:rat]: ((plus_plus_rat @ A @ (uminus_uminus_rat @ A)) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5170_add_Oright__inverse)). 185.47/93.68 thf(19023,plain,((! [A:rat]: ((plus_plus_rat @ A @ (uminus_uminus_rat @ A)) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3430])). 185.47/93.68 thf(5575,axiom,((power_power_complex = (^ [A:complex,B:nat]: (if_complex @ (B = zero_zero_nat) @ one_one_complex @ (times_times_complex @ A @ (power_power_complex @ A @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2958_power__eq__if)). 185.47/93.68 thf(26288,plain,(((power_power_complex) = (^ [A:complex,B:nat]: (if_complex @ (B = zero_zero_nat) @ one_one_complex @ (times_times_complex @ A @ (power_power_complex @ A @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5575])). 185.47/93.68 thf(4072,axiom,((! [A:num,B:num,C:num]: ((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) != (modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ C)) @ (numeral_numeral_int @ (bit0 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6610_cong__exp__iff__simps_I12_J)). 185.47/93.68 thf(21049,plain,((! [A:num,B:num,C:num]: ~ ((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ C)) @ (numeral_numeral_int @ (bit0 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4072])). 185.47/93.68 thf(5298,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3996_less__induct)). 185.47/93.68 thf(25242,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5298])). 185.47/93.68 thf(3492,axiom,((! [A:rat]: ? [B:int]: (! [C:int]: ((C = B) <= ((ord_less_rat @ A @ (ring_1_of_int_rat @ (plus_plus_int @ C @ one_one_int))) & (ord_less_eq_rat @ (ring_1_of_int_rat @ C) @ A))) & (ord_less_rat @ A @ (ring_1_of_int_rat @ (plus_plus_int @ B @ one_one_int))) & (ord_less_eq_rat @ (ring_1_of_int_rat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7367_floor__exists1)). 185.47/93.68 thf(19224,plain,((! [A:rat]: ? [B:int]: (! [C:int]: ((C = B) | ~ ((ord_less_rat @ A @ (ring_1_of_int_rat @ (plus_plus_int @ C @ one_one_int))) & (ord_less_eq_rat @ (ring_1_of_int_rat @ C) @ A))) & (ord_less_rat @ A @ (ring_1_of_int_rat @ (plus_plus_int @ B @ one_one_int))) & (ord_less_eq_rat @ (ring_1_of_int_rat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3492])). 185.47/93.68 thf(5466,axiom,((! [A:num,B:num]: ((bit0 @ A) != (bit1 @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6472_verit__eq__simplify_I14_J)). 185.47/93.68 thf(25840,plain,((! [A:num,B:num]: ~ ((bit0 @ A) = (bit1 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5466])). 185.47/93.68 thf(5528,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_757_diff__cancel2)). 185.47/93.68 thf(26141,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5528])). 185.47/93.68 thf(4255,axiom,((! [A:real]: (sums_real @ (^ [B:nat]: (times_times_real @ (divide_divide_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (semiri2265585572941072030t_real @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) @ (cos_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8280_cos__paired)). 185.47/93.68 thf(21618,plain,((! [A:real]: (sums_real @ (^ [B:nat]: (times_times_real @ (divide_divide_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (semiri2265585572941072030t_real @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (power_power_real @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) @ (cos_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4255])). 185.47/93.68 thf(7461,axiom,((! [A:real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2485_power__0)). 185.47/93.68 thf(33149,plain,((! [A:real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7461])). 185.47/93.68 thf(517,axiom,((vEBT_VEBT_minNull @ (vEBT_Leaf @ ($false) @ ($false)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1950_VEBT__internal_OminNull_Osimps_I1_J)). 185.47/93.68 thf(9470,plain,((vEBT_VEBT_minNull @ (vEBT_Leaf @ ($false) @ ($false)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[517])). 185.47/93.68 thf(4536,axiom,((! [A:real,B:nat,C:real]: (((power_power_real @ A @ (suc @ B)) = (power_power_real @ C @ (suc @ B))) => ((ord_less_eq_real @ zero_zero_real @ A) => ((A = C) <= (ord_less_eq_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2750_power__inject__base)). 185.47/93.68 thf(22531,plain,((! [A:real,B:nat,C:real]: (((power_power_real @ A @ (suc @ B)) = (power_power_real @ C @ (suc @ B))) => ((ord_less_eq_real @ zero_zero_real @ A) => ((A = C) | ~ (ord_less_eq_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4536])). 185.47/93.68 thf(1918,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) <= (ord_less_int @ zero_zero_int @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2376_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)). 185.47/93.68 thf(14138,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) | ~ (ord_less_int @ zero_zero_int @ C) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1918])). 185.47/93.68 thf(3751,axiom,((! [A:real,B:nat,C:nat]: ((comm_s7457072308508201937r_real @ A @ (plus_plus_nat @ B @ C)) = (times_times_real @ (comm_s7457072308508201937r_real @ A @ B) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8520_pochhammer__product_H)). 185.47/93.68 thf(20045,plain,((! [A:real,B:nat,C:nat]: ((comm_s7457072308508201937r_real @ A @ (plus_plus_nat @ B @ C)) = (times_times_real @ (comm_s7457072308508201937r_real @ A @ B) @ (comm_s7457072308508201937r_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3751])). 185.47/93.68 thf(5940,axiom,((! [A:real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1482_mult__zero__left)). 185.47/93.68 thf(27661,plain,((! [A:real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5940])). 185.47/93.68 thf(3308,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = ((ord_less_int @ B @ A) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4032_not__less__iff__gr__or__eq)). 185.47/93.68 thf(18634,plain,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = ((ord_less_int @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3308])). 185.47/93.68 thf(379,axiom,((! [A:(nat > real)]: (((! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B))) => ((ord_less_real @ zero_zero_real @ (suminf_real @ A)) = (? [B:nat]: (ord_less_real @ zero_zero_real @ (A @ B))))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7710_suminf__pos__iff)). 185.47/93.68 thf(8997,plain,((! [A:(nat > real)]: (((! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B))) => ((ord_less_real @ zero_zero_real @ (suminf_real @ (A))) = (? [B:nat]: (ord_less_real @ zero_zero_real @ (A @ B))))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])). 185.47/93.68 thf(2015,axiom,((! [A:nat,B:int,C:int]: ((bit_ri631733984087533419it_int @ A @ (minus_minus_int @ (bit_ri631733984087533419it_int @ A @ B) @ (bit_ri631733984087533419it_int @ A @ C))) = (bit_ri631733984087533419it_int @ A @ (minus_minus_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4691_signed__take__bit__diff)). 185.47/93.68 thf(14472,plain,((! [A:nat,B:int,C:int]: ((bit_ri631733984087533419it_int @ A @ (minus_minus_int @ (bit_ri631733984087533419it_int @ A @ B) @ (bit_ri631733984087533419it_int @ A @ C))) = (bit_ri631733984087533419it_int @ A @ (minus_minus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015])). 185.47/93.68 thf(2297,axiom,((! [A:complex]: (ord_less_eq_real @ (uminus_uminus_real @ (real_V1022390504157884413omplex @ A)) @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7428_complex__mod__minus__le__complex__mod)). 185.47/93.68 thf(15351,plain,((! [A:complex]: (ord_less_eq_real @ (uminus_uminus_real @ (real_V1022390504157884413omplex @ A)) @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2297])). 185.47/93.68 thf(3410,axiom,((! [A:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2197_not__numeral__le__zero)). 185.47/93.68 thf(18960,plain,((! [A:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3410])). 185.47/93.68 thf(3352,axiom,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5926_neg__numeral__le__one)). 185.47/93.68 thf(18779,plain,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3352])). 185.47/93.68 thf(4359,axiom,((! [A:int,B:(int > (int > $o)),C:int]: ((ord_less_int @ A @ zero_zero_int) => ((B @ (divide_divide_int @ C @ A) @ (modulo_modulo_int @ C @ A)) = (! [D:int,E:int]: (((ord_less_eq_int @ E @ zero_zero_int) & (C = (plus_plus_int @ (times_times_int @ A @ D) @ E)) & (ord_less_int @ A @ E)) => (B @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3065_split__neg__lemma)). 185.47/93.68 thf(21964,plain,((! [A:int,B:(int > (int > $o)),C:int]: ((ord_less_int @ A @ zero_zero_int) => ((B @ (divide_divide_int @ C @ A) @ (modulo_modulo_int @ C @ A)) = (! [D:int,E:int]: (((ord_less_eq_int @ E @ zero_zero_int) & (C = (plus_plus_int @ (times_times_int @ A @ D) @ E)) & (ord_less_int @ A @ E)) => (B @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4359])). 185.47/93.68 thf(3248,axiom,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) != zero_zero_int) => ((bit_se2923211474154528505it_int @ A @ (minus_minus_int @ B @ one_one_int)) = (minus_minus_int @ (bit_se2923211474154528505it_int @ A @ B) @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9291_take__bit__decr__eq)). 185.47/93.68 thf(18447,plain,((! [A:nat,B:int]: ((~ ((bit_se2923211474154528505it_int @ A @ B) = zero_zero_int)) => ((bit_se2923211474154528505it_int @ A @ (minus_minus_int @ B @ one_one_int)) = (minus_minus_int @ (bit_se2923211474154528505it_int @ A @ B) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3248])). 185.47/93.68 thf(2695,axiom,((! [A:complex,B:num,C:complex]: (((divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B)) = C) = (((A = (times_times_complex @ C @ (numera6690914467698888265omplex @ B))) <= ((numera6690914467698888265omplex @ B) != zero_zero_complex)) & (((numera6690914467698888265omplex @ B) = zero_zero_complex) => (C = zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1823_divide__eq__eq__numeral1_I1_J)). 185.47/93.68 thf(16702,plain,((! [A:complex,B:num,C:complex]: (((divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B)) = C) = (((A = (times_times_complex @ C @ (numera6690914467698888265omplex @ B))) | ((numera6690914467698888265omplex @ B) = zero_zero_complex)) & (((numera6690914467698888265omplex @ B) = zero_zero_complex) => (C = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2695])). 185.47/93.68 thf(5619,axiom,((! [A:real,B:nat,C:nat]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_nat @ C @ B)) <= (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1863_power__strict__decreasing__iff)). 185.47/93.68 thf(26433,plain,((! [A:real,B:nat,C:nat]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_nat @ C @ B)) | ~ (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5619])). 185.47/93.68 thf(7370,axiom,((! [A:int,B:nat,C:nat]: ((A != zero_zero_int) => ((dvd_dvd_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = ((dvd_dvd_int @ A @ one_one_int) | (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4914_dvd__power__iff)). 185.47/93.68 thf(32829,plain,((! [A:int,B:nat,C:nat]: ((~ (A = zero_zero_int)) => ((dvd_dvd_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = ((dvd_dvd_int @ A @ one_one_int) | (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7370])). 185.47/93.68 thf(1242,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3275_minf_I5_J)). 185.47/93.68 thf(11899,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242])). 185.47/93.68 thf(6601,axiom,((! [A:int]: ((^ [B:int]: (times_times_int @ B @ A)) = (times_times_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1337_mult__commute__abs)). 185.47/93.68 thf(30008,plain,((! [A:int]: ((^ [B:int]: (times_times_int @ B @ A)) = (times_times_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6601])). 185.47/93.68 thf(5109,axiom,((! [A:rat,B:rat,C:num]: (((divide_divide_rat @ A @ B) = (uminus_uminus_rat @ (numeral_numeral_rat @ C))) = (((B != zero_zero_rat) => (A = (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B))) & (((uminus_uminus_rat @ (numeral_numeral_rat @ C)) = zero_zero_rat) <= (B = zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6161_divide__eq__eq__numeral_I2_J)). 185.47/93.68 thf(24549,plain,((! [A:rat,B:rat,C:num]: (((divide_divide_rat @ A @ B) = (uminus_uminus_rat @ (numeral_numeral_rat @ C))) = (((~ (B = zero_zero_rat)) => (A = (times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ C)) @ B))) & (((uminus_uminus_rat @ (numeral_numeral_rat @ C)) = zero_zero_rat) | ~ (B = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5109])). 185.47/93.68 thf(6188,axiom,((! [A:nat,B:nat,C:nat]: (((semiri1316708129612266289at_nat @ A) = (power_power_nat @ (semiri1316708129612266289at_nat @ B) @ C)) = (A = (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6950_of__nat__power__eq__of__nat__cancel__iff)). 185.47/93.68 thf(28571,plain,((! [A:nat,B:nat,C:nat]: (((semiri1316708129612266289at_nat @ A) = (power_power_nat @ (semiri1316708129612266289at_nat @ B) @ C)) = (A = (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6188])). 185.47/93.68 thf(5157,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ B) @ A) = (modulo_modulo_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1597_mod__add__self1)). 185.47/93.68 thf(24741,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ B) @ A) = (modulo_modulo_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5157])). 185.47/93.68 thf(3095,axiom,((! [A:complex,B:complex,C:complex]: (((A != zero_zero_complex) => ((plus_plus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (times_times_complex @ C @ A)) @ A))) & ((A = zero_zero_complex) => ((plus_plus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6166_add__divide__eq__if__simps_I3_J)). 185.47/93.68 thf(17973,plain,((! [A:complex,B:complex,C:complex]: (((~ (A = zero_zero_complex)) => ((plus_plus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (times_times_complex @ C @ A)) @ A))) & ((A = zero_zero_complex) => ((plus_plus_complex @ (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) @ C) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3095])). 185.47/93.68 thf(7457,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ (suc @ A) @ B) @ (times_times_nat @ (suc @ A) @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1100_Suc__mult__less__cancel1)). 185.47/93.68 thf(33116,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ (suc @ A) @ B) @ (times_times_nat @ (suc @ A) @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7457])). 185.47/93.68 thf(6354,axiom,((! [A:nat,B:nat,C:product_prod_nat_nat]: (((nat_prod_decode_aux @ A @ B) = C) => (((C = (nat_prod_decode_aux @ (suc @ A) @ (minus_minus_nat @ B @ (suc @ A)))) <= (~ (ord_less_eq_nat @ B @ A))) & ((ord_less_eq_nat @ B @ A) => (C = (product_Pair_nat_nat @ B @ (minus_minus_nat @ A @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9748_prod__decode__aux_Oelims)). 185.47/93.68 thf(29126,plain,((! [A:nat,B:nat,C:product_prod_nat_nat]: (((nat_prod_decode_aux @ A @ B) = C) => (((C = (nat_prod_decode_aux @ (suc @ A) @ (minus_minus_nat @ B @ (suc @ A)))) | (ord_less_eq_nat @ B @ A)) & ((ord_less_eq_nat @ B @ A) => (C = (product_Pair_nat_nat @ B @ (minus_minus_nat @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6354])). 185.47/93.68 thf(2197,axiom,((plus_plus_rat = (^ [A:rat,B:rat]: (plus_plus_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_add_Ocommute)). 185.47/93.68 thf(15052,plain,(((plus_plus_rat) = (^ [A:rat,B:rat]: (plus_plus_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2197])). 185.47/93.68 thf(4284,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C)) = (ord_less_eq_rat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_add__le__cancel__left)). 185.47/93.68 thf(21698,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C)) = (ord_less_eq_rat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4284])). 185.47/93.68 thf(5398,axiom,((! [A:num,B:num]: ((plus_plus_num @ (bit1 @ A) @ (bit1 @ B)) = (bit0 @ (plus_plus_num @ (plus_plus_num @ A @ B) @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6408_semiring__norm_I10_J)). 185.47/93.68 thf(25590,plain,((! [A:num,B:num]: ((plus_plus_num @ (bit1 @ A) @ (bit1 @ B)) = (bit0 @ (plus_plus_num @ (plus_plus_num @ A @ B) @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5398])). 185.47/93.68 thf(1276,axiom,((! [A:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5933_neg__numeral__le__neg__one)). 185.47/93.68 thf(11999,plain,((! [A:num]: (ord_less_eq_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276])). 185.47/93.68 thf(2398,axiom,((! [A:real,B:real]: ((A != B) = ((ord_less_real @ A @ B) | (ord_less_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4058_linorder__neq__iff)). 185.47/93.68 thf(15667,plain,((! [A:real,B:real]: ((~ (A = B)) = ((ord_less_real @ A @ B) | (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2398])). 185.47/93.68 thf(6560,axiom,((! [A:nat]: ((? [B:nat]: (A = (suc @ B))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2100_not0__implies__Suc)). 185.47/93.68 thf(29873,plain,((! [A:nat]: (? [B:nat]: (A = (suc @ B)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6560])). 185.47/93.68 thf(6893,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_add__diff__cancel__left_H)). 185.47/93.68 thf(31110,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6893])). 185.47/93.68 thf(6138,axiom,(((neg_nu3179335615603231917ec_rat @ zero_zero_rat) = (uminus_uminus_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6797_dbl__dec__simps_I2_J)). 185.47/93.68 thf(28348,plain,(((neg_nu3179335615603231917ec_rat @ zero_zero_rat) = (uminus_uminus_rat @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6138])). 185.47/93.68 thf(6717,axiom,((! [A:vEBT_VEBT,B:nat]: (((accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ A @ B)) => ((! [C:$o,D:$o]: ((~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B))) <= (A = (vEBT_Leaf @ C @ D)))) => (((! [C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F)) => (((B = D) | (B = C)) <= (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F) @ B))))) => ((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G) @ B)) => ((B = D) | (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) | (B = C))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G)))) => (~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E)) => ((accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E) @ B)) => (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))))))))) <= (! [C:list_VEBT_VEBT,D:vEBT_VEBT]: ((~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ C @ D) @ B))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ C @ D))))))) <= (~ (vEBT_VEBT_membermima @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3123_VEBT__internal_Omembermima_Opelims_I3_J)). 185.47/93.69 thf(30381,plain,((! [A:vEBT_VEBT,B:nat]: (((accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ A @ B)) => ((! [C:$o,D:$o]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) | ~ (A = (vEBT_Leaf @ C @ D)))) => (((! [C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F)) => ((B = D) | (B = C) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F) @ B))))) => ((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G) @ B)) => ((B = D) | (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) | (B = C))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G)))) => (~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E)) => ((accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E) @ B)) => (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))))))))) | ~ (! [C:list_VEBT_VEBT,D:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ C @ D) @ B)) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ C @ D))))))) | (vEBT_VEBT_membermima @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6717])). 185.47/93.69 thf(1825,axiom,((! [A:num]: ~ (ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5939_not__one__le__neg__numeral)). 185.47/93.69 thf(13846,plain,((! [A:num]: ~ (ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825])). 185.47/93.69 thf(5322,axiom,((! [A:real]: ((one_one_real = A) = (A = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_one__reorient)). 185.47/93.69 thf(25314,plain,((! [A:real]: ((one_one_real = A) = (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5322])). 185.47/93.69 thf(3324,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (sqrt @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8121_real__sqrt__gt__0__iff)). 185.47/93.69 thf(18683,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (sqrt @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3324])). 185.47/93.69 thf(1557,axiom,((! [A:num,B:num,C:int]: ((plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ (plus_plus_num @ A @ B))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5323_semiring__norm_I168_J)). 185.47/93.69 thf(12893,plain,((! [A:num,B:num,C:int]: ((plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ B)) @ C)) = (plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ (plus_plus_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557])). 185.47/93.69 thf(6210,axiom,((! [A:int]: ((minus_minus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3140_minus__int__code_I1_J)). 185.47/93.69 thf(28632,plain,((! [A:int]: ((minus_minus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6210])). 185.47/93.69 thf(7312,axiom,((! [A:num,B:num]: (((modulo_modulo_int @ (numeral_numeral_int @ one) @ (numeral_numeral_int @ (bit0 @ A))) = (modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ B)) @ (numeral_numeral_int @ (bit0 @ A)))) = ((modulo_modulo_int @ (numeral_numeral_int @ B) @ (numeral_numeral_int @ A)) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6702_cong__exp__iff__simps_I7_J)). 185.47/93.69 thf(32642,plain,((! [A:num,B:num]: (((modulo_modulo_int @ (numeral_numeral_int @ one) @ (numeral_numeral_int @ (bit0 @ A))) = (modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ B)) @ (numeral_numeral_int @ (bit0 @ A)))) = ((modulo_modulo_int @ (numeral_numeral_int @ B) @ (numeral_numeral_int @ A)) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7312])). 185.47/93.69 thf(1305,axiom,(((cos_real @ (times_times_real @ (divide_divide_real @ (numeral_numeral_real @ (bit1 @ one)) @ (numeral_numeral_real @ (bit0 @ one))) @ pi)) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7814_cos__3over2__pi)). 185.47/93.69 thf(12080,plain,(((cos_real @ (times_times_real @ (divide_divide_real @ (numeral_numeral_real @ (bit1 @ one)) @ (numeral_numeral_real @ (bit0 @ one))) @ pi)) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305])). 185.47/93.69 thf(146,axiom,((! [A:int,B:nat,C:int]: (((power_power_int @ (ring_1_of_int_int @ A) @ B) = (ring_1_of_int_int @ C)) = ((power_power_int @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6985_of__int__eq__of__int__power__cancel__iff)). 185.47/93.69 thf(8203,plain,((! [A:int,B:nat,C:int]: (((power_power_int @ (ring_1_of_int_int @ A) @ B) = (ring_1_of_int_int @ C)) = ((power_power_int @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 185.47/93.69 thf(2130,axiom,((! [A:real,B:(int > real),C:int,D:int]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [E:int,F:int]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_int @ E @ F))) => (ord_less_real @ A @ (B @ D))) <= (ord_less_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4325_order__le__less__subst1)). 185.47/93.69 thf(14823,plain,((! [A:real,B:(int > real),C:int,D:int]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [E:int,F:int]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_int @ E @ F))) => (ord_less_real @ A @ (B @ D))) | ~ (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2130])). 185.47/93.69 thf(6161,axiom,((! [A:int,B:int]: ((times_times_int @ (uminus_uminus_int @ A) @ B) = (uminus_uminus_int @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5070_mult__minus__left)). 185.47/93.69 thf(28465,plain,((! [A:int,B:int]: ((times_times_int @ (uminus_uminus_int @ A) @ B) = (uminus_uminus_int @ (times_times_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6161])). 185.47/93.69 thf(281,axiom,((! [A:nat,B:complex]: ((times_times_complex @ (semiri8010041392384452111omplex @ (suc @ A)) @ (gbinomial_complex @ (plus_plus_complex @ B @ one_one_complex) @ (suc @ A))) = (times_times_complex @ (plus_plus_complex @ B @ one_one_complex) @ (gbinomial_complex @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8532_Suc__times__gbinomial)). 185.47/93.69 thf(8649,plain,((! [A:nat,B:complex]: ((times_times_complex @ (semiri8010041392384452111omplex @ (suc @ A)) @ (gbinomial_complex @ (plus_plus_complex @ B @ one_one_complex) @ (suc @ A))) = (times_times_complex @ (plus_plus_complex @ B @ one_one_complex) @ (gbinomial_complex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 185.47/93.69 thf(4502,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((((minus_minus_complex @ (divide1717551699836669952omplex @ C @ A) @ (divide1717551699836669952omplex @ D @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (times_times_complex @ C @ B) @ (times_times_complex @ D @ A)) @ (times_times_complex @ A @ B))) <= (B != zero_zero_complex)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2768_diff__frac__eq)). 185.47/93.69 thf(22408,plain,((! [A:complex,B:complex,C:complex,D:complex]: (((minus_minus_complex @ (divide1717551699836669952omplex @ C @ A) @ (divide1717551699836669952omplex @ D @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (times_times_complex @ C @ B) @ (times_times_complex @ D @ A)) @ (times_times_complex @ A @ B))) | (B = zero_zero_complex) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4502])). 185.47/93.69 thf(4746,axiom,((! [A:int,B:nat,C:nat]: ((ord_less_int @ one_one_int @ A) => ((ord_less_eq_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) => (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_900_power__le__imp__le__exp)). 185.47/93.69 thf(23216,plain,((! [A:int,B:nat,C:nat]: ((ord_less_int @ one_one_int @ A) => ((ord_less_eq_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) => (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4746])). 185.47/93.69 thf(1904,axiom,((! [A:num]: ((numeral_numeral_rat @ (bit0 @ A)) = (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1359_numeral__code_I2_J)). 185.47/93.69 thf(14094,plain,((! [A:num]: ((numeral_numeral_rat @ (bit0 @ A)) = (plus_plus_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1904])). 185.47/93.69 thf(506,axiom,((! [A:int]: (((ring_1_of_int_int @ A) = one_one_int) = (A = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6963_of__int__eq__1__iff)). 185.47/93.69 thf(9434,plain,((! [A:int]: (((ring_1_of_int_int @ A) = one_one_int) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])). 185.47/93.69 thf(6213,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ B)) = (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A != zero_zero_real)) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_real @ zero_zero_real @ A)) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4979_zero__less__power__eq)). 185.47/93.69 thf(28641,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ B)) = (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & ~ (A = zero_zero_real)) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_real @ zero_zero_real @ A)) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6213])). 185.47/93.69 thf(4563,axiom,((! [A:rat,B:rat,C:rat]: ((((plus_plus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = C) <= (A = zero_zero_rat)) & ((A != zero_zero_rat) => ((plus_plus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (divide_divide_rat @ (plus_plus_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6167_add__divide__eq__if__simps_I3_J)). 185.47/93.69 thf(22615,plain,((! [A:rat,B:rat,C:rat]: ((((plus_plus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = C) | ~ (A = zero_zero_rat)) & ((~ (A = zero_zero_rat)) => ((plus_plus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (divide_divide_rat @ (plus_plus_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4563])). 185.47/93.69 thf(7335,axiom,((! [A:complex,B:nat,C:nat]: ((power_power_complex @ A @ (times_times_nat @ B @ C)) = (power_power_complex @ (power_power_complex @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_power__mult)). 185.47/93.69 thf(32722,plain,((! [A:complex,B:nat,C:nat]: ((power_power_complex @ A @ (times_times_nat @ B @ C)) = (power_power_complex @ (power_power_complex @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7335])). 185.47/93.69 thf(1205,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6648_sum_OatLeast0__atMost__Suc)). 185.47/93.69 thf(11785,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205])). 185.47/93.69 thf(2000,axiom,((! [A:real,B:(num > real),C:num,D:num]: ((ord_less_eq_real @ A @ (B @ C)) => (((ord_less_real @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F))))) <= (ord_less_num @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4323_order__le__less__subst1)). 185.47/93.69 thf(14418,plain,((! [A:real,B:(num > real),C:num,D:num]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) | ~ (ord_less_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2000])). 185.47/93.69 thf(1050,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (minus_minus_int @ B @ C)) = (ord_less_int @ (plus_plus_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_800_less__diff__eq)). 185.47/93.69 thf(11305,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (minus_minus_int @ B @ C)) = (ord_less_int @ (plus_plus_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050])). 185.47/93.69 thf(3266,axiom,((! [A:rat,B:rat,C:nat]: (((ord_less_eq_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2446_power__mono)). 185.47/93.69 thf(18500,plain,((! [A:rat,B:rat,C:nat]: (((ord_less_eq_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ (power_power_rat @ A @ C) @ (power_power_rat @ B @ C))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3266])). 185.47/93.69 thf(2054,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (? [C:rat]: ((ord_less_rat @ A @ C) & (ord_less_rat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3975_dense)). 185.47/93.69 thf(14592,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ B) => (? [C:rat]: ((ord_less_rat @ A @ C) & (ord_less_rat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2054])). 185.47/93.69 thf(7,axiom,((! [A:real]: (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ (nat2 @ (archim7802044766580827645g_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9301_real__nat__ceiling__ge)). 185.47/93.69 thf(7747,plain,((! [A:real]: (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ (nat2 @ (archim7802044766580827645g_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 185.47/93.69 thf(2050,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ C) <= (ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_add__less__imp__less__right)). 185.47/93.69 thf(14582,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ C) | ~ (ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050])). 185.47/93.69 thf(1800,axiom,((! [A:nat,B:nat,C:(nat > rat),D:rat]: ((((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F)))) => (ord_less_eq_rat @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3956_ord__le__eq__subst)). 185.47/93.69 thf(13761,plain,((! [A:nat,B:nat,C:(nat > rat),D:rat]: (((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_rat @ (C @ E) @ (C @ F)))) => (ord_less_eq_rat @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800])). 185.47/93.69 thf(3772,axiom,((! [A:int,B:int,C:int,D:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ D)) = (plus_plus_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_add__diff__add)). 185.47/93.69 thf(20123,plain,((! [A:int,B:int,C:int,D:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ D)) = (plus_plus_int @ (minus_minus_int @ A @ C) @ (minus_minus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3772])). 185.47/93.69 thf(5810,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((A != zero_zero_nat) => ((((dvd_dvd_nat @ B @ D) => (((divide_divide_nat @ C @ A) = (divide_divide_nat @ D @ B)) = ((times_times_nat @ C @ B) = (times_times_nat @ A @ D)))) <= (dvd_dvd_nat @ A @ C)) <= (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4839_dvd__div__div__eq__mult)). 185.47/93.69 thf(27131,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((~ (A = zero_zero_nat)) => (((dvd_dvd_nat @ B @ D) => (((divide_divide_nat @ C @ A) = (divide_divide_nat @ D @ B)) = ((times_times_nat @ C @ B) = (times_times_nat @ A @ D)))) | ~ (dvd_dvd_nat @ A @ C) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5810])). 185.47/93.69 thf(868,axiom,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => ((((ord_less_real @ one_one_real @ (groups129246275422532515t_real @ C @ A)) <= (! [D:nat]: ((ord_less_eq_real @ one_one_real @ (C @ D)) <= (member_nat @ D @ A)))) <= (ord_less_real @ one_one_real @ (C @ B))) <= (member_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8872_less__1__prod2)). 185.47/93.69 thf(10695,plain,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => ((ord_less_real @ one_one_real @ (groups129246275422532515t_real @ (C) @ A)) | ~ (! [D:nat]: ((ord_less_eq_real @ one_one_real @ (C @ D)) | ~ (member_nat @ D @ A))) | ~ (ord_less_real @ one_one_real @ (C @ B)) | ~ (member_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[868])). 185.47/93.69 thf(5531,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2101_Zero__not__Suc)). 185.47/93.69 thf(26151,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5531])). 185.47/93.69 thf(6232,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F))))) <= (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ F @ E)))) <= (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3258_minf_I1_J)). 185.47/93.69 thf(28698,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F)))) | ~ (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ F @ E))) | ~ (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6232])). 185.47/93.69 thf(2954,axiom,((! [A:num,B:nat,C:nat]: ((ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ (semiri1314217659103216013at_int @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7134_numeral__power__le__of__nat__cancel__iff)). 185.47/93.69 thf(17521,plain,((! [A:num,B:nat,C:nat]: ((ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ (semiri1314217659103216013at_int @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2954])). 185.47/93.69 thf(4645,axiom,((! [A:code_integer]: (dvd_dvd_Code_integer @ one_one_Code_integer @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4635_one__dvd)). 185.47/93.69 thf(22879,plain,((! [A:code_integer]: (dvd_dvd_Code_integer @ one_one_Code_integer @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4645])). 185.47/93.69 thf(6330,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1715_diff__add__zero)). 185.47/93.69 thf(29033,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6330])). 185.47/93.69 thf(1890,axiom,(((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one)) = (uminus1351360451143612070nteger @ one_one_Code_integer))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5992_uminus__numeral__One)). 185.47/93.69 thf(14054,plain,(((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one)) = (uminus1351360451143612070nteger @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890])). 185.47/93.69 thf(5935,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (times_times_nat @ B @ C)) = (power_power_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_power__mult)). 185.47/93.69 thf(27644,plain,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (times_times_nat @ B @ C)) = (power_power_int @ (power_power_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5935])). 185.47/93.69 thf(2119,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (ord_less_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5062_neg__less__iff__less)). 185.47/93.69 thf(14787,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (ord_less_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2119])). 185.47/93.69 thf(5702,axiom,((! [A:complex,B:complex,C:num]: ((times_times_complex @ (minus_minus_complex @ A @ B) @ (numera6690914467698888265omplex @ C)) = (minus_minus_complex @ (times_times_complex @ A @ (numera6690914467698888265omplex @ C)) @ (times_times_complex @ B @ (numera6690914467698888265omplex @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_left__diff__distrib__numeral)). 185.47/93.69 thf(26701,plain,((! [A:complex,B:complex,C:num]: ((times_times_complex @ (minus_minus_complex @ A @ B) @ (numera6690914467698888265omplex @ C)) = (minus_minus_complex @ (times_times_complex @ A @ (numera6690914467698888265omplex @ C)) @ (times_times_complex @ B @ (numera6690914467698888265omplex @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5702])). 185.47/93.69 thf(2228,axiom,((~ (ord_less_int @ one_one_int @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5753_less__minus__one__simps_I4_J)). 185.47/93.69 thf(15139,plain,((~ (ord_less_int @ one_one_int @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2228])). 185.47/93.69 thf(5651,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1040_le__SucE)). 185.47/93.69 thf(26536,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5651])). 185.47/93.69 thf(6705,axiom,((! [A:int]: ((gbinomial_int @ A @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8418_gbinomial__0_I1_J)). 185.47/93.69 thf(30344,plain,((! [A:int]: ((gbinomial_int @ A @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6705])). 185.47/93.69 thf(5735,axiom,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ C @ A) => (ord_less_eq_num @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3896_dual__order_Otrans)). 185.47/93.69 thf(26813,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ C @ A) => (ord_less_eq_num @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5735])). 185.47/93.69 thf(6860,axiom,((! [A:num,B:num]: ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) != (numera6690914467698888265omplex @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5537_neg__numeral__neq__numeral)). 185.47/93.69 thf(30986,plain,((! [A:num,B:num]: ~ ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6860])). 185.47/93.69 thf(3179,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4155_leI)). 185.47/93.69 thf(18237,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3179])). 185.47/93.69 thf(3151,axiom,((! [A:real,B:real,C:num]: ((ord_less_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ C))) = (ord_less_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_less__divide__eq__numeral1_I1_J)). 185.47/93.69 thf(18147,plain,((! [A:real,B:real,C:num]: ((ord_less_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ C))) = (ord_less_real @ (times_times_real @ A @ (numeral_numeral_real @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3151])). 185.47/93.69 thf(2662,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ (sin_complex @ A) @ (sin_complex @ B)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sin_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (cos_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7854_sin__plus__sin)). 185.47/93.69 thf(16554,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ (sin_complex @ A) @ (sin_complex @ B)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sin_complex @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one))))) @ (cos_complex @ (divide1717551699836669952omplex @ (minus_minus_complex @ A @ B) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2662])). 185.47/93.69 thf(722,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((((! [D:nat]: (((C @ D) = zero_zero_int) <= (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups3539618377306564664at_int @ C @ A) = (groups3539618377306564664at_int @ C @ B))) <= (ord_less_eq_set_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6086_sum_Omono__neutral__right)). 185.47/93.69 thf(10137,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: (((! [D:nat]: (((C @ D) = zero_zero_int) | ~ (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups3539618377306564664at_int @ (C) @ A) = (groups3539618377306564664at_int @ (C) @ B))) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[722])). 185.47/93.69 thf(4702,axiom,((! [A:real,B:num,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ (numeral_numeral_real @ B)) @ C) = (ord_less_eq_real @ A @ (times_times_real @ C @ (numeral_numeral_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_divide__le__eq__numeral1_I1_J)). 185.47/93.69 thf(23077,plain,((! [A:real,B:num,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ (numeral_numeral_real @ B)) @ C) = (ord_less_eq_real @ A @ (times_times_real @ C @ (numeral_numeral_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4702])). 185.47/93.69 thf(2992,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) = (((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ A)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2225_mult__le__0__iff)). 185.47/93.69 thf(17653,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) = (((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ A)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2992])). 185.47/93.69 thf(542,axiom,((! [A:int]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ one_one_int) = (ord_less_eq_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7085_of__int__le__1__iff)). 185.47/93.69 thf(9537,plain,((! [A:int]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ one_one_int) = (ord_less_eq_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[542])). 185.47/93.69 thf(7378,axiom,((! [A:num,B:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = zero_zero_nat) = ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1942_cong__exp__iff__simps_I2_J)). 185.47/93.69 thf(32852,plain,((! [A:num,B:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = zero_zero_nat) = ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7378])). 185.47/93.69 thf(3976,axiom,((! [A:rat,B:rat,C:rat]: (((divide_divide_rat @ A @ B) = (divide_divide_rat @ C @ B)) = ((A = C) | (B = zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1579_divide__cancel__right)). 185.47/93.69 thf(20768,plain,((! [A:rat,B:rat,C:rat]: (((divide_divide_rat @ A @ B) = (divide_divide_rat @ C @ B)) = ((A = C) | (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3976])). 185.47/93.69 thf(6540,axiom,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3158_times__int__code_I2_J)). 185.47/93.69 thf(29808,plain,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6540])). 185.47/93.69 thf(5263,axiom,((! [A:num]: ~ (ord_less_num @ A @ one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_semiring__norm_I75_J)). 185.47/93.69 thf(25099,plain,((! [A:num]: ~ (ord_less_num @ A @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5263])). 185.47/93.69 thf(2007,axiom,((! [A:int,B:int]: ((minus_minus_int @ A @ (modulo_modulo_int @ A @ B)) = (times_times_int @ B @ (divide_divide_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2557_minus__mod__eq__mult__div)). 185.47/93.69 thf(14442,plain,((! [A:int,B:int]: ((minus_minus_int @ A @ (modulo_modulo_int @ A @ B)) = (times_times_int @ B @ (divide_divide_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2007])). 185.47/93.69 thf(3858,axiom,((! [A:(nat > real),B:(nat > real),C:real,D:real]: ((((ord_less_eq_real @ C @ D) <= (sums_real @ B @ D)) <= (sums_real @ A @ C)) <= (! [E:nat]: (ord_less_eq_real @ (A @ E) @ (B @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8153_sums__le)). 185.47/93.69 thf(20393,plain,((! [A:(nat > real),B:(nat > real),C:real,D:real]: ((ord_less_eq_real @ C @ D) | ~ (sums_real @ (B) @ D) | ~ (sums_real @ (A) @ C) | ~ (! [E:nat]: (ord_less_eq_real @ (A @ E) @ (B @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3858])). 185.47/93.69 thf(5312,axiom,((! [A:num,B:num]: (((numeral_numeral_int @ A) = (numeral_numeral_int @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_numeral__eq__iff)). 185.47/93.69 thf(25282,plain,((! [A:num,B:num]: (((numeral_numeral_int @ A) = (numeral_numeral_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5312])). 185.47/93.69 thf(5656,axiom,((! [A:real]: ((root @ (suc @ zero_zero_nat) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9158_real__root__Suc__0)). 185.47/93.69 thf(26554,plain,((! [A:real]: ((root @ (suc @ zero_zero_nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5656])). 185.47/93.69 thf(4210,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) = (((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ B @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ B) & (ord_less_rat @ A @ zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2436_divide__less__0__iff)). 185.47/93.69 thf(21472,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) = (((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ B @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ B) & (ord_less_rat @ A @ zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4210])). 185.47/93.69 thf(2551,axiom,((! [A:nat]: ~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7311_not__zle__0__negative)). 185.47/93.69 thf(16193,plain,((! [A:nat]: ~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2551])). 185.47/93.69 thf(4057,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ A @ C) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3254_pinf_I7_J)). 185.47/93.69 thf(21005,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ A @ C) | ~ (ord_less_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4057])). 185.47/93.69 thf(5522,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2341_zero__less__mult__pos)). 185.47/93.69 thf(26119,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5522])). 185.47/93.69 thf(4126,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((A = (plus_plus_rat @ B @ C)) => ((plus_plus_rat @ D @ A) = (plus_plus_rat @ B @ (plus_plus_rat @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_group__cancel_Oadd2)). 185.47/93.69 thf(21217,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((A = (plus_plus_rat @ B @ C)) => ((plus_plus_rat @ D @ A) = (plus_plus_rat @ B @ (plus_plus_rat @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4126])). 185.47/93.69 thf(4078,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ B @ C)) <= (ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2575_mult__left__less__imp__less)). 185.47/93.69 thf(21068,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ B @ C)) | ~ (ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4078])). 185.47/93.69 thf(1338,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ B @ C) => ((divide_divide_int @ (divide_divide_int @ C @ A) @ (divide_divide_int @ B @ A)) = (divide_divide_int @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4676_div__div__div__same)). 185.47/93.69 thf(12194,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ B @ C) => ((divide_divide_int @ (divide_divide_int @ C @ A) @ (divide_divide_int @ B @ A)) = (divide_divide_int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338])). 185.47/93.69 thf(5037,axiom,(((semiri5044797733671781792omplex @ one_one_nat) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7958_fact__1)). 185.47/93.69 thf(24214,plain,(((semiri5044797733671781792omplex @ one_one_nat) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5037])). 185.47/93.69 thf(1770,axiom,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ (divide_divide_rat @ A @ B) @ C) = (divide_divide_rat @ A @ (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_divide__divide__eq__left)). 185.47/93.69 thf(13659,plain,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ (divide_divide_rat @ A @ B) @ C) = (divide_divide_rat @ A @ (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770])). 185.47/93.69 thf(2682,axiom,((! [A:real,B:real]: ? [C:real]: ! [D:real]: (((~ (dvd_dvd_real @ A @ (plus_plus_real @ D @ B))) = (~ (dvd_dvd_real @ A @ (plus_plus_real @ D @ B)))) <= (ord_less_real @ D @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4704_minf_I10_J)). 185.47/93.69 thf(16667,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2682])). 185.47/93.69 thf(2606,axiom,((! [A:num]: ((numera6620942414471956472nteger @ A) != (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5776_numeral__neq__neg__one)). 185.47/93.69 thf(16382,plain,((! [A:num]: ~ ((numera6620942414471956472nteger @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2606])). 185.47/93.69 thf(1928,axiom,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4591_dvd__triv__left)). 185.47/93.69 thf(14165,plain,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1928])). 185.47/93.69 thf(48,axiom,((! [A:complex,B:nat]: (((A != one_one_complex) => ((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ B)) @ (minus_minus_complex @ one_one_complex @ A)))) & (((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)) = (semiri8010041392384452111omplex @ B)) <= (A = one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7605_sum__gp__strict)). 185.47/93.69 thf(7887,plain,((! [A:complex,B:nat]: (((~ (A = one_one_complex)) => ((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ B)) @ (minus_minus_complex @ one_one_complex @ A)))) & (((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)) = (semiri8010041392384452111omplex @ B)) | ~ (A = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 185.47/93.69 thf(5437,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7048_of__nat__less__of__nat__power__cancel__iff)). 185.47/93.69 thf(25740,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5437])). 185.47/93.69 thf(317,axiom,((! [A:nat]: ((groups2906978787729119204at_rat @ (gbinomial_rat @ (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (semiri681578069525770553at_rat @ A)) @ one_one_rat)) @ (set_ord_atMost_nat @ A)) = (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8630_gbinomial__r__part__sum)). 185.47/93.69 thf(8793,plain,((! [A:nat]: ((groups2906978787729119204at_rat @ (gbinomial_rat @ (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (semiri681578069525770553at_rat @ A)) @ one_one_rat)) @ (set_ord_atMost_nat @ A)) = (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 185.47/93.69 thf(5068,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((C != A) <= (ord_less_num @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3267_minf_I3_J)). 185.47/93.69 thf(24396,plain,((! [A:num]: ? [B:num]: ! [C:num]: (~ (C = A) | ~ (ord_less_num @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5068])). 185.47/93.69 thf(5345,axiom,((! [A:real]: ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit1 @ one)) @ A)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))) @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit1 @ one)))) @ (times_times_real @ (numeral_numeral_real @ (bit1 @ one)) @ (cos_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7918_cos__treble__cos)). 185.47/93.69 thf(25390,plain,((! [A:real]: ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit1 @ one)) @ A)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))) @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit1 @ one)))) @ (times_times_real @ (numeral_numeral_real @ (bit1 @ one)) @ (cos_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5345])). 185.47/93.69 thf(2790,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => ((ord_less_eq_rat @ B @ one_one_rat) => (ord_less_eq_rat @ (times_times_rat @ B @ A) @ A))) <= (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2673_mult__left__le__one__le)). 185.47/93.69 thf(16993,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => ((ord_less_eq_rat @ B @ one_one_rat) => (ord_less_eq_rat @ (times_times_rat @ B @ A) @ A))) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2790])). 185.47/93.69 thf(421,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (cos_real @ A)) <= (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7900_cos__gt__zero)). 185.47/93.69 thf(9130,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (cos_real @ A)) | ~ (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[421])). 185.47/93.69 thf(5363,axiom,((! [A:nat,B:nat,C:nat]: (((comm_s4663373288045622133er_nat @ C @ B) = (times_times_nat @ (comm_s4663373288045622133er_nat @ C @ A) @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ C @ (semiri1316708129612266289at_nat @ A)) @ (minus_minus_nat @ B @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8543_pochhammer__product)). 185.47/93.69 thf(25485,plain,((! [A:nat,B:nat,C:nat]: (((comm_s4663373288045622133er_nat @ C @ B) = (times_times_nat @ (comm_s4663373288045622133er_nat @ C @ A) @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ C @ (semiri1316708129612266289at_nat @ A)) @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5363])). 185.47/93.69 thf(4608,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ C) <= (ord_less_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_add__less__imp__less__right)). 185.47/93.69 thf(22756,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ C) | ~ (ord_less_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4608])). 185.47/93.69 thf(7551,axiom,((~ (vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) | ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_960_i1)). 185.47/93.69 thf(33437,plain,((~ (vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))))) | ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7551])). 185.47/93.69 thf(1288,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_add__left__imp__eq)). 185.47/93.69 thf(12031,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288])). 185.47/93.69 thf(4998,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_V8194947554948674370ptions @ A @ C) = (vEBT_vebt_member @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_both__member__options__equiv__member)). 185.47/93.69 thf(24096,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_V8194947554948674370ptions @ A @ C) = (vEBT_vebt_member @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4998])). 185.47/93.69 thf(550,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_real @ A @ one_one_real) => ((ord_less_real @ (arccos @ A) @ pi) & (ord_less_real @ zero_zero_real @ (arccos @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8372_arccos__lt__bounded)). 185.47/93.69 thf(9559,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_real @ A @ one_one_real) => ((ord_less_real @ (arccos @ A) @ pi) & (ord_less_real @ zero_zero_real @ (arccos @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[550])). 185.47/93.69 thf(3885,axiom,((! [A:nat]: ((vEBT_VEBT_set_vebt @ (vEBT_vebt_buildup @ A)) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_buildup__gives__empty)). 185.47/93.69 thf(20474,plain,((! [A:nat]: ((vEBT_VEBT_set_vebt @ (vEBT_vebt_buildup @ A)) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3885])). 185.47/93.69 thf(4018,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_rat @ (abs_abs_rat @ B) @ A)) <= (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6712_power2__le__iff__abs__le)). 185.47/93.69 thf(20891,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_rat @ (abs_abs_rat @ B) @ A)) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4018])). 185.47/93.69 thf(7690,axiom,((! [A:num,B:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ one) @ (numeral_numeral_nat @ (bit0 @ A))) != (modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ B)) @ (numeral_numeral_nat @ (bit0 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2157_cong__exp__iff__simps_I6_J)). 185.47/93.69 thf(33812,plain,((! [A:num,B:num]: ~ ((modulo_modulo_nat @ (numeral_numeral_nat @ one) @ (numeral_numeral_nat @ (bit0 @ A))) = (modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ B)) @ (numeral_numeral_nat @ (bit0 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7690])). 185.47/93.69 thf(706,axiom,((! [A:(nat > rat)]: ((groups73079841787564623at_rat @ A @ bot_bot_set_nat) = one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8643_prod_Oempty)). 185.47/93.69 thf(10087,plain,((! [A:(nat > rat)]: ((groups73079841787564623at_rat @ (A) @ bot_bot_set_nat) = one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[706])). 185.47/93.69 thf(809,axiom,((! [A:real]: (ord_less_real @ (arctan @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7763_arctan__ubound)). 185.47/93.69 thf(10483,plain,((! [A:real]: (ord_less_real @ (arctan @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[809])). 185.47/93.69 thf(5859,axiom,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) <= (ord_less_eq_num @ (C @ B) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3924_order__subst2)). 185.47/93.69 thf(27398,plain,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ (ord_less_eq_num @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5859])). 185.47/93.69 thf(6586,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3089_verit__comp__simplify1_I2_J)). 185.47/93.69 thf(29959,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6586])). 185.47/93.69 thf(7309,axiom,((zero_zero_int != (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5719_zero__neq__neg__one)). 185.47/93.69 thf(32627,plain,((~ (zero_zero_int = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7309])). 185.47/93.69 thf(4297,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ (plus_plus_real @ A @ C)) <= (ord_less_real @ B @ C)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2641_add__strict__increasing2)). 185.47/93.69 thf(21734,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ B @ (plus_plus_real @ A @ C)) | ~ (ord_less_real @ B @ C) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4297])). 185.47/93.69 thf(2408,axiom,((ord_less_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2391_less__numeral__extra_I1_J)). 185.47/93.69 thf(15699,plain,((ord_less_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2408])). 185.47/93.69 thf(5284,axiom,((! [A:(nat > nat),B:set_nat,C:nat]: ((? [D:nat]: ((member_nat @ D @ B) & (ord_less_nat @ zero_zero_nat @ (A @ D)))) <= ((groups3542108847815614940at_nat @ A @ B) = (suc @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6596_sum__SucD)). 