0.06/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.15 % Command : run_Leo-III %s %d 0.15/0.36 % Computer : n012.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 05:27:59 EDT 2022 0.15/0.37 % CPUTime : 0.93/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 3.52/1.63 % [INFO] Parsing done (725ms). 3.52/1.64 % [INFO] Running in sequential loop mode. 3.99/1.83 % [INFO] eprover registered as external prover. 3.99/1.84 % [INFO] cvc4 registered as external prover. 3.99/1.84 % [INFO] Scanning for conjecture ... 6.85/2.62 % [INFO] Found a conjecture and 10255 axioms. Running axiom selection ... 12.63/6.06 % [INFO] Axiom selection finished. Selected 8254 axioms (removed 2001 axioms). 18.41/9.23 % [INFO] Problem is higher-order (TPTP THF). 18.90/9.37 % [INFO] Type checking passed. 18.90/9.38 % [CONFIG] Using configuration: timeout(120) with strategy. Searching for refutation ... 153.18/68.24 % External prover 'cvc4' found a proof! 153.18/68.24 % [INFO] Killing All external provers ... 153.18/68.24 % Time passed: 67727ms (effective reasoning time: 66590ms) 153.18/68.24 % Solved by strategy 153.18/68.26 % Axioms used in derivation (8254): fact_350_Ex__list__of__length, fact_5985_and__numerals_I2_J, fact_6539_of__nat__eq__1__iff, fact_3649_Euclidean__Division_Opos__mod__bound, fact_2833_dual__order_Ostrict__implies__not__eq, fact_1527_double__zero__sym, fact_4699_mult__minus1, fact_9955_tanh__real__at__top, fact_2787_antisym__conv3, help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T, fact_7827_double__gauss__sum__from__Suc__0, fact_378_length__induct, fact_7822_arith__series, fact_2682_order__subst2, fact_3542_mod__le__divisor, fact_4025_dvd__power__same, fact_5040_neg__numeral__less__numeral, fact_4196_is__unit__div__mult__cancel__left, fact_1301_max__add__distrib__right, fact_2832_order_Ostrict__implies__not__eq, fact_4842_take__bit__of__1, fact_8633_prod_Ozero__middle, fact_8993_inverse__less__iff__less, fact_644_power__Suc2, fact_5156_less__minus__one__simps_I1_J, fact_4940_less__minus__iff, fact_4808_mult__neg__numeral__simps_I2_J, fact_3533_minus__mod__eq__mult__div, fact_9258_pos__less__divideR__eq, fact_2283_unique__euclidean__semiring__numeral__class_Odiv__less, fact_8000_power__diff__sumr2, fact_8957_polyfun__extremal__lemma, fact_863_VEBT__internal_Ooption__shift_Osimps_I2_J, fact_9439_nat__plus__as__int, fact_9451_nat__div__distrib, fact_4483_minf_I7_J, fact_2374_diff__frac__eq, fact_474_real__divide__square__eq, fact_6503_of__nat__0__eq__iff, fact_3936_dvdI, fact_2932_order__less__imp__not__eq2, fact_8305_Suc__times__gbinomial, fact_6667_of__nat__less__0__iff, fact_6617_of__nat__power__le__of__nat__cancel__iff, fact_560_div2__Suc__Suc, fact_3770_finite__has__maximal, fact_4631_mult__minus__left, fact_2516_exp__not__zero__imp__exp__diff__not__zero, fact_8164_of__nat__code, fact_1147_add__mono__thms__linordered__semiring_I4_J, fact_3154_order__le__less, fact_1117_add__left__imp__eq, fact_5845_of__int__less__of__int__power__cancel__iff, fact_4950_neg__numeral__neq__numeral, fact_2458_zero__power2, fact_1377_square__diff__one__factored, fact_2177_divide__eq__eq, fact_4649_ln__less__cancel__iff, fact_8354_fact__double, fact_2565_invar__vebt_Ocases, fact_332_one__plus__numeral__commute, fact_2482_less__eq__div__iff__mult__less__eq, fact_3815_dvd__mult__cancel__right, fact_5288_uminus__power__if, fact_5874_of__int__less__neg__numeral__power__cancel__iff, fact_30_less__divide__eq__numeral1_I1_J, fact_5200_eq__minus__divide__eq, fact_5055_ab__group__add__class_Oab__left__minus, fact_4781_semiring__norm_I168_J, fact_1491_mult__zero__right, fact_4210_bit__eq__rec, fact_6265_or__not__num__neg_Osimps_I8_J, fact_3807_dbl__simps_I2_J, fact_3073_order_Oorder__iff__strict, fact_8300_le__mult__floor, fact_2831_order_Ostrict__implies__not__eq, fact_2678_order__subst2, fact_3028_leI, fact_4920_le__minus__iff, fact_7775_sum__natinterval__diff, fact_5287_uminus__power__if, fact_6536_of__nat__mult, fact_9118_binomial__altdef__nat, fact_948_max_OorderI, fact_6410_flip__bit__eq__if, fact_3479_cong__exp__iff__simps_I4_J, fact_2157_divide__less__cancel, fact_4351_of__bool__not__iff, fact_3459_mod__add__eq, fact_5782_of__int__add, fact_613_lift__Suc__antimono__le, fact_1315_add__le__less__mono, fact_4261_zero__le__even__power, fact_6610_of__nat__power__less__of__nat__cancel__iff, fact_4474_minf_I4_J, fact_2811_linorder__less__wlog, fact_5670_signed__take__bit__numeral__minus__bit1, fact_5516_abs__ge__zero, fact_9107_binomial__ge__n__over__k__pow__k, fact_5093_one__neq__neg__numeral, fact_9064_inverse__le__imp__le__neg, fact_2815_order_Ostrict__trans, fact_3441_mod__mult__right__eq, fact_9305_exp__two__pi__i, fact_5302_take__bit__eq__0__iff, fact_5034_zero__neq__neg__numeral, fact_4053_is__unit__mult__iff, fact_6090_AND__upper1_H_H, fact_5603_lemma__interval__lt, fact_5142_not__zero__le__neg__numeral, fact_9641_csqrt_Ocode, fact_2858_order__less__trans, fact_4218_dvd__power, fact_7505_sum_Oinsert__if, fact_1568_diff__self__eq__0, fact_8344_pochhammer__minus, fact_8451_prod_OatMost__Suc, fact_5807_dbl__dec__simps_I5_J, fact_31__C4_C, fact_4100_div__unit__dvd__iff, fact_844_mult__diff__mult, fact_6722_of__nat__mask__eq, fact_6612_of__nat__le__of__nat__power__cancel__iff, fact_4855_diff__numeral__special_I11_J, fact_6416_exp__eq__0__imp__not__bit, fact_842_mult__diff__mult, fact_2745_ord__eq__le__trans, fact_4625_mult__minus__right, fact_7059_suminf__pos, fact_3196_order__neq__le__trans, fact_6750_real__of__nat__div__aux, fact_1595_double__add__less__zero__iff__single__add__less__zero, fact_9114_times__binomial__minus1__eq, fact_1615_mult__cancel__right2, fact_99_numeral__plus__numeral, fact_4195_is__unitE, fact_91_numeral__times__numeral, fact_4264_zero__less__power__eq, fact_6798_int__eq__iff__numeral, fact_6423_stable__imp__bit__iff__odd, fact_7929_sums__Suc__imp, fact_1239_comm__semiring__class_Odistrib, fact_2529_power__minus__mult, fact_2293_frac__le, fact_2193_one__is__add, fact_1734_zero__less__divide__1__iff, fact_1458_VEBT__internal_Omembermima_Osimps_I4_J, fact_4575_add__0__iff, fact_3388_mod__mod__trivial, fact_7273_le__powr__iff, fact_6019_and__numerals_I4_J, fact_5069_zero__neq__neg__one, fact_2520_power__diff__power__eq, fact_4552_set__decode__0, fact_9009_zero__less__binomial__iff, fact_8302_floor__le__iff, fact_1505_add__0, fact_691_less__add__eq__less, fact_4433_pinf_I2_J, fact_2646_ord__le__eq__subst, fact_4801_semiring__norm_I172_J, fact_2351_add__frac__eq, fact_5070_zero__neq__neg__one, fact_6905_norm__power, fact_4164_div__mult__unit2, fact_1371_ordered__ring__class_Ole__add__iff1, fact_8740_prod_OlessThan__Suc__shift, fact_6326_bit__numeral__Bit0__Suc__iff, fact_609_lift__Suc__mono__less__iff, fact_4481_minf_I5_J, fact_8140_Maclaurin__cos__expansion2, fact_9230_vector__fraction__eq__iff, fact_5882_arctan__monotone, fact_5386_semiring__norm_I88_J, fact_696_add__leD2, fact_283_less__numeral__extra_I4_J, fact_1187_add__less__imp__less__left, fact_3415_mod__mult__self4, fact_2109_pos__add__strict, fact_52_numeral__eq__iff, fact_3789_nat__dvd__1__iff__1, fact_2212_vebt__member_Osimps_I3_J, fact_8004_power__half__series, fact_626_less__Suc__eq__le, fact_296_power__one__over, fact_9436_sgn__mod, fact_840_diff__mult__distrib, fact_9351_imaginary__unit_Ocode, fact_1561_le0, fact_9216_scaleR__left__distrib, fact_10073_VEBT__internal_Ovalid_H_Opelims_I1_J, fact_8105_fact__le__power, fact_8054_cos__coeff__0, fact_7174_sin__times__sin, fact_5700_add__neg__numeral__special_I5_J, fact_683_less__mono__imp__le__mono, fact_2716_dual__order_Oeq__iff, fact_9662_csqrt__principal, fact_2331_neg__divide__less__eq, fact_631_less__add__Suc2, fact_3603_old_Oprod_Oinject, fact_1518_add__cancel__left__right, fact_2839_linorder__neqE, fact_2527_power__eq__if, fact_9036_inverse__numeral__1, fact_1673_one__eq__divide__iff, fact_8882_polyfun__linear__factor__root, fact_1440_divide__divide__eq__left_H, fact_5719_inc_Osimps_I2_J, fact_405_list__ball__nth, fact_9029_negative__imp__inverse__negative, fact_6366_bit__numeral__iff, fact_6973_cos__periodic__pi, fact_5266_take__bit__eq__mod, fact_1097_mult_Oleft__commute, fact_6328_bit__numeral__Bit1__Suc__iff, fact_2908_order__less__not__sym, fact_1011_option_Odistinct_I1_J, fact_5319_minus__one__power__iff, fact_5616_numeral__Bit1__div__2, fact_4001_one__dvd, fact_700_trans__le__add1, fact_2979_subset__eq, fact_6999_neg__numeral__less__ceiling, fact_1005_option_Oexhaust, fact_2464_power__decreasing, fact_2459_zero__power2, fact_2782_ord__less__eq__trans, fact_5974_bit_Odisj__one__right, fact_2635_ex__nat__less, fact_8568_prod_Orelated, fact_9266_sin__def, fact_86_mult__numeral__left__semiring__numeral, fact_2610_order__refl, fact_4526_pinf_I9_J, fact_9444_nat__less__eq__zless, fact_1468_deg1Leaf, fact_1482_mult__cancel__left, fact_569_Nat_OlessE, fact_8026_mono__SucI2, fact_8243_pochhammer__0__left, fact_8249_gbinomial__addition__formula, fact_5238_pos__less__minus__divide__eq, fact_4333_length__replicate, fact_7733_set__encode__def, fact_5292_neg__one__power__add__eq__neg__one__power__diff, fact_6658_of__nat__less__of__int__iff, fact_3902_even__succ__div__2, fact_6331_zero__less__log__cancel__iff, fact_2248_mult__strict__mono, fact_8155_sin__coeff__Suc, fact_5823_of__int__less__numeral__iff, fact_4370_odd__of__bool__self, fact_211_list__update__id, fact_2708_dual__order_Otrans, fact_2467_self__le__power, fact_7010_sin__cos__squared__add, fact_734_succ__list__to__short, fact_3606_old_Oprod_Oinject, fact_7951_sums__If__finite__set_H, fact_855_Nat_Odiff__add__assoc2, fact_3968_mult__dvd__mono, fact_9290_sin__minus__converges, fact_1941_power__strict__mono, fact_4646_add__minus__cancel, fact_8224_le__floor__iff, fact_9175_central__binomial__lower__bound, fact_6984_one__less__ceiling, fact_7241_Complex__eq__numeral, fact_1174_add__mono__thms__linordered__semiring_I1_J, fact_2622_i0__less, fact_8766_fact__prod, fact_3578_divmod__digit__1_I1_J, fact_1131_add_Oleft__cancel, fact_6881_pi__series, fact_4407_split__of__bool, fact_46_inthall, fact_228_power__inject__exp, fact_2292_frac__less, fact_7298_tan__total__pos, fact_4728_take__bit__numeral__1, fact_7235_powr__mono2, fact_393_list__eq__iff__nth__eq, fact_1409_mult__commute__abs, fact_5767_of__int__le__iff, fact_7418_sum__nonneg, fact_2736_order__antisym, fact_5597_cong__exp__iff__simps_I13_J, fact_4864_Power_Oring__1__class_Opower__minus__even, fact_7375_cos__of__real__pi__half, fact_2258_add__strict__increasing2, fact_9557_set__bit__nat__def, fact_813_diff__Suc__1, fact_1567_mult__is__0, fact_8450_prod_OatMost__Suc, fact_1683_power__zero__numeral, fact_9681_complex__unit__circle, fact_7172_cos__treble__cos, fact_721_succ__min, fact_6837_abs__sin__le__one, fact_507_field__sum__of__halves, fact_8611_prod_Oin__pairs__0, fact_322_one__le__numeral, fact_1388_times__divide__eq__left, fact_1836_not__less__zero, fact_8942_gbinomial__partial__sum__poly, fact_8068_fact__2, fact_5605_numeral__code_I3_J, fact_2117_add__neg__neg, fact_9547_push__bit__nonnegative__int__iff, fact_4051_is__unit__mult__iff, fact_5908_of__int__neg__numeral, fact_2226_mult__le__less__imp__less, fact_5326_signed__take__bit__eq__take__bit__shift, fact_4880_diff__numeral__special_I4_J, fact_3078_order_Ostrict__iff__order, fact_2724_order__trans, fact_3409_bits__mod__div__trivial, fact_6124_or__one__eq, fact_9274_summable__norm__cos, fact_4746_diff__numeral__special_I12_J, fact_3089_order_Ostrict__trans2, fact_7873_lessThan__subset__iff, fact_7249_ge__one__powr__ge__zero, fact_6195_subset__insertI, fact_6902_norm__mult, fact_9055_mult__inverse__of__nat__commute, fact_3438_add__self__mod__2, fact_9046_power__mult__power__inverse__commute, fact_2198_less__imp__add__positive, fact_7276_ln__powr__bound2, fact_5835_numeral__power__eq__of__int__cancel__iff, fact_5405_abs__le__zero__iff, fact_5938_and_Oidem, fact_1866_divisors__zero, fact_4112_dvd__power__le, fact_3840_dvd__mult__div__cancel, fact_7667_sum_OatLeast__Suc__atMost, fact_3562_div__exp__mod__exp__eq, fact_5103_diff__conv__add__uminus, fact_3380_Bolzano, fact_6126_or__one__eq, fact_4780_semiring__norm_I168_J, fact_5743_take__bit__numeral__bit1, fact_5954_or_Oleft__neutral, fact_4337_of__bool__or__iff, fact_7368_norm__of__real__addn, fact_9406_arcsin__def, fact_9634_plus__complex_Osimps_I1_J, fact_2535_vebt__pred_Osimps_I6_J, fact_8145_Maclaurin__sin__expansion4, fact_1130_add_Oleft__cancel, fact_7406_sum__distrib__left, fact_8285_pochhammer__of__nat__eq__0__iff, fact_6677_of__nat__neq__0, fact_3494_unique__euclidean__semiring__numeral__class_Omod__less, fact_3802_div__dvd__div, fact_3085_order_Ostrict__trans1, fact_6897_zero__less__norm__iff, fact_2387_nat__mult__le__cancel1, fact_4871_power__minus__odd, fact_2028_add__nonneg__nonneg, fact_4153_even__numeral, fact_5749_of__int__code__if, fact_3964_mult__dvd__mono, fact_6403_bit__not__int__iff_H, fact_4163_div__mult__unit2, fact_7202_ceiling__log__nat__eq__if, fact_6749_less__log__of__power, fact_2748_order__class_Oorder__eq__iff, fact_4099_div__unit__dvd__iff, fact_2533_split__div_H, fact_9110_binomial__antimono, fact_314_power__strict__increasing, fact_1563_add__is__0, fact_2235_mult__le__cancel__left__neg, fact_8159_pochhammer__double, fact_8452_prod_Ocl__ivl__Suc, fact_6159_singleton__insert__inj__eq_H, fact_2287_divide__nonpos__neg, fact_7527_sum__nonneg__0, fact_244_one__add__one, fact_9658_cmod__Re__le__iff, fact_6055_or__eq__0__iff, fact_3956_dvd__mult__left, fact_3030_leI, fact_5256_add__divide__eq__if__simps_I6_J, fact_4832_neg__numeral__less__neg__one__iff, fact_8912_sum_Oin__pairs__0, fact_1200_add__mono__thms__linordered__field_I1_J, fact_5980_and__nonnegative__int__iff, fact_7767_cos__int__times__real, fact_4032_dvd__diff__nat, fact_2282_div__positive, fact_5528_abs__triangle__ineq3, fact_1385_divide__divide__eq__left, fact_7540_sum_OatLeastAtMost__rev, fact_7783_mask__eq__sum__exp, fact_2777_ord__eq__less__trans, fact_6463_bit__sum__mult__2__cases, fact_3536_minus__mod__eq__div__mult, fact_3414_mod__mult__self4, fact_9437_nat__abs__mult__distrib, fact_5711_diff__numeral__special_I6_J, fact_5438_zdiv__numeral__Bit1, fact_6527_of__nat__le__iff, fact_9506_split__root, fact_456__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_061_A_Iif_Ax_A_061_Ami_Athen_Athe_A_Ivebt__mint_Asummary_J_A_K_A2_A_094_A_Ideg_Adiv_A2_J_A_L_Athe_A_Ivebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__mint_Asummary_J_J_J_Aelse_Ax_J_092_060close_062, fact_10207_prod__encode__def, fact_5996_one__le__exp__iff, fact_9655_abs__Im__le__cmod, fact_7227_norm__cos__sin, fact_4442_pinf_I4_J, fact_3589_product__nth, fact_496_both__member__options__from__chilf__to__complete__tree, fact_4307_flip__bit__0, fact_1960_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_5218_power__minus, fact_3389_mod__mod__trivial, fact_4243_even__set__bit__iff, fact_5972_bit_Odisj__one__left, fact_5240_neg__less__minus__divide__eq, fact_3432_Suc__times__numeral__mod__eq, fact_6340_log__le__zero__cancel__iff, fact_1784_one__div__two__eq__zero, fact_9__C12_C, fact_3119_dual__order_Ostrict__trans1, fact_6065_not__exp__less__zero, fact_6058_exp__times__arg__commute, fact_1774_zero__eq__power2, fact_918_le__max__iff__disj, fact_2154_divide__strict__right__mono__neg, fact_3465_power__mod, fact_5393_abs__add__abs, fact_3955_dvd__mult__left, fact_6595_numeral__power__eq__of__nat__cancel__iff, fact_9422_nat__numeral__diff__1, fact_8222_pochhammer__fact, fact_8858_prod__mono2, fact_3453_mod__add__right__eq, fact_5299_signed__take__bit__int__less__eq__self__iff, fact_7395_sum__mono, fact_2158_divide__less__0__iff, fact_6896_norm__numeral, fact_7281_tan__60, fact_1511_add__cancel__right__right, fact_265_numeral__le__one__iff, fact_1624_mult__cancel__left1, fact_9197_scaleR__minus1__left, fact_5849_numeral__power__le__of__int__cancel__iff, fact_5275_pos__le__minus__divide__eq, fact_5792_zero__less__arctan__iff, fact_1076_mult__1, fact_9774_zero__int__def, fact_703_le__cube, fact_6566_of__nat__power__eq__of__nat__cancel__iff, fact_3864_unit__mult__div__div, fact_4938_less__minus__iff, fact_2410_mult__less__cancel__right2, fact_7492_sum_Orelated, fact_3088_order_Ostrict__trans2, fact_3124_dual__order_Ostrict__trans1, fact_6231_finite__ranking__induct, fact_3317_VEBT__internal_Onaive__member_Opelims_I1_J, fact_9636_abs__Re__le__cmod, fact_1715_div__by__Suc__0, fact_8282_pochhammer__of__nat__eq__0__iff, fact_5418_abs__power__minus, fact_591_le__Suc__eq, fact_8894_pochhammer__prod__rev, fact_8916_polynomial__product, fact_4985_minus__divide__divide, fact_4061_dvd__mult__unit__iff_H, fact_6113_take__bit__eq__mask__iff, fact_2262_add__strict__increasing, fact_2465_self__le__power, fact_7016_cos__npi__int, fact_7847_geometric__deriv__sums, fact_2751_order__class_Oorder__eq__iff, fact_114_le__divide__eq__numeral1_I1_J, fact_1889_zero__neq__one, fact_9537_xor__Suc__0__eq, fact_3040_antisym__conv1, fact_1856_mult__left__cancel, fact_1384_divide__divide__eq__right, fact_2228_mult__right__le__imp__le, fact_2254_mult__le__cancel__right, fact_1525_add__cancel__left__left, fact_2807_exists__least__iff, fact_2490_mult__eq__if, fact_2304_mult__le__one, fact_7442_sum__mono__inv, fact_7163_ceiling__eq, fact_9491_real__root__lt__1__iff, fact_2628_bot__nat__def, fact_4673_neg__less__eq__nonneg, fact_1484_mult__cancel__left, fact_7155_cos__times__cos, fact_5966_and_Oleft__neutral, fact_8295_pochhammer__product_H, fact_8264_pochhammer__rec, fact_6456_real__less__lsqrt, fact_4500_pinf_I8_J, fact_7260_complex__mult, fact_327_numeral__One, fact_4825_not__neg__one__le__neg__numeral__iff, fact_2120_add__neg__neg, fact_3945_dvd__mult, fact_1240_ring__class_Oring__distribs_I1_J, fact_2551_Suc__n__div__2__gt__zero, fact_8336_gbinomial__minus, fact_1357_diff__less__eq, fact_7190_cos__double__sin, fact_6601_real__of__nat__eq__numeral__power__cancel__iff, fact_628_le__imp__less__Suc, fact_4667_neg__le__0__iff__le, fact_4185_mod__eq__dvd__iff__nat, fact_4652_mod__minus__minus, fact_8328_pochhammer__absorb__comp, fact_6894_norm__one, fact_8050_fact__1, fact_9135_fact__binomial, fact_5419_abs__power__minus, fact_5675_take__bit__Suc__minus__bit1, fact_8525_prod_OatMost__shift, fact_2661_ord__eq__le__subst, fact_3977_dvd__triv__right, fact_829_diff__le__mono, fact_3941_dvd__def, fact_394_list__eq__iff__nth__eq, fact_3332_atLeastatMost__empty, fact_3963_dvd__triv__left, fact_6380_bit__or__int__iff, fact_8104_fact__le__power, fact_606_lift__Suc__mono__less__iff, fact_6131_or__int__rec, fact_3957_dvd__mult__left, fact_6344_bit__numeral__simps_I2_J, fact_7005_cos__npi2, fact_527_old_Onat_Oinject, fact_7654_sum__shift__lb__Suc0__0, fact_4807_mult__neg__numeral__simps_I1_J, fact_3943_dvd__def, fact_8072_fact__ge__zero, fact_7886_sums__mult2, fact_4557_add__scale__eq__noteq, fact_494__C10_C, fact_8092_fact__dvd, fact_260_one__plus__numeral, fact_506_left__add__mult__distrib, fact_9469_floor__eq4, fact_9490_real__root__gt__1__iff, fact_4047_dvd__div__eq__0__iff, fact_8872_sum__gp__basic, fact_9174_binomial__code, fact_519_even__odd__cases, fact_6988_ceiling__diff__numeral, fact_9275_pos__le__minus__divideR__eq, fact_8242_pochhammer__0__left, fact_7353_of__real__neg__numeral, fact_3683_surj__pair, fact_3843_div__add, fact_3882_even__mod__2__iff, fact_8219_pochhammer__fact, fact_453_self__le__ge2__pow, fact_6012_or__numerals_I5_J, fact_9826_nat__of__char__less__256, fact_7408_sum__distrib__left, fact_4995_mod__minus__right, fact_9441_or__nat__def, fact_3951_dvd__mult2, fact_1886_zero__neq__one, fact_9264_sin__converges, fact_1221_diff__eq__diff__less, fact_141_numeral__Bit0, fact_6824_complex__mod__triangle__ineq2, fact_1171_add__mono, fact_3981_dvd__add, fact_5318_minus__one__power__iff, fact_6820_int__of__nat__induct, fact_285_less__numeral__extra_I4_J, fact_7264_powr__less__iff, fact_9388_ln__neg__is__const, fact_127_is__num__normalize_I1_J, fact_6461_real__sqrt__ge__abs1, fact_5635_num_Osize_I6_J, fact_4529_pinf_I9_J, fact_5053_add_Oinverse__unique, fact_3004_realpow__pos__nth, fact_488_semiring__norm_I78_J, fact_7125_sin__zero__abs__cos__one, fact_3948_dvd__mult, fact_8056_fact__Suc__0, fact_4129_dvd__diffD1, fact_4883_diff__numeral__special_I3_J, fact_7962_sum__lessThan__telescope_H, fact_9671_complex__eq__0, fact_8049_fact__1, fact_8376_prod_Oneutral__const, fact_10127_nth__upt, fact_4742_add__neg__numeral__special_I8_J, fact_4948_neg__numeral__neq__numeral, fact_2936_order__less__imp__not__less, fact_5589_numeral__Bit1, fact_6470_real__sqrt__power__even, fact_4571_even__signed__take__bit__iff, fact_7707_arccos__less__mono, fact_2778_ord__eq__less__trans, fact_2038_add__decreasing2, fact_4889_dbl__simps_I4_J, fact_9466_nat__less__iff, fact_4157_unit__eq__div1, fact_1654_mult__divide__mult__cancel__left__if, fact_5614_abs__add__one__gt__zero, fact_1681_power__zero__numeral, fact_9095_binomial__fact__lemma, fact_3213_order__le__less__subst1, fact_6823_nat__int__comparison_I3_J, fact_6360_real__sqrt__pow2, fact_3192_order__neq__le__trans, fact_3394_mod__add__self1, fact_3145_order_Ostrict__implies__order, fact_564_enat__less__induct, fact_8226_le__floor__add, fact_1262_left__diff__distrib_H, fact_7303_tan__bound__pi2, fact_2753_le__cases3, fact_5047_eq__neg__iff__add__eq__0, fact_2214_vebt__insert_Ocases, fact_4601_num_Osize__gen_I2_J, fact_801_max_Oabsorb3, fact_4202_odd__even__add, fact_6448_bit__int__def, fact_8784_even__prod__iff, fact_5_high__bound__aux, fact_35__C1_C, fact_9346_hyperbolic__pythagoras, fact_4547_option_Osize__gen_I2_J, fact_9106_choose__rising__sum_I2_J, fact_3927_division__decomp, fact_1086_add__diff__cancel__right_H, fact_6041_and_Oleft__commute, fact_9764_unbounded__k__infinite, fact_2181_right__inverse__eq, fact_9062_inverse__le__imp__le, fact_2049_not__one__le__zero, fact_8563_prod_Orelated, fact_4911_take__bit__of__2, fact_2385_diff__Suc__less, fact_18_notemp, fact_2260_add__strict__increasing, fact_9251_real__vector__eq__affinity, fact_14__092_060open_062both__member__options_A_ItreeList_A_B_Ahigh_Ama_An_J_A_Ilow_Ama_An_J_092_060close_062, fact_5002_cond__case__prod__eta, fact_8015_sums__if_H, fact_9748_vebt__mint_Opelims, fact_4550_signed__take__bit__Suc, fact_7481_sum__strict__mono__ex1, fact_8180_pochhammer__0, fact_5206_mult__1s__ring__1_I2_J, fact_2505_power2__eq__imp__eq, fact_7903_sums__split__initial__segment, fact_6177_and__nat__numerals_I4_J, fact_4582_crossproduct__noteq, fact_7290_tan__minus__45, fact_6454_odd__bit__iff__bit__pred, fact_6696_unique__euclidean__semiring__with__nat__class_Oof__nat__div, fact_8626_prod_OatLeastAtMost__rev, fact_5687_le__Suc__numeral, fact_9323_sinh__le__cosh__real, fact_9433_zless__nat__eq__int__zless, fact_5033_zero__neq__neg__numeral, fact_9708_card__atMost, fact_74_numeral__le__iff, fact_4756_neg__one__eq__numeral__iff, fact_1366_eq__add__iff1, fact_1144_group__cancel_Oadd1, fact_1749_div__mult__self1, fact_9261_summable__exp__generic, fact_9170_choose__alternating__sum, fact_5651_abs__square__less__1, fact_6961_of__int__ceiling__cancel, fact_6554_of__nat__1, fact_9149_binomial__ring, fact_3071_order_Oorder__iff__strict, fact_8046_fact__0, fact_9541_xor__nat__numerals_I3_J, fact_5199_eq__minus__divide__eq, fact_3711_max__def__raw, fact_2573_buildup__gives__valid, fact_7398_sum__product, fact_5844_of__int__less__of__int__power__cancel__iff, fact_9093_reals__Archimedean, fact_6064_and__eq__minus__1__iff, fact_1688_power__Suc0__right, fact_1074_mult__1, fact_4734_dbl__simps_I1_J, fact_7774_sum__natinterval__diff, fact_4743_add__neg__numeral__special_I8_J, fact_735_pred__list__to__short, fact_2075_mult__strict__left__mono__neg, fact_3075_order_Ostrict__iff__order, fact_209_length__list__update, fact_5443_semiring__norm_I3_J, fact_2578_set__bit__0, fact_5313_minus__power__mult__self, fact_3256_linorder__le__less__linear, fact_7802_double__arith__series, fact_9777_one__int__def, fact_8845_gbinomial__parallel__sum, fact_2128_zero__less__one, fact_6498_of__nat__0, fact_1185_add__less__imp__less__right, fact_2758_lt__ex, fact_1271_diff__diff__eq, fact_2325_divide__strict__left__mono, fact_261_one__plus__numeral, fact_1788_power2__eq__iff__nonneg, fact_4432_pinf_I2_J, fact_2690_order__subst1, fact_4892_power__minus1__even, fact_2518_power__diff__power__eq, fact_337_numerals_I1_J, fact_2327_mult__imp__div__pos__less, fact_4972_one__neq__neg__one, fact_3596_product__nth, fact_3831_dvd__add__times__triv__right__iff, fact_1728_divide__le__0__1__iff, fact_3093_order_Ostrict__trans2, fact_4654_take__bit__of__0, fact_2339_divide__eq__eq__numeral_I1_J, fact_1336_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, fact_6259_Diff__single__insert, fact_133_mult__numeral__1__right, fact_4826_le__divide__eq__numeral1_I2_J, fact_576_less__Suc__eq, fact_1112_add__right__imp__eq, fact_6806_powser__zero, fact_3585_flip__bit__Suc, fact_9660_plus__complex_Ocode, fact_152_left__add__twice, fact_6737_real__of__nat__div, fact_2344_divide__add__eq__iff, fact_6526_of__nat__le__iff, fact_6922_norm__power__ineq, fact_1581_le__add__same__cancel2, fact_3554_unique__euclidean__semiring__numeral__class_Omod__mult2__eq, fact_4952_minus__mult__commute, fact_8080_fact__ge__1, fact_6596_numeral__power__eq__of__nat__cancel__iff, fact_1136_add_Oassoc, fact_4590_set__decode__def, fact_5421_semiring__norm_I7_J, fact_8210_of__int__floor__le, fact_6893_norm__one, fact_4206_odd__one, fact_2242_mult__right__less__imp__less, fact_5431_tanh__real__nonneg__iff, fact_5054_ab__group__add__class_Oab__left__minus, fact_9043_field__class_Ofield__divide__inverse, fact_2323_zero__less__two, fact_3509_mod__mult__div__eq, fact_6856_zdiff__int__split, fact_4141_dvd__div__eq__mult, fact_5897_of__int__nonneg, fact_4913_take__bit__add, fact_6828_int__ops_I7_J, fact_4004_one__dvd, fact_2306_mult__left__le, fact_4286_ex__min__if__finite, fact_9770_Suc__funpow, fact_7166_cos__60, fact_95_add__numeral__left, fact_2427_divide__left__mono__neg, fact_5555_abs__eq__mult, fact_532__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lx_O_ASome_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_3553_unique__euclidean__semiring__numeral__class_Omod__mult2__eq, fact_5157_less__minus__one__simps_I1_J, fact_2802_dual__order_Oirrefl, fact_2356_add__divide__eq__if__simps_I2_J, fact_7926_sum__eq__1__iff, fact_7297_powr__neg__numeral, fact_3961_dvd__triv__left, fact_9218_scaleR__conv__of__real, fact_6295_and__nat__rec, fact_5048_eq__neg__iff__add__eq__0, fact_4727_take__bit__Suc__1, fact_5838_of__int__eq__numeral__power__cancel__iff, fact_2429_mult__imp__div__pos__le, fact_1083_mult_Oright__neutral, fact_9558_flip__bit__nat__def, fact_3029_leI, fact_1416_lambda__one, fact_5203_mult__1s__ring__1_I1_J, fact_5586_abs__diff__less__iff, fact_8228_int__add__floor, fact_7880_powser__sums__zero__iff, fact_227_power__inject__exp, fact_6867_exp__bound__half, fact_122_div__mult2__numeral__eq, fact_4419_replicate__eqI, fact_4975_one__neq__neg__one, fact_2202_nat__mult__less__cancel1, fact_97_numeral__plus__numeral, fact_1992_mult__nonpos__nonpos, fact_220_numeral__eq__one__iff, fact_8636_prod_Ozero__middle, fact_4501_pinf_I8_J, fact_3814_dvd__mult__cancel__right, fact_4642_minus__add__cancel, fact_2119_add__neg__neg, help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T, fact_9072_inverse__add, fact_7372_sum__zero__power_H, fact_5830_of__int__1__less__iff, fact_1684_power__zero__numeral, fact_5916_numeral__BitM, fact_582_less__trans__Suc, fact_3233_order__less__le__subst1, fact_1126_add_Ocommute, fact_7300_tan__less__zero, fact_6868_exp__bound__half, fact_3859_dbl__simps_I5_J, fact_3496_unique__euclidean__semiring__numeral__class_Opos__mod__sign, fact_6408_Icc__eq__insert__lb__nat, fact_10205_le__prod__encode__2, fact_1951_not__numeral__le__zero, fact_3169_linorder__not__le, fact_8273_pochhammer__rec_H, fact_4683_less__neg__neg, fact_326_not__numeral__less__one, fact_8059_fact__Suc__0, fact_7913_sums__mult2__iff, fact_4128_dvd__diffD, fact_2470_one__less__power, fact_1634_nonzero__mult__div__cancel__left, fact_8270_pochhammer__Suc, fact_4294_inf__period_I3_J, fact_2476_power__diff, fact_1061_add__left__cancel, fact_604_lift__Suc__mono__less, fact_2842_linorder__neqE, fact_4066_unit__mult__left__cancel, fact_2701_antisym, fact_6385_bit__1__iff, fact_5394_abs__add__abs, help_If_2_1_If_001t__Nat__Onat_T, fact_4524_exp__div__exp__eq, fact_1775_zero__eq__power2, fact_3946_dvd__mult, fact_3872_even__mult__iff, fact_8158_floor__log__nat__eq__powr__iff, fact_5179_not__neg__one__less__neg__numeral, fact_2675_order__subst2, fact_2761_gt__ex, fact_8991_inverse__negative__iff__negative, fact_2627_half__negative__int__iff, fact_193__C11_C, fact_9734_less__eq__nat_Osimps_I2_J, fact_3980_dvd__add, fact_7311_tan__diff, fact_8334_pochhammer__same, fact_4616_neg__less__iff__less, fact_9207_fraction__scaleR__times, fact_7928_sums__mult__D, fact_859_vebt__mint_Osimps_I2_J, fact_1067_add__le__cancel__left, fact_2554_vebt__member_Oelims_I1_J, fact_7402_sum__distrib__right, fact_482_member__correct, fact_4725_ln__eq__zero__iff, fact_9628_Re__divide__of__nat, fact_4095_div__plus__div__distrib__dvd__right, fact_5773_of__int__1, fact_5210_divide__eq__minus__1__iff, fact_714_invar__vebt_Ointros_I5_J, fact_5662_take__bit__Suc__bit1, fact_1962_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_3856_div__diff, fact_2645_linorder__le__cases, fact_5625_power3__eq__cube, fact_9034_Suc__times__binomial__eq, fact_3262_order__le__imp__less__or__eq, fact_3971_dvd__mult__right, fact_6147_round__unique_H, fact_5682_eq__numeral__Suc, fact_3663_verit__comp__simplify1_I2_J, fact_8454_prod_Ocl__ivl__Suc, fact_5733_nat__intermed__int__val, fact_3442_mod__mult__left__eq, fact_9070_division__ring__inverse__add, fact_5839_of__int__eq__numeral__power__cancel__iff, fact_8205_floor__minus__divide__eq__div__numeral, fact_6220_or__not__num__neg_Osimps_I5_J, fact_6951_square__norm__one, fact_2210_diff__add__0, fact_6088_exp__ge__add__one__self, fact_5746_dbl__inc__simps_I3_J, fact_9023_inverse__less__imp__less, fact_3680_prod__cases, fact_6779_minus__pi__half__less__zero, fact_4533_pinf_I10_J, fact_5515_abs__ge__zero, fact_448_power__even__eq, fact_4115_power__le__dvd, fact_9169_choose__linear__sum, fact_3033_nless__le, fact_3812_dvd__mult__cancel__left, fact_8948_sum__gp0, fact_1055_add__right__cancel, fact_3170_linorder__not__le, fact_6573_of__nat__of__bool, fact_3611_prod_Oinject, fact_1732_divide__eq__eq__numeral1_I1_J, fact_1305_max__add__distrib__left, fact_2497_convex__bound__lt, fact_7017_summable__comparison__test, fact_4927_le__imp__neg__le, fact_7854_monoI2, fact_7162_ceiling__divide__lower, fact_3819_dvd__times__left__cancel__iff, fact_6524_of__nat__le__iff, fact_2625_not__real__square__gt__zero, fact_8519_prod__atLeastAtMost__code, fact_4096_unit__div__cancel, fact_1036_div__by__1, fact_1008_option_OdiscI, fact_34_not__min__Null__member, fact_570_Suc__lessD, fact_9208_fraction__scaleR__times, fact_719_set__vebt__set__vebt_H__valid, fact_3630_length__product, fact_2691_order__subst1, fact_1448_is__pred__in__set__def, fact_2443_frac__le__eq, fact_3253_linorder__le__less__linear, fact_8182_pochhammer__0, fact_8955_polyfun__diff__alt, fact_5209_divide__eq__minus__1__iff, fact_7877_sum_OlessThan__Suc, fact_8070_fact__ge__zero, fact_1172_add__mono, fact_6405_atLeast0__atMost__Suc, fact_1633_nonzero__mult__div__cancel__left, fact_4108_dvd__power__le, fact_7640_sum_Osubset__diff, fact_3849_unit__div__1__unit, fact_5448_zero__less__power__abs__iff, fact_8977_Maclaurin__sin__bound, fact_2856_order__less__asym_H, fact_8127_fact__reduce, fact_1813_power__0__left, fact_8445_prod_OlessThan__Suc, fact_6079_mult__exp__exp, fact_4121_le__imp__power__dvd, fact_4208_bit__eq__rec, fact_7894_sums__divide, fact_585_not__less__less__Suc__eq, fact_263_numeral__le__one__iff, fact_3695_verit__comp__simplify1_I3_J, fact_9447_nat__add__distrib, fact_5401_tanh__real__le__iff, help_If_1_1_If_001t__Extended____Nat__Oenat_T, fact_1453_less__half__sum, fact_4584_crossproduct__noteq, fact_4666_neg__le__0__iff__le, fact_4994_mod__minus__right, fact_1188_add__less__imp__less__left, fact_5147_neg__numeral__less__zero, fact_9445_nat__le__eq__zle, fact_2068_mult__strict__right__mono__neg, fact_790_max_Oabsorb2, fact_3608_prod_Oinject, fact_5411_zero__less__abs__iff, fact_1562_Nat_Oadd__0__right, help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T, fact_1228_distrib__right, fact_6735_reals__Archimedean3, fact_4308_flip__bit__0, fact_9362_cosh__zero__iff, fact_8783_even__prod__iff, fact_9604_and__not__numerals_I7_J, fact_9768_xor__minus__numerals_I1_J, fact_7657_sum_OatLeast0__atMost__Suc, fact_9475_real__root__zero, fact_443_power4__eq__xxxx, fact_1771_power__strict__decreasing__iff, fact_2808_linorder__less__wlog, fact_5888_semiring__norm_I28_J, fact_1678_power__0__Suc, fact_1814_power__0__left, fact_7037_summable__mult__D, fact_2350_add__frac__num, fact_8635_prod_Ozero__middle, fact_722_greater__shift, fact_8102_fact__le__power, fact_8447_prod_OlessThan__Suc, fact_9074_field__class_Ofield__inverse, fact_8286_pochhammer__eq__0__iff, fact_4089_div__mult__div__if__dvd, fact_498_del__x__mi__lets__in__not__minNull, fact_9647_Im__divide__numeral, fact_8631_Iic__subset__Iio__iff, fact_1590_add__le__same__cancel1, fact_5631_abs__le__square__iff, fact_9762_nat__descend__induct, fact_7997_diff__power__eq__sum, fact_1870_mult__not__zero, fact_5094_square__eq__1__iff, fact_4954_minus__mult__commute, fact_8962_fact__code, fact_1801_vebt__delete_Osimps_I1_J, fact_2140_divide__nonpos__nonneg, fact_1741_div__mult__self4, fact_8494_prod__mono, fact_1612_sum__squares__eq__zero__iff, fact_8734_prod_OatLeast__Suc__atMost, fact_1180_add__mono__thms__linordered__semiring_I3_J, fact_1339_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, fact_9484_real__root__one, fact_4177_is__unit__power__iff, fact_1012_option_Odistinct_I1_J, fact_3497_unique__euclidean__semiring__numeral__class_Opos__mod__sign, fact_760_minminNull, fact_4392_zero__less__eq__of__bool, fact_9814_integer__of__num_I2_J, fact_8011_sum__less__suminf2, fact_5678_dbl__dec__simps_I3_J, fact_4558_add__scale__eq__noteq, fact_9589_xor__int__def, fact_9401_arccos__def, fact_7711_arcsin__less__mono, fact_8946_root__polyfun, fact_4391_zero__less__eq__of__bool, fact_78_numeral__less__iff, fact_7178_cos__times__sin, fact_9453_nat__power__eq, fact_7189_cos__one__2pi, fact_6848_pos__int__cases, fact_5706_diff__numeral__special_I5_J, fact_4922_le__minus__iff, fact_2667_linorder__linear, fact_8471_prod_Odistrib, fact_73__092_060open_062both__member__options_Asummary_A_Ihigh_Ama_An_J_092_060close_062, fact_8179_floor__one, fact_1190_add__strict__right__mono, fact_9688_complex__mult__cnj, fact_7299_tan__pos__pi2__le, fact_6909_nonzero__norm__divide, fact_4745_diff__numeral__special_I12_J, fact_5325_take__bit__int__eq__self, fact_5271_take__bit__nat__def, fact_4041_subset__divisors__dvd, fact_6459_sqrt__sum__squares__le__sum__abs, fact_5523_abs__mult__less, fact_2570_vebt__member_Osimps_I2_J, fact_647_power__Suc2, fact_1682_power__zero__numeral, fact_7124_ceiling__divide__eq__div, fact_1198_add__strict__mono, fact_1560_bot__nat__0_Oextremum, fact_657_nat__less__induct, fact_5779_of__int__mult, fact_361_power__commutes, fact_4923_minus__le__iff, fact_5902_of__int__pos, fact_4876_even__take__bit__eq, fact_2246_mult__less__cancel__left, fact_1830_le__numeral__extra_I3_J, fact_2462_power__decreasing, fact_5560_abs__eq__iff_H, fact_8929_Cauchy__product__sums, fact_282_le__numeral__extra_I4_J, fact_928_max_Ocobounded1, fact_367_power__commuting__commutes, fact_6398_log__def, fact_77_numeral__le__iff, fact_2528_power__eq__if, fact_1516_add__cancel__right__left, fact_9113_choose__reduce__nat, fact_1569_diff__0__eq__0, fact_158_mult__2__right, fact_3428_bits__one__mod__two__eq__one, fact_2268_add__nonpos__neg, fact_5866_of__int__le__neg__numeral__power__cancel__iff, fact_6520_of__nat__less__iff, fact_2405_vebt__insert_Osimps_I3_J, fact_7826_gauss__sum, fact_5462_Suc__div__eq__add3__div__numeral, fact_1027_le__add__diff__inverse2, fact_5064_le__minus__one__simps_I4_J, fact_6643_of__nat__le__numeral__power__cancel__iff, fact_7325_of__real__eq__1__iff, fact_1578_double__add__le__zero__iff__single__add__le__zero, fact_858_nat__minus__add__max, fact_2878_ord__less__eq__subst, fact_3411_mod__div__trivial, fact_224_one__eq__numeral__iff, fact_6841_zless__iff__Suc__zadd, fact_6892_norm__le__zero__iff, fact_3925_dvd__productE, fact_2261_add__strict__increasing, fact_5057_ab__group__add__class_Oab__left__minus, fact_3591_product__nth, fact_6437_and__exp__eq__0__iff__not__bit, fact_1646_nonzero__mult__divide__mult__cancel__right2, fact_5947_bit_Oconj__zero__left, fact_1284_diff__diff__eq2, fact_3327_VEBT__internal_Omembermima_Opelims_I1_J, fact_1743_div__mult__self3, fact_8483_prod_Onested__swap_H, fact_7158_sin__squared__eq, fact_6507_of__nat__eq__0__iff, fact_1585_le__add__same__cancel1, fact_5351_signed__take__bit__Suc__minus__bit1, fact_4225_even__two__times__div__two, fact_2150_zero__le__power, fact_5402_semiring__norm_I80_J, fact_1383_divide__divide__eq__right, fact_51_numeral__eq__iff, fact_617_lift__Suc__mono__le, fact_6864_sin__mono__le__eq, fact_2166_nonzero__eq__divide__eq, fact_699_add__le__mono1, fact_4739_add__neg__numeral__special_I7_J, fact_7912_sums__mult2__iff, fact_6871_sin__mono__less__eq, fact_10173_min__diff, fact_2404_div__less__dividend, fact_447_power2__eq__square, fact_3702_verit__sum__simplify, fact_3785_dbl__simps_I3_J, fact_8263_pochhammer__rec, fact_2126_not__one__less__zero, fact_6865_sin__monotone__2pi__le, fact_6927_norm__triangle__ineq, fact_9586_or__not__numerals_I1_J, fact_7188_cos__ge__zero, fact_9523_odd__real__root__pow, fact_2057_zero__less__one__class_Ozero__le__one, fact_2574_inrange, fact_6000_exp__ln, fact_5139_neg__numeral__le__zero, fact_7308_tan__add, help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T, fact_2345_add__divide__eq__iff, fact_808_right__diff__distrib__numeral, fact_1637_div__mult__mult1__if, fact_5333_take__bit__Suc, fact_5459_power__even__abs__numeral, fact_2873_ord__less__eq__subst, fact_1044_add__diff__cancel__left, fact_5927_floor__exists, fact_9363_cosh__zero__iff, fact_8144_Maclaurin__sin__expansion3, fact_2483_dividend__less__times__div, fact_5859_of__int__eq__neg__numeral__power__cancel__iff, fact_504_less__eq__real__def, fact_4986_minus__divide__divide, fact_5114_take__bit__flip__bit__eq, fact_1800_VEBT__internal_Omembermima_Osimps_I1_J, fact_3818_dvd__times__left__cancel__iff, fact_4721_take__bit__0, fact_8125_fact__reduce, fact_1337_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, fact_6032_of__int__or__eq, fact_8306_Suc__times__gbinomial, fact_7169_cos__double__cos, fact_6133_and__int__rec, fact_3576_divmod__digit__1_I1_J, fact_5595_power__minus__Bit1, fact_7306_arctan__tan, fact_70_Collect__cong, fact_4663_neg__0__le__iff__le, fact_621_Suc__le__eq, fact_3712_max__def__raw, fact_4485_minf_I7_J, fact_6140_mask__eq__exp__minus__1, fact_8849_fact__eq__fact__times, fact_8321_gbinomial__rec, fact_4113_power__le__dvd, fact_1159_add__le__imp__le__right, fact_10137_map__add__upt, fact_1042_diff__add__cancel, fact_2044_add__decreasing, fact_1436_times__divide__times__eq, fact_6702_pi__not__less__zero, fact_6402_le__real__sqrt__sumsq, fact_5520_abs__of__pos, fact_1356_less__diff__eq, fact_5587_numeral__Bit1, fact_2771_order_Oasym, fact_328_numeral__One, fact_3251_order__less__le__subst2, fact_8368_gbinomial__partial__row__sum, fact_9368_sinh__def, fact_7378_arcsin__minus__1, fact_5728_numeral__inc, fact_6330_real__sqrt__four, fact_3673_Pair__inject, fact_6914_norm__mult__less, fact_8870_sum__gp__basic, fact_6680_div__mult2__eq_H, fact_5265_take__bit__eq__mod, fact_6815_sin__le__one, fact_6112_exp__le, fact_9421_one__less__nat__eq, fact_7400_sum__product, fact_1724_diff__is__0__eq_H, fact_2208_One__nat__def, fact_3147_dual__order_Ostrict__implies__order, fact_893_power2__diff, fact_4052_is__unit__mult__iff, fact_2430_pos__le__divide__eq, fact_9211_real__scaleR__def, fact_6137_ex__le__of__int, fact_5430_tanh__real__neg__iff, fact_161_mult__2__right, fact_6375_bit__or__iff, fact_4930_compl__mono, fact_5716_add__inc, fact_3224_order__le__less__subst2, fact_3918_power__le__zero__eq__numeral, fact_9225_scaleR__le__cancel__left, fact_2394_length__pos__if__in__set, fact_372_power__mult, fact_7215_tan__periodic__pi, fact_4323_of__bool__eq_I2_J, fact_4435_pinf_I2_J, fact_2001_mult__mono_H, fact_7673_sum__Suc__diff, fact_204_power__one__right, fact_2124_not__one__less__zero, fact_6665_of__nat__0__le__iff, fact_9827_range__nat__of__char, fact_2650_ord__le__eq__subst, fact_5646_abs__sqrt__wlog, fact_3263_order__le__imp__less__or__eq, fact_3072_order_Oorder__iff__strict, fact_10181_take__upt, fact_9587_atLeast0__lessThan__Suc, fact_7282_powr__def, fact_140_mult__numeral__1, fact_9385_cot__periodic, fact_4611_neg__le__iff__le, fact_733_mintlistlength, fact_4056_dvd__mult__unit__iff, fact_9735_max__Suc2, fact_6031_or__numerals_I7_J, fact_9612_or__not__numerals_I5_J, fact_1799_VEBT__internal_Onaive__member_Osimps_I1_J, fact_1289_add__diff__eq, fact_2509_zero__le__power2, fact_6390_disjunctive__add, fact_376_length__induct, fact_1947_vebt__maxt_Osimps_I1_J, fact_9514_sgn__real__def, fact_3283_bot_Oextremum__strict, fact_5237_pos__minus__divide__less__eq, fact_2865_ord__eq__less__subst, fact_2108_pos__add__strict, fact_6697_unique__euclidean__semiring__with__nat__class_Oof__nat__div, fact_2337_eq__divide__eq__numeral_I1_J, fact_7804_double__arith__series, fact_1225_combine__common__factor, fact_2172_divide__eq__imp, fact_8315_pochhammer__product, fact_3500_cong__exp__iff__simps_I1_J, fact_1368_ordered__ring__class_Ole__add__iff2, fact_9581_ex__nat__less__eq, fact_5982_or__nonnegative__int__iff, fact_4465_minf_I2_J, fact_1053_mul__shift, fact_493_both__member__options__from__complete__tree__to__child, fact_8206_neg__numeral__less__floor, fact_7167_cos__30, fact_2355_add__divide__eq__if__simps_I2_J, fact_5116_dvd__div__neg, fact_1706_max__0__1_I1_J, fact_1630_nonzero__mult__div__cancel__right, fact_7600_sum_Omono__neutral__right, fact_2664_ord__eq__le__subst, fact_4018_div__div__div__same, fact_5019_take__bit__tightened__less__eq__int, fact_1991_mult__left__mono, fact_7377_sin__of__real__pi__half, fact_1924_mult__0, fact_8314_pochhammer__product, fact_1492_mult__zero__right, fact_6676_of__nat__neq__0, fact_2281_div__positive, fact_23__C2_C, fact_1483_mult__cancel__left, fact_2008_not__numeral__less__zero, fact_2705_dual__order_Otrans, fact_8313_pochhammer__product, fact_7358_sin__arcsin, fact_1957_zero__le__numeral, fact_3037_nless__le, fact_7009_sin__cos__squared__add, fact_6788_of__nat__code__if, fact_9254_neg__divideR__le__eq, fact_9823_card__UNIV__char, fact_7291_tan__inverse, fact_6005_and__numerals_I5_J, fact_1412_lambda__one, fact_2853_order__less__asym_H, fact_1338_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_1359_square__diff__square__factored, fact_3505_cong__exp__iff__simps_I8_J, fact_1295_diff__eq__eq, fact_4364_in__set__replicate, fact_3988_dvd__add__left__iff, fact_4174_is__unit__div__mult2__eq, fact_419_all__nth__imp__all__set, fact_7245_powr__inj, fact_7547_sum__pos2, fact_1258_right__diff__distrib_H, fact_3579_mult__less__iff1, fact_769_max_Oleft__idem, fact_5537_abs__le__D2, fact_9508_real__root__le__mono, fact_7797_mask__eq__sum__exp__nat, fact_3922_even__succ__div__exp, fact_8157_sin__coeff__def, fact_3640_finite__M__bounded__by__nat, fact_9310_sinh__real__nonpos__iff, fact_5067_le__minus__one__simps_I2_J, fact_9423_nat__less__numeral__power__cancel__iff, fact_8304_floor__eq2, fact_3862_even__Suc, fact_1985_mult__right__mono, fact_4136_unit__dvdE, fact_5193_nonzero__neg__divide__eq__eq2, fact_2608_order__refl, fact_6365_bit__numeral__iff, fact_9199_scaleR__collapse, fact_9731_nat_Odisc__eq__case_I1_J, fact_6979_ceiling__le__numeral, fact_8730_prod_OatLeast0__atMost__Suc, fact_7265_less__powr__iff, fact_1410_mult__commute__abs, fact_8904_prod_Oin__pairs, fact_9747_vebt__maxt_Opelims, fact_1400_del__in__range, fact_5062_le__minus__one__simps_I4_J, fact_8575_prod_Oinsert__if, fact_7139_ceiling__split, fact_1253_comm__monoid__mult__class_Omult__1, fact_1222_diff__strict__mono, fact_2818_not__less__iff__gr__or__eq, fact_7192_cos__arctan, fact_461__092_060open_062vebt__member_Asummary_A_Ihigh_Ama_An_J_092_060close_062, fact_3096_order_Ostrict__iff__not, fact_4503_minf_I6_J, fact_346_neq__if__length__neq, fact_5551_tanh__real__lt__1, fact_7212_powr__gt__zero, fact_9237_scaleR__le__0__iff, fact_5604_numeral__code_I3_J, fact_4457_minf_I1_J, fact_339_power__le__imp__le__exp, fact_8756_polyfun__eq__coeffs, fact_661_nat__le__linear, fact_6141_mask__eq__exp__minus__1, fact_2920_linorder__less__linear, fact_1426_numeral__code_I2_J, fact_6477_real__sqrt__sum__squares__less, fact_5615_numeral__Bit1__div__2, fact_9316_i__even__power, fact_3123_dual__order_Ostrict__trans1, fact_7541_sum_OatLeastAtMost__rev, fact_6322_real__sqrt__le__1__iff, fact_5109_ab__group__add__class_Oab__diff__conv__add__uminus, fact_5090_one__neq__neg__numeral, fact_1978_split__mult__neg__le, fact_1269_left__diff__distrib, fact_5545_abs__less__iff, fact_8098_fact__less__mono, fact_6740_mod__mult2__eq_H, fact_254_numeral__plus__one, fact_3891_power__less__zero__eq__numeral, fact_1040_add__diff__cancel, fact_6022_and__minus__numerals_I5_J, fact_8006_real__sum__nat__ivl__bounded2, fact_5763_of__int__numeral, fact_4387_of__bool__conj, fact_6692_of__nat__mono, fact_7655_sum__shift__lb__Suc0__0, fact_8926_gbinomial__sum__lower__neg, fact_9493_real__root__le__1__iff, fact_5163_neg__numeral__le__one, fact_8139_Maclaurin__cos__expansion, fact_7350_arccos__minus__1, fact_5159_less__minus__one__simps_I3_J, fact_3247_order__less__le__subst2, fact_5701_add__neg__numeral__special_I6_J, fact_1350_diff__le__eq, fact_6635_of__nat__less__numeral__power__cancel__iff, fact_662_le__antisym, fact_4598_take__bit__rec, fact_638_plus__1__eq__Suc, fact_6355_bit__minus__numeral__int_I2_J, fact_4002_one__dvd, fact_3483_div__add1__eq, fact_4737_add__neg__numeral__special_I7_J, fact_651_power__gt1, fact_2189_All__less__Suc2, fact_10191_vimage__Suc__insert__0, fact_2576_set__bit__0, fact_6673_of__nat__neq__0, fact_1753_nonzero__divide__mult__cancel__right, fact_446_power2__eq__square, fact_6407_atLeastAtMostSuc__conv, fact_6488_of__nat__eq__iff, fact_4618_neg__less__iff__less, fact_7517_sum__nonneg__leq__bound, fact_4778_ln__le__zero__iff, fact_6745_pi__ge__two, fact_589_not__less__eq__eq, fact_1288_add__diff__eq, fact_5024_take__bit__int__greater__self__iff, fact_523__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062summin_O_ASome_Asummin_A_061_Avebt__mint_Asummary_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_9051_inverse__eq__divide, fact_7805