185.47/93.69 thf(25198,plain,((! [A:(nat > nat),B:set_nat,C:nat]: (? [D:nat]: ((member_nat @ D @ B) & (ord_less_nat @ zero_zero_nat @ (A @ D))) | ~ ((groups3542108847815614940at_nat @ (A) @ B) = (suc @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5284])). 185.47/93.69 thf(4227,axiom,((! [A:complex]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ zero_zero_real) = (A = zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7451_norm__le__zero__iff)). 185.47/93.69 thf(21528,plain,((! [A:complex]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ zero_zero_real) = (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4227])). 185.47/93.69 thf(7126,axiom,((! [A:nat,B:real]: (((ord_less_eq_real @ one_one_real @ (root @ A @ B)) = (ord_less_eq_real @ one_one_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9173_real__root__ge__1__iff)). 185.47/93.69 thf(31980,plain,((! [A:nat,B:real]: (((ord_less_eq_real @ one_one_real @ (root @ A @ B)) = (ord_less_eq_real @ one_one_real @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7126])). 185.47/93.69 thf(6301,axiom,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_num @ B @ C) => (ord_less_num @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4208_order_Ostrict__trans1)). 185.47/93.69 thf(28929,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_num @ B @ C) => (ord_less_num @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6301])). 185.47/93.69 thf(6479,axiom,((! [A:rat,B:nat]: ((power_power_rat @ (uminus_uminus_rat @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_rat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5429_Power_Oring__1__class_Opower__minus__even)). 185.47/93.69 thf(29588,plain,((! [A:rat,B:nat]: ((power_power_rat @ (uminus_uminus_rat @ A) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_rat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6479])). 185.47/93.69 thf(7422,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_int @ (abs_abs_int @ B) @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6713_power2__le__iff__abs__le)). 185.47/93.69 thf(33016,plain,((! [A:int,B:int]: (((ord_less_eq_int @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_int @ (abs_abs_int @ B) @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7422])). 185.47/93.69 thf(5767,axiom,((! [A:real,B:real,C:num]: (((complex2 @ A @ B) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = ((A = (uminus_uminus_real @ (numeral_numeral_real @ C))) & (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8014_Complex__eq__neg__numeral)). 185.47/93.69 thf(26912,plain,((! [A:real,B:real,C:num]: (((complex2 @ A @ B) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = ((A = (uminus_uminus_real @ (numeral_numeral_real @ C))) & (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5767])). 185.47/93.69 thf(4929,axiom,(((^ [A:real]: (A)) = (times_times_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1353_lambda__one)). 185.47/93.69 thf(23866,plain,(((^ [A:real]: (A)) = (times_times_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4929])). 185.47/93.69 thf(2222,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4159_leI)). 185.47/93.69 thf(15124,plain,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2222])). 185.47/93.69 thf(5664,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (modulo_modulo_nat @ A @ B)) = (modulo_modulo_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7247_of__nat__mod)). 185.47/93.69 thf(26586,plain,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (modulo_modulo_nat @ A @ B)) = (modulo_modulo_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5664])). 185.47/93.69 thf(4931,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4546_even__diff__nat)). 185.47/93.69 thf(23869,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4931])). 185.47/93.69 thf(1833,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ A @ C) <= (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3995_ord__less__eq__trans)). 185.47/93.69 thf(13873,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1833])). 185.47/93.69 thf(3738,axiom,((! [A:nat,B:nat]: (ord_less_eq_real @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B)) @ (divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7269_real__of__nat__div4)). 185.47/93.69 thf(20006,plain,((! [A:nat,B:nat]: (ord_less_eq_real @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B)) @ (divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3738])). 185.47/93.69 thf(7535,axiom,((! [A:num]: ((sqr @ (bit0 @ A)) = (bit0 @ (bit0 @ (sqr @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9848_sqr_Osimps_I2_J)). 185.47/93.69 thf(33393,plain,((! [A:num]: ((sqr @ (bit0 @ A)) = (bit0 @ (bit0 @ (sqr @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7535])). 185.47/93.69 thf(6724,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4041_order_Ostrict__implies__not__eq)). 185.47/93.69 thf(30426,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6724])). 185.47/93.69 thf(3636,axiom,((! [A:num]: ((neg_nu5851722552734809277nc_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (neg_nu3811975205180677377ec_int @ (numeral_numeral_int @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6863_dbl__inc__simps_I1_J)). 185.47/93.69 thf(19669,plain,((! [A:num]: ((neg_nu5851722552734809277nc_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (neg_nu3811975205180677377ec_int @ (numeral_numeral_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3636])). 185.47/93.69 thf(1951,axiom,((! [A:int,B:int]: ((plus_plus_int @ (modulo_modulo_int @ A @ B) @ (times_times_int @ (divide_divide_int @ A @ B) @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2536_mod__div__mult__eq)). 185.47/93.69 thf(14261,plain,((! [A:int,B:int]: ((plus_plus_int @ (modulo_modulo_int @ A @ B) @ (times_times_int @ (divide_divide_int @ A @ B) @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1951])). 185.47/93.69 thf(4602,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => (~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ C @ D @ E) @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1915_VEBT__internal_Ovalid_H_Ocases)). 185.47/93.69 thf(22739,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => (~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ C @ D @ E) @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4602])). 185.47/93.69 thf(4333,axiom,((~ (ord_less_eq_rat @ one_one_rat @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2268_not__one__le__zero)). 185.47/93.69 thf(21882,plain,((~ (ord_less_eq_rat @ one_one_rat @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4333])). 185.47/93.69 thf(4524,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_rat @ (power_power_rat @ (semiri681578069525770553at_rat @ A) @ B) @ (semiri681578069525770553at_rat @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7065_of__nat__le__of__nat__power__cancel__iff)). 185.47/93.69 thf(22494,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_rat @ (power_power_rat @ (semiri681578069525770553at_rat @ A) @ B) @ (semiri681578069525770553at_rat @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4524])). 185.47/93.69 thf(5389,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_nat__add__left__cancel__less)). 185.47/93.69 thf(25564,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5389])). 185.47/93.69 thf(1529,axiom,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (root @ A @ B) @ (root @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9184_real__root__le__mono)). 185.47/93.69 thf(12805,plain,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (root @ A @ B) @ (root @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529])). 185.47/93.69 thf(444,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ zero_zero_int @ (ring_1_of_int_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7287_of__int__pos)). 185.47/93.69 thf(9211,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ zero_zero_int @ (ring_1_of_int_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[444])). 185.47/93.69 thf(2089,axiom,((! [A:real,B:real]: ((invers8013647133539491842omplex @ (complex2 @ A @ B)) = (complex2 @ (divide_divide_real @ A @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (divide_divide_real @ (uminus_uminus_real @ B) @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9011_complex__inverse)). 185.47/93.69 thf(14700,plain,((! [A:real,B:real]: ((invers8013647133539491842omplex @ (complex2 @ A @ B)) = (complex2 @ (divide_divide_real @ A @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (divide_divide_real @ (uminus_uminus_real @ B) @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2089])). 185.47/93.69 thf(4558,axiom,((! [A:int,B:nat]: ((ord_less_int @ one_one_int @ A) => (ord_less_int @ (power_power_int @ A @ B) @ (times_times_int @ A @ (power_power_int @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_power__less__power__Suc)). 185.47/93.69 thf(22600,plain,((! [A:int,B:nat]: ((ord_less_int @ one_one_int @ A) => (ord_less_int @ (power_power_int @ A @ B) @ (times_times_int @ A @ (power_power_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4558])). 185.47/93.69 thf(4725,axiom,((! [A:num,B:num]: ((ord_less_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_numeral__less__iff)). 185.47/93.69 thf(23153,plain,((! [A:num,B:num]: ((ord_less_rat @ (numeral_numeral_rat @ A) @ (numeral_numeral_rat @ B)) = (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4725])). 185.47/93.69 thf(7584,axiom,((! [A:nat,B:nat]: ((product_fst_nat_nat @ (divmod_nat @ A @ B)) = (divide_divide_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9763_fst__divmod__nat)). 185.47/93.69 thf(33525,plain,((! [A:nat,B:nat]: ((product_fst_nat_nat @ (divmod_nat @ A @ B)) = (divide_divide_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7584])). 185.47/93.69 thf(5486,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2941_zero__le__power2)). 185.47/93.69 thf(26003,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5486])). 185.47/93.69 thf(6263,axiom,((times_times_nat = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ zero_zero_nat @ (plus_plus_nat @ B @ (times_times_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2917_mult__eq__if)). 185.47/93.69 thf(28805,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ zero_zero_nat @ (plus_plus_nat @ B @ (times_times_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6263])). 185.47/93.69 thf(3254,axiom,((! [A:(nat > rat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_rat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_eq_rat @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1075_lift__Suc__mono__le)). 185.47/93.69 thf(18464,plain,((! [A:(nat > rat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_rat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_eq_rat @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3254])). 185.47/93.69 thf(4447,axiom,((! [A:nat]: ((ord_less_real @ zero_zero_real @ (semiri5074537144036343181t_real @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7022_of__nat__0__less__iff)). 185.47/93.69 thf(22239,plain,((! [A:nat]: ((ord_less_real @ zero_zero_real @ (semiri5074537144036343181t_real @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4447])). 185.47/93.69 thf(1450,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) <= (ord_less_rat @ zero_zero_rat @ B)) <= (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2660_divide__nonpos__pos)). 185.47/93.69 thf(12567,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ B) @ zero_zero_rat) | ~ (ord_less_rat @ zero_zero_rat @ B) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450])). 185.47/93.69 thf(479,axiom,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((ord_less_eq_rat @ (groups2906978787729119204at_rat @ B @ A) @ (groups2906978787729119204at_rat @ C @ A)) <= (! [D:nat]: ((ord_less_eq_rat @ (B @ D) @ (C @ D)) <= (member_nat @ D @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5597_sum__mono)). 185.47/93.69 thf(9350,plain,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((ord_less_eq_rat @ (groups2906978787729119204at_rat @ (B) @ A) @ (groups2906978787729119204at_rat @ (C) @ A)) | ~ (! [D:nat]: ((ord_less_eq_rat @ (B @ D) @ (C @ D)) | ~ (member_nat @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])). 185.47/93.69 thf(3930,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (ord_max_nat @ A @ C) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3676_max_OboundedI)). 185.47/93.69 thf(20622,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ (ord_max_nat @ A @ C) @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3930])). 185.47/93.69 thf(7553,axiom,((! [A:num,B:num,C:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ C)) @ (numeral_numeral_nat @ (bit0 @ B)))) = ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (modulo_modulo_nat @ (numeral_numeral_nat @ C) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2040_cong__exp__iff__simps_I9_J)). 185.47/93.69 thf(33442,plain,((! [A:num,B:num,C:num]: (((modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (modulo_modulo_nat @ (numeral_numeral_nat @ (bit0 @ C)) @ (numeral_numeral_nat @ (bit0 @ B)))) = ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (modulo_modulo_nat @ (numeral_numeral_nat @ C) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7553])). 185.47/93.69 thf(5725,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7224_of__nat__less__imp__less)). 185.47/93.69 thf(26786,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5725])). 185.47/93.69 thf(3086,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ (times_times_rat @ B @ A) @ (times_times_rat @ C @ A)) = (ord_less_rat @ B @ C)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3372_mult__less__iff1)). 185.47/93.69 thf(17941,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ (times_times_rat @ B @ A) @ (times_times_rat @ C @ A)) = (ord_less_rat @ B @ C)) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3086])). 185.47/93.69 thf(1828,axiom,((! [A:real]: ((((tan_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (divide_divide_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (tan_real @ A)) @ (minus_minus_real @ one_one_real @ (power_power_real @ (tan_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))) <= ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) != zero_zero_real)) <= ((cos_real @ A) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7950_tan__double)). 185.47/93.69 thf(13855,plain,((! [A:real]: (((tan_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (divide_divide_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (tan_real @ A)) @ (minus_minus_real @ one_one_real @ (power_power_real @ (tan_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))) | ((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = zero_zero_real) | ((cos_real @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828])). 185.47/93.69 thf(2668,axiom,((! [A:real]: (((sin_real @ A) = zero_zero_real) => ((real_V7735802525324610683m_real @ (cos_real @ A)) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7824_sin__zero__norm__cos__one)). 185.47/93.69 thf(16571,plain,((! [A:real]: (((sin_real @ A) = zero_zero_real) => ((real_V7735802525324610683m_real @ (cos_real @ A)) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2668])). 185.47/93.69 thf(2178,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7234_unique__euclidean__semiring__with__nat__class_Oof__nat__div)). 185.47/93.69 thf(14995,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2178])). 185.47/93.69 thf(619,axiom,((! [A:set_nat,B:set_nat,C:nat,D:(nat > rat)]: ((finite_finite_nat @ A) => (((((ord_less_rat @ (groups2906978787729119204at_rat @ D @ B) @ (groups2906978787729119204at_rat @ D @ A)) <= (! [E:nat]: ((member_nat @ E @ A) => (ord_less_eq_rat @ zero_zero_rat @ (D @ E))))) <= (ord_less_rat @ zero_zero_rat @ (D @ C))) <= (member_nat @ C @ (minus_minus_set_nat @ A @ B))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6248_sum__strict__mono2)). 185.47/93.69 thf(9787,plain,((! [A:set_nat,B:set_nat,C:nat,D:(nat > rat)]: ((finite_finite_nat @ A) => ((ord_less_rat @ (groups2906978787729119204at_rat @ (D) @ B) @ (groups2906978787729119204at_rat @ (D) @ A)) | ~ (! [E:nat]: ((member_nat @ E @ A) => (ord_less_eq_rat @ zero_zero_rat @ (D @ E)))) | ~ (ord_less_rat @ zero_zero_rat @ (D @ C)) | ~ (member_nat @ C @ (minus_minus_set_nat @ A @ B)) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[619])). 185.47/93.69 thf(576,axiom,((! [A:real]: ? [B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) & ((tan_real @ B) = A) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8060_lemma__tan__total1)). 185.47/93.69 thf(9643,plain,((! [A:real]: ? [B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) & ((tan_real @ B) = A) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[576])). 185.47/93.69 thf(4402,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3976_less__imp__neq)). 185.47/93.69 thf(22099,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4402])). 185.47/93.69 thf(6080,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (power_power_rat @ A @ (suc @ B)) @ one_one_rat) <= (ord_less_rat @ A @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2876_power__Suc__less__one)). 185.47/93.69 thf(28136,plain,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ (power_power_rat @ A @ (suc @ B)) @ one_one_rat) | ~ (ord_less_rat @ A @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6080])). 185.47/93.69 thf(7090,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (bit_se2925701944663578781it_nat @ A @ C) @ (bit_se2925701944663578781it_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9273_take__bit__tightened__less__eq__nat)). 185.47/93.69 thf(31869,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (bit_se2925701944663578781it_nat @ A @ C) @ (bit_se2925701944663578781it_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7090])). 185.47/93.69 thf(5370,axiom,((ord_less_eq_nat @ xa @ ma)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74__092_060open_062x_A_092_060le_062_Ama_092_060close_062)). 185.47/93.69 thf(25507,plain,((ord_less_eq_nat @ xa @ ma)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5370])). 185.47/93.69 thf(2348,axiom,((! [A:nat,B:nat,C:nat]: ((groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ (binomial @ A @ D) @ (binomial @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C)) = (binomial @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8947_vandermonde)). 185.47/93.69 thf(15508,plain,((! [A:nat,B:nat,C:nat]: ((groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ (binomial @ A @ D) @ (binomial @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C)) = (binomial @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2348])). 185.47/93.69 thf(2957,axiom,(((ring_17405671764205052669omplex @ one_one_int) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6966_of__int__1)). 185.47/93.69 thf(17528,plain,(((ring_17405671764205052669omplex @ one_one_int) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2957])). 185.47/93.69 thf(5852,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2455_zero__less__power)). 185.47/93.69 thf(27371,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5852])). 185.47/93.69 thf(6037,axiom,((! [A:int,B:nat,C:nat]: ((ord_less_int @ zero_zero_int @ A) => (((ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (ord_less_nat @ C @ B)) <= (ord_less_int @ A @ one_one_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1866_power__strict__decreasing__iff)). 185.47/93.69 thf(28004,plain,((! [A:int,B:nat,C:nat]: ((ord_less_int @ zero_zero_int @ A) => (((ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = (ord_less_nat @ C @ B)) | ~ (ord_less_int @ A @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6037])). 185.47/93.69 thf(7053,axiom,((! [A:num]: ((unique5055182867167087721od_nat @ one @ (bit0 @ A)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6808_divmod__algorithm__code_I3_J)). 185.47/93.69 thf(31758,plain,((! [A:num]: ((unique5055182867167087721od_nat @ one @ (bit0 @ A)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7053])). 185.47/93.69 thf(3461,axiom,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4594_dvd__triv__left)). 185.47/93.69 thf(19109,plain,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3461])). 185.47/93.69 thf(3279,axiom,((! [A:complex,B:complex,C:nat,D:nat]: (((dvd_dvd_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ D)) <= (ord_less_eq_nat @ C @ D)) <= (dvd_dvd_complex @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4800_dvd__power__le)). 185.47/93.69 thf(18542,plain,((! [A:complex,B:complex,C:nat,D:nat]: ((dvd_dvd_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ D)) | ~ (ord_less_eq_nat @ C @ D) | ~ (dvd_dvd_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3279])). 185.47/93.69 thf(1331,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ B) @ B) = (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1651_add__less__same__cancel2)). 185.47/93.69 thf(12171,plain,((! [A:rat,B:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ B) @ B) = (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331])). 185.47/93.69 thf(3262,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_nat @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))) => (ord_less_nat @ (C @ A) @ D)) <= ((C @ B) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4086_ord__less__eq__subst)). 185.47/93.69 thf(18483,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => (((! [E:real,F:real]: ((ord_less_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))) => (ord_less_nat @ (C @ A) @ D)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3262])). 185.47/93.69 thf(1016,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ B) = (ord_less_eq_rat @ (uminus_uminus_rat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5512_minus__le__iff)). 185.47/93.69 thf(11208,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ A) @ B) = (ord_less_eq_rat @ (uminus_uminus_rat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016])). 185.47/93.69 thf(2252,axiom,((! [A:num,B:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ (times_times_int @ (bit_ri631733984087533419it_int @ (pred_numeral @ A) @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6772_signed__take__bit__numeral__bit1)). 185.47/93.69 thf(15218,plain,((! [A:num,B:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ (times_times_int @ (bit_ri631733984087533419it_int @ (pred_numeral @ A) @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2252])). 185.47/93.69 thf(488,axiom,((! [A:num]: ((ord_max_int @ zero_zero_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3619_max__0__1_I3_J)). 185.47/93.69 thf(9378,plain,((! [A:num]: ((ord_max_int @ zero_zero_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[488])). 185.47/93.69 thf(3420,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) <= (ord_less_rat @ B @ zero_zero_rat)) <= (ord_less_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2428_divide__neg__neg)). 185.47/93.69 thf(18991,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) | ~ (ord_less_rat @ B @ zero_zero_rat) | ~ (ord_less_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3420])). 185.47/93.69 thf(3626,axiom,((! [A:int,B:int,C:nat]: (((power_power_int @ (divide_divide_int @ B @ A) @ C) = (divide_divide_int @ (power_power_int @ B @ C) @ (power_power_int @ A @ C))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4785_div__power)). 185.47/93.69 thf(19637,plain,((! [A:int,B:int,C:nat]: (((power_power_int @ (divide_divide_int @ B @ A) @ C) = (divide_divide_int @ (power_power_int @ B @ C) @ (power_power_int @ A @ C))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3626])). 185.47/93.69 thf(2125,axiom,((! [A:complex,B:complex]: ((((cos_complex @ B) != zero_zero_complex) => ((minus_minus_complex @ one_one_complex @ (times_times_complex @ (tan_complex @ A) @ (tan_complex @ B))) = (divide1717551699836669952omplex @ (cos_complex @ (plus_plus_complex @ A @ B)) @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B))))) <= ((cos_complex @ A) != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8080_lemma__tan__add1)). 185.47/93.69 thf(14806,plain,((! [A:complex,B:complex]: (((~ ((cos_complex @ B) = zero_zero_complex)) => ((minus_minus_complex @ one_one_complex @ (times_times_complex @ (tan_complex @ A) @ (tan_complex @ B))) = (divide1717551699836669952omplex @ (cos_complex @ (plus_plus_complex @ A @ B)) @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B))))) | ((cos_complex @ A) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2125])). 185.47/93.69 thf(2989,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ (bit_ri631733984087533419it_int @ A @ B) @ B) = (ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6240_signed__take__bit__int__less__eq__self__iff)). 185.47/93.69 thf(17644,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ (bit_ri631733984087533419it_int @ A @ B) @ B) = (ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2989])). 185.47/93.69 thf(544,axiom,((! [A:real,B:real]: (((((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_eq_real @ (sin_real @ A) @ (sin_real @ B)) = (ord_less_eq_real @ A @ B))) <= (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B)) <= (ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7902_sin__mono__le__eq)). 185.47/93.69 thf(9542,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_eq_real @ (sin_real @ A) @ (sin_real @ B)) = (ord_less_eq_real @ A @ B))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) | ~ (ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[544])). 185.47/93.69 thf(7192,axiom,((ord_less_eq_nat @ one_one_nat @ na)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557__092_060open_0621_A_092_060le_062_An_092_060close_062)). 185.47/93.69 thf(32228,plain,((ord_less_eq_nat @ one_one_nat @ na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7192])). 185.47/93.69 thf(2280,axiom,((! [A:rat,B:rat]: ((abs_abs_rat @ (times_times_rat @ A @ B)) = (times_times_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6459_abs__mult)). 185.47/93.69 thf(15300,plain,((! [A:rat,B:rat]: ((abs_abs_rat @ (times_times_rat @ A @ B)) = (times_times_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2280])). 185.47/93.69 thf(6677,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2117_not__less0)). 185.47/93.69 thf(30257,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6677])). 185.47/93.69 thf(1669,axiom,((! [A:int,B:int,C:int,D:int]: (((dvd_dvd_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) <= (dvd_dvd_int @ C @ D)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4589_mult__dvd__mono)). 185.47/93.69 thf(13328,plain,((! [A:int,B:int,C:int,D:int]: ((dvd_dvd_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) | ~ (dvd_dvd_int @ C @ D) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669])). 185.47/93.69 thf(6017,axiom,((ord_less_eq_num = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4196_order_Oorder__iff__strict)). 185.47/93.69 thf(27947,plain,(((ord_less_eq_num) = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6017])). 185.47/93.69 thf(3583,axiom,((! [A:real,B:real,C:real]: ((((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = B) <= (A = zero_zero_real)) & ((A != zero_zero_real) => ((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (plus_plus_real @ (times_times_real @ B @ A) @ C) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2745_add__divide__eq__if__simps_I1_J)). 185.47/93.69 thf(19505,plain,((! [A:real,B:real,C:real]: ((((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = B) | ~ (A = zero_zero_real)) & ((~ (A = zero_zero_real)) => ((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (plus_plus_real @ (times_times_real @ B @ A) @ C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3583])). 185.47/93.69 thf(3740,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (sqrt @ A) @ (sqrt @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8152_real__sqrt__le__mono)). 185.47/93.69 thf(20013,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (sqrt @ A) @ (sqrt @ B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3740])). 185.47/93.69 thf(3754,axiom,((! [A:int,B:int]: ((plus_plus_int @ (bit_se725231765392027082nd_int @ A @ B) @ (bit_se1409905431419307370or_int @ A @ B)) = (plus_plus_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9424_plus__and__or)). 185.47/93.69 thf(20054,plain,((! [A:int,B:int]: ((plus_plus_int @ (bit_se725231765392027082nd_int @ A @ B) @ (bit_se1409905431419307370or_int @ A @ B)) = (plus_plus_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3754])). 185.47/93.69 thf(3263,axiom,((! [A:rat,B:rat,C:(rat > real),D:real]: (((ord_less_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_rat @ E @ F))))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4331_order__le__less__subst2)). 185.47/93.69 thf(18491,plain,((! [A:rat,B:rat,C:(rat > real),D:real]: (((ord_less_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_rat @ E @ F))))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3263])). 185.47/93.69 thf(2673,axiom,((! [A:(nat > rat),B:nat,C:nat]: ((! [D:nat]: (ord_less_rat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_rat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1060_lift__Suc__mono__less__iff)). 185.47/93.69 thf(16590,plain,((! [A:(nat > rat),B:nat,C:nat]: ((! [D:nat]: (ord_less_rat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_rat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2673])). 185.47/93.69 thf(1191,axiom,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ B) = (((ord_less_int @ A @ one_one_int) <= (ord_less_eq_int @ zero_zero_int @ B)) & ((ord_less_int @ one_one_int @ A) <= (ord_less_eq_int @ B @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2829_mult__less__cancel__right2)). 185.47/93.69 thf(11744,plain,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ B) = (((ord_less_int @ A @ one_one_int) | ~ (ord_less_eq_int @ zero_zero_int @ B)) & ((ord_less_int @ one_one_int @ A) | ~ (ord_less_eq_int @ B @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191])). 185.47/93.69 thf(3256,axiom,((! [A:nat,B:nat]: ((semiri681578069525770553at_rat @ (divide_divide_nat @ A @ B)) = (divide_divide_rat @ (minus_minus_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ (modulo_modulo_nat @ A @ B))) @ (semiri681578069525770553at_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7302_field__char__0__class_Oof__nat__div)). 185.47/93.69 thf(18470,plain,((! [A:nat,B:nat]: ((semiri681578069525770553at_rat @ (divide_divide_nat @ A @ B)) = (divide_divide_rat @ (minus_minus_rat @ (semiri681578069525770553at_rat @ A) @ (semiri681578069525770553at_rat @ (modulo_modulo_nat @ A @ B))) @ (semiri681578069525770553at_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3256])). 185.47/93.69 thf(3406,axiom,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7233_of__nat__mono)). 185.47/93.69 thf(18948,plain,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3406])). 185.47/93.69 thf(7275,axiom,((! [A:real,B:num]: ((power_power_real @ (uminus_uminus_real @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus_uminus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6615_power__minus__Bit1)). 185.47/93.69 thf(32510,plain,((! [A:real,B:num]: ((power_power_real @ (uminus_uminus_real @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (uminus_uminus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit1 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7275])). 185.47/93.69 thf(7058,axiom,(((minus_minus_rat @ one_one_rat @ one_one_rat) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1713_diff__numeral__special_I9_J)). 185.47/93.69 thf(31771,plain,(((minus_minus_rat @ one_one_rat @ one_one_rat) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7058])). 185.47/93.69 thf(6993,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((A @ C) => (A @ (suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2106_nat__induct)). 185.47/93.69 thf(31523,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ C) => (A @ (suc @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6993])). 185.47/93.69 thf(3298,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (times_times_int @ B @ A)) = (((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_int @ one_one_int @ B)) & ((ord_less_int @ B @ one_one_int) <= (ord_less_eq_int @ A @ zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2826_mult__less__cancel__right1)). 185.47/93.69 thf(18596,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (times_times_int @ B @ A)) = (((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_int @ one_one_int @ B)) & ((ord_less_int @ B @ one_one_int) | ~ (ord_less_eq_int @ A @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3298])). 185.47/93.69 thf(3395,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ (times_times_complex @ B @ A) @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1680_nonzero__mult__div__cancel__right)). 185.47/93.69 thf(18914,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ (times_times_complex @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3395])). 185.47/93.69 thf(189,axiom,((! [A:real]: (ord_less_real @ (tanh_real @ A) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6538_tanh__real__lt__1)). 185.47/93.69 thf(8341,plain,((! [A:real]: (ord_less_real @ (tanh_real @ A) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 185.47/93.69 thf(5493,axiom,((! [A:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7011_of__nat__le__0__iff)). 185.47/93.69 thf(26026,plain,((! [A:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5493])). 185.47/93.69 thf(1397,axiom,((ord_less_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_4222_order_Ostrict__iff__not)). 185.47/93.69 thf(12391,plain,(((ord_less_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)],[1397])). 185.47/93.69 thf(4178,axiom,((! [A:complex,B:nat]: ((power_power_complex @ (divide1717551699836669952omplex @ one_one_complex @ A) @ B) = (divide1717551699836669952omplex @ one_one_complex @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_843_power__one__over)). 185.47/93.69 thf(21378,plain,((! [A:complex,B:nat]: ((power_power_complex @ (divide1717551699836669952omplex @ one_one_complex @ A) @ B) = (divide1717551699836669952omplex @ one_one_complex @ (power_power_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4178])). 185.47/93.69 thf(6502,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) => ((ord_less_eq_num @ A @ B) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4169_antisym__conv1)). 185.47/93.69 thf(29674,plain,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) => ((ord_less_eq_num @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6502])). 185.47/93.69 thf(2216,axiom,((! [A:num]: ((abs_abs_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6377_abs__neg__numeral)). 185.47/93.69 thf(15109,plain,((! [A:num]: ((abs_abs_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A))) = (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2216])). 185.47/93.69 thf(3727,axiom,((~ (ord_less_rat @ zero_zero_rat @ (uminus_uminus_rat @ one_one_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5921_less__minus__one__simps_I3_J)). 185.47/93.69 thf(19970,plain,((~ (ord_less_rat @ zero_zero_rat @ (uminus_uminus_rat @ one_one_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3727])). 185.47/93.69 thf(118,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (log @ A @ B) @ one_one_real) = (ord_less_eq_real @ B @ A))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9031_log__le__one__cancel__iff)). 185.47/93.69 thf(8115,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (log @ A @ B) @ one_one_real) = (ord_less_eq_real @ B @ A))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 185.47/93.69 thf(66,axiom,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ A @ (set_ord_atMost_nat @ B)) = (times_times_int @ (A @ zero_zero_nat) @ (groups705719431365010083at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8773_prod_OatMost__shift)). 185.47/93.69 thf(7946,plain,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (A) @ (set_ord_atMost_nat @ B)) = (times_times_int @ (A @ zero_zero_nat) @ (groups705719431365010083at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 185.47/93.69 thf(5499,axiom,((! [A:real,B:real]: (((plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1904_sum__power2__eq__zero__iff)). 185.47/93.69 thf(26045,plain,((! [A:real,B:real]: (((plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5499])). 185.47/93.69 thf(2549,axiom,((! [A:rat,B:rat,C:rat]: (((((divide_divide_rat @ B @ A) = (divide_divide_rat @ C @ A)) = (B = C)) <= (dvd_dvd_rat @ A @ C)) <= (dvd_dvd_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4665_dvd__div__eq__iff)). 185.47/93.69 thf(16186,plain,((! [A:rat,B:rat,C:rat]: ((((divide_divide_rat @ B @ A) = (divide_divide_rat @ C @ A)) = (B = C)) | ~ (dvd_dvd_rat @ A @ C) | ~ (dvd_dvd_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2549])). 185.47/93.69 thf(4576,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ one_one_Code_integer) = ((dvd_dvd_Code_integer @ B @ one_one_Code_integer) & (dvd_dvd_Code_integer @ A @ one_one_Code_integer))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4747_is__unit__mult__iff)). 185.47/93.69 thf(22660,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ one_one_Code_integer) = ((dvd_dvd_Code_integer @ B @ one_one_Code_integer) & (dvd_dvd_Code_integer @ A @ one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4576])). 185.47/93.69 thf(7706,axiom,(((ord_less_nat @ (vEBT_VEBT_low @ xa @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) & (ord_less_nat @ (vEBT_VEBT_high @ xa @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25__092_060open_062high_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ax_An_A_060_A2_A_094_An_092_060close_062)). 185.47/93.69 thf(33860,plain,(((ord_less_nat @ (vEBT_VEBT_low @ xa @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) & (ord_less_nat @ (vEBT_VEBT_high @ xa @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7706])). 185.47/93.69 thf(6064,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ (modulo_modulo_nat @ B @ C)) @ C) = (modulo_modulo_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1970_mod__mult__right__eq)). 185.47/93.69 thf(28085,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ (modulo_modulo_nat @ B @ C)) @ C) = (modulo_modulo_nat @ (times_times_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6064])). 185.47/93.69 thf(4147,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (times_times_int @ B @ A)) = (((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ one_one_int @ B)) & ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ B @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2814_mult__le__cancel__right1)). 185.47/93.69 thf(21282,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (times_times_int @ B @ A)) = (((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ one_one_int @ B)) & ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ B @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4147])). 185.47/93.69 thf(6190,axiom,((! [A:nat,B:num]: ((bit_ri631733984087533419it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (bit_ri631733984087533419it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5454_signed__take__bit__Suc__minus__bit0)). 185.47/93.69 thf(28577,plain,((! [A:nat,B:num]: ((bit_ri631733984087533419it_int @ (suc @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ B)))) = (times_times_int @ (bit_ri631733984087533419it_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ B))) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6190])). 185.47/93.69 thf(5459,axiom,((! [A:int]: ((times_times_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ one))) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5981_mult__1s__ring__1_I2_J)). 185.47/93.69 thf(25819,plain,((! [A:int]: ((times_times_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ one))) = (uminus_uminus_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5459])). 185.47/93.69 thf(547,axiom,((! [A:nat]: ((cos_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ pi)) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7810_cos__2npi)). 185.47/93.69 thf(9551,plain,((! [A:nat]: ((cos_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ pi)) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[547])). 185.47/93.69 thf(4274,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (((plus_plus_int @ A @ B) = zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int)))) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2282_add__nonpos__eq__0__iff)). 185.47/93.69 thf(21670,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (((plus_plus_int @ A @ B) = zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int)))) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4274])). 185.47/93.69 thf(6203,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_752_diff__le__mono)). 185.47/93.69 thf(28613,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6203])). 185.47/93.69 thf(6089,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ (times_times_nat @ B @ C)) @ B) = (modulo_modulo_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1779_mod__mult__self2)). 185.47/93.69 thf(28170,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ (times_times_nat @ B @ C)) @ B) = (modulo_modulo_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6089])). 185.47/93.69 thf(6728,axiom,((! [A:nat]: ((compow_nat_nat @ A @ suc) = (plus_plus_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9808_Suc__funpow)). 185.47/93.69 thf(30440,plain,((! [A:nat]: ((compow_nat_nat @ A @ suc) = (plus_plus_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6728])). 185.47/93.69 thf(2454,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) & (ord_less_eq_rat @ A @ B)) => (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_add__mono__thms__linordered__semiring_I1_J)). 185.47/93.69 thf(15865,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ C @ D) & (ord_less_eq_rat @ A @ B)) => (ord_less_eq_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2454])). 185.47/93.69 thf(1172,axiom,((~ (dvd_dvd_int @ zero_zero_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4702_not__is__unit__0)). 185.47/93.69 thf(11690,plain,((~ (dvd_dvd_int @ zero_zero_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172])). 185.47/93.69 thf(2609,axiom,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ A) = (((ord_less_int @ B @ one_one_int) <= (ord_less_eq_int @ zero_zero_int @ A)) & ((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_int @ one_one_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2823_mult__less__cancel__left2)). 185.47/93.69 thf(16393,plain,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ A) = (((ord_less_int @ B @ one_one_int) | ~ (ord_less_eq_int @ zero_zero_int @ A)) & ((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_int @ one_one_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2609])). 185.47/93.69 thf(6440,axiom,((! [A:(nat > $o),B:nat]: ((? [C:nat]: (A @ (times_times_nat @ B @ C))) = (? [C:nat]: ((A @ C) & (dvd_dvd_nat @ B @ (plus_plus_nat @ C @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4827_unity__coeff__ex)). 185.47/93.69 thf(29454,plain,((! [A:(nat > $o),B:nat]: ((? [C:nat]: (A @ (times_times_nat @ B @ C))) = (? [C:nat]: ((A @ C) & (dvd_dvd_nat @ B @ (plus_plus_nat @ C @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6440])). 185.47/93.69 thf(3909,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) <= (ord_less_eq_rat @ B @ zero_zero_rat)) <= (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2240_mult__nonpos__nonpos)). 185.47/93.69 thf(20552,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ zero_zero_rat @ (times_times_rat @ A @ B)) | ~ (ord_less_eq_rat @ B @ zero_zero_rat) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3909])). 185.47/93.69 thf(6950,axiom,((! [A:nat,B:int,C:int]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((ord_less_eq_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) <= (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4945_power__mono__odd)). 185.47/93.69 thf(31303,plain,((! [A:nat,B:int,C:int]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((ord_less_eq_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) | ~ (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6950])). 185.47/93.69 thf(7286,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4055_order__less__asym)). 185.47/93.69 thf(32545,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7286])). 185.47/93.69 thf(4688,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (~ (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3322_minf_I8_J)). 185.47/93.69 thf(23025,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (~ (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4688])). 185.47/93.69 thf(3471,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ A @ B)) = (((B = zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ A)) | (ord_less_int @ zero_zero_int @ B) | (dvd_dvd_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4929_mod__int__pos__iff)). 185.47/93.69 thf(19156,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ A @ B)) = (((B = zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ A)) | (ord_less_int @ zero_zero_int @ B) | (dvd_dvd_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3471])). 185.47/93.69 thf(148,axiom,((! [A:real,B:real]: (((((arcsin @ A) = (arcsin @ B)) = (A = B)) <= (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real)) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8314_arcsin__eq__iff)). 185.47/93.69 thf(8209,plain,((! [A:real,B:real]: ((((arcsin @ A) = (arcsin @ B)) = (A = B)) | ~ (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 185.47/93.69 thf(4574,axiom,((ord_less_int @ (uminus_uminus_int @ one_one_int) @ zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5916_less__minus__one__simps_I1_J)). 185.47/93.69 thf(22656,plain,((ord_less_int @ (uminus_uminus_int @ one_one_int) @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4574])). 185.47/93.69 thf(3436,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (bit1 @ A)) = (plus_plus_complex @ (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A)) @ one_one_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6600_numeral__Bit1)). 185.47/93.69 thf(19040,plain,((! [A:num]: ((numera6690914467698888265omplex @ (bit1 @ A)) = (plus_plus_complex @ (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A)) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3436])). 185.47/93.69 thf(7724,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_power2__nat__le__imp__le)). 185.47/93.69 thf(33910,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7724])). 185.47/93.69 thf(2873,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((arctan @ A) = (suminf_real @ (^ [B:nat]: (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (times_times_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))) @ (power_power_real @ A @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7529_arctan__series)). 185.47/93.69 thf(17265,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((arctan @ A) = (suminf_real @ (^ [B:nat]: (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (times_times_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))) @ (power_power_real @ A @ (plus_plus_nat @ (times_times_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2873])). 185.47/93.69 thf(3231,axiom,((~ (ord_less_eq_int @ one_one_int @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5717_le__minus__one__simps_I4_J)). 185.47/93.69 thf(18401,plain,((~ (ord_less_eq_int @ one_one_int @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3231])). 185.47/93.69 thf(4989,axiom,((ord_less_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2390_less__numeral__extra_I1_J)). 185.47/93.69 thf(24070,plain,((ord_less_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4989])). 185.47/93.69 thf(7397,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2061_mult__left__cancel)). 185.47/93.69 thf(32909,plain,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7397])). 185.47/93.69 thf(5115,axiom,((! [A:nat,B:real]: (((root @ A @ (abs_abs_real @ B)) = (abs_abs_real @ (root @ A @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9186_real__root__abs)). 185.47/93.69 thf(24564,plain,((! [A:nat,B:real]: (((root @ A @ (abs_abs_real @ B)) = (abs_abs_real @ (root @ A @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5115])). 185.47/93.69 thf(93,axiom,((! [A:nat]: ((set_or4665077453230672383an_nat @ (suc @ zero_zero_nat) @ A) = (minus_minus_set_nat @ (set_ord_lessThan_nat @ A) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9570_atLeast1__lessThan__eq__remove0)). 185.47/93.69 thf(8038,plain,((! [A:nat]: ((set_or4665077453230672383an_nat @ (suc @ zero_zero_nat) @ A) = (minus_minus_set_nat @ (set_ord_lessThan_nat @ A) @ (insert_nat @ zero_zero_nat @ bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 185.47/93.69 thf(4753,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ B) = ((ord_less_eq_rat @ A @ B) & (ord_less_eq_rat @ (uminus_uminus_rat @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6518_abs__le__iff)). 185.47/93.69 thf(23242,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ B) = ((ord_less_eq_rat @ A @ B) & (ord_less_eq_rat @ (uminus_uminus_rat @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4753])). 185.47/93.69 thf(1494,axiom,((! [A:complex]: (((suminf_complex @ (power_power_complex @ A)) = (divide1717551699836669952omplex @ one_one_complex @ (minus_minus_complex @ one_one_complex @ A))) <= (ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7641_suminf__geometric)). 185.47/93.69 thf(12702,plain,((! [A:complex]: (((suminf_complex @ (power_power_complex @ A)) = (divide1717551699836669952omplex @ one_one_complex @ (minus_minus_complex @ one_one_complex @ A))) | ~ (ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494])). 185.47/93.69 thf(2933,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ (uminus_uminus_rat @ (divide_divide_rat @ B @ C))) = (((~ (ord_less_rat @ zero_zero_rat @ C)) => (((ord_less_rat @ C @ zero_zero_rat) => (ord_less_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ A @ C))) & ((ord_less_rat @ A @ zero_zero_rat) <= (~ (ord_less_rat @ C @ zero_zero_rat))))) & ((ord_less_rat @ (times_times_rat @ A @ C) @ (uminus_uminus_rat @ B)) <= (ord_less_rat @ zero_zero_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6145_less__minus__divide__eq)). 185.47/93.69 thf(17460,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ (uminus_uminus_rat @ (divide_divide_rat @ B @ C))) = (((~ (ord_less_rat @ zero_zero_rat @ C)) => (((ord_less_rat @ C @ zero_zero_rat) => (ord_less_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ A @ C))) & ((ord_less_rat @ A @ zero_zero_rat) | (ord_less_rat @ C @ zero_zero_rat)))) & ((ord_less_rat @ (times_times_rat @ A @ C) @ (uminus_uminus_rat @ B)) | ~ (ord_less_rat @ zero_zero_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2933])). 185.47/93.69 thf(7622,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_int @ (power_power_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_power__even__eq)). 185.47/93.69 thf(33629,plain,((! [A:int,B:nat]: ((power_power_int @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (power_power_int @ (power_power_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7622])). 185.47/93.69 thf(7217,axiom,((! [A:(nat > complex),B:complex]: ((sums_complex @ (^ [C:nat]: (times_times_complex @ (A @ C) @ (power_power_complex @ zero_zero_complex @ C))) @ B) = ((A @ zero_zero_nat) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8137_powser__sums__zero__iff)). 185.47/93.69 thf(32316,plain,((! [A:(nat > complex),B:complex]: ((sums_complex @ (^ [C:nat]: (times_times_complex @ (A @ C) @ (power_power_complex @ zero_zero_complex @ C))) @ B) = ((A @ zero_zero_nat) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7217])). 185.47/93.69 thf(11,axiom,((! [A:(nat > rat),B:nat,C:rat]: ((minus_minus_rat @ (groups2906978787729119204at_rat @ A @ (set_ord_lessThan_nat @ B)) @ (times_times_rat @ (semiri681578069525770553at_rat @ B) @ C)) = (groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7584_sumr__diff__mult__const2)). 185.47/93.69 thf(7759,plain,((! [A:(nat > rat),B:nat,C:rat]: ((minus_minus_rat @ (groups2906978787729119204at_rat @ (A) @ (set_ord_lessThan_nat @ B)) @ (times_times_rat @ (semiri681578069525770553at_rat @ B) @ C)) = (groups2906978787729119204at_rat @ (^ [D:nat]: (minus_minus_rat @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 185.47/93.69 thf(7482,axiom,((! [A:real,B:num]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ zero_zero_real) = ((ord_less_real @ A @ zero_zero_real) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4537_power__less__zero__eq__numeral)). 185.47/93.69 thf(33216,plain,((! [A:real,B:num]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ zero_zero_real) = ((ord_less_real @ A @ zero_zero_real) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7482])). 185.47/93.69 thf(4512,axiom,((! [A:num]: ~ (ord_le3102999989581377725nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5936_not__numeral__le__neg__one)). 185.47/93.69 thf(22455,plain,((! [A:num]: ~ (ord_le3102999989581377725nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4512])). 185.47/93.69 thf(2565,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ one_one_real @ (powr_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9095_gr__one__powr)). 185.47/93.69 thf(16235,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ one_one_real @ (powr_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2565])). 185.47/93.69 thf(1894,axiom,((! [A:real]: (((powr_real @ A @ one_one_real) = A) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9075_powr__one__gt__zero__iff)). 185.47/93.69 thf(14065,plain,((! [A:real]: (((powr_real @ A @ one_one_real) = A) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894])). 185.47/93.69 thf(1601,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => ((ord_less_eq_real @ (minus_minus_real @ C @ B) @ D) <= (ord_less_eq_real @ C @ (plus_plus_real @ D @ B))))) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1195_add__le__add__imp__diff__le)). 185.47/93.69 thf(13043,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => ((ord_less_eq_real @ (minus_minus_real @ C @ B) @ D) | ~ (ord_less_eq_real @ C @ (plus_plus_real @ D @ B))))) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601])). 185.47/93.69 thf(3588,axiom,((! [A:real,B:real]: (((exp_real @ (plus_plus_real @ A @ B)) = (times_times_real @ (exp_real @ A) @ (exp_real @ B))) <= ((times_times_real @ A @ B) = (times_times_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8173_exp__add__commuting)). 185.47/93.69 thf(19526,plain,((! [A:real,B:real]: (((exp_real @ (plus_plus_real @ A @ B)) = (times_times_real @ (exp_real @ A) @ (exp_real @ B))) | ~ ((times_times_real @ A @ B) = (times_times_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3588])). 185.47/93.69 thf(1037,axiom,((! [A:num]: ((neg_nu7009210354673126013omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu7009210354673126013omplex @ (numera6690914467698888265omplex @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5268_dbl__simps_I1_J)). 185.47/93.69 thf(11271,plain,((! [A:num]: ((neg_nu7009210354673126013omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu7009210354673126013omplex @ (numera6690914467698888265omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037])). 185.47/93.69 thf(3250,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3967_lt__ex)). 185.47/93.69 thf(18453,plain,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3250])). 185.47/93.69 thf(2750,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_int @ C @ A)) & ((ord_less_int @ A @ C) <= (ord_less_eq_int @ zero_zero_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2596_mult__less__cancel__right)). 185.47/93.69 thf(16871,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_int @ C @ A)) & ((ord_less_int @ A @ C) | ~ (ord_less_eq_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2750])). 185.47/93.69 thf(4985,axiom,((! [A:int]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1899_power2__less__eq__zero__iff)). 185.47/93.69 thf(24039,plain,((! [A:int]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4985])). 185.47/93.69 thf(4228,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => ((cos_real @ (arcsin @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8307_cos__arcsin)). 185.47/93.69 thf(21531,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => ((cos_real @ (arcsin @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4228])). 185.47/93.69 thf(1930,axiom,((! [A:num,B:nat]: ((minus_minus_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (minus_minus_nat @ (pred_numeral @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6790_diff__numeral__Suc)). 185.47/93.69 thf(14170,plain,((! [A:num,B:nat]: ((minus_minus_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (minus_minus_nat @ (pred_numeral @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930])). 185.47/93.69 thf(1361,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) <= (ord_less_real @ one_one_real @ A)) <= (ord_less_real @ (powr_real @ A @ B) @ (powr_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9089_powr__less__cancel)). 185.47/93.69 thf(12267,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ B @ C) | ~ (ord_less_real @ one_one_real @ A) | ~ (ord_less_real @ (powr_real @ A @ B) @ (powr_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361])). 185.47/93.69 thf(1251,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9375_AND__upper1)). 185.47/93.69 thf(11928,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251])). 