_double__arith__series, fact_1993_mult__nonpos__nonpos, fact_1425_numeral__code_I2_J, fact_6034_of__int__mask__eq, fact_8976_round__altdef, fact_5611_power__numeral__odd, fact_4_high__def, fact_1621_mult__cancel__left2, fact_4610_Compl__subset__Compl__iff, fact_7768_cos__int__times__real, fact_1075_mult__1, fact_7895_sums__divide, fact_6531_of__nat__add, fact_1534_div__by__0, fact_6009_or__numerals_I3_J, fact_455_power2__nat__le__imp__le, fact_1558_neq0__conv, fact_1651_nonzero__mult__divide__mult__cancel__left, fact_5843_of__int__le__of__int__power__cancel__iff, fact_1226_combine__common__factor, fact_8118_cos__coeff__def, fact_6275_finite__remove__induct, fact_7514_nonzero__of__real__divide, fact_6600_real__of__nat__eq__numeral__power__cancel__iff, fact_4252_mod2__eq__if, fact_2725_order__trans, fact_1664_zero__eq__1__divide__iff, fact_10111_inj__Suc, fact_8755_polyfun__eq__coeffs, fact_9704_cnj__add__mult__eq__Re, fact_5282_take__bit__int__def, fact_8073_fact__not__neg, fact_2504_power2__le__imp__le, fact_2881_ord__less__eq__subst, fact_3103_dense__le__bounded, fact_2270_add__nonpos__neg, fact_2373_diff__frac__eq, fact_5739_nat__ivt__aux, fact_2919_linorder__less__linear, fact_1877_add_Ocomm__neutral, fact_2000_mult__mono_H, fact_4249_oddE, fact_6949_norm__triangle__ineq3, fact_4213_dvd__power__iff, fact_8738_prod_Onat__ivl__Suc_H, fact_9366_cosh__def, fact_6563_of__nat__eq__of__nat__power__cancel__iff, fact_5452_power2__abs, fact_9161_real__le__abs__sinh, fact_3705_neg__zmod__mult__2, fact_2866_ord__eq__less__subst, fact_9387_cot__npi, fact_9282_pos__less__minus__divideR__eq, fact_4450_pinf_I5_J, fact_2081_zero__less__mult__pos2, fact_10142_upt__add__eq__append, fact_6924_norm__add__leD, fact_2862_order__less__trans, fact_5294_neg__one__power__add__eq__neg__one__power__diff, fact_9144_plus__inverse__ge__2, fact_6668_of__nat__less__0__iff, fact_1479_mult__cancel__right, fact_1103_mult_Oassoc, fact_2602_dual__order_Orefl, fact_1031_Suc__double__not__eq__double, fact_9075_field__class_Ofield__inverse, fact_5899_of__int__leD, fact_9465_Suc__nat__eq__nat__zadd1, fact_5233_ln__mult, fact_2830_order_Ostrict__implies__not__eq, fact_4375_bits__1__div__exp, fact_1445_vebt__insert_Osimps_I5_J, fact_7992_sum__gp__strict, fact_4695_add__neg__numeral__simps_I3_J, fact_9315_power2__i, fact_2252_mult__left__less__imp__less, fact_3623_length__product, fact_9669_Im__power2, fact_5239_neg__minus__divide__less__eq, fact_1499_mult__zero__left, fact_6482_arsinh__real__def, fact_7569_norm__less__p1, fact_4901_neg__one__odd__power, fact_3115_dual__order_Ostrict__iff__order, fact_2409_vebt__maxt_Oelims, fact_2078_mult__less__cancel__left__pos, fact_8984_inverse__divide, fact_291_left__right__inverse__power, fact_2361_power__le__imp__le__base, fact_1156_one__reorient, fact_4810_mult__neg__numeral__simps_I2_J, fact_8211_floor__less__cancel, fact_938_max_OboundedI, fact_3703_verit__eq__simplify_I10_J, fact_5692_max__numeral__Suc, fact_8040_sumr__cos__zero__one, fact_5389_abs__numeral, fact_9240_split__scaleR__neg__le, fact_4802_semiring__norm_I172_J, fact_5815_of__int__0__less__iff, fact_2537_power2__less__imp__less, fact_3104_dual__order_Oorder__iff__strict, fact_9511_real__root__gt__zero, fact_9349_arcosh__cosh__real, fact_1297_group__cancel_Osub1, fact_5963_exp__zero, fact_9611_or__not__numerals_I6_J, fact_5556_abs__mult__pos, fact_1641_div__mult__mult2, fact_5977_mask__0, fact_8811_fold__atLeastAtMost__nat_Osimps, fact_654_less__not__refl2, fact_1964_zero__le__mult__iff, fact_3402_mod__mult__self2__is__0, fact_5694_dbl__dec__simps_I2_J, fact_212_list__update__id, fact_9709_card__Collect__le__nat, fact_2046_add__decreasing, fact_7788_sum_Oin__pairs, fact_8598_prod__dvd__prod__subset2, fact_175_nth__list__update__eq, fact_7985_suminf__split__initial__segment, fact_6561_of__nat__eq__of__nat__power__cancel__iff, fact_148_less__mult__imp__div__less, fact_2924_order__less__imp__not__eq, fact_8176_gbinomial__0_I1_J, fact_3960_dvd__triv__left, fact_4953_minus__mult__commute, fact_4752_numeral__eq__neg__one__iff, fact_5037_not__numeral__less__neg__numeral, fact_9568_XOR__upper, fact_6093_exp__minus__inverse, fact_3061_less__le__not__le, fact_2305_mult__le__one, fact_351_Ex__list__of__length, fact_8388_prod_Oinfinite, fact_3095_order_Ostrict__iff__not, fact_6870_sin__less__zero, fact_5184_not__numeral__less__neg__one, fact_4926_le__imp__neg__le, fact_7153_sin__cos__le1, fact_7156_cos__plus__cos, fact_8747_prod_OSuc__reindex__ivl, fact_7196_cos__zero__iff__int, fact_2550_nat__bit__induct, fact_5900_of__int__leD, fact_3765_rev__finite__subset, fact_9664_sin__n__Im__cis__pow__n, fact_8544_power__sum, fact_6663_of__nat__0__le__iff, fact_6419_bit__Suc, fact_2438_divide__le__eq__1, fact_256_numeral__plus__one, fact_3182_order__less__imp__le, fact_1363_eq__add__iff2, fact_5740_take__bit__numeral__minus__bit0, fact_1199_add__mono__thms__linordered__field_I1_J, fact_9336_cosh__real__nonpos__le__iff, fact_5890_inc__BitM__eq, fact_7176_sin__times__cos, fact_6024_and__numerals_I7_J, fact_9257_pos__divideR__less__eq, fact_9089_inverse__less__1__iff, fact_8061_fact__Suc, fact_7570_norm__less__p1, fact_9518_real__root__strict__increasing, fact_9737_diff__Suc, fact_1319_add__mono__thms__linordered__field_I4_J, fact_8311_gbinomial__trinomial__revision, fact_1839_gr__zeroI, fact_9332_sinh__diff, fact_2032_add__increasing2, fact_6156_insert__subset, fact_3847_unit__div, fact_5639_cong__exp__iff__simps_I11_J, fact_7817_arcsin__lbound, fact_5052_add_Oinverse__unique, fact_8147_Maclaurin__sin__expansion, fact_3574_set__bit__Suc, fact_5718_inc_Osimps_I1_J, fact_9554_bit__xor__int__iff, fact_2548_zero__le__even__power_H, fact_2474_power__diff, fact_5992_mask__Suc__0, fact_7317_arcosh__def, fact_5220_power__minus__Bit0, fact_1656_diff__numeral__special_I9_J, fact_6399_signed__take__bit__eq__if__positive, fact_9501_real__root__inverse, fact_1165_add__right__mono, fact_6218_or__not__num__neg_Osimps_I7_J, fact_7222_powr__log__cancel, fact_7262_tan__def, fact_2098_mult__neg__pos, fact_468_field__less__half__sum, fact_851_add__diff__inverse__nat, fact_6559_of__nat__power, fact_4633_mult__minus__left, fact_7963_sum__lessThan__telescope, fact_9594_or__not__numerals_I4_J, fact_5997_exp__le__one__iff, fact_4497_pinf_I6_J, fact_8836_sum_OatMost__shift, fact_1158_add__le__imp__le__right, fact_9312_cosh__0, fact_9743_Suc__0__mod__numeral, fact_1666_eq__divide__eq__1, fact_1546_bits__div__0, fact_9801_integer__of__num__triv_I2_J, fact_5714_signed__take__bit__numeral__minus__bit0, fact_9233_eq__vector__fraction__iff, fact_9212_scaleR__right__distrib, fact_3824_dvd__add__times__triv__left__iff, fact_4741_add__neg__numeral__special_I8_J, fact_5123_dvd__neg__div, fact_1347_add__le__imp__le__diff, fact_349_neq__if__length__neq, fact_1748_div__mult__self2, fact_1871_mult__not__zero, fact_3448_mod__mult__cong, fact_8087_fact__mono, fact_4477_minf_I5_J, fact_7791_arccos, fact_7117_of__int__ceiling__diff__one__le, fact_2587_max__bot2, fact_8379_prod_Oempty, fact_8972_choose__even__sum, fact_5976_mask__eq__0__iff, fact_4717_divide__minus1, fact_4132_dbl__def, fact_9352_cosh__double, fact_2402_div__less__iff__less__mult, fact_2764_less__imp__neq, fact_3547_modulo__nat__def, fact_3932_dvdE, fact_4522_exp__div__exp__eq, fact_6128_one__or__eq, fact_9121_frac__add, fact_84_mult__numeral__left__semiring__numeral, fact_2561_VEBT__internal_Oexp__split__high__low_I2_J, fact_157_mult__2__right, fact_9742_drop__bit__nat__def, fact_5757_dbl__dec__simps_I1_J, fact_8167_gchoose__row__sum__weighted, fact_2723_order__trans, fact_5323_div__pos__neg__trivial, fact_4383_one__mod__2__pow__eq, fact_7672_sum__Suc__diff, fact_5642_cong__exp__iff__simps_I7_J, fact_1149_ab__semigroup__add__class_Oadd__ac_I1_J, fact_6925_norm__triangle__le, fact_3314_vebt__member_Opelims_I3_J, fact_7049_suminf__divide, fact_107_distrib__right__numeral, fact_4378_one__div__2__pow__eq, fact_9186_mult__scaleR__right, fact_6603_real__of__nat__eq__numeral__power__cancel__iff, fact_6143_real__exp__bound__lemma, fact_8735_prod_OatLeast__Suc__atMost, fact_612_lift__Suc__antimono__le, fact_1237_comm__semiring__class_Odistrib, fact_1212_diff__right__mono, fact_4019_div__div__div__same, fact_7223_tan__npi, fact_4182_dvd__mult__cancel, fact_1882_comm__monoid__add__class_Oadd__0, fact_5403_semiring__norm_I73_J, fact_9488_real__root__ge__0__iff, fact_1_bit__split__inv, fact_6580_of__nat__le__0__iff, fact_2136_le__iff__diff__le__0, fact_701_trans__le__add2, fact_9350_Complex__eq__i, fact_5175_not__one__le__neg__numeral, fact_5699_add__neg__numeral__special_I5_J, fact_743_not__None__eq, fact_831_le__diff__iff, fact_9027_inverse__negative__imp__negative, fact_120_div__mult2__numeral__eq, fact_9808_image__Suc__atMost, fact_8481_prod_OatMost__Suc__shift, fact_5984_and__numerals_I2_J, fact_8178_gbinomial__0_I1_J, fact_7771_arccos__cos2, fact_5613_abs__add__one__gt__zero, fact_6852_negative__zless__0, fact_1176_add__mono__thms__linordered__semiring_I1_J, fact_3437_not__mod2__eq__Suc__0__eq__0, fact_8883_polyfun__linear__factor__root, fact_1331_less__add__one, fact_2204_mult__less__mono2, fact_7015_cos__3over2__pi, fact_1650_nonzero__mult__divide__mult__cancel__left2, fact_1610_diff__gt__0__iff__gt, fact_9163_tan__sec, fact_390_Skolem__list__nth, fact_4685_less__neg__neg, fact_9192_scaleR__scaleR, fact_803_diff__diff__left, fact_4722_take__bit__0, fact_1133_add_Oassoc, fact_3450_mod__mult__eq, fact_4148_dvd__div__div__eq__mult, fact_1620_mult__cancel__left2, fact_3949_dvd__mult2, fact_5077_less__minus__one__simps_I4_J, fact_6337_signed__take__bit__nonnegative__iff, fact_6830_zdiv__int, fact_5917_numeral__BitM, fact_5825_of__int__numeral__less__iff, fact_1255_comm__monoid__mult__class_Omult__1, fact_4237_dvd__power__iff__le, fact_2056_zero__less__one__class_Ozero__le__one, fact_6001_exp__ln__iff, fact_72__092_060open_062invar__vebt_A_ItreeList_A_B_Asummin_J_An_092_060close_062, fact_8520_prod__atLeastAtMost__code, fact_89_numeral__times__numeral, fact_4916_take__bit__tightened, fact_3776_finite__has__minimal, fact_4109_dvd__power__le, fact_3313_vebt__member_Opelims_I1_J, fact_3741_finite__maxlen, fact_6899_norm__not__less__zero, fact_8231_gbinomial__pochhammer, fact_368_power__commuting__commutes, fact_8834_polyfun__eq__0, fact_4049_dvd__div__eq__0__iff, fact_6912_power__eq__imp__eq__norm, fact_5235_ln__div, fact_6521_of__nat__less__iff, fact_3517_div__mult__mod__eq, fact_4709_diff__minus__eq__add, fact_6560_of__nat__power, fact_1917_less__eq__nat_Osimps_I1_J, fact_1030_add__def, fact_6522_of__nat__less__iff, fact_1755_nonzero__divide__mult__cancel__left, fact_1245_ring__class_Oring__distribs_I2_J, fact_9292_cos__minus__converges, fact_2099_mult__neg__pos, fact_4650_ln__inj__iff, fact_4331_of__bool__eq__1__iff, fact_8442_sum_OatMost__Suc, fact_5940_or_Oright__idem, fact_1822_VEBT_Oexhaust, fact_4690_ab__left__minus, fact_5878_mult__of__int__commute, fact_4641_minus__add__cancel, fact_2933_order__less__imp__not__less, fact_890_nat__less__add__iff2, fact_629_less__natE, fact_8204_floor__one__divide__eq__div__numeral, fact_146_divide__numeral__1, fact_6487_of__nat__eq__iff, fact_3462_mod__diff__cong, fact_4788_diff__numeral__simps_I3_J, fact_1219_diff__strict__left__mono, fact_8318_gbinomial__factors, fact_1632_nonzero__mult__div__cancel__left, fact_4521_inf__period_I2_J, fact_6163_round__numeral, fact_8789_prod_Oremove, fact_8238_gbinomial__of__nat__symmetric, fact_3160_order__less__le, fact_3419_mod__mult__self2, fact_239_power__add__numeral, fact_2364_div__add__self2, fact_4971_is__num__normalize_I8_J, fact_5385_semiring__norm_I89_J, fact_6216_or__not__num__neg_Osimps_I4_J, fact_3966_mult__dvd__mono, fact_1629_nonzero__mult__div__cancel__right, fact_8441_sum_OatMost__Suc, fact_6374_bit__and__iff, fact_1502_add__0, fact_8065_fact__2, fact_2696_Orderings_Oorder__eq__iff, fact_4205_odd__one, fact_3836_unit__prod, fact_4035_bezout__lemma__nat, fact_5134_ln__less__zero, fact_9629_Re__divide__of__real, fact_812_Nat_Odiff__diff__right, fact_6361_real__sqrt__sum__squares__mult__squared__eq, fact_4346_of__bool__less__one__iff, fact_7108_summable__norm, fact_6901_norm__mult, fact_990_combine__options__cases, fact_8170_gbinomial__0_I2_J, fact_3294_max__absorb2, fact_9408_powr__int, fact_9087_inverse__le__iff, fact_5697_add__neg__numeral__special_I5_J, fact_8762_fact__prod, fact_9739_drop__bit__of__Suc__0, fact_9724_drop__bit__numeral__minus__bit1, fact_4059_mult__unit__dvd__iff, fact_5152_le__minus__one__simps_I1_J, fact_2810_linorder__less__wlog, fact_9263_sin__converges, fact_2859_order__less__trans, fact_2275_add__neg__nonpos, fact_1496_mult__zero__left, fact_1375_less__add__iff1, fact_4873_power__minus__odd, fact_5553_dense__eq0__I, fact_8650_less__1__prod, fact_6017_or__minus__numerals_I6_J, fact_4000_one__dvd, fact_4909_take__bit__of__2, fact_3221_order__le__less__subst1, fact_7513_nonzero__of__real__divide, fact_5490_power__abs, fact_2176_divide__eq__eq, fact_7110_cos__diff, fact_6910_nonzero__norm__divide, fact_5219_power__minus__Bit0, fact_1779_power__mono__iff, fact_2369_divide__diff__eq__iff, fact_2036_add__decreasing2, fact_1442_add__divide__distrib, fact_423_all__set__conv__all__nth, fact_9083_binomial__absorb__comp, fact_9056_mult__inverse__of__int__commute, fact_2673_order__eq__refl, fact_8941_gbinomial__partial__sum__poly, fact_9353_cosh__double, fact_318_power__increasing, fact_2167_nonzero__eq__divide__eq, fact_4414_split__of__bool__asm, fact_9329_cosh__diff, fact_5999_take__bit__minus__one__eq__mask, fact_2320_zero__less__two, fact_6966_ceiling__one, fact_4329_of__bool__eq__1__iff, fact_5722_abs__mod__less, fact_6886_norm__mult__numeral2, fact_233_power__strict__increasing__iff, fact_1489_mult__eq__0__iff, fact_1358_diff__less__eq, fact_6007_and__numerals_I3_J, fact_3531_minus__mult__div__eq__mod, fact_4106_div__power, fact_2419_mult__le__cancel__right2, fact_6588_of__nat__0__less__iff, fact_4262_zero__le__even__power, fact_433_nth__list__update, fact_9467_nat__mult__distrib__neg, fact_3229_order__le__less__subst2, fact_9249_real__vector__affinity__eq, fact_3571_divmod__digit__1_I2_J, fact_7359_sum_Ocl__ivl__Suc, fact_1192_add__strict__left__mono, fact_7981_power__diff__1__eq, fact_8420_prod_Odelta, fact_2073_mult__strict__left__mono, fact_2496_divide__le__eq__numeral_I1_J, fact_6593_numeral__power__eq__of__nat__cancel__iff, fact_1124_add_Ocommute, fact_2805_dual__order_Oirrefl, fact_8319_gbinomial__factors, fact_1229_distrib__right, fact_3153_order__le__less, fact_4358_Bex__set__replicate, fact_3168_linorder__not__le, fact_3151_dual__order_Ostrict__implies__order, fact_4799_semiring__norm_I171_J, fact_3470_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend, fact_614_lift__Suc__antimono__le, fact_6215_subset__Diff__insert, fact_7778_sum__telescope_H_H, fact_5317_minus__one__power__iff, fact_5388_semiring__norm_I84_J, fact_6341_one__le__log__cancel__iff, fact_5817_of__int__less__0__iff, fact_2776_ord__eq__less__trans, fact_5446_semiring__norm_I79_J, fact_4866_Parity_Oring__1__class_Opower__minus__even, fact_4851_diff__numeral__special_I10_J, fact_10169_min__Suc__numeral, fact_6858_sin__pi__divide__n__ge__0, fact_1215_diff__eq__diff__less__eq, fact_7238_powr__mono, fact_7140_summable__ratio__test, fact_3122_dual__order_Ostrict__trans1, fact_445_power2__eq__square, fact_313_power__strict__increasing, fact_9468_nat__abs__int__diff, fact_7820_arcsin__sin, fact_5921_real__of__int__div2, fact_3026_leD, fact_3379_unset__bit__0, fact_4710_uminus__add__conv__diff, fact_4731_signed__take__bit__of__minus__1, fact_3829_dvd__add__times__triv__right__iff, fact_7145_cos__two__less__zero, fact_6654_bit__of__nat__iff__bit, fact_1665_one__divide__eq__0__iff, fact_8324_gbinomial__index__swap, fact_3440_mod__mult__right__eq, fact_7109_summable__norm, fact_1184_add__less__imp__less__right, fact_2191_less__Suc__eq__0__disj, fact_399_nth__mem, fact_6047_or_Ocommute, fact_3406_bits__mod__by__1, fact_8268_pochhammer__Suc, fact_8995_binomial__1, fact_8920_pochhammer__Suc__prod__rev, fact_2180_right__inverse__eq, fact_2386_power__gt__expt, fact_4161_unit__eq__div2, fact_8752_sum__telescope, fact_2218_vebt__pred_Osimps_I3_J, fact_592_Suc__le__D, fact_596_nat__arith_Osuc1, fact_1988_mult__left__mono, fact_370_power__divide, fact_3190_order__le__neq__trans, fact_1169_add__left__mono, fact_3917_power__le__zero__eq__numeral, fact_7836_arcsin__pi, fact_5869_neg__numeral__power__le__of__int__cancel__iff, fact_5106_ab__group__add__class_Oab__diff__conv__add__uminus, fact_8168_gchoose__row__sum__weighted, fact_1346_add__le__imp__le__diff, fact_8195_floor__diff__one, fact_159_mult__2__right, fact_1760_Suc__pred, fact_1751_div__mult__self1, fact_4973_one__neq__neg__one, fact_6310_real__sqrt__zero, fact_3467_mod__Suc__eq, fact_6829_int__ops_I2_J, fact_6968_summable__cmult__iff, fact_6025_and__numerals_I7_J, fact_7819_arcsin__bounded, fact_5285_power2__eq__1__iff, fact_9430_unset__bit__nat__def, fact_2096_mult__pos__neg, fact_1160_add__le__imp__le__left, fact_3548_split__mod, fact_102_num__double, fact_7776_sum__natinterval__diff, fact_4658_case__prod__conv, fact_2021_add__nonneg__eq__0__iff, fact_2485_split__div, fact_2750_order__class_Oorder__eq__iff, fact_4664_neg__0__le__iff__le, fact_677_power__odd__eq, fact_3234_order__less__le__subst1, fact_9053_binomial__le__pow, fact_1512_add__cancel__right__right, fact_9020_norm__inverse__le__norm, fact_3797_dvd__add__triv__right__iff, fact_9119_frac__eq, fact_6389_real__sqrt__eq__zero__cancel, fact_7191_cos__double__sin, fact_4691_ab__left__minus, fact_3817_dvd__mult__cancel__right, fact_1921_add__eq__self__zero, fact_8964_fact__code, fact_6642_of__nat__le__numeral__power__cancel__iff, fact_8482_prod_OatMost__Suc__shift, fact_7216_powr__eq__one__iff, fact_4134_finite__divisors__nat, fact_9598_int__numeral__not__or__num__neg, fact_7480_sum__strict__mono__ex1, fact_7266_log__less__iff, fact_4332_replicate__eq__replicate, fact_167_in__children__def, fact_2755_nle__le, fact_9301_sinh__converges, fact_3320_set__bit__nonnegative__int__iff, fact_3881_even__mod__2__iff, fact_6372_real__sqrt__minus, fact_7789_sum_Oin__pairs, fact_1390_vebt__pred_Osimps_I4_J, fact_841_diff__mult__distrib2, fact_1616_mult__cancel__right2, fact_8213_pochhammer__pos, fact_8266_pochhammer__rec, fact_4135_div2__even__ext__nat, fact_4288_even__mod__4__div__2, fact_6854_sin__gt__zero__02, fact_2715_dual__order_Oeq__iff, fact_5893_real__of__int__div, fact_9146_binomial__ring, fact_7305_arctan__unique, fact_100_numeral__plus__numeral, fact_3852_unit__div__1__div__1, fact_9375_norm__cis, fact_6475_unset__bit__eq, fact_7095_complete__algebra__summable__geometric, fact_6439_real__le__lsqrt, fact_8770_prod__mono__strict, fact_3191_order__neq__le__trans, fact_6333_one__less__log__cancel__iff, fact_1413_lambda__one, fact_2095_mult__pos__neg, fact_9736_max__Suc1, fact_3621_mod__neg__neg__trivial, fact_2030_add__nonneg__nonneg, fact_1727_nat__mult__div__cancel__disj, fact_7722_sum__le__suminf, fact_7974_sum_OatLeast1__atMost__eq, fact_1415_lambda__one, fact_1208_diff__mono, fact_9200_scaleR__collapse, fact_4599_take__bit__rec, fact_2257_add__strict__increasing2, fact_5363_case__prodI2, fact_3177_order__less__imp__le, fact_7449_sum__cong__Suc, fact_1332_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, fact_5322_minus__1__div__exp__eq__int, fact_850_less__diff__conv, fact_1275_add__implies__diff, fact_9341_cosh__real__nonneg__less__iff, fact_2434_divide__left__mono, fact_6472_arith__geo__mean__sqrt, fact_5978_mask__0, fact_323_not__numeral__less__one, fact_6941_norm__diff__ineq, fact_977_max_Ostrict__order__iff, fact_2461_zero__power2, fact_115_divide__le__eq__numeral1_I1_J, fact_4665_neg__le__0__iff__le, fact_5883_arctan__less__iff, fact_3054_dense__le, fact_6148_of__int__round__abs__le, fact_5621_cong__exp__iff__simps_I3_J, fact_3248_order__less__le__subst2, fact_4902_take__bit__Suc__0, fact_4848_diff__numeral__special_I10_J, fact_10079_mono__ge2__power__minus__self, fact_3985_dvd__add__left__iff, fact_5440_semiring__norm_I8_J, fact_9300_sinh__converges, fact_1881_comm__monoid__add__class_Oadd__0, fact_1687_power__Suc0__right, fact_4890_power__minus1__even, fact_5244_eq__divide__eq__numeral_I2_J, fact_4519_inf__period_I2_J, fact_8335_round__def, fact_1099_mult_Ocommute, fact_7976_one__diff__power__eq, fact_6879_sin__zero__lemma, fact_780_diff__Suc__Suc, fact_7244_powr__less__mono2, fact_6223_finite__ranking__induct, fact_9426_nat__le__numeral__power__cancel__iff, fact_8082_fact__fact__dvd__fact, fact_2541_sum__power2__le__zero__iff, fact_3261_order__le__imp__less__or__eq, fact_4463_minf_I2_J, fact_9091_inverse__diff__inverse, fact_9450_nat__abs__triangle__ineq, fact_9540_xor__nat__numerals_I4_J, fact_154_left__add__twice, fact_6336_log__eq__one, fact_6388_real__sqrt__ge__zero, fact_6378_bit__unset__bit__iff, fact_2634_ile0__eq, fact_641_power__Suc, fact_6412_log__base__change, fact_5167_neg__one__le__numeral, fact_5524_abs__mult__less, fact_131_mult__numeral__1__right, fact_4268_even__mask__div__iff_H, fact_5656_divmod_H__nat__def, fact_1216_diff__strict__right__mono, fact_8151_fact__ge__Suc__0__nat, fact_1927_vebt__delete_Osimps_I3_J, fact_454_power2__nat__le__eq__le, fact_4749_numeral__eq__neg__one__iff, fact_594_le__SucE, fact_5693_dbl__dec__simps_I2_J, fact_9715_card__less, fact_1793_zero__less__power2, fact_6455_set__decode__plus__power__2, fact_1794_power__decreasing__iff, fact_388_Skolem__list__nth, fact_7313_lemma__tan__add1, fact_7714_norm__of__real__diff, fact_2679_order__subst2, fact_6926_norm__triangle__le, fact_5021_take__bit__nonnegative, fact_2333_divide__less__eq, fact_6706_of__nat__mod, fact_1444_diff__divide__distrib, fact_6479_take__bit__Suc__from__most, fact_1043_diff__add__cancel, fact_8808_prod_Oub__add__nat, fact_3564_divmod__digit__0_I1_J, fact_3973_dvd__mult__right, fact_4468_minf_I3_J, fact_4857_minus__1__div__2__eq, fact_8051_fact__1, fact_5056_ab__group__add__class_Oab__left__minus, fact_1795_power__decreasing__iff, fact_6834_sin__x__ge__neg__x, fact_8793_prod_Oremove, fact_1897_nat_Odistinct_I1_J, fact_4389_of__bool__conj, fact_2849_linorder__neq__iff, fact_4816_neg__numeral__le__iff, fact_6081_exp__diff, fact_8342_pochhammer__minus_H, fact_7927_sums__mult__D, fact_4563_signed__take__bit__numeral__of__1, fact_2397_nat__diff__split__asm, fact_3397_unset__bit__nonnegative__int__iff, fact_4782_semiring__norm_I168_J, fact_2848_linorder__neq__iff, fact_3742_finite__maxlen, fact_7122_cos__mono__less__eq, fact_1642_div__mult__mult1, fact_5680_pred__numeral__simps_I1_J, fact_5229_real__0__le__add__iff, fact_8196_floor__numeral__power, fact_7326_of__real__eq__1__iff, fact_6962_summable__iff__shift, fact_4736_dbl__simps_I1_J, fact_6552_of__nat__1, fact_6846_sin__zero__iff__int2, fact_8148_fact__mono__nat, fact_3875_odd__add, fact_264_numeral__le__one__iff, fact_4763_minus__one__mult__self, fact_6028_or__numerals_I6_J, fact_4178_unit__imp__mod__eq__0, fact_262_numeral__le__one__iff, fact_3350_atLeastatMost__empty__iff2, fact_7301_tan__mono__le__eq, fact_2786_antisym__conv3, fact_1476_not__gr__zero, fact_5772_of__int__1, fact_5013_case__prodE2, fact_3460_mod__diff__right__eq, fact_753_max__less__iff__conj, fact_5073_numeral__times__minus__swap, fact_5466_Suc__mod__eq__add3__mod__numeral, fact_4689_add_Oright__inverse, fact_2455_power__strict__decreasing, fact_9799_pow_Osimps_I2_J, fact_1636_div__mult__mult1__if, fact_1884_comm__monoid__add__class_Oadd__0, fact_1983_mult__right__mono, fact_6368_real__sqrt__le__mono, fact_8350_floor__log__eq__powr__iff, fact_4908_take__bit__of__exp, fact_6976_sin__cos__squared__add3, fact_4455_pinf_I7_J, fact_6438_real__sqrt__unique, fact_7567_arcsin__eq__iff, fact_2240_mult__strict__mono_H, fact_3515_div__mult__mod__eq, fact_9644_Im__divide__of__real, fact_4968_is__num__normalize_I8_J, fact_2100_mult__neg__pos, fact_8374_atMost__iff, fact_6626_of__nat__zero__less__power__iff, fact_9570_xor__int__unfold, fact_417_all__nth__imp__all__set, fact_7161_cos__squared__eq, fact_4024_dvd__power__same, fact_9052_inverse__eq__divide, fact_6411_sqrt2__less__2, fact_3176_linorder__not__less, fact_6639_numeral__power__le__of__nat__cancel__iff, fact_9529_ln__root, fact_9189_scaleR__one, fact_2383_n__less__m__mult__n, fact_8609_prod_Oin__pairs__0, fact_3405_mod__by__1, fact_9618_Chebyshev__sum__upper__nat, fact_2023_add__nonneg__eq__0__iff, fact_3321_set__bit__negative__int__iff, fact_1411_mult__commute__abs, fact_605_lift__Suc__mono__less__iff, fact_3830_dvd__add__times__triv__right__iff, fact_5752_of__int__code__if, fact_4440_pinf_I3_J, fact_4546_vebt__buildup_Opelims, fact_4681_neg__less__pos, fact_7973_sum_OatLeast1__atMost__eq, fact_7019_summable__comparison__test_H, fact_7363_sum_Ocl__ivl__Suc, fact_2508_zero__le__power2, fact_2828_order_Ostrict__implies__not__eq, fact_8743_prod_OlessThan__Suc__shift, fact_2353_add__divide__eq__if__simps_I1_J, fact_4630_minus__mult__minus, fact_1858_no__zero__divisors, fact_6329_bit__numeral__Bit1__Suc__iff, fact_4759_left__minus__one__mult__self, fact_1909_not0__implies__Suc, fact_4472_minf_I4_J, fact_116_yhelper, fact_1506_zero__eq__add__iff__both__eq__0, fact_5230_real__add__le__0__iff, fact_79_numeral__less__iff, fact_3863_even__Suc__Suc__iff, fact_7371_arcsin__1, fact_3975_dvd__triv__right, fact_10170_min__numeral__Suc, fact_3795_dvd__add__triv__right__iff, fact_4072_dvd__div__mult, fact_6525_of__nat__le__iff, fact_8754_sum__telescope, fact_6936_norm__diff__triangle__le, fact_7310_tan__diff, fact_2088_zero__less__mult__iff, fact_9168_binomial__r__part__sum, fact_1918_bot__nat__0_Oextremum__unique, fact_7070_summable__0__powser, fact_9627_complex__Re__numeral, fact_9443_nat__div__as__int, fact_4636_minus__add__distrib, fact_3915_odd__two__times__div__two__succ, fact_1855_mult__left__cancel, fact_1395_set__vebt_H__def, fact_1653_mult__divide__mult__cancel__left__if, fact_9013_inverse__eq__divide__neg__numeral, fact_8994_binomial__0__Suc, fact_2227_mult__right__le__imp__le, fact_2092_mult__pos__pos, fact_4854_diff__numeral__special_I11_J, fact_2401_nat__mult__div__cancel1, fact_7882_sum__diff__distrib, fact_919_le__max__iff__disj, fact_3139_order_Ostrict__implies__order, fact_3854_unit__div__1__div__1, fact_1674_divide__eq__1__iff, fact_6023_and__minus__numerals_I1_J, fact_6980_ceiling__less__one, fact_5599_cong__exp__iff__simps_I12_J, fact_3520_mod__div__decomp, fact_6433_bit__iff__odd, fact_7798_gauss__sum__nat, fact_1143_group__cancel_Oadd1, fact_3600_pred__none__empty, fact_3484_div__add1__eq, fact_8280_pochhammer__of__nat__eq__0__lemma, fact_3225_order__le__less__subst2, fact_7416_mod__sum__eq, fact_6151_or__minus__numerals_I1_J, fact_8922_pochhammer__Suc__prod__rev, fact_5930_tanh__real__altdef, fact_1773_zero__eq__power2, fact_9461_bit__nat__iff, fact_312_power__less__imp__less__exp, fact_7490_sum_Orelated, fact_8310_gbinomial__trinomial__revision, fact_2637_vebt__buildup_Osimps_I1_J, fact_5832_of__int__less__1__iff, fact_3633_bounded__nat__set__is__finite, fact_746_not__Some__eq, fact_5258_even__minus, fact_1033_div__by__1, fact_7057_suminf__eq__zero__iff, fact_7025_summable__ignore__initial__segment, fact_5283_power2__eq__1__iff, fact_2479_div__geq, fact_5118_dvd__div__neg, fact_10070_VEBT__internal_Ovalid_H_Oelims_I3_J, fact_6432_log__divide, fact_741_vebt__mint_Osimps_I3_J, fact_4784_diff__numeral__simps_I2_J, fact_4289_even__even__mod__4__iff, fact_7718_sum_Oub__add__nat, fact_4965_group__cancel_Oneg1, fact_873_nat__diff__add__eq2, fact_4719_minus__mod__self1, fact_9575_not__negative__int__iff, fact_1329_less__add__one, fact_6349_bit__minus__numeral__Bit1__Suc__iff, fact_10177_min__Suc1, fact_59_mem__Collect__eq, fact_1572_max__nat_Oneutr__eq__iff, fact_7638_sum_Osubset__diff, fact_8088_fact__mono, fact_3825_dvd__add__times__triv__left__iff, fact_3001_realpow__pos__nth2, fact_6130_OR__upper, fact_9033_Suc__times__binomial, fact_3094_order_Ostrict__trans2, fact_4569_signed__take__bit__int__less__exp, fact_9196_scaleR__power, fact_2294_sum__squares__ge__zero, fact_3431_mod2__Suc__Suc, fact_6666_of__nat__0__le__iff, fact_6919_norm__add__less, fact_5342_ln__one__plus__pos__lower__bound, fact_9042_divide__inverse, fact_2407_vebt__delete_Osimps_I6_J, fact_4076_div__mult__swap, fact_9512_real__root__strict__decreasing, fact_6611_of__nat__power__less__of__nat__cancel__iff, fact_1778_power__mono__iff, fact_671_div__nat__eqI, fact_1829_le__numeral__extra_I3_J, fact_2291_frac__less2, fact_1472_member__valid__both__member__options, fact_5453_power2__abs, fact_874_max_Oleft__commute, fact_7316_tan__half, fact_8043_sin__paired, fact_3390_bits__mod__0, fact_4220_dvd__mult__cancel1, fact_8744_prod_OSuc__reindex__ivl, fact_1089_add__diff__cancel__right, fact_6662_of__nat__0__le__iff, fact_3031_leI, fact_10167_min__0L, fact_5140_neg__numeral__le__zero, fact_2359_power__inject__base, fact_4227_even__two__times__div__two, fact_5724_pred__numeral__def, fact_7294_add__tan__eq, fact_8130_Maclaurin__zero, fact_5840_of__int__power__le__of__int__cancel__iff, fact_5278_minus__divide__le__eq, fact_6182_round__neg__numeral, fact_8914_sum_Oin__pairs__0, fact_6935_norm__diff__triangle__le, fact_8444_prod_OlessThan__Suc, fact_6080_mult__exp__exp, fact_1485_mult__cancel__left, fact_2900_order__less__subst2, fact_4492_bits__induct, fact_4192_evenE, fact_588_full__nat__induct, fact_7134_sin__double, fact_5712_diff__numeral__special_I6_J, fact_8396_prod_Oinfinite, fact_3060_less__le__not__le, fact_1990_mult__left__mono, fact_807_right__diff__distrib__numeral, fact_1270_diff__diff__eq, fact_1259_right__diff__distrib_H, fact_4970_is__num__normalize_I8_J, fact_1942_power__strict__mono, fact_7182_sin__diff__sin, fact_2768_less__imp__neq, fact_2050_not__one__le__zero, fact_5398_abs__divide, fact_1553_divide__cancel__left, fact_508_invar__vebt_Ointros_I4_J, fact_5390_abs__numeral, fact_4488_of__bool__odd__eq__mod__2, fact_8963_fact__code, fact_4083_dvd__div__mult2__eq, fact_646_power__Suc2, fact_4900_neg__one__odd__power, fact_2522_less__2__cases, fact_1776_zero__eq__power2, fact_4260_zero__le__odd__power, fact_5196_nonzero__neg__divide__eq__eq, fact_5809_pred__numeral__simps_I2_J, fact_1173_add__mono, fact_6049_and_Oassoc, fact_4626_mult__minus__right, fact_4046_dvd__div__eq__0__iff, fact_6898_zero__less__norm__iff, fact_1139_group__cancel_Oadd2, fact_1122_add_Oleft__commute, fact_2037_add__decreasing2, fact_3801_dvd__1__left, fact_7875_sum_OlessThan__Suc, fact_6168_or__nat__numerals_I4_J, fact_5525_abs__triangle__ineq2__sym, fact_1606_add__less__same__cancel1, fact_2072_mult__strict__left__mono, fact_6585_of__nat__Suc, fact_853_Nat_Ole__diff__conv2, fact_4979_minus__diff__minus, fact_839_diff__add__inverse2, fact_1494_mult__zero__right, fact_5338_stable__imp__take__bit__eq, fact_5645_abs__sqrt__wlog, fact_1535_div__by__0, fact_9963_tendsto__arctan__at__top, fact_5895_BitM__plus__one, fact_7327_of__real__mult, fact_554_max__0__1_I6_J, fact_8464_prod_Onot__neutral__contains__not__neutral, fact_2431_pos__divide__le__eq, fact_8103_fact__le__power, fact_7568_arcsin__le__mono, fact_1556_divide__eq__0__iff, fact_2864_ord__eq__less__subst, fact_802_diff__diff__cancel, fact_451_power__even__eq, fact_4048_dvd__div__eq__0__iff, fact_4395_of__bool__less__eq__one, fact_8064_fact__Suc, fact_5540_abs__le__iff, fact_4379_one__div__2__pow__eq, fact_4159_unit__eq__div1, fact_2897_order__less__subst1, fact_1286_diff__diff__eq2, fact_6040_bit_Oconj__disj__distrib, fact_6441_real__sqrt__sum__squares__eq__cancel2, fact_242_power__add__numeral2, fact_9418_nat__eq__numeral__power__cancel__iff, fact_1832_zero__less__iff__neq__zero, fact_6842_norm__exp, fact_624_Suc__le__lessD, fact_8191_one__le__floor, fact_321_one__le__numeral, fact_1509_add__eq__0__iff__both__eq__0, fact_5295_realpow__square__minus__le, fact_524_mint__member, fact_5105_diff__conv__add__uminus, fact_886_power2__commute, fact_876_max_Oleft__commute, fact_723_less__shift, fact_4964_group__cancel_Oneg1, fact_5074_numeral__times__minus__swap, fact_3851_unit__div__1__unit, fact_7112_cos__add, fact_5100_group__cancel_Osub2, fact_9745_prod__decode__aux_Osimps, fact_4369_odd__of__bool__self, fact_731_succ__correct, fact_5026_not__numeral__le__neg__numeral, fact_9378_cis__2pi, fact_2876_ord__less__eq__subst, fact_9576_atLeastLessThan__singleton, fact_2659_ord__eq__le__subst, fact_2484_dividend__less__div__times, fact_6768_bit__nat__def, fact_1380_real__average__minus__second, fact_7659_sum_OatLeast0__atMost__Suc, fact_6946_power__eq__1__iff, fact_4487_of__bool__odd__eq__mod__2, fact_3059_less__le__not__le, fact_7099_ceiling__le__iff, fact_6960_sincos__total__2pi, fact_7154_cos__times__cos, fact_6184_and__Suc__0__eq, fact_9585_and__not__numerals_I1_J, fact_4637_minus__add__distrib, fact_3421_mod__mult__self1, fact_5455_dvd__numeral__simp, fact_4147_dvd__div__iff__mult, fact_5488_abs__one, fact_2641_order__antisym__conv, fact_2728_order_Otrans, fact_2501_scaling__mono, fact_1432_power__numeral__even, fact_1353_linordered__semidom__class_Oadd__diff__inverse, fact_4958_square__eq__iff, fact_6594_numeral__power__eq__of__nat__cancel__iff, fact_3657_Euclidean__Division_Opos__mod__sign, fact_6975_sin__cos__squared__add3, fact_6616_of__nat__power__le__of__nat__cancel__iff, fact_2266_add__pos__nonneg, fact_1197_add__strict__mono, fact_7085_suminf__pos2, fact_7246_gr__one__powr, fact_2892_order__less__subst1, fact_2473_power__diff, fact_2981_equalityE, fact_9761_bit__cut__integer__def, fact_9224_scaleR__right__mono, fact_300_set__update__subsetI, fact_9691_Re__complex__div__lt__0, fact_1344_diff__add, fact_10190_vimage__Suc__insert__Suc, fact_4266_Euclid__induct, fact_5028_not__numeral__le__neg__numeral, fact_9131_binomial__strict__mono, fact_2798_dual__order_Oasym, fact_6319_real__sqrt__lt__1__iff, fact_3126_dual__order_Ostrict__trans2, fact_1671_divide__self, fact_7129_powser__split__head_I2_J, fact_8448_prod_OatMost__Suc, fact_4859_minus__1__mod__2__eq, fact_4809_mult__neg__numeral__simps_I2_J, fact_9360_sinh__field__def, fact_6101_even__or__iff, fact_6923_norm__add__leD, fact_4620_neg__numeral__eq__iff, fact_4587_option_Osize__gen_I1_J, fact_5027_not__numeral__le__neg__numeral, fact_1690_less__Suc0, fact_847_Suc__diff__le, fact_5058_add__eq__0__iff, fact_6836_sin__ge__minus__one, fact_2640_order__antisym__conv, fact_4384_dvd__antisym, fact_3920_semiring__parity__class_Oeven__mask__iff, fact_543_max__number__of_I1_J, fact_9272_summable__norm__sin, fact_5953_or_Oright__neutral, fact_9455_div__abs__eq__div__nat, fact_1811_power__0__left, fact_9354_tanh__add, fact_4030_mod__mod__cancel, fact_4150_dvd__div__div__eq__mult, fact_6406_atLeastAtMost__insertL, fact_4415_split__of__bool__asm, fact_571_Suc__lessE, fact_7781_summable__partial__sum__bound, fact_5813_of__int__0__le__iff, fact_989_max_Ostrict__coboundedI2, fact_5263_take__bit__Suc__bit0, fact_2439_convex__bound__le, fact_4126_nat__dvd__not__less, fact_3056_less__le__not__le, fact_2090_mult__pos__neg2, fact_4204_odd__even__add, fact_5269_take__bit__nat__eq__self, fact_708_add__mult__distrib, fact_1514_add__cancel__right__left, fact_6783_le__log2__of__power, fact_2466_self__le__power, fact_8947_sum__gp0, fact_7860_monoseq__def, fact_4396_of__bool__less__eq__one, fact_235_power__strict__increasing__iff, fact_9596_bit__minus__int__iff, fact_4496_pinf_I6_J, fact_1273_diff__diff__eq, fact_7365_sum__zero__power, fact_1631_nonzero__mult__div__cancel__left, fact_3055_less__le__not__le, fact_1573_max__nat_Oright__neutral, fact_1875_add_Ogroup__left__neutral, fact_2889_order__less__subst1, fact_6634_of__nat__less__numeral__power__cancel__iff, fact_121_div__mult2__numeral__eq, fact_5958_take__bit__and, fact_640_power__Suc, fact_9452_nat__div__distrib_H, fact_2151_power__mono, fact_8291_pochhammer__of__nat__eq__0__lemma_H, fact_2223_mult__less__le__imp__less, fact_8017_sum__split__even__odd, fact_4480_minf_I5_J, fact_4486_minf_I7_J, fact_1605_add__less__same__cancel1, fact_3412_mod__div__trivial, fact_5915_numeral__BitM, fact_6678_div__mult2__eq_H, fact_6802_sin__npi2, fact_5626_power3__eq__cube, fact_5132_ln__bound, fact_6383_bit__numeral__simps_I1_J, fact_1153_one__reorient, fact_1609_diff__ge__0__iff__ge, fact_6859_sin__45, fact_6688_of__nat__less__imp__less, fact_8832_zero__polynom__imp__zero__coeffs, fact_4878_diff__numeral__special_I4_J, fact_2354_add__divide__eq__if__simps_I1_J, fact_7060_suminf__pos, fact_6826_int__plus, fact_1757_power__eq__0__iff, fact_1850_mult__right__cancel, fact_3884_odd__Suc__div__two, fact_4295_inf__period_I3_J, fact_9758_VEBT__internal_OminNull_Opelims_I2_J, fact_6883_norm__divide__numeral, fact_4107_div__power, fact_2489_VEBT__internal_Onaive__member_Oelims_I3_J, fact_5994_one__less__exp__iff, fact_4536_minf_I9_J, fact_6094_mask__Suc__double, fact_2165_zero__less__power, fact_6504_of__nat__0__eq__iff, fact_4304_triangle__def, fact_2066_mult__strict__right__mono, fact_9081_binomial__Suc__Suc__eq__times, fact_2315_sum__squares__gt__zero__iff, fact_4711_uminus__add__conv__diff, fact_5834_numeral__power__eq__of__int__cancel__iff, fact_6974_cos__periodic__pi2, fact_9245_scaleR__nonpos__nonpos, fact_3455_mod__add__left__eq, fact_5527_abs__triangle__ineq3, fact_3202_order__le__less__trans, fact_4352_Suc__0__mod__eq, fact_3916_odd__two__times__div__two__succ, fact_5268_take__bit__nat__less__exp, fact_6965_ceiling__numeral, fact_3986_dvd__add__left__iff, fact_5758_dbl__dec__simps_I1_J, fact_1370_ordered__ring__class_Ole__add__iff1, fact_2308_mult__left__le, fact_3401_mod__mult__self1__is__0, fact_8106_diffs__def, fact_7662_sum_Onat__ivl__Suc_H, fact_3301_max__absorb1, fact_259_one__plus__numeral, fact_5296_num_Osize__gen_I1_J, fact_6985_ceiling__add__numeral, fact_603_lift__Suc__mono__less, fact_6904_norm__divide, fact_4608_Compl__anti__mono, fact_9372_csqrt__ii, fact_2225_mult__le__less__imp__less, fact_9674_complex__neq__0, fact_9176_sin__x__sin__y, fact_5347_tanh__ln__real, fact_898_max_OcoboundedI2, fact_8839_sum_OatMost__shift, fact_3382_mult__le__cancel__iff1, fact_8074_fact__not__neg, fact_510_insert__simp__norm, fact_8799_prod_Oinsert__remove, fact_8490_atMost__def, fact_2972_equalityD2, fact_1233_distrib__left, fact_583_less__Suc__induct, fact_5059_add__eq__0__iff, fact_6669_of__nat__less__0__iff, fact_8338_gbinomial__reduce__nat, fact_10147_sum__list__upt, fact_5279_le__minus__divide__eq, fact_7770_sin__int__times__real, fact_7285_tan__total, fact_8765_fact__prod, fact_5685_less__Suc__numeral, fact_705_mult__le__mono, fact_658_infinite__descent, fact_2555_vebt__member_Oelims_I3_J, fact_3_pow__sum, fact_377_length__induct, fact_2440_convex__bound__le, fact_2105_mult__neg__neg, fact_5790_of__int__power, fact_1062_add__le__cancel__right, fact_2536_vebt__succ_Osimps_I5_J, fact_3185_order__le__neq__trans, fact_8149_fact__ge__self, fact_4996_mod__minus__cong, fact_9295_exp__series__add__commuting, fact_4430_pinf_I1_J, fact_5521_abs__triangle__ineq, fact_2420_mult__le__cancel__right1, fact_1726_less__one, fact_3900_zero__less__power__eq__numeral, fact_3487_mod__less__divisor, fact_3668_verit__comp__simplify1_I1_J, fact_2222_mult__less__le__imp__less, fact_9829_String_Ochar__of__ascii__of, fact_3816_dvd__mult__cancel__right, fact_7013_ceiling__less__neg__numeral, fact_4792_semiring__norm_I170_J, fact_2034_add__increasing2, fact_9675_Re__divide, fact_6325_real__sqrt__mult__self, fact_6145_exp__lower__Taylor__quadratic, fact_8261_real__of__int__floor__gt__diff__one, fact_4874_even__take__bit__eq, fact_1981_mult__le__0__iff, help_If_1_1_If_001t__Int__Oint_T, fact_7315_tan__half, fact_9952_filterlim__pow__at__bot__even, fact_6890_norm__neg__numeral, fact_7782_mask__eq__sum__exp, fact_1971_mult__nonneg__nonpos, fact_4290_inf__period_I4_J, fact_3206_order__less__le__trans, fact_7374_cos__of__real__pi__half, fact_8742_prod_OlessThan__Suc__shift, fact_6538_of__nat__eq__1__iff, fact_2006_mult__mono, fact_2133_less__numeral__extra_I1_J, fact_2083_zero__less__mult__pos2, fact_8547_prod_Oshift__bounds__cl__nat__ivl, fact_3080_order_Ostrict__iff__order, fact_3199_order__le__less__trans, fact_4191_evenE, fact_6394_bit__take__bit__iff, fact_5300_signed__take__bit__int__greater__self__iff, fact_8443_sum_OatMost__Suc, fact_1398_del__x__not__mi__new__node__nil, fact_8919_pochhammer__Suc__prod__rev, fact_8169_of__int__floor__cancel, fact_6413_bit__imp__take__bit__positive, fact_1611_diff__gt__0__iff__gt, fact_6311_real__sqrt__less__iff, fact_151_numeral__Bit0__div__2, fact_5950_and__zero__eq, fact_8032_monoseq__Suc, fact_3857_concat__bit__nonnegative__iff, fact_7639_sum_Osubset__diff, fact_9187_mult__scaleR__left, fact_6530_of__nat__add, fact_4277_even__mult__exp__div__exp__iff, fact_5277_neg__le__minus__divide__eq, fact_8317_floor__divide__lower, fact_1473_VEBT_Oinject_I2_J, fact_8227_floor__add__int, fact_2861_order__less__trans, fact_8010_sum__less__suminf2, fact_3112_dual__order_Ostrict__iff__order, fact_6062_less__eq__mask, fact_3165_order__less__le, fact_6440_lemma__real__divide__sqrt__less, fact_4793_semiring__norm_I170_J, fact_363_power__mult__distrib, fact_2915_order__less__imp__triv, fact_1594_double__add__less__zero__iff__single__add__less__zero, fact_5904_of__int__lessD, fact_595_Suc__leD, fact_4888_dbl__simps_I4_J, fact_6765_log__base__pow, fact_3584_flip__bit__Suc, fact_3490_mod__if, fact_9165_choose__alternating__linear__sum, fact_9567_push__bit__minus__one, fact_1720_nat__power__eq__Suc__0__iff, fact_6729_of__nat__diff, fact_2375_add__divide__eq__if__simps_I4_J, fact_1517_add__cancel__right__left, fact_7218_powr__one__gt__zero__iff, fact_8234_floor__power, fact_4428_pinf_I1_J, fact_5023_not__take__bit__negative, fact_6008_or__numerals_I3_J, fact_287_one__le__power, fact_8505_prod__pos, fact_9108_binomial__maximum_H, fact_7240_Complex__eq__1, fact_4924_minus__le__iff, fact_6804_sin__npi__int, fact_2276_add__neg__nonpos, fact_6162_singleton__insert__inj__eq, fact_9141_choose__row__sum, fact_2426_field__le__mult__one__interval, fact_5534_abs__leI, fact_6353_real__sqrt__abs, fact_7001_cos__two__pi, fact_2851_linorder__neq__iff, fact_4962_add_Oinverse__distrib__swap, fact_341_one__power2, fact_2106_mult__neg__neg, fact_6930_norm__triangle__mono, fact_6891_norm__le__zero__iff, fact_2127_not__one__less__zero, fact_3782_concat__bit__Suc, fact_739_vebt__insert_Osimps_I4_J, fact_124_div__le__mono, fact_4447_pinf_I5_J, fact_7137_ceiling__unique, fact_8246_pochhammer__0__left, fact_7250_powr__divide, fact_9513_sqrt__def, fact_1626_nonzero__mult__div__cancel__right, fact_1267_left__diff__distrib, fact_537_Suc__le__mono, fact_4495_pinf_I6_J, fact_5627_numeral__3__eq__3, fact_8362_pochhammer__code, fact_3850_unit__div__1__unit, fact_9515_root__abs__power, fact_5467_divmod__algorithm__code_I4_J, fact_9723_floor__real__def, fact_6644_even__of__nat, fact_3475_cong__exp__iff__simps_I9_J, fact_5331_power__minus1__odd, fact_9374_cis__minus__pi__half, fact_8005_real__sum__nat__ivl__bounded2, fact_3378_unset__bit__0, fact_1861_no__zero__divisors, fact_5853_numeral__power__less__of__int__cancel__iff, fact_4776_take__bit__of__1__eq__0__iff, fact_1977_split__mult__neg__le, fact_8951_gbinomial__partial__sum__poly__xpos, fact_9638_one__natural_Orsp, fact_6773_log__of__power__less, fact_9464_nat__2, fact_9373_Arg__ii, fact_492_summaxma, fact_5091_one__neq__neg__numeral, fact_5995_exp__less__one__iff, fact_9136_binomial__fact, fact_3486_mod__induct, fact_2835_dual__order_Ostrict__implies__not__eq, fact_4071_unit__mult__right__cancel, fact_3518_mod__div__decomp, fact_1467_Leaf__0__not, fact_2589_vebt__succ_Opelims, fact_939_max_OboundedI, fact_5619_odd__numeral, fact_7825_gauss__sum, fact_2784_less__induct, fact_2492_vebt__pred_Osimps_I5_J, fact_8075_fact__not__neg, fact_5912_dbl__inc__def, fact_3796_dvd__add__triv__right__iff, fact_649_power__gt1, fact_4075_div__mult__swap, fact_8390_prod_Oinfinite, fact_1669_divide__self__if, fact_4074_dvd__div__mult, fact_1029_mul__def, fact_10155_tl__upt, fact_4247_even__diff__iff, fact_9677_csqrt__unique, fact_6615_of__nat__le__of__nat__power__cancel__iff, fact_3903_even__succ__div__2, fact_3552_unique__euclidean__semiring__numeral__class_Omod__mult2__eq, fact_6738_mod__mult2__eq_H, fact_7088_cos__one__sin__zero, fact_4669_less__eq__neg__nonpos, fact_3693_zmod__zmult2__eq, fact_8100_fact__mod, fact_5663_abs__ln__one__plus__x__minus__x__bound__nonneg, fact_2906_order__less__subst2, fact_9370_sinh__ln__real, fact_3907_even__succ__div__two, fact_4137_unit__dvdE, fact_8527_atMost__Suc, fact_1154_one__reorient, fact_8880_pochhammer__Suc__prod, fact_5231_ln__ge__zero__imp__ge__one, fact_5855_of__int__less__numeral__power__cancel__iff, fact_8289_pochhammer__of__nat__eq__0__lemma_H, fact_4154_unit__div__eq__0__iff, fact_7107_abs__cos__le__one, fact_7209_ceiling__log__eq__powr__iff, fact_8233_gbinomial__pochhammer_H, fact_6042_and_Oleft__commute, fact_8208_floor__minus__one__divide__eq__div__numeral, fact_1051_add__diff__cancel__left_H, fact_8020_mono__SucI1, fact_6430_log__mult, fact_4224_mod__nat__eqI, fact_3512_mod__div__mult__eq, fact_7149_cos__total, fact_118_allvalidinlist, fact_1711_max__0__1_I2_J, fact_9631_Re__divide__numeral, fact_7957_sum_OlessThan__Suc__shift, fact_574_less__SucI, fact_8223_pochhammer__fact, fact_561_Suc__1, fact_2486_add__eq__if, fact_3877_odd__add, fact_8239_pochhammer__nonneg, fact_8260_real__of__int__floor__add__one__ge, fact_5794_arctan__le__zero__iff, fact_9348_sinh__square__eq, fact_2437_le__divide__eq__1, fact_828_diff__le__self, fact_5148_neg__numeral__less__zero, fact_1703_mult__eq__1__iff, fact_8019_sum__pos__lt__pair, fact_9539_horner__sum__of__bool__2__less, fact_7123_cos__monotone__minus__pi__0_H, fact_7366_norm__of__real__add1, fact_548_max__0__1_I5_J, fact_3434_not__mod__2__eq__1__eq__0, fact_1849_zero__neq__numeral, fact_4431_pinf_I1_J, fact_6144_take__bit__eq__mask__iff__exp__dvd, fact_4256_parity__cases, fact_3429_one__mod__two__eq__one, fact_8218_pochhammer__neq__0__mono, fact_9676_csqrt__square, fact_3586_div__less__mono, fact_4694_add__neg__numeral__simps_I3_J, fact_1480_mult__cancel__right, fact_2367_div__add__self1, fact_2422_mult__le__cancel__left2, fact_9130_binomial__strict__antimono, fact_3511_mod__mult__div__eq, fact_6324_real__sqrt__abs2, fact_8768_sum_Onested__swap_H, fact_988_max_Ostrict__coboundedI2, fact_6132_mask__nat__def, fact_1864_divisors__zero, fact_4274_even__mask__div__iff, fact_868_nat__eq__add__iff1, fact_1708_max__0__1_I1_J, fact_2841_linorder__neqE, fact_1547_bits__div__0, fact_1538_div__0, fact_1015_option_Osel, fact_934_max_Oorder__iff, fact_7995_lemma__termdiff1, fact_2182_power__0, fact_4491_bits__induct, fact_6636_numeral__power__le__of__nat__cancel__iff, fact_4831_divide__eq__eq__numeral1_I2_J, fact_2116_add__pos__pos, fact_5634_abs__square__eq__1, fact_2697_Orderings_Oorder__eq__iff, fact_5531