185.47/93.69 thf(3984,axiom,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (sqrt @ (plus_plus_real @ (power_power_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (plus_plus_real @ C @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (sqrt @ (plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8228_real__sqrt__sum__squares__triangle__ineq)). 185.47/93.69 thf(20789,plain,((! [A:real,B:real,C:real,D:real]: (ord_less_eq_real @ (sqrt @ (plus_plus_real @ (power_power_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (plus_plus_real @ C @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (sqrt @ (plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ D @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3984])). 185.47/93.69 thf(2798,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= (ord_less_real @ C @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_add__le__less__mono)). 185.47/93.69 thf(17024,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ (ord_less_real @ C @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2798])). 185.47/93.69 thf(7341,axiom,((! [A:num]: ((minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (plus_plus_num @ A @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5450_diff__numeral__special_I4_J)). 185.47/93.69 thf(32741,plain,((! [A:num]: ((minus_minus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (plus_plus_num @ A @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7341])). 185.47/93.69 thf(6182,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ (times_times_nat @ B @ A) @ C) = (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4742_mult__unit__dvd__iff)). 185.47/93.69 thf(28534,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ (times_times_nat @ B @ A) @ C) = (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6182])). 185.47/93.69 thf(4610,axiom,((! [A:num,B:nat,C:nat]: ((ord_less_real @ (power_power_real @ (numeral_numeral_real @ A) @ B) @ (semiri5074537144036343181t_real @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7124_numeral__power__less__of__nat__cancel__iff)). 185.47/93.69 thf(22761,plain,((! [A:num,B:nat,C:nat]: ((ord_less_real @ (power_power_real @ (numeral_numeral_real @ A) @ B) @ (semiri5074537144036343181t_real @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4610])). 185.47/93.69 thf(7459,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1848_nat__mult__le__cancel__disj)). 185.47/93.69 thf(33143,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7459])). 185.47/93.69 thf(7033,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1003_Suc__diff__diff)). 185.47/93.69 thf(31690,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7033])). 185.47/93.69 thf(4468,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ A) => (ord_less_rat @ zero_zero_rat @ (power_power_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2454_zero__less__power)). 185.47/93.69 thf(22303,plain,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ A) => (ord_less_rat @ zero_zero_rat @ (power_power_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4468])). 185.47/93.69 thf(6,axiom,((! [A:num,B:num]: ((archim7802044766580827645g_real @ (uminus_uminus_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)))) = (uminus_uminus_int @ (divide_divide_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9066_ceiling__minus__divide__eq__div__numeral)). 185.47/93.69 thf(7744,plain,((! [A:num,B:num]: ((archim7802044766580827645g_real @ (uminus_uminus_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)))) = (uminus_uminus_int @ (divide_divide_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 185.47/93.69 thf(3168,axiom,((ord_less_rat = (^ [A:rat,B:rat]: (ord_less_rat @ (minus_minus_rat @ A @ B) @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2425_less__iff__diff__less__0)). 185.47/93.69 thf(18203,plain,(((ord_less_rat) = (^ [A:rat,B:rat]: (ord_less_rat @ (minus_minus_rat @ A @ B) @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3168])). 185.47/93.69 thf(1963,axiom,((! [A:num]: ~ (ord_less_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5956_not__one__less__neg__numeral)). 185.47/93.69 thf(14300,plain,((! [A:num]: ~ (ord_less_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963])). 185.47/93.69 thf(4776,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ zero_zero_int) => ((divide_divide_int @ A @ B) = (uminus_uminus_int @ one_one_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6276_div__pos__neg__trivial)). 185.47/93.69 thf(23346,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ zero_zero_int) => ((divide_divide_int @ A @ B) = (uminus_uminus_int @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4776])). 185.47/93.69 thf(1550,axiom,((ord_less_eq_rat = (^ [A:rat,B:rat]: ((A = B) | (ord_less_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4195_order_Oorder__iff__strict)). 185.47/93.69 thf(12876,plain,(((ord_less_eq_rat) = (^ [A:rat,B:rat]: ((A = B) | (ord_less_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550])). 185.47/93.69 thf(1716,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_5506_le__minus__iff)). 185.47/93.69 thf(13473,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)],[1716])). 185.47/93.69 thf(3341,axiom,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ (plus_plus_nat @ A @ C) @ A)) @ (set_ord_atMost_nat @ B)) = (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ one_one_nat) @ (plus_plus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8944_choose__rising__sum_I1_J)). 185.47/93.69 thf(18734,plain,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ (plus_plus_nat @ A @ C) @ A)) @ (set_ord_atMost_nat @ B)) = (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ one_one_nat) @ (plus_plus_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3341])). 185.47/93.69 thf(6345,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((? [C:real]: ((ord_less_real @ zero_zero_real @ C) & ((power_power_real @ C @ A) = B) & ! [D:real]: ((((power_power_real @ D @ A) = B) & (ord_less_real @ zero_zero_real @ D)) => (D = C)))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3100_realpow__pos__nth__unique)). 185.47/93.69 thf(29094,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & ((power_power_real @ C @ A) = B) & ! [D:real]: ((((power_power_real @ D @ A) = B) & (ord_less_real @ zero_zero_real @ D)) => (D = C))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6345])). 185.47/93.69 thf(3606,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (((ord_less_rat @ C @ B) & (ord_less_rat @ A @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2361_mult__less__cancel__left__disj)). 185.47/93.69 thf(19577,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ A @ C)) = (((ord_less_rat @ C @ B) & (ord_less_rat @ A @ zero_zero_rat)) | ((ord_less_rat @ zero_zero_rat @ A) & (ord_less_rat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3606])). 185.47/93.69 thf(2206,axiom,((! [A:real,B:real]: (((? [C:nat]: (ord_less_real @ (power_power_real @ B @ C) @ A)) <= (ord_less_real @ B @ one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3097_real__arch__pow__inv)). 185.47/93.69 thf(15076,plain,((! [A:real,B:real]: (? [C:nat]: (ord_less_real @ (power_power_real @ B @ C) @ A) | ~ (ord_less_real @ B @ one_one_real) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2206])). 185.47/93.69 thf(4928,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1534_add__eq__0__iff__both__eq__0)). 185.47/93.69 thf(23863,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4928])). 185.47/93.69 thf(4679,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (bit0 @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1357_numeral__code_I2_J)). 185.47/93.69 thf(22993,plain,((! [A:num]: ((numera6690914467698888265omplex @ (bit0 @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4679])). 185.47/93.69 thf(3999,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1810_divide__less__eq__1__neg)). 185.47/93.69 thf(20831,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3999])). 185.47/93.69 thf(595,axiom,((! [A:nat]: ((ord_less_eq_real @ zero_zero_real @ (sin_real @ (divide_divide_real @ pi @ (semiri5074537144036343181t_real @ A)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7891_sin__pi__divide__n__ge__0)). 185.47/93.69 thf(9711,plain,((! [A:nat]: ((ord_less_eq_real @ zero_zero_real @ (sin_real @ (divide_divide_real @ pi @ (semiri5074537144036343181t_real @ A)))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[595])). 185.47/93.69 thf(2925,axiom,(((neg_nu3179335615603231917ec_rat @ one_one_rat) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6777_dbl__dec__simps_I3_J)). 185.47/93.69 thf(17431,plain,(((neg_nu3179335615603231917ec_rat @ one_one_rat) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2925])). 185.47/93.69 thf(5869,axiom,((! [A:num,B:num]: (((bit1 @ A) = (bit1 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6312_semiring__norm_I90_J)). 185.47/93.69 thf(27426,plain,((! [A:num,B:num]: (((bit1 @ A) = (bit1 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5869])). 185.47/93.69 thf(3917,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se8568078237143864401it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9752_drop__bit__nonnegative__int__iff)). 185.47/93.69 thf(20580,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se8568078237143864401it_int @ A @ B)) = (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3917])). 185.47/93.69 thf(5108,axiom,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option_nat > $o)),C:option_nat]: (((A = none_P5556105721700978146at_nat) => (B @ A @ C)) => (((B @ A @ C) <= (! [D:product_prod_nat_nat,E:nat]: ((A = (some_P7363390416028606310at_nat @ D)) => ((C = (some_nat @ E)) => (B @ A @ C))))) <= ((C = none_nat) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1177_combine__options__cases)). 185.47/93.69 thf(24532,plain,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option_nat > $o)),C:option_nat]: (((A = none_P5556105721700978146at_nat) => (B @ A @ C)) => ((B @ A @ C) | ~ (! [D:product_prod_nat_nat,E:nat]: ((A = (some_P7363390416028606310at_nat @ D)) => ((C = (some_nat @ E)) => (B @ A @ C)))) | ~ ((C = none_nat) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5108])). 185.47/93.69 thf(6436,axiom,((ord_less_num = (^ [A:num,B:num]: ((B != A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4236_dual__order_Ostrict__iff__order)). 185.47/93.69 thf(29431,plain,(((ord_less_num) = (^ [A:num,B:num]: (~ (B = A) & (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6436])). 185.47/93.69 thf(3601,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (bit_se2002935070580805687sk_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9219_less__eq__mask)). 185.47/93.69 thf(19564,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (bit_se2002935070580805687sk_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3601])). 185.47/93.69 thf(4994,axiom,((! [A:nat]: ((power_power_int @ (uminus_uminus_int @ one_one_int) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6294_power__minus1__odd)). 185.47/93.69 thf(24082,plain,((! [A:nat]: ((power_power_int @ (uminus_uminus_int @ one_one_int) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4994])). 185.47/93.69 thf(351,axiom,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ B))) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7662_summable__mult2)). 185.47/93.69 thf(8908,plain,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ B))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])). 185.47/93.69 thf(6472,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1156_left__diff__distrib_H)). 185.47/93.69 thf(29565,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6472])). 185.47/93.69 thf(2533,axiom,((! [A:num]: ((neg_numeral_dbl_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (neg_numeral_dbl_real @ (numeral_numeral_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5266_dbl__simps_I1_J)). 185.47/93.69 thf(16130,plain,((! [A:num]: ((neg_numeral_dbl_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (neg_numeral_dbl_real @ (numeral_numeral_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2533])). 185.47/93.69 thf(2541,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ (abs_abs_rat @ A) @ B)) = ((A != zero_zero_rat) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6421_zero__less__power__abs__iff)). 185.47/93.69 thf(16160,plain,((! [A:rat,B:nat]: ((ord_less_rat @ zero_zero_rat @ (power_power_rat @ (abs_abs_rat @ A) @ B)) = (~ (A = zero_zero_rat) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2541])). 185.47/93.69 thf(2983,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => ((ord_less_int @ B @ A) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4006_linorder__cases)). 185.47/93.69 thf(17626,plain,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => ((ord_less_int @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2983])). 185.47/93.69 thf(6693,axiom,((power_power_rat = (^ [A:rat,B:nat]: (if_rat @ (B = zero_zero_nat) @ one_one_rat @ (times_times_rat @ A @ (power_power_rat @ A @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2960_power__eq__if)). 185.47/93.69 thf(30305,plain,(((power_power_rat) = (^ [A:rat,B:nat]: (if_rat @ (B = zero_zero_nat) @ one_one_rat @ (times_times_rat @ A @ (power_power_rat @ A @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6693])). 185.47/93.69 thf(1641,axiom,((! [A:rat]: ((zero_zero_rat = (plus_plus_rat @ A @ A)) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1512_double__zero__sym)). 185.47/93.69 thf(13192,plain,((! [A:rat]: ((zero_zero_rat = (plus_plus_rat @ A @ A)) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641])). 185.47/93.69 thf(3559,axiom,((! [A:real,B:real]: ((one_one_real = (divide_divide_real @ A @ B)) = ((A = B) & (B != zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1736_one__eq__divide__iff)). 185.47/93.69 thf(19432,plain,((! [A:real,B:real]: ((one_one_real = (divide_divide_real @ A @ B)) = ((A = B) & ~ (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3559])). 185.47/93.69 thf(5337,axiom,((! [A:rat,B:rat]: ((plus_plus_rat @ A @ (plus_plus_rat @ A @ B)) = (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_left__add__twice)). 185.47/93.69 thf(25368,plain,((! [A:rat,B:rat]: ((plus_plus_rat @ A @ (plus_plus_rat @ A @ B)) = (plus_plus_rat @ (times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5337])). 185.47/93.69 thf(1233,axiom,((! [A:real,B:real]: ((real_V1022390504157884413omplex @ (times_times_complex @ (real_V4546457046886955230omplex @ A) @ (plus_plus_complex @ (real_V4546457046886955230omplex @ (cos_real @ B)) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sin_real @ B)))))) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9150_cmod__complex__polar)). 185.47/93.69 thf(11871,plain,((! [A:real,B:real]: ((real_V1022390504157884413omplex @ (times_times_complex @ (real_V4546457046886955230omplex @ A) @ (plus_plus_complex @ (real_V4546457046886955230omplex @ (cos_real @ B)) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sin_real @ B)))))) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233])). 185.47/93.69 thf(4956,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D)) <= ((A = B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_add__mono__thms__linordered__semiring_I4_J)). 185.47/93.69 thf(23959,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D)) | ~ ((A = B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4956])). 185.47/93.69 thf(4773,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7500_norm__triangle__le__diff)). 185.47/93.69 thf(23339,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4773])). 185.47/93.69 thf(5811,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_781_nat__mult__1__right)). 185.47/93.69 thf(27135,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5811])). 185.47/93.69 thf(795,axiom,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => ((((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (B = D) @ (C @ D) @ one_one_complex)) @ A) = one_one_complex) <= (~ (member_nat @ B @ A))) & ((member_nat @ B @ A) => ((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (B = D) @ (C @ D) @ one_one_complex)) @ A) = (C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8677_prod_Odelta_H)). 185.47/93.69 thf(10443,plain,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => ((((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (B = D) @ (C @ D) @ one_one_complex)) @ A) = one_one_complex) | (member_nat @ B @ A)) & ((member_nat @ B @ A) => ((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (B = D) @ (C @ D) @ one_one_complex)) @ A) = (C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[795])). 185.47/93.69 thf(1343,axiom,((! [A:num,B:nat,C:nat]: ((ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ (semiri1314217659103216013at_int @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7123_numeral__power__less__of__nat__cancel__iff)). 185.47/93.69 thf(12208,plain,((! [A:num,B:nat,C:nat]: ((ord_less_int @ (power_power_int @ (numeral_numeral_int @ A) @ B) @ (semiri1314217659103216013at_int @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343])). 185.47/93.69 thf(7025,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_vebt_member @ A @ B) = C) => ((! [D:$o,E:$o]: ((C = (~ (((D) <= (B = zero_zero_nat)) & (((B = one_one_nat) & ((B = one_one_nat) => (E))) <= (B != zero_zero_nat))))) <= (A = (vEBT_Leaf @ D @ E)))) => (((? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))) => (C)) => (((C) <= (? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F)))) => ((~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT]: ((C = (~ ((B != D) => ((B != E) => (~ (ord_less_nat @ B @ D) & ((~ (ord_less_nat @ E @ B) & (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))) <= (~ (ord_less_nat @ E @ B)))) <= (~ (ord_less_nat @ B @ D)))))))) <= (? [H:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))))) <= ((C) <= (? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3003_vebt__member_Oelims_I1_J)). 185.47/93.69 thf(31636,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_vebt_member @ A @ B) = C) => ((! [D:$o,E:$o]: ((C = (~ (((D) | ~ (B = zero_zero_nat)) & (((B = one_one_nat) & ((B = one_one_nat) => (E))) | (B = zero_zero_nat))))) | ~ (A = (vEBT_Leaf @ D @ E)))) => (((? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))) => (C)) => (((C) | ~ (? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F)))) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT]: ((C = (~ ((~ (B = D)) => ((~ (B = E)) => (~ (ord_less_nat @ B @ D) & ((~ (ord_less_nat @ E @ B) & (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))) | (ord_less_nat @ E @ B))) | (ord_less_nat @ B @ D))))))) | ~ (? [H:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H))))) | ~ ((C) | ~ (? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7025])). 185.47/93.69 thf(1184,axiom,((! [A:nat,B:real]: (sums_real @ (^ [C:nat]: (times_times_real @ (if_real @ (C = A) @ one_one_real @ zero_zero_real) @ (power_power_real @ B @ C))) @ (power_power_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8200_powser__sums__if)). 185.47/93.69 thf(11722,plain,((! [A:nat,B:real]: (sums_real @ (^ [C:nat]: (times_times_real @ (if_real @ (C = A) @ one_one_real @ zero_zero_real) @ (power_power_real @ B @ C))) @ (power_power_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184])). 185.47/93.69 thf(4340,axiom,((! [A:nat]: ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (plus_plus_rat @ (semiri681578069525770553at_rat @ A) @ one_one_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7346_double__gauss__sum)). 185.47/93.69 thf(21900,plain,((! [A:nat]: ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ (semiri681578069525770553at_rat) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (plus_plus_rat @ (semiri681578069525770553at_rat @ A) @ one_one_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4340])). 185.47/93.69 thf(4163,axiom,((! [A:num,B:nat,C:int]: ((ord_less_real @ (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7172_neg__numeral__power__less__of__int__cancel__iff)). 185.47/93.69 thf(21334,plain,((! [A:num,B:nat,C:int]: ((ord_less_real @ (power_power_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B) @ (ring_1_of_int_real @ C)) = (ord_less_int @ (power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4163])). 185.47/93.69 thf(2040,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ zero_zero_real @ A)) | ((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2439_zero__less__divide__iff)). 185.47/93.69 thf(14551,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ zero_zero_real @ A)) | ((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2040])). 185.47/93.69 thf(7581,axiom,((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ res @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ res @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34__092_060open_062both__member__options_A_ItreeList_A_B_Ahigh_Ares_A_Ideg_Adiv_A2_J_J_A_Ilow_Ares_A_Ideg_Adiv_A2_J_J_092_060close_062)). 185.47/93.69 thf(33518,plain,((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ res @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ res @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7581])). 185.47/93.69 thf(2900,axiom,((! [A:nat]: ((semiri1406184849735516958ct_int @ (suc @ A)) = (times_times_int @ (semiri1314217659103216013at_int @ (suc @ A)) @ (semiri1406184849735516958ct_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7968_fact__Suc)). 185.47/93.69 thf(17355,plain,((! [A:nat]: ((semiri1406184849735516958ct_int @ (suc @ A)) = (times_times_int @ (semiri1314217659103216013at_int @ (suc @ A)) @ (semiri1406184849735516958ct_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2900])). 185.47/93.69 thf(5508,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ B @ A)) = (B = A)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4000_antisym__conv3)). 185.47/93.69 thf(26074,plain,((! [A:nat,B:nat]: (((~ (ord_less_nat @ B @ A)) = (B = A)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5508])). 185.47/93.69 thf(5564,axiom,((! [A:nat]: ((power_power_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1744_power__0__Suc)). 185.47/93.69 thf(26253,plain,((! [A:nat]: ((power_power_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5564])). 185.47/93.69 thf(2016,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real) <= (ord_less_eq_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2287_add__nonpos__nonpos)). 185.47/93.69 thf(14475,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real) | ~ (ord_less_eq_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016])). 185.47/93.69 thf(3249,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_add__diff__cancel__left_H)). 185.47/93.69 thf(18450,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3249])). 185.47/93.69 thf(5948,axiom,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2273_linordered__nonzero__semiring__class_Ozero__le__one)). 185.47/93.69 thf(27686,plain,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5948])). 185.47/93.69 thf(5746,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (times_times_nat @ B @ C)) => (ord_less_nat @ (divide_divide_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_less__mult__imp__div__less)). 185.47/93.69 thf(26850,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (times_times_nat @ B @ C)) => (ord_less_nat @ (divide_divide_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5746])). 185.47/93.69 thf(1180,axiom,((! [A:num,B:num]: ((bit_se8568078237143864401it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (bit_se8568078237143864401it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (inc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9750_drop__bit__numeral__minus__bit1)). 185.47/93.69 thf(11712,plain,((! [A:num,B:num]: ((bit_se8568078237143864401it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (bit_se8568078237143864401it_int @ (pred_numeral @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (inc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180])). 185.47/93.69 thf(5361,axiom,((! [A:int,B:nat]: (((ord_less_int @ one_one_int @ (power_power_int @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2901_one__less__power)). 185.47/93.69 thf(25479,plain,((! [A:int,B:nat]: ((ord_less_int @ one_one_int @ (power_power_int @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5361])). 185.47/93.69 thf(2174,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ (times_times_rat @ B @ A) @ C)) = (dvd_dvd_rat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4473_dvd__add__times__triv__left__iff)). 185.47/93.69 thf(14984,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ (plus_plus_rat @ (times_times_rat @ B @ A) @ C)) = (dvd_dvd_rat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2174])). 185.47/93.69 thf(5646,axiom,((! [A:num]: ((abs_abs_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6376_abs__neg__numeral)). 185.47/93.69 thf(26522,plain,((! [A:num]: ((abs_abs_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5646])). 185.47/93.69 thf(6145,axiom,((! [A:num]: ((ring_17405671764205052669omplex @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7297_of__int__neg__numeral)). 185.47/93.69 thf(28370,plain,((! [A:num]: ((ring_17405671764205052669omplex @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6145])). 185.47/93.69 thf(5301,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_783_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse)). 185.47/93.69 thf(25250,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5301])). 185.47/93.69 thf(2116,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4263_dual__order_Ostrict__implies__order)). 185.47/93.69 thf(14779,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2116])). 185.47/93.69 thf(7723,axiom,((! [A:rat,B:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = B) | (A = (uminus_uminus_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6182_power2__eq__iff)). 185.47/93.69 thf(33907,plain,((! [A:rat,B:rat]: (((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = B) | (A = (uminus_uminus_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7723])). 185.47/93.69 thf(3528,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ D)) = (plus_plus_rat @ (minus_minus_rat @ A @ C) @ (minus_minus_rat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_713_add__diff__add)). 185.47/93.69 thf(19339,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ C @ D)) = (plus_plus_rat @ (minus_minus_rat @ A @ C) @ (minus_minus_rat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3528])). 185.47/93.69 thf(6367,axiom,((! [A:complex,B:complex,C:complex]: ((((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (uminus1482373934393186551omplex @ C)) <= (A = zero_zero_complex)) & (((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ B @ (times_times_complex @ C @ A)) @ A)) <= (A != zero_zero_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6172_add__divide__eq__if__simps_I5_J)). 185.47/93.69 thf(29168,plain,((! [A:complex,B:complex,C:complex]: ((((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (uminus1482373934393186551omplex @ C)) | ~ (A = zero_zero_complex)) & (((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ B @ (times_times_complex @ C @ A)) @ A)) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6367])). 185.47/93.69 thf(1225,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9544_or__not__numerals_I9_J)). 185.47/93.69 thf(11843,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ B)))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225])). 185.47/93.69 thf(4023,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3981_order_Oasym)). 185.47/93.69 thf(20913,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4023])). 185.47/93.69 thf(4123,axiom,((! [A:nat]: ((set_or4665077453230672383an_nat @ A @ zero_zero_nat) = bot_bot_set_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9564_atLeastLessThan0)). 185.47/93.69 thf(21209,plain,((! [A:nat]: ((set_or4665077453230672383an_nat @ A @ zero_zero_nat) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4123])). 185.47/93.69 thf(4621,axiom,((gbinomial_real = (^ [A:real,B:nat]: (divide_divide_real @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (comm_s7457072308508201937r_real @ (uminus_uminus_real @ A) @ B)) @ (semiri2265585572941072030t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8456_gbinomial__pochhammer)). 185.47/93.69 thf(22799,plain,(((gbinomial_real) = (^ [A:real,B:nat]: (divide_divide_real @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (comm_s7457072308508201937r_real @ (uminus_uminus_real @ A) @ B)) @ (semiri2265585572941072030t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4621])). 185.47/93.69 thf(5553,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (((modulo_modulo_nat @ (plus_plus_nat @ one_one_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (plus_plus_nat @ one_one_nat @ (modulo_modulo_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4417_even__succ__mod__exp)). 185.47/93.69 thf(26221,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (((modulo_modulo_nat @ (plus_plus_nat @ one_one_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (plus_plus_nat @ one_one_nat @ (modulo_modulo_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5553])). 185.47/93.69 thf(5165,axiom,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_bits__div__by__1)). 185.47/93.69 thf(24768,plain,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5165])). 185.47/93.69 thf(3099,axiom,((! [A:vEBT_VEBT]: ((? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C))) <= (vEBT_invar_vebt @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1472_deg__1__Leaf)). 185.47/93.69 thf(17989,plain,((! [A:vEBT_VEBT]: (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)) | ~ (vEBT_invar_vebt @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3099])). 185.47/93.69 thf(6964,axiom,((! [A:rat]: ((minus_minus_rat @ A @ A) = zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1558_diff__self)). 185.47/93.69 thf(31388,plain,((! [A:rat]: ((minus_minus_rat @ A @ A) = zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6964])). 185.47/93.69 thf(1851,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((C != A) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3240_pinf_I4_J)). 185.47/93.69 thf(13941,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (C = A) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1851])). 185.47/93.69 thf(3361,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6475_abs__ge__zero)). 185.47/93.69 thf(18804,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3361])). 185.47/93.69 thf(7501,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) <= (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1062_lift__Suc__mono__less__iff)). 185.47/93.69 thf(33288,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) | ~ (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7501])). 185.47/93.69 thf(3175,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ (uminus_uminus_rat @ (divide_divide_rat @ B @ C))) = (((ord_less_eq_rat @ (times_times_rat @ A @ C) @ (uminus_uminus_rat @ B)) <= (ord_less_rat @ zero_zero_rat @ C)) & ((~ (ord_less_rat @ zero_zero_rat @ C)) => (((~ (ord_less_rat @ C @ zero_zero_rat)) => (ord_less_eq_rat @ A @ zero_zero_rat)) & ((ord_less_rat @ C @ zero_zero_rat) => (ord_less_eq_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ A @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6207_le__minus__divide__eq)). 185.47/93.69 thf(18221,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_eq_rat @ A @ (uminus_uminus_rat @ (divide_divide_rat @ B @ C))) = (((ord_less_eq_rat @ (times_times_rat @ A @ C) @ (uminus_uminus_rat @ B)) | ~ (ord_less_rat @ zero_zero_rat @ C)) & ((~ (ord_less_rat @ zero_zero_rat @ C)) => (((~ (ord_less_rat @ C @ zero_zero_rat)) => (ord_less_eq_rat @ A @ zero_zero_rat)) & ((ord_less_rat @ C @ zero_zero_rat) => (ord_less_eq_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ A @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3175])). 185.47/93.69 thf(953,axiom,((! [A:set_nat,B:set_nat,C:(nat > complex),D:(nat > complex)]: (((ord_less_eq_set_nat @ B @ A) => (((! [E:nat]: ((member_nat @ E @ B) => ((C @ E) = (D @ E)))) => ((groups2073611262835488442omplex @ C @ A) = (groups2073611262835488442omplex @ D @ B))) <= (! [E:nat]: (((C @ E) = zero_zero_complex) <= (member_nat @ E @ (minus_minus_set_nat @ A @ B)))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6069_sum_Omono__neutral__cong__right)). 185.47/93.69 thf(10998,plain,((! [A:set_nat,B:set_nat,C:(nat > complex),D:(nat > complex)]: (((ord_less_eq_set_nat @ B @ A) => (((! [E:nat]: ((member_nat @ E @ B) => ((C @ E) = (D @ E)))) => ((groups2073611262835488442omplex @ (C) @ A) = (groups2073611262835488442omplex @ (D) @ B))) | ~ (! [E:nat]: (((C @ E) = zero_zero_complex) | ~ (member_nat @ E @ (minus_minus_set_nat @ A @ B)))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[953])). 185.47/93.69 thf(2256,axiom,((! [A:rat,B:nat]: ((ord_less_eq_rat @ one_one_rat @ (power_power_rat @ A @ B)) <= (ord_less_eq_rat @ one_one_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_835_one__le__power)). 185.47/93.69 thf(15230,plain,((! [A:rat,B:nat]: ((ord_less_eq_rat @ one_one_rat @ (power_power_rat @ A @ B)) | ~ (ord_less_eq_rat @ one_one_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2256])). 185.47/93.69 thf(428,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((log @ B @ (powr_real @ A @ C)) = (times_times_real @ C @ (log @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9104_log__powr)). 185.47/93.69 thf(9156,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((log @ B @ (powr_real @ A @ C)) = (times_times_real @ C @ (log @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])). 185.47/93.69 thf(2961,axiom,((! [A:real,B:real]: ((cos_real @ (minus_minus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)) @ (times_times_real @ (sin_real @ A) @ (sin_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7822_cos__diff)). 185.47/93.69 thf(17544,plain,((! [A:real,B:real]: ((cos_real @ (minus_minus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)) @ (times_times_real @ (sin_real @ A) @ (sin_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2961])). 185.47/93.69 thf(261,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((real_V4546457046886955230omplex @ (sqrt @ A)) = (csqrt @ (real_V4546457046886955230omplex @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9192_of__real__sqrt)). 185.47/93.69 thf(8589,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((real_V4546457046886955230omplex @ (sqrt @ A)) = (csqrt @ (real_V4546457046886955230omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 185.47/93.69 thf(4755,axiom,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) => ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_Code_integer) <= (ord_le3102999989581377725nteger @ A @ one_one_Code_integer))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6265_square__le__1)). 185.47/93.69 thf(23247,plain,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) => ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_Code_integer) | ~ (ord_le3102999989581377725nteger @ A @ one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4755])). 185.47/93.69 thf(5905,axiom,((! [A:nat,B:nat]: ((bit_se2161824704523386999it_nat @ (suc @ A) @ B) = (plus_plus_nat @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2161824704523386999it_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3035_flip__bit__Suc)). 185.47/93.69 thf(27555,plain,((! [A:nat,B:nat]: ((bit_se2161824704523386999it_nat @ (suc @ A) @ B) = (plus_plus_nat @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2161824704523386999it_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5905])). 185.47/93.69 thf(3849,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5086_add__minus__cancel)). 185.47/93.69 thf(20361,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3849])). 185.47/93.69 thf(7529,axiom,((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4904_odd__one)). 185.47/93.69 thf(33379,plain,((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7529])). 185.47/93.69 thf(1526,axiom,((! [A:complex,B:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7505_norm__triangle__ineq4)). 185.47/93.69 thf(12798,plain,((! [A:complex,B:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526])). 185.47/93.69 thf(5083,axiom,((! [A:nat]: ((binomial @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8425_binomial__n__0)). 185.47/93.69 thf(24440,plain,((! [A:nat]: ((binomial @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5083])). 185.47/93.69 thf(1212,axiom,((! [A:real]: ~ (ord_less_eq_real @ (exp_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8168_not__exp__le__zero)). 185.47/93.69 thf(11807,plain,((! [A:real]: ~ (ord_less_eq_real @ (exp_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212])). 185.47/93.69 thf(4854,axiom,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ (divide_divide_rat @ A @ C) @ (divide_divide_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_add__divide__distrib)). 185.47/93.69 thf(23586,plain,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ (plus_plus_rat @ A @ B) @ C) = (plus_plus_rat @ (divide_divide_rat @ A @ C) @ (divide_divide_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4854])). 185.47/93.69 thf(2809,axiom,((! [A:complex]: ((times_times_complex @ (exp_complex @ A) @ A) = (times_times_complex @ A @ (exp_complex @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8144_exp__times__arg__commute)). 185.47/93.69 thf(17059,plain,((! [A:complex]: ((times_times_complex @ (exp_complex @ A) @ A) = (times_times_complex @ A @ (exp_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2809])). 185.47/93.69 thf(6772,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2118_less__zeroE)). 185.47/93.69 thf(30646,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6772])). 185.47/93.69 thf(1247,axiom,((! [A:nat,B:nat]: (((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ B)) @ A) != zero_zero_real) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8517_pochhammer__of__nat__eq__0__lemma_H)). 185.47/93.69 thf(11914,plain,((! [A:nat,B:nat]: (~ ((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ B)) @ A) = zero_zero_real) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247])). 185.47/93.69 thf(7133,axiom,((! [A:num,B:num,C:(num > num),D:num]: (((ord_less_num @ (C @ B) @ D) => ((ord_less_num @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4338_order__le__less__subst2)). 185.47/93.69 thf(32017,plain,((! [A:num,B:num,C:(num > num),D:num]: (((ord_less_num @ (C @ B) @ D) => ((ord_less_num @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7133])). 185.47/93.69 thf(5200,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4045_dual__order_Ostrict__implies__not__eq)). 185.47/93.69 thf(24873,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5200])). 185.47/93.69 thf(840,axiom,((! [A:rat,B:nat]: ((times_times_rat @ (gbinomial_rat @ A @ B) @ A) = (plus_plus_rat @ (times_times_rat @ (semiri681578069525770553at_rat @ B) @ (gbinomial_rat @ A @ B)) @ (times_times_rat @ (semiri681578069525770553at_rat @ (suc @ B)) @ (gbinomial_rat @ A @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8484_gbinomial__mult__1_H)). 185.47/93.69 thf(10590,plain,((! [A:rat,B:nat]: ((times_times_rat @ (gbinomial_rat @ A @ B) @ A) = (plus_plus_rat @ (times_times_rat @ (semiri681578069525770553at_rat @ B) @ (gbinomial_rat @ A @ B)) @ (times_times_rat @ (semiri681578069525770553at_rat @ (suc @ B)) @ (gbinomial_rat @ A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[840])). 185.47/93.69 thf(2405,axiom,((! [A:int,B:nat,C:nat]: (((ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) => (ord_less_nat @ B @ C)) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_power__less__imp__less__exp)). 185.47/93.69 thf(15690,plain,((! [A:int,B:nat,C:nat]: (((ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) => (ord_less_nat @ B @ C)) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2405])). 185.47/93.69 thf(4652,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((((plus_plus_complex @ (divide1717551699836669952omplex @ C @ A) @ (divide1717551699836669952omplex @ D @ B)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (times_times_complex @ C @ B) @ (times_times_complex @ D @ A)) @ (times_times_complex @ A @ B))) <= (B != zero_zero_complex)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2741_add__frac__eq)). 185.47/93.69 thf(22901,plain,((! [A:complex,B:complex,C:complex,D:complex]: (((plus_plus_complex @ (divide1717551699836669952omplex @ C @ A) @ (divide1717551699836669952omplex @ D @ B)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (times_times_complex @ C @ B) @ (times_times_complex @ D @ A)) @ (times_times_complex @ A @ B))) | (B = zero_zero_complex) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4652])). 185.47/93.69 thf(1615,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_eq_real @ (times_times_real @ B @ A) @ (uminus_uminus_real @ C))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6214_pos__le__minus__divide__eq)). 185.47/93.69 thf(13096,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_eq_real @ (times_times_real @ B @ A) @ (uminus_uminus_real @ C))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615])). 185.47/93.69 thf(1131,axiom,((! [A:nat,B:num]: ((((set_or4665077453230672383an_nat @ A @ (numeral_numeral_nat @ B)) = (insert_nat @ (pred_numeral @ B) @ (set_or4665077453230672383an_nat @ A @ (pred_numeral @ B)))) <= (ord_less_eq_nat @ A @ (pred_numeral @ B))) & ((~ (ord_less_eq_nat @ A @ (pred_numeral @ B))) => ((set_or4665077453230672383an_nat @ A @ (numeral_numeral_nat @ B)) = bot_bot_set_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9567_atLeastLessThan__nat__numeral)). 185.47/93.69 thf(11563,plain,((! [A:nat,B:num]: ((((set_or4665077453230672383an_nat @ A @ (numeral_numeral_nat @ B)) = (insert_nat @ (pred_numeral @ B) @ (set_or4665077453230672383an_nat @ A @ (pred_numeral @ B)))) | ~ (ord_less_eq_nat @ A @ (pred_numeral @ B))) & ((~ (ord_less_eq_nat @ A @ (pred_numeral @ B))) => ((set_or4665077453230672383an_nat @ A @ (numeral_numeral_nat @ B)) = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131])). 185.47/93.69 thf(2751,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4257_order_Ostrict__implies__order)). 185.47/93.69 thf(16874,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2751])). 185.47/93.69 thf(4234,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (times_times_int @ A @ B) @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1755_mod__mult__self1__is__0)). 185.47/93.69 thf(21549,plain,((! [A:int,B:int]: ((modulo_modulo_int @ (times_times_int @ A @ B) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4234])). 185.47/93.69 thf(5540,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = zero_zero_nat) => (? [C:nat]: (A = (times_times_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1931_mod__eq__0D)). 185.47/93.69 thf(26184,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = zero_zero_nat) => (? [C:nat]: (A = (times_times_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5540])). 185.47/93.69 thf(7031,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((divide_divide_nat @ B @ A) = zero_zero_nat) = (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4842_unit__div__eq__0__iff)). 185.47/93.69 thf(31680,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((divide_divide_nat @ B @ A) = zero_zero_nat) = (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7031])). 185.47/93.69 thf(701,axiom,((! [A:int,B:int]: ((ring_1_of_int_int @ (minus_minus_int @ A @ B)) = (minus_minus_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6978_of__int__diff)). 185.47/93.69 thf(10073,plain,((! [A:int,B:int]: ((ring_1_of_int_int @ (minus_minus_int @ A @ B)) = (minus_minus_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[701])). 185.47/93.69 thf(2773,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= (ord_less_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_add__le__less__mono)). 185.47/93.69 thf(16943,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2773])). 185.47/93.69 thf(476,axiom,((! [A:(nat > real),B:real,C:set_nat,D:real,E:(nat > real)]: ((sums_real @ A @ B) => (((D = (plus_plus_real @ B @ (groups6591440286371151544t_real @ (^ [F:nat]: (minus_minus_real @ (E @ F) @ (A @ F))) @ C))) => (sums_real @ (^ [F:nat]: (if_real @ (member_nat @ F @ C) @ (E @ F) @ (A @ F))) @ D)) <= (finite_finite_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8212_sums__If__finite__set_H)). 185.47/93.69 thf(9331,plain,((! [A:(nat > real),B:real,C:set_nat,D:real,E:(nat > real)]: ((sums_real @ (A) @ B) => (((D = (plus_plus_real @ B @ (groups6591440286371151544t_real @ (^ [F:nat]: (minus_minus_real @ (E @ F) @ (A @ F))) @ C))) => (sums_real @ (^ [F:nat]: (if_real @ (member_nat @ F @ C) @ (E @ F) @ (A @ F))) @ D)) | ~ (finite_finite_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[476])). 185.47/93.69 thf(6222,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((C = D) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_add__mono__thms__linordered__semiring_I3_J)). 185.47/93.69 thf(28667,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((C = D) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6222])). 185.47/93.69 thf(1957,axiom,((! [A:int,B:nat]: ((ord_less_int @ A @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) => (ord_less_eq_int @ (plus_plus_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ B))) @ (bit_ri631733984087533419it_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6300_signed__take__bit__int__greater__eq)). 185.47/93.69 thf(14278,plain,((! [A:int,B:nat]: ((ord_less_int @ A @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) => (ord_less_eq_int @ (plus_plus_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ B))) @ (bit_ri631733984087533419it_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1957])). 185.47/93.69 thf(2021,axiom,((! [A:nat]: ~ (ord_less_int @ (semiri1314217659103216013at_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7211_of__nat__less__0__iff)). 185.47/93.69 thf(14490,plain,((! [A:nat]: ~ (ord_less_int @ (semiri1314217659103216013at_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2021])). 185.47/93.69 thf(5106,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((((power_power_nat @ B @ A) = (power_power_nat @ C @ A)) = (B = C)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2140_power__eq__iff__eq__base)). 185.47/93.69 thf(24510,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((((power_power_nat @ B @ A) = (power_power_nat @ C @ A)) = (B = C)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5106])). 185.47/93.69 thf(5018,axiom,(((uminus_uminus_int @ zero_zero_int) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5056_add_Oinverse__neutral)). 185.47/93.69 thf(24159,plain,(((uminus_uminus_int @ zero_zero_int) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5018])). 185.47/93.69 thf(4247,axiom,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))) @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6447_zmod__numeral__Bit1)). 185.47/93.69 thf(21594,plain,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4247])). 185.47/93.69 thf(2373,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ A) = (((ord_less_real @ A @ zero_zero_real) => (ord_less_eq_real @ one_one_real @ B)) & ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ B @ one_one_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2809_mult__le__cancel__left2)). 185.47/93.69 thf(15585,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ A) = (((ord_less_real @ A @ zero_zero_real) => (ord_less_eq_real @ one_one_real @ B)) & ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ B @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2373])). 185.47/93.69 thf(752,axiom,((! [A:complex,B:nat]: ((gbinomial_complex @ (plus_plus_complex @ A @ one_one_complex) @ (suc @ B)) = (times_times_complex @ (gbinomial_complex @ A @ B) @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ one_one_complex) @ (semiri8010041392384452111omplex @ (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8559_gbinomial__rec)). 185.47/93.69 thf(10250,plain,((! [A:complex,B:nat]: ((gbinomial_complex @ (plus_plus_complex @ A @ one_one_complex) @ (suc @ B)) = (times_times_complex @ (gbinomial_complex @ A @ B) @ (divide1717551699836669952omplex @ (plus_plus_complex @ A @ one_one_complex) @ (semiri8010041392384452111omplex @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[752])). 185.47/93.69 thf(2098,axiom,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) => ((ord_less_eq_rat @ A @ B) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4168_antisym__conv1)). 185.47/93.69 thf(14723,plain,((! [A:rat,B:rat]: ((~ (ord_less_rat @ A @ B)) => ((ord_less_eq_rat @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2098])). 185.47/93.69 thf(320,axiom,((! [A:real,B:real]: ((((ord_less_real @ (arcsin @ A) @ (arcsin @ B)) = (ord_less_real @ A @ B)) <= (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real)) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8316_arcsin__less__mono)). 185.47/93.69 thf(8801,plain,((! [A:real,B:real]: (((ord_less_real @ (arcsin @ A) @ (arcsin @ B)) = (ord_less_real @ A @ B)) | ~ (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 185.47/93.69 thf(3941,axiom,((! [A:int,B:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (ord_less_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5061_neg__less__iff__less)). 185.47/93.69 thf(20659,plain,((! [A:int,B:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (ord_less_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3941])). 185.47/93.69 thf(1867,axiom,((! [A:nat,B:nat,C:int]: (((ord_less_eq_int @ one_one_int @ C) => (ord_less_eq_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_877_power__increasing)). 185.47/93.69 thf(13986,plain,((! [A:nat,B:nat,C:int]: (((ord_less_eq_int @ one_one_int @ C) => (ord_less_eq_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867])). 185.47/93.69 thf(2976,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (ord_max_nat @ A @ B) @ C) = (ord_max_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3760_nat__add__max__left)). 185.47/93.69 thf(17597,plain,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (ord_max_nat @ A @ B) @ C) = (ord_max_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2976])). 185.47/93.69 thf(69,axiom,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_real @ (groups129246275422532515t_real @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8696_prod_OlessThan__Suc)). 185.47/93.69 thf(7955,plain,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_real @ (groups129246275422532515t_real @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 185.47/93.69 thf(7702,axiom,((! [A:num]: ((A != one) => ((~ (! [B:num]: (A != (bit1 @ B)))) <= (! [B:num]: (A != (bit0 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6529_num_Oexhaust)). 185.47/93.69 thf(33848,plain,((! [A:num]: ((~ (A = one)) => (~ (! [B:num]: ~ (A = (bit1 @ B))) | ~ (! [B:num]: ~ (A = (bit0 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7702])). 185.47/93.69 thf(955,axiom,(((im @ one_one_complex) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9671_one__complex_Osimps_I2_J)). 185.47/93.69 thf(11009,plain,(((im @ one_one_complex) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[955])). 185.47/93.69 thf(3211,axiom,((! [A:nat,B:num,C:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (numeral_numeral_real @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7127_of__nat__le__numeral__power__cancel__iff)). 185.47/93.69 thf(18342,plain,((! [A:nat,B:num,C:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (numeral_numeral_real @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3211])). 185.47/93.69 thf(270,axiom,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ A) @ B) = ((ord_le6747313008572928689nteger @ A @ B) & (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6527_abs__less__iff)). 185.47/93.69 thf(8616,plain,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (abs_abs_Code_integer @ A) @ B) = ((ord_le6747313008572928689nteger @ A @ B) & (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 185.47/93.69 thf(4073,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_3961_linorder__le__cases)). 185.47/93.69 thf(21053,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)],[4073])). 185.47/93.69 thf(4364,axiom,((! [A:int,B:nat,C:int]: (((ord_less_int @ A @ C) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2684_power__less__imp__less__base)). 185.47/93.69 thf(21981,plain,((! [A:int,B:nat,C:int]: ((ord_less_int @ A @ C) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4364])). 185.47/93.69 thf(4793,axiom,((! [A:rat,B:(num > rat),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F)))) => (ord_less_eq_rat @ A @ (B @ D)))) <= (ord_less_eq_rat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3910_order__subst1)). 185.47/93.69 thf(23399,plain,((! [A:rat,B:(num > rat),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F)))) => (ord_less_eq_rat @ A @ (B @ D)))) | ~ (ord_less_eq_rat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4793])). 185.47/93.69 thf(5581,axiom,((! [A:nat]: (ord_less_eq_real @ (times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ A)) @ (semiri2265585572941072030t_real @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8043_square__fact__le__2__fact)). 185.47/93.69 thf(26305,plain,((! [A:nat]: (ord_less_eq_real @ (times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ A)) @ (semiri2265585572941072030t_real @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5581])). 185.47/93.69 thf(7729,axiom,((bit_se8570568707652914677it_nat = (^ [A:nat,B:nat]: (divide_divide_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9765_drop__bit__nat__def)). 185.47/93.69 thf(33921,plain,(((bit_se8570568707652914677it_nat) = (^ [A:nat,B:nat]: (divide_divide_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7729])). 185.47/93.69 thf(3830,axiom,((! [A:int,B:num]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (numeral_numeral_rat @ B)) = (ord_less_int @ A @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7078_of__int__less__numeral__iff)). 185.47/93.69 thf(20297,plain,((! [A:int,B:num]: ((ord_less_rat @ (ring_1_of_int_rat @ A) @ (numeral_numeral_rat @ B)) = (ord_less_int @ A @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3830])). 185.47/93.69 thf(4009,axiom,((! [A:real,B:real,C:real,D:real]: ((times_times_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ D)) = (divide_divide_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_times__divide__times__eq)). 185.47/93.69 thf(20865,plain,((! [A:real,B:real,C:real,D:real]: ((times_times_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ D)) = (divide_divide_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4009])). 185.47/93.69 thf(5771,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ B @ A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4152_leD)). 185.47/93.69 thf(26933,plain,((! [A:num,B:num]: (~ (ord_less_num @ B @ A) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5771])). 185.47/93.69 thf(2588,axiom,((! [A:num]: (ord_less_eq_rat @ zero_zero_rat @ (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2191_zero__le__numeral)). 185.47/93.69 thf(16326,plain,((! [A:num]: (ord_less_eq_rat @ zero_zero_rat @ (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2588])). 185.47/93.69 thf(1256,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ C) <= (dvd_dvd_real @ (times_times_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4596_dvd__mult__left)). 185.47/93.69 thf(11943,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ C) | ~ (dvd_dvd_real @ (times_times_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256])). 185.47/93.69 thf(4307,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_add__right__cancel)). 185.47/93.69 thf(21763,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4307])). 185.47/93.69 thf(3933,axiom,((! [A:int]: ? [B:int]: (ord_less_int @ B @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3969_lt__ex)). 185.47/93.69 thf(20631,plain,((! [A:int]: ? [B:int]: (ord_less_int @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3933])). 185.47/93.69 thf(1561,axiom,((! [A:nat,B:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6906_of__nat__le__iff)). 185.47/93.69 thf(12904,plain,((! [A:nat,B:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561])). 185.47/93.69 thf(6581,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) => (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3005_odd__0__le__power__imp__0__le)). 185.47/93.69 thf(29944,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) => (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6581])). 185.47/93.69 thf(3469,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ zero_zero_rat) => ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2630_add__nonpos__neg)). 185.47/93.69 thf(19151,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ zero_zero_rat) => ((ord_less_rat @ B @ zero_zero_rat) => (ord_less_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3469])). 185.47/93.69 thf(5094,axiom,((! [A:nat]: ((bit_se6528837805403552850or_nat @ A @ (suc @ zero_zero_nat)) = (minus_minus_nat @ (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9447_xor__Suc__0__eq)). 185.47/93.69 thf(24472,plain,((! [A:nat]: ((bit_se6528837805403552850or_nat @ A @ (suc @ zero_zero_nat)) = (minus_minus_nat @ (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5094])). 185.47/93.69 thf(5007,axiom,((! [A:num]: ((ord_less_rat @ one_one_rat @ (numeral_numeral_rat @ A)) = (ord_less_num @ one @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_one__less__numeral__iff)). 185.47/93.69 thf(24127,plain,((! [A:num]: ((ord_less_rat @ one_one_rat @ (numeral_numeral_rat @ A)) = (ord_less_num @ one @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5007])). 