_nonzero__abs__divide, fact_1230_distrib__right, fact_4273_even__mask__div__iff, fact_9255_pos__le__divideR__eq, fact_6518_of__nat__numeral, fact_3228_order__le__less__subst2, fact_6759_pi__half__neq__zero, fact_9496_real__root__divide, fact_2544_sum__power2__gt__zero__iff, fact_9049_power__mult__inverse__distrib, fact_2836_dual__order_Ostrict__implies__not__eq, fact_6495_of__nat__0, fact_559_add__2__eq__Suc_H, fact_8351_gbinomial__absorption_H, fact_971_max_Ostrict__boundedE, fact_5541_abs__ge__minus__self, fact_1009_option_OdiscI, fact_9416_zero__less__nat__eq, fact_9690_Re__complex__div__gt__0, fact_4843_take__bit__of__1, fact_3491_mod__geq, fact_4125_bezout__add__strong__nat, fact_4668_less__eq__neg__nonpos, fact_6035_take__bit__eq__mask, fact_7090_sin__add, fact_2303_mult__le__one, fact_8943_root__polyfun, fact_3268_bot_Oextremum__uniqueI, fact_4758_left__minus__one__mult__self, fact_7032_summable__mult2, fact_2514_exp__add__not__zero__imp__left, fact_9221_of__real__def, fact_6682_less__imp__of__nat__less, fact_1738_divide__less__eq__1__neg, fact_2135_less__numeral__extra_I1_J, fact_553_max__0__1_I6_J, fact_8545_power__sum, fact_7773_cos__arcsin__nonzero, fact_3699_verit__sum__simplify, fact_3996_dvd__unit__imp__unit, fact_5321_signed__take__bit__int__eq__self, fact_1601_less__add__same__cancel1, fact_5955_or_Oleft__neutral, fact_1129_add_Oright__cancel, fact_1627_nonzero__mult__div__cancel__right, fact_9017_mult__commute__imp__mult__inverse__commute, fact_724_helpyd, fact_1797_sum__power2__eq__zero__iff, fact_4761_minus__one__mult__self, fact_6219_or__not__num__neg_Osimps_I3_J, fact_1035_div__by__1, fact_5284_power2__eq__1__iff, fact_1874_add_Ogroup__left__neutral, fact_4110_dvd__power__le, fact_1223_diff__strict__mono, fact_5805_dbl__inc__simps_I5_J, fact_8114_fact__numeral, fact_1979_split__mult__neg__le, fact_6428_real__le__rsqrt, fact_1842_less__numeral__extra_I3_J, fact_9026_less__imp__inverse__less__neg, fact_2542_sum__power2__ge__zero, fact_6367_real__sqrt__less__mono, fact_4863_Power_Oring__1__class_Opower__minus__even, fact_9538_Suc__0__xor__eq, fact_8517_prod__atLeastAtMost__code, fact_9150_real__inv__sqrt__pow2, fact_3435_not__mod__2__eq__0__eq__1, fact_5095_square__eq__1__iff, fact_2310_power__less__imp__less__base, fact_6346_bit__minus__numeral__Bit0__Suc__iff, fact_8066_fact__2, fact_6119_exp__double, fact_1790_power2__less__eq__zero__iff, fact_2487_VEBT__internal_Onaive__member_Oelims_I1_J, fact_9415_zless__nat__conj, fact_6460_real__sqrt__ge__abs2, fact_689_trans__less__add1, fact_4117_power__le__dvd, fact_9428_nat__mono, fact_3983_dvd__add, fact_2285_unique__euclidean__semiring__numeral__class_Odiv__less, fact_4461_minf_I1_J, fact_843_mult__diff__mult, fact_4959_square__eq__iff, fact_2054_linordered__nonzero__semiring__class_Ozero__le__one, fact_5487_abs__one, fact_1879_add_Ocomm__neutral, fact_8062_fact__Suc, fact_4735_dbl__simps_I1_J, fact_3692_mod__pos__neg__trivial, fact_7842_gauss__sum__from__Suc__0, fact_1292_eq__diff__eq, fact_3858_concat__bit__negative__iff, fact_2867_ord__eq__less__subst, fact_7080_summable__rabs, fact_837_diff__cancel2, fact_1052_add__shift, fact_4556_diff__shunt__var, fact_1803_VEBT__internal_Onaive__member_Osimps_I2_J, fact_1006_option_Oexhaust, fact_6808_sin__pi__half, fact_5195_nonzero__neg__divide__eq__eq, fact_2468_one__less__power, fact_6512_of__nat__eq__0__iff, fact_5447_semiring__norm_I74_J, fact_3065_not__le__imp__less, fact_7772_arccos__minus, fact_5172_not__numeral__le__neg__one, fact_2421_mult__le__cancel__right1, fact_4253_mod2__eq__if, fact_3422_mod__by__Suc__0, fact_6758_real__archimedian__rdiv__eq__0, fact_5905_of__int__neg__numeral, fact_5119_dvd__div__neg, fact_10192_finite__vimage__Suc__iff, fact_6629_numeral__power__less__of__nat__cancel__iff, fact_2850_linorder__neq__iff, fact_4678_neg__0__less__iff__less, fact_2371_diff__divide__eq__iff, fact_5049_eq__neg__iff__add__eq__0, fact_1396_zdiv__numeral__Bit0, fact_9663_cmod__le, fact_6695_unique__euclidean__semiring__with__nat__class_Oof__nat__div, fact_7666_sum_OatLeast__Suc__atMost, fact_7318_cos__arcsin, fact_5785_of__int__power__eq__of__int__cancel__iff, fact_6270_remove__induct, fact_7369_norm__of__real__addn, fact_9680_complex__abs__le__norm, fact_9605_or__not__numerals_I3_J, fact_4226_even__two__times__div__two, fact_3326_vebt__member_Opelims_I2_J, fact_345_one__power2, fact_943_max_OboundedE, fact_4988_minus__divide__right, fact_1207_add__mono__thms__linordered__field_I5_J, fact_2094_mult__pos__pos, fact_306_power__gt1__lemma, fact_5261_power2__eq__iff, fact_8209_floor__mono, fact_1564_mult__cancel2, fact_1146_add__mono__thms__linordered__semiring_I4_J, fact_6784_log2__of__power__less, fact_6134_mask__half__int, fact_693_le__add1, fact_2229_mult__right__le__imp__le, fact_9481_real__root__eq__0__iff, fact_4716_divide__minus1, fact_2870_ord__eq__less__subst, fact_5842_of__int__le__of__int__power__cancel__iff, fact_6748_log__of__power__eq, fact_1201_add__mono__thms__linordered__field_I1_J, fact_5721_add__One, fact_9285_exp__def, fact_7381_norm__sum, fact_8094_choose__dvd, fact_2273_add__nonneg__pos, fact_4839_power2__minus, fact_4211_dvd__power__iff, fact_3675_Pair__inject, fact_410_in__set__conv__nth, fact_1943_vebt__delete_Ocases, fact_5410_zero__less__abs__iff, fact_1231_distrib__right, fact_1466_deg__not__0, fact_3184_order__le__neq__trans, fact_2840_linorder__neqE, fact_9379_cis__mult, fact_3068_order_Oorder__iff__strict, fact_6792_of__nat__code__if, fact_9345_hyperbolic__pythagoras, fact_5252_minus__divide__diff__eq__iff, fact_1028_le__add__diff__inverse2, fact_5450_abs__power2, fact_7838_le__arcsin__iff, fact_1094_linorder__neqE__linordered__idom, fact_4235_power__mono__odd, fact_6396_bit__of__bool__iff, fact_5579_abs__diff__triangle__ineq, fact_9579_bit__not__int__iff, fact_8841_sum__up__index__split, fact_690_trans__less__add2, fact_4706_diff__minus__eq__add, fact_5250_add__divide__eq__if__simps_I3_J, fact_6036_take__bit__eq__mask, fact_3546_mod__mult2__eq, fact_5610_power__numeral__odd, fact_5216_power__minus, fact_3590_product__nth, fact_7686_arccos__less__arccos, fact_2880_ord__less__eq__subst, fact_3522_cancel__div__mod__rules_I1_J, fact_3039_antisym__conv1, fact_8322_gbinomial__negated__upper, fact_3929_dvdE, fact_8113_fact__numeral, fact_2713_dual__order_Oantisym, fact_386_nth__equalityI, fact_3787_even__succ__mod__exp, fact_8183_pochhammer__0, fact_7955_suminf__le__const, fact_593_le__SucI, fact_3570_mod__double__modulus, fact_2917_order__less__imp__triv, fact_4216_dvd__power, fact_6742_field__char__0__class_Oof__nat__div, fact_7784_sum__gp__multiplied, fact_2695_Orderings_Oorder__eq__iff, fact_1457_pred__empty, fact_9728_drop__bit__Suc__minus__bit0, fact_727_pred__member, fact_6582_of__nat__Suc, fact_8888_sum__power__shift, fact_8918_polynomial__product, fact_7646_sum__diff, fact_8262_real__of__int__floor__ge__diff__one, fact_4443_pinf_I4_J, fact_6631_numeral__power__less__of__nat__cancel__iff, fact_6056_or__eq__0__iff, fact_4869_Parity_Oring__1__class_Opower__minus__even, fact_5088_numeral__neq__neg__one, fact_5812_of__int__0__le__iff, fact_1658_diff__numeral__special_I9_J, fact_7324_of__real__1, fact_6630_numeral__power__less__of__nat__cancel__iff, fact_6474_set__bit__eq, fact_1389_vebt__succ_Osimps_I3_J, fact_6434_bit__iff__odd, fact_7179_sin__plus__sin, fact_2051_not__one__le__zero, fact_6173_subset__Compl__singleton, fact_5350_divmod__nat__if, fact_375_power__mult, fact_3092_order_Ostrict__trans2, fact_6471_real__sqrt__sum__squares__mult__ge__zero, fact_913_max_Oabsorb__iff1, fact_4470_minf_I3_J, fact_511_insert__simp__excp, fact_555_mult__Suc__right, fact_7269_powr__neg__one, fact_7011_cos__2npi, fact_6339_zero__le__log__cancel__iff, fact_1460_VEBT__internal_Omembermima_Osimps_I5_J, fact_1210_diff__left__mono, fact_9771_max__nat_Osemilattice__neutr__order__axioms, fact_7811_double__gauss__sum, fact_4572_signed__take__bit__int__greater__eq__self__iff, fact_4242_even__set__bit__iff, fact_675_power__odd__eq, fact_1268_left__diff__distrib, fact_6835_sin__ge__zero, fact_9063_le__imp__inverse__le, fact_9811_lessThan__Suc__eq__insert__0, fact_2042_add__increasing, fact_10204_prod__encode__prod__decode__aux, fact_8890_sum__power__shift, fact_2265_add__pos__nonneg, fact_4454_pinf_I7_J, fact_6089_and__less__eq, fact_3837_dvd__div__mult__self, fact_2824_dual__order_Ostrict__trans, fact_539_max__Suc__Suc, fact_6747_pi__half__neq__two, fact_5596_power__minus__Bit1, fact_93_add__numeral__left, fact_4852_diff__numeral__special_I11_J, fact_7044_suminf__mult, fact_80_numeral__less__iff, fact_4818_neg__numeral__le__iff, fact_6548_of__nat__1__eq__iff, fact_6698_of__nat__dvd__iff, fact_1737_divide__less__eq__1__pos, fact_3894_even__plus__one__iff, fact_1878_add_Ocomm__neutral, fact_1662_div__self, fact_8090_fact__dvd, fact_1264_right__diff__distrib, fact_2408_vebt__mint_Oelims, fact_9235_Real__Vector__Spaces_Ole__add__iff1, fact_5425_semiring__norm_I72_J, fact_1860_no__zero__divisors, fact_1477_not__gr__zero, fact_2445_power__Suc__less, fact_6937_norm__triangle__ineq4, fact_5045_neg__eq__iff__add__eq__0, fact_1848_zero__neq__numeral, fact_4956_square__eq__iff, fact_3246_order__less__le__subst2, fact_2662_ord__eq__le__subst, fact_1827_zero__le, fact_9602_prod__Suc__Suc__fact, fact_9601_prod__Suc__fact, fact_3399_mod__less, fact_5254_add__divide__eq__if__simps_I5_J, fact_3245_order__less__le__subst2, fact_933_max_Oorder__iff, fact_5162_take__bit__decr__eq, fact_5933_and_Oright__idem, fact_869_nat__eq__add__iff2, fact_2278_add__neg__nonpos, fact_9509_real__root__power, fact_2916_order__less__imp__triv, fact_487_delt__out__of__range, fact_5044_neg__eq__iff__add__eq__0, fact_6464_bit__sum__mult__2__cases, fact_8843_sum__up__index__split, fact_7030_summable__mult, fact_44_inthall, fact_7796_sin__cos__eq, fact_3530_minus__mult__div__eq__mod, fact_4945_numeral__neq__neg__numeral, fact_6931_norm__diff__triangle__less, fact_1449_is__succ__in__set__def, fact_9544_xor__nat__unfold, fact_5862_neg__numeral__power__eq__of__int__cancel__iff, fact_7959_sum_OlessThan__Suc__shift, fact_2363_div__add__self2, fact_4123_mod__eq__dvd__iff, fact_5089_numeral__neq__neg__one, fact_8352_gbinomial__absorption_H, fact_4644_add__minus__cancel, fact_9498_real__root__commute, fact_1402_del__x__mi__lets__in, fact_6849_int__cases3, fact_4862_Power_Oring__1__class_Opower__minus__even, fact_6637_numeral__power__le__of__nat__cancel__iff, fact_500__092_060open_062Some_Asummin_A_061_Avebt__mint_Asummary_092_060close_062, fact_5316_minus__one__power__iff, fact_9651_csqrt__of__real__nonpos, fact_5827_of__int__1__le__iff, fact_7328_of__real__mult, fact_7193_sincos__total__pi, fact_9656_times__complex_Osimps_I2_J, fact_1934_lambda__zero, fact_6993_ceiling__less__zero, fact_728_pred__corr, fact_4932_compl__le__swap1, fact_3344_atLeastatMost__empty__iff, fact_8440_sum_OatMost__Suc, fact_959_max_Omono, fact_8071_fact__ge__zero, fact_4102_dvd__div__unit__iff, fact_1846_zero__neq__numeral, fact_730_pred__correct, fact_9334_cosh__real__nonneg, fact_6945_power__eq__1__iff, fact_1713_max__0__1_I2_J, fact_711_nat__mult__1__right, fact_2274_add__nonneg__pos, fact_8063_fact__Suc, fact_392_list__eq__iff__nth__eq, fact_5334_take__bit__Suc, fact_6728_of__nat__diff, fact_8757_prod_OatLeast1__atMost__eq, fact_825_less__imp__diff__less, help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T, fact_5133_ln__gt__zero__imp__gt__one, fact_1937_lambda__zero, fact_3947_dvd__mult, fact_5324_take__bit__int__eq__self__iff, fact_1323_less__1__mult, fact_2759_lt__ex, fact_2480_Suc__diff__eq__diff__pred, fact_1263_left__diff__distrib_H, fact_5993_mask__Suc__0, fact_5180_not__neg__one__less__neg__numeral, fact_4436_pinf_I2_J, fact_3003_vebt__buildup_Osimps_I2_J, fact_4627_minus__mult__minus, fact_8624_prod_Onat__diff__reindex, fact_3258_order__le__imp__less__or__eq, fact_8038_sum__bounds__lt__plus1, fact_8044_fact__0, fact_4978_minus__diff__minus, fact_3791_dvd__add__triv__left__iff, fact_2846_order__less__asym, fact_8518_prod__atLeastAtMost__code, fact_9399_cot__def, fact_8053_fact__1, fact_1224_combine__common__factor, fact_9054_mult__inverse__of__nat__commute, fact_7999_power__diff__sumr2, fact_5183_not__one__less__neg__numeral, fact_83_mult__numeral__left__semiring__numeral, fact_9358_cosh__field__def, fact_9066_zero__less__binomial, fact_4009_dvd__div__eq__iff, fact_1614_mult__cancel__right2, fact_5674_dbl__dec__simps_I4_J, fact_6649_mult__of__nat__commute, fact_119__C111_C, fact_9247_scaleR__2, fact_9178_sums__cos__x__plus__y, fact_5709_diff__numeral__special_I6_J, fact_4805_mult__neg__numeral__simps_I1_J, fact_4257_zero__le__power__eq, fact_241_power__add__numeral2, fact_5975_mask__eq__0__iff, fact_1640_div__mult__mult2, fact_3408_bits__mod__div__trivial, fact_3933_dvdE, fact_513_nat__mult__eq__1__iff, fact_9485_real__root__eq__1__iff, fact_5632_abs__le__square__iff, fact_8220_pochhammer__fact, fact_7267_less__log__iff, fact_6944_norm__triangle__ineq2, fact_4765_mod__minus1__right, fact_4787_diff__numeral__simps_I2_J, fact_1838_gr__zeroI, fact_9622_valid__eq1, fact_1508_add__eq__0__iff__both__eq__0, fact_9299_exp__first__terms, fact_3638_finite__list, fact_2413_mult__less__cancel__right1, fact_8099_fact__less__mono, fact_8278_pochhammer__of__nat__eq__0__lemma, fact_1403_del__x__mi__lets__in__minNull, fact_4167_unit__div__commute, fact_5068_zero__neq__neg__one, fact_6850_zmult__zless__mono2__lemma, fact_2138_divide__right__mono__neg, fact_483_semiring__norm_I6_J, fact_618_lift__Suc__mono__le, fact_8007_real__sum__nat__ivl__bounded2, fact_2710_dual__order_Oantisym, fact_4269_even__mask__div__iff_H, fact_3835_unit__prod, fact_110_distrib__left__numeral, fact_8057_fact__Suc__0, fact_3403_mod__mult__self2__is__0, fact_2896_order__less__subst1, fact_9324_sinh__less__cosh__real, fact_4896_neg__one__even__power, fact_856_Nat_Ole__imp__diff__is__add, fact_8966_gbinomial__r__part__sum, fact_2803_dual__order_Oirrefl, fact_2763_dense, fact_536_misiz, fact_3433_not__mod__2__eq__1__eq__0, fact_6387_real__sqrt__gt__zero, fact_7914_sums__mult__iff, fact_6057_exp__less__cancel, fact_5558_abs__eq__iff_H, fact_4005_one__dvd, fact_7142_mult__ceiling__le, fact_90_numeral__times__numeral, fact_1532_add_Oright__neutral, fact_6515_of__nat__numeral, fact_4733_dbl__simps_I1_J, fact_9001_inverse__le__iff__le, fact_2779_ord__less__eq__trans, fact_9158_tan__cot, fact_7761_convex__sum__bound__le, fact_1772_power__strict__decreasing__iff, fact_6558_of__nat__power, fact_4190_evenE, fact_4042_concat__bit__assoc, fact_6586_of__nat__Suc, fact_4313_of__bool__less__eq__iff, fact_1661_div__self, fact_3834_unit__prod, fact_1522_add__cancel__left__left, fact_2775_ord__eq__less__trans, fact_6730_of__nat__diff, fact_6118_exp__half__le2, fact_9281_pos__minus__divideR__less__eq, fact_4635_minus__add__distrib, fact_5080_less__minus__one__simps_I2_J, fact_6096_less__mask, fact_3426_Suc__mod__mult__self1, fact_4258_zero__le__power__eq, fact_356_ex__power__ivl1, fact_3860_dbl__simps_I5_J, fact_3660_verit__la__disequality, fact_2233_mult__le__cancel__left__pos, fact_3665_verit__comp__simplify1_I2_J, fact_6499_of__nat__0, fact_5072_numeral__times__minus__swap, fact_3100_order_Ostrict__iff__not, fact_538_add__Suc__right, fact_9417_diff__nat__numeral, fact_4101_div__unit__dvd__iff, fact_584_strict__inc__induct, fact_9479_sgn__le__0__iff, fact_4162_unit__eq__div2, fact_9798_sqr__conv__mult, fact_8846_gbinomial__parallel__sum, fact_4082_dvd__div__mult2__eq, fact_9205_inverse__scaleR__times, fact_3461_mod__diff__left__eq, fact_249_power__increasing__iff, fact_5168_neg__one__le__numeral, fact_8134_Maclaurin__zero, fact_6787_of__nat__code__if, fact_1854_mult__left__cancel, fact_6142_exp__bound, fact_4819_neg__numeral__less__iff, fact_6575_of__nat__of__bool, fact_8959_polyfun__diff, fact_904_max_OcoboundedI1, fact_4643_add__minus__cancel, fact_9552_push__bit__of__Suc__0, fact_9804_image__Suc__atLeastAtMost, fact_179_list__update__beyond, fact_6192_subset__insertI2, fact_3990_dvd__add__right__iff, fact_4498_pinf_I8_J, fact_8857_prod__mono2, fact_8750_sum_OatMost__Suc__shift, fact_7708_arccos__ubound, fact_7456_sum__le__included, fact_1582_le__add__same__cancel2, fact_310_power__less__imp__less__exp, fact_9098_real__arch__inverse, fact_7936_sums__Suc__iff, fact_2477_power__diff, fact_8934_gbinomial__Suc, fact_2657_ord__eq__le__subst, fact_6092_exp__minus__inverse, fact_697_le__Suc__ex, fact_8978_inverse__mult__distrib, fact_231_power__mult__numeral, fact_9500_real__root__mult__exp, fact_1949_VEBT__internal_OminNull_Oelims_I3_J, fact_8269_pochhammer__Suc, fact_620_Suc__leI, fact_1162_add__le__imp__le__left, fact_1193_add__strict__left__mono, fact_6959_cos__pi__eq__zero, fact_8625_prod_Onat__diff__reindex, fact_2149_zero__le__power, fact_7996_diff__power__eq__sum, fact_8953_polyfun__diff__alt, fact_4272_even__mask__div__iff, fact_147_divide__numeral__1, fact_1702_one__eq__mult__iff, fact_6877_exp__bound__lemma, fact_2236_mult__le__cancel__left__neg, fact_1317_add__mono__thms__linordered__field_I3_J, fact_6108_one__and__eq, fact_2256_mult__le__cancel__left, fact_1310_add__less__le__mono, fact_5352_abs__ln__one__plus__x__minus__x__bound, fact_9565_push__bit__nat__def, fact_9757_VEBT__internal_OminNull_Opelims_I3_J, fact_5189_neg__one__less__numeral, fact_463_member__bound, fact_4036_bezout1__nat, fact_9014_real__sqrt__inverse, fact_4198_is__unit__div__mult__cancel__left, fact_3473_unique__euclidean__semiring__numeral__class_Opos__mod__bound, fact_171_set__swap, fact_4564_signed__take__bit__Suc__bit0, fact_9185_mult__scaleR__right, fact_4475_minf_I4_J, fact_6604_of__nat__less__of__nat__power__cancel__iff, fact_117__C7b_C, fact_8172_gbinomial__0_I2_J, fact_8561_prod_Orelated, fact_257_one__plus__numeral, fact_5741_nat0__intermed__int__val, fact_9637_Re__csqrt, fact_5574_abs__of__neg, fact_8928_polynomial__product__nat, fact_2017_add__nonpos__eq__0__iff, fact_6010_or__numerals_I1_J, fact_2774_ord__eq__less__trans, fact_8214_pochhammer__pos, fact_3984_dvd__add__left__iff, fact_1953_not__numeral__le__zero, fact_6528_of__nat__add, fact_1093_linorder__neqE__linordered__idom, fact_3928_division__decomp, fact_3794_dvd__add__triv__left__iff, fact_3189_order__le__neq__trans, fact_8944_root__polyfun, fact_9302_cosh__converges, fact_9476_real__root__Suc__0, fact_7841_gauss__sum__from__Suc__0, fact_2612_subset__antisym, fact_5833_of__int__less__1__iff, fact_4882_diff__numeral__special_I3_J, fact_389_Skolem__list__nth, fact_1961_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_6303_signed__take__bit__eq__take__bit__minus, fact_9242_scaleR__nonneg__nonneg, fact_3383_mult__le__cancel__iff2, fact_3063_not__le__imp__less, fact_3488_mod__Suc__le__divisor, fact_2168_nonzero__divide__eq__eq, fact_2396_nat__one__le__power, fact_2079_mult__less__cancel__left__neg, fact_6358_bit__mod__2__iff, fact_5341_divmod__step__nat__def, fact_685_add__less__mono, fact_6071_or__greater__eq, fact_6418_bit__Suc, fact_720_pred__max, fact_2343_divide__add__eq__iff, fact_8997_binomial__Suc__Suc, fact_2852_linorder__neq__iff, fact_9040_divide__inverse__commute, fact_8192_floor__less__one, fact_6323_log__one, fact_3445_mult__mod__right, fact_9435_nat__int__add, fact_2952_Collect__mono__iff, fact_1920_le__0__eq, fact_362_power__mult__distrib, fact_1045_add__diff__cancel__left, fact_4925_minus__le__iff, fact_8198_numeral__less__floor, fact_1447_vebt__succ_Osimps_I6_J, fact_6906_norm__power, fact_686_not__add__less1, fact_4515_exp__mod__exp, fact_467_div__exp__eq, fact_4013_dvd__div__eq__cancel, fact_5153_le__minus__one__simps_I3_J, fact_2069_mult__strict__right__mono__neg, fact_5820_of__int__le__numeral__iff, fact_5400_tanh__real__less__iff, fact_6125_or__one__eq, fact_5726_numeral__inc, fact_10068_VEBT__internal_Ovalid_H_Oelims_I2_J, fact_4149_dvd__div__div__eq__mult, fact_4343_zero__less__of__bool__iff, fact_7186_cos__double, fact_9767_xor__minus__numerals_I2_J, fact_6790_of__nat__code__if, fact_2630_enat__0__less__mult__iff, fact_2263_add__pos__nonneg, fact_8987_binomial__n__n, fact_101_numeral__plus__numeral, fact_9740_drop__bit__nat__eq, fact_6793_monoseq__arctan__series, fact_7901_sums__iff__shift, fact_6853_negD, fact_6139_ex__less__of__int, fact_3678_prod__cases, fact_4259_zero__le__odd__power, fact_7067_summable__zero__power_H, fact_2341_less__divide__eq__1, fact_7709_arccos__cos, fact_8283_pochhammer__of__nat__eq__0__iff, fact_1157_add__le__imp__le__right, fact_7845_lemma__termdiff2, fact_5903_of__int__lessD, fact_9700_complex__norm__square, fact_1443_diff__divide__distrib, fact_5961_take__bit__or, fact_9402_pi__half, fact_4171_unit__div__mult__swap, fact_4532_pinf_I10_J, fact_8272_pochhammer__Suc, fact_7453_sum_Oshift__bounds__cl__Suc__ivl, fact_1379_real__average__minus__first, fact_1435_times__divide__times__eq, fact_1478_mult__cancel__right, fact_7656_sum_OatLeast0__atMost__Suc, fact_2144_divide__right__mono, fact_1986_mult__right__mono__neg, fact_1386_divide__divide__eq__left, fact_180_list__update__beyond, fact_2076_mult__strict__left__mono__neg, fact_226_power__inject__exp, fact_2290_divide__le__cancel, fact_2147_less__iff__diff__less__0, fact_9749_fst__divmod__nat, fact_8522_prod_OatMost__shift, fact_7448_sum__cong__Suc, fact_2162_divide__neg__neg, fact_7336_of__real__add, fact_4747_diff__numeral__special_I12_J, fact_4684_less__neg__neg, fact_2706_dual__order_Otrans, fact_597_add__Suc, fact_5489_power__abs, fact_1965_mult__nonneg__nonpos2, fact_2731_order_Otrans, fact_1628_nonzero__mult__div__cancel__right, fact_6647_real__arch__simple, fact_5429_tanh__real__pos__iff, fact_183_both__member__options__ding, fact_4732_signed__take__bit__of__minus__1, fact_8732_prod_OatLeast__Suc__atMost, fact_4484_minf_I7_J, fact_1046_add__diff__cancel__left, fact_3581_verit__le__mono__div, fact_8312_pochhammer__product, fact_1309_max__diff__distrib__left, fact_343_one__power2, fact_6664_of__nat__0__le__iff, fact_7219_powr__le__cancel__iff, fact_5391_abs__mult__self__eq, fact_5501_verit__eq__simplify_I14_J, fact_8844_atLeast1__atMost__eq__remove0, fact_8530_prod_Ointer__filter, fact_7247_powr__le1, fact_5643_Suc__div__eq__add3__div, fact_2968_subset__iff, fact_653_less__not__refl, fact_5518_abs__not__less__zero, fact_0__C3_C, fact_5797_dbl__inc__simps_I2_J, fact_4298_unity__coeff__ex, fact_5412_abs__neg__numeral, fact_2453_power__Suc__less__one, fact_3021_leD, fact_8988_inverse__nonnegative__iff__nonnegative, fact_8468_prod_Onot__neutral__contains__not__neutral, fact_8958_polyfun__diff, fact_1821_VEBT_Odistinct_I1_J, fact_2794_linorder__cases, fact_9333_cosh__real__pos, fact_2877_ord__less__eq__subst, fact_8276_pochhammer__rec_H, fact_8758_prod_OatLeast1__atMost__eq, fact_4068_unit__mult__left__cancel, fact_295_power__one__over, fact_5345_ln__2__less__1, fact_7715_arccos__cos__eq__abs, fact_566_nat__add__max__right, fact_7104_cos__mono__le__eq, fact_324_not__numeral__less__one, fact_9824_UNIV__char__of__nat, fact_1625_mult__cancel__left1, fact_8974_choose__even__sum, fact_1257_right__diff__distrib_H, fact_3242_order__less__le__subst2, fact_2185_power__0, fact_8367_gbinomial__partial__row__sum, fact_6796_sin__cos__npi, fact_10166_min__Suc__Suc, fact_565_nat__add__max__left, fact_2863_ord__eq__less__subst, fact_9088_one__le__inverse, fact_5640_cong__exp__iff__simps_I11_J, fact_1111_add__right__imp__eq, fact_8476_mod__prod__eq, fact_7183_cos__diff__cos, fact_4687_add_Oright__inverse, fact_9003_right__inverse, fact_5286_power2__eq__1__iff, fact_347_neq__if__length__neq, fact_1570_max__nat_Oeq__neutr__iff, fact_2988_subsetD, fact_2894_order__less__subst1, fact_7251_powr__mult, fact_9696_Im__complex__div__ge__0, fact_1834_gr__implies__not__zero, fact_8375_prod_Oneutral__const, fact_1717_nat__0__less__mult__iff, fact_8052_fact__1, fact_4140_dvd__div__eq__mult, fact_8112_fact__numeral, fact_3164_order__less__le, fact_8012_one__diff__power__eq_H, fact_9477_real__root__eq__iff, fact_9239_scaleR__mono_H, fact_2019_add__nonpos__eq__0__iff, fact_449_power__even__eq, fact_9809_atLeast0__atMost__Suc__eq__insert__0, fact_7943_powser__sums__if, fact_1930_power__eq__imp__eq__base, fact_4372_of__bool__half__eq__0, fact_2904_order__less__subst2, fact_4769_max__number__of_I4_J, fact_1334_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, fact_1905_zero__induct, fact_3806_concat__bit__0, fact_516_nat__add__left__cancel__less, fact_4903_take__bit__Suc__0, fact_8216_pochhammer__eq__0__mono, fact_3556_divmod__digit__0_I2_J, fact_5852_numeral__power__less__of__int__cancel__iff, fact_1950_vebt__succ_Osimps_I1_J, fact_1901_old_Onat_Oexhaust, fact_520_deg__SUcn__Node, fact_8200_one__less__floor, fact_9298_exp__first__terms, fact_6565_of__nat__eq__of__nat__power__cancel__iff, fact_6109_one__and__eq, fact_1583_le__add__same__cancel1, fact_10172_nat__mult__min__right, fact_1970_mult__nonpos__nonneg, fact_5470_divmod__algorithm__code_I8_J, fact_1756_power__eq__0__iff, fact_2160_divide__pos__neg, fact_4267_even__mask__div__iff_H, fact_6445_real__sqrt__sum__squares__ge1, fact_2178_frac__eq__eq, fact_9795_pow_Osimps_I3_J, fact_1135_add_Oassoc, fact_2280_div__positive, fact_5776_of__int__eq__1__iff, fact_3499_cong__exp__iff__simps_I2_J, fact_5423_semiring__norm_I14_J, fact_1106_mult_Oassoc, fact_8806_prod_Oub__add__nat, fact_1236_comm__semiring__class_Odistrib, fact_2460_zero__power2, fact_5638_power__even__abs, fact_4302_unity__coeff__ex, fact_1065_add__le__cancel__left, fact_6447_log__eq__div__ln__mult__log, fact_1002_split__option__ex, fact_9294_exp__series__add__commuting, fact_7670_sum_OSuc__reindex__ivl, fact_5901_of__int__pos, fact_3632_zmod__numeral__Bit0, fact_9005_left__inverse, fact_6509_of__nat__eq__0__iff, fact_2086_zero__less__mult__pos, fact_8126_fact__reduce, fact_6122_semiring__bit__operations__class_Oeven__mask__iff, fact_2733_order__antisym, fact_4997_mod__minus__cong, fact_7331_of__real__divide, fact_4169_unit__div__mult__swap, fact_785_max_Obounded__iff, fact_2656_ord__eq__le__subst, fact_428_set__update__memI, fact_2875_ord__less__eq__subst, fact_2080_mult__less__cancel__left__neg, fact_9404_cot__gt__zero, fact_1944_vebt__member_Ocases, fact_330_numeral__One, fact_9019_choose__one, fact_9293_complex__inverse, fact_2302_mult__le__one, fact_6719_of__nat__or__eq, fact_5079_less__minus__one__simps_I2_J, fact_6435_bit__iff__odd, fact_4790_diff__numeral__simps_I3_J, fact_2549_zero__le__even__power_H, fact_5482_abs__le__D1, fact_1110_ab__semigroup__mult__class_Omult__ac_I1_J, fact_1430_power__numeral__even, fact_149_numeral__Bit0__div__2, fact_342_one__power2, fact_6772_linear__plus__1__le__power, fact_3086_order_Ostrict__trans1, fact_557_lesseq__shift, fact_4686_add_Oright__inverse, fact_5609_power__numeral__odd, fact_1469_deg__1__Leaf, fact_9284_exp__converges, fact_1450_discrete, fact_9661_scaleR__complex_Ocode, fact_2663_ord__eq__le__subst, fact_9412_sum__count__set, fact_982_max_Ostrict__coboundedI1, fact_9746_Suc__0__div__numeral, fact_8523_prod_OatMost__shift, fact_4540_minf_I9_J, fact_2562_VEBT__internal_Omembermima_Oelims_I2_J, fact_6003_and__numerals_I1_J, fact_2284_unique__euclidean__semiring__numeral__class_Odiv__less, fact_692_add__leE, fact_4885_signed__take__bit__Suc__minus__bit0, fact_7100_ceiling__le, fact_1862_no__zero__divisors, fact_4621_neg__numeral__eq__iff, fact_3219_order__le__less__subst1, fact_5187_neg__one__less__numeral, fact_5580_abs__diff__triangle__ineq, fact_5329_power__minus1__odd, fact_1071_add__less__cancel__left, fact_3620_mod__pos__pos__trivial, fact_1931_power__eq__iff__eq__base, fact_9021_norm__inverse__le__norm, fact_763_option_Oinject, fact_1796_power__decreasing__iff, fact_8232_gbinomial__pochhammer_H, fact_1899_old_Onat_Odistinct_I1_J, fact_4397_of__bool__less__eq__one, fact_7833_sum__gp__offset, fact_281_le__numeral__extra_I4_J, fact_9279_neg__minus__divideR__less__eq, fact_887_power2__commute, fact_7274_powr__le__iff, fact_4672_neg__less__eq__nonneg, fact_9695_Im__complex__div__lt__0, fact_8069_fact__2, fact_5337_take__bit__int__greater__eq, fact_8831_norm__prod__diff, fact_953_max_OorderE, fact_8842_sum__up__index__split, fact_512_del__single__cont, fact_3839_dvd__div__mult__self, fact_3198_order__le__less__trans, fact_3136_dual__order_Ostrict__iff__not, fact_6671_of__nat__less__0__iff, fact_401_nth__mem, fact_1321_add__mono__thms__linordered__field_I4_J, fact_1313_add__le__less__mono, fact_7883_sums__le, fact_7360_sum_Ocl__ivl__Suc, fact_5463_divmod__algorithm__code_I3_J, fact_7721_sum__le__suminf, fact_1579_double__add__le__zero__iff__single__add__le__zero, fact_9030_positive__imp__inverse__positive, fact_7181_sin__diff__sin, fact_2043_add__increasing, fact_4844_add__neg__numeral__special_I9_J, fact_3174_linorder__not__less, fact_534_Suc__mono, fact_214_nth__list__update__neq, fact_9409_divide__int__unfold, fact_6681_less__imp__of__nat__less, fact_8935_gbinomial__Suc, fact_1733_divide__eq__eq__numeral1_I1_J, fact_5477_divmod__algorithm__code_I6_J, fact_2898_order__less__subst2, fact_8194_floor__diff__numeral, fact_6485_machin__Euler, fact_2721_linorder__wlog, fact_8146_Maclaurin__sin__expansion2, fact_1555_divide__eq__0__iff, fact_6381_not__bit__1__Suc, fact_2684_order__subst1, help_If_1_1_If_001t__Complex__Ocomplex_T, fact_9625_csqrt_Osimps_I1_J, fact_1643_div__mult__mult1, fact_4542_minf_I10_J, fact_2539_power2__less__imp__less, fact_8924_polyfun__eq__const, fact_666_size__neq__size__imp__neq, fact_2183_power__0, fact_9024_less__imp__inverse__less, fact_4270_power__le__zero__eq, fact_9945_tendsto__arctan__at__bot, fact_9210_scaleR__half__double, fact_8484_prod_Onested__swap_H, fact_6240_finite__linorder__min__induct, fact_3240_order__less__le__subst1, fact_7092_sin__diff, fact_7814_Sum__Icc__nat, fact_2097_mult__pos__neg, fact_7445_sum__mono__inv, fact_2243_mult__right__less__imp__less, fact_9256_pos__divideR__le__eq, fact_3604_old_Oprod_Oinject, fact_1689_power__Suc0__right, fact_4705_mult__minus1__right, fact_2507_power2__eq__imp__eq, fact_1677_power__0__Suc, fact_4156_unit__div__eq__0__iff, fact_2809_linorder__less__wlog, fact_2452_power__Suc__less__one, fact_317_power__increasing, fact_7485_sum_Orelated, fact_1141_group__cancel_Oadd1, fact_4891_power__minus1__even, fact_1649_nonzero__mult__divide__mult__cancel__left2, fact_7160_cos__squared__eq, fact_92_add__numeral__left, fact_4086_dvd__mult__imp__div, fact_9171_choose__alternating__sum, fact_6952_square__norm__one, fact_6778_log__of__power__le, fact_1857_mult__left__cancel, fact_2039_add__decreasing2, fact_2860_order__less__trans, fact_5730_even__abs__add__iff, fact_5851_of__int__le__numeral__power__cancel__iff, fact_9679_Im__divide, fact_2170_eq__divide__imp, fact_2922_linorder__less__linear, fact_6809_sin__periodic, fact_5734_dbl__dec__def, fact_4581_crossproduct__eq, fact_8559_prod_Orelated, fact_3870_pow__divides__pow__iff, fact_4382_one__mod__2__pow__eq, fact_8810_fold__atLeastAtMost__nat_Oelims, fact_1936_lambda__zero, fact_2963_subset__refl, fact_2309_mult__left__le, fact_4403_of__bool__def, fact_4605_power__numeral, fact_4783_semiring__norm_I168_J, fact_1820_zero__power, fact_9037_inverse__unique, fact_6727_of__nat__diff, fact_2171_eq__divide__imp, fact_7065_cos__le__one, fact_8341_pochhammer__minus_H, fact_2556_odd__0__le__power__imp__0__le, fact_357_ex__power__ivl2, fact_1132_add_Oleft__cancel, fact_531_maxt__corr__help, fact_2488_VEBT__internal_Onaive__member_Oelims_I2_J, fact_2206_diff__less, fact_9361_sinh__field__def, fact_2249_mult__strict__mono, fact_2122_add__less__zeroD, fact_1348_le__diff__eq, fact_1589_add__le__same__cancel1, fact_3493_le__mod__geq, fact_8767_sum_Onested__swap_H, fact_6537_of__nat__mult, fact_7272_log__le__iff, fact_2376_add__divide__eq__if__simps_I4_J, fact_5800_dbl__inc__simps_I4_J, fact_7135_sin__double, fact_4105_div__power, fact_3561_div__exp__mod__exp__eq, fact_8741_prod_OlessThan__Suc__shift, fact_5257_even__minus, fact_6764_le__log__of__power, fact_9223_scaleR__right__mono__neg, fact_3391_bits__mod__0, fact_85_mult__numeral__left__semiring__numeral, fact_9505_sgn__power__root, fact_7843_arsinh__def, fact_2382_n__less__n__mult__m, fact_6963_cos__zero, fact_2388_nat__induct__non__zero, fact_8122_fact__num__eq__if, fact_4152_even__numeral, fact_7098_suminf__split__head, fact_6006_and__numerals_I3_J, fact_9405_tan__cot_H, fact_3436_not__mod__2__eq__0__eq__1, fact_4974_one__neq__neg__one, fact_2031_add__nonneg__nonneg, fact_9297_exp__first__term, fact_6994_zero__le__ceiling, fact_9381_of__real__sqrt, fact_815_diff__Suc__diff__eq1, fact_5051_add_Oinverse__unique, fact_9446_le__nat__iff, fact_1463_vebt__pred_Oelims, fact_3529_div__mult1__eq, fact_9432_nat__mono__iff, fact_7769_sin__int__times__real, fact_2895_order__less__subst1, fact_6803_sin__npi, fact_2255_mult__le__cancel__left, fact_1057_add__right__cancel, fact_3053_dense__ge, fact_4513_exp__mod__exp, fact_6661_bit__Suc__0__iff, fact_7180_sin__plus__sin, fact_4544_minf_I10_J, fact_3252_linorder__le__less__linear, fact_5620_odd__numeral, fact_1183_add__less__imp__less__right, fact_1037_div__by__1, fact_5127_real__minus__mult__self__le, fact_9153_pochhammer__binomial__sum, fact_6138_ex__of__int__less, fact_1178_add__mono__thms__linordered__semiring_I2_J, fact_9076_division__ring__inverse__diff, fact_6578_of__nat__le__0__iff, fact_1913_not__less0, fact_5788_of__int__eq__of__int__power__cancel__iff, fact_1102_mult_Ocommute, fact_7002_cos__periodic, fact_9806_zero__notin__Suc__image, fact_3732_sum_Ofinite__Collect__op, fact_4613_neg__le__iff__le, fact_8902_Cauchy__product, fact_4188_even__zero, fact_4921_le__minus__iff, fact_6675_of__nat__neq__0, fact_8136_termdiff__converges, fact_599_Suc__mult__cancel1, fact_9503_real__sgn__eq, fact_3232_order__less__le__subst1, fact_5629_lemma__interval, fact_9377_cis__pi__half, fact_6510_of__nat__eq__0__iff, fact_9786_num__of__nat_Osimps_I1_J, fact_6051_or_Oassoc, fact_5923_even__of__int__iff, fact_7536_sum__power__add, fact_3965_mult__dvd__mono, fact_1365_eq__add__iff1, fact_4682_neg__less__pos, fact_234_power__strict__increasing__iff, fact_2746_ord__eq__le__trans, fact_9265_sin__def, fact_2498_convex__bound__lt, fact_7806_double__arith__series, fact_395_list__eq__iff__nth__eq, fact_6379_bit__unset__bit__iff, fact_6478_arcosh__real__def, fact_1597_less__add__same__cancel2, fact_5226_take__bit__numeral__minus__1__eq, fact_2324_divide__strict__left__mono__neg, fact_5962_take__bit__or, fact_132_mult__numeral__1__right, fact_6599_real__of__nat__eq__numeral__power__cancel__iff, fact_477_semiring__norm_I85_J, fact_9209_scaleR__half__double, fact_880_max_Ocommute, fact_1680_power__0__Suc, fact_549_max__0__1_I5_J, fact_6427_real__less__rsqrt, fact_2211_mult__eq__self__implies__10, fact_6462_ln__sqrt, fact_4939_less__minus__iff, fact_7093_summable__geometric, fact_1792_zero__less__power2, fact_1759_power__eq__0__iff, fact_623_inc__induct, fact_1446_vebt__pred_Osimps_I7_J, fact_4606_power__numeral, fact_5768_of__int__le__iff, fact_5708_diff__numeral__special_I5_J, fact_1648_nonzero__mult__divide__mult__cancel__right, fact_7937_sums__zero__iff__shift, fact_1060_add__left__cancel, help_If_1_1_If_001t__Nat__Onat_T, fact_8078_fact__gt__zero, fact_5751_of__int__code__if, fact_7647_sum__diff, fact_4467_minf_I3_J, fact_1752_nonzero__divide__mult__cancel__right, fact_4624_mult__minus__right, fact_6645_even__of__nat, fact_7899_lessThan__def, fact_2288_divide__nonneg__pos, fact_480_bits__div__by__1, fact_9458_le__nat__floor, fact_4648_div__minus__minus, fact_2545_sum__power2__gt__zero__iff, fact_3697_verit__comp__simplify1_I3_J, fact_7821_arith__series, fact_4444_pinf_I4_J, fact_4588_option_Osize__gen_I1_J, fact_284_less__numeral__extra_I4_J, fact_5723_mult__inc, fact_6744_nat__less__real__le, fact_8307_gbinomial__absorption, fact_882_max_Oassoc, fact_8308_gbinomial__absorption, fact_1524_add__cancel__left__left, fact_6978_zero__less__ceiling, fact_1251_comm__monoid__mult__class_Omult__1, fact_19_nothprolist, fact_4516_inf__period_I1_J, fact_8474_prod__power__distrib, fact_4312_of__bool__less__eq__iff, fact_2517_exp__not__zero__imp__exp__diff__not__zero, fact_6882_arctan__series, fact_1645_nonzero__mult__divide__mult__cancel__right2, fact_7287_tan__monotone_H, fact_2632_iadd__is__0, fact_205_power__one__right, fact_6839_int__Suc, fact_1213_diff__right__mono, fact_9311_sinh__real__nonneg__iff, fact_6546_of__nat__1__eq__iff, fact_5046_eq__neg__iff__add__eq__0, fact_1081_mult_Oright__neutral, fact_1349_le__diff__eq, fact_5803_dbl__inc__simps_I5_J, fact_2155_divide__strict__right__mono, fact_5801_dbl__inc__simps_I4_J, fact_4906_take__bit__of__exp, fact_725_helpypredd, fact_8193_floor__neg__numeral, fact_1324_less__1__mult, fact_8809_prod_Oub__add__nat, fact_9291_cos__minus__converges, fact_3424_Suc__mod__mult__self3, fact_2415_mult__less__cancel__left2, fact_2059_zero__less__one__class_Ozero__le__one, fact_1227_combine__common__factor, fact_9325_cosh__add, fact_4197_is__unit__div__mult__cancel__left, fact_3439_mod2__gr__0, fact_3376_double__eq__0__iff, fact_1274_add__implies__diff, fact_304_power__gt1__lemma, fact_7283_lemma__tan__total, fact_9953_sqrt__at__top, fact_1825_vebt__pred_Osimps_I1_J, fact_374_power__mult, fact_4085_dvd__mult__imp__div, fact_6357_bit__mod__2__iff, fact_8330_floor__divide__upper, fact_7944_powser__sums__if, fact_3889_power__less__zero__eq, fact_6751_nat__approx__posE, fact_4899_neg__one__odd__power, fact_1528_add_Oright__neutral, fact_6713_take__bit__of__nat, fact_2503_power2__le__imp__le, fact_4951_neg__numeral__neq__numeral, fact_1211_diff__left__mono, fact_6948_norm__diff__triangle__ineq, fact_6833_sin__gt__zero, fact_664_le__trans, fact_8217_pochhammer__neq__0__mono, fact_9244_scaleR__nonpos__nonneg, fact_1791_power2__less__eq__zero__iff, fact_6085_mask__Suc__exp, fact_9152_pochhammer__binomial__sum, fact_4165_div__mult__unit2, fact_329_numeral__One, fact_7452_sum_Oshift__bounds__cl__Suc__ivl, fact_567_nat__mult__max__left, fact_245_one__add__one, fact_9278_neg__minus__divideR__le__eq, fact_5744_arctan__double, fact_1244_ring__class_Oring__distribs_I2_J, fact_3043_antisym__conv1, fact_75_numeral__le__iff, fact_4726_take__bit__Suc__1, fact_3066_not__le__imp__less, fact_7651_sum__shift__lb__Suc0__0, fact_2791_linorder__cases, fact_5567_zero__le__power__abs, fact_7138_ceiling__eq__iff, fact_6029_or__numerals_I6_J, fact_3492_nat__mod__eq__iff, fact_7194_sin__cos__sqrt, fact_1189_add__strict__right__mono, fact_5174_not__numeral__le__neg__one, fact_5197_minus__divide__eq__eq, fact_8257_gbinomial__mult__1_H, fact_3940_dvd__def, fact_8830_norm__prod__diff, fact_8014_one__diff__power__eq_H, fact_1397_del__x__not__mi, fact_6614_of__nat__le__of__nat__power__cancel__iff, fact_4026_dvd__mod, fact_8013_one__diff__power__eq_H, fact_3648_neg__mod__bound, fact_2195_option_Osize_I4_J, fact_3909_even__succ__div__two, fact_7795_sin__cos__eq, fact_3845_div__add, fact_1623_mult__cancel__left1, fact_3896_even__diff, fact_3489_mod__eq__0D, fact_7785_sum__gp__multiplied, fact_3377_unset__bit__0, fact_9234_Real__Vector__Spaces_Ole__add__iff2, fact_7252_divide__powr__uminus, fact_5932_or__int__unfold, fact_6382_not__bit__1__Suc, fact_3887_zero__le__power__eq__numeral, help_If_2_1_If_001t__Real__Oreal_T, fact_2319_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq, fact_7834_sum__gp__offset, fact_602_lift__Suc__mono__less, fact_9665_Re__exp, fact_9796_sqr_Osimps_I2_J, fact_7978_one__diff__power__eq, fact_9367_cosh__ln__real, fact_5208_mult__1s__ring__1_I2_J, fact_7800_minus__sin__cos__eq, fact_5204_mult__1s__ring__1_I1_J, fact_3209_order__less__le__trans, fact_1041_diff__add__cancel, fact_528_nat_Oinject, fact_5082_nonzero__minus__divide__divide, fact_5821_of__int__le__numeral__iff, fact_4541_minf_I10_J, fact_8886_polyfun__linear__factor, fact_1242_ring__class_Oring__distribs_I1_J, fact_8347_pochhammer__minus, fact_9566_push__bit__int__def, fact_8455_prod_Ocl__ivl__Suc, fact_6982_one__le__ceiling, fact_9577_and__minus__minus__numerals, fact_8470_prod_Odistrib, fact_6091_AND__upper2_H_H, fact_4887_dbl__simps_I4_J, fact_872_nat__diff__add__eq1, fact_7713_norm__of__real__diff, fact_3804_div__dvd__div, fact_7253_log__base__powr, fact_9201_norm__scaleR, fact_1054_add__right__cancel, fact_1895_power__not__zero, fact_6480_sqrt__sum__squares__half__less, fact_4482_minf_I7_J, fact_9712_card__atLeastAtMost, fact_991_combine__options__cases, fact_28_nnvalid, fact_1903_nat__induct, fact_1744_div__mult__self3, fact_3449_mod__mult__cong, fact_4119_le__imp__power__dvd, fact_8346_pochhammer__minus, fact_8939_sum_Ozero__middle, fact_3997_unit__imp__dvd, fact_1904_diff__induct, fact_1531_add_Oright__neutral, fact_9482_real__root__less__iff, fact_3779_arcosh__1, fact_2121_add__less__zeroD, fact_98_numeral__plus__numeral, fact_3239_order__less__le__subst1, fact_6633_of__nat__less__numeral__power__cancel__iff, fact_704_le__square, help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T, fact_9578_or__minus__minus__numerals, fact_7931_sums__Suc, fact_1454_vebt__delete_Osimps_I7_J, fact_1900_nat_OdiscI, fact_9640_cos__n__Re__cis__pow__n, fact_4701_mult__minus1, fact_2757_nle__le, fact_2626_half__nonnegative__int__iff, fact_9269_cos__def, fact_4850_diff__numeral__special_I10_J, fact_4755_neg__one__eq__numeral__iff, fact_6__C9_C, fact_275_subset__code_I1_J, fact_7351_sum__abs__ge__zero, fact_9960_tendsto__exp__limit__at__top, fact_82_mult__numeral__left__semiring__numeral, fact_544_max__number__of_I1_J, fact_7261_tan__def, fact_6574_of__nat__of__bool, fact_2342_divide__less__eq__1, help_If_2_1_If_001t__Code____Numeral__Ointeger_T, fact_6990_ceiling__numeral__power, fact_1587_add__le__same__cancel2, fact_2739_ord__le__eq__trans, fact_6342_log__le__one__cancel__iff, fact_8124_fact__num__eq__if, fact_6928_norm__triangle__ineq, fact_7878_sum_OlessThan__Suc, fact_4027_dvd__mod, fact_4401_of__bool__def, fact_3704_pos__zmod__mult__2, fact_6020_and__numerals_I6_J, fact_6484_machin, fact_9527_real__root__increasing, fact_5486_abs__mult, fact_8761_bounded__imp__summable, fact_7544_arccos__le__mono, fact_4720_ln__le__cancel__iff, fact_5212_uminus__numeral__One, fact_1374_less__add__iff1, fact_9190_scaleR__one, fact_2563_arith__geo__mean, fact_4918_take__bit__tightened__less__eq__nat, fact_4910_take__bit__of__2, fact_2436_divide__le__eq, fact_5968_and_Oright__neutral, fact_4877_diff__numeral__special_I4_J, fact_5507_case__prodD, fact_4011_dvd__div__eq__iff, fact_3823_dvd__times__right__cancel__iff, fact_8979_inverse__mult__distrib, fact_2572_vebt__succ_Oelims, fact_6444_real__sqrt__sum__squares__ge2, fact_9228_scaleR__left__mono__neg, fact_9057_mult__inverse__of__int__commute, fact_3609_prod_Oinject, fact_7385_sum__norm__le, fact_7762_convex__sum__bound__le, fact_3798_dvd__add__triv__right__iff, fact_3755_finite__has__minimal2, fact_4142_div__dvd__iff__mult, fact_1984_mult__right__mono, fact_7225_tan__periodic__nat, fact_1833_zero__less__iff__neq__zero, fact_2530_power__minus__mult, fact_8016_sums__if, fact_2298_mult__left__le__one__le, fact_3277_bot_Oextremum, fact_9608_atLeastLessThan__nat__numeral, fact_4347_of__bool__less__one__iff, fact_8353_floor__log2__div2, fact_3618_flip__bit__negative__int__iff, fact_1266_right__diff__distrib, fact_4124_mod__eq__dvd__iff, fact_818_add__diff__add, fact_3959_dvd__triv__left, fact_229_power__mult__numeral, fact_1351_diff__le__eq, fact_5750_of__int__code__if, fact_3567_mult__exp__mod__exp__eq, fact_5628_Suc3__eq__add__3, fact_6569_of__nat__power__eq__of__nat__cancel__iff, fact_2164_zero__less__power, fact_4915_take__bit__tightened, fact_2931_order__less__imp__not__eq2, fact_8292_pochhammer__product_H, fact_6840_int__ops_I4_J, fact_4241_even__set__bit__iff, fact_215_nth__list__update__neq, fact_8252_gbinomial__absorb__comp, fact_236_power__add__numeral, fact_4104_dvd__div__unit__iff, fact_1121_add_Oleft__commute, fact_8129_fact__reduce, fact_1399_del__x__not__mia, fact_3144_order_Ostrict__implies__order, fact_1966_mult__nonneg__nonpos2, fact_878_max_Ocommute, fact_5303_take__bit__eq__0__iff, fact_1537_div__by__0, fact_2334_power__le__one, fact_9769_sub__BitM__One__eq, fact_403_list__ball__nth, fact_305_power__gt1__lemma, fact_9654_scaleR__complex_Osimps_I2_J, fact_860_vebt__maxt_Osimps_I2_J, fact_8925_polyfun__eq__const, fact_2366_div__add__self1, fact_6188_or__minus__numerals_I3_J, fact_9380_DeMoivre, fact_4704_mult__minus1__right, fact_1354_linordered__semidom__class_Oadd__diff__inverse, fact_1704_add__gr__0, fact_6186_or__minus__numerals_I4_J, fact_87_numeral__times__numeral, fact_5043_neg__eq__iff__add__eq__0, fact_7965_sum__lessThan__telescope, fact_5872_neg__numeral__power__less__of__int__cancel__iff, fact_4738_add__neg__numeral__special_I7_J, fact_7229_tan__periodic, fact_3506_mult__div__mod__eq, fact_1127_add_Oright__cancel, fact_6878_sin__zero__iff__int, fact_6442_real__sqrt__sum__squares__eq__cancel, fact_5737_take__bit__numeral__bit0, fact_355_nat__1__add__1, fact_1073_add__less__cancel__left, fact_3278_bot_Oextremum, fact_2595_subset__empty, fact_3976_dvd__triv__right, fact_7242_complex__add, fact_6077_exp__add__commuting, fact_8236_gbinomial__Suc__Suc, fact_9427_nat__numeral__as__int, fact_9177_sin__x__sin__y, fact_9198_scaleR__minus1__left, fact_4373_of__bool__half__eq__0, fact_8255_gbinomial__mult__1, fact_2577_set__bit__0, fact_1604_add__less__same__cancel2, fact_7848_monoI1, fact_240_power__add__numeral2, fact_9648_Im__divide__of__nat, fact_6467_bit__rec, fact_4183_nat__mult__dvd__cancel1, fact_1406_pred__lesseq__max, fact_3919_semiring__parity__class_Oeven__mask__iff, fact_7956_sum_OlessThan__Suc__shift, fact_9015_power__inverse, fact_9483_real__root__le__iff, fact_9068_one__less__inverse__iff, fact_9084_inverse__powr, fact_1577_zero__le__double__add__iff__zero__le__single__add, fact_9280_neg__less__minus__divideR__eq, fact_3249_order__less__le__subst2, fact_6977_ceiling__le__zero, fact_3744_finite__maxlen, fact_8733_prod_OatLeast__Suc__atMost, fact_10141_map__decr__upt, fact_9096_forall__pos__mono__1, fact_1777_power__mono__iff, fact_4065_mult__unit__dvd__iff_H, fact_8887_polyfun__linear__factor, fact_1232_distrib__left, fact_5101_group__cancel_Osub2, fact_1279_diff__add__eq__diff__diff__swap, help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T, fact_4934_compl__le__swap2, fact_6175_or__nat__numerals_I1_J, fact_5657_power__mono__even, fact_7799_minus__sin__cos__eq, fact_36__C5_OIH_C_I1_J, fact_2141_divide__nonneg__nonpos, fact_6903_norm__divide, fact_6059_exp__times__arg__commute, fact_795_max_Oabsorb1, fact_4698_mult__minus1, fact_2245_mult__less__cancel__left, fact_5273_take__bit__int__less__exp, fact_2954_set__eq__subset, fact_6027_or__numerals_I4_J, fact_2481_Suc__pred_H, fact_7958_sum_OlessThan__Suc__shift, fact_9776_uminus__int_Oabs__eq, fact_5223_take__bit__Suc__minus__1__eq, fact_3446_mod__mult__mult2, fact_8403_atMost__subset__iff, fact_2400_div__le__mono