185.47/93.69 thf(4042,axiom,((! [A:real]: ? [B:nat]: (ord_less_real @ A @ (semiri5074537144036343181t_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7434_reals__Archimedean2)). 185.47/93.69 thf(20962,plain,((! [A:real]: ? [B:nat]: (ord_less_real @ A @ (semiri5074537144036343181t_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4042])). 185.47/93.69 thf(7631,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4910_bit__eq__rec)). 185.47/93.69 thf(33661,plain,((((=) @ nat) = (^ [A:nat,B:nat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7631])). 185.47/93.69 thf(2385,axiom,((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5911_le__minus__one__simps_I1_J)). 185.47/93.69 thf(15622,plain,((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2385])). 185.47/93.69 thf(3904,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (times_times_real @ B @ C)) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4601_dvd__mult2)). 185.47/93.69 thf(20535,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (times_times_real @ B @ C)) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3904])). 185.47/93.69 thf(6597,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2124_le__0__eq)). 185.47/93.69 thf(29996,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6597])). 185.47/93.69 thf(3028,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5516_le__imp__neg__le)). 185.47/93.69 thf(17757,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A)) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3028])). 185.47/93.69 thf(5960,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((A != B) => (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4005_linorder__cases)). 185.47/93.69 thf(27732,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (A = B)) => (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5960])). 185.47/93.69 thf(4312,axiom,((! [A:real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1566_div__0)). 185.47/93.69 thf(21778,plain,((! [A:real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4312])). 185.47/93.69 thf(6731,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ B @ A) @ C) @ A) = (plus_plus_nat @ B @ (divide_divide_nat @ C @ A))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1834_div__mult__self3)). 185.47/93.69 thf(30450,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ B @ A) @ C) @ A) = (plus_plus_nat @ B @ (divide_divide_nat @ C @ A))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6731])). 185.47/93.69 thf(6640,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ A @ (bit0 @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9456_or__minus__numerals_I4_J)). 185.47/93.69 thf(30133,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ B)))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ A @ (bit0 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6640])). 185.47/93.69 thf(3053,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((B @ D) != zero_zero_complex) & (member_nat @ D @ A))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((plus_plus_complex @ (B @ D) @ (C @ D)) != zero_zero_complex) & (member_nat @ D @ A))))) <= (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((C @ D) != zero_zero_complex))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3543_sum_Ofinite__Collect__op)). 185.47/93.69 thf(17839,plain,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((B @ D) = zero_zero_complex) & (member_nat @ D @ A))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((plus_plus_complex @ (B @ D) @ (C @ D)) = zero_zero_complex) & (member_nat @ D @ A))))) | ~ (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((C @ D) = zero_zero_complex))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3053])). 185.47/93.69 thf(5380,axiom,((! [A:nat,B:nat]: ? [C:nat]: ! [D:nat]: ((ord_less_nat @ C @ D) => ((~ (dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B))) = (~ (dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4716_pinf_I10_J)). 185.47/93.69 thf(25539,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5380])). 185.47/93.69 thf(5194,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9394_and__nat__numerals_I1_J)). 185.47/93.69 thf(24855,plain,((! [A:num]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5194])). 185.47/93.69 thf(328,axiom,((! [A:real]: ((ord_less_eq_real @ (ln_ln_real @ A) @ (minus_minus_real @ A @ one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6201_ln__le__minus__one)). 185.47/93.69 thf(8833,plain,((! [A:real]: ((ord_less_eq_real @ (ln_ln_real @ A) @ (minus_minus_real @ A @ one_one_real)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 185.47/93.69 thf(713,axiom,((! [A:nat,B:nat,C:(nat > rat)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & (((groups2906978787729119204at_rat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_rat) <= (ord_less_nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6430_sum_Ocl__ivl__Suc)). 185.47/93.69 thf(10105,plain,((! [A:nat,B:nat,C:(nat > rat)]: (((~ (ord_less_nat @ (suc @ A) @ B)) => ((groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_plus_rat @ (groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A))))) & (((groups2906978787729119204at_rat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_rat) | ~ (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[713])). 185.47/93.69 thf(4811,axiom,((! [A:int]: ~ (! [B:nat,C:nat]: (A != (abs_Integ @ (product_Pair_nat_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9814_eq__Abs__Integ)). 185.47/93.69 thf(23452,plain,((! [A:int]: ~ (! [B:nat,C:nat]: ~ (A = (abs_Integ @ (product_Pair_nat_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4811])). 185.47/93.69 thf(4061,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9299_nat__plus__as__int)). 185.47/93.69 thf(21015,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4061])). 185.47/93.69 thf(37,axiom,((! [A:real,B:nat]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (sin_real @ A) @ (groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (sin_coeff @ C) @ (power_power_real @ A @ C))) @ (set_ord_lessThan_nat @ B)))) @ (times_times_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ (abs_abs_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8955_Maclaurin__sin__bound)). 185.47/93.69 thf(7851,plain,((! [A:real,B:nat]: (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (sin_real @ A) @ (groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (sin_coeff @ C) @ (power_power_real @ A @ C))) @ (set_ord_lessThan_nat @ B)))) @ (times_times_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ (abs_abs_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 185.47/93.69 thf(4260,axiom,((! [A:rat,B:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ A) @ (plus_plus_rat @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5092_minus__add__cancel)). 185.47/93.69 thf(21630,plain,((! [A:rat,B:rat]: ((plus_plus_rat @ (uminus_uminus_rat @ A) @ (plus_plus_rat @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4260])). 185.47/93.69 thf(2461,axiom,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (minus_minus_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_add__diff__cancel__left)). 185.47/93.69 thf(15884,plain,((! [A:real,B:real,C:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) = (minus_minus_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2461])). 185.47/93.69 thf(2538,axiom,((! [A:real,B:real,C:(real > num),D:num]: ((((C @ B) = D) => ((ord_less_num @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_num @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4085_ord__less__eq__subst)). 185.47/93.69 thf(16145,plain,((! [A:real,B:real,C:(real > num),D:num]: ((((C @ B) = D) => ((ord_less_num @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_num @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2538])). 185.47/93.69 thf(4289,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ B @ zero_zero_int) => (ord_less_eq_int @ (divide_divide_int @ A @ B) @ zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3054_div__nonneg__neg__le0)). 185.47/93.69 thf(21712,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ B @ zero_zero_int) => (ord_less_eq_int @ (divide_divide_int @ A @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4289])). 185.47/93.69 thf(3085,axiom,((! [A:rat,B:rat,C:(rat > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4352_order__less__le__subst2)). 185.47/93.69 thf(17937,plain,((! [A:rat,B:rat,C:(rat > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3085])). 185.47/93.69 thf(3306,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ B)) = ((B != zero_zero_real) & ((ord_less_real @ C @ A) <= (ord_less_real @ B @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2437_divide__less__cancel)). 185.47/93.69 thf(18628,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ B)) = (~ (B = zero_zero_real) & ((ord_less_real @ C @ A) | ~ (ord_less_real @ B @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3306])). 185.47/93.69 thf(3939,axiom,((! [A:nat,B:(rat > nat),C:rat,D:rat]: ((A = (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_rat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3940_ord__eq__le__subst)). 185.47/93.69 thf(20648,plain,((! [A:nat,B:(rat > nat),C:rat,D:rat]: ((A = (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_rat @ E @ F))) => (ord_less_eq_nat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3939])). 185.47/93.69 thf(6576,axiom,((! [A:num]: ((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ one_one_rat) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_numeral__le__one__iff)). 185.47/93.69 thf(29927,plain,((! [A:num]: ((ord_less_eq_rat @ (numeral_numeral_rat @ A) @ one_one_rat) = (ord_less_eq_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6576])). 185.47/93.69 thf(5620,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri1316708129612266289at_nat @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (semiri1316708129612266289at_nat @ B) @ (semiri1316708129612266289at_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7264_of__nat__diff)). 185.47/93.69 thf(26437,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri1316708129612266289at_nat @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (semiri1316708129612266289at_nat @ B) @ (semiri1316708129612266289at_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5620])). 185.47/93.69 thf(4382,axiom,((! [A:int,B:int,C:int]: ((((dvd_dvd_int @ (divide_divide_int @ B @ A) @ C) = (dvd_dvd_int @ B @ (times_times_int @ C @ A))) <= (dvd_dvd_int @ A @ B)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4834_div__dvd__iff__mult)). 185.47/93.69 thf(22037,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ (divide_divide_int @ B @ A) @ C) = (dvd_dvd_int @ B @ (times_times_int @ C @ A))) | ~ (dvd_dvd_int @ A @ B) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4382])). 185.47/93.69 thf(3822,axiom,(((neg_nu5219082963157363817nc_rat @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7003_dbl__inc__simps_I4_J)). 185.47/93.69 thf(20275,plain,(((neg_nu5219082963157363817nc_rat @ (uminus_uminus_rat @ one_one_rat)) = (uminus_uminus_rat @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3822])). 185.47/93.69 thf(900,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:(nat > complex),E:(nat > complex)]: (((ord_less_eq_set_nat @ B @ A) => ((ord_less_eq_set_nat @ C @ A) => (((((groups2073611262835488442omplex @ D @ B) = (groups2073611262835488442omplex @ E @ C)) <= ((groups2073611262835488442omplex @ D @ A) = (groups2073611262835488442omplex @ E @ A))) <= (! [F:nat]: ((member_nat @ F @ (minus_minus_set_nat @ A @ C)) => ((E @ F) = zero_zero_complex)))) <= (! [F:nat]: (((D @ F) = zero_zero_complex) <= (member_nat @ F @ (minus_minus_set_nat @ A @ B))))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6109_sum_Osame__carrierI)). 185.47/93.69 thf(10809,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:(nat > complex),E:(nat > complex)]: (((ord_less_eq_set_nat @ B @ A) => ((ord_less_eq_set_nat @ C @ A) => (((groups2073611262835488442omplex @ (D) @ B) = (groups2073611262835488442omplex @ (E) @ C)) | ~ ((groups2073611262835488442omplex @ (D) @ A) = (groups2073611262835488442omplex @ (E) @ A)) | ~ (! [F:nat]: ((member_nat @ F @ (minus_minus_set_nat @ A @ C)) => ((E @ F) = zero_zero_complex))) | ~ (! [F:nat]: (((D @ F) = zero_zero_complex) | ~ (member_nat @ F @ (minus_minus_set_nat @ A @ B))))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[900])). 185.47/93.69 thf(5989,axiom,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((power_power_real @ (root @ A @ B) @ A) = B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9196_real__root__pow__pos)). 185.47/93.69 thf(27857,plain,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((power_power_real @ (root @ A @ B) @ A) = B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5989])). 185.47/93.69 thf(1333,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ A @ B))) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2634_add__pos__nonneg)). 185.47/93.69 thf(12177,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ A @ B))) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333])). 185.47/93.69 thf(691,axiom,((! [A:complex,B:complex]: ((if_complex @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Complex__Ocomplex_T)). 185.47/93.69 thf(10036,plain,((! [A:complex,B:complex]: ((if_complex @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[691])). 185.47/93.69 thf(1846,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ A @ (bit_se2923211474154528505it_int @ B @ A)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9343_take__bit__int__greater__eq__self__iff)). 185.47/93.69 thf(13926,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ A @ (bit_se2923211474154528505it_int @ B @ A)) = (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1846])). 185.47/93.69 thf(7684,axiom,((vEBT_VEBT_high = (^ [A:nat,B:nat]: (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_high__def)). 185.47/93.69 thf(33797,plain,(((vEBT_VEBT_high) = (^ [A:nat,B:nat]: (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7684])). 185.47/93.69 thf(6682,axiom,(((minus_minus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ one_one_complex)) = (numera6690914467698888265omplex @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5417_diff__numeral__special_I11_J)). 185.47/93.69 thf(30273,plain,(((minus_minus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ one_one_complex)) = (numera6690914467698888265omplex @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6682])). 185.47/93.69 thf(6131,axiom,((! [A:num,B:nat,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ A) @ B) @ (times_times_nat @ (numeral_numeral_nat @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_distrib__left__numeral)). 185.47/93.69 thf(28316,plain,((! [A:num,B:nat,C:nat]: ((times_times_nat @ (numeral_numeral_nat @ A) @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ A) @ B) @ (times_times_nat @ (numeral_numeral_nat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6131])). 185.47/93.69 thf(2358,axiom,((! [A:real,B:real]: ((dvd_dvd_real @ A @ B) => (((divide_divide_real @ B @ A) = zero_zero_real) = (B = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4725_dvd__div__eq__0__iff)). 185.47/93.69 thf(15540,plain,((! [A:real,B:real]: ((dvd_dvd_real @ A @ B) => (((divide_divide_real @ B @ A) = zero_zero_real) = (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2358])). 185.47/93.69 thf(1960,axiom,((! [A:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A)) @ A)) @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7637_of__int__round__abs__le)). 185.47/93.69 thf(14288,plain,((! [A:rat]: (ord_less_eq_rat @ (abs_abs_rat @ (minus_minus_rat @ (ring_1_of_int_rat @ (archim7778729529865785530nd_rat @ A)) @ A)) @ (divide_divide_rat @ one_one_rat @ (numeral_numeral_rat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1960])). 185.47/93.69 thf(2490,axiom,((! [A:int,B:int]: (A = (plus_plus_int @ (times_times_int @ (divide_divide_int @ A @ B) @ B) @ (modulo_modulo_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2542_mod__div__decomp)). 185.47/93.69 thf(15989,plain,((! [A:int,B:int]: (A = (plus_plus_int @ (times_times_int @ (divide_divide_int @ A @ B) @ B) @ (modulo_modulo_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2490])). 185.47/93.69 thf(2943,axiom,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2738_add__frac__num)). 185.47/93.69 thf(17488,plain,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2943])). 185.47/93.69 thf(6305,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (minus_minus_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_848_nat__diff__add__eq2)). 185.47/93.69 thf(28941,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (minus_minus_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6305])). 185.47/93.69 thf(7557,axiom,(((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2889_zero__power2)). 185.47/93.69 thf(33454,plain,(((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7557])). 185.47/93.69 thf(4121,axiom,((! [A:int,B:nat]: ((ord_less_eq_nat @ (nat2 @ A) @ B) = (ord_less_eq_int @ A @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9293_nat__le__iff)). 185.47/93.69 thf(21204,plain,((! [A:int,B:nat]: ((ord_less_eq_nat @ (nat2 @ A) @ B) = (ord_less_eq_int @ A @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4121])). 185.47/93.69 thf(3563,axiom,((numeral_numeral_nat = (^ [A:num]: (suc @ (pred_numeral @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6820_numeral__eq__Suc)). 185.47/93.69 thf(19445,plain,(((numeral_numeral_nat) = (^ [A:num]: (suc @ (pred_numeral @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3563])). 185.47/93.69 thf(6475,axiom,((! [A:rat,B:nat]: (((ord_less_eq_rat @ (power_power_rat @ A @ (suc @ B)) @ A) <= (ord_less_eq_rat @ A @ one_one_rat)) <= (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2872_power__Suc__le__self)). 185.47/93.69 thf(29575,plain,((! [A:rat,B:nat]: ((ord_less_eq_rat @ (power_power_rat @ A @ (suc @ B)) @ A) | ~ (ord_less_eq_rat @ A @ one_one_rat) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6475])). 185.47/93.69 thf(767,axiom,(((plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit1 @ (bit0 @ one))) @ (arctan @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit1 @ (bit1 @ one)))))) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (arctan @ (divide_divide_real @ (numeral_numeral_real @ (bit1 @ one)) @ (numeral_numeral_real @ (bit1 @ (bit1 @ (bit1 @ (bit1 @ (bit0 @ (bit0 @ one))))))))))) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7769_machin__Euler)). 185.47/93.69 thf(10340,plain,(((plus_plus_real @ (times_times_real @ (numeral_numeral_real @ (bit1 @ (bit0 @ one))) @ (arctan @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit1 @ (bit1 @ one)))))) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (arctan @ (divide_divide_real @ (numeral_numeral_real @ (bit1 @ one)) @ (numeral_numeral_real @ (bit1 @ (bit1 @ (bit1 @ (bit1 @ (bit0 @ (bit0 @ one))))))))))) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[767])). 185.47/93.69 thf(2883,axiom,((! [A:real,B:real]: (((plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real) => (~ (! [C:real]: (((ord_less_real @ C @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => ((A = (cos_real @ C)) => (B != (sin_real @ C)))) <= (ord_less_eq_real @ zero_zero_real @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7890_sincos__total__2pi)). 185.47/93.69 thf(17295,plain,((! [A:real,B:real]: (((plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real) => (~ (! [C:real]: (((ord_less_real @ C @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => ((A = (cos_real @ C)) => (~ (B = (sin_real @ C))))) | ~ (ord_less_eq_real @ zero_zero_real @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2883])). 185.47/93.69 thf(6357,axiom,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8413_binomial__eq__0__iff)). 185.47/93.69 thf(29139,plain,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6357])). 185.47/93.69 thf(1129,axiom,((! [A:rat,B:rat,C:rat]: ((A != zero_zero_rat) => ((plus_plus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (plus_plus_rat @ C @ (times_times_rat @ B @ A)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2737_add__num__frac)). 185.47/93.69 thf(11557,plain,((! [A:rat,B:rat,C:rat]: ((~ (A = zero_zero_rat)) => ((plus_plus_rat @ B @ (divide_divide_rat @ C @ A)) = (divide_divide_rat @ (plus_plus_rat @ C @ (times_times_rat @ B @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129])). 185.47/93.69 thf(866,axiom,((! [A:(nat > real),B:set_nat]: (ord_less_eq_real @ zero_zero_real @ (groups6591440286371151544t_real @ (^ [C:nat]: (abs_abs_real @ (A @ C))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6415_sum__abs__ge__zero)). 185.47/93.69 thf(10691,plain,((! [A:(nat > real),B:set_nat]: (ord_less_eq_real @ zero_zero_real @ (groups6591440286371151544t_real @ (^ [C:nat]: (abs_abs_real @ (A @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[866])). 185.47/93.69 thf(2158,axiom,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2076_comm__monoid__add__class_Oadd__0)). 185.47/93.69 thf(14924,plain,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2158])). 185.47/93.69 thf(2310,axiom,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ A @ (suc @ B)) = (times_times_rat @ (comm_s4028243227959126397er_rat @ A @ B) @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8496_pochhammer__Suc)). 185.47/93.69 thf(15393,plain,((! [A:rat,B:nat]: ((comm_s4028243227959126397er_rat @ A @ (suc @ B)) = (times_times_rat @ (comm_s4028243227959126397er_rat @ A @ B) @ (plus_plus_rat @ A @ (semiri681578069525770553at_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2310])). 185.47/93.69 thf(3311,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = zero_zero_real) = ((B = zero_zero_real) | (A = zero_zero_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1584_divide__eq__0__iff)). 185.47/93.69 thf(18643,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = zero_zero_real) = ((B = zero_zero_real) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3311])). 185.47/93.69 thf(6891,axiom,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ A @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ A @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8491_pochhammer__rec)). 185.47/93.69 thf(31106,plain,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ A @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ A @ one_one_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6891])). 185.47/93.69 thf(1070,axiom,((! [A:nat,B:set_nat]: ((~ (finite_finite_nat @ B)) <= (! [C:nat]: ((? [D:nat]: ((member_nat @ D @ B) & (ord_less_nat @ C @ D))) <= (ord_less_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7919_unbounded__k__infinite)). 185.47/93.69 thf(11362,plain,((! [A:nat,B:set_nat]: (~ (finite_finite_nat @ B) | ~ (! [C:nat]: (? [D:nat]: ((member_nat @ D @ B) & (ord_less_nat @ C @ D)) | ~ (ord_less_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070])). 185.47/93.69 thf(1011,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (times_3573771949741848930nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) | (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4515_even__mult__iff)). 185.47/93.69 thf(11194,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (times_3573771949741848930nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) | (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011])). 185.47/93.69 thf(7569,axiom,((! [A:rat]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_rat @ (times_times_rat @ (times_times_rat @ A @ A) @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_power4__eq__xxxx)). 185.47/93.69 thf(33486,plain,((! [A:rat]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_rat @ (times_times_rat @ (times_times_rat @ A @ A) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7569])). 185.47/93.69 thf(5233,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9367_and__minus__numerals_I6_J)). 185.47/93.69 thf(24987,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5233])). 185.47/93.69 thf(7520,axiom,((~ (! [A:nat]: ((some_nat @ A) != (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ pr)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_944__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxy_O_ASome_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Apr_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 185.47/93.69 thf(33345,plain,((~ (! [A:nat]: ~ ((some_nat @ A) = (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ pr)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7520])). 185.47/93.69 thf(6454,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (times_times_int @ B @ C)) = (times_times_int @ B @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_mult_Oleft__commute)). 185.47/93.69 thf(29495,plain,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (times_times_int @ B @ C)) = (times_times_int @ B @ (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6454])). 185.47/93.69 thf(1303,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ B @ C) <= (ord_less_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_add__less__imp__less__left)). 185.47/93.69 thf(12076,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ B @ C) | ~ (ord_less_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303])). 185.47/93.69 thf(1462,axiom,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ A) @ (abs_abs_real @ (divide_divide_real @ (minus_minus_real @ (exp_real @ A) @ (inverse_inverse_real @ (exp_real @ A))) @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8979_real__le__abs__sinh)). 185.47/93.69 thf(12605,plain,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ A) @ (abs_abs_real @ (divide_divide_real @ (minus_minus_real @ (exp_real @ A) @ (inverse_inverse_real @ (exp_real @ A))) @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462])). 185.47/93.69 thf(5671,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4153_leD)). 185.47/93.69 thf(26607,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5671])). 185.47/93.69 thf(3268,axiom,((! [A:real,B:real,C:real]: ((A = (divide_divide_real @ B @ C)) = ((((times_times_real @ A @ C) = B) <= (C != zero_zero_real)) & ((C = zero_zero_real) => (A = zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2471_eq__divide__eq)). 185.47/93.69 thf(18506,plain,((! [A:real,B:real,C:real]: ((A = (divide_divide_real @ B @ C)) = ((((times_times_real @ A @ C) = B) | (C = zero_zero_real)) & ((C = zero_zero_real) => (A = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3268])). 185.47/93.69 thf(777,axiom,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((((groups2906978787729119204at_rat @ (^ [D:nat]: (divide_divide_rat @ (times_times_rat @ (B @ D) @ (power_power_rat @ zero_zero_rat @ D)) @ (C @ D))) @ A) = (divide_divide_rat @ (B @ zero_zero_nat) @ (C @ zero_zero_nat))) <= ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))) & (((groups2906978787729119204at_rat @ (^ [D:nat]: (divide_divide_rat @ (times_times_rat @ (B @ D) @ (power_power_rat @ zero_zero_rat @ D)) @ (C @ D))) @ A) = zero_zero_rat) <= (~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6445_sum__zero__power_H)). 185.47/93.69 thf(10379,plain,((! [A:set_nat,B:(nat > rat),C:(nat > rat)]: ((((groups2906978787729119204at_rat @ (^ [D:nat]: (divide_divide_rat @ (times_times_rat @ (B @ D) @ (power_power_rat @ zero_zero_rat @ D)) @ (C @ D))) @ A) = (divide_divide_rat @ (B @ zero_zero_nat) @ (C @ zero_zero_nat))) | ~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))) & (((groups2906978787729119204at_rat @ (^ [D:nat]: (divide_divide_rat @ (times_times_rat @ (B @ D) @ (power_power_rat @ zero_zero_rat @ D)) @ (C @ D))) @ A) = zero_zero_rat) | ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[777])). 185.47/93.69 thf(7369,axiom,((! [A:nat,B:list_VEBT_VEBT,C:nat]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ B)) => ((set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ (nth_VEBT_VEBT @ B @ C)) @ C @ (nth_VEBT_VEBT @ B @ A))) = (set_VEBT_VEBT2 @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3648_set__swap)). 185.47/93.69 thf(32825,plain,((! [A:nat,B:list_VEBT_VEBT,C:nat]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ B)) => ((set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ (nth_VEBT_VEBT @ B @ C)) @ C @ (nth_VEBT_VEBT @ B @ A))) = (set_VEBT_VEBT2 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7369])). 185.47/93.69 thf(6183,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_mult__le__mono1)). 185.47/93.69 thf(28538,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6183])). 185.47/93.69 thf(6032,axiom,((! [A:rat,B:rat]: ((times_times_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (times_times_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5077_minus__mult__minus)). 185.47/93.69 thf(27989,plain,((! [A:rat,B:rat]: ((times_times_rat @ (uminus_uminus_rat @ A) @ (uminus_uminus_rat @ B)) = (times_times_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6032])). 185.47/93.69 thf(7264,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2309_add__decreasing)). 185.47/93.69 thf(32478,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7264])). 185.47/93.69 thf(6172,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((((vEBT_vebt_member @ A @ D) => (ord_less_eq_nat @ C @ D)) <= ((vEBT_vebt_mint @ A) = (some_nat @ C))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_956_mint__corr__help)). 185.47/93.69 thf(28502,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((vEBT_vebt_member @ A @ D) => (ord_less_eq_nat @ C @ D)) | ~ ((vEBT_vebt_mint @ A) = (some_nat @ C)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6172])). 185.47/93.69 thf(682,axiom,((! [A:complex,B:complex]: (((im @ A) = (im @ B)) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) = (ord_less_eq_real @ (abs_abs_real @ (re @ A)) @ (abs_abs_real @ (re @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9678_cmod__Re__le__iff)). 185.47/93.69 thf(10009,plain,((! [A:complex,B:complex]: (((im @ A) = (im @ B)) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) = (ord_less_eq_real @ (abs_abs_real @ (re @ A)) @ (abs_abs_real @ (re @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[682])). 185.47/93.69 thf(3220,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ C @ B)) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1199_add__le__imp__le__diff)). 185.47/93.69 thf(18369,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (minus_minus_real @ C @ B)) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3220])). 185.47/93.69 thf(1455,axiom,((! [A:rat]: ((zero_zero_rat = (divide_divide_rat @ one_one_rat @ A)) = (A = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1722_zero__eq__1__divide__iff)). 185.47/93.69 thf(12583,plain,((! [A:rat]: ((zero_zero_rat = (divide_divide_rat @ one_one_rat @ A)) = (A = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455])). 185.47/93.69 thf(6549,axiom,((! [A:num]: ((ring_1_of_int_rat @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7298_of__int__neg__numeral)). 185.47/93.69 thf(29836,plain,((! [A:num]: ((ring_1_of_int_rat @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6549])). 185.47/93.69 thf(2211,axiom,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ D @ A) = (plus_plus_real @ (uminus_uminus_real @ B) @ (minus_minus_real @ D @ C))) <= (A = (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5782_group__cancel_Osub2)). 185.47/93.69 thf(15091,plain,((! [A:real,B:real,C:real,D:real]: (((minus_minus_real @ D @ A) = (plus_plus_real @ (uminus_uminus_real @ B) @ (minus_minus_real @ D @ C))) | ~ (A = (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2211])). 185.47/93.69 thf(2793,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (plus_plus_int @ C @ D)) = (dvd_dvd_int @ A @ (plus_plus_int @ (plus_plus_int @ C @ (times_times_int @ E @ B)) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4819_zdvd__period)). 185.47/93.69 thf(17003,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (plus_plus_int @ C @ D)) = (dvd_dvd_int @ A @ (plus_plus_int @ (plus_plus_int @ C @ (times_times_int @ E @ B)) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2793])). 185.47/93.69 thf(6456,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3272_minf_I4_J)). 185.47/93.69 thf(29501,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6456])). 185.47/93.69 thf(7629,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((divide_divide_nat @ (plus_plus_nat @ A @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4551_odd__succ__div__two)). 185.47/93.69 thf(33656,plain,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((divide_divide_nat @ (plus_plus_nat @ A @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7629])). 185.47/93.69 thf(1083,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = A) = (B = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1523_add__cancel__left__right)). 185.47/93.69 thf(11401,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = A) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083])). 185.47/93.69 thf(3803,axiom,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (times_times_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)) @ (comm_s7457072308508201937r_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8498_pochhammer__rec_H)). 185.47/93.69 thf(20222,plain,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (times_times_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)) @ (comm_s7457072308508201937r_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3803])). 185.47/93.69 thf(5574,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (divide_divide_nat @ C @ B) @ (divide_divide_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2791_div__le__mono2)). 185.47/93.69 thf(26285,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (divide_divide_nat @ C @ B) @ (divide_divide_nat @ C @ A)) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5574])). 185.47/93.69 thf(254,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se6526347334894502574or_int @ A @ B)) = ((ord_less_eq_int @ zero_zero_int @ A) = (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9488_xor__nonnegative__int__iff)). 185.47/93.69 thf(8557,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_se6526347334894502574or_int @ A @ B)) = ((ord_less_eq_int @ zero_zero_int @ A) = (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 185.47/93.69 thf(4112,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_real @ C @ (divide_divide_real @ B @ (numeral_numeral_real @ (bit0 @ one)))) => (((ord_less_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ B) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_eq_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8275_sqrt__sum__squares__half__less)). 185.47/93.69 thf(21177,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_real @ C @ (divide_divide_real @ B @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_real @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ B) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_eq_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4112])). 185.47/93.69 thf(1150,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ C @ D) => (ord_less_rat @ (minus_minus_rat @ A @ D) @ (minus_minus_rat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_701_diff__strict__mono)). 185.47/93.69 thf(11627,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ A @ B) => ((ord_less_rat @ C @ D) => (ord_less_rat @ (minus_minus_rat @ A @ D) @ (minus_minus_rat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150])). 185.47/93.69 thf(7713,axiom,((! [A:nat]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_power2__eq__square)). 185.47/93.69 thf(33878,plain,((! [A:nat]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7713])). 185.47/93.69 thf(2834,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (ord_less_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_add__less__cancel__right)). 185.47/93.69 thf(17135,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (ord_less_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2834])). 185.47/93.69 thf(7199,axiom,((! [A:nat,B:nat,C:nat]: ((((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_Nat_Ole__imp__diff__is__add)). 185.47/93.69 thf(32245,plain,((! [A:nat,B:nat,C:nat]: ((((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7199])). 185.47/93.69 thf(3581,axiom,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ B) = one_one_rat) = ((A = B) & (B != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1740_divide__eq__1__iff)). 185.47/93.69 thf(19500,plain,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ B) = one_one_rat) = ((A = B) & ~ (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3581])). 185.47/93.69 thf(1807,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((C != A) <= (ord_less_real @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3265_minf_I3_J)). 185.47/93.69 thf(13787,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (C = A) | ~ (ord_less_real @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1807])). 185.47/93.69 thf(2614,axiom,((! [A:real]: ((real_V1022390504157884413omplex @ (plus_plus_complex @ (real_V4546457046886955230omplex @ (cos_real @ A)) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sin_real @ A))))) = one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9149_cmod__unit__one)). 185.47/93.69 thf(16407,plain,((! [A:real]: ((real_V1022390504157884413omplex @ (plus_plus_complex @ (real_V4546457046886955230omplex @ (cos_real @ A)) @ (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sin_real @ A))))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2614])). 185.47/93.69 thf(1108,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) => (((ord_less_real @ (divide_divide_real @ A @ D) @ (divide_divide_real @ B @ C)) <= (ord_less_real @ C @ D)) <= (ord_less_real @ zero_zero_real @ C))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2649_frac__less2)). 185.47/93.69 thf(11494,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_real @ (divide_divide_real @ A @ D) @ (divide_divide_real @ B @ C)) | ~ (ord_less_real @ C @ D) | ~ (ord_less_real @ zero_zero_real @ C))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108])). 185.47/93.69 thf(2001,axiom,((! [A:nat,B:nat]: (((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ B)) @ A) != zero_zero_complex) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8514_pochhammer__of__nat__eq__0__lemma_H)). 185.47/93.69 thf(14422,plain,((! [A:nat,B:nat]: (~ ((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ B)) @ A) = zero_zero_complex) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2001])). 185.47/93.69 thf(2258,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_max_nat @ A @ B) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3563_max_Oabsorb2)). 185.47/93.69 thf(15236,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_max_nat @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2258])). 185.47/93.69 thf(3052,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((divide_divide_int @ (uminus_uminus_int @ B) @ A) = (uminus_uminus_int @ (divide_divide_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5813_dvd__neg__div)). 185.47/93.69 thf(17836,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((divide_divide_int @ (uminus_uminus_int @ B) @ A) = (uminus_uminus_int @ (divide_divide_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3052])). 185.47/93.69 thf(7006,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = (suc @ zero_zero_nat)) = ((A = (suc @ zero_zero_nat)) & (B = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1788_mult__eq__1__iff)). 185.47/93.69 thf(31572,plain,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = (suc @ zero_zero_nat)) = ((A = (suc @ zero_zero_nat)) & (B = (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7006])). 185.47/93.69 thf(6670,axiom,((! [A:num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_818_one__le__numeral)). 185.47/93.69 thf(30237,plain,((! [A:num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6670])). 185.47/93.69 thf(3765,axiom,((! [A:int,B:int]: ((~ ((A != zero_zero_int) => (! [C:int]: ((C != zero_zero_int) => ((dvd_dvd_int @ C @ one_one_int) => ((((divide_divide_int @ one_one_int @ C) = A) => (((divide_divide_int @ B @ A) != (times_times_int @ B @ C)) <= ((times_times_int @ A @ C) = one_one_int))) <= ((divide_divide_int @ one_one_int @ A) = C))))))) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4893_is__unitE)). 185.47/93.69 thf(20090,plain,((! [A:int,B:int]: (~ ((~ (A = zero_zero_int)) => (! [C:int]: ((~ (C = zero_zero_int)) => ((dvd_dvd_int @ C @ one_one_int) => ((((divide_divide_int @ one_one_int @ C) = A) => (~ ((divide_divide_int @ B @ A) = (times_times_int @ B @ C)) | ~ ((times_times_int @ A @ C) = one_one_int))) | ~ ((divide_divide_int @ one_one_int @ A) = C)))))) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3765])). 185.47/93.69 thf(5696,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1116_vebt__pred_Osimps_I4_J)). 185.47/93.69 thf(26685,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5696])). 185.47/93.69 thf(3810,axiom,((! [A:nat]: (ord_less_eq_real @ (semiri2265585572941072030t_real @ A) @ (semiri5074537144036343181t_real @ (power_power_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8025_fact__le__power)). 185.47/93.69 thf(20243,plain,((! [A:nat]: (ord_less_eq_real @ (semiri2265585572941072030t_real @ A) @ (semiri5074537144036343181t_real @ (power_power_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3810])). 185.47/93.69 thf(7450,axiom,((! [A:num,B:num]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (numeral_numeral_rat @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5350_mult__neg__numeral__simps_I1_J)). 185.47/93.69 thf(33096,plain,((! [A:num,B:num]: ((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))) = (numeral_numeral_rat @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7450])). 185.47/93.69 thf(2652,axiom,((! [A:real,B:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6034_real__add__less__0__iff)). 185.47/93.69 thf(16526,plain,((! [A:real,B:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2652])). 185.47/93.69 thf(7131,axiom,((! [A:option_nat,B:(option_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: ((((B @ A @ C) <= (C = none_P5556105721700978146at_nat)) => ((! [D:nat,E:product_prod_nat_nat]: ((A = (some_nat @ D)) => ((C = (some_P7363390416028606310at_nat @ E)) => (B @ A @ C)))) => (B @ A @ C))) <= ((B @ A @ C) <= (A = none_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1179_combine__options__cases)). 185.47/93.69 thf(31997,plain,((! [A:option_nat,B:(option_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: ((((B @ A @ C) | ~ (C = none_P5556105721700978146at_nat)) => ((! [D:nat,E:product_prod_nat_nat]: ((A = (some_nat @ D)) => ((C = (some_P7363390416028606310at_nat @ E)) => (B @ A @ C)))) => (B @ A @ C))) | ~ ((B @ A @ C) | ~ (A = none_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7131])). 185.47/93.69 thf(7176,axiom,((! [A:num,B:num]: ((A != B) = ((ord_less_num @ B @ A) | (ord_less_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4060_linorder__neq__iff)). 185.47/93.69 thf(32175,plain,((! [A:num,B:num]: ((~ (A = B)) = ((ord_less_num @ B @ A) | (ord_less_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7176])). 185.47/93.69 thf(7694,axiom,((! [A:int]: ((power_power_int @ (abs_abs_int @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6428_power2__abs)). 185.47/93.69 thf(33826,plain,((! [A:int]: ((power_power_int @ (abs_abs_int @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7694])). 185.47/93.69 thf(2383,axiom,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ C)) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7497_norm__add__leD)). 185.47/93.69 thf(15617,plain,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ C)) | ~ (ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2383])). 185.47/93.69 thf(645,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((A != one_one_real) => ((ord_less_real @ zero_zero_real @ B) => (((ord_less_real @ zero_zero_real @ C) => ((log @ A @ C) = (times_times_real @ (divide_divide_real @ (ln_ln_real @ B) @ (ln_ln_real @ A)) @ (log @ B @ C)))) <= (B != one_one_real))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9053_log__eq__div__ln__mult__log)). 185.47/93.69 thf(9874,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((~ (A = one_one_real)) => ((ord_less_real @ zero_zero_real @ B) => (((ord_less_real @ zero_zero_real @ C) => ((log @ A @ C) = (times_times_real @ (divide_divide_real @ (ln_ln_real @ B) @ (ln_ln_real @ A)) @ (log @ B @ C)))) | (B = one_one_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[645])). 185.47/93.69 thf(3761,axiom,((! [A:nat,B:(nat > real),C:real]: ((! [D:nat]: ((ord_less_nat @ D @ A) => ((B @ D) = zero_zero_real))) => ((sums_real @ (^ [D:nat]: (B @ (plus_plus_nat @ D @ A))) @ C) = (sums_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8192_sums__zero__iff__shift)). 185.47/93.69 thf(20073,plain,((! [A:nat,B:(nat > real),C:real]: ((! [D:nat]: ((ord_less_nat @ D @ A) => ((B @ D) = zero_zero_real))) => ((sums_real @ (^ [D:nat]: (B @ (plus_plus_nat @ D @ A))) @ C) = (sums_real @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3761])). 185.47/93.69 thf(97,axiom,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_nat @ (groups708209901874060359at_nat @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8698_prod_OlessThan__Suc)). 185.47/93.69 thf(8051,plain,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_nat @ (groups708209901874060359at_nat @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[97])). 185.47/93.69 thf(5791,axiom,((! [A:(num > (num > $o)),B:num,C:num]: ((! [D:num,E:num]: ((ord_less_eq_num @ D @ E) => (A @ D @ E))) => ((A @ B @ C) <= (! [D:num,E:num]: ((A @ D @ E) <= (A @ E @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3881_linorder__wlog)). 185.47/93.69 thf(26992,plain,((! [A:(num > (num > $o)),B:num,C:num]: ((! [D:num,E:num]: ((ord_less_eq_num @ D @ E) => (A @ D @ E))) => ((A @ B @ C) | ~ (! [D:num,E:num]: ((A @ D @ E) | ~ (A @ E @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5791])). 185.47/93.69 thf(5999,axiom,((! [A:nat,B:rat]: ((dvd_dvd_rat @ B @ (power_power_rat @ B @ A)) <= ((B = one_one_rat) | (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4917_dvd__power)). 185.47/93.69 thf(27889,plain,((! [A:nat,B:rat]: ((dvd_dvd_rat @ B @ (power_power_rat @ B @ A)) | ~ ((B = one_one_rat) | (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5999])). 185.47/93.69 thf(6266,axiom,((! [A:num,B:num]: ((minus_minus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (nat2 @ (minus_minus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9256_diff__nat__numeral)). 185.47/93.69 thf(28814,plain,((! [A:num,B:num]: ((minus_minus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (nat2 @ (minus_minus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6266])). 185.47/93.69 thf(4924,axiom,(((uminus_uminus_rat @ zero_zero_rat) = zero_zero_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5058_add_Oinverse__neutral)). 185.47/93.69 thf(23852,plain,(((uminus_uminus_rat @ zero_zero_rat) = zero_zero_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4924])). 185.47/93.69 thf(5483,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((~ (! [C:nat]: ((B != (suc @ C)) <= (ord_less_nat @ A @ C)))) <= (B != (suc @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1022_Nat_OlessE)). 185.47/93.69 thf(25992,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: (~ (B = (suc @ C)) | ~ (ord_less_nat @ A @ C))) | (B = (suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5483])). 185.47/93.69 thf(1429,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_add__strict__right__mono)). 185.47/93.69 thf(12503,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429])). 185.47/93.69 thf(1416,axiom,((! [A:num]: ((inc @ (bitM @ A)) = (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9384_inc__BitM__eq)). 185.47/93.69 thf(12459,plain,((! [A:num]: ((inc @ (bitM @ A)) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416])). 185.47/93.69 thf(805,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => (ord_less_eq_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5650_ln__add__one__self__le__self2)). 185.47/93.69 thf(10472,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => (ord_less_eq_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[805])). 185.47/93.69 thf(1356,axiom,((! [A:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (exp_real @ A)) @ (plus_plus_real @ one_one_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (real_V7735802525324610683m_real @ A)))) <= (ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8272_exp__bound__lemma)). 185.47/93.69 thf(12253,plain,((! [A:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (exp_real @ A)) @ (plus_plus_real @ one_one_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (real_V7735802525324610683m_real @ A)))) | ~ (ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356])). 185.47/93.69 thf(1487,axiom,((! [A:complex,B:complex,C:complex]: (((B = (divide1717551699836669952omplex @ C @ A)) = ((times_times_complex @ B @ A) = C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2458_nonzero__eq__divide__eq)). 185.47/93.69 thf(12679,plain,((! [A:complex,B:complex,C:complex]: (((B = (divide1717551699836669952omplex @ C @ A)) = ((times_times_complex @ B @ A) = C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487])). 185.47/93.69 thf(4456,axiom,((! [A:num]: (ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5901_neg__numeral__less__zero)). 185.47/93.69 thf(22267,plain,((! [A:num]: (ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4456])). 185.47/93.69 thf(3730,axiom,((! [A:real,B:real,C:real]: (((dvd_dvd_real @ A @ (plus_plus_real @ B @ C)) <= (dvd_dvd_real @ A @ C)) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4652_dvd__add)). 185.47/93.69 thf(19979,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ B @ C)) | ~ (dvd_dvd_real @ A @ C) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3730])). 185.47/93.69 thf(2970,axiom,((! [A:num,B:num,C:(num > real),D:real]: (((ord_less_real @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_less_real @ (C @ A) @ D))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4336_order__le__less__subst2)). 185.47/93.69 thf(17575,plain,((! [A:num,B:num,C:(num > real),D:real]: (((ord_less_real @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_less_real @ (C @ A) @ D))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2970])). 185.47/93.69 thf(1002,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2248_zero__le__square)). 185.47/93.69 thf(11162,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002])). 185.47/93.69 thf(247,axiom,((! [A:num]: ((archim6058952711729229775r_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A))) = (divide_divide_int @ one_one_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9082_floor__one__divide__eq__div__numeral)). 185.47/93.69 thf(8516,plain,((! [A:num]: ((archim6058952711729229775r_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A))) = (divide_divide_int @ one_one_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 185.47/93.69 thf(2684,axiom,((! [A:real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1511_double__zero__sym)). 185.47/93.69 thf(16671,plain,((! [A:real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2684])). 185.47/93.69 thf(5482,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((dvd_dvd_nat @ A @ C) => ((((times_times_nat @ C @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ A)) | ((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ C @ E) @ A))) => (? [F:nat,G:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) & (((times_times_nat @ B @ F) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ B @ C) @ G) @ A)) | ((times_times_nat @ (plus_plus_nat @ B @ C) @ F) = (plus_plus_nat @ (times_times_nat @ B @ G) @ A))) & (dvd_dvd_nat @ A @ B))))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4816_bezout__lemma__nat)). 185.47/93.69 thf(25981,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((dvd_dvd_nat @ A @ C) => ((((times_times_nat @ C @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ A)) | ((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ C @ E) @ A))) => (? [F:nat,G:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) & (((times_times_nat @ B @ F) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ B @ C) @ G) @ A)) | ((times_times_nat @ (plus_plus_nat @ B @ C) @ F) = (plus_plus_nat @ (times_times_nat @ B @ G) @ A))) & (dvd_dvd_nat @ A @ B))))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5482])). 185.47/93.69 thf(4496,axiom,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7242_zle__int)). 185.47/93.69 thf(22392,plain,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4496])). 185.47/93.69 thf(2869,axiom,((! [A:nat]: (ord_less_eq_real @ one_one_real @ (semiri2265585572941072030t_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7998_fact__ge__1)). 185.47/93.69 thf(17252,plain,((! [A:nat]: (ord_less_eq_real @ one_one_real @ (semiri2265585572941072030t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2869])). 185.47/93.69 thf(466,axiom,((! [A:(nat > real),B:nat,C:nat,D:nat]: ((groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ C) @ (plus_plus_nat @ D @ C))) = (groups6591440286371151544t_real @ (^ [E:nat]: (A @ (plus_plus_nat @ E @ C))) @ (set_or1269000886237332187st_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6537_sum_Oshift__bounds__cl__nat__ivl)). 185.47/93.69 thf(9299,plain,((! [A:(nat > real),B:nat,C:nat,D:nat]: ((groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ C) @ (plus_plus_nat @ D @ C))) = (groups6591440286371151544t_real @ (^ [E:nat]: (A @ (plus_plus_nat @ E @ C))) @ (set_or1269000886237332187st_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[466])). 185.47/93.69 thf(6921,axiom,((! [A:real,B:real,C:num]: ((A = (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ C)))) = (((A = zero_zero_real) <= ((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real)) & (((times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ C))) = B) <= ((uminus_uminus_real @ (numeral_numeral_real @ C)) != zero_zero_real)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5383_eq__divide__eq__numeral1_I2_J)). 185.47/93.69 thf(31199,plain,((! [A:real,B:real,C:num]: ((A = (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ C)))) = (((A = zero_zero_real) | ~ ((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real)) & (((times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ C))) = B) | ((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6921])). 185.47/93.69 thf(5598,axiom,((! [A:real]: ((sqrt @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8139_real__sqrt__abs)). 185.47/93.69 thf(26359,plain,((! [A:real]: ((sqrt @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5598])). 185.47/93.69 thf(1873,axiom,((! [A:nat,B:int]: ((bit_se7879613467334960850it_int @ (suc @ A) @ B) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se7879613467334960850it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3114_set__bit__Suc)). 185.47/93.69 thf(14001,plain,((! [A:nat,B:int]: ((bit_se7879613467334960850it_int @ (suc @ A) @ B) = (plus_plus_int @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se7879613467334960850it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1873])). 185.47/93.69 thf(6370,axiom,((! [A:nat,B:nat]: (((vEBT_vebt_pred @ summary @ A) = (some_nat @ B)) = (vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ summary) @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562__C4_Ohyps_C_I3_J)). 185.47/93.69 thf(29183,plain,((! [A:nat,B:nat]: (((vEBT_vebt_pred @ summary @ A) = (some_nat @ B)) = (vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ summary) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6370])). 185.47/93.69 thf(6019,axiom,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_num @ B @ C) => (ord_less_num @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4070_order__less__trans)). 185.47/93.69 thf(27951,plain,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_num @ B @ C) => (ord_less_num @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6019])). 185.47/93.69 thf(2952,axiom,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_diff__add__cancel)). 185.47/93.69 thf(17516,plain,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2952])). 185.47/93.69 thf(4181,axiom,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))) = (suminf_real @ (^ [A:nat]: (divide_divide_real @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ one_one_real) @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7644_pi__series)). 185.47/93.69 thf(21387,plain,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))) = (suminf_real @ (^ [A:nat]: (divide_divide_real @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ A) @ one_one_real) @ (semiri5074537144036343181t_real @ (plus_plus_nat @ (times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4181])). 185.47/93.69 thf(6590,axiom,(((semiri773545260158071498ct_rat @ zero_zero_nat) = one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7954_fact__0)). 185.47/93.69 thf(29976,plain,(((semiri773545260158071498ct_rat @ zero_zero_nat) = one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6590])). 185.47/93.69 thf(2343,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (uminus_uminus_rat @ (divide_divide_rat @ A @ B)) @ C) = (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ (uminus_uminus_rat @ A) @ (times_times_rat @ C @ B))) & ((((ord_less_rat @ zero_zero_rat @ C) <= (~ (ord_less_rat @ B @ zero_zero_rat))) & ((ord_less_rat @ (times_times_rat @ C @ B) @ (uminus_uminus_rat @ A)) <= (ord_less_rat @ B @ zero_zero_rat))) <= (~ (ord_less_rat @ zero_zero_rat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6147_minus__divide__less__eq)). 