2, fact_5696_dbl__dec__simps_I2_J, fact_9678_inverse__complex_Osimps_I2_J, fact_6298_of__int__round__ge, fact_5353_semiring__norm_I90_J, fact_2279_field__le__epsilon, fact_3868_unit__div__mult__self, fact_5098_group__cancel_Osub2, fact_3924_even__succ__div__exp, fact_4092_div__plus__div__distrib__dvd__left, fact_7078_summable__norm__comparison__test, fact_4960_add_Oinverse__distrib__swap, fact_1598_less__add__same__cancel2, fact_625_le__less__Suc__eq, fact_9613_atLeast1__lessThan__eq__remove0, fact_9035_inverse__numeral__1, fact_2379_numeral__1__eq__Suc__0, fact_4836_divide__less__eq__numeral1_I2_J, fact_5829_of__int__le__1__iff, fact_1497_mult__zero__left, fact_9270_cos__def, fact_9425_numeral__power__le__nat__cancel__iff, fact_2621_div__neg__neg__trivial, fact_2604_dual__order_Orefl, fact_8201_floor__le__one, fact_7991_sum__gp__strict, fact_1050_add__diff__cancel__left_H, fact_8199_floor__le__numeral, fact_5066_le__minus__one__simps_I2_J, fact_7334_of__real__power, fact_2546_not__sum__power2__lt__zero, fact_3407_bits__mod__by__1, fact_1639_div__mult__mult2, fact_530_mint__corr__help, fact_8731_prod_OatLeast0__atMost__Suc, fact_6672_of__nat__neq__0, fact_6838_int__cases4, fact_1721_zero__less__diff, fact_5576_abs__if, fact_444_power2__eq__square, fact_7248_powr__mono__both, fact_5981_and__negative__int__iff, fact_6997_numeral__le__ceiling, fact_207_length__list__update, fact_8359_pochhammer__times__pochhammer__half, fact_2521_less__2__cases__iff, fact_1088_add__diff__cancel__right, fact_1593_zero__less__double__add__iff__zero__less__single__add, fact_2027_add__nonpos__nonpos, fact_5251_minus__divide__diff__eq__iff, fact_1873_add_Ogroup__left__neutral, fact_9456_nat__mod__distrib, fact_3726_prod_Ofinite__Collect__op, fact_1429_power__numeral__even, fact_5885_arctan__le__iff, fact_9607_or__not__numerals_I7_J, fact_6810_sin__2npi, fact_1367_eq__add__iff1, fact_2913_order__less__imp__triv, fact_4969_is__num__normalize_I8_J, fact_1586_add__le__same__cancel2, fact_10178_min__Suc2, fact_7829_double__gauss__sum__from__Suc__0, fact_4977_minus__diff__minus, fact_4179_unit__imp__mod__eq__0, fact_4293_inf__period_I4_J, fact_8975_choose__even__sum, fact_1976_mult__nonneg__nonneg, fact_3205_order__less__le__trans, fact_5155_le__minus__one__simps_I3_J, fact_7979_power__diff__1__eq, fact_5149_neg__numeral__less__zero, fact_243_power__add__numeral2, fact_679_less__imp__le__nat, fact_9260_neg__less__divideR__eq, fact_2929_order__less__imp__not__eq2, fact_994_combine__options__cases, fact_485_semiring__norm_I11_J, fact_6958_summable__arctan__series, fact_7314_tan__total__pi4, fact_9517_real__root__pos__pos, fact_5647_power2__le__iff__abs__le, fact_3736_sum_Ofinite__Collect__op, fact_688_add__less__mono1, fact_8760_bounded__imp__summable, fact_9693_Re__complex__div__le__0, fact_9525_real__root__power__cancel, fact_8288_pochhammer__of__nat__eq__0__lemma_H, fact_745_not__Some__eq, fact_4175_is__unit__power__iff, fact_2114_add__pos__pos, fact_7056_suminf__eq__zero__iff, fact_2711_dual__order_Oantisym, fact_5550_sin__bound__lemma, fact_1696_max__0__1_I4_J, fact_3045_antisym__conv1, fact_4221_dvd__mult__cancel2, fact_3025_leD, fact_9227_scaleR__le__cancel__left__pos, fact_113_distrib__left__numeral, fact_3810_dvd__mult__cancel__left, fact_5480_abs__ge__self, help_If_2_1_If_001t__Extended____Nat__Oenat_T, fact_2893_order__less__subst1, fact_3118_dual__order_Ostrict__trans1, fact_6756_exp__divide__power__eq, fact_9548_push__bit__negative__int__iff, fact_800_max_Oabsorb3, fact_1481_mult__cancel__right, fact_2145_divide__le__0__iff, fact_4827_divide__le__eq__numeral1_I2_J, fact_8128_fact__reduce, fact_3828_dvd__add__times__triv__left__iff, fact_2012_zero__less__numeral, fact_2633_i0__lb, fact_198_power__one, fact_3666_verit__comp__simplify1_I2_J, fact_4408_split__of__bool, fact_6628_numeral__power__less__of__nat__cancel__iff, fact_2703_antisym, fact_4081_dvd__div__mult2__eq, fact_8885_polyfun__linear__factor, fact_1148_ab__semigroup__add__class_Oadd__ac_I1_J, fact_3822_dvd__times__right__cancel__iff, fact_668_size__neq__size__imp__neq, fact_7742_sum__strict__mono2, fact_4593_artanh__def, fact_8121_fact__num__eq__if, fact_4531_pinf_I10_J, fact_9530_log__root, fact_9440_nat__times__as__int, fact_6734_exp__of__nat__mult, fact_1686_power__Suc0__right, fact_5305_take__bit__int__less__self__iff, fact_8008_real__sum__nat__ivl__bounded2, fact_6264_or__not__num__neg_Osimps_I2_J, fact_473_semiring__norm_I87_J, fact_9571_Sum__Ico__nat, fact_439_list__update__same__conv, fact_5264_take__bit__Suc__bit0, fact_575_Ex__less__Suc, fact_608_lift__Suc__mono__less__iff, fact_4062_dvd__mult__unit__iff_H, fact_9652_imaginary__unit_Osimps_I2_J, fact_8477_mod__prod__eq, fact_6650_mult__of__nat__commute, fact_10171_nat__mult__min__left, fact_5387_semiring__norm_I86_J, fact_4961_add_Oinverse__distrib__swap, fact_2689_order__subst1, fact_4803_semiring__norm_I172_J, fact_4928_le__imp__neg__le, fact_202_power__one__right, fact_1018_option_Oexpand, fact_1922_plus__nat_Oadd__0, fact_9592_and__not__numerals_I4_J, fact_8111_fact__numeral, fact_9564_set__bit__int__def, fact_4886_dbl__simps_I4_J, fact_6100_even__or__iff, fact_3325_set__bit__greater__eq, fact_10075_mono__Suc, fact_5914_real__of__int__div__aux, fact_2207_Euclidean__Division_Odiv__eq__0__iff, fact_6847_zero__less__imp__eq__int, fact_8153_fact__diff__Suc, fact_4292_inf__period_I4_J, fact_6164_round__1, fact_9727_drop__bit__minus__one, fact_6547_of__nat__1__eq__iff, fact_5828_of__int__le__1__iff, fact_8815_prod_Odelta__remove, fact_3800_dvd__1__iff__1, fact_2152_power__mono, fact_1789_power2__eq__iff__nonneg, fact_3557_divmod__digit__0_I2_J, fact_4275_even__mult__exp__div__exp__iff, fact_1343_add__le__add__imp__diff__le, fact_4714_div__minus1__right, fact_6014_and__minus__numerals_I2_J, fact_5989_or__numerals_I2_J, fact_6794_lemma__termdiff3, fact_8333_pochhammer__same, fact_4811_mult__neg__numeral__simps_I2_J, fact_993_combine__options__cases, fact_5557_abs__mult__pos, fact_9714_card__less__Suc, fact_7356_cos__of__real__pi, fact_5242_less__minus__divide__eq, fact_10071_VEBT__internal_Ovalid_H_Opelims_I3_J, fact_7924_sum__SucD, fact_5898_of__int__nonneg, fact_4982_div__minus__right, fact_9371_Arg__minus__ii, fact_1603_add__less__same__cancel2, fact_1660_div__self, fact_7906_sums__iff__shift_H, fact_4493_pinf_I6_J, fact_8296_pochhammer__product_H, fact_9134_fact__binomial, fact_4868_Parity_Oring__1__class_Opower__minus__even, fact_3550_unset__bit__Suc, fact_9470_even__nat__iff, fact_4324_of__bool__eq_I2_J, fact_21__C114_C, fact_6723_of__nat__mask__eq, fact_2674_order__subst2, fact_8397_prod_Oinfinite, fact_250_power__increasing__iff, fact_4201_is__unit__div__mult__cancel__right, fact_6362_set__encode__insert, fact_5406_abs__le__self__iff, fact_7236_powr__less__mono, fact_9220_of__real__def, fact_4655_real__add__minus__iff, fact_2411_mult__less__cancel__right2, fact_3410_bits__mod__div__trivial, fact_8901_Cauchy__product, fact_5097_square__eq__1__iff, fact_6607_of__nat__less__of__nat__power__cancel__iff, fact_1077_mult__1, fact_1576_zero__le__double__add__iff__zero__le__single__add, fact_7816_arcsin__lt__bounded, fact_7685_arccos__lbound, fact_2418_mult__le__cancel__right2, fact_4527_pinf_I9_J, fact_8542_power__sum, fact_2658_ord__eq__le__subst, fact_9172_choose__alternating__sum, fact_5289_uminus__power__if, fact_2756_nle__le, fact_7478_sum__strict__mono__ex1, fact_1722_div__less, fact_6315_real__sqrt__gt__0__iff, fact_8637_prod_Ozero__middle, fact_1580_le__add__same__cancel2, fact_8973_choose__even__sum, fact_1679_power__0__Suc, fact_5173_not__numeral__le__neg__one, fact_9673_inverse__complex_Osimps_I1_J, fact_2631_not__iless0, fact_2104_not__square__less__zero, fact_4214_dvd__power, fact_5784_of__int__power__eq__of__int__cancel__iff, fact_3197_order__neq__le__trans, fact_6493_abs__of__nat, fact_3879_even__add, fact_514_nat__1__eq__mult__iff, fact_5117_dvd__div__neg, fact_8039_sum__bounds__lt__plus1, fact_2838_linorder__neqE, fact_4715_div__minus1__right, fact_4506_minf_I6_J, fact_2511_power2__less__0, fact_4576_add__0__iff, fact_9813_integer__of__num__triv_I1_J, fact_2692_order__subst1, fact_5190_neg__numeral__less__one, fact_2352_add__frac__eq, fact_3082_order_Ostrict__trans1, fact_9314_norm__ii, fact_6393_bit__take__bit__iff, fact_581_Suc__less__SucD, fact_9308_sinh__real__neg__iff, fact_5979_exp__eq__one__iff, help_If_1_1_If_001t__Code____Numeral__Ointeger_T, fact_2417_mult__less__cancel__left1, fact_6502_of__nat__0__eq__iff, fact_7710_arcsin__less__arcsin, fact_6746_nat__le__real__less, fact_6542_of__nat__eq__1__iff, fact_128_times__div__less__eq__dividend, fact_7042_suminf__mult2, fact_2230_mult__left__le__imp__le, fact_6350_bit__0, fact_1840_field__lbound__gt__zero, fact_2239_mult__strict__mono_H, fact_7450_complex__of__real__mult__Complex, fact_2005_mult__mono, fact_5439_semiring__norm_I10_J, fact_8764_fact__prod, fact_4680_neg__less__pos, fact_3861_dbl__simps_I5_J, fact_9765_infinite__nat__iff__unbounded, fact_3105_dual__order_Oorder__iff__strict, fact_535_Suc__less__eq, fact_4628_minus__mult__minus, fact_3504_cong__exp__iff__simps_I8_J, fact_5449_zero__less__power__abs__iff, fact_2513_exp__add__not__zero__imp__right, fact_4822_take__bit__of__Suc__0, fact_5787_of__int__eq__of__int__power__cancel__iff, help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T, fact_1837_not__less__zero, fact_7668_sum_OSuc__reindex__ivl, fact_9524_real__root__pos__unique, fact_9725_drop__bit__nonnegative__int__iff, fact_1747_div__mult__self2, fact_7271_le__log__iff, fact_1217_diff__strict__right__mono, fact_17_hlbound, fact_6165_and__nat__numerals_I3_J, fact_3381_mult__le__cancel__iff1, fact_187_power2__sum, fact_6699_of__nat__dvd__iff, fact_4034_bezout__add__nat, fact_9188_mult__scaleR__left, fact_7649_sum__diff, fact_9574_not__nonnegative__int__iff, fact_1114_add__right__imp__eq, fact_2899_order__less__subst2, fact_6185_or__minus__numerals_I8_J, fact_1701_max__0__1_I3_J, fact_5798_dbl__inc__simps_I2_J, fact_3846_unit__div, fact_1847_zero__neq__numeral, fact_2250_mult__left__less__imp__less, fact_3978_dvd__triv__right, fact_7939_lessThan__nat__numeral, fact_6895_norm__numeral, fact_3821_dvd__times__right__cancel__iff, fact_1584_le__add__same__cancel1, fact_6069_not__exp__le__zero, fact_9128_vandermonde, fact_6210_subset__singletonD, fact_9775_int__def, fact_6391_disjunctive__add, fact_6969_summable__divide__iff, fact_1668_divide__self__if, fact_8141_Maclaurin__minus__cos__expansion, fact_684_add__lessD1, fact_1695_max__0__1_I4_J, fact_308_power__less__power__Suc, fact_2142_divide__nonneg__nonneg, fact_4016_dvd__div__eq__cancel, fact_1967_mult__nonneg__nonpos2, fact_4446_pinf_I4_J, fact_162_mult__2, fact_6821_nat__int__comparison_I2_J, fact_8045_fact__0, fact_817_add__diff__add, fact_7063_le__of__int__ceiling, fact_3218_order__le__less__subst1, fact_3687_old_Oprod_Oexhaust, fact_4478_minf_I5_J, fact_9562_concat__bit__eq, fact_2512_exp__add__not__zero__imp__right, fact_8171_gbinomial__0_I2_J, fact_6110_and__one__eq, fact_176_nth__list__update__eq, fact_5707_diff__numeral__special_I5_J, fact_9694_Im__complex__div__gt__0, fact_8917_polynomial__product, fact_5248_minus__divide__add__eq__iff, fact_4640_minus__add__cancel, fact_7488_sum_Orelated, fact_5483_abs__le__D1, fact_5826_of__int__1__le__iff, fact_1619_mult__cancel__right1, fact_3480_cong__exp__iff__simps_I4_J, fact_3032_nless__le, fact_5742_take__bit__numeral__bit1, fact_8160_pochhammer__double, fact_6689_of__nat__less__imp__less, fact_1438_divide__divide__times__eq, fact_7322_sin__arccos, fact_1504_add__0, fact_1138_group__cancel_Oadd2, fact_1500_mult__zero__left, fact_8961_fact__code, fact_1541_div__0, fact_9078_Suc__times__binomial__add, fact_3827_dvd__add__times__triv__left__iff, fact_5584_abs__diff__le__iff, fact_3935_dvdI, fact_4043_not__is__unit__0, fact_7136_ceiling__correct, fact_7082_suminf__pos__iff, fact_7003_cos__2pi__minus, fact_5348_divmod__algorithm__code_I5_J, fact_4103_dvd__div__unit__iff, fact_9340_cosh__real__nonpos__less__iff, fact_3587_product__nth, fact_2316_sum__squares__gt__zero__iff, fact_1404_del__x__mia, fact_3602_verit__eq__simplify_I8_J, fact_8366_pochhammer__code, fact_7765_arccos__bounded, fact_6114_tanh__altdef, fact_3062_not__le__imp__less, fact_6822_zle__int, fact_4238_even__unset__bit__iff, fact_10131_atLeast__upt, fact_8254_gbinomial__mult__1, fact_9086_inverse__less__iff, fact_8634_prod_Ozero__middle, fact_5135_ln__gt__zero, fact_2071_mult__less__cancel__left__disj, fact_2332_less__divide__eq, fact_6998_ceiling__le__neg__numeral, fact_1427_numeral__code_I2_J, fact_4570_even__signed__take__bit__iff, fact_5150_le__minus__one__simps_I1_J, fact_3312_vebt__insert_Opelims, fact_558_add__2__eq__Suc, fact_7150_sincos__principal__value, fact_2605_dual__order_Orefl, fact_4980_minus__diff__minus, fact_1723_nat__zero__less__power__iff, fact_9424_numeral__power__less__nat__cancel__iff, fact_3322_imult__is__0, fact_4155_unit__div__eq__0__iff, fact_7173_sin__times__sin, fact_3217_order__le__less__subst1, fact_9007_inverse__eq__divide__numeral, fact_4317_of__bool__less__iff, fact_7940_sum_Onat__diff__reindex, fact_849_diff__less__mono, fact_5889_semiring__norm_I27_J, fact_7977_one__diff__power__eq, fact_5308_divide__le__eq__numeral_I2_J, fact_6885_norm__mult__numeral2, fact_2139_divide__nonpos__nonpos, fact_6217_or__not__num__neg_Osimps_I6_J, fact_7164_cos__double__less__one, fact_5083_nonzero__minus__divide__divide, fact_2707_dual__order_Otrans, fact_4151_even__numeral, fact_4798_semiring__norm_I171_J, fact_5679_dbl__dec__simps_I3_J, fact_7793_cos__sin__eq, fact_9682_inverse__complex_Ocode, fact_4748_diff__numeral__special_I12_J, fact_1959_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_8337_gbinomial__minus, fact_7151_ceiling__divide__upper, fact_5445_semiring__norm_I16_J, fact_10135_upt__conv__Cons__Cons, fact_2326_mult__imp__less__div__pos, fact_1246_mult_Ocomm__neutral, fact_1730_eq__divide__eq__numeral1_I1_J, fact_7187_cos__gt__zero__pi, fact_3417_mod__mult__self3, fact_10076_mono__times__nat, fact_6989_ceiling__diff__one, fact_2765_less__imp__neq, fact_432_nth__list__update, fact_6918_norm__triangle__lt, fact_197_power__one, fact_2772_order_Oasym, fact_884_max_Oassoc, fact_909_max_Oabsorb__iff2, fact_6309_real__sqrt__eq__zero__cancel__iff, fact_5437_abs__of__nonpos, fact_7869_lessThan__iff, fact_3464_power__mod, fact_6568_of__nat__power__eq__of__nat__cancel__iff, fact_103__C6_C, fact_5907_of__int__neg__numeral, fact_2113_add__pos__pos, fact_1470_deg__1__Leafy, fact_5717_numeral__eq__Suc, fact_3019_int__power__div__base, fact_7787_sum_Oin__pairs, fact_598_add__Suc__shift, fact_6972_cos__pi, fact_2935_order__less__imp__not__less, fact_9556_XOR__lower, fact_4186_prod__decode__aux_Ocases, fact_9267_cos__converges, fact_8571_prod_Oinsert__if, fact_6953_norm__power__diff, fact_289_one__le__power, fact_7121_cos__monotone__0__pi, fact_4341_zero__less__of__bool__iff, fact_9797_sqr_Osimps_I1_J, fact_1107_ab__semigroup__mult__class_Omult__ac_I1_J, fact_758_max_Oabsorb4, fact_2559_odd__power__less__zero, fact_5910_int__less__real__le, fact_867_less__diff__conv2, fact_3972_dvd__mult__right, fact_5720_inc_Osimps_I3_J, fact_1166_add__right__mono, fact_10174_concat__bit__assoc__sym, fact_2937_order__less__imp__not__less, fact_4697_add__neg__numeral__simps_I3_J, fact_3545_mod__eq__nat1E, fact_10157_powr__real__of__int_H, fact_3267_bot_Oextremum__uniqueI, fact_2882_ord__less__eq__subst, fact_5293_neg__one__power__add__eq__neg__one__power__diff, fact_8327_pochhammer__absorb__comp, fact_663_eq__imp__le, fact_3362_atLeastAtMost__iff, fact_632_less__iff__Suc__add, fact_2599_buildup__nothing__in__min__max, fact_7665_sum_OatLeast__Suc__atMost, fact_3510_mod__mult__div__eq, fact_1391_divmod__step__eq, fact_216_numeral__eq__one__iff, fact_8188_zero__less__floor, fact_665_le__refl, fact_7387_sum__norm__le, fact_4517_inf__period_I1_J, fact_6457_sqrt__sum__squares__le__sum, fact_268_one__less__numeral__iff, fact_9632_complex__Re__le__cmod, fact_6860_sin__gt__zero2, fact_5120_dvd__neg__div, fact_10118_atLeastLessThan__add__Un, fact_8905_prod_Oin__pairs, fact_5964_exp__zero, fact_8256_gbinomial__mult__1_H, fact_5039_neg__numeral__less__numeral, fact_656_less__irrefl__nat, fact_601_lift__Suc__mono__less, fact_9812_atMost__Suc__eq__insert__0, fact_5392_abs__mult__self__eq, fact_6103_exp__ge__add__one__self__aux, fact_7064_ceiling__less__cancel, fact_10132_atLeastLessThan__upt, fact_587_nat__induct__at__least, fact_4849_diff__numeral__special_I10_J, fact_8197_floor__divide__eq__div__numeral, fact_4718_minus__mod__self1, fact_5594_power__minus__Bit1, fact_1865_divisors__zero, fact_8534_prod_Ointer__filter, fact_1318_add__mono__thms__linordered__field_I3_J, fact_1145_add__mono__thms__linordered__semiring_I4_J, fact_3901_even__succ__div__2, fact_5652_abs__square__less__1, fact_4462_minf_I2_J, fact_6679_div__mult2__eq_H, fact_5217_power__minus, fact_5312_minus__power__mult__self, fact_5957_exp__less__cancel__iff, fact_6404_log__ln, fact_1498_mult__zero__left, fact_3273_bot_Oextremum__unique, fact_3593_product__nth, fact_3897_odd__Suc__minus__one, fact_8131_Maclaurin__zero, fact_9238_scaleR__mono, fact_816_diff__commute, fact_4507_minf_I6_J, fact_660_Nat_Oex__has__greatest__nat, fact_9031_nonzero__inverse__mult__distrib, fact_633_less__imp__Suc__add, fact_2169_nonzero__divide__eq__eq, fact_1195_add__strict__mono, fact_4271_power__le__zero__eq, fact_9951_filterlim__pow__at__bot__odd, fact_2500_half__gt__zero, fact_3625_length__product, fact_5457_divmod__algorithm__code_I2_J, fact_6082_exp__diff, fact_7053_suminf__nonneg, fact_2299_mult__left__le__one__le, fact_1781_bits__1__div__2, fact_8284_pochhammer__of__nat__eq__0__iff, fact_698_add__le__mono, fact_687_not__add__less2, fact_6991_summable__geometric__iff, fact_5654_divmod__def, fact_4145_dvd__div__iff__mult, fact_3129_dual__order_Ostrict__trans2, fact_9657_cmod__Im__le__iff, fact_6099_even__and__iff, fact_182_list__update__beyond, fact_2718_dual__order_Oeq__iff, fact_1493_mult__zero__right, fact_7809_double__gauss__sum, fact_7220_numeral__powr__numeral__real, fact_5729_numeral__inc, fact_5854_of__int__less__numeral__power__cancel__iff, fact_6086_mask__Suc__exp, fact_9147_binomial__ring, fact_965_less__max__iff__disj, fact_2566_vebt__insert_Oelims, fact_9193_scaleR__eq__iff, fact_2377_vebt__member_Osimps_I4_J, fact_4138_unit__dvdE, fact_1552_divide__cancel__right, fact_2564_invar__vebt_Osimps, fact_3631_length__product, fact_5171_neg__numeral__le__neg__one, fact_3427_bits__one__mod__two__eq__one, fact_1987_mult__right__mono__neg, fact_412_in__set__conv__nth, fact_2448_power__Suc__le__self, fact_5236_take__bit__minus__small__eq, fact_5875_of__int__less__neg__numeral__power__cancel__iff, fact_4867_Parity_Oring__1__class_Opower__minus__even, fact_7815_arccos__le__pi2, fact_5165_neg__numeral__le__one, fact_4250_oddE, fact_958_max_Omono, fact_2340_divide__eq__eq__numeral_I1_J, fact_7329_of__real__numeral, fact_4744_add__neg__numeral__special_I8_J, fact_5606_numeral__code_I3_J, fact_6947_norm__diff__triangle__ineq, fact_9018_mult__commute__imp__mult__inverse__commute, fact_2065_mult__strict__right__mono, fact_6105_lemma__exp__total, fact_5182_not__one__less__neg__numeral, fact_9273_summable__norm__cos, fact_2934_order__less__imp__not__less, fact_1261_left__diff__distrib_H, fact_8152_dvd__fact, fact_4794_semiring__norm_I170_J, fact_4551_signed__take__bit__Suc, fact_9785_num__of__nat__numeral__eq, fact_4173_is__unit__div__mult2__eq, fact_2568_vebt__delete_Osimps_I4_J, fact_5837_of__int__eq__numeral__power__cancel__iff, fact_2007_mult__mono, fact_7115_sin__zero__norm__cos__one, fact_5340_stable__imp__take__bit__eq, fact_7757_convex__sum__bound__le, fact_9127_sum__choose__diagonal, fact_810_Nat_Oadd__diff__assoc, fact_7539_complex__of__real__add__Complex, fact_2598_empty__subsetI, fact_8258_floor__eq, fact_600_lift__Suc__mono__less, fact_7201_sincos__total__2pi__le, fact_2685_order__subst1, fact_2237_mult__less__cancel__right, fact_4458_minf_I1_J, fact_6352_bit__0, fact_3950_dvd__mult2, fact_2525_power__eq__if, fact_7288_tan__mono__lt__eq, fact_4187_even__zero, fact_7007_sin__cos__squared__add2, fact_8950_gbinomial__sum__nat__pow2, fact_1844_less__numeral__extra_I3_J, fact_5753_dbl__inc__simps_I1_J, fact_1296_group__cancel_Osub1, fact_820_zero__induct__lemma, fact_5078_less__minus__one__simps_I4_J, fact_3456_mod__add__cong, fact_6235_finite__linorder__max__induct, fact_9137_binomial__fact, fact_1958_zero__le__numeral, fact_6501_of__nat__0__eq__iff, fact_9090_one__le__inverse__iff, fact_983_max_Ostrict__coboundedI1, fact_5339_stable__imp__take__bit__eq, fact_3485_mod__Suc, fact_1739_divide__less__0__1__iff, fact_353_Ex__list__of__length, fact_8567_prod_Orelated, fact_5686_pred__numeral__simps_I3_J, fact_5050_add_Oinverse__unique, fact_8343_pochhammer__minus_H, fact_7289_lemma__tan__total1, fact_6786_exp__ge__one__plus__x__over__n__power__n, fact_9331_sinh__diff, fact_9025_inverse__less__imp__less__neg, fact_3038_nless__le, fact_1325_add__mono1, fact_9643_integer__of__int__code, fact_4015_dvd__div__eq__cancel, fact_4144_div__dvd__iff__mult, fact_4594_divmod__step__def, fact_94_add__numeral__left, fact_8316_pochhammer__product, fact_9784_num__of__nat_Osimps_I2_J, fact_2365_div__add__self2, fact_6084_not__mask__negative__int, fact_9499_real__root__mult, fact_2874_ord__less__eq__subst, fact_9246_scaleR__left__le__one__le, fact_5433_zero__le__divide__abs__iff, fact_1278_diff__add__eq__diff__diff__swap, fact_1364_eq__add__iff2, fact_7362_sum_Ocl__ivl__Suc, fact_1635_nonzero__mult__div__cancel__left, fact_4545_minf_I10_J, fact_3238_order__less__le__subst1, fact_7543_arccos__eq__iff, fact_9303_cosh__converges, fact_8355_fact__double, fact_4617_neg__less__iff__less, fact_8323_gbinomial__negated__upper, fact_7494_sum__strict__mono, fact_5307_le__divide__eq__numeral_I2_J, fact_627_less__eq__Suc__le, fact_929_max_Ocobounded1, fact_3418_mod__mult__self2, fact_3323_zero__one__enat__neq_I1_J, fact_9099_sqrt__divide__self__eq, fact_7987_suminf__minus__initial__segment, fact_6540_of__nat__eq__1__iff, fact_7076_summable__powser__ignore__initial__segment, fact_3563_div__exp__mod__exp__eq, fact_3513_mod__div__mult__eq, fact_7184_cos__diff__cos, fact_2064_mult__less__cancel__right__disj, fact_464_dsimp, fact_2300_mult__right__le__one__le, fact_2603_dual__order_Orefl, fact_5298_signed__take__bit__int__greater__eq__minus__exp, fact_8749_sum_OatMost__Suc__shift, fact_8449_prod_OatMost__Suc, fact_5234_ln__eq__minus__one, fact_577_not__less__eq, fact_1243_ring__class_Oring__distribs_I2_J, fact_2456_power__strict__decreasing, fact_4523_exp__div__exp__eq, fact_8120_fact__num__eq__if, fact_5143_not__zero__le__neg__numeral, fact_5793_arctan__less__zero__iff, fact_9179_sums__cos__x__plus__y, fact_1405_pred__less__length__list, fact_6107_ln__x__over__x__mono, fact_2053_linordered__nonzero__semiring__class_Ozero__le__one, fact_7258_powr__add, fact_2666_linorder__linear, fact_4600_take__bit__rec, fact_563_Suc__inject, fact_1423_set__vebt__def, fact_2301_mult__right__le__one__le, fact_4255_parity__cases, fact_7152_cos__45, fact_1345_add__le__imp__le__diff, fact_8326_pochhammer__absorb__comp, fact_9478_root__0, fact_5732_take__bit__numeral__minus__bit1, fact_7038_summable__zero__power, fact_3365_bounded__Max__nat, fact_2322_zero__less__two, fact_6146_round__unique, fact_3468_mod__