185.47/93.69 thf(15493,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (uminus_uminus_rat @ (divide_divide_rat @ A @ B)) @ C) = (((ord_less_rat @ zero_zero_rat @ B) => (ord_less_rat @ (uminus_uminus_rat @ A) @ (times_times_rat @ C @ B))) & ((((ord_less_rat @ zero_zero_rat @ C) | (ord_less_rat @ B @ zero_zero_rat)) & ((ord_less_rat @ (times_times_rat @ C @ B) @ (uminus_uminus_rat @ A)) | ~ (ord_less_rat @ B @ zero_zero_rat))) | (ord_less_rat @ zero_zero_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2343])). 185.47/93.69 thf(170,axiom,((! [A:real,B:real,C:real]: ((times_times_complex @ (real_V4546457046886955230omplex @ A) @ (complex2 @ B @ C)) = (complex2 @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9140_complex__of__real__mult__Complex)). 185.47/93.69 thf(8277,plain,((! [A:real,B:real,C:real]: ((times_times_complex @ (real_V4546457046886955230omplex @ A) @ (complex2 @ B @ C)) = (complex2 @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 185.47/93.69 thf(7155,axiom,((! [A:nat,B:nat,C:rat]: (((ord_less_eq_rat @ zero_zero_rat @ C) => ((ord_less_eq_rat @ (power_power_rat @ C @ B) @ (power_power_rat @ C @ A)) <= (ord_less_eq_rat @ C @ one_one_rat))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2884_power__decreasing)). 185.47/93.69 thf(32100,plain,((! [A:nat,B:nat,C:rat]: (((ord_less_eq_rat @ zero_zero_rat @ C) => ((ord_less_eq_rat @ (power_power_rat @ C @ B) @ (power_power_rat @ C @ A)) | ~ (ord_less_eq_rat @ C @ one_one_rat))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7155])). 185.47/93.69 thf(607,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((~ ((member_nat @ A @ C) <= (member_nat @ A @ B))) <= (member_nat @ A @ (minus_minus_set_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1315_DiffE)). 185.47/93.69 thf(9752,plain,((! [A:nat,B:set_nat,C:set_nat]: (~ ((member_nat @ A @ C) | ~ (member_nat @ A @ B)) | ~ (member_nat @ A @ (minus_minus_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[607])). 185.47/93.69 thf(971,axiom,((! [A:int,B:int]: ((divide_divide_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) = (semiri1314217659103216013at_int @ (divide_divide_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9321_div__abs__eq__div__nat)). 185.47/93.69 thf(11067,plain,((! [A:int,B:int]: ((divide_divide_int @ (abs_abs_int @ A) @ (abs_abs_int @ B)) = (semiri1314217659103216013at_int @ (divide_divide_nat @ (nat2 @ (abs_abs_int @ A)) @ (nat2 @ (abs_abs_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[971])). 185.47/93.69 thf(446,axiom,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ A @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups708209901874060359at_nat @ (^ [C:nat]: (times_times_nat @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) @ (set_ord_atMost_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8845_prod_Oin__pairs__0)). 185.47/93.69 thf(9215,plain,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (A) @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups708209901874060359at_nat @ (^ [C:nat]: (times_times_nat @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) @ (set_ord_atMost_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[446])). 185.47/93.69 thf(7077,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2330_mult__pos__pos)). 185.47/93.69 thf(31825,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7077])). 185.47/93.69 thf(5818,axiom,((! [A:num,B:(num > num),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_num @ A @ (B @ D)))) <= (ord_less_num @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4348_order__less__le__subst1)). 185.47/93.69 thf(27251,plain,((! [A:num,B:(num > num),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_num @ A @ (B @ D)))) | ~ (ord_less_num @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5818])). 185.47/93.69 thf(4973,axiom,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = ((B != A) & (ord_less_eq_num @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3843_nle__le)). 185.47/93.69 thf(24007,plain,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = (~ (B = A) & (ord_less_eq_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4973])). 185.47/93.69 thf(1339,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6360_abs__le__zero__iff)). 185.47/93.69 thf(12198,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339])). 185.47/93.69 thf(1503,axiom,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ (plus_plus_int @ A @ B)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5090_minus__add__cancel)). 185.47/93.69 thf(12729,plain,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ (plus_plus_int @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503])). 185.47/93.69 thf(6956,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => ((dvd_dvd_nat @ A @ C) => ((dvd_dvd_nat @ A @ B) <= (ord_less_eq_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4810_dvd__diffD)). 185.47/93.69 thf(31324,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => ((dvd_dvd_nat @ A @ C) => ((dvd_dvd_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6956])). 185.47/93.69 thf(5590,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2497_add__is__1)). 185.47/93.69 thf(26332,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5590])). 185.47/93.69 thf(6941,axiom,((! [A:num]: ((plus_plus_num @ (bit0 @ A) @ one) = (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6410_semiring__norm_I5_J)). 185.47/93.69 thf(31273,plain,((! [A:num]: ((plus_plus_num @ (bit0 @ A) @ one) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6941])). 185.47/93.69 thf(7297,axiom,(((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_one__add__one)). 185.47/93.69 thf(32592,plain,(((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7297])). 185.47/93.69 thf(6115,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1133_comm__semiring__class_Odistrib)). 185.47/93.69 thf(28265,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6115])). 185.47/93.69 thf(1164,axiom,((! [A:nat]: (ord_less_real @ zero_zero_real @ (semiri2265585572941072030t_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7994_fact__gt__zero)). 185.47/93.69 thf(11668,plain,((! [A:nat]: (ord_less_real @ zero_zero_real @ (semiri2265585572941072030t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164])). 185.47/93.69 thf(6925,axiom,((! [A:real]: ((sqrt @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (sqrt @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8143_real__sqrt__minus)). 185.47/93.69 thf(31216,plain,((! [A:real]: ((sqrt @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6925])). 185.47/93.69 thf(2711,axiom,((! [A:int,B:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_diff__add__cancel)). 185.47/93.69 thf(16756,plain,((! [A:int,B:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2711])). 185.47/93.69 thf(65,axiom,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_rat @ (groups73079841787564623at_rat @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8697_prod_OlessThan__Suc)). 185.47/93.69 thf(7943,plain,((! [A:(nat > rat),B:nat]: ((groups73079841787564623at_rat @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_rat @ (groups73079841787564623at_rat @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 185.47/93.69 thf(3519,axiom,((bit_se1409905431419307370or_int = (^ [A:int,B:int]: (if_int @ ((A = (uminus_uminus_int @ one_one_int)) | (B = (uminus_uminus_int @ one_one_int))) @ (uminus_uminus_int @ one_one_int) @ (if_int @ (A = zero_zero_int) @ B @ (if_int @ (B = zero_zero_int) @ A @ (plus_plus_int @ (ord_max_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9407_or__int__unfold)). 185.47/93.69 thf(19313,plain,(((bit_se1409905431419307370or_int) = (^ [A:int,B:int]: (if_int @ ((A = (uminus_uminus_int @ one_one_int)) | (B = (uminus_uminus_int @ one_one_int))) @ (uminus_uminus_int @ one_one_int) @ (if_int @ (A = zero_zero_int) @ B @ (if_int @ (B = zero_zero_int) @ A @ (plus_plus_int @ (ord_max_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3519])). 185.47/93.69 thf(6291,axiom,((! [A:nat,B:real]: (((power_power_real @ (root @ A @ B) @ A) = B) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9199_odd__real__root__pow)). 185.47/93.69 thf(28898,plain,((! [A:nat,B:real]: (((power_power_real @ (root @ A @ B) @ A) = B) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6291])). 185.47/93.69 thf(622,axiom,((! [A:int,B:nat,C:int]: ((ord_less_eq_int @ (power_power_int @ (ring_1_of_int_int @ A) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_eq_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7097_of__int__le__of__int__power__cancel__iff)). 185.47/93.69 thf(9795,plain,((! [A:int,B:nat,C:int]: ((ord_less_eq_int @ (power_power_int @ (ring_1_of_int_int @ A) @ B) @ (ring_1_of_int_int @ C)) = (ord_less_eq_int @ (power_power_int @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[622])). 185.47/93.69 thf(2416,axiom,((! [A:(nat > nat),B:set_nat,C:nat]: ((times_times_nat @ (groups3542108847815614940at_nat @ A @ B) @ C) = (groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ (A @ D) @ C)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5613_sum__distrib__right)). 185.47/93.69 thf(15726,plain,((! [A:(nat > nat),B:set_nat,C:nat]: ((times_times_nat @ (groups3542108847815614940at_nat @ (A) @ B) @ C) = (groups3542108847815614940at_nat @ (^ [D:nat]: (times_times_nat @ (A @ D) @ C)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2416])). 185.47/93.69 thf(4418,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (bit_se2002935070580805687sk_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9213_mask__nat__positive__iff)). 185.47/93.69 thf(22143,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (bit_se2002935070580805687sk_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4418])). 185.47/93.69 thf(4606,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (~ (ord_less_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4154_leD)). 185.47/93.69 thf(22751,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => (~ (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4606])). 185.47/93.69 thf(4729,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((ord_less_int @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4198_order_Oorder__iff__strict)). 185.47/93.69 thf(23165,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((ord_less_int @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4729])). 185.47/93.69 thf(6197,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1034_Suc__less__SucD)). 185.47/93.69 thf(28598,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6197])). 185.47/93.69 thf(2754,axiom,((ord_less_rat @ zero_zero_rat @ one_one_rat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2385_zero__less__one)). 185.47/93.69 thf(16888,plain,((ord_less_rat @ zero_zero_rat @ one_one_rat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2754])). 185.47/93.69 thf(3649,axiom,((! [A:nat]: ((ord_less_eq_real @ (divide_divide_real @ (power_power_real @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))) @ A) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A))) @ (semiri5074537144036343181t_real @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8614_central__binomial__lower__bound)). 185.47/93.69 thf(19720,plain,((! [A:nat]: ((ord_less_eq_real @ (divide_divide_real @ (power_power_real @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))) @ A) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A))) @ (semiri5074537144036343181t_real @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3649])). 185.47/93.69 thf(3119,axiom,((! [A:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ A) @ zero_zero_rat) = (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1615_double__add__le__zero__iff__single__add__le__zero)). 185.47/93.69 thf(18053,plain,((! [A:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ A) @ zero_zero_rat) = (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3119])). 185.47/93.69 thf(3255,axiom,((! [A:nat,B:nat]: ((divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) = (plus_plus_real @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B)) @ (divide_divide_real @ (semiri5074537144036343181t_real @ (modulo_modulo_nat @ A @ B)) @ (semiri5074537144036343181t_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7318_real__of__nat__div__aux)). 185.47/93.69 thf(18467,plain,((! [A:nat,B:nat]: ((divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) = (plus_plus_real @ (semiri5074537144036343181t_real @ (divide_divide_nat @ A @ B)) @ (divide_divide_real @ (semiri5074537144036343181t_real @ (modulo_modulo_nat @ A @ B)) @ (semiri5074537144036343181t_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3255])). 185.47/93.69 thf(7691,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ A @ B) @ (binomial @ A @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8527_binomial__maximum)). 185.47/93.69 thf(33816,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ A @ B) @ (binomial @ A @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7691])). 185.47/93.69 thf(167,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6935_of__int__le__iff)). 185.47/93.69 thf(8268,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B)) = (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 185.47/93.69 thf(4019,axiom,((! [A:num,B:num]: ((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit0 @ B)) = (produc2626176000494625587at_nat @ (^ [C:nat,D:nat]: (product_Pair_nat_nat @ C @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) @ (unique5055182867167087721od_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7158_divmod__algorithm__code_I5_J)). 185.47/93.69 thf(20895,plain,((! [A:num,B:num]: ((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit0 @ B)) = (produc2626176000494625587at_nat @ (^ [C:nat,D:nat]: (product_Pair_nat_nat @ C @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) @ (unique5055182867167087721od_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4019])). 185.47/93.69 thf(5587,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_nat @ B @ C) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ B)) @ A @ E @ F) @ C) = (some_nat @ B))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_pred__max)). 185.47/93.69 thf(26322,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_nat @ B @ C) => ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ B)) @ A @ E @ F) @ C) = (some_nat @ B))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5587])). 185.47/93.69 thf(4531,axiom,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3107_verit__sum__simplify)). 185.47/93.69 thf(22516,plain,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4531])). 185.47/93.69 thf(2250,axiom,((! [A:num,B:real,C:real]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (divide_divide_real @ B @ C)) = (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) @ B)) & ((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ B @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C))) & ((~ (ord_less_real @ C @ zero_zero_real)) => (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6220_less__divide__eq__numeral_I2_J)). 185.47/93.69 thf(15213,plain,((! [A:num,B:real,C:real]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (divide_divide_real @ B @ C)) = (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) @ B)) & ((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ B @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C))) & ((~ (ord_less_real @ C @ zero_zero_real)) => (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2250])). 185.47/93.69 thf(5617,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_989_nat_Oinject)). 185.47/93.69 thf(26426,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5617])). 185.47/93.69 thf(2481,axiom,((! [A:int,B:int]: (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2983_sum__power2__ge__zero)). 185.47/93.69 thf(15949,plain,((! [A:int,B:int]: (ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2481])). 185.47/93.69 thf(1316,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ B) => (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6456_abs__le__D1)). 185.47/93.69 thf(12121,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ B) => (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316])). 185.47/93.69 thf(4598,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4188_not__le__imp__less)). 185.47/93.69 thf(22729,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4598])). 185.47/93.69 thf(6554,axiom,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2149_lambda__zero)). 185.47/93.69 thf(29851,plain,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6554])). 185.47/93.69 thf(6075,axiom,((! [A:(nat > real),B:real]: ((sums_real @ (^ [C:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ zero_zero_real @ (A @ (divide_divide_nat @ (minus_minus_nat @ C @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ B) <= (sums_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8251_sums__if_H)). 185.47/93.69 thf(28122,plain,((! [A:(nat > real),B:real]: ((sums_real @ (^ [C:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ zero_zero_real @ (A @ (divide_divide_nat @ (minus_minus_nat @ C @ one_one_nat) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ B) | ~ (sums_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6075])). 185.47/93.69 thf(24,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ A) => ((! [C:nat]: (ord_less_real @ zero_zero_real @ (plus_plus_real @ (A @ (plus_plus_nat @ B @ (times_times_nat @ (suc @ (suc @ zero_zero_nat)) @ C))) @ (A @ (plus_plus_nat @ B @ (plus_plus_nat @ (times_times_nat @ (suc @ (suc @ zero_zero_nat)) @ C) @ one_one_nat)))))) => (ord_less_real @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B)) @ (suminf_real @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7768_sum__pos__lt__pair)). 185.47/93.69 thf(7808,plain,((! [A:(nat > real),B:nat]: ((summable_real @ (A)) => ((! [C:nat]: (ord_less_real @ zero_zero_real @ (plus_plus_real @ (A @ (plus_plus_nat @ B @ (times_times_nat @ (suc @ (suc @ zero_zero_nat)) @ C))) @ (A @ (plus_plus_nat @ B @ (plus_plus_nat @ (times_times_nat @ (suc @ (suc @ zero_zero_nat)) @ C) @ one_one_nat)))))) => (ord_less_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B)) @ (suminf_real @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 185.47/93.69 thf(3737,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1857_divide__le__eq__1__pos)). 185.47/93.69 thf(20002,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3737])). 185.47/93.69 thf(6750,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (uminus1351360451143612070nteger @ A)) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6178_even__minus)). 185.47/93.69 thf(30559,plain,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (uminus1351360451143612070nteger @ A)) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6750])). 185.47/93.69 thf(7497,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) <= (ord_less_eq_nat @ B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2207_mult__nonneg__nonpos2)). 185.47/93.69 thf(33276,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) | ~ (ord_less_eq_nat @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7497])). 185.47/93.69 thf(3320,axiom,((! [A:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5729_ab__group__add__class_Oab__left__minus)). 185.47/93.69 thf(18670,plain,((! [A:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3320])). 185.47/93.69 thf(6742,axiom,((! [A:nat,B:nat,C:nat]: ((((power_power_nat @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B))) <= (ord_less_eq_nat @ B @ C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2907_power__diff)). 185.47/93.69 thf(30490,plain,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B))) | ~ (ord_less_eq_nat @ B @ C) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6742])). 185.47/93.69 thf(4429,axiom,((minus_minus_real = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5787_diff__conv__add__uminus)). 185.47/93.69 thf(22179,plain,(((minus_minus_real) = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4429])). 185.47/93.69 thf(982,axiom,((! [A:nat,B:nat,C:nat]: (((semiri681578069525770553at_rat @ A) = (power_power_rat @ (semiri681578069525770553at_rat @ B) @ C)) = (A = (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6951_of__nat__power__eq__of__nat__cancel__iff)). 185.47/93.69 thf(11099,plain,((! [A:nat,B:nat,C:nat]: (((semiri681578069525770553at_rat @ A) = (power_power_rat @ (semiri681578069525770553at_rat @ B) @ C)) = (A = (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[982])). 185.47/93.69 thf(3456,axiom,((! [A:num,B:int,C:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ A) @ B) @ (times_times_int @ (numeral_numeral_int @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_distrib__left__numeral)). 185.47/93.69 thf(19096,plain,((! [A:num,B:int,C:int]: ((times_times_int @ (numeral_numeral_int @ A) @ (plus_plus_int @ B @ C)) = (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ A) @ B) @ (times_times_int @ (numeral_numeral_int @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3456])). 185.47/93.69 thf(3386,axiom,((! [A:real]: (((? [B:nat]: ((A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) <= ((cos_real @ A) = zero_zero_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7943_cos__zero__lemma)). 185.47/93.69 thf(18882,plain,((! [A:real]: (? [B:nat]: ((A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ ((cos_real @ A) = zero_zero_real) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3386])). 185.47/93.69 thf(3495,axiom,((divide_divide_nat = (^ [A:nat,B:nat]: (nat2 @ (divide_divide_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9303_nat__div__as__int)). 185.47/93.69 thf(19237,plain,(((divide_divide_nat) = (^ [A:nat,B:nat]: (nat2 @ (divide_divide_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3495])). 185.47/93.69 thf(5372,axiom,((! [A:rat,B:rat]: ((times_times_rat @ (uminus_uminus_rat @ A) @ B) = (times_times_rat @ A @ (uminus_uminus_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5548_minus__mult__commute)). 185.47/93.69 thf(25511,plain,((! [A:rat,B:rat]: ((times_times_rat @ (uminus_uminus_rat @ A) @ B) = (times_times_rat @ A @ (uminus_uminus_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5372])). 185.47/93.69 thf(4027,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) => ((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2610_mult__right__le__imp__le)). 185.47/93.69 thf(20923,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) => ((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4027])). 185.47/93.69 thf(4446,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4734_unit__mult__left__cancel)). 185.47/93.69 thf(22235,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4446])). 185.47/93.69 thf(1772,axiom,((! [A:real]: ((sums_real @ (power_power_real @ A) @ (divide_divide_real @ one_one_real @ (minus_minus_real @ one_one_real @ A))) <= (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8236_geometric__sums)). 185.47/93.69 thf(13665,plain,((! [A:real]: ((sums_real @ (power_power_real @ A) @ (divide_divide_real @ one_one_real @ (minus_minus_real @ one_one_real @ A))) | ~ (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772])). 185.47/93.69 thf(1285,axiom,((! [A:rat,B:rat,C:rat]: ((B = C) <= ((plus_plus_rat @ A @ B) = (plus_plus_rat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_add__left__imp__eq)). 185.47/93.69 thf(12022,plain,((! [A:rat,B:rat,C:rat]: ((B = C) | ~ ((plus_plus_rat @ A @ B) = (plus_plus_rat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285])). 185.47/93.69 thf(5650,axiom,((! [A:num]: ((sqr @ (bit1 @ A)) = (bit1 @ (bit0 @ (plus_plus_num @ (sqr @ A) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9851_sqr_Osimps_I3_J)). 185.47/93.69 thf(26533,plain,((! [A:num]: ((sqr @ (bit1 @ A)) = (bit1 @ (bit0 @ (plus_plus_num @ (sqr @ A) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5650])). 185.47/93.69 thf(4703,axiom,((! [A:int,B:int]: ((((ord_less_eq_int @ B @ one_one_int) => (ord_less_eq_int @ (times_times_int @ B @ A) @ A)) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2674_mult__left__le__one__le)). 185.47/93.69 thf(23080,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ one_one_int) => (ord_less_eq_int @ (times_times_int @ B @ A) @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4703])). 185.47/93.69 thf(6713,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((A @ C) <= (! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1046_full__nat__induct)). 185.47/93.69 thf(30368,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((A @ C) | ~ (! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6713])). 185.47/93.69 thf(464,axiom,((! [A:complex,B:complex]: ((re @ (plus_plus_complex @ A @ B)) = (plus_plus_real @ (re @ A) @ (re @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9643_plus__complex_Osimps_I1_J)). 185.47/93.69 thf(9293,plain,((! [A:complex,B:complex]: ((re @ (plus_plus_complex @ A @ B)) = (plus_plus_real @ (re @ A) @ (re @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[464])). 185.47/93.69 thf(1113,axiom,((! [A:real,B:real]: ((sin_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (sin_real @ A) @ (cos_real @ B)) @ (times_times_real @ (cos_real @ A) @ (sin_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7817_sin__add)). 185.47/93.69 thf(11509,plain,((! [A:real,B:real]: ((sin_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (sin_real @ A) @ (cos_real @ B)) @ (times_times_real @ (cos_real @ A) @ (sin_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113])). 185.47/93.69 thf(7236,axiom,((! [A:real]: ((sqrt @ (times_times_real @ A @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8131_real__sqrt__abs2)). 185.47/93.69 thf(32389,plain,((! [A:real]: ((sqrt @ (times_times_real @ A @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7236])). 185.47/93.69 thf(7601,axiom,((vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ summary) @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ pr)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35__092_060open_062is__pred__in__set_A_Iset__vebt_H_Asummary_J_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_Apr_092_060close_062)). 185.47/93.69 thf(33577,plain,((vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ summary) @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ pr)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7601])). 185.47/93.69 thf(326,axiom,((! [A:set_nat,B:(nat > complex)]: (((~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))) => ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (B @ C) @ (power_power_complex @ zero_zero_complex @ C))) @ A) = zero_zero_complex)) & (((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (B @ C) @ (power_power_complex @ zero_zero_complex @ C))) @ A) = (B @ zero_zero_nat)) <= ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6434_sum__zero__power)). 185.47/93.69 thf(8822,plain,((! [A:set_nat,B:(nat > complex)]: (((~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))) => ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (B @ C) @ (power_power_complex @ zero_zero_complex @ C))) @ A) = zero_zero_complex)) & (((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (B @ C) @ (power_power_complex @ zero_zero_complex @ C))) @ A) = (B @ zero_zero_nat)) | ~ ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 185.47/93.69 thf(298,axiom,((! [A:real,B:(nat > nat),C:set_nat]: ((power_power_real @ A @ (groups3542108847815614940at_nat @ B @ C)) = (groups129246275422532515t_real @ (^ [D:nat]: (power_power_real @ A @ (B @ D))) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8786_power__sum)). 185.47/93.69 thf(8706,plain,((! [A:real,B:(nat > nat),C:set_nat]: ((power_power_real @ A @ (groups3542108847815614940at_nat @ (B) @ C)) = (groups129246275422532515t_real @ (^ [D:nat]: (power_power_real @ A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 185.47/93.69 thf(2909,axiom,((! [A:complex]: ((times_times_complex @ imaginary_unit @ (times_times_complex @ imaginary_unit @ A)) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8986_complex__i__mult__minus)). 185.47/93.69 thf(17384,plain,((! [A:complex]: ((times_times_complex @ imaginary_unit @ (times_times_complex @ imaginary_unit @ A)) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2909])). 185.47/93.69 thf(7421,axiom,((! [A:num]: ((numeral_numeral_int @ A) != (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5773_numeral__neq__neg__one)). 185.47/93.69 thf(33012,plain,((! [A:num]: ~ ((numeral_numeral_int @ A) = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7421])). 185.47/93.69 thf(5977,axiom,((one_one_real != (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5550_one__neq__neg__one)). 185.47/93.69 thf(27820,plain,((~ (one_one_real = (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5977])). 185.47/93.69 thf(3473,axiom,((! [A:$o,B:$o]: ((ord_less_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B)) = ((B) & ~ (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5116_of__bool__less__iff)). 185.47/93.69 thf(19161,plain,((! [A:$o,B:$o]: ((ord_less_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B)) = ((B) & ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3473])). 185.47/93.69 thf(7596,axiom,(((power_power_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_902_one__power2)). 185.47/93.69 thf(33565,plain,(((power_power_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7596])). 185.47/93.69 thf(505,axiom,((! [A:rat,B:rat]: ((if_rat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Rat__Orat_T)). 185.47/93.69 thf(9431,plain,((! [A:rat,B:rat]: ((if_rat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])). 185.47/93.69 thf(2006,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (plus_plus_int @ (divide_divide_int @ A @ C) @ (if_int @ ((modulo_modulo_int @ B @ C) = zero_zero_int) @ one_one_int @ zero_zero_int)) @ (divide_divide_int @ B @ C)) <= (ord_less_int @ zero_zero_int @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3063_verit__le__mono__div__int)). 185.47/93.69 thf(14439,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (plus_plus_int @ (divide_divide_int @ A @ C) @ (if_int @ ((modulo_modulo_int @ B @ C) = zero_zero_int) @ one_one_int @ zero_zero_int)) @ (divide_divide_int @ B @ C)) | ~ (ord_less_int @ zero_zero_int @ C) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2006])). 185.47/93.69 thf(406,axiom,((! [A:real]: ((((ln_ln_real @ A) = zero_zero_real) = (A = one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5237_ln__eq__zero__iff)). 185.47/93.69 thf(9083,plain,((! [A:real]: ((((ln_ln_real @ A) = zero_zero_real) = (A = one_one_real)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])). 185.47/93.69 thf(3535,axiom,((! [A:int,B:int]: ((A = B) | ~ (ord_less_eq_int @ A @ B) | ~ (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3085_verit__la__disequality)). 185.47/93.69 thf(19360,plain,((! [A:int,B:int]: ((A = B) | ~ (ord_less_eq_int @ A @ B) | ~ (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3535])). 185.47/93.69 thf(810,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:(nat > complex),E:(nat > complex)]: ((finite_finite_nat @ A) => (((ord_less_eq_set_nat @ C @ A) => ((! [F:nat]: ((member_nat @ F @ (minus_minus_set_nat @ A @ B)) => ((D @ F) = zero_zero_complex))) => ((((groups2073611262835488442omplex @ D @ B) = (groups2073611262835488442omplex @ E @ C)) = ((groups2073611262835488442omplex @ D @ A) = (groups2073611262835488442omplex @ E @ A))) <= (! [F:nat]: ((member_nat @ F @ (minus_minus_set_nat @ A @ C)) => ((E @ F) = zero_zero_complex)))))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6119_sum_Osame__carrier)). 185.47/93.69 thf(10485,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:(nat > complex),E:(nat > complex)]: ((finite_finite_nat @ A) => (((ord_less_eq_set_nat @ C @ A) => ((! [F:nat]: ((member_nat @ F @ (minus_minus_set_nat @ A @ B)) => ((D @ F) = zero_zero_complex))) => ((((groups2073611262835488442omplex @ (D) @ B) = (groups2073611262835488442omplex @ (E) @ C)) = ((groups2073611262835488442omplex @ (D) @ A) = (groups2073611262835488442omplex @ (E) @ A))) | ~ (! [F:nat]: ((member_nat @ F @ (minus_minus_set_nat @ A @ C)) => ((E @ F) = zero_zero_complex)))))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[810])). 185.47/93.69 thf(4946,axiom,((! [A:nat,B:nat]: (((nat_set_decode @ (plus_plus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)) = (insert_nat @ A @ (nat_set_decode @ B))) <= (~ (member_nat @ A @ (nat_set_decode @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9438_set__decode__plus__power__2)). 185.47/93.69 thf(23927,plain,((! [A:nat,B:nat]: (((nat_set_decode @ (plus_plus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)) = (insert_nat @ A @ (nat_set_decode @ B))) | (member_nat @ A @ (nat_set_decode @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4946])). 185.47/93.69 thf(2184,axiom,((! [A:rat]: (ord_less_eq_rat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3087_verit__comp__simplify1_I2_J)). 185.47/93.69 thf(15012,plain,((! [A:rat]: (ord_less_eq_rat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2184])). 185.47/93.69 thf(2138,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => ((plus_plus_int @ B @ (minus_minus_int @ A @ B)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1214_linordered__semidom__class_Oadd__diff__inverse)). 185.47/93.69 thf(14846,plain,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => ((plus_plus_int @ B @ (minus_minus_int @ A @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2138])). 185.47/93.69 thf(7614,axiom,(((some_nat @ maxy) = (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_940__092_060open_062Some_Amaxy_A_061_Avebt__maxt_A_ItreeList_A_B_Athe_A_Ivebt__pred_Asummary_A_Ihigh_Ax_A_Ideg_Adiv_A2_J_J_J_J_092_060close_062)). 185.47/93.69 thf(33611,plain,(((some_nat @ maxy) = (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7614])). 185.47/93.69 thf(3697,axiom,((! [A:int]: ~ (ord_less_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4016_dual__order_Oirrefl)). 185.47/93.69 thf(19865,plain,((! [A:int]: ~ (ord_less_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3697])). 185.47/93.69 thf(6207,axiom,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4943_power__mono__odd)). 185.47/93.69 thf(28623,plain,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6207])). 185.47/93.69 thf(1446,axiom,((! [A:int,B:int]: (((A != B) => (ord_less_int @ A @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4302_order__le__neq__trans)). 185.47/93.69 thf(12555,plain,((! [A:int,B:int]: (((~ (A = B)) => (ord_less_int @ A @ B)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446])). 185.47/93.69 thf(5797,axiom,((! [A:vEBT_VEBT,B:nat,C:option_nat]: (((vEBT_vebt_pred @ A @ B) = C) => ((((C != none_nat) <= (B = zero_zero_nat)) <= (? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E)))) => (((! [D:$o,E:$o]: (((? [F:nat]: (B = (suc @ (suc @ F)))) => (~ (((C = (some_nat @ one_one_nat)) <= (E)) & ((~ (E)) => (((~ (D)) => (C = none_nat)) & ((C = (some_nat @ zero_zero_nat)) <= (D))))))) <= (A = (vEBT_Leaf @ D @ E)))) => (((((? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F))) => (C != none_nat)) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)) => (~ (((~ (ord_less_nat @ E @ B)) => (C = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) @ (if_option_nat @ ((vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_nat)) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ D @ B) @ (some_nat @ D) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat))) & ((C = (some_nat @ E)) <= (ord_less_nat @ E @ B)))))))) <= ((? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F))) => (C != none_nat))) <= ((? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))) => (C != none_nat)))) <= (! [D:$o]: (((B = (suc @ zero_zero_nat)) => (~ (((~ (D)) => (C = none_nat)) & ((D) => (C = (some_nat @ zero_zero_nat)))))) <= (? [E:$o]: (A = (vEBT_Leaf @ D @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1459_vebt__pred_Oelims)). 185.47/93.69 thf(27029,plain,((! [A:vEBT_VEBT,B:nat,C:option_nat]: (((vEBT_vebt_pred @ A @ B) = C) => ((~ (C = none_nat) | ~ (B = zero_zero_nat) | ~ (? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E)))) => (((! [D:$o,E:$o]: (((? [F:nat]: (B = (suc @ (suc @ F)))) => (~ (((C = (some_nat @ one_one_nat)) | ~ (E)) & ((~ (E)) => (((~ (D)) => (C = none_nat)) & ((C = (some_nat @ zero_zero_nat)) | ~ (D))))))) | ~ (A = (vEBT_Leaf @ D @ E)))) => ((((? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F))) => (~ (C = none_nat))) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)) => (~ (((~ (ord_less_nat @ E @ B)) => (C = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) @ (if_option_nat @ ((vEBT_VEBT_greater @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ~ ((vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat)) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_pred @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ (if_option_nat @ (ord_less_nat @ D @ B) @ (some_nat @ D) @ none_nat) @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_pred @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat))) & ((C = (some_nat @ E)) | ~ (ord_less_nat @ E @ B)))))))) | ~ ((? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F))) => (~ (C = none_nat))) | ~ ((? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))) => (~ (C = none_nat))))) | ~ (! [D:$o]: (((B = (suc @ zero_zero_nat)) => (~ (((~ (D)) => (C = none_nat)) & ((D) => (C = (some_nat @ zero_zero_nat)))))) | ~ (? [E:$o]: (A = (vEBT_Leaf @ D @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5797])). 185.47/93.69 thf(5110,axiom,((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ deg)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_thisvalid)). 185.47/93.69 thf(24552,plain,((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ deg)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5110])). 185.47/93.69 thf(1686,axiom,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ C @ B) => (ord_less_rat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3276_minf_I5_J)). 185.47/93.69 thf(13377,plain,((! [A:rat]: ? [B:rat]: ! [C:rat]: ((ord_less_rat @ C @ B) => (ord_less_rat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686])). 185.47/93.69 thf(6169,axiom,((! [A:int]: ((times_times_int @ A @ (numeral_numeral_int @ one)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_mult__numeral__1__right)). 185.47/93.69 thf(28491,plain,((! [A:int]: ((times_times_int @ A @ (numeral_numeral_int @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6169])). 185.47/93.69 thf(3928,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ C @ A) => (ord_less_int @ C @ B)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4250_dual__order_Ostrict__trans2)). 185.47/93.69 thf(20616,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ C @ A) => (ord_less_int @ C @ B)) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3928])). 185.47/93.69 thf(5184,axiom,((! [A:real,B:nat]: ((sqrt @ (power_power_real @ A @ B)) = (power_power_real @ (sqrt @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8148_real__sqrt__power)). 185.47/93.69 thf(24825,plain,((! [A:real,B:nat]: ((sqrt @ (power_power_real @ A @ B)) = (power_power_real @ (sqrt @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5184])). 185.47/93.69 thf(5730,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ (suc @ B) @ A) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2911_Suc__diff__eq__diff__pred)). 185.47/93.69 thf(26798,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ (suc @ B) @ A) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5730])). 185.47/93.69 thf(5147,axiom,((! [A:num,B:num]: (((uminus_uminus_int @ (numeral_numeral_int @ A)) = (uminus_uminus_int @ (numeral_numeral_int @ B))) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5065_neg__numeral__eq__iff)). 185.47/93.69 thf(24709,plain,((! [A:num,B:num]: (((uminus_uminus_int @ (numeral_numeral_int @ A)) = (uminus_uminus_int @ (numeral_numeral_int @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5147])). 185.47/93.69 thf(6369,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4284_linorder__not__le)). 185.47/93.69 thf(29180,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6369])). 185.47/93.69 thf(4129,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => (((dvd_dvd_int @ C @ (divide_divide_int @ B @ A)) = (dvd_dvd_int @ (times_times_int @ C @ A) @ B)) <= (dvd_dvd_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4837_dvd__div__iff__mult)). 185.47/93.69 thf(21228,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => (((dvd_dvd_int @ C @ (divide_divide_int @ B @ A)) = (dvd_dvd_int @ (times_times_int @ C @ A) @ B)) | ~ (dvd_dvd_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4129])). 185.47/93.69 thf(7445,axiom,((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4905_odd__one)). 185.47/93.69 thf(33083,plain,((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7445])). 185.47/93.69 thf(987,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (suc @ (numeral_numeral_nat @ (bitM @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8966_eval__nat__numeral_I2_J)). 185.47/93.69 thf(11114,plain,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (suc @ (numeral_numeral_nat @ (bitM @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[987])). 185.47/93.69 thf(6483,axiom,((! [A:num,B:rat,C:rat]: (((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = (divide_divide_rat @ B @ C)) = (((C = zero_zero_rat) => ((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = zero_zero_rat)) & (((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C) = B) <= (C != zero_zero_rat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6158_eq__divide__eq__numeral_I2_J)). 185.47/93.69 thf(29603,plain,((! [A:num,B:rat,C:rat]: (((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = (divide_divide_rat @ B @ C)) = (((C = zero_zero_rat) => ((uminus_uminus_rat @ (numeral_numeral_rat @ A)) = zero_zero_rat)) & (((times_times_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ C) = B) | (C = zero_zero_rat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6483])). 185.47/93.69 thf(5088,axiom,((! [A:nat,B:nat]: (((bit_se2925701944663578781it_nat @ A @ B) = B) = (ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9326_take__bit__nat__eq__self__iff)). 185.47/93.69 thf(24453,plain,((! [A:nat,B:nat]: (((bit_se2925701944663578781it_nat @ A @ B) = B) = (ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5088])). 185.47/93.69 thf(6280,axiom,((! [A:rat,B:num]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_rat @ (times_times_rat @ A @ (power_power_rat @ A @ (numeral_numeral_nat @ B))) @ (power_power_rat @ A @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6634_power__numeral__odd)). 185.47/93.69 thf(28866,plain,((! [A:rat,B:num]: ((power_power_rat @ A @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_rat @ (times_times_rat @ A @ (power_power_rat @ A @ (numeral_numeral_nat @ B))) @ (power_power_rat @ A @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6280])). 185.47/93.69 thf(3351,axiom,((! [A:rat,B:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_add__diff__cancel__right_H)). 185.47/93.69 thf(18776,plain,((! [A:rat,B:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3351])). 185.47/93.69 thf(5189,axiom,((! [A:num,B:num]: ((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) != (numera6620942414471956472nteger @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5539_neg__numeral__neq__numeral)). 185.47/93.69 thf(24840,plain,((! [A:num,B:num]: ~ ((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (numera6620942414471956472nteger @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5189])). 185.47/93.69 thf(7276,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (power_power_nat @ A @ B) @ one_one_nat) <= (ord_less_eq_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2721_power__le__one)). 185.47/93.69 thf(32513,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (power_power_nat @ A @ B) @ one_one_nat) | ~ (ord_less_eq_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7276])). 185.47/93.69 thf(1902,axiom,((! [A:real]: ? [B:int]: ((ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ B @ one_one_int))) & ! [C:int]: (((ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ C @ one_one_int))) & (ord_less_eq_real @ (ring_1_of_int_real @ C) @ A)) => (C = B)) & (ord_less_eq_real @ (ring_1_of_int_real @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7366_floor__exists1)). 185.47/93.69 thf(14087,plain,((! [A:real]: ? [B:int]: ((ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ B @ one_one_int))) & ! [C:int]: (((ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ C @ one_one_int))) & (ord_less_eq_real @ (ring_1_of_int_real @ C) @ A)) => (C = B)) & (ord_less_eq_real @ (ring_1_of_int_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1902])). 185.47/93.69 thf(4091,axiom,((! [A:nat,B:nat,C:(nat > int),D:(nat > int)]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ A) => ((groups705719431365010083at_int @ (^ [E:nat]: (if_int @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_int @ (E = B) @ one_one_int @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups705719431365010083at_int @ (^ [E:nat]: (if_int @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8870_prod_Ozero__middle)). 185.47/93.69 thf(21112,plain,((! [A:nat,B:nat,C:(nat > int),D:(nat > int)]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ A) => ((groups705719431365010083at_int @ (^ [E:nat]: (if_int @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_int @ (E = B) @ one_one_int @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups705719431365010083at_int @ (^ [E:nat]: (if_int @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4091])). 185.47/93.69 thf(4211,axiom,((! [A:nat,B:nat,C:complex]: ((((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = zero_zero_complex) <= (ord_less_nat @ A @ B)) & ((~ (ord_less_nat @ A @ B)) => ((((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (semiri8010041392384452111omplex @ (minus_minus_nat @ (plus_plus_nat @ A @ one_one_nat) @ B))) <= (C = one_one_complex)) & ((C != one_one_complex) => ((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (power_power_complex @ C @ B) @ (power_power_complex @ C @ (suc @ A))) @ (minus_minus_complex @ one_one_complex @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6845_sum__gp)). 185.47/93.69 thf(21475,plain,((! [A:nat,B:nat,C:complex]: ((((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = zero_zero_complex) | ~ (ord_less_nat @ A @ B)) & ((~ (ord_less_nat @ A @ B)) => ((((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (semiri8010041392384452111omplex @ (minus_minus_nat @ (plus_plus_nat @ A @ one_one_nat) @ B))) | ~ (C = one_one_complex)) & ((~ (C = one_one_complex)) => ((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (divide1717551699836669952omplex @ (minus_minus_complex @ (power_power_complex @ C @ B) @ (power_power_complex @ C @ (suc @ A))) @ (minus_minus_complex @ one_one_complex @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4211])). 185.47/93.69 thf(5764,axiom,((! [A:num]: ((ord_less_int @ one_one_int @ (numeral_numeral_int @ A)) = (ord_less_num @ one @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_one__less__numeral__iff)). 185.47/93.69 thf(26903,plain,((! [A:num]: ((ord_less_int @ one_one_int @ (numeral_numeral_int @ A)) = (ord_less_num @ one @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5764])). 185.47/93.69 thf(2261,axiom,(((plus_plus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5276_add__neg__numeral__special_I7_J)). 185.47/93.69 thf(15245,plain,(((plus_plus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2261])). 185.47/93.69 thf(2918,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ C) => ((ord_less_eq_rat @ (minus_minus_rat @ C @ B) @ D) <= (ord_less_eq_rat @ C @ (plus_plus_rat @ D @ B)))) <= (ord_less_eq_rat @ C @ (plus_plus_rat @ D @ B))) <= (ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1196_add__le__add__imp__diff__le)). 185.47/93.69 thf(17409,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ C) => ((ord_less_eq_rat @ (minus_minus_rat @ C @ B) @ D) | ~ (ord_less_eq_rat @ C @ (plus_plus_rat @ D @ B)))) | ~ (ord_less_eq_rat @ C @ (plus_plus_rat @ D @ B)) | ~ (ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2918])). 185.47/93.69 thf(59,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (^ [C:nat]: (minus_minus_int @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_int @ (A @ zero_zero_nat) @ (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7587_sum__lessThan__telescope_H)). 185.47/93.69 thf(7925,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (^ [C:nat]: (minus_minus_int @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_int @ (A @ zero_zero_nat) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 185.47/93.69 thf(6245,axiom,((((=) @ int) = (^ [A:int,B:int]: ((minus_minus_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2093_eq__iff__diff__eq__0)). 185.47/93.69 thf(28746,plain,((((=) @ int) = (^ [A:int,B:int]: ((minus_minus_int @ A @ B) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6245])). 185.47/93.69 thf(439,axiom,(((exp_complex @ (times_times_complex @ imaginary_unit @ (times_times_complex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one))))) = one_one_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9137_exp__two__pi__i_H)). 185.47/93.69 thf(9198,plain,(((exp_complex @ (times_times_complex @ imaginary_unit @ (times_times_complex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one))))) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[439])). 185.47/93.69 thf(3717,axiom,((! [A:rat,B:rat,C:(rat > real),D:real]: (((ord_less_real @ (C @ B) @ D) => ((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4113_order__less__subst2)). 185.47/93.69 thf(19940,plain,((! [A:rat,B:rat,C:(rat > real),D:real]: (((ord_less_real @ (C @ B) @ D) => ((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3717])). 185.47/93.69 thf(5863,axiom,((modulo_modulo_nat = (^ [A:nat,B:nat]: (minus_minus_nat @ A @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2567_modulo__nat__def)). 185.47/93.69 thf(27411,plain,(((modulo_modulo_nat) = (^ [A:nat,B:nat]: (minus_minus_nat @ A @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5863])). 185.47/93.69 thf(1399,axiom,((! [A:int,B:int,C:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (minus_minus_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_add__diff__cancel__right)). 185.47/93.69 thf(12395,plain,((! [A:int,B:int,C:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B)) = (minus_minus_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399])). 185.47/93.69 thf(474,axiom,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_int @ (groups705719431365010083at_int @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8703_prod_OatMost__Suc)). 185.47/93.69 thf(9325,plain,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_int @ (groups705719431365010083at_int @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[474])). 185.47/93.69 thf(7195,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (minus_minus_nat @ C @ B)) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1201_add__le__imp__le__diff)). 185.47/93.69 thf(32235,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (minus_minus_nat @ C @ B)) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7195])). 185.47/93.69 thf(294,axiom,((! [A:real]: (((log @ (numeral_numeral_real @ (bit0 @ (bit1 @ (bit0 @ one)))) @ A) = (times_times_real @ (log @ (numeral_numeral_real @ (bit0 @ (bit1 @ (bit0 @ one)))) @ (exp_real @ one_one_real)) @ (ln_ln_real @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9060_log__base__10__eq2)). 185.47/93.69 thf(8692,plain,((! [A:real]: (((log @ (numeral_numeral_real @ (bit0 @ (bit1 @ (bit0 @ one)))) @ A) = (times_times_real @ (log @ (numeral_numeral_real @ (bit0 @ (bit1 @ (bit0 @ one)))) @ (exp_real @ one_one_real)) @ (ln_ln_real @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 185.47/93.69 thf(6022,axiom,((! [A:num]: ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6660_odd__numeral)). 185.47/93.69 thf(27959,plain,((! [A:num]: ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6022])). 185.47/93.69 thf(1025,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (abs_abs_real @ A)) = (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6372_zero__less__abs__iff)). 185.47/93.69 thf(11236,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (abs_abs_real @ A)) = (~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025])). 185.47/93.69 thf(1404,axiom,((! [A:nat,B:vEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ (replicate_VEBT_VEBT @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5131_length__replicate)). 185.47/93.69 thf(12412,plain,((! [A:nat,B:vEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ (replicate_VEBT_VEBT @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404])). 185.47/93.69 thf(923,axiom,((! [A:set_nat,B:set_nat,C:(nat > real)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => ((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_real))) => ((groups129246275422532515t_real @ C @ B) = (groups129246275422532515t_real @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8927_prod_Omono__neutral__left)). 185.47/93.69 thf(10896,plain,((! [A:set_nat,B:set_nat,C:(nat > real)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => ((! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = one_one_real))) => ((groups129246275422532515t_real @ (C) @ B) = (groups129246275422532515t_real @ (C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[923])). 185.47/93.69 thf(482,axiom,((! [A:complex,B:num]: ((re @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B))) = (divide_divide_real @ (re @ A) @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9640_Re__divide__numeral)). 185.47/93.69 thf(9357,plain,((! [A:complex,B:num]: ((re @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B))) = (divide_divide_real @ (re @ A) @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[482])). 185.47/93.69 thf(6628,axiom,(((uminus_uminus_rat @ (numeral_numeral_rat @ one)) = (uminus_uminus_rat @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5991_uminus__numeral__One)). 185.47/93.69 thf(30097,plain,(((uminus_uminus_rat @ (numeral_numeral_rat @ one)) = (uminus_uminus_rat @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6628])). 185.47/93.69 thf(6173,axiom,((! [A:complex]: ((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (minus_minus_complex @ one_one_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7862_cos__double__sin)). 185.47/93.69 thf(28506,plain,((! [A:complex]: ((cos_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (minus_minus_complex @ one_one_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (power_power_complex @ (sin_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6173])). 185.47/93.69 thf(4976,axiom,(((abs_abs_int @ (uminus_uminus_int @ one_one_int)) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6380_abs__neg__one)). 185.47/93.69 thf(24016,plain,(((abs_abs_int @ (uminus_uminus_int @ one_one_int)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4976])). 185.47/93.69 thf(6977,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (suc @ (minus_minus_nat @ B @ A))) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ (suc @ B))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1014_diff__Suc__diff__eq1)). 185.47/93.69 thf(31476,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (suc @ (minus_minus_nat @ B @ A))) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ (suc @ B))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6977])). 185.47/93.69 thf(6140,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_3858_ord__eq__le__trans)). 185.47/93.69 thf(28353,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)],[6140])). 185.47/93.69 thf(7432,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ B) = (plus_plus_nat @ B @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_mult__Suc)). 185.47/93.69 thf(33044,plain,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ B) = (plus_plus_nat @ B @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7432])). 185.47/93.69 thf(1402,axiom,((! [A:(nat > real),B:real]: ((sums_real @ (^ [C:nat]: (A @ (suc @ C))) @ B) = (sums_real @ A @ (plus_plus_real @ B @ (A @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8187_sums__Suc__iff)). 185.47/93.69 thf(12406,plain,((! [A:(nat > real),B:real]: ((sums_real @ (^ [C:nat]: (A @ (suc @ C))) @ B) = (sums_real @ (A) @ (plus_plus_real @ B @ (A @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402])). 185.47/93.69 thf(7407,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1793_nat__0__less__mult__iff)). 185.47/93.69 thf(32966,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7407])). 185.47/93.69 thf(1079,axiom,((! [A:rat]: ? [B:int]: (ord_less_eq_rat @ A @ (ring_1_of_int_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7437_ex__le__of__int)). 185.47/93.69 thf(11390,plain,((! [A:rat]: ? [B:int]: (ord_less_eq_rat @ A @ (ring_1_of_int_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079])). 185.47/93.69 thf(3411,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_rat @ B @ (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = (ord_less_rat @ (uminus_uminus_rat @ C) @ (times_times_rat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6149_neg__less__minus__divide__eq)). 185.47/93.69 thf(18963,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ A @ zero_zero_rat) => ((ord_less_rat @ B @ (uminus_uminus_rat @ (divide_divide_rat @ C @ A))) = (ord_less_rat @ (uminus_uminus_rat @ C) @ (times_times_rat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3411])). 185.47/93.69 thf(2670,axiom,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((minus_minus_int @ D @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (minus_minus_int @ D @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5783_group__cancel_Osub2)). 185.47/93.69 thf(16578,plain,((! [A:int,B:int,C:int,D:int]: ((A = (plus_plus_int @ B @ C)) => ((minus_minus_int @ D @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (minus_minus_int @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2670])). 185.47/93.69 thf(3992,axiom,((! [A:real,B:real,C:real]: ((powr_real @ (powr_real @ A @ B) @ C) = (powr_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9086_powr__powr)). 185.47/93.69 thf(20810,plain,((! [A:real,B:real,C:real]: ((powr_real @ (powr_real @ A @ B) @ C) = (powr_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3992])). 185.47/93.69 thf(7290,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_power__strict__increasing__iff)). 185.47/93.69 thf(32557,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7290])). 185.47/93.69 thf(1878,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ (divide_divide_int @ A @ B)) = ((ord_less_int @ zero_zero_int @ B) & (ord_less_eq_int @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3059_nonneg1__imp__zdiv__pos__iff)). 185.47/93.69 thf(14018,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ (divide_divide_int @ A @ B)) = ((ord_less_int @ zero_zero_int @ B) & (ord_less_eq_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878])). 185.47/93.69 thf(149,axiom,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7796_cos__pi__half)). 185.47/93.69 thf(8213,plain,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 185.47/93.69 thf(4525,axiom,(((archim8280529875227126926d_real @ one_one_real) = one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7548_round__1)). 185.47/93.69 thf(22497,plain,(((archim8280529875227126926d_real @ one_one_real) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4525])). 185.47/93.69 thf(5831,axiom,((! [A:nat]: ((one_one_nat = (semiri1316708129612266289at_nat @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6926_of__nat__1__eq__iff)). 185.47/93.69 thf(27290,plain,((! [A:nat]: ((one_one_nat = (semiri1316708129612266289at_nat @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5831])). 185.47/93.69 thf(4881,axiom,((! [A:(int > (int > $o)),B:set_nat,C:(nat > int),D:(nat > int)]: ((((finite_finite_nat @ B) => ((A @ (groups3539618377306564664at_int @ C @ B) @ (groups3539618377306564664at_int @ D @ B)) <= (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))))) <= (! [E:int,F:int,G:int,H:int]: ((A @ (plus_plus_int @ E @ F) @ (plus_plus_int @ G @ H)) <= ((A @ E @ G) & (A @ F @ H))))) <= (A @ zero_zero_int @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5865_sum_Orelated)). 185.47/93.69 thf(23674,plain,((! [A:(int > (int > $o)),B:set_nat,C:(nat > int),D:(nat > int)]: (((finite_finite_nat @ B) => ((A @ (groups3539618377306564664at_int @ (C) @ B) @ (groups3539618377306564664at_int @ (D) @ B)) | ~ (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))))) | ~ (! [E:int,F:int,G:int,H:int]: ((A @ (plus_plus_int @ E @ F) @ (plus_plus_int @ G @ H)) | ~ ((A @ E @ G) & (A @ F @ H)))) | ~ (A @ zero_zero_int @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4881])). 185.47/93.69 thf(7726,axiom,((! [A:num]: ((one_one_nat = (numeral_numeral_nat @ A)) = (one = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_one__eq__numeral__iff)). 185.47/93.69 thf(33914,plain,((! [A:num]: ((one_one_nat = (numeral_numeral_nat @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7726])). 185.47/93.69 thf(1915,axiom,((! [A:(complex > $o),B:complex]: ((? [C:complex]: (A @ (times_times_complex @ B @ C))) = (? [C:complex]: ((A @ C) & (dvd_dvd_complex @ B @ (plus_plus_complex @ C @ zero_zero_complex))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4824_unity__coeff__ex)). 185.47/93.69 thf(14127,plain,((! [A:(complex > $o),B:complex]: ((? [C:complex]: (A @ (times_times_complex @ B @ C))) = (? [C:complex]: ((A @ C) & (dvd_dvd_complex @ B @ (plus_plus_complex @ C @ zero_zero_complex))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1915])). 185.47/93.69 thf(2029,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((? [C:real]: ((ord_less_real @ zero_zero_real @ C) & (ord_less_real @ C @ A) & (ord_less_real @ C @ B))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2025_field__lbound__gt__zero)). 185.47/93.69 thf(14514,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & (ord_less_real @ C @ A) & (ord_less_real @ C @ B)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2029])). 185.47/93.69 thf(4707,axiom,((! [A:rat,B:rat]: ((A = B) => (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3930_order__eq__refl)). 185.47/93.69 thf(23097,plain,((! [A:rat,B:rat]: ((A = B) => (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4707])). 185.47/93.69 thf(2340,axiom,((! [A:real,B:nat]: ((power_power_real @ (divide_divide_real @ one_one_real @ A) @ B) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_844_power__one__over)). 185.47/93.69 thf(15484,plain,((! [A:real,B:nat]: ((power_power_real @ (divide_divide_real @ one_one_real @ A) @ B) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2340])). 185.47/93.69 thf(4940,axiom,((! [A:complex,B:complex]: ((power_power_complex @ (minus_minus_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_complex @ (plus_plus_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_908_power2__diff)). 185.47/93.69 thf(23908,plain,((! [A:complex,B:complex]: ((power_power_complex @ (minus_minus_complex @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_complex @ (plus_plus_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4940])). 185.47/93.69 thf(2761,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sqrt @ A)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8165_real__sqrt__ge__zero)). 185.47/93.69 thf(16908,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sqrt @ A)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2761])). 185.47/93.69 thf(6527,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: (((vEBT_vebt_member @ A @ C) <= (vEBT_V8194947554948674370ptions @ A @ C)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_valid__member__both__member__options)). 185.47/93.69 thf(29768,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_vebt_member @ A @ C) | ~ (vEBT_V8194947554948674370ptions @ A @ C) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6527])). 185.47/93.69 thf(2693,axiom,((! [A:rat,B:rat]: ((~ (ord_less_eq_rat @ A @ B)) = (ord_less_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4282_linorder__not__le)). 185.47/93.69 thf(16696,plain,((! [A:rat,B:rat]: ((~ (ord_less_eq_rat @ A @ B)) = (ord_less_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2693])). 185.47/93.69 thf(3956,axiom,((! [A:num,B:num]: ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5370_neg__numeral__le__iff)). 185.47/93.69 thf(20703,plain,((! [A:num,B:num]: ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3956])). 185.47/93.69 thf(1524,axiom,((! [A:(nat > real),B:real,C:(nat > real),D:real]: (((sums_real @ C @ D) => (sums_real @ (^ [E:nat]: (plus_plus_real @ (A @ E) @ (C @ E))) @ (plus_plus_real @ B @ D))) <= (sums_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8158_sums__add)). 185.47/93.69 thf(12793,plain,((! [A:(nat > real),B:real,C:(nat > real),D:real]: (((sums_real @ (C) @ D) => (sums_real @ (^ [E:nat]: (plus_plus_real @ (A @ E) @ (C @ E))) @ (plus_plus_real @ B @ D))) | ~ (sums_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524])). 185.47/93.69 thf(3144,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((ord_less_int @ A @ B) & (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_add__mono__thms__linordered__field_I3_J)). 185.47/93.69 thf(18125,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ ((ord_less_int @ A @ B) & (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3144])). 185.47/93.69 thf(5881,axiom,((! [A:nat,B:nat]: ((? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & (dvd_dvd_nat @ C @ B) & ((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4882_bezout__add__strong__nat)). 185.47/93.69 thf(27463,plain,((! [A:nat,B:nat]: (? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & (dvd_dvd_nat @ C @ B) & ((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5881])). 185.47/93.69 thf(4322,axiom,((! [A:rat,B:rat]: (((ord_less_rat @ one_one_rat @ (divide_divide_rat @ B @ A)) = (ord_less_rat @ A @ B)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1817_less__divide__eq__1__pos)). 185.47/93.69 thf(21847,plain,((! [A:rat,B:rat]: (((ord_less_rat @ one_one_rat @ (divide_divide_rat @ B @ A)) = (ord_less_rat @ A @ B)) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4322])). 185.47/93.69 thf(2248,axiom,((! [A:rat,B:rat]: ? [C:rat]: ! [D:rat]: ((ord_less_rat @ D @ C) => ((~ (dvd_dvd_rat @ A @ (plus_plus_rat @ D @ B))) = (~ (dvd_dvd_rat @ A @ (plus_plus_rat @ D @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4705_minf_I10_J)). 185.47/93.69 thf(15209,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2248])). 185.47/93.69 thf(1546,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4269_order__le__less)). 185.47/93.69 thf(12855,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546])). 185.47/93.69 thf(3015,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_5036_neg__le__iff__le)). 185.47/93.69 thf(17718,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)],[3015])). 185.47/93.69 thf(6167,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ A @ B)) = ((ord_less_eq_nat @ B @ A) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2792_div__greater__zero__iff)). 185.47/93.69 thf(28485,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ A @ B)) = ((ord_less_eq_nat @ B @ A) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6167])). 185.47/93.69 thf(5369,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) = ((A = zero_zero_int) | (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1495_mult__eq__0__iff)). 185.47/93.69 thf(25504,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) = ((A = zero_zero_int) | (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5369])). 185.47/93.69 thf(6281,axiom,((! [A:real,B:real]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B) => (ord_less_real @ A @ (sqrt @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8213_real__less__rsqrt)). 185.47/93.69 thf(28869,plain,((! [A:real,B:real]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B) => (ord_less_real @ A @ (sqrt @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6281])). 185.47/93.69 thf(2230,axiom,((! [A:int,B:int]: ? [C:int]: ! [D:int]: (((dvd_dvd_int @ A @ (plus_plus_int @ D @ B)) = (dvd_dvd_int @ A @ (plus_plus_int @ D @ B))) <= (ord_less_int @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4722_pinf_I9_J)). 185.47/93.69 thf(15145,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2230])). 185.47/93.69 thf(5614,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2024_zero__le)). 185.47/93.69 thf(26417,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5614])). 185.47/93.69 thf(5130,axiom,((! [A:complex,B:num,C:num]: ((power_power_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (power_power_complex @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_power__mult__numeral)). 185.47/93.69 thf(24615,plain,((! [A:complex,B:num,C:num]: ((power_power_complex @ (power_power_complex @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ C)) = (power_power_complex @ A @ (numeral_numeral_nat @ (times_times_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5130])). 185.47/93.69 thf(1438,axiom,((! [A:num]: ((semiri1314217659103216013at_int @ (numeral_numeral_nat @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6902_of__nat__numeral)). 185.47/93.69 thf(12530,plain,((! [A:num]: ((semiri1314217659103216013at_int @ (numeral_numeral_nat @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438])). 185.47/93.69 thf(3159,axiom,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ (divide_divide_rat @ A @ B) @ C) = (divide_divide_rat @ A @ (times_times_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_divide__divide__eq__left_H)). 185.47/93.69 thf(18174,plain,((! [A:rat,B:rat,C:rat]: ((divide_divide_rat @ (divide_divide_rat @ A @ B) @ C) = (divide_divide_rat @ A @ (times_times_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3159])). 185.47/93.69 thf(4026,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => (dvd_dvd_rat @ A @ (times_times_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4607_dvd__mult)). 185.47/93.69 thf(20920,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ A @ B) => (dvd_dvd_rat @ A @ (times_times_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4026])). 185.47/93.69 thf(4670,axiom,((! [A:int,B:int]: ((ord_less_int @ (abs_abs_int @ A) @ B) = ((ord_less_int @ A @ B) & (ord_less_int @ (uminus_uminus_int @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6525_abs__less__iff)). 185.47/93.69 thf(22956,plain,((! [A:int,B:int]: ((ord_less_int @ (abs_abs_int @ A) @ B) = ((ord_less_int @ A @ B) & (ord_less_int @ (uminus_uminus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4670])). 185.47/93.69 thf(7163,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4040_order_Ostrict__implies__not__eq)). 185.47/93.69 thf(32132,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7163])). 185.47/93.69 thf(3873,axiom,((dvd_dvd_int = (^ [A:int,B:int]: ? [C:int]: (B = (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4614_dvd__def)). 185.47/93.69 thf(20436,plain,(((dvd_dvd_int) = (^ [A:int,B:int]: ? [C:int]: (B = (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3873])). 185.47/93.69 thf(4353,axiom,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ A @ (plus_plus_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_741_diff__diff__eq)). 185.47/93.69 thf(21942,plain,((! [A:rat,B:rat,C:rat]: ((minus_minus_rat @ (minus_minus_rat @ A @ B) @ C) = (minus_minus_rat @ A @ (plus_plus_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4353])). 185.47/93.69 thf(5867,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (times_times_nat @ C @ B)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4608_dvd__mult)). 185.47/93.69 thf(27421,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (times_times_nat @ C @ B)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5867])). 185.47/93.69 thf(2550,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (plus_plus_rat @ B @ A)) = (ord_less_rat @ zero_zero_rat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1643_less__add__same__cancel2)). 185.47/93.69 thf(16190,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (plus_plus_rat @ B @ A)) = (ord_less_rat @ zero_zero_rat @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2550])). 185.47/93.69 thf(56,axiom,((! [A:nat]: (((set_ord_lessThan_nat @ A) = bot_bot_set_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7572_lessThan__empty__iff)). 185.47/93.69 thf(7915,plain,((! [A:nat]: (((set_ord_lessThan_nat @ A) = bot_bot_set_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 185.47/93.69 thf(388,axiom,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => (((ord_less_eq_real @ (tan_real @ A) @ (tan_real @ B)) <= (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8069_tan__mono__le)). 185.47/93.69 thf(9023,plain,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_eq_real @ (tan_real @ A) @ (tan_real @ B)) | ~ (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])). 185.47/93.69 thf(6969,axiom,((! [A:real]: ((power_power_real @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1770_power__Suc0__right)). 185.47/93.69 thf(31403,plain,((! [A:real]: ((power_power_real @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6969])). 185.47/93.69 thf(7333,axiom,((! [A:num,B:num]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5339_mult__neg__numeral__simps_I3_J)). 185.47/93.69 thf(32716,plain,((! [A:num,B:num]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7333])). 185.47/93.69 thf(1940,axiom,((! [A:real,B:real]: (((plus_plus_real @ (minus_minus_real @ B @ A) @ A) = B) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_978_le__add__diff__inverse2)). 185.47/93.69 thf(14225,plain,((! [A:real,B:real]: (((plus_plus_real @ (minus_minus_real @ B @ A) @ A) = B) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1940])). 185.47/93.69 thf(6895,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_896_nat__less__add__iff2)). 185.47/93.69 thf(31117,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6895])). 185.47/93.69 thf(2698,axiom,((! [A:num]: ((neg_nu5851722552734809277nc_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7008_dbl__inc__simps_I5_J)). 185.47/93.69 thf(16711,plain,((! [A:num]: ((neg_nu5851722552734809277nc_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2698])). 185.47/93.69 thf(2246,axiom,((! [A:nat,B:nat,C:set_nat]: ((((finite_finite_nat @ C) => (? [D:nat]: (vEBT_is_pred_in_set @ C @ B @ D))) <= (vEBT_VEBT_min_in_set @ C @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3375_obtain__set__pred)). 185.47/93.69 thf(15204,plain,((! [A:nat,B:nat,C:set_nat]: (((finite_finite_nat @ C) => (? [D:nat]: (vEBT_is_pred_in_set @ C @ B @ D))) | ~ (vEBT_VEBT_min_in_set @ C @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2246])). 185.47/93.69 thf(6058,axiom,((! [A:int,B:num]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ B))) = (((numeral_numeral_nat @ B) = zero_zero_nat) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_int @ zero_zero_int @ A)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (A != zero_zero_int)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4549_zero__less__power__eq__numeral)). 185.47/93.69 thf(28062,plain,((! [A:int,B:num]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ B))) = (((numeral_numeral_nat @ B) = zero_zero_nat) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_int @ zero_zero_int @ A)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & ~ (A = zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6058])). 185.47/93.69 thf(4349,axiom,((ord_less_eq_real @ zero_zero_real @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2275_zero__less__one__class_Ozero__le__one)). 185.47/93.69 thf(21930,plain,((ord_less_eq_real @ zero_zero_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4349])). 185.47/93.69 thf(1992,axiom,((! [A:int,B:nat,C:int]: (((power_power_int @ A @ (suc @ B)) = (power_power_int @ C @ (suc @ B))) => ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ C) => (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2753_power__inject__base)). 185.47/93.69 thf(14390,plain,((! [A:int,B:nat,C:int]: (((power_power_int @ A @ (suc @ B)) = (power_power_int @ C @ (suc @ B))) => ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ C) => (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992])). 185.47/93.69 thf(4587,axiom,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ A @ B) = (plus_plus_rat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_add__right__cancel)). 185.47/93.69 thf(22692,plain,((! [A:rat,B:rat,C:rat]: (((plus_plus_rat @ A @ B) = (plus_plus_rat @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4587])). 185.47/93.69 thf(6304,axiom,((! [A:num]: ((semiri2265585572941072030t_real @ (numeral_numeral_nat @ A)) = (times_times_real @ (numeral_numeral_real @ A) @ (semiri2265585572941072030t_real @ (pred_numeral @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8040_fact__numeral)). 185.47/93.69 thf(28938,plain,((! [A:num]: ((semiri2265585572941072030t_real @ (numeral_numeral_nat @ A)) = (times_times_real @ (numeral_numeral_real @ A) @ (semiri2265585572941072030t_real @ (pred_numeral @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6304])). 185.47/93.69 thf(2418,axiom,((! [A:int,B:nat]: (((nat2 @ (power_power_int @ A @ B)) = (power_power_nat @ (nat2 @ A) @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9318_nat__power__eq)). 185.47/93.69 thf(15732,plain,((! [A:int,B:nat]: (((nat2 @ (power_power_int @ A @ B)) = (power_power_nat @ (nat2 @ A) @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2418])). 185.47/93.69 thf(4684,axiom,((! [A:int,B:nat]: (((ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => ((bit_se2923211474154528505it_int @ B @ (uminus_uminus_int @ A)) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ A))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9357_take__bit__minus__small__eq)). 185.47/93.69 thf(23013,plain,((! [A:int,B:nat]: (((ord_less_eq_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => ((bit_se2923211474154528505it_int @ B @ (uminus_uminus_int @ A)) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ A))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4684])). 185.47/93.69 thf(4361,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((dvd_dvd_int @ A @ B) => (((divide_divide_int @ B @ A) = C) = (B = (times_times_int @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4831_dvd__div__eq__mult)). 185.47/93.69 thf(21971,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((dvd_dvd_int @ A @ B) => (((divide_divide_int @ B @ A) = C) = (B = (times_times_int @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4361])). 185.47/93.69 thf(1656,axiom,((! [A:$o,B:$o,C:$o,D:$o]: (((vEBT_Leaf @ A @ B) = (vEBT_Leaf @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1478_VEBT_Oinject_I2_J)). 185.47/93.69 thf(13247,plain,((! [A:$o,B:$o,C:$o,D:$o]: (((vEBT_Leaf @ A @ B) = (vEBT_Leaf @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656])). 185.47/93.69 thf(2518,axiom,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ B) => ((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5814_dvd__neg__div)). 185.47/93.69 thf(16081,plain,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ B) => ((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2518])). 185.47/93.69 thf(7526,axiom,((! [A:num,B:num,C:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ C)) = (times_times_complex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_mult__numeral__left__semiring__numeral)). 185.47/93.69 thf(33369,plain,((! [A:num,B:num,C:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ C)) = (times_times_complex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7526])). 185.47/93.69 thf(6522,axiom,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1044_Suc__n__not__le__n)). 185.47/93.69 thf(29741,plain,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6522])). 185.47/93.69 thf(306,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ B @ (sgn_sgn_int @ C))) = ((dvd_dvd_int @ A @ B) | (C = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9218_dvd__mult__sgn__iff)). 185.47/93.69 thf(8758,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ B @ (sgn_sgn_int @ C))) = ((dvd_dvd_int @ A @ B) | (C = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 185.47/93.69 thf(7574,axiom,((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4889_even__zero)). 185.47/93.69 thf(33501,plain,((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7574])). 185.47/93.69 thf(7672,axiom,((! [A:real]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_real @ (times_times_real @ (times_times_real @ A @ A) @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_power4__eq__xxxx)). 185.47/93.69 thf(33765,plain,((! [A:real]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (times_times_real @ (times_times_real @ (times_times_real @ A @ A) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7672])). 185.47/93.69 thf(4908,axiom,((real_V975177566351809787t_real = (^ [A:real,B:real]: (abs_abs_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10133_dist__real__def)). 185.47/93.69 thf(23787,plain,(((real_V975177566351809787t_real) = (^ [A:real,B:real]: (abs_abs_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4908])). 185.47/93.69 thf(3356,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ zero_zero_rat @ (plus_plus_rat @ A @ B))) <= (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2292_add__nonneg__nonneg)). 185.47/93.69 thf(18791,plain,((! [A:rat,B:rat]: (((ord_less_eq_rat @ zero_zero_rat @ B) => (ord_less_eq_rat @ zero_zero_rat @ (plus_plus_rat @ A @ B))) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3356])). 185.47/93.69 thf(7109,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ B @ A)) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4976_zero__le__even__power)). 185.47/93.69 thf(31925,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ B @ A)) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7109])). 185.47/93.69 thf(1839,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3812_order__refl)). 185.47/93.69 thf(13894,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1839])). 185.47/93.69 thf(471,axiom,((! [A:real]: ((cos_real @ (plus_plus_real @ pi @ A)) = (uminus_uminus_real @ (cos_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7784_cos__periodic__pi2)). 185.47/93.69 thf(9314,plain,((! [A:real]: ((cos_real @ (plus_plus_real @ pi @ A)) = (uminus_uminus_real @ (cos_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[471])). 185.47/93.69 thf(1586,axiom,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (times_times_int @ (modulo_modulo_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ (times_times_int @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1974_mod__mult__left__eq)). 185.47/93.69 thf(12984,plain,((! [A:int,B:int,C:int]: ((modulo_modulo_int @ (times_times_int @ (modulo_modulo_int @ A @ B) @ C) @ B) = (modulo_modulo_int @ (times_times_int @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586])). 185.47/93.69 thf(2845,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => (((divide_divide_int @ B @ A) = zero_zero_int) = (B = zero_zero_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4728_dvd__div__eq__0__iff)). 185.47/93.69 thf(17177,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => (((divide_divide_int @ B @ A) = zero_zero_int) = (B = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2845])). 185.47/93.69 thf(2600,axiom,((! [A:int,B:int]: ((((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) = (divide_divide_int @ B @ A)) <= (ord_less_int @ (modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ A)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2489_divmod__digit__0_I1_J)). 185.47/93.69 thf(16363,plain,((! [A:int,B:int]: (((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) = (divide_divide_int @ B @ A)) | ~ (ord_less_int @ (modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ A) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2600])). 185.47/93.69 thf(1514,axiom,((! [A:nat,B:int]: (((ord_less_int @ zero_zero_int @ B) => ((divide_divide_int @ (power_power_int @ B @ A) @ B) = (power_power_int @ B @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3098_int__power__div__base)). 185.47/93.69 thf(12761,plain,((! [A:nat,B:int]: (((ord_less_int @ zero_zero_int @ B) => ((divide_divide_int @ (power_power_int @ B @ A) @ B) = (power_power_int @ B @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1514])). 185.47/93.69 thf(3335,axiom,((! [A:rat,B:nat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2450_zero__le__power)). 185.47/93.69 thf(18716,plain,((! [A:rat,B:nat]: ((ord_less_eq_rat @ zero_zero_rat @ A) => (ord_less_eq_rat @ zero_zero_rat @ (power_power_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3335])). 185.47/93.69 thf(873,axiom,((! [A:complex,B:complex]: (((cos_complex @ A) != zero_zero_complex) => (((cos_complex @ B) != zero_zero_complex) => ((plus_plus_complex @ (tan_complex @ A) @ (tan_complex @ B)) = (divide1717551699836669952omplex @ (sin_complex @ (plus_plus_complex @ A @ B)) @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8063_add__tan__eq)). 185.47/93.69 thf(10713,plain,((! [A:complex,B:complex]: ((~ ((cos_complex @ A) = zero_zero_complex)) => ((~ ((cos_complex @ B) = zero_zero_complex)) => ((plus_plus_complex @ (tan_complex @ A) @ (tan_complex @ B)) = (divide1717551699836669952omplex @ (sin_complex @ (plus_plus_complex @ A @ B)) @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[873])). 185.47/93.69 thf(7172,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2079_comm__monoid__add__class_Oadd__0)). 185.47/93.69 thf(32164,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7172])). 185.47/93.69 thf(6938,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085_Suc__le__eq)). 185.47/93.69 thf(31263,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6938])). 185.47/93.69 thf(4777,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A)))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ one @ (bitM @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9445_or__minus__numerals_I1_J)). 185.47/93.69 thf(23350,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A)))) = (uminus_uminus_int @ (numeral_numeral_int @ (bit_or_not_num_neg @ one @ (bitM @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4777])). 185.47/93.69 thf(6356,axiom,((! [A:nat]: ((modulo_modulo_nat @ one_one_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (zero_n2687167440665602831ol_nat @ (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5483_one__mod__2__pow__eq)). 185.47/93.69 thf(29136,plain,((! [A:nat]: ((modulo_modulo_nat @ one_one_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (zero_n2687167440665602831ol_nat @ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6356])). 185.47/93.69 thf(1743,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat]: ((ord_less_eq_nat @ (B @ D) @ (C @ D)) <= (member_nat @ D @ A))) => ((groups3542108847815614940at_nat @ (^ [D:nat]: (minus_minus_nat @ (C @ D) @ (B @ D))) @ A) = (minus_minus_nat @ (groups3542108847815614940at_nat @ C @ A) @ (groups3542108847815614940at_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6535_sum__subtractf__nat)). 185.47/93.69 thf(13574,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat]: ((ord_less_eq_nat @ (B @ D) @ (C @ D)) | ~ (member_nat @ D @ A))) => ((groups3542108847815614940at_nat @ (^ [D:nat]: (minus_minus_nat @ (C @ D) @ (B @ D))) @ A) = (minus_minus_nat @ (groups3542108847815614940at_nat @ (C) @ A) @ (groups3542108847815614940at_nat @ (B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743])). 185.47/93.69 thf(3301,axiom,((! [A:real,B:real,C:real]: ((divide_divide_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_divide__divide__eq__right)). 185.47/93.69 thf(18606,plain,((! [A:real,B:real,C:real]: ((divide_divide_real @ A @ (divide_divide_real @ B @ C)) = (divide_divide_real @ (times_times_real @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3301])). 185.47/93.69 thf(4131,axiom,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (bit_se2000444600071755411sk_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9221_mask__nonnegative__int)). 185.47/93.69 thf(21236,plain,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (bit_se2000444600071755411sk_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4131])). 185.47/93.69 thf(5424,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5465_neg__one__even__power)). 185.47/93.69 thf(25667,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5424])). 185.47/93.69 thf(3867,axiom,((! [A:int,B:(num > int),C:num,D:num]: ((ord_less_int @ A @ (B @ C)) => (((ord_less_int @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_less_eq_num @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4350_order__less__le__subst1)). 185.47/93.69 thf(20417,plain,((! [A:int,B:(num > int),C:num,D:num]: ((ord_less_int @ A @ (B @ C)) => ((ord_less_int @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_less_eq_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3867])). 185.47/93.69 thf(3108,axiom,((! [A:int,B:int,C:int,D:int]: ((divide_divide_rat @ (fract @ A @ B) @ (fract @ C @ D)) = (fract @ (times_times_int @ A @ D) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9930_divide__rat)). 185.47/93.69 thf(18021,plain,((! [A:int,B:int,C:int,D:int]: ((divide_divide_rat @ (fract @ A @ B) @ (fract @ C @ D)) = (fract @ (times_times_int @ A @ D) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3108])). 185.47/93.69 thf(5222,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_V8194947554948674370ptions @ (vEBT_vebt_insert @ A @ D) @ C) <= (vEBT_V8194947554948674370ptions @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_valid__insert__both__member__options__pres)). 185.47/93.69 thf(24940,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_V8194947554948674370ptions @ (vEBT_vebt_insert @ A @ D) @ C) | ~ (vEBT_V8194947554948674370ptions @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5222])). 185.47/93.69 thf(419,axiom,((! [A:nat,B:int,C:nat,D:int,E:int]: ((bit_concat_bit @ A @ B @ (bit_concat_bit @ C @ D @ E)) = (bit_concat_bit @ (plus_plus_nat @ C @ A) @ (bit_concat_bit @ A @ B @ D) @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3838_concat__bit__assoc)). 185.47/93.69 thf(9124,plain,((! [A:nat,B:int,C:nat,D:int,E:int]: ((bit_concat_bit @ A @ B @ (bit_concat_bit @ C @ D @ E)) = (bit_concat_bit @ (plus_plus_nat @ C @ A) @ (bit_concat_bit @ A @ B @ D) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])). 185.47/93.69 thf(1542,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ (sin_real @ A)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7839_sin__x__ge__neg__x)). 185.47/93.69 thf(12844,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ (sin_real @ A)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542])). 185.47/93.69 thf(783,axiom,((! [A:(nat > rat),B:nat,C:nat]: ((groups2906978787729119204at_rat @ A @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups2906978787729119204at_rat @ (^ [D:nat]: (plus_plus_rat @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6749_sum_Oin__pairs)). 185.47/93.69 thf(10403,plain,((! [A:(nat > rat),B:nat,C:nat]: ((groups2906978787729119204at_rat @ (A) @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups2906978787729119204at_rat @ (^ [D:nat]: (plus_plus_rat @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[783])). 185.47/93.69 thf(3806,axiom,((dvd_dvd_real = (^ [A:real,B:real]: ? [C:real]: (B = (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4611_dvd__def)). 185.47/93.69 thf(20231,plain,(((dvd_dvd_real) = (^ [A:real,B:real]: ? [C:real]: (B = (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3806])). 185.47/93.69 thf(5266,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ A @ B)) => ((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B))) <= (C = ((((B = one_one_nat) & ((E) <= (B = one_one_nat))) <= (B != zero_zero_nat)) & ((D) <= (B = zero_zero_nat))))))) => ((~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ D @ (suc @ E) @ F @ G)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ (suc @ E) @ F @ G) @ B))) <= (C = (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)))))))) <= (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ zero_zero_nat @ E @ F) @ B))) <= (~ (C))) <= (A = (vEBT_Node @ D @ zero_zero_nat @ E @ F))))))) <= ((vEBT_V5719532721284313246member @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3118_VEBT__internal_Onaive__member_Opelims_I1_J)). 185.47/93.69 thf(25108,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ A @ B)) => ((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)) | ~ (C = ((((B = one_one_nat) & ((E) | ~ (B = one_one_nat))) | (B = zero_zero_nat)) & ((D) | ~ (B = zero_zero_nat))))))) => (~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ D @ (suc @ E) @ F @ G)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ (suc @ E) @ F @ G) @ B)) | ~ (C = (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))))))) | ~ (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ zero_zero_nat @ E @ F) @ B)) | (C) | ~ (A = (vEBT_Node @ D @ zero_zero_nat @ E @ F))))))) | ~ ((vEBT_V5719532721284313246member @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5266])). 185.47/93.69 thf(4175,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ C @ zero_zero_rat) => (ord_less_eq_rat @ (times_times_rat @ B @ C) @ (times_times_rat @ A @ C))) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2233_mult__right__mono__neg)). 185.47/93.69 thf(21366,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_eq_rat @ C @ zero_zero_rat) => (ord_less_eq_rat @ (times_times_rat @ B @ C) @ (times_times_rat @ A @ C))) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4175])). 185.47/93.69 thf(4988,axiom,((! [A:num]: ((minus_minus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ one_one_rat) = (uminus_uminus_rat @ (numeral_numeral_rat @ (plus_plus_num @ A @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5452_diff__numeral__special_I4_J)). 185.47/93.69 thf(24067,plain,((! [A:num]: ((minus_minus_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ one_one_rat) = (uminus_uminus_rat @ (numeral_numeral_rat @ (plus_plus_num @ A @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4988])). 185.47/93.69 thf(1590,axiom,((! [A:rat,B:(rat > rat),C:rat,D:rat]: ((A = (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F)))) => (ord_less_eq_rat @ A @ (B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3938_ord__eq__le__subst)). 185.47/93.69 thf(12997,plain,((! [A:rat,B:(rat > rat),C:rat,D:rat]: ((A = (B @ C)) => ((ord_less_eq_rat @ C @ D) => ((! [E:rat,F:rat]: ((ord_less_eq_rat @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F)))) => (ord_less_eq_rat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590])). 185.47/93.69 thf(3082,axiom,((! [A:complex,B:complex,C:num]: (((divide1717551699836669952omplex @ A @ B) = (numera6690914467698888265omplex @ C)) = (((A = (times_times_complex @ (numera6690914467698888265omplex @ C) @ B)) <= (B != zero_zero_complex)) & (((numera6690914467698888265omplex @ C) = zero_zero_complex) <= (B = zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2726_divide__eq__eq__numeral_I1_J)). 185.47/93.69 thf(17927,plain,((! [A:complex,B:complex,C:num]: (((divide1717551699836669952omplex @ A @ B) = (numera6690914467698888265omplex @ C)) = (((A = (times_times_complex @ (numera6690914467698888265omplex @ C) @ B)) | (B = zero_zero_complex)) & (((numera6690914467698888265omplex @ C) = zero_zero_complex) | ~ (B = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3082])). 185.47/93.69 thf(7534,axiom,((! [A:rat,B:rat]: ((power_power_rat @ (minus_minus_rat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ (minus_minus_rat @ B @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_893_power2__commute)). 185.47/93.69 thf(33390,plain,((! [A:rat,B:rat]: ((power_power_rat @ (minus_minus_rat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_rat @ (minus_minus_rat @ B @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7534])). 185.47/93.69 thf(2080,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B))) = ((B != zero_zero_rat) | (A != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2689_sum__squares__gt__zero__iff)). 185.47/93.69 thf(14672,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ (plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B))) = (~ (B = zero_zero_rat) | ~ (A = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2080])). 185.47/93.69 thf(6726,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_not__less__eq__eq)). 185.47/93.69 thf(30433,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6726])). 185.47/93.69 thf(7507,axiom,((! [A:nat]: (ord_less_nat @ (bit_se2002935070580805687sk_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9230_mask__nat__less__exp)). 185.47/93.69 thf(33308,plain,((! [A:nat]: (ord_less_nat @ (bit_se2002935070580805687sk_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7507])). 185.47/93.69 thf(2028,axiom,((! [A:rat,B:rat]: ((abs_abs_rat @ (divide_divide_rat @ A @ B)) = (divide_divide_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6351_abs__divide)). 185.47/93.69 thf(14511,plain,((! [A:rat,B:rat]: ((abs_abs_rat @ (divide_divide_rat @ A @ B)) = (divide_divide_rat @ (abs_abs_rat @ A) @ (abs_abs_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2028])). 185.47/93.69 thf(2810,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (modulo_modulo_int @ A @ B) @ B) = (modulo_modulo_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1476_mod__mod__trivial)). 185.47/93.69 thf(17062,plain,((! [A:int,B:int]: ((modulo_modulo_int @ (modulo_modulo_int @ A @ B) @ B) = (modulo_modulo_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2810])). 185.47/93.69 thf(4464,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((! [B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ B @ C) @ D))) => (((! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ D) @ E @ F) @ G))) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ B) @ C @ D) @ E))))) <= (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ zero_zero_nat @ D @ E) @ F)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2151_VEBT__internal_Omembermima_Ocases)). 185.47/93.69 thf(22291,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((! [B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ B @ C) @ D))) => (((! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ D) @ E @ F) @ G))) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ B) @ C @ D) @ E))))) | ~ (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ zero_zero_nat @ D @ E) @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4464])). 185.47/93.69 thf(6088,axiom,((! [A:num]: ((size_size_num @ (bit0 @ A)) = (plus_plus_nat @ (size_size_num @ A) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2776_num_Osize_I5_J)). 185.47/93.69 thf(28167,plain,((! [A:num]: ((size_size_num @ (bit0 @ A)) = (plus_plus_nat @ (size_size_num @ A) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6088])). 185.47/93.69 thf(5973,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (((plus_plus_nat @ A @ C) = B) & (ord_less_nat @ zero_zero_nat @ C))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2502_less__imp__add__positive)). 185.47/93.69 thf(27807,plain,((! [A:nat,B:nat]: (? [C:nat]: (((plus_plus_nat @ A @ C) = B) & (ord_less_nat @ zero_zero_nat @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5973])). 185.47/93.69 thf(3336,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) <= (ord_less_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2434_divide__pos__pos)). 185.47/93.69 thf(18719,plain,((! [A:rat,B:rat]: ((ord_less_rat @ zero_zero_rat @ A) => ((ord_less_rat @ zero_zero_rat @ (divide_divide_rat @ A @ B)) | ~ (ord_less_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3336])). 185.47/93.69 thf(909,axiom,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ A @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups705719431365010083at_int @ (^ [C:nat]: (times_times_int @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) @ (set_ord_atMost_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8846_prod_Oin__pairs__0)). 185.47/93.69 thf(10845,plain,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (A) @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups705719431365010083at_int @ (^ [C:nat]: (times_times_int @ (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) @ (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) @ (set_ord_atMost_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[909])). 185.47/93.69 thf(1820,axiom,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ B @ A) <= (A = (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4617_dvdI)). 185.47/93.69 thf(13827,plain,((! [A:rat,B:rat,C:rat]: ((dvd_dvd_rat @ B @ A) | ~ (A = (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1820])). 185.47/93.69 thf(3516,axiom,((! [A:real]: ((ord_less_real @ A @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5151_less__neg__neg)). 185.47/93.69 thf(19304,plain,((! [A:real]: ((ord_less_real @ A @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3516])). 185.47/93.69 thf(2200,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ B @ (times_3573771949741848930nteger @ A @ C)) = (dvd_dvd_Code_integer @ B @ C)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4738_dvd__mult__unit__iff_H)). 185.47/93.69 thf(15059,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ B @ (times_3573771949741848930nteger @ A @ C)) = (dvd_dvd_Code_integer @ B @ C)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2200])). 185.47/93.69 thf(694,axiom,((! [A:real]: ((ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real) => (summable_real @ (power_power_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7722_summable__geometric)). 185.47/93.69 thf(10045,plain,((! [A:real]: ((ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real) => (summable_real @ (power_power_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[694])). 185.47/93.69 thf(5173,axiom,((! [A:(nat > $o),B:$o]: ((A @ (zero_n2687167440665602831ol_nat @ B)) = (((A @ zero_zero_nat) <= (~ (B))) & ((B) => (A @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5680_split__of__bool)). 185.47/93.69 thf(24792,plain,((! [A:(nat > $o),B:$o]: ((A @ (zero_n2687167440665602831ol_nat @ B)) = (((A @ zero_zero_nat) | (B)) & ((B) => (A @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5173])). 185.47/93.69 thf(3603,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ B @ (plus_plus_real @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2637_add__strict__increasing)). 185.47/93.69 thf(19568,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ B @ (plus_plus_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3603])). 185.47/93.69 thf(3842,axiom,((! [A:set_nat]: ((A != bot_bot_set_nat) => ((~ (finite_finite_nat @ A)) <= (! [B:nat]: ((member_nat @ B @ A) => (? [C:nat]: ((ord_less_nat @ B @ C) & (member_nat @ C @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4432_infinite__growing)). 185.47/93.69 thf(20339,plain,((! [A:set_nat]: ((~ (A = bot_bot_set_nat)) => (~ (finite_finite_nat @ A) | ~ (! [B:nat]: ((member_nat @ B @ A) => (? [C:nat]: ((ord_less_nat @ B @ C) & (member_nat @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3842])). 185.47/93.69 thf(4031,axiom,(((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ one_one_complex) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5273_add__neg__numeral__special_I8_J)). 185.47/93.69 thf(20933,plain,(((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ one_one_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4031])). 185.47/93.69 thf(1098,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3110_verit__sum__simplify)). 185.47/93.69 thf(11462,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098])). 185.47/93.69 thf(572,axiom,(((sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = zero_zero_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7797_sin__two__pi)). 185.47/93.69 thf(9633,plain,(((sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[572])). 185.47/93.69 thf(7365,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (A = B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_add__mono__thms__linordered__semiring_I2_J)). 185.47/93.69 thf(32812,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) & (A = B)) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7365])). 185.47/93.69 thf(6609,axiom,((! [A:nat,B:nat,C:real]: ((root @ A @ (root @ B @ C)) = (root @ B @ (root @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9179_real__root__commute)). 185.47/93.69 thf(30031,plain,((! [A:nat,B:nat,C:real]: ((root @ A @ (root @ B @ C)) = (root @ B @ (root @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6609])). 185.47/93.69 thf(3233,axiom,((semiri8010041392384452111omplex = (^ [A:nat]: (if_complex @ (A = zero_zero_nat) @ zero_zero_complex @ (produc1917071388513777916omplex @ (^ [B:nat,C:nat]: (if_complex @ (C = zero_zero_nat) @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (semiri8010041392384452111omplex @ B)) @ (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (semiri8010041392384452111omplex @ B)) @ one_one_complex))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7523_of__nat__code__if)). 185.47/93.69 thf(18406,plain,(((semiri8010041392384452111omplex) = (^ [A:nat]: (if_complex @ (A = zero_zero_nat) @ zero_zero_complex @ (produc1917071388513777916omplex @ (^ [B:nat,C:nat]: (if_complex @ (C = zero_zero_nat) @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (semiri8010041392384452111omplex @ B)) @ (plus_plus_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (semiri8010041392384452111omplex @ B)) @ one_one_complex))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3233])). 185.47/93.69 thf(6930,axiom,((! [A:$o]: ((semiri1316708129612266289at_nat @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n2687167440665602831ol_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6997_of__nat__of__bool)). 185.47/93.69 thf(31231,plain,((! [A:$o]: ((semiri1316708129612266289at_nat @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n2687167440665602831ol_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6930])). 185.47/93.69 thf(1058,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7261_nat__leq__as__int)). 185.47/93.69 thf(11330,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058])). 185.47/93.69 thf(20,axiom,((! [A:(nat > real),B:(nat > real),C:nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) @ (A @ D) @ (B @ D))) @ (set_ord_lessThan_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) @ (set_ord_lessThan_nat @ C)) @ (groups6591440286371151544t_real @ (^ [D:nat]: (B @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) @ one_one_nat))) @ (set_ord_lessThan_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7629_sum__split__even__odd)). 185.47/93.69 thf(7791,plain,((! [A:(nat > real),B:(nat > real),C:nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) @ (A @ D) @ (B @ D))) @ (set_ord_lessThan_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) = (plus_plus_real @ (groups6591440286371151544t_real @ (^ [D:nat]: (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) @ (set_ord_lessThan_nat @ C)) @ (groups6591440286371151544t_real @ (^ [D:nat]: (B @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) @ one_one_nat))) @ (set_ord_lessThan_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 185.47/93.69 thf(724,axiom,((! [A:real,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (gbinomial_real @ A @ C) @ (minus_minus_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ C)))) @ (set_ord_atMost_nat @ B)) = (times_times_real @ (divide_divide_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ B) @ one_one_real) @ (numeral_numeral_real @ (bit0 @ one))) @ (gbinomial_real @ A @ (plus_plus_nat @ B @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8620_gbinomial__partial__row__sum)). 185.47/93.69 thf(10146,plain,((! [A:real,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (gbinomial_real @ A @ C) @ (minus_minus_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one))) @ (semiri5074537144036343181t_real @ C)))) @ (set_ord_atMost_nat @ B)) = (times_times_real @ (divide_divide_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ B) @ one_one_real) @ (numeral_numeral_real @ (bit0 @ one))) @ (gbinomial_real @ A @ (plus_plus_nat @ B @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[724])). 185.47/93.69 thf(6746,axiom,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (((ord_less_eq_real @ zero_zero_real @ B) => (A = B)) <= (ord_less_eq_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2937_power2__eq__imp__eq)). 185.47/93.69 thf(30544,plain,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (((ord_less_eq_real @ zero_zero_real @ B) => (A = B)) | ~ (ord_less_eq_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6746])). 185.47/93.69 thf(794,axiom,((! [A:real]: ((sin_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (sin_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7801_sin__periodic)). 185.47/93.69 thf(10440,plain,((! [A:real]: ((sin_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (sin_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[794])). 185.47/93.69 thf(4344,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((((plus_plus_real @ B @ (times_times_real @ A @ D)) != (plus_plus_real @ C @ (times_times_real @ A @ E))) <= ((D != E) & (B = C))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5011_add__scale__eq__noteq)). 185.47/93.69 thf(21913,plain,((! [A:real,B:real,C:real,D:real,E:real]: (~ ((plus_plus_real @ B @ (times_times_real @ A @ D)) = (plus_plus_real @ C @ (times_times_real @ A @ E))) | ~ (~ (D = E) & (B = C)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4344])). 185.47/93.69 thf(3574,axiom,((! [A:nat,B:nat]: (dvd_dvd_rat @ (times_times_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ B)) @ (semiri773545260158071498ct_rat @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8019_fact__fact__dvd__fact)). 185.47/93.69 thf(19476,plain,((! [A:nat,B:nat]: (dvd_dvd_rat @ (times_times_rat @ (semiri773545260158071498ct_rat @ A) @ (semiri773545260158071498ct_rat @ B)) @ (semiri773545260158071498ct_rat @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3574])). 185.47/93.69 thf(6112,axiom,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ (root @ A @ B)) = (ord_less_real @ zero_zero_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9166_real__root__gt__0__iff)). 185.47/93.69 thf(28256,plain,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ (root @ A @ B)) = (ord_less_real @ zero_zero_real @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6112])). 185.47/93.69 thf(918,axiom,((! [A:real,B:real]: ((((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) => ((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_real @ (tan_real @ A) @ (tan_real @ B)) = (ord_less_real @ A @ B)))) <= (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8059_tan__mono__lt__eq)). 185.47/93.69 thf(10877,plain,((! [A:real,B:real]: (((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) => ((ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((ord_less_real @ (tan_real @ A) @ (tan_real @ B)) = (ord_less_real @ A @ B)))) | ~ (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[918])). 185.47/93.69 thf(2033,axiom,((! [A:rat]: (ord_less_eq_rat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3809_order__refl)). 185.47/93.69 thf(14528,plain,((! [A:rat]: (ord_less_eq_rat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033])). 185.47/93.69 thf(6575,axiom,((! [A:rat,B:rat]: ((minus_minus_rat @ (uminus_uminus_rat @ A) @ B) = (minus_minus_rat @ (uminus_uminus_rat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5573_minus__diff__commute)). 185.47/93.69 thf(29924,plain,((! [A:rat,B:rat]: ((minus_minus_rat @ (uminus_uminus_rat @ A) @ B) = (minus_minus_rat @ (uminus_uminus_rat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6575])). 185.47/93.69 thf(5156,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ C) => (((divide_divide_nat @ B @ A) = (divide_divide_nat @ C @ A)) = (B = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4666_dvd__div__eq__iff)). 185.47/93.69 thf(24737,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ C) => (((divide_divide_nat @ B @ A) = (divide_divide_nat @ C @ A)) = (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5156])). 185.47/93.69 thf(4425,axiom,((! [A:rat]: ((plus_plus_rat @ A @ zero_zero_rat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3108_verit__sum__simplify)). 185.47/93.69 thf(22162,plain,((! [A:rat]: ((plus_plus_rat @ A @ zero_zero_rat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4425])). 185.47/93.69 thf(7331,axiom,((! [A:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real) = ((abs_abs_real @ A) = one_one_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6688_abs__square__eq__1)). 185.47/93.69 thf(32709,plain,((! [A:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real) = ((abs_abs_real @ A) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7331])). 185.47/93.69 thf(1972,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ A)) = (divide1717551699836669952omplex @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5762_nonzero__minus__divide__divide)). 185.47/93.69 thf(14330,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ A)) = (divide1717551699836669952omplex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1972])). 185.47/93.69 thf(5529,axiom,((! [A:product_prod_nat_nat]: ~ (! [B:nat,C:nat]: (A != (product_Pair_nat_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3433_old_Oprod_Oexhaust)). 185.47/93.69 thf(26144,plain,((! [A:product_prod_nat_nat]: ~ (! [B:nat,C:nat]: ~ (A = (product_Pair_nat_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5529])). 185.47/93.69 thf(7576,axiom,((! [A:int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1870_zero__eq__power2)). 185.47/93.69 thf(33506,plain,((! [A:int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7576])). 185.47/93.69 thf(5097,axiom,(((^ [A:rat]: (zero_zero_rat)) = (times_times_rat @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2148_lambda__zero)). 185.47/93.69 thf(24481,plain,(((^ [A:rat]: (zero_zero_rat)) = (times_times_rat @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5097])). 185.47/93.69 thf(6618,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_mint @ A) = (some_nat @ C)) <= (vEBT_VEBT_min_in_set @ (vEBT_VEBT_set_vebt @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_950_mint__sound)). 185.47/93.69 thf(30065,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_mint @ A) = (some_nat @ C)) | ~ (vEBT_VEBT_min_in_set @ (vEBT_VEBT_set_vebt @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6618])). 185.47/93.69 thf(2122,axiom,((! [A:int,B:int]: ((~ (! [C:int]: (B != (times_times_int @ A @ C)))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4624_dvdE)). 185.47/93.69 thf(14796,plain,((! [A:int,B:int]: (~ (! [C:int]: ~ (B = (times_times_int @ A @ C))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2122])). 185.47/93.69 thf(5593,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ (suc @ D) @ (suc @ E)) <= (A @ D @ E))) => (A @ B @ C))) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2105_diff__induct)). 185.47/93.69 thf(26344,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ (suc @ D) @ (suc @ E)) | ~ (A @ D @ E))) => (A @ B @ C))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5593])). 185.47/93.69 thf(6082,axiom,((! [A:rat,B:rat]: (((uminus_uminus_rat @ A) = B) = ((uminus_uminus_rat @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5494_minus__equation__iff)). 185.47/93.69 thf(28142,plain,((! [A:rat,B:rat]: (((uminus_uminus_rat @ A) = B) = ((uminus_uminus_rat @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6082])). 185.47/93.69 thf(5320,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_Nat_Oadd__diff__assoc)). 185.47/93.69 thf(25306,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5320])). 185.47/93.69 thf(4310,axiom,((! [A:set_nat]: ((? [B:nat]: (member_nat @ B @ A)) = (A != bot_bot_set_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1376_ex__in__conv)). 185.47/93.69 thf(21773,plain,((! [A:set_nat]: ((? [B:nat]: (member_nat @ B @ A)) = (~ (A = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4310])). 185.47/93.69 thf(4356,axiom,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (divide_divide_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ one_one_rat @ one_one_rat))) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_857_less__half__sum)). 185.47/93.69 thf(21956,plain,((! [A:rat,B:rat]: ((ord_less_rat @ A @ (divide_divide_rat @ (plus_plus_rat @ A @ B) @ (plus_plus_rat @ one_one_rat @ one_one_rat))) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4356])). 185.47/93.69 thf(5256,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3137_int__distrib_I3_J)). 185.47/93.69 thf(25072,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (minus_minus_int @ A @ B) @ C) = (minus_minus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5256])). 185.47/93.69 thf(5063,axiom,((! [A:real]: ((power_power_real @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_power__one__right)). 185.47/93.69 thf(24383,plain,((! [A:real]: ((power_power_real @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5063])). 185.47/93.69 thf(6211,axiom,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_four__x__squared)). 185.47/93.69 thf(28635,plain,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6211])). 185.47/93.69 thf(7348,axiom,((! [A:int,B:int,C:nat]: (((times_times_int @ A @ B) = one_one_int) => ((times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_842_left__right__inverse__power)). 185.47/93.69 thf(32761,plain,((! [A:int,B:int,C:nat]: (((times_times_int @ A @ B) = one_one_int) => ((times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7348])). 185.47/93.69 thf(7137,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) => (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4157_leI)). 185.47/93.69 thf(32029,plain,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) => (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7137])). 185.47/93.69 thf(638,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (arctan @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6784_zero__le__arctan__iff)). 185.47/93.69 thf(9848,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (arctan @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[638])). 185.47/93.69 thf(1948,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat) <= (ord_less_eq_rat @ B @ zero_zero_rat)) <= (ord_less_eq_rat @ A @ zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2288_add__nonpos__nonpos)). 185.47/93.69 thf(14251,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (plus_plus_rat @ A @ B) @ zero_zero_rat) | ~ (ord_less_eq_rat @ B @ zero_zero_rat) | ~ (ord_less_eq_rat @ A @ zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1948])). 185.47/93.69 thf(3899,axiom,((! [A:nat,B:nat,C:(nat > int),D:nat]: (((groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_int @ (groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D))))) <= (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6695_sum_Oub__add__nat)). 185.47/93.69 thf(20512,plain,((! [A:nat,B:nat,C:(nat > int),D:nat]: (((groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_int @ (groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D))))) | ~ (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3899])). 185.47/93.69 thf(3133,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4291_order__less__imp__le)). 185.47/93.69 thf(18093,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3133])). 185.47/93.69 thf(6212,axiom,((! [A:int]: ((minus_minus_int @ A @ A) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1545_cancel__comm__monoid__add__class_Odiff__cancel)). 185.47/93.69 thf(28638,plain,((! [A:int]: ((minus_minus_int @ A @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6212])). 185.47/93.69 thf(340,axiom,((! [A:int,B:int]: (((ord_max_int @ A @ B) = B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3581_max_Oabsorb4)). 185.47/93.69 thf(8876,plain,((! [A:int,B:int]: (((ord_max_int @ A @ B) = B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])). 185.47/93.69 thf(2449,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ (^ [B:nat]: (if_rat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri681578069525770553at_rat @ (binomial @ A @ B)) @ zero_zero_rat)) @ (set_ord_atMost_nat @ A))) = (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8627_choose__odd__sum)). 185.47/93.69 thf(15840,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ (groups2906978787729119204at_rat @ (^ [B:nat]: (if_rat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri681578069525770553at_rat @ (binomial @ A @ B)) @ zero_zero_rat)) @ (set_ord_atMost_nat @ A))) = (power_power_rat @ (numeral_numeral_rat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2449])). 185.47/93.69 thf(5135,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2032_not__less__zero)). 185.47/93.69 thf(24660,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5135])). 185.47/93.69 thf(1812,axiom,((ord_less_real @ (uminus_uminus_real @ one_one_real) @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5748_less__minus__one__simps_I2_J)). 185.47/93.69 thf(13802,plain,((ord_less_real @ (uminus_uminus_real @ one_one_real) @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1812])). 185.47/93.69 thf(3047,axiom,((! [A:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5196_mult__minus1__right)). 185.47/93.69 thf(17821,plain,((! [A:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3047])). 185.47/93.69 thf(3955,axiom,((! [A:real,B:real,C:real]: ((divide_divide_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_add__divide__distrib)). 185.47/93.69 thf(20700,plain,((! [A:real,B:real,C:real]: ((divide_divide_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3955])). 185.47/93.69 thf(6371,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) => ((divide_divide_nat @ C @ (times_times_nat @ A @ B)) = (divide_divide_nat @ (divide_divide_nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4760_dvd__div__mult2__eq)). 185.47/93.69 thf(29186,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) => ((divide_divide_nat @ C @ (times_times_nat @ A @ B)) = (divide_divide_nat @ (divide_divide_nat @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6371])). 185.47/93.69 thf(636,axiom,((! [A:(nat > real),B:(nat > real),C:set_nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (A @ D) @ (B @ D))) @ C) = (minus_minus_real @ (groups6591440286371151544t_real @ A @ C) @ (groups6591440286371151544t_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5625_sum__subtractf)). 185.47/93.69 thf(9842,plain,((! [A:(nat > real),B:(nat > real),C:set_nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (A @ D) @ (B @ D))) @ C) = (minus_minus_real @ (groups6591440286371151544t_real @ (A) @ C) @ (groups6591440286371151544t_real @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[636])). 185.47/93.69 thf(1614,axiom,((! [A:num]: ((~ (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)))) = (A != one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5376_not__neg__one__le__neg__numeral__iff)). 185.47/93.69 thf(13092,plain,((! [A:num]: ((~ (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)))) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614])). 185.47/93.69 thf(1483,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4290_linorder__not__less)). 185.47/93.69 thf(12669,plain,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483])). 185.47/93.69 thf(1064,axiom,((! [A:nat]: ((ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ zero_zero_rat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7010_of__nat__le__0__iff)). 185.47/93.69 thf(11345,plain,((! [A:nat]: ((ord_less_eq_rat @ (semiri681578069525770553at_rat @ A) @ zero_zero_rat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064])). 185.47/93.69 thf(1474,axiom,((! [A:complex,B:complex,C:complex,D:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ C @ D))) @ (plus_plus_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ C)) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7515_norm__diff__triangle__ineq)). 185.47/93.69 thf(12643,plain,((! [A:complex,B:complex,C:complex,D:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ C @ D))) @ (plus_plus_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ C)) @ (real_V1022390504157884413omplex @ (minus_minus_complex @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474])). 185.47/93.69 thf(2999,axiom,((! [A:real,B:real,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (dvd_dvd_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ D))) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4798_dvd__power__le)). 185.47/93.69 thf(17673,plain,((! [A:real,B:real,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (dvd_dvd_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ D))) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2999])). 185.47/93.69 thf(178,axiom,((! [A:real]: ((times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ A)) = (complex2 @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9145_i__complex__of__real)). 185.47/93.69 thf(8305,plain,((! [A:real]: ((times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ A)) = (complex2 @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 185.47/93.69 thf(5925,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1096_less__add__Suc1)). 185.47/93.69 thf(27616,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5925])). 185.47/93.69 thf(354,axiom,((ord_less_real @ (ln_ln_real @ (numeral_numeral_real @ (bit0 @ one))) @ one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6305_ln__2__less__1)). 185.47/93.69 thf(8918,plain,((ord_less_real @ (ln_ln_real @ (numeral_numeral_real @ (bit0 @ one))) @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 185.47/93.69 thf(2276,axiom,((! [A:nat,B:real]: (((gbinomial_real @ B @ A) = (times_times_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A)) @ (gbinomial_real @ (minus_minus_real @ B @ one_one_real) @ (minus_minus_nat @ A @ one_one_nat)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8599_gbinomial__absorption_H)). 185.47/93.69 thf(15287,plain,((! [A:nat,B:real]: (((gbinomial_real @ B @ A) = (times_times_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A)) @ (gbinomial_real @ (minus_minus_real @ B @ one_one_real) @ (minus_minus_nat @ A @ one_one_nat)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2276])). 185.47/93.69 thf(4683,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ one_one_rat) => (((ord_less_eq_rat @ B @ one_one_rat) => (ord_less_eq_rat @ (times_times_rat @ A @ B) @ one_one_rat)) <= (ord_less_eq_rat @ zero_zero_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2666_mult__le__one)). 185.47/93.69 thf(23010,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ one_one_rat) => (((ord_less_eq_rat @ B @ one_one_rat) => (ord_less_eq_rat @ (times_times_rat @ A @ B) @ one_one_rat)) | ~ (ord_less_eq_rat @ zero_zero_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4683])). 185.47/93.69 thf(3295,axiom,((! [A:real,B:real]: ((times_times_real @ (cos_real @ A) @ (sin_real @ B)) = (divide_divide_real @ (minus_minus_real @ (sin_real @ (plus_plus_real @ A @ B)) @ (sin_real @ (minus_minus_real @ A @ B))) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7853_cos__times__sin)). 185.47/93.69 thf(18587,plain,((! [A:real,B:real]: ((times_times_real @ (cos_real @ A) @ (sin_real @ B)) = (divide_divide_real @ (minus_minus_real @ (sin_real @ (plus_plus_real @ A @ B)) @ (sin_real @ (minus_minus_real @ A @ B))) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3295])). 185.47/93.69 thf(4104,axiom,((! [A:rat,B:nat]: ((abs_abs_rat @ (power_power_rat @ (uminus_uminus_rat @ A) @ B)) = (abs_abs_rat @ (power_power_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6385_abs__power__minus)). 185.47/93.69 thf(21153,plain,((! [A:rat,B:nat]: ((abs_abs_rat @ (power_power_rat @ (uminus_uminus_rat @ A) @ B)) = (abs_abs_rat @ (power_power_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4104])). 185.47/93.69 thf(1307,axiom,((! [A:complex,B:nat]: ((times_times_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ (comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ A) @ B)) = (times_times_complex @ A @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ one_one_complex) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8568_pochhammer__absorb__comp)). 185.47/93.69 thf(12085,plain,((! [A:complex,B:nat]: ((times_times_complex @ (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ (comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ A) @ B)) = (times_times_complex @ A @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ one_one_complex) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307])). 185.47/93.69 thf(1146,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1617_le__add__same__cancel2)). 185.47/93.69 thf(11616,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146])). 185.47/93.69 thf(5759,axiom,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_mult__1)). 185.47/93.69 thf(26888,plain,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5759])). 185.47/93.69 thf(6567,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: (((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) <= ((some_nat @ C) = (vEBT_vebt_mint @ A))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_943_misiz)). 185.47/93.69 thf(29892,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ ((some_nat @ C) = (vEBT_vebt_mint @ A)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6567])). 185.47/93.69 thf(6928,axiom,((! [A:real]: (((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6264_square__le__1)). 185.47/93.69 thf(31226,plain,((! [A:real]: ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) | ~ (ord_less_eq_real @ A @ one_one_real) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6928])). 185.47/93.69 thf(1819,axiom,((! [A:nat]: ((abs_abs_int @ (semiri1314217659103216013at_int @ A)) = (semiri1314217659103216013at_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6873_abs__of__nat)). 185.47/93.69 thf(13824,plain,((! [A:nat]: ((abs_abs_int @ (semiri1314217659103216013at_int @ A)) = (semiri1314217659103216013at_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1819])). 185.47/93.69 thf(4501,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2291_add__nonneg__nonneg)). 185.47/93.69 thf(22405,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4501])). 185.47/93.69 thf(3514,axiom,((! [A:(rat > (rat > $o)),B:rat]: ((A @ (abs_abs_rat @ B) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) <= (! [C:rat]: ((A @ C @ (power_power_rat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) <= (ord_less_eq_rat @ zero_zero_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6708_abs__sqrt__wlog)). 185.47/93.69 thf(19298,plain,((! [A:(rat > (rat > $o)),B:rat]: ((A @ (abs_abs_rat @ B) @ (power_power_rat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (! [C:rat]: ((A @ C @ (power_power_rat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (ord_less_eq_rat @ zero_zero_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3514])). 185.47/93.69 thf(5399,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (vEBT_VEBT_greater @ (some_nat @ B) @ (some_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_greater__shift)). 185.47/93.69 thf(25593,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (vEBT_VEBT_greater @ (some_nat @ B) @ (some_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5399])). 185.47/93.69 thf(7709,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4516_even__mult__iff)). 185.47/93.69 thf(33867,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7709])). 185.47/93.69 thf(6405,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1517_add__cancel__left__left)). 185.47/93.69 thf(29327,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6405])). 185.47/93.69 thf(7669,axiom,((! [A:code_integer]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5401_power2__minus)). 185.47/93.69 thf(33758,plain,((! [A:code_integer]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7669])). 185.47/93.69 thf(5538,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_real @ (times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ B @ A))) @ (semiri2265585572941072030t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8035_choose__dvd)). 185.47/93.69 thf(26180,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_real @ (times_times_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ B @ A))) @ (semiri2265585572941072030t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5538])). 185.47/93.69 thf(7544,axiom,(((inc @ one) = (bit0 @ one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9377_inc_Osimps_I1_J)). 185.47/93.69 thf(33418,plain,(((inc @ one) = (bit0 @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7544])). 185.47/93.69 thf(5129,axiom,((! [A:num]: ((bit_or_not_num_neg @ (bit1 @ A) @ one) = one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9465_or__not__num__neg_Osimps_I7_J)). 185.47/93.69 thf(24612,plain,((! [A:num]: ((bit_or_not_num_neg @ (bit1 @ A) @ one) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5129])). 185.47/93.69 thf(6676,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4301_order__le__neq__trans)). 185.47/93.69 thf(30254,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6676])). 185.47/93.69 thf(5919,axiom,((! [A:nat]: ((bit_se1412395901928357646or_nat @ A @ (suc @ zero_zero_nat)) = (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9480_or__Suc__0__eq)). 185.47/93.69 thf(27597,plain,((! [A:nat]: ((bit_se1412395901928357646or_nat @ A @ (suc @ zero_zero_nat)) = (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5919])). 185.47/93.69 thf(2212,axiom,((! [A:int]: (((modulo_modulo_int @ (uminus_uminus_int @ one_one_int) @ A) = (minus_minus_int @ A @ one_one_int)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6243_zmod__minus1)). 185.47/93.69 thf(15096,plain,((! [A:int]: (((modulo_modulo_int @ (uminus_uminus_int @ one_one_int) @ A) = (minus_minus_int @ A @ one_one_int)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2212])). 185.47/93.69 thf(2936,axiom,((! [A:rat,B:rat]: ~ (ord_less_rat @ (plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B)) @ zero_zero_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2686_not__sum__squares__lt__zero)). 185.47/93.69 thf(17469,plain,((! [A:rat,B:rat]: ~ (ord_less_rat @ (plus_plus_rat @ (times_times_rat @ A @ A) @ (times_times_rat @ B @ B)) @ zero_zero_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2936])). 185.47/93.69 thf(1324,axiom,((! [A:rat,B:rat]: (((ord_less_eq_rat @ (times_times_rat @ A @ B) @ zero_zero_rat) <= (ord_less_eq_rat @ B @ zero_zero_rat)) <= (ord_less_eq_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2214_mult__nonneg__nonpos)). 185.47/93.69 thf(12144,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (times_times_rat @ A @ B) @ zero_zero_rat) | ~ (ord_less_eq_rat @ B @ zero_zero_rat) | ~ (ord_less_eq_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324])). 185.47/93.69 thf(7653,axiom,(((plus_plus_num @ one @ one) = (bit0 @ one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_semiring__norm_I2_J)). 185.47/93.69 thf(33716,plain,(((plus_plus_num @ one @ one) = (bit0 @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7653])). 185.47/93.69 thf(2744,axiom,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5899_neg__numeral__less__zero)). 185.47/93.69 thf(16856,plain,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2744])). 185.47/93.69 thf(5469,axiom,((! [A:rat,B:rat,C:rat]: (((A = zero_zero_rat) => ((minus_minus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (uminus_uminus_rat @ C))) & ((A != zero_zero_rat) => ((minus_minus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (divide_divide_rat @ (minus_minus_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6176_add__divide__eq__if__simps_I6_J)). 185.47/93.69 thf(25851,plain,((! [A:rat,B:rat,C:rat]: (((A = zero_zero_rat) => ((minus_minus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (uminus_uminus_rat @ C))) & ((~ (A = zero_zero_rat)) => ((minus_minus_rat @ (uminus_uminus_rat @ (divide_divide_rat @ B @ A)) @ C) = (divide_divide_rat @ (minus_minus_rat @ (uminus_uminus_rat @ B) @ (times_times_rat @ C @ A)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5469])). 185.47/93.69 thf(7231,axiom,((! [A:nat,B:real]: (((times_times_real @ (sgn_sgn_real @ (root @ A @ B)) @ (power_power_real @ (abs_abs_real @ (root @ A @ B)) @ A)) = B) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9340_sgn__power__root)). 185.47/93.69 thf(32374,plain,((! [A:nat,B:real]: (((times_times_real @ (sgn_sgn_real @ (root @ A @ B)) @ (power_power_real @ (abs_abs_real @ (root @ A @ B)) @ A)) = B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7231])). 185.47/93.69 thf(1289,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((A != B) & (C != D)) = ((plus_plus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)) != (plus_plus_rat @ (times_times_rat @ A @ D) @ (times_times_rat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6290_crossproduct__noteq)). 185.47/93.69 thf(12035,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((~ (A = B) & ~ (C = D)) = (~ ((plus_plus_rat @ (times_times_rat @ A @ C) @ (times_times_rat @ B @ D)) = (plus_plus_rat @ (times_times_rat @ A @ D) @ (times_times_rat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289])). 185.47/93.69 thf(6598,axiom,((! [A:complex,B:nat]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ B) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5995_power__minus)). 185.47/93.69 thf(29999,plain,((! [A:complex,B:nat]: ((power_power_complex @ (uminus1482373934393186551omplex @ A) @ B) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (power_power_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6598])). 185.47/93.69 thf(7485,axiom,((! [A:vEBT_VEBT,B:nat]: (((! [C:nat,D:nat]: ((? [E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F))) => (~ ((B = D) | (B = C))))) => ((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: ((~ ((((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) | (B = D) | (B = C))) <= (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G))))) => (~ (! [C:nat,D:list_VEBT_VEBT]: ((? [E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E))) => (~ (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))))))))) <= (vEBT_VEBT_membermima @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1455_VEBT__internal_Omembermima_Oelims_I2_J)). 185.47/93.69 thf(33225,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:nat,D:nat]: ((? [E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F))) => (~ ((B = D) | (B = C))))) => ((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: (~ ((((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F))) | (B = D) | (B = C)) | ~ (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G))))) => (~ (! [C:nat,D:list_VEBT_VEBT]: ((? [E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E))) => (~ (((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))))))))) | ~ (vEBT_VEBT_membermima @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7485])). 185.47/93.69 thf(1780,axiom,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D)) = (plus_plus_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_712_add__diff__add)). 185.47/93.69 thf(13697,plain,((! [A:real,B:real,C:real,D:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ D)) = (plus_plus_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780])). 185.47/93.69 thf(5915,axiom,((! [A:nat]: ((groups3542108847815614940at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) = (divide_divide_nat @ (times_times_nat @ A @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6755_gauss__sum__nat)). 185.47/93.69 thf(27584,plain,((! [A:nat]: ((groups3542108847815614940at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) = (divide_divide_nat @ (times_times_nat @ A @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5915])). 185.47/93.69 thf(6402,axiom,((! [A:num,B:nat,C:int]: (((power_power_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ B) = (ring_17405671764205052669omplex @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7149_neg__numeral__power__eq__of__int__cancel__iff)). 185.47/93.69 thf(29287,plain,((! [A:num,B:nat,C:int]: (((power_power_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ B) = (ring_17405671764205052669omplex @ C)) = ((power_power_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6402])). 185.47/93.69 thf(7319,axiom,((bit_se6528837805403552850or_nat = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ B @ (if_nat @ (B = zero_zero_nat) @ A @ (plus_plus_nat @ (modulo_modulo_nat @ (plus_plus_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (numeral_numeral_nat @ (bit0 @ one))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se6528837805403552850or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9482_xor__nat__unfold)). 185.47/93.69 thf(32665,plain,(((bit_se6528837805403552850or_nat) = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ B @ (if_nat @ (B = zero_zero_nat) @ A @ (plus_plus_nat @ (modulo_modulo_nat @ (plus_plus_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (numeral_numeral_nat @ (bit0 @ one))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se6528837805403552850or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7319])). 185.47/93.69 thf(6199,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4231_dual__order_Oorder__iff__strict)). 185.47/93.69 thf(28603,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6199])). 185.47/93.69 thf(3480,axiom,((! [A:rat,B:rat]: ((~ (ord_less_eq_rat @ A @ B)) => (ord_less_eq_rat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3958_linorder__le__cases)). 185.47/93.69 thf(19188,plain,((! [A:rat,B:rat]: ((~ (ord_less_eq_rat @ A @ B)) => (ord_less_eq_rat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3480])). 185.47/93.69 thf(1893,axiom,((! [A:int,B:int]: (((abs_abs_int @ A) = B) = (((A = (uminus_uminus_int @ B)) | (A = B)) & (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6557_abs__eq__iff_H)). 185.47/93.69 thf(14062,plain,((! [A:int,B:int]: (((abs_abs_int @ A) = B) = (((A = (uminus_uminus_int @ B)) | (A = B)) & (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1893])). 185.47/93.69 thf(1510,axiom,((! [A:int,B:int,C:int,D:int]: ((minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (plus_plus_int @ (times_times_int @ A @ (minus_minus_int @ B @ D)) @ (times_times_int @ (minus_minus_int @ A @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_806_mult__diff__mult)). 185.47/93.69 thf(12749,plain,((! [A:int,B:int,C:int,D:int]: ((minus_minus_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ D)) = (plus_plus_int @ (times_times_int @ A @ (minus_minus_int @ B @ D)) @ (times_times_int @ (minus_minus_int @ A @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510])). 185.47/93.69 thf(6563,axiom,((! [A:rat,B:nat]: ((times_times_rat @ (power_power_rat @ A @ B) @ A) = (times_times_rat @ A @ (power_power_rat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_power__commutes)). 185.47/93.69 thf(29881,plain,((! [A:rat,B:nat]: ((times_times_rat @ (power_power_rat @ A @ B) @ A) = (times_times_rat @ A @ (power_power_rat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6563])). 185.47/93.69 thf(5245,axiom,((! [A:rat,B:rat,C:rat]: (((times_times_rat @ A @ B) = (times_times_rat @ C @ B)) = ((B = zero_zero_rat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1503_mult__cancel__right)). 185.47/93.69 thf(25026,plain,((! [A:rat,B:rat,C:rat]: (((times_times_rat @ A @ B) = (times_times_rat @ C @ B)) = ((B = zero_zero_rat) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5245])). 185.47/93.69 thf(3968,axiom,((! [A:num]: ((bitM @ (inc @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9385_BitM__inc__eq)). 185.47/93.69 thf(20737,plain,((! [A:num]: ((bitM @ (inc @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3968])). 185.47/93.69 thf(553,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ B @ (powr_real @ A @ C)) = (ord_less_real @ (log @ A @ B) @ C))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9109_less__powr__iff)). 185.47/93.69 thf(9568,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ B @ (powr_real @ A @ C)) = (ord_less_real @ (log @ A @ B) @ C))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[553])). 185.47/93.69 thf(4812,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1142_distrib__right)). 185.47/93.69 thf(23456,plain,((! [A:int,B:int,C:int]: ((times_times_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4812])). 185.47/93.69 thf(5704,axiom,((! [A:num]: ((abs_abs_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6335_abs__numeral)). 185.47/93.69 thf(26706,plain,((! [A:num]: ((abs_abs_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5704])). 185.47/93.69 thf(4327,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)) <= (ord_less_eq_rat @ C @ D)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_add__less__le__mono)). 185.47/93.69 thf(21864,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D)) | ~ (ord_less_eq_rat @ C @ D) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4327])). 185.47/93.69 thf(5652,axiom,((! [A:nat]: ((minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat) = (groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6744_mask__eq__sum__exp)). 185.47/93.69 thf(26539,plain,((! [A:nat]: ((minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat) = (groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one))) @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5652])). 185.47/93.69 thf(1727,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => ((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (times_times_complex @ B @ A) @ C) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2732_add__divide__eq__iff)). 185.47/93.69 thf(13524,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => ((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (times_times_complex @ B @ A) @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727])). 185.47/93.69 thf(2181,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2400_add__pos__pos)). 185.47/93.69 thf(15003,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2181])). 185.47/93.69 thf(51,axiom,((! [A:(nat > real),B:real]: ((summable_real @ A) => ((! [C:nat]: (ord_less_eq_real @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ C)) @ B)) => (ord_less_eq_real @ (suminf_real @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7718_suminf__le__const)). 185.47/93.69 thf(7900,plain,((! [A:(nat > real),B:real]: ((summable_real @ (A)) => ((! [C:nat]: (ord_less_eq_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ C)) @ B)) => (ord_less_eq_real @ (suminf_real @ (A)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 185.47/93.69 thf(6113,axiom,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (times_times_rat @ A @ B) @ C) = (times_times_rat @ A @ (times_times_rat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_ab__semigroup__mult__class_Omult__ac_I1_J)). 185.47/93.69 thf(28260,plain,((! [A:rat,B:rat,C:rat]: ((times_times_rat @ (times_times_rat @ A @ B) @ C) = (times_times_rat @ A @ (times_times_rat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6113])). 185.47/93.69 thf(644,axiom,((! [A:real,B:real]: (((((tan_real @ (plus_plus_real @ A @ B)) = (divide_divide_real @ (plus_plus_real @ (tan_real @ A) @ (tan_real @ B)) @ (minus_minus_real @ one_one_real @ (times_times_real @ (tan_real @ A) @ (tan_real @ B))))) <= ((cos_real @ (plus_plus_real @ A @ B)) != zero_zero_real)) <= ((cos_real @ B) != zero_zero_real)) <= ((cos_real @ A) != zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8085_tan__add)). 185.47/93.69 thf(9870,plain,((! [A:real,B:real]: (((tan_real @ (plus_plus_real @ A @ B)) = (divide_divide_real @ (plus_plus_real @ (tan_real @ A) @ (tan_real @ B)) @ (minus_minus_real @ one_one_real @ (times_times_real @ (tan_real @ A) @ (tan_real @ B))))) | ((cos_real @ (plus_plus_real @ A @ B)) = zero_zero_real) | ((cos_real @ B) = zero_zero_real) | ((cos_real @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[644])). 185.47/93.69 thf(871,axiom,((! [A:real,B:real,C:real]: (((A != one_one_real) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ zero_zero_real @ C) => ((log @ A @ (divide_divide_real @ B @ C)) = (minus_minus_real @ (log @ A @ B) @ (log @ A @ C)))))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9046_log__divide)). 185.47/93.69 thf(10706,plain,((! [A:real,B:real,C:real]: (((~ (A = one_one_real)) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ zero_zero_real @ C) => ((log @ A @ (divide_divide_real @ B @ C)) = (minus_minus_real @ (log @ A @ B) @ (log @ A @ C)))))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[871])). 185.47/93.69 thf(778,axiom,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C)))) = (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7701_summable__powser__split__head)). 185.47/93.69 thf(10389,plain,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C)))) = (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[778])). 185.47/93.69 thf(3731,axiom,((! [A:rat,B:rat,C:rat,D:rat]: ((minus_minus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ D)) = (plus_plus_rat @ (times_times_rat @ A @ (minus_minus_rat @ B @ D)) @ (times_times_rat @ (minus_minus_rat @ A @ C) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_805_mult__diff__mult)). 185.47/93.69 thf(19982,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((minus_minus_rat @ (times_times_rat @ A @ B) @ (times_times_rat @ C @ D)) = (plus_plus_rat @ (times_times_rat @ A @ (minus_minus_rat @ B @ D)) @ (times_times_rat @ (minus_minus_rat @ A @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3731])). 185.47/93.69 thf(6656,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_ab__semigroup__mult__class_Omult__ac_I1_J)). 185.47/93.69 thf(30187,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6656])). 185.47/93.69 thf(635,axiom,((! [A:real,B:real,C:real]: (((A != one_one_real) => (((minus_minus_real @ (log @ A @ B) @ C) = (log @ A @ (times_times_real @ B @ (powr_real @ A @ (uminus_uminus_real @ C))))) <= (ord_less_real @ zero_zero_real @ B))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9129_log__minus__eq__powr)). 185.47/93.69 thf(9838,plain,((! [A:real,B:real,C:real]: (((~ (A = one_one_real)) => (((minus_minus_real @ (log @ A @ B) @ C) = (log @ A @ (times_times_real @ B @ (powr_real @ A @ (uminus_uminus_real @ C))))) | ~ (ord_less_real @ zero_zero_real @ B))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[635])). 185.47/93.69 thf(2984,axiom,((! [A:int,B:int,C:(int > rat),D:rat]: ((ord_less_int @ A @ B) => ((ord_less_eq_rat @ (C @ B) @ D) => ((! [E:int,F:int]: ((ord_less_rat @ (C @ E) @ (C @ F)) <= (ord_less_int @ E @ F))) => (ord_less_rat @ (C @ A) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4360_order__less__le__subst2)). 185.47/93.69 thf(17629,plain,((! [A:int,B:int,C:(int > rat),D:rat]: ((ord_less_int @ A @ B) => ((ord_less_eq_rat @ (C @ B) @ D) => ((! [E:int,F:int]: ((ord_less_rat @ (C @ E) @ (C @ F)) | ~ (ord_less_int @ E @ F))) => (ord_less_rat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2984])). 185.47/93.69 thf(1274,axiom,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (plus_plus_rat @ A @ B)) = (plus_plus_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5568_add_Oinverse__distrib__swap)). 185.47/93.69 thf(11992,plain,((! [A:rat,B:rat]: ((uminus_uminus_rat @ (plus_plus_rat @ A @ B)) = (plus_plus_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274])). 185.47/93.69 thf(4015,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ C @ D) & (ord_less_eq_rat @ A @ B)) => (ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_add__mono__thms__linordered__field_I4_J)). 185.47/93.69 thf(20884,plain,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_rat @ C @ D) & (ord_less_eq_rat @ A @ B)) => (ord_less_rat @ (plus_plus_rat @ A @ C) @ (plus_plus_rat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4015])). 185.47/93.69 thf(2687,axiom,((! [A:real]: (ord_less_eq_real @ (cos_real @ A) @ one_one_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7832_cos__le__one)). 185.47/93.69 thf(16679,plain,((! [A:real]: (ord_less_eq_real @ (cos_real @ A) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2687])). 185.47/93.69 thf(5504,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ (power_power_nat @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1067_power__Suc2)). 185.47/93.69 thf(26062,plain,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ (power_power_nat @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5504])). 185.47/93.69 thf(4826,axiom,(((real_V7735802525324610683m_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7454_norm__one)). 185.47/93.69 thf(23503,plain,(((real_V7735802525324610683m_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4826])). 185.47/93.69 thf(665,axiom,((! [A:complex,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (gbinomial_complex @ A @ C) @ (minus_minus_complex @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ (bit0 @ one))) @ (semiri8010041392384452111omplex @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (times_times_complex @ (divide1717551699836669952omplex @ (semiri8010041392384452111omplex @ (suc @ B)) @ (numera6690914467698888265omplex @ (bit0 @ one))) @ (gbinomial_complex @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8409_gchoose__row__sum__weighted)). 185.47/93.69 thf(9954,plain,((! [A:complex,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (gbinomial_complex @ A @ C) @ (minus_minus_complex @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ (bit0 @ one))) @ (semiri8010041392384452111omplex @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (times_times_complex @ (divide1717551699836669952omplex @ (semiri8010041392384452111omplex @ (suc @ B)) @ (numera6690914467698888265omplex @ (bit0 @ one))) @ (gbinomial_complex @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[665])). 185.47/93.69 thf(1166,axiom,((ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2694_zero__less__two)). 185.47/93.69 thf(11675,plain,((ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166])). 185.47/93.69 thf(2730,axiom,((bit_se725231765392027082nd_int = (^ [A:int,B:int]: (if_int @ ((B = zero_zero_int) | (A = zero_zero_int)) @ zero_zero_int @ (if_int @ (A = (uminus_uminus_int @ one_one_int)) @ B @ (if_int @ (B = (uminus_uminus_int @ one_one_int)) @ A @ (plus_plus_int @ (times_times_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9362_and__int__unfold)). 185.47/93.69 thf(16813,plain,(((bit_se725231765392027082nd_int) = (^ [A:int,B:int]: (if_int @ ((B = zero_zero_int) | (A = zero_zero_int)) @ zero_zero_int @ (if_int @ (A = (uminus_uminus_int @ one_one_int)) @ B @ (if_int @ (B = (uminus_uminus_int @ one_one_int)) @ A @ (plus_plus_int @ (times_times_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2730])). 185.47/93.69 thf(6667,axiom,((! [A:$o,B:$o]: ((ord_less_eq_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B)) = ((B) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5109_of__bool__less__eq__iff)). 185.47/93.69 thf(30222,plain,((! [A:$o,B:$o]: ((ord_less_eq_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B)) = ((B) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6667])). 185.47/93.69 thf(3935,axiom,((zero_zero_rat = (fract @ zero_zero_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9945_Zero__rat__def)). 185.47/93.69 thf(20635,plain,((zero_zero_rat = (fract @ zero_zero_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3935])). 185.47/93.69 thf(4431,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (ord_less_real @ (sqrt @ A) @ B)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8238_real__less__lsqrt)). 185.47/93.69 thf(22183,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (ord_less_real @ (sqrt @ A) @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4431])). 185.47/93.69 thf(7260,axiom,((! [A:num]: ((ord_less_eq_num @ A @ one) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_le__num__One__iff)). 185.47/93.69 thf(32466,plain,((! [A:num]: ((ord_less_eq_num @ A @ one) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7260])). 185.47/93.69 thf(6450,axiom,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_911_power2__diff)). 185.47/93.69 thf(29483,plain,((! [A:int,B:int]: ((power_power_int @ (minus_minus_int @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_int @ (plus_plus_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6450])). 185.47/93.69 thf(6251,axiom,(((neg_nu6075765906172075777c_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit1 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6761_dbl__dec__simps_I4_J)). 185.47/93.69 thf(28761,plain,(((neg_nu6075765906172075777c_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit1 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6251])). 185.47/93.69 thf(3315,axiom,((! [A:nat,B:num]: (((semiri1314217659103216013at_int @ A) = (numeral_numeral_int @ B)) = (A = (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6871_int__eq__iff__numeral)). 185.47/93.69 thf(18655,plain,((! [A:nat,B:num]: (((semiri1314217659103216013at_int @ A) = (numeral_numeral_int @ B)) = (A = (numeral_numeral_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3315])). 185.47/93.69 thf(5964,axiom,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_mult_Oright__neutral)). 185.47/93.69 thf(27743,plain,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5964])). 185.47/93.69 thf(3782,axiom,((! [A:complex,B:complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7509_norm__diff__ineq)). 185.47/93.69 thf(20155,plain,((! [A:complex,B:complex]: (ord_less_eq_real @ (minus_minus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3782])). 185.47/93.69 thf(5496,axiom,((! [A:int]: ((times_times_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_mult__2__right)). 185.47/93.69 thf(26035,plain,((! [A:int]: ((times_times_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = (plus_plus_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5496])). 185.47/93.69 thf(5673,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3989_ord__eq__less__trans)). 185.47/93.69 thf(26612,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5673])). 185.47/93.69 thf(2941,axiom,((! [A:nat]: ((divide_divide_int @ one_one_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (zero_n2684676970156552555ol_int @ (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5481_one__div__2__pow__eq)). 185.47/93.69 thf(17484,plain,((! [A:nat]: ((divide_divide_int @ one_one_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (zero_n2684676970156552555ol_int @ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2941])). 185.47/93.69 thf(3508,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:$o,F:$o]: ((vEBT_Node @ A @ B @ C @ D) != (vEBT_Leaf @ E @ F)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2012_VEBT_Odistinct_I1_J)). 185.47/93.69 thf(19279,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:$o,F:$o]: ~ ((vEBT_Node @ A @ B @ C @ D) = (vEBT_Leaf @ E @ F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3508])). 185.47/93.69 thf(4047,axiom,((! [A:(nat > real),B:real]: ((sums_real @ A @ (plus_plus_real @ B @ (A @ zero_zero_nat))) <= (sums_real @ (^ [C:nat]: (A @ (suc @ C))) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8188_sums__Suc)). 185.47/93.69 thf(20977,plain,((! [A:(nat > real),B:real]: ((sums_real @ (A) @ (plus_plus_real @ B @ (A @ zero_zero_nat))) | ~ (sums_real @ (^ [C:nat]: (A @ (suc @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4047])). 185.47/93.69 thf(5434,axiom,((nat_set_decode = (^ [A:nat]: (collect_nat @ (^ [B:nat]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4885_set__decode__def)). 185.47/93.69 thf(25699,plain,(((nat_set_decode) = (^ [A:nat]: (collect_nat @ (^ [B:nat]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5434])). 185.47/93.69 thf(5006,axiom,((! [A:num]: (one_one_rat != (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5770_one__neq__neg__numeral)). 185.47/93.69 thf(24123,plain,((! [A:num]: ~ (one_one_rat = (uminus_uminus_rat @ (numeral_numeral_rat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5006])). 185.47/93.69 thf(6393,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat,E:nat]: ((A @ D @ E) <= (A @ E @ D))) => (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3882_linorder__wlog)). 185.47/93.69 thf(29255,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((! [D:nat,E:nat]: ((A @ D @ E) | ~ (A @ E @ D))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6393])). 185.47/93.69 thf(3388,axiom,((! [A:int,B:int,C:$o,D:$o]: ((A = B) => ((((ord_less_eq_int @ zero_zero_int @ A) & (C)) = ((D) & (ord_less_eq_int @ zero_zero_int @ B))) <= ((ord_less_eq_int @ zero_zero_int @ B) => (C = D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3330_conj__le__cong)). 185.47/93.69 thf(18890,plain,((! [A:int,B:int,C:$o,D:$o]: ((A = B) => ((((ord_less_eq_int @ zero_zero_int @ A) & (C)) = ((D) & (ord_less_eq_int @ zero_zero_int @ B))) | ~ ((ord_less_eq_int @ zero_zero_int @ B) => (C = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3388])). 185.47/93.69 thf(1817,axiom,((! [A:num,B:num]: ~ (ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5695_not__numeral__le__neg__numeral)). 185.47/93.69 thf(13817,plain,((! [A:num,B:num]: ~ (ord_less_eq_rat @ (numeral_numeral_rat @ A) @ (uminus_uminus_rat @ (numeral_numeral_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1817])). 185.47/93.69 thf(121,axiom,((! [A:complex]: (ord_less_eq_real @ (abs_abs_real @ (re @ A)) @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9646_abs__Re__le__cmod)). 185.47/93.69 thf(8125,plain,((! [A:complex]: (ord_less_eq_real @ (abs_abs_real @ (re @ A)) @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 185.47/93.69 thf(250,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) => ((ord_less_eq_real @ (arccos @ A) @ (arccos @ B)) = (ord_less_eq_real @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8364_arccos__le__mono)). 185.47/93.69 thf(8525,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) => ((ord_less_eq_real @ (arccos @ A) @ (arccos @ B)) = (ord_less_eq_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 185.47/93.69 thf(5509,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ B @ A) => (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4807_dvd__pos__nat)). 185.47/93.69 thf(26077,plain,((! [A:nat,B:nat]: (((dvd_dvd_nat @ B @ A) => (ord_less_nat @ zero_zero_nat @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5509])). 185.47/93.69 thf(1341,axiom,((bit_ri631733984087533419it_int = (^ [A:nat,B:int]: (minus_minus_int @ (bit_se2923211474154528505it_int @ (suc @ A) @ (plus_plus_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9356_signed__take__bit__eq__take__bit__shift)). 185.47/93.69 thf(12203,plain,(((bit_ri631733984087533419it_int) = (^ [A:nat,B:int]: (minus_minus_int @ (bit_se2923211474154528505it_int @ (suc @ A) @ (plus_plus_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341])). 185.47/93.69 thf(978,axiom,((! [A:num,B:num,C:num]: (((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ C)) @ (numeral_numeral_int @ (bit0 @ B)))) = ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (modulo_modulo_int @ (numeral_numeral_int @ C) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2041_cong__exp__iff__simps_I9_J)). 185.47/93.69 thf(11086,plain,((! [A:num,B:num,C:num]: (((modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (modulo_modulo_int @ (numeral_numeral_int @ (bit0 @ C)) @ (numeral_numeral_int @ (bit0 @ B)))) = ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (modulo_modulo_int @ (numeral_numeral_int @ C) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[978])). 185.47/93.69 thf(2194,axiom,((! [A:rat,B:rat]: (dvd_dvd_rat @ A @ (times_times_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4592_dvd__triv__left)). 185.47/93.69 thf(15044,plain,((! [A:rat,B:rat]: (dvd_dvd_rat @ A @ (times_times_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2194])). 185.47/93.69 thf(5281,axiom,((power_power_nat = (^ [A:nat,B:nat]: (if_nat @ (B = zero_zero_nat) @ one_one_nat @ (times_times_nat @ A @ (power_power_nat @ A @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2961_power__eq__if)). 185.47/93.69 thf(25190,plain,(((power_power_nat) = (^ [A:nat,B:nat]: (if_nat @ (B = zero_zero_nat) @ one_one_nat @ (times_times_nat @ A @ (power_power_nat @ A @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5281])). 185.47/93.69 thf(5140,axiom,((! [A:nat]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_nat @ (times_times_nat @ A @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6669_power3__eq__cube)). 185.47/93.69 thf(24677,plain,((! [A:nat]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_nat @ (times_times_nat @ A @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5140])). 185.47/93.69 thf(4266,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ B) => (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6455_abs__le__D1)). 185.47/93.69 thf(21649,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ (abs_abs_rat @ A) @ B) => (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4266])). 185.47/93.69 thf(3556,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) => (ord_less_eq_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_add__le__imp__le__left)). 185.47/93.69 thf(19427,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C)) => (ord_less_eq_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3556])). 185.47/93.69 thf(716,axiom,((! [A:set_nat,B:set_nat,C:(nat > rat)]: (((ord_less_eq_set_nat @ B @ A) => ((groups2906978787729119204at_rat @ C @ (minus_minus_set_nat @ A @ B)) = (minus_minus_rat @ (groups2906978787729119204at_rat @ C @ A) @ (groups2906978787729119204at_rat @ C @ B)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6133_sum__diff)). 185.47/93.69 thf(10118,plain,((! [A:set_nat,B:set_nat,C:(nat > rat)]: (((ord_less_eq_set_nat @ B @ A) => ((groups2906978787729119204at_rat @ (C) @ (minus_minus_set_nat @ A @ B)) = (minus_minus_rat @ (groups2906978787729119204at_rat @ (C) @ A) @ (groups2906978787729119204at_rat @ (C) @ B)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[716])). 185.47/93.69 thf(361,axiom,((! [A:(nat > real),B:real]: ((summable_real @ A) => ((~ (! [C:nat]: ~ (! [D:nat]: ((! [E:nat]: (ord_less_real @ (real_V7735802525324610683m_real @ (groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ D @ E))) @ B)) <= (ord_less_eq_nat @ C @ D))))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7747_summable__partial__sum__bound)). 185.47/93.69 thf(8940,plain,((! [A:(nat > real),B:real]: ((summable_real @ (A)) => (~ (! [C:nat]: ~ (! [D:nat]: (! [E:nat]: (ord_less_real @ (real_V7735802525324610683m_real @ (groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ D @ E))) @ B) | ~ (ord_less_eq_nat @ C @ D)))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])). 185.47/93.69 thf(1835,axiom,((! [A:int,B:int,C:int,D:int]: (((B != zero_zero_int) => ((plus_plus_rat @ (fract @ C @ A) @ (fract @ D @ B)) = (fract @ (plus_plus_int @ (times_times_int @ C @ B) @ (times_times_int @ D @ A)) @ (times_times_int @ A @ B)))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9932_add__rat)). 185.47/93.69 thf(13881,plain,((! [A:int,B:int,C:int,D:int]: (((~ (B = zero_zero_int)) => ((plus_plus_rat @ (fract @ C @ A) @ (fract @ D @ B)) = (fract @ (plus_plus_int @ (times_times_int @ C @ B) @ (times_times_int @ D @ A)) @ (times_times_int @ A @ B)))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1835])). 185.47/93.69 thf(2545,axiom,((! [A:nat,B:(real > nat),C:real,D:real]: ((((ord_less_nat @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F))))) <= (ord_less_real @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4076_ord__eq__less__subst)). 185.47/93.69 thf(16171,plain,((! [A:nat,B:(real > nat),C:real,D:real]: ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_real @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2545])). 185.47/93.69 thf(3146,axiom,((! [A:num]: ((semiri5074537144036343181t_real @ (numeral_numeral_nat @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6903_of__nat__numeral)). 185.47/93.69 thf(18130,plain,((! [A:num]: ((semiri5074537144036343181t_real @ (numeral_numeral_nat @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3146])). 185.47/93.69 thf(3694,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ B @ D)) @ E) => (ord_less_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ D)) @ (plus_plus_real @ C @ E))) <= (ord_less_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7498_norm__diff__triangle__less)). 185.47/93.69 thf(19856,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ B @ D)) @ E) => (ord_less_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ D)) @ (plus_plus_real @ C @ E))) | ~ (ord_less_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3694])). 185.47/93.69 thf(5699,axiom,((! [A:nat]: (ord_less_eq_real @ one_one_real @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_964_two__realpow__ge__one)). 185.47/93.69 thf(26693,plain,((! [A:nat]: (ord_less_eq_real @ one_one_real @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5699])). 185.47/93.69 thf(1082,axiom,((! [A:real,B:(int > real),C:int,D:int]: ((ord_less_real @ A @ (B @ C)) => (((! [E:int,F:int]: ((ord_less_int @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) <= (ord_less_int @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4102_order__less__subst1)). 185.47/93.69 thf(11397,plain,((! [A:real,B:(int > real),C:int,D:int]: ((ord_less_real @ A @ (B @ C)) => (((! [E:int,F:int]: ((ord_less_int @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) | ~ (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082])). 185.47/93.69 thf(3106,axiom,((! [A:rat,B:(rat > rat),C:rat,D:rat]: ((((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F)))) => (ord_less_rat @ A @ (B @ D))) <= (ord_less_rat @ C @ D)) <= (ord_less_rat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4104_order__less__subst1)). 185.47/93.69 thf(18014,plain,((! [A:rat,B:(rat > rat),C:rat,D:rat]: (((! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F)))) => (ord_less_rat @ A @ (B @ D))) | ~ (ord_less_rat @ C @ D) | ~ (ord_less_rat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3106])). 185.47/93.69 thf(2794,axiom,((dvd_dvd_Code_integer = (^ [A:code_integer,B:code_integer]: ? [C:code_integer]: (B = (times_3573771949741848930nteger @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4610_dvd__def)). 185.47/93.69 thf(17007,plain,(((dvd_dvd_Code_integer) = (^ [A:code_integer,B:code_integer]: ? [C:code_integer]: (B = (times_3573771949741848930nteger @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2794])). 185.47/93.69 thf(4158,axiom,((! [A:int,B:int]: ((ord_less_int @ (modulo_modulo_int @ B @ A) @ A) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1923_unique__euclidean__semiring__numeral__class_Opos__mod__bound)). 185.47/93.69 thf(21319,plain,((! [A:int,B:int]: ((ord_less_int @ (modulo_modulo_int @ B @ A) @ A) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4158])). 185.47/93.69 thf(4194,axiom,((! [A:rat,B:num,C:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ B)) @ C) = (ord_less_eq_rat @ A @ (times_times_rat @ C @ (numeral_numeral_rat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_divide__le__eq__numeral1_I1_J)). 185.47/93.69 thf(21429,plain,((! [A:rat,B:num,C:rat]: ((ord_less_eq_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ B)) @ C) = (ord_less_eq_rat @ A @ (times_times_rat @ C @ (numeral_numeral_rat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4194])). 185.47/93.69 thf(3387,axiom,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (minus_minus_rat @ A @ B) @ C) = (ord_less_rat @ A @ (plus_plus_rat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_802_diff__less__eq)). 185.47/93.69 thf(18887,plain,((! [A:rat,B:rat,C:rat]: ((ord_less_rat @ (minus_minus_rat @ A @ B) @ C) = (ord_less_rat @ A @ (plus_plus_rat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3387])). 185.47/93.69 thf(2151,axiom,((! [A:rat,B:rat,C:(rat > int),D:int]: ((((ord_less_int @ (C @ A) @ D) <= (! [E:rat,F:rat]: ((ord_less_int @ (C @ E) @ (C @ F)) <= (ord_less_rat @ E @ F)))) <= ((C @ B) = D)) <= (ord_less_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4092_ord__less__eq__subst)). 185.47/93.69 thf(14899,plain,((! [A:rat,B:rat,C:(rat > int),D:int]: ((ord_less_int @ (C @ A) @ D) | ~ (! [E:rat,F:rat]: ((ord_less_int @ (C @ E) @ (C @ F)) | ~ (ord_less_rat @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_less_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2151])). 185.47/93.69 thf(7415,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ A) @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_high__inv)). 185.47/93.69 thf(32992,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7415])). 185.47/93.69 thf(6156,axiom,(((num_of_nat @ zero_zero_nat) = one)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9841_num__of__nat_Osimps_I1_J)). 185.47/93.69 thf(28447,plain,(((num_of_nat @ zero_zero_nat) = one)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6156])). 185.47/93.69 thf(4726,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((C != A) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3274_minf_I4_J)). 185.47/93.69 thf(23156,plain,((! [A:int]: ? [B:int]: ! [C:int]: (~ (C = A) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4726])). 185.47/93.69 thf(377,axiom,((! [A:(nat > real)]: ((! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C))) => (topolo6980174941875973593q_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8346_monoI2)). 185.47/93.69 thf(8991,plain,((! [A:(nat > real)]: ((! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C))) => (topolo6980174941875973593q_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])). 185.47/93.69 thf(36,axiom,((! [A:real,B:real,C:nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (times_times_real @ (power_power_real @ (plus_plus_real @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_real @ A @ D)) @ (power_power_real @ A @ C))) @ (set_ord_lessThan_nat @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (power_power_real @ A @ D) @ (minus_minus_real @ (power_power_real @ (plus_plus_real @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_real @ A @ (minus_minus_nat @ C @ D))))) @ (set_ord_lessThan_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7611_lemma__termdiff1)). 185.47/93.69 thf(7848,plain,((! [A:real,B:real,C:nat]: ((groups6591440286371151544t_real @ (^ [D:nat]: (minus_minus_real @ (times_times_real @ (power_power_real @ (plus_plus_real @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_real @ A @ D)) @ (power_power_real @ A @ C))) @ (set_ord_lessThan_nat @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (power_power_real @ A @ D) @ (minus_minus_real @ (power_power_real @ (plus_plus_real @ A @ B) @ (minus_minus_nat @ C @ D)) @ (power_power_real @ A @ (minus_minus_nat @ C @ D))))) @ (set_ord_lessThan_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 185.47/93.69 thf(750,axiom,((! [A:nat,B:real]: ((ord_less_eq_real @ (power_power_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A)) @ A) @ (gbinomial_real @ B @ A)) <= (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8481_gbinomial__ge__n__over__k__pow__k)). 185.47/93.69 thf(10245,plain,((! [A:nat,B:real]: ((ord_less_eq_real @ (power_power_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A)) @ A) @ (gbinomial_real @ B @ A)) | ~ (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[750])). 185.47/93.69 thf(6311,axiom,((! [A:nat]: (((power_power_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ one_one_int)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5471_neg__one__odd__power)). 185.47/93.69 thf(28960,plain,((! [A:nat]: (((power_power_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ one_one_int)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6311])). 185.47/93.69 thf(2045,axiom,((! [A:rat,B:rat]: (((uminus_uminus_rat @ A) = B) = ((plus_plus_rat @ A @ B) = zero_zero_rat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5746_neg__eq__iff__add__eq__0)). 185.47/93.69 thf(14568,plain,((! [A:rat,B:rat]: (((uminus_uminus_rat @ A) = B) = ((plus_plus_rat @ A @ B) = zero_zero_rat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045])). 185.47/93.69 thf(196,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: (((~ ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A))) => ((groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (times_times_real @ (B @ D) @ (power_power_real @ zero_zero_real @ D)) @ (C @ D))) @ A) = zero_zero_real)) & (((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A)) => ((groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (times_times_real @ (B @ D) @ (power_power_real @ zero_zero_real @ D)) @ (C @ D))) @ A) = (divide_divide_real @ (B @ zero_zero_nat) @ (C @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6446_sum__zero__power_H)). 185.47/93.69 thf(8363,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: (((~ ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A))) => ((groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (times_times_real @ (B @ D) @ (power_power_real @ zero_zero_real @ D)) @ (C @ D))) @ A) = zero_zero_real)) & (((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A)) => ((groups6591440286371151544t_real @ (^ [D:nat]: (divide_divide_real @ (times_times_real @ (B @ D) @ (power_power_real @ zero_zero_real @ D)) @ (C @ D))) @ A) = (divide_divide_real @ (B @ zero_zero_nat) @ (C @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 185.47/93.69 thf(3059,axiom,((! [A:(nat > $o),B:(nat > (nat > $o))]: ((finite_finite_nat @ (collect_nat @ A)) => ((finite_finite_nat @ (collect_nat @ (^ [C:nat]: ? [D:nat]: ((B @ C @ D) & (A @ D))))) = (! [C:nat]: ((A @ C) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: (B @ D @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3446_finite__Collect__bounded__ex)). 185.47/93.69 thf(17861,plain,((! [A:(nat > $o),B:(nat > (nat > $o))]: ((finite_finite_nat @ (collect_nat @ (A))) => ((finite_finite_nat @ (collect_nat @ (^ [C:nat]: ? [D:nat]: ((B @ C @ D) & (A @ D))))) = (! [C:nat]: ((A @ C) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: (B @ D @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3059])). 185.47/93.69 thf(5250,axiom,((! [A:real,B:real]: ((times_times_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (times_times_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5074_minus__mult__minus)). 185.47/93.69 thf(25041,plain,((! [A:real,B:real]: ((times_times_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (times_times_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5250])). 185.47/93.69 thf(5561,axiom,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (times_times_nat @ B @ C)) = (power_power_real @ (power_power_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_power__mult)). 185.47/93.69 thf(26244,plain,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (times_times_nat @ B @ C)) = (power_power_real @ (power_power_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5561])). 185.47/93.69 thf(3173,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ A) => (ord_less_eq_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3898_dual__order_Otrans)). 185.47/93.69 thf(18214,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ C @ A) => (ord_less_eq_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3173])). 185.47/93.69 thf(2910,axiom,((! [A:int]: (((ring_17405671764205052669omplex @ A) = one_one_complex) = (A = one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6962_of__int__eq__1__iff)). 185.47/93.69 thf(17387,plain,((! [A:int]: (((ring_17405671764205052669omplex @ A) = one_one_complex) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2910])). 185.47/93.69 thf(7565,axiom,((! [A:list_VEBT_VEBT,B:nat]: ((list_u1324408373059187874T_VEBT @ A @ B @ (nth_VEBT_VEBT @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3601_list__update__id)). 185.47/93.69 thf(33474,plain,((! [A:list_VEBT_VEBT,B:nat]: ((list_u1324408373059187874T_VEBT @ A @ B @ (nth_VEBT_VEBT @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7565])). 185.47/93.69 thf(7252,axiom,((! [A:real,B:real,C:nat]: ((power_power_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_power__mult__distrib)). 185.47/93.69 thf(32438,plain,((! [A:real,B:real,C:nat]: ((power_power_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7252])). 185.47/93.69 thf(6537,axiom,((sqr = (^ [A:num]: (times_times_num @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9849_sqr__conv__mult)). 185.47/93.69 thf(29800,plain,(((sqr) = (^ [A:num]: (times_times_num @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6537])). 185.47/93.69 thf(1730,axiom,((! [A:real]: ((ord_less_real @ (divide_divide_real @ A @ (sqrt @ (numeral_numeral_real @ (bit0 @ one)))) @ A) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8223_lemma__real__divide__sqrt__less)). 185.47/93.69 thf(13534,plain,((! [A:real]: ((ord_less_real @ (divide_divide_real @ A @ (sqrt @ (numeral_numeral_real @ (bit0 @ one)))) @ A) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730])). 185.47/93.69 thf(7382,axiom,((! [A:nat]: (((semiri2265585572941072030t_real @ A) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ A @ one_one_nat)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8052_fact__reduce)). 185.47/93.69 thf(32866,plain,((! [A:nat]: (((semiri2265585572941072030t_real @ A) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (semiri2265585572941072030t_real @ (minus_minus_nat @ A @ one_one_nat)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7382])). 185.47/93.69 thf(618,axiom,((! [A:rat,B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (times_times_rat @ (gbinomial_rat @ A @ C) @ (minus_minus_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))) @ (semiri681578069525770553at_rat @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (times_times_rat @ (divide_divide_rat @ (semiri681578069525770553at_rat @ (suc @ B)) @ (numeral_numeral_rat @ (bit0 @ one))) @ (gbinomial_rat @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8410_gchoose__row__sum__weighted)). 185.47/93.69 thf(9784,plain,((! [A:rat,B:nat]: ((groups2906978787729119204at_rat @ (^ [C:nat]: (times_times_rat @ (gbinomial_rat @ A @ C) @ (minus_minus_rat @ (divide_divide_rat @ A @ (numeral_numeral_rat @ (bit0 @ one))) @ (semiri681578069525770553at_rat @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) = (times_times_rat @ (divide_divide_rat @ (semiri681578069525770553at_rat @ (suc @ B)) @ (numeral_numeral_rat @ (bit0 @ one))) @ (gbinomial_rat @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[618])). 185.47/93.69 thf(5889,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7359_double__gauss__sum__from__Suc__0)). 185.47/93.69 thf(27495,plain,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (groups3542108847815614940at_nat @ (semiri1316708129612266289at_nat) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5889])). 185.47/93.69 thf(1653,axiom,((! [A:(rat > $o),B:(rat > $o),C:(rat > $o),D:(rat > $o)]: (((? [E:rat]: ! [F:rat]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) <= (ord_less_rat @ F @ E))) <= (? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => ((C @ F) = (D @ F))))) <= (? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3256_minf_I1_J)). 185.47/93.69 thf(13230,plain,((! [A:(rat > $o),B:(rat > $o),C:(rat > $o),D:(rat > $o)]: (? [E:rat]: ! [F:rat]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) | ~ (ord_less_rat @ F @ E)) | ~ (? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => ((C @ F) = (D @ F)))) | ~ (? [E:rat]: ! [F:rat]: ((ord_less_rat @ F @ E) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653])). 185.47/93.69 thf(3195,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((((modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (plus_plus_int @ (modulo_modulo_int @ B @ A) @ A)) | ((modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (modulo_modulo_int @ B @ A))) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2525_mod__double__modulus)). 185.47/93.69 thf(18285,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => (((modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (plus_plus_int @ (modulo_modulo_int @ B @ A) @ A)) | ((modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) = (modulo_modulo_int @ B @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3195])). 185.47/93.69 thf(3764,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((dvd_dvd_int @ B @ C) = (dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4813_zdvd__mono)). 185.47/93.69 thf(20086,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((dvd_dvd_int @ B @ C) = (dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3764])). 185.47/93.69 thf(2830,axiom,((! [A:int,B:int]: (((ord_less_rat @ one_one_rat @ (fract @ B @ A)) = (ord_less_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9949_one__less__Fract__iff)). 185.47/93.69 thf(17123,plain,((! [A:int,B:int]: (((ord_less_rat @ one_one_rat @ (fract @ B @ A)) = (ord_less_int @ A @ B)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2830])). 185.47/93.69 thf(1806,axiom,((semiri773545260158071498ct_rat = (^ [A:nat]: (if_rat @ (A = zero_zero_nat) @ one_one_rat @ (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8047_fact__num__eq__if)). 185.47/93.69 thf(13785,plain,(((semiri773545260158071498ct_rat) = (^ [A:nat]: (if_rat @ (A = zero_zero_nat) @ one_one_rat @ (times_times_rat @ (semiri681578069525770553at_rat @ A) @ (semiri773545260158071498ct_rat @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1806])). 185.47/93.69 thf(3660,axiom,((! [A:real]: (((powr_real @ A @ one_one_real) = A) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9074_powr__one)). 185.47/93.69 thf(19750,plain,((! [A:real]: (((powr_real @ A @ one_one_real) = A) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3660])). 185.47/93.69 thf(3285,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (sin_complex @ A) @ (cos_complex @ B)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (sin_complex @ (plus_plus_complex @ A @ B)) @ (sin_complex @ (minus_minus_complex @ A @ B))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7850_sin__times__cos)). 185.47/93.69 thf(18559,plain,((! [A:complex,B:complex]: ((times_times_complex @ (sin_complex @ A) @ (cos_complex @ B)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (sin_complex @ (plus_plus_complex @ A @ B)) @ (sin_complex @ (minus_minus_complex @ A @ B))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3285])). 185.47/93.69 thf(470,axiom,((! [A:(nat > real),B:real]: (((suminf_real @ (^ [C:nat]: (divide_divide_real @ (A @ C) @ B))) = (divide_divide_real @ (suminf_real @ A) @ B)) <= (summable_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7683_suminf__divide)). 185.47/93.69 thf(9310,plain,((! [A:(nat > real),B:real]: (((suminf_real @ (^ [C:nat]: (divide_divide_real @ (A @ C) @ B))) = (divide_divide_real @ (suminf_real @ (A)) @ B)) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[470])). 185.47/93.69 thf(7628,axiom,((! [A:num]: (one != (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3111_verit__eq__simplify_I10_J)). 185.47/93.69 thf(33652,plain,((! [A:num]: ~ (one = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7628])). 185.47/93.69 thf(3448,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => ((ord_less_eq_int @ B @ one_one_int) => (ord_less_eq_int @ (times_times_int @ A @ B) @ one_one_int))) <= (ord_less_eq_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2668_mult__le__one)). 185.47/93.69 thf(19072,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => ((ord_less_eq_int @ B @ one_one_int) => (ord_less_eq_int @ (times_times_int @ A @ B) @ one_one_int))) | ~ (ord_less_eq_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3448])). 185.47/93.69 thf(2729,axiom,((! [A:complex,B:complex,C:complex]: ((A = (divide1717551699836669952omplex @ B @ C)) = (((C != zero_zero_complex) => ((times_times_complex @ A @ C) = B)) & ((A = zero_zero_complex) <= (C = zero_zero_complex)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2470_eq__divide__eq)). 185.47/93.69 thf(16810,plain,((! [A:complex,B:complex,C:complex]: ((A = (divide1717551699836669952omplex @ B @ C)) = (((~ (C = zero_zero_complex)) => ((times_times_complex @ A @ C) = B)) & ((A = zero_zero_complex) | ~ (C = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2729])). 185.47/93.69 thf(3322,axiom,((! [A:rat,B:(nat > rat),C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((ord_less_rat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F)))))) <= (ord_less_rat @ A @ (B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4106_order__less__subst1)). 185.47/93.69 thf(18675,plain,((! [A:rat,B:(nat > rat),C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((ord_less_rat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_less_rat @ (B @ E) @ (B @ F)))))) | ~ (ord_less_rat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3322])). 185.47/93.69 thf(5478,axiom,(((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ one_one_complex)) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5283_diff__numeral__special_I12_J)). 185.47/93.69 thf(25966,plain,(((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ one_one_complex)) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5478])). 185.47/93.69 thf(2189,axiom,((! [A:nat,B:nat,C:(vEBT_VEBT > $o),D:vEBT_VEBT]: (((C @ D) => (C @ (nth_VEBT_VEBT @ (replicate_VEBT_VEBT @ B @ D) @ A))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5019_intind)). 185.47/93.69 thf(15024,plain,((! [A:nat,B:nat,C:(vEBT_VEBT > $o),D:vEBT_VEBT]: (((C @ D) => (C @ (nth_VEBT_VEBT @ (replicate_VEBT_VEBT @ B @ D) @ A))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2189])). 185.47/93.69 thf(5452,axiom,((! [A:real]: ((zero_zero_real = A) = (A = zero_zero_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1926_zero__reorient)). 185.47/93.69 thf(25799,plain,((! [A:real]: ((zero_zero_real = A) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5452])). 185.47/93.69 thf(4165,axiom,((! [A:num]: (ord_less_eq_rat @ one_one_rat @ (numeral_numeral_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_817_one__le__numeral)). 185.47/93.69 thf(21340,plain,((! [A:num]: (ord_less_eq_rat @ one_one_rat @ (numeral_numeral_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4165])). 185.47/93.69 thf(5722,axiom,((! [A:complex]: (((times_times_complex @ A @ A) = one_one_complex) = ((A = (uminus1482373934393186551omplex @ one_one_complex)) | (A = one_one_complex))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5779_square__eq__1__iff)). 185.47/93.69 thf(26777,plain,((! [A:complex]: (((times_times_complex @ A @ A) = one_one_complex) = ((A = (uminus1482373934393186551omplex @ one_one_complex)) | (A = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5722])). 185.47/93.69 thf(5865,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2017_mod__less__eq__dividend)). 185.47/93.69 thf(27416,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5865])). 185.47/93.69 thf(4992,axiom,((res = (the_nat @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_965_snd)). 185.47/93.69 thf(24077,plain,((res = (the_nat @ (vEBT_VEBT_add @ (vEBT_VEBT_mul @ (some_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_pred @ summary @ (vEBT_VEBT_high @ xa @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4992])). 185.47/93.69 thf(7509,axiom,((! [A:option_nat]: ((! [B:nat]: (A != (some_nat @ B))) = (A = none_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_not__Some__eq)). 185.47/93.69 thf(33313,plain,((! [A:option_nat]: ((! [B:nat]: ~ (A = (some_nat @ B))) = (A = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7509])). 185.47/93.69 thf(84,axiom,((! [A:rat,B:nat]: ((minus_minus_rat @ (power_power_rat @ A @ B) @ one_one_rat) = (times_times_rat @ (minus_minus_rat @ A @ one_one_rat) @ (groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7597_power__diff__1__eq)). 185.47/93.69 thf(8006,plain,((! [A:rat,B:nat]: ((minus_minus_rat @ (power_power_rat @ A @ B) @ one_one_rat) = (times_times_rat @ (minus_minus_rat @ A @ one_one_rat) @ (groups2906978787729119204at_rat @ (power_power_rat @ A) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 185.47/93.69 thf(4471,axiom,((! [A:complex,B:nat]: (((comm_s2602460028002588243omplex @ A @ B) = zero_zero_complex) = (? [C:nat]: ((ord_less_nat @ C @ B) & (A = (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8501_pochhammer__eq__0__iff)). 185.47/93.69 thf(22313,plain,((! [A:complex,B:nat]: (((comm_s2602460028002588243omplex @ A @ B) = zero_zero_complex) = (? [C:nat]: ((ord_less_nat @ C @ B) & (A = (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4471])). 185.47/93.69 thf(4554,axiom,((! [A:real,B:nat]: (((ord_less_eq_real @ (power_power_real @ (minus_minus_real @ one_one_real @ (divide_divide_real @ A @ (semiri5074537144036343181t_real @ B))) @ B) @ (exp_real @ (uminus_uminus_real @ A))) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8269_exp__ge__one__minus__x__over__n__power__n)). 185.47/93.69 thf(22588,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ (power_power_real @ (minus_minus_real @ one_one_real @ (divide_divide_real @ A @ (semiri5074537144036343181t_real @ B))) @ B) @ (exp_real @ (uminus_uminus_real @ A))) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4554])). 185.47/93.69 thf(6163,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((modulo_modulo_nat @ B @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4873_unit__imp__mod__eq__0)). 185.47/93.69 thf(28472,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((modulo_modulo_nat @ B @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6163])). 185.47/93.69 thf(2226,axiom,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ B @ (times_times_rat @ C @ A)) => (ord_less_rat @ (divide_divide_rat @ B @ A) @ C)) <= (ord_less_rat @ zero_zero_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2708_mult__imp__div__pos__less)). 185.47/93.69 thf(15134,plain,((! [A:rat,B:rat,C:rat]: (((ord_less_rat @ B @ (times_times_rat @ C @ A)) => (ord_less_rat @ (divide_divide_rat @ B @ A) @ C)) | ~ (ord_less_rat @ zero_zero_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2226])). 185.47/93.69 thf(6328,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1072_power__Suc)). 185.47/93.69 thf(29026,plain,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6328])). 185.47/93.69 thf(5120,axiom,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4017_exists__least__iff)). 185.47/93.69 thf(24580,plain,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5120])). 185.47/93.69 thf(1491,axiom,((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ one_one_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5713_le__minus__one__simps_I2_J)). 185.47/93.69 thf(12694,plain,((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491])). 185.47/93.69 thf(4662,axiom,((! [A:num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2259_zero__less__numeral)). 185.47/93.69 thf(22933,plain,((! [A:num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4662])). 185.47/93.69 thf(897,axiom,((! [A:real]: ((sin_real @ (minus_minus_real @ A @ pi)) = (uminus_uminus_real @ (sin_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7790_sin__minus__pi)). 185.47/93.69 thf(10800,plain,((! [A:real]: ((sin_real @ (minus_minus_real @ A @ pi)) = (uminus_uminus_real @ (sin_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[897])). 185.47/93.69 thf(6714,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4141_order__less__imp__not__eq2)). 185.47/93.69 thf(30372,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6714])). 185.47/93.69 thf(1975,axiom,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:int]: ((A @ (nat2 @ B)) & (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9283_ex__nat)). 185.47/93.69 thf(14340,plain,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:int]: ((A @ (nat2 @ B)) & (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975])). 185.47/93.69 thf(7223,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4261_order_Ostrict__implies__order)). 185.47/93.69 thf(32353,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7223])). 185.47/93.69 thf(7084,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((product_Pair_nat_nat @ A @ B) = (product_Pair_nat_nat @ C @ D)) => (~ ((B != D) <= (A = C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3418_Pair__inject)). 185.47/93.69 thf(31848,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((product_Pair_nat_nat @ A @ B) = (product_Pair_nat_nat @ C @ D)) => (~ (~ (B = D) | ~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7084])). 185.47/93.69 thf(924,axiom,((! [A:nat,B:int,C:int,D:nat]: ((bit_se1146084159140164899it_int @ (bit_concat_bit @ A @ B @ C) @ D) = (((ord_less_eq_nat @ A @ D) & (bit_se1146084159140164899it_int @ C @ (minus_minus_nat @ D @ A))) | ((ord_less_nat @ D @ A) & (bit_se1146084159140164899it_int @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9433_bit__concat__bit__iff)). 185.47/93.69 thf(10902,plain,((! [A:nat,B:int,C:int,D:nat]: ((bit_se1146084159140164899it_int @ (bit_concat_bit @ A @ B @ C) @ D) = (((ord_less_eq_nat @ A @ D) & (bit_se1146084159140164899it_int @ C @ (minus_minus_nat @ D @ A))) | ((ord_less_nat @ D @ A) & (bit_se1146084159140164899it_int @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[924])). 185.47/93.69 thf(4183,axiom,((! [A:int,B:(rat > int),C:rat,D:rat]: ((A = (B @ C)) => (((ord_less_int @ A @ (B @ D)) <= (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_int @ (B @ E) @ (B @ F))))) <= (ord_less_rat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4082_ord__eq__less__subst)). 185.47/93.69 thf(21391,plain,((! [A:int,B:(rat > int),C:rat,D:rat]: ((A = (B @ C)) => ((ord_less_int @ A @ (B @ D)) | ~ (! [E:rat,F:rat]: ((ord_less_rat @ E @ F) => (ord_less_int @ (B @ E) @ (B @ F)))) | ~ (ord_less_rat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4183])). 185.47/93.69 thf(1425,axiom,((! [A:rat,B:rat,C:rat]: ((A = (plus_plus_rat @ B @ C)) => ((uminus_uminus_rat @ A) = (plus_plus_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5563_group__cancel_Oneg1)). 185.47/93.69 thf(12488,plain,((! [A:rat,B:rat,C:rat]: ((A = (plus_plus_rat @ B @ C)) => ((uminus_uminus_rat @ A) = (plus_plus_rat @ (uminus_uminus_rat @ B) @ (uminus_uminus_rat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425])). 185.47/93.69 thf(2734,axiom,((! [A:int]: (((abs_abs_int @ A) = A) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6370_abs__of__nonneg)). 185.47/93.69 thf(16827,plain,((! [A:int]: (((abs_abs_int @ A) = A) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2734])). 185.47/93.69 thf(5543,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4879_dvd__imp__le)). 185.47/93.69 thf(26193,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5543])). 185.47/93.69 thf(4627,axiom,((minus_minus_rat = (^ [A:rat,B:rat]: (plus_plus_rat @ A @ (uminus_uminus_rat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5795_ab__group__add__class_Oab__diff__conv__add__uminus)). 185.47/93.69 thf(22826,plain,(((minus_minus_rat) = (^ [A:rat,B:rat]: (plus_plus_rat @ A @ (uminus_uminus_rat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4627])). 185.47/93.69 thf(2679,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) => (ord_less_eq_real @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_add__le__imp__le__right)). 185.47/93.69 thf(16659,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ C @ B)) => (ord_less_eq_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2679])). 185.47/93.69 thf(5554,axiom,((! [A:nat,B:nat,C:nat]: (((~ (! [D:nat]: (C != (plus_plus_nat @ A @ (times_times_nat @ B @ D))))) <= (ord_less_eq_nat @ A @ C)) <= ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2176_mod__eq__nat2E)). 185.47/93.69 thf(26225,plain,((! [A:nat,B:nat,C:nat]: (~ (! [D:nat]: ~ (C = (plus_plus_nat @ A @ (times_times_nat @ B @ D)))) | ~ (ord_less_eq_nat @ A @ C) | ~ ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5554])). 185.47/93.69 thf(4300,axiom,((! [A:num]: ((ring_1_of_int_real @ (numeral_numeral_int @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6937_of__int__numeral)). 185.47/93.69 thf(21744,plain,((! [A:num]: ((ring_1_of_int_real @ (numeral_numeral_int @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4300])). 185.47/93.69 thf(7117,axiom,(((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one)) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5990_uminus__numeral__One)). 185.47/93.69 thf(31953,plain,(((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one)) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7117])). 185.47/93.69 thf(123,axiom,((! [A:real,B:nat,C:real]: (((ord_less_eq_real @ (semiri5074537144036343181t_real @ B) @ (log @ A @ C)) <= (ord_less_real @ one_one_real @ A)) <= (ord_less_eq_real @ (power_power_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9047_le__log__of__power)). 185.47/93.69 thf(8130,plain,((! [A:real,B:nat,C:real]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ B) @ (log @ A @ C)) | ~ (ord_less_real @ one_one_real @ A) | ~ (ord_less_eq_real @ (power_power_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 185.47/93.69 thf(4508,axiom,((! [A:rat,B:nat,C:nat]: (((ord_less_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) => (ord_less_nat @ B @ C)) <= (ord_less_rat @ one_one_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_867_power__less__imp__less__exp)). 185.47/93.69 thf(22437,plain,((! [A:rat,B:nat,C:nat]: (((ord_less_rat @ (power_power_rat @ A @ B) @ (power_power_rat @ A @ C)) => (ord_less_nat @ B @ C)) | ~ (ord_less_rat @ one_one_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4508])). 185.47/93.69 thf(965,axiom,((! [A:nat]: ((sin_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ pi)) = zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7809_sin__2npi)). 185.47/93.69 thf(11048,plain,((! [A:nat]: ((sin_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ pi)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[965])). 185.47/93.69 thf(3482,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) <= (! [D:real]: ((ord_less_real @ A @ D) => ((ord_less_eq_real @ D @ C) <= (ord_less_real @ D @ B))))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4225_dense__le__bounded)). 185.47/93.69 thf(19193,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) | ~ (! [D:real]: ((ord_less_real @ A @ D) => ((ord_less_eq_real @ D @ C) | ~ (ord_less_real @ D @ B)))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3482])). 185.47/93.69 thf(5807,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (C != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3268_minf_I3_J)). 185.47/93.69 thf(27120,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5807])). 185.47/93.69 thf(520,axiom,((! [A:real]: (ord_less_real @ (minus_minus_real @ A @ one_one_real) @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9114_real__of__int__floor__gt__diff__one)). 185.47/93.69 thf(9479,plain,((! [A:real]: (ord_less_real @ (minus_minus_real @ A @ one_one_real) @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[520])). 185.47/93.69 thf(1859,axiom,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => (~ (ord_less_rat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4151_leD)). 185.47/93.69 thf(13962,plain,((! [A:rat,B:rat]: ((ord_less_eq_rat @ A @ B) => (~ (ord_less_rat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1859])). 185.47/93.69 thf(2658,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_eq_int @ C @ A) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3317_minf_I6_J)). 185.47/93.69 thf(16543,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_eq_int @ C @ A) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2658])). 185.47/93.69 thf(4050,axiom,(((semiri8010041392384452111omplex @ zero_zero_nat) = zero_zero_complex)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6882_of__nat__0)). 185.47/93.69 thf(20984,plain,(((semiri8010041392384452111omplex @ zero_zero_nat) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4050])). 185.47/93.69 thf(4862,axiom,((! [A:nat,B:nat,C:(nat > int)]: (((plus_plus_int @ (groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_int @ (C @ A) @ (groups3539618377306564664at_int @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6675_sum_OSuc__reindex__ivl)). 185.47/93.69 thf(23610,plain,((! [A:nat,B:nat,C:(nat > int)]: (((plus_plus_int @ (groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_int @ (C @ A) @ (groups3539618377306564664at_int @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4862])). 185.47/93.69 thf(1662,axiom,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Collect__mem__eq)). 185.47/93.69 thf(13306,plain,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662])). 185.47/93.69 thf(864,axiom,(((arcsin @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8310_arcsin__minus__1)). 185.47/93.69 thf(10686,plain,(((arcsin @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[864])). 185.47/93.69 thf(6657,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_less__iff__Suc__add)). 185.47/93.69 thf(30190,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6657])). 185.47/93.69 thf(2271,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2449_zero__le__power)). 185.47/93.69 thf(15272,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2271])). 185.47/93.69 thf(7149,axiom,((! [A:nat,B:code_integer]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (power_8256067586552552935nteger @ B @ A))) & (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ B @ A))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6188_uminus__power__if)). 185.47/93.69 thf(32079,plain,((! [A:nat,B:code_integer]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (power_8256067586552552935nteger @ B @ A))) & (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ B @ A))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7149])). 185.47/93.69 thf(7454,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_3873_order_Otrans)). 185.47/93.69 thf(33107,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)],[7454])). 185.47/93.69 thf(4738,axiom,((! [A:rat,B:rat,C:rat,D:rat]: (((ord_less_eq_rat @ (minus_minus_rat @ A @ D) @ (minus_minus_rat @ B @ C)) <= (ord_less_eq_rat @ C @ D)) <= (ord_less_eq_rat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_diff__mono)). 185.47/93.69 thf(23192,plain,((! [A:rat,B:rat,C:rat,D:rat]: ((ord_less_eq_rat @ (minus_minus_rat @ A @ D) @ (minus_minus_rat @ B @ C)) | ~ (ord_less_eq_rat @ C @ D) | ~ (ord_less_eq_rat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4738])). 185.47/93.69 thf(5463,axiom,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ (comm_s4663373288045622133er_nat @ A @ B) @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8495_pochhammer__Suc)). 185.47/93.69 thf(25831,plain,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ (comm_s4663373288045622133er_nat @ A @ B) @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5463])). 185.47/93.69 thf(3611,axiom,((! [A:real,B:nat]: ((sin_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ pi) @ (numeral_numeral_real @ (bit0 @ one))))) = (cos_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ pi) @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7870_sin__expansion__lemma)). 185.47/93.69 thf(19592,plain,((! [A:real,B:nat]: ((sin_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ pi) @ (numeral_numeral_real @ (bit0 @ one))))) = (cos_real @ (plus_plus_real @ A @ (divide_divide_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ pi) @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3611])). 185.47/93.69 thf(2147,axiom,((! [A:num,B:num]: ~ (ord_le3102999989581377725nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5694_not__numeral__le__neg__numeral)). 185.47/93.69 thf(14884,plain,((! [A:num,B:num]: ~ (ord_le3102999989581377725nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2147])). 185.47/93.69 thf(4390,axiom,((! [A:num]: (ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ one_one_rat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5945_neg__numeral__less__one)). 185.47/93.69 thf(22066,plain,((! [A:num]: (ord_less_rat @ (uminus_uminus_rat @ (numeral_numeral_rat @ A)) @ one_one_rat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4390])). 185.47/93.69 thf(2688,axiom,((! [A:nat,B:int]: ~ (ord_less_int @ (bit_se2923211474154528505it_int @ A @ B) @ zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9280_not__take__bit__negative)). 185.47/93.69 thf(16681,plain,((! [A:nat,B:int]: ~ (ord_less_int @ (bit_se2923211474154528505it_int @ A @ B) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2688])). 185.47/93.69 thf(2468,axiom,((! [A:int]: (((plus_plus_int @ A @ A) = zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3026_double__eq__0__iff)). 185.47/93.69 thf(15906,plain,((! [A:int]: (((plus_plus_int @ A @ A) = zero_zero_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2468])). 185.47/93.69 thf(7023,axiom,((! [A:nat,B:real]: (((ord_less_eq_real @ (root @ A @ B) @ one_one_real) = (ord_less_eq_real @ B @ one_one_real)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9172_real__root__le__1__iff)). 185.47/93.69 thf(31630,plain,((! [A:nat,B:real]: (((ord_less_eq_real @ (root @ A @ B) @ one_one_real) = (ord_less_eq_real @ B @ one_one_real)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7023])). 185.47/93.69 thf(7368,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (suc @ A) @ B) <= ((suc @ A) != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1025_Suc__lessI)). 185.47/93.69 thf(32822,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (suc @ A) @ B) | ((suc @ A) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7368])). 185.47/93.69 thf(4532,axiom,((! [A:int]: ((bit_se7879613467334960850it_int @ zero_zero_nat @ A) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3021_set__bit__0)). 185.47/93.69 thf(22519,plain,((! [A:int]: ((bit_se7879613467334960850it_int @ zero_zero_nat @ A) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4532])). 185.47/93.69 thf(1969,axiom,((! [A:num]: ((pred_numeral @ (bit0 @ A)) = (numeral_numeral_nat @ (bitM @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8958_pred__numeral__simps_I2_J)). 185.47/93.69 thf(14320,plain,((! [A:num]: ((pred_numeral @ (bit0 @ A)) = (numeral_numeral_nat @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1969])). 185.47/93.69 thf(6955,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_add__left__imp__eq)). 185.47/93.69 thf(31320,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6955])). 185.47/93.69 thf(1301,axiom,((! [A:int]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ one_one_rat) = (ord_less_eq_int @ A @ one_one_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7084_of__int__le__1__iff)). 185.47/93.69 thf(12070,plain,((! [A:int]: ((ord_less_eq_rat @ (ring_1_of_int_rat @ A) @ one_one_rat) = (ord_less_eq_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301])). 185.47/93.69 thf(7391,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) <= (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4583_dvd__mult__right)). 185.47/93.69 thf(32892,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) | ~ (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7391])). 185.47/93.69 thf(6711,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7347_double__gauss__sum)). 185.47/93.69 thf(30362,plain,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (groups3542108847815614940at_nat @ (semiri1316708129612266289at_nat) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6711])). 185.47/93.69 thf(7377,axiom,((! [A:num,B:complex,C:complex]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (divide1717551699836669952omplex @ B @ C)) = (((C = zero_zero_complex) => ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = zero_zero_complex)) & ((C != zero_zero_complex) => ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ C) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6157_eq__divide__eq__numeral_I2_J)). 185.47/93.69 thf(32849,plain,((! [A:num,B:complex,C:complex]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (divide1717551699836669952omplex @ B @ C)) = (((C = zero_zero_complex) => ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = zero_zero_complex)) & ((~ (C = zero_zero_complex)) => ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ C) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7377])). 185.47/93.69 thf(7538,axiom,((! [A:real]: ((power_power_real @ (abs_abs_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6427_power2__abs)). 185.47/93.69 thf(33401,plain,((! [A:real]: ((power_power_real @ (abs_abs_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7538])). 185.47/93.69 thf(1388,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) => (ord_less_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8011_fact__less__mono)). 185.47/93.69 thf(12359,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) => (ord_less_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388])). 185.47/93.69 thf(3987,axiom,((! [A:rat,B:nat]: ((ord_less_rat @ (power_power_rat @ A @ B) @ (times_times_rat @ A @ (power_power_rat @ A @ B))) <= (ord_less_rat @ one_one_rat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_863_power__less__power__Suc)). 185.47/93.69 thf(20795,plain,((! [A:rat,B:nat]: ((ord_less_rat @ (power_power_rat @ A @ B) @ (times_times_rat @ A @ (power_power_rat @ A @ B))) | ~ (ord_less_rat @ one_one_rat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3987])). 185.47/93.69 thf(7072,axiom,((! [A:(nat > nat),B:nat]: ((sums_nat @ (^ [C:nat]: (A @ (suc @ C))) @ B) => (sums_nat @ A @ (plus_plus_nat @ B @ (A @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8189_sums__Suc)). 185.47/93.69 thf(31812,plain,((! [A:(nat > nat),B:nat]: ((sums_nat @ (^ [C:nat]: (A @ (suc @ C))) @ B) => (sums_nat @ (A) @ (plus_plus_nat @ B @ (A @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7072])). 185.47/93.69 thf(6420,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ A)) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4438_dvd__add__triv__right__iff)). 185.47/93.69 thf(29382,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ A)) = (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6420])). 185.47/93.69 thf(4550,axiom,((! [A:num,B:num]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (numera6620942414471956472nteger @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5351_mult__neg__numeral__simps_I1_J)). 185.47/93.69 thf(22575,plain,((! [A:num,B:num]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (numera6620942414471956472nteger @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4550])). 185.47/93.69 thf(4154,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2356_mult__strict__left__mono)). 185.47/93.69 thf(21308,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4154])). 185.47/93.69 thf(4605,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ B) @ B) = (ord_less_eq_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9279_take__bit__int__less__eq__self__iff)). 185.47/93.69 thf(22748,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ B) @ B) = (ord_less_eq_int @ zero_zero_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4605])). 185.47/93.69 thf(884,axiom,((! [A:set_nat,B:set_nat,C:(nat > complex),D:(nat > complex)]: ((((! [E:nat]: ((member_nat @ E @ (minus_minus_set_nat @ A @ B)) => ((C @ E) = zero_zero_complex))) => (((groups2073611262835488442omplex @ D @ B) = (groups2073611262835488442omplex @ C @ A)) <= (! [E:nat]: (((D @ E) = (C @ E)) <= (member_nat @ E @ B))))) <= (ord_less_eq_set_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6079_sum_Omono__neutral__cong__left)). 185.47/93.69 thf(10750,plain,((! [A:set_nat,B:set_nat,C:(nat > complex),D:(nat > complex)]: (((! [E:nat]: ((member_nat @ E @ (minus_minus_set_nat @ A @ B)) => ((C @ E) = zero_zero_complex))) => (((groups2073611262835488442omplex @ (D) @ B) = (groups2073611262835488442omplex @ (C) @ A)) | ~ (! [E:nat]: (((D @ E) = (C @ E)) | ~ (member_nat @ E @ B))))) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[884])). 185.47/93.69 thf(3749,axiom,((! [A:int]: ((ord_less_eq_real @ zero_zero_real @ (ring_1_of_int_real @ A)) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7030_of__int__0__le__iff)). 185.47/93.69 thf(20039,plain,((! [A:int]: ((ord_less_eq_real @ zero_zero_real @ (ring_1_of_int_real @ A)) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3749])). 185.47/93.69 thf(6898,axiom,((ord_less_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2386_zero__less__one)). 185.47/93.69 thf(31127,plain,((ord_less_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6898])). 185.47/93.69 thf(6881,axiom,((! [A:code_integer]: ((abs_abs_Code_integer @ (uminus1351360451143612070nteger @ A)) = (abs_abs_Code_integer @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6355_abs__minus__cancel)). 185.47/93.69 thf(31072,plain,((! [A:code_integer]: ((abs_abs_Code_integer @ (uminus1351360451143612070nteger @ A)) = (abs_abs_Code_integer @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6881])). 185.47/93.69 thf(6410,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3984_order_Oasym)). 185.47/93.69 thf(29342,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6410])). 185.47/93.69 thf(4796,axiom,((! [A:complex]: ((ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real) => (sums_complex @ (^ [B:nat]: (times_times_complex @ (semiri8010041392384452111omplex @ (suc @ B)) @ (power_power_complex @ A @ B))) @ (divide1717551699836669952omplex @ one_one_complex @ (power_power_complex @ (minus_minus_complex @ one_one_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8282_geometric__deriv__sums)). 185.47/93.69 thf(23410,plain,((! [A:complex]: ((ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real) => (sums_complex @ (^ [B:nat]: (times_times_complex @ (semiri8010041392384452111omplex @ (suc @ B)) @ (power_power_complex @ A @ B))) @ (divide1717551699836669952omplex @ one_one_complex @ (power_power_complex @ (minus_minus_complex @ one_one_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4796])). 185.47/93.69 thf(1638,axiom,((one_one_rat = (fract @ one_one_int @ one_one_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9943_One__rat__def)). 185.47/93.69 thf(13182,plain,((one_one_rat = (fract @ one_one_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638])). 185.47/93.69 thf(4984,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ A @ (divide_divide_nat @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2916_dividend__less__times__div)). 185.47/93.69 thf(24036,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ A @ (divide_divide_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4984])). 185.47/93.69 thf(2466,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (minus_minus_int @ B @ C)) <= (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4661_dvd__diff)). 185.47/93.69 thf(15899,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ A @ (minus_minus_int @ B @ C)) | ~ (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2466])). 185.47/93.69 thf(208,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (bit_ri7919022796975470100ot_int @ zero_zero_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9535_or__not__numerals_I7_J)). 185.47/93.69 thf(8405,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (bit_ri7919022796975470100ot_int @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 185.47/93.69 thf(7645,axiom,((((ord_less_nat @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList)) & (vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) | (za = ma) | (za = mi))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102__C20_C)). 185.47/93.69 thf(33693,plain,((((ord_less_nat @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ treeList)) & (vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ za @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one)))))) | (za = ma) | (za = mi))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7645])). 185.47/93.69 thf(1157,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (sqrt @ (times_times_real @ A @ B)) @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8257_arith__geo__mean__sqrt)). 185.47/93.69 thf(11648,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (sqrt @ (times_times_real @ A @ B)) @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157])). 185.47/93.69 thf(1241,axiom,((! [A:nat]: ((bit_ri631733984087533419it_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4451_signed__take__bit__of__0)). 185.47/93.69 thf(11896,plain,((! [A:nat]: ((bit_ri631733984087533419it_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241])). 185.47/93.69 thf(1120,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (plus_plus_real @ (semiri5074537144036343181t_real @ B) @ one_one_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7309_nat__le__real__less)). 185.47/93.69 thf(11529,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (plus_plus_real @ (semiri5074537144036343181t_real @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120])). 185.47/93.69 thf(7491,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: ((B = (plus_plus_nat @ A @ C)) => (C = zero_zero_nat)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2399_canonically__ordered__monoid__add__class_OlessE)). 185.47/93.69 thf(33256,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ((B = (plus_plus_nat @ A @ C)) => (C = zero_zero_nat))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7491])). 185.47/93.69 thf(7280,axiom,((! [A:num]: (one != (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6331_semiring__norm_I84_J)). 185.47/93.69 thf(32525,plain,((! [A:num]: ~ (one = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7280])). 185.47/93.69 thf(2499,axiom,((! [A:rat,B:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_add__diff__cancel__left_H)). 185.47/93.69 thf(16017,plain,((! [A:rat,B:rat]: ((minus_minus_rat @ (plus_plus_rat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2499])). 185.47/93.69 thf(1794,axiom,((! [A:nat]: ~ (ord_less_real @ (semiri2265585572941072030t_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7990_fact__not__neg)). 185.47/93.69 thf(13743,plain,((! [A:nat]: ~ (ord_less_real @ (semiri2265585572941072030t_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794])). 185.47/93.69 thf(6701,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ A @ (suc @ (suc @ (suc @ B)))) = (modulo_modulo_nat @ A @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6443_mod__Suc__eq__mod__add3)). 185.47/93.69 thf(30332,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ A @ (suc @ (suc @ (suc @ B)))) = (modulo_modulo_nat @ A @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6701])). 185.47/93.69 thf(6226,axiom,((! [A:real]: ((powr_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) = (abs_abs_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9084_square__powr__half)). 185.47/93.69 thf(28680,plain,((! [A:real]: ((powr_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6226])). 185.47/93.69 thf(4437,axiom,((! [A:rat,B:(num > rat),C:num,D:num]: ((ord_less_rat @ A @ (B @ C)) => ((ord_less_eq_num @ C @ D) => ((ord_less_rat @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4347_order__less__le__subst1)). 185.47/93.69 thf(22206,plain,((! [A:rat,B:(num > rat),C:num,D:num]: ((ord_less_rat @ A @ (B @ C)) => ((ord_less_eq_num @ C @ D) => ((ord_less_rat @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_rat @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4437])). 185.47/93.69 thf(7201,axiom,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2484_power__0)). 185.47/93.69 thf(32252,plain,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7201])). 185.47/93.69 thf(5821,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se4205575877204974255it_nat @ A @ B)) = ((A = zero_zero_nat) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4951_even__unset__bit__iff)). 185.47/93.69 thf(27262,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se4205575877204974255it_nat @ A @ B)) = ((A = zero_zero_nat) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5821])). 185.47/93.69 thf(2986,axiom,((! [A:real,B:real]: ((times_times_real @ (sin_real @ A) @ (cos_real @ B)) = (divide_divide_real @ (plus_plus_real @ (sin_real @ (plus_plus_real @ A @ B)) @ (sin_real @ (minus_minus_real @ A @ B))) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7851_sin__times__cos)). 185.47/93.69 thf(17634,plain,((! [A:real,B:real]: ((times_times_real @ (sin_real @ A) @ (cos_real @ B)) = (divide_divide_real @ (plus_plus_real @ (sin_real @ (plus_plus_real @ A @ B)) @ (sin_real @ (minus_minus_real @ A @ B))) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2986])). 185.47/93.69 thf(3840,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) => (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9057_le__log2__of__power)). 185.47/93.69 thf(20324,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) => (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3840])). 185.47/93.69 thf(3584,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ B) <= (ord_less_real @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4239_dual__order_Ostrict__trans1)). 185.47/93.69 thf(19513,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ B) | ~ (ord_less_real @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3584])). 185.47/93.69 thf(6546,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2301_add__decreasing2)). 185.47/93.69 thf(29827,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6546])). 185.47/93.69 thf(274,axiom,((! [A:(nat > real),B:real]: ((summable_real @ A) => ((times_times_real @ (suminf_real @ A) @ B) = (suminf_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7677_suminf__mult2)). 185.47/93.69 thf(8628,plain,((! [A:(nat > real),B:real]: ((summable_real @ (A)) => ((times_times_real @ (suminf_real @ (A)) @ B) = (suminf_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 185.47/93.69 thf(2457,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_eq_real @ A @ C) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3308_pinf_I8_J)). 185.47/93.69 thf(15872,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_eq_real @ A @ C) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2457])). 185.47/93.69 thf(7087,axiom,((! [A:num]: ((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ A)) = zero_zero_int))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1749_power__zero__numeral)). 185.47/93.69 thf(31861,plain,((! [A:num]: ((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7087])). 185.47/93.69 thf(6387,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_mult__1)). 185.47/93.69 thf(29235,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6387])). 185.47/93.69 thf(4565,axiom,((! [A:int]: ~ (ord_less_int @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4097_order__less__irrefl)). 185.47/93.69 thf(22624,plain,((! [A:int]: ~ (ord_less_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4565])). 185.47/93.69 thf(3675,axiom,((! [A:nat]: ((semiri2265585572941072030t_real @ (suc @ A)) = (times_times_real @ (semiri5074537144036343181t_real @ (suc @ A)) @ (semiri2265585572941072030t_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7970_fact__Suc)). 185.47/93.69 thf(19794,plain,((! [A:nat]: ((semiri2265585572941072030t_real @ (suc @ A)) = (times_times_real @ (semiri5074537144036343181t_real @ (suc @ A)) @ (semiri2265585572941072030t_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3675])). 185.47/93.69 thf(2627,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (sin_real @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7830_sin__x__le__x)). 185.47/93.69 thf(16447,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (sin_real @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2627])). 185.47/93.69 thf(1606,axiom,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ B) = one_one_rat) = ((B = A) & (B != zero_zero_rat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1728_divide__eq__eq__1)). 185.47/93.69 thf(13061,plain,((! [A:rat,B:rat]: (((divide_divide_rat @ A @ B) = one_one_rat) = ((B = A) & ~ (B = zero_zero_rat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1606])). 185.47/93.69 thf(5600,axiom,((! [A:num]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (uminus_uminus_real @ one_one_real)) = (A = one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5286_numeral__eq__neg__one__iff)). 185.47/93.69 thf(26364,plain,((! [A:num]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (uminus_uminus_real @ one_one_real)) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5600])). 185.47/93.69 thf(3097,axiom,((! [A:int,B:int]: ((A != B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4042_order_Ostrict__implies__not__eq)). 185.47/93.69 thf(17982,plain,((! [A:int,B:int]: (~ (A = B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3097])). 185.47/93.69 thf(132,axiom,((! [A:(nat > real),B:set_nat,C:(nat > real),D:set_nat]: ((times_times_real @ (groups6591440286371151544t_real @ A @ B) @ (groups6591440286371151544t_real @ C @ D)) = (groups6591440286371151544t_real @ (^ [E:nat]: (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (A @ E) @ (C @ F))) @ D)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5610_sum__product)). 185.47/93.69 thf(8157,plain,((! [A:(nat > real),B:set_nat,C:(nat > real),D:set_nat]: ((times_times_real @ (groups6591440286371151544t_real @ (A) @ B) @ (groups6591440286371151544t_real @ (C) @ D)) = (groups6591440286371151544t_real @ (^ [E:nat]: (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (A @ E) @ (C @ F))) @ D)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 185.47/93.69 thf(4872,axiom,((! [A:real,B:real]: ((cos_real @ (plus_plus_real @ A @ B)) = (minus_minus_real @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)) @ (times_times_real @ (sin_real @ A) @ (sin_real @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7823_cos__add)). 185.47/93.69 thf(23646,plain,((! [A:real,B:real]: ((cos_real @ (plus_plus_real @ A @ B)) = (minus_minus_real @ (times_times_real @ (cos_real @ A) @ (cos_real @ B)) @ (times_times_real @ (sin_real @ A) @ (sin_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4872])). 185.47/93.69 thf(4250,axiom,(((semiri1314217659103216013at_int @ zero_zero_nat) = zero_zero_int)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6883_of__nat__0)). 185.47/93.69 thf(21602,plain,(((semiri1314217659103216013at_int @ zero_zero_nat) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4250])). 185.47/93.69 thf(2904,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1131_comm__semiring__class_Odistrib)). 185.47/93.69 thf(17365,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2904])). 185.47/93.69 thf(5275,axiom,((! [A:nat]: ((gbinomial_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8417_gbinomial__0_I1_J)). 185.47/93.69 thf(25158,plain,((! [A:nat]: ((gbinomial_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5275])). 185.47/93.69 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185.57/93.70 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 185.57/93.70 % [INFO] Killing All external provers ... 185.79/93.93 EOF