less__eq__dividend, fact_10133_atLeastAtMost__upt, fact_1566_mult__0__right, fact_8143_Maclaurin__exp__lt, fact_1134_add_Oassoc, fact_9670_Re__power2, fact_4509_minf_I8_J, fact_8728_prod_OatLeast0__atMost__Suc, fact_5892_real__of__int__div4, fact_3759_finite__subset, fact_4236_odd__pos, fact_2412_mult__less__cancel__right1, fact_4490_bits__induct, fact_8142_cos__paired, fact_6102_even__or__iff, fact_8985_inverse__divide, fact_4063_mult__unit__dvd__iff_H, fact_6875_sin__arctan, fact_8623_atMost__nat__numeral, fact_3937_dvdI, fact_5115_take__bit__flip__bit__eq, fact_2792_linorder__cases, fact_4834_neg__numeral__less__neg__one__iff, fact_5408_abs__of__nonneg, fact_3020_leD, fact_4580_crossproduct__eq, fact_8279_pochhammer__of__nat__eq__0__lemma, fact_309_power__less__power__Suc, fact_4434_pinf_I2_J, fact_503_real__arch__pow, fact_15__C115_C, fact_5178_not__neg__one__less__neg__numeral, fact_4146_dvd__div__iff__mult, fact_7376_sin__of__real__pi__half, fact_2328_pos__less__divide__eq, fact_6817_int__ops_I3_J, fact_4813_mult__neg__numeral__simps_I3_J, fact_3302_max__absorb1, fact_3502_cong__exp__iff__simps_I6_J, fact_9079_nonzero__inverse__eq__divide, fact_6767_log__nat__power, fact_4561_signed__take__bit__of__0, fact_2688_order__subst1, fact_2018_add__nonpos__eq__0__iff, fact_286_less__numeral__extra_I4_J, fact_3110_dual__order_Oorder__iff__strict, fact_6166_and__nat__numerals_I1_J, fact_9191_scaleR__scaleR, fact_188_power2__sum, fact_3166_order__less__le, fact_4028_dvd__mod, fact_9082_choose__mult, fact_3535_minus__mod__eq__mult__div, fact_2526_power__eq__if, fact_1181_add__mono__thms__linordered__semiring_I3_J, fact_1168_add__left__mono, fact_2295_sum__squares__ge__zero, fact_1647_nonzero__mult__divide__mult__cancel__right, fact_3568_mult__exp__mod__exp__eq, fact_9521_odd__real__root__power__cancel, fact_4615_compl__le__compl__iff, fact_9164_choose__alternating__linear__sum, fact_9588_unset__bit__int__def, fact_1340_le__add__diff, fact_48_numeral__eq__iff, fact_2175_eq__divide__eq, fact_1298_group__cancel_Osub1, fact_4656_concat__bit__of__zero__2, fact_1911_gr__implies__not0, fact_9232_eq__vector__fraction__iff, fact_7257_Complex__eq__neg__numeral, fact_1140_group__cancel_Oadd2, fact_4088_div__mult__div__if__dvd, fact_3117_dual__order_Ostrict__iff__order, fact_5552_tanh__real__gt__neg1, fact_9326_cosh__add, fact_4998_mod__minus__eq, fact_5030_neg__numeral__le__numeral, fact_7295_add__tan__eq, fact_2289_divide__nonneg__neg, fact_2909_order__less__not__sym, fact_6938_norm__triangle__ineq4, fact_3516_div__mult__mod__eq, fact_2903_order__less__subst2, fact_6451_even__bit__succ__iff, fact_501__092_060open_062Some_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_092_060close_062, fact_9646_Re__power__real, fact_3195_order__neq__le__trans, fact_6781_arctan__lbound, fact_1401_del__x__mi, fact_611_lift__Suc__antimono__le, fact_6684_less__imp__of__nat__less, fact_8980_inverse__1, fact_572_Suc__lessI, fact_178_nth__list__update__eq, fact_5469_zmod__numeral__Bit1, fact_6450_even__bit__succ__iff, fact_7905_sums__iff__shift_H, fact_1068_add__less__cancel__right, fact_9407_modulo__int__unfold, fact_6299_of__int__round__gt, fact_8250_gbinomial__addition__formula, fact_4181_dvd__imp__le, fact_5160_less__minus__one__simps_I3_J, fact_269_one__less__numeral__iff, fact_1155_one__reorient, fact_336_one__plus__numeral__commute, fact_5661_take__bit__Suc__bit1, fact_4865_Power_Oring__1__class_Opower__minus__even, fact_2132_less__numeral__extra_I1_J, fact_4800_semiring__norm_I172_J, fact_6863_sin__inj__pi, fact_2871_ord__eq__less__subst, fact_3328_VEBT__internal_Omembermima_Opelims_I3_J, fact_5224_take__bit__Suc__minus__1__eq, fact_4427_pinf_I1_J, fact_9553_flip__bit__int__def, fact_3527_div__mult1__eq, fact_7198_cos__zero__iff, fact_806_left__diff__distrib__numeral, fact_8325_gbinomial__index__swap, fact_5022_take__bit__int__less__eq__self__iff, fact_9306_sinh__real__less__iff, fact_5649_abs__square__le__1, fact_9182_exp__first__two__terms, fact_7428_sum__nonpos, fact_5320_signed__take__bit__int__eq__self__iff, fact_670_size__neq__size__imp__neq, fact_9672_norm__complex__def, fact_4619_neg__numeral__eq__iff, fact_5255_add__divide__eq__if__simps_I6_J, fact_6726_of__nat__diff, fact_6517_of__nat__numeral, fact_5715_num__induct, fact_2444_power__Suc__less, fact_9217_scaleR__left__distrib, fact_7538_Complex__add__complex__of__real, fact_1767_le__divide__eq__1__neg, fact_529_VEBT_Oinject_I1_J, fact_2812_linorder__less__wlog, fact_7915_sums__mult__iff, fact_1459_VEBT__internal_Onaive__member_Osimps_I3_J, fact_9241_split__scaleR__pos__le, fact_4840_power2__minus, fact_4548_option_Osize__gen_I2_J, fact_1548_bits__div__0, fact_5042_neg__eq__iff__add__eq__0, fact_1085_add__diff__cancel__right_H, fact_6942_norm__diff__ineq, fact_7813_arith__series__nat, fact_2414_mult__less__cancel__left2, fact_311_power__less__imp__less__exp, fact_6889_norm__neg__numeral, fact_6983_ceiling__le__one, fact_5243_eq__divide__eq__numeral_I2_J, fact_4777_take__bit__of__1__eq__0__iff, fact_6775_Bernoulli__inequality, fact_6468_bit__rec, fact_3543_nat__mod__eq__lemma, fact_1869_mult__not__zero, fact_8548_prod_Oshift__bounds__cl__nat__ivl, fact_9667_times__complex_Ocode, fact_4077_div__mult__swap, fact_2918_linorder__less__linear, fact_460_post__member__pre__member, fact_7168_cos__one__2pi__int, fact_682_le__neq__implies__less, fact_7320_sum__gp, fact_9507_real__root__less__mono, fact_4632_mult__minus__left, fact_4345_of__bool__less__one__iff, fact_9504_root__sgn__power, fact_33__C7_C, fact_3514_mod__div__mult__eq, fact_533_lessI, fact_4847_add__neg__numeral__special_I9_J, fact_5867_neg__numeral__power__le__of__int__cancel__iff, fact_7006_ceiling__minus__divide__eq__div__numeral, fact_8186_floor__less__zero, fact_108_distrib__right__numeral, fact_4623_mult__minus__right, fact_9510_real__root__abs, fact_2457_zero__power2, fact_8237_gbinomial__of__nat__symmetric, fact_3241_order__less__le__subst1, fact_9790_num__of__nat__plus__distrib, fact_6135_exists__least__lemma, fact_10140_upt__conv__Cons, fact_8293_pochhammer__product_H, fact_4054_dvd__mult__unit__iff, fact_3478_mod__eq__self__iff__div__eq__0, fact_5343_signed__take__bit__int__greater__eq, fact_7143_ceiling__less__iff, fact_1372_less__add__iff2, fact_871_nat__le__add__iff2, fact_279_le__numeral__extra_I4_J, fact_9719_subset__eq__atLeast0__lessThan__card, fact_4130_less__eq__dvd__minus, fact_5032_zero__neq__neg__numeral, fact_3942_dvd__def, fact_6373_bit__and__iff, fact_9215_scaleR__left_Oadd, fact_9789_num__of__nat__double, fact_1565_mult__cancel1, fact_7147_cos__two__le__zero, fact_8458_prod_Oneutral, fact_8896_fact__div__fact, fact_5465_mod__Suc__eq__mod__add3, fact_3994_dvd__unit__imp__unit, fact_7296_powr__half__sqrt, fact_2349_add__frac__num, fact_9489_real__root__le__0__iff, fact_9959_tendsto__power__div__exp__0, fact_1536_div__by__0, fact_7175_sin__times__cos, fact_3532_minus__mult__div__eq__mod, fact_4448_pinf_I5_J, fact_2267_add__nonpos__neg, fact_1608_diff__ge__0__iff__ge, fact_2336_power__le__one, fact_7889_sums__mult, fact_9419_numeral__power__eq__nat__cancel__iff, fact_7239_one__complex_Ocode, fact_4244_even__flip__bit__iff, fact_5863_neg__numeral__power__eq__of__int__cancel__iff, fact_2494_VEBT__internal_Omembermima_Oelims_I3_J, fact_9519_real__root__decreasing, fact_2760_gt__ex, fact_4693_ab__left__minus, fact_6733_exp__of__nat__mult, fact_457_semiring__norm_I69_J, fact_4565_signed__take__bit__mult, fact_450_power__even__eq, fact_7337_arccos__1, fact_1785_one__div__two__eq__zero, fact_3458_mod__add__eq, fact_294_left__right__inverse__power, fact_145_numeral__Bit0, fact_8907_sum__atLeastAtMost__code, fact_6429_sqrt__le__D, fact_3572_divmod__digit__1_I2_J, fact_253_numeral__plus__one, fact_4008_dvd__div__eq__iff, fact_4251_mod2__eq__if, fact_3895_even__diff, fact_6400_real__div__sqrt, fact_7980_power__diff__1__eq, fact_6335_log__less__cancel__iff, fact_7674_sum__Suc__diff, fact_9145_binomial__ring, fact_7839_arccos__cos__eq__abs__2pi, fact_1667_divide__eq__eq__1, fact_8116_termdiff__converges__all, fact_8930_Cauchy__product__sums, fact_6332_log__less__zero__cancel__iff, fact_255_numeral__plus__one, fact_8954_polyfun__diff__alt, fact_857_diff__Suc__eq__diff__pred, fact_5564_abs__minus__le__zero, fact_9105_choose__rising__sum_I1_J, fact_5547_abs__real__def, fact_3211_order__less__le__trans, fact_9115_ex__inverse__of__nat__less, fact_2259_add__strict__increasing2, fact_4473_minf_I4_J, fact_5789_of__int__power, fact_1431_power__numeral__even, fact_9309_sinh__real__pos__iff, fact_6401_sqrt__add__le__add__sqrt, fact_2101_mult__less__0__iff, fact_5451_abs__power2, fact_4912_signed__take__bit__minus, fact_436_list__update__same__conv, fact_1754_nonzero__divide__mult__cancel__left, fact_7967_sumr__diff__mult__const2, fact_200_power__one, fact_3869_unit__div__mult__self, fact_944_max_OboundedE, fact_8807_prod_Oub__add__nat, fact_1819_zero__power, fact_695_add__leD1, fact_333_one__plus__numeral__commute, fact_9730_drop__bit__Suc__minus__bit1, fact_5665_divmod__divmod__step, fact_5428_semiring__norm_I77_J, fact_6718_of__nat__or__eq, fact_9462_divide__int__def, fact_2184_power__0, fact_2538_power2__less__imp__less, fact_9788_num__of__nat__One, fact_832_eq__diff__iff, fact_4622_neg__numeral__eq__iff, fact_4388_of__bool__conj, fact_1841_less__numeral__extra_I3_J, fact_3254_linorder__le__less__linear, fact_5122_dvd__neg__div, fact_9288_summable__norm__exp, fact_4583_crossproduct__noteq, fact_3958_dvd__mult__left, fact_826_diff__le__mono2, fact_4510_minf_I8_J, fact_276_L2__set__mult__ineq__lemma, fact_7027_summable__divide, fact_5738_take__bit__numeral__bit0, fact_5971_bit_Odisj__one__left, fact_5358_case__prodI, fact_6827_int__ops_I5_J, fact_1659_div__self, fact_10067_VEBT__internal_Ovalid_H_Oelims_I1_J, fact_6305_log__base__10__eq2, fact_4815_mult__neg__numeral__simps_I3_J, fact_7535_sum__power__add, fact_4453_pinf_I7_J, fact_3157_order__le__less, fact_2843_order__less__asym, fact_4520_inf__period_I2_J, fact_6127_one__or__eq, fact_6799_negative__zless, fact_6369_real__sqrt__divide, fact_778_geqmaxNone, fact_2700_antisym, fact_217_numeral__eq__one__iff, fact_4376_bits__1__div__exp, fact_5422_semiring__norm_I9_J, fact_8189_floor__le__zero, fact_5108_ab__group__add__class_Oab__diff__conv__add__uminus, fact_6655_bit__of__nat__iff__bit, fact_1539_div__0, fact_8281_pochhammer__of__nat__eq__0__lemma, fact_6414_bit__concat__bit__iff, fact_3526_cancel__div__mod__rules_I2_J, fact_252_numeral__plus__one, fact_8406_prod_Odelta_H, fact_2552_div__2__gt__zero, fact_6720_of__nat__or__eq, fact_5618_odd__numeral, fact_7051_powser__insidea, fact_2241_mult__strict__mono_H, fact_9492_real__root__ge__1__iff, fact_2790_antisym__conv3, fact_7361_sum_Ocl__ivl__Suc, fact_134_mult__numeral__1__right, fact_6584_of__nat__Suc, fact_3781_gcd__nat__induct, fact_4949_neg__numeral__neq__numeral, fact_7091_sin__diff, fact_4143_div__dvd__iff__mult, fact_1441_add__divide__distrib, fact_5535_abs__le__D2, fact_9365_cosh__def, fact_8047_fact__0, fact_3641_finite__less__ub, fact_5327_take__bit__incr__eq, fact_1115_add__left__imp__eq, fact_1672_one__eq__divide__iff, fact_1320_add__mono__thms__linordered__field_I4_J, fact_509_nested__mint, fact_1542_div__0, fact_1963_zero__le__mult__iff, fact_7835_arcsin, fact_3101_order_Ostrict__iff__not, fact_1908_Zero__not__Suc, fact_6351_bit__0, fact_9364_cmod__unit__one, fact_5214_uminus__numeral__One, fact_8356_floor__log__nat__eq__if, fact_8473_prod__power__distrib, fact_2729_order_Otrans, fact_2717_dual__order_Oeq__iff, fact_435_nth__list__update, fact_7233_powr__less__mono2__neg, fact_6725_ex__less__of__nat__mult, fact_8656_less__1__prod, fact_1152_one__reorient, fact_6203_insert__mono, fact_5161_less__minus__one__simps_I3_J, fact_6364_bit__disjunctive__add__iff, fact_3682_surj__pair, fact_5084_nonzero__minus__divide__right, fact_6026_or__numerals_I4_J, fact_9580_all__nat__less__eq, fact_1676_power__0__Suc, fact_6613_of__nat__le__of__nat__power__cancel__iff, fact_5690_diff__numeral__Suc, fact_2800_dual__order_Oasym, fact_4919_take__bit__mult, fact_9559_bit__push__bit__iff__int, fact_5814_of__int__0__less__iff, fact_9194_scaleR__eq__iff, fact_6933_norm__triangle__le__diff, fact_9229_scaleR__left__mono, fact_223_one__eq__numeral__iff, fact_9111_binomial__maximum, fact_3227_order__le__less__subst2, fact_6458_sqrt__even__pow2, fact_1893_power__not__zero, fact_4602_power__numeral, fact_2888_order__less__subst1, fact_8202_neg__numeral__le__floor, fact_6739_mod__mult2__eq_H, fact_5891_BitM__inc__eq, fact_8138_Maclaurin__exp__le, fact_7971_summableI__nonneg__bounded, fact_8881_pochhammer__Suc__prod, fact_2084_zero__less__mult__pos, fact_5988_or__numerals_I2_J, fact_5112_take__bit__set__bit__eq, fact_24__092_060open_062length_AtreeList_A_061_Alength_A_ItreeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_J_092_060close_062, fact_1119_add_Oleft__commute, fact_1204_add__mono__thms__linordered__field_I2_J, fact_771_max_Oleft__idem, fact_6623_of__nat__zero__less__power__iff, fact_7846_geometric__deriv__sums, fact_2102_mult__less__0__iff, fact_7947_powser__sums__zero, fact_3658_neg__mod__sign, fact_1487_mult__eq__0__iff, fact_10194_set__encode__vimage__Suc, fact_4330_of__bool__eq__1__iff, fact_1691_zero__less__Suc, fact_1290_eq__diff__eq, fact_1831_le__numeral__extra_I3_J, fact_6296_or__nat__unfold, fact_3413_mod__div__trivial, help_If_2_1_If_001t__Complex__Ocomplex_T, fact_5761_of__int__numeral, fact_9590_not__int__div__2, fact_2926_order__less__imp__not__eq, fact_5941_or_Oleft__idem, fact_777_power__minus__is__div, fact_5221_power__minus__Bit0, fact_9773_eq__Abs__Integ, fact_320_one__le__numeral, fact_5104_diff__conv__add__uminus, fact_3416_mod__mult__self3, fact_1069_add__less__cancel__right, fact_8981_inverse__1, fact_2891_order__less__subst1, fact_1252_comm__monoid__mult__class_Omult__1, fact_3067_order_Oorder__iff__strict, fact_630_less__add__Suc1, fact_8967_gbinomial__r__part__sum, fact_371_power__divide, fact_1049_add__diff__cancel__left_H, fact_3534_minus__mod__eq__mult__div, fact_2013_zero__less__numeral, fact_1408_mult__commute__abs, fact_7277_tan__45, fact_440_power4__eq__xxxx, fact_6436_and__exp__eq__0__iff__not__bit, fact_1254_comm__monoid__mult__class_Omult__1, fact_238_power__add__numeral, fact_8871_sum__gp__basic, fact_1948_vebt__pred_Osimps_I2_J, fact_3392_mod__add__self2, fact_8746_prod_OSuc__reindex__ivl, fact_1766_le__divide__eq__1__pos, fact_8968_choose__odd__sum, fact_7330_of__real__numeral, fact_1685_power__zero__numeral, fact_9077_division__ring__inverse__diff, fact_2780_ord__less__eq__trans, fact_8096_choose__dvd, fact_6791_of__nat__code__if, fact_5060_add__eq__0__iff, fact_652_nat__neq__iff, fact_6550_of__nat__1, fact_3231_order__le__less__subst2, fact_1663_div__self, fact_6621_real__of__nat__less__numeral__iff, fact_5113_take__bit__set__bit__eq, fact_4772_max__number__of_I3_J, fact_2384_one__less__mult, fact_9028_inverse__positive__imp__positive, fact_6785_Bernoulli__inequality__even, fact_2686_order__subst1, fact_5272_ln__diff__le, fact_636_mult__Suc, fact_8294_pochhammer__product_H, fact_8086_fact__mono, fact_88_numeral__times__numeral, fact_4914_take__bit__add, fact_3005_realpow__pos__nth__unique, fact_9071_division__ring__inverse__add, fact_7444_sum__mono__inv, fact_6320_real__sqrt__gt__1__iff, fact_170_valid__insert__both__member__options__add, fact_3537_minus__mod__eq__div__mult, fact_706_mult__le__mono1, fact_2312_power__less__imp__less__base, fact_5865_of__int__le__neg__numeral__power__cancel__iff, fact_1100_mult_Ocommute, fact_765_max_Oright__idem, fact_196__092_060open_062x_A_092_060noteq_062_Ami_A_092_060or_062_Ax_A_092_060noteq_062_Ama_092_060close_062, fact_6624_of__nat__zero__less__power__iff, fact_4653_take__bit__of__0, fact_2720_linorder__wlog, fact_5582_abs__triangle__ineq4, fact_1096_mult_Oleft__commute, fact_5128_minus__real__def, fact_3215_order__le__less__subst1, fact_2885_order__less__irrefl, fact_7468_sum__nonneg__eq__0__iff, fact_4476_minf_I4_J, fact_6424_bit__iff__idd__imp__stable, fact_6780_arctan__bounded, fact_8085_fact__fact__dvd__fact, fact_9582_atLeastLessThanSuc__atLeastAtMost, fact_2174_eq__divide__eq, fact_3132_dual__order_Ostrict__iff__not, fact_1994_mult__left__mono__neg, fact_2712_dual__order_Oantisym, fact_4014_dvd__div__eq__cancel, fact_2179_frac__eq__eq, fact_7887_sums__mult2, fact_9328_sinh__add, fact_1312_add__less__le__mono, fact_1824_vebt__insert_Osimps_I1_J, fact_6453_odd__bit__iff__bit__pred, fact_3404_mod__by__1, fact_4445_pinf_I4_J, fact_1926_minus__nat_Odiff__0, fact_2205_mult__less__mono1, fact_7047_suminf__add, fact_2215_vebt__pred_Ocases, fact_4055_dvd__mult__unit__iff, fact_6652_mult__of__nat__commute, fact_2974_equalityD1, fact_3243_order__less__le__subst2, fact_3838_dvd__div__mult__self, fact_8309_floor__divide__real__eq__div, fact_1975_mult__nonneg__nonneg, fact_6386_bit__1__iff, fact_9060_frac__lt__1, fact_1316_add__mono__thms__linordered__field_I3_J, fact_8060_fact__Suc, fact_3395_mod__add__self1, fact_2905_order__less__subst2, fact_7319_sum__gp, fact_2087_zero__less__mult__iff, fact_6683_less__imp__of__nat__less, fact_466_div__exp__eq, fact_5759_dbl__dec__simps_I1_J, fact_5529_abs__triangle__ineq2, fact_5754_dbl__inc__simps_I1_J, fact_4562_signed__take__bit__Suc__1, fact_9321_sinh__plus__cosh, fact_9738_drop__bit__int__def, fact_5569_abs__div__pos, fact_4707_diff__minus__eq__add, fact_6917_norm__triangle__lt, fact_2887_order__less__irrefl, fact_7832_double__gauss__sum__from__Suc__0, fact_9729_drop__bit__numeral__minus__bit0, fact_1588_add__le__same__cancel2, fact_7415_sum__divide__distrib, fact_5549_num_Oexhaust, fact_4766_mod__minus1__right, fact_5808_dbl__dec__simps_I5_J, fact_5973_bit_Odisj__one__right, fact_6691_of__nat__mono, fact_2845_order__less__asym, fact_9214_scaleR__left_Oadd, fact_846_Suc__diff__Suc, fact_2253_mult__le__cancel__right, fact_9248_scaleR__2, fact_6862_sin__30, fact_7004_cos__npi, fact_8492_prod__nonneg, fact_5766_of__int__eq__numeral__iff, fact_1025_le__add__diff__inverse, fact_7292_log__minus__eq__powr, fact_4963_add_Oinverse__distrib__swap, fact_914_max_Oabsorb__iff1, fact_4228_even__iff__mod__2__eq__zero, fact_2793_linorder__cases, fact_6564_of__nat__eq__of__nat__power__cancel__iff, fact_7966_sumr__diff__mult__const2, fact_1235_distrib__left, fact_1989_mult__left__mono, fact_1896_num_Osize_I4_J, fact_1780_Suc__diff__1, fact_7946_powser__sums__zero, fact_7904_sums__split__initial__segment, fact_6120_exp__double, fact_4797_semiring__norm_I171_J, fact_5925_arctan__add, fact_5987_and__numerals_I8_J, fact_9120_log__inverse, fact_8083_fact__fact__dvd__fact, fact_1887_zero__neq__one, fact_5085_nonzero__minus__divide__right, fact_9701_complex__add__cnj, fact_7933_sums__Suc, fact_6516_of__nat__numeral, fact_9551_xor__negative__int__iff, fact_4823_not__neg__one__le__neg__numeral__iff, fact_680_le__eq__less__or__eq, fact_1892_power__not__zero, fact_8949_gbinomial__sum__nat__pow2, fact_9104_sum__choose__lower, fact_2883_order__less__irrefl, fact_6753_of__nat__less__two__power, fact_1935_lambda__zero, fact_4833_neg__numeral__less__neg__one__iff, fact_8983_inverse__eq__1__iff, fact_2506_power2__eq__imp__eq, fact_7159_sin__squared__eq, fact_8253_gbinomial__ge__n__over__k__pow__k, fact_4305_vebt__buildup_Oelims, fact_221_one__eq__numeral__iff, fact_6074_AND__upper2, fact_222_one__eq__numeral__iff, fact_1369_ordered__ring__class_Ole__add__iff2, fact_4296_inf__period_I3_J, fact_5176_not__one__le__neg__numeral, fact_383_power__add, fact_6705_of__nat__mod, fact_2234_mult__le__cancel__left__pos, fact_8627_prod_OatLeastAtMost__rev, fact_3109_dual__order_Oorder__iff__strict, fact_1912_less__zeroE, fact_515_nat__add__left__cancel__le, fact_3904_odd__succ__div__two, fact_2822_not__less__iff__gr__or__eq, fact_3701_verit__sum__simplify, fact_9335_cosh__real__nonneg__le__iff, fact_7777_sum__telescope_H_H, fact_1327_add__mono1, fact_3451_mod__mult__eq, fact_29_divide__less__eq__numeral1_I1_J, fact_6598_real__of__nat__eq__numeral__power__cancel__iff, fact_732_local_Opower__def, fact_8274_pochhammer__rec_H, fact_7243_powr__mono2_H, fact_6653_mult__of__nat__commute, fact_976_max_Ostrict__order__iff, fact_2999_Diff__mono, fact_7012_cos__int__2pin, fact_6054_bit_Odisj__zero__right, fact_8133_Maclaurin__zero, fact_9253_neg__le__divideR__eq, fact_830_Nat_Odiff__diff__eq, fact_3050_antisym__conv2, fact_4779_ln__ge__zero__iff, fact_7332_of__real__divide, fact_9593_and__not__numerals_I2_J, fact_7105_cos__monotone__0__pi__le, fact_3387_low__def, fact_4070_unit__mult__right__cancel, fact_2159_divide__pos__pos, fact_7113_cos__add, fact_6466_bit__rec, fact_1769_divide__le__eq__1__neg, fact_9542_xor__nat__numerals_I2_J, fact_2910_order__less__not__sym, fact_4239_even__unset__bit__iff, fact_2296_sum__squares__le__zero__iff, fact_9116_power__diff__conv__inverse, fact_7812_double__gauss__sum, fact_3244_order__less__le__subst2, fact_5409_abs__of__nonneg, fact_6939_norm__triangle__sub, fact_4967_group__cancel_Oneg1, fact_7671_sum_OSuc__reindex__ivl, fact_8430_prod_Oinsert, fact_8275_pochhammer__rec_H, fact_6176_and__nat__numerals_I2_J, fact_635_Suc__mult__le__cancel1, fact_5909_int__le__real__less, fact_8945_root__polyfun, fact_354_list__update__swap, fact_5404_abs__le__zero__iff, fact_1194_add__strict__left__mono, fact_5836_numeral__power__eq__of__int__cancel__iff, fact_674_power__odd__eq, fact_1809_VEBT__internal_Onaive__member_Ocases, fact_7969_sumr__diff__mult__const2, fact_2346_add__divide__eq__iff, fact_6421_stable__imp__bit__iff__odd, fact_8931_gbinomial__Suc, fact_8303_floor__correct, fact_8345_pochhammer__minus, fact_1919_bot__nat__0_Oextremum__uniqueI, fact_3356_Icc__eq__Icc, fact_2153_power__mono, fact_8361_pochhammer__code, fact_6620_numeral__less__real__of__nat__iff, fact_7367_norm__of__real__add1, fact_3143_order_Ostrict__implies__order, fact_5896_one__plus__BitM, fact_3146_dual__order_Ostrict__implies__order, fact_475_mi__eq__ma__no__ch, fact_1644_div__mult__mult1, fact_6789_of__nat__code__if, fact_10168_min__0R, fact_6557_of__nat__power, fact_1439_divide__divide__eq__left_H, fact_2927_order__less__imp__not__eq, fact_1034_div__by__1, fact_7199_cos__expansion__lemma, fact_1182_add__mono__thms__linordered__semiring_I3_J, fact_1314_add__le__less__mono, fact_6818_complex__mod__minus__le__complex__mod, fact_5796_dbl__inc__simps_I2_J, fact_1853_mult__right__cancel, fact_10182_drop__upt, fact_4942_verit__negate__coefficient_I2_J, fact_452_less__exp, fact_7146_cos__is__zero, fact_1523_add__cancel__left__left, fact_1770_power__strict__decreasing__iff, fact_4723_ln__less__zero__iff, fact_5873_of__int__less__neg__numeral__power__cancel__iff, fact_2540_sum__power2__le__zero__iff, fact_4638_minus__add__distrib, fact_2449_power__Suc__le__self, fact_9000_prod__eq__1__iff, fact_6709_of__nat__max, fact_7716_sum_Oub__add__nat, fact_5444_artanh__minus__real, fact_8271_pochhammer__Suc, fact_1355_less__diff__eq, fact_1205_add__mono__thms__linordered__field_I5_J, fact_2519_power__diff__power__eq, fact_5791_of__int__power, fact_5311_square__le__1, fact_9420_nat__ceiling__le__eq, fact_4591_signed__take__bit__rec, fact_1342_add__le__add__imp__diff__le, fact_4452_pinf_I7_J, fact_6486_exp__ge__one__minus__x__over__n__power__n, fact_478_bits__div__by__1, fact_4703_mult__minus1__right, fact_8915_sum_Oin__pairs__0, fact_7275_ln__powr__bound, fact_1090_add__diff__cancel__right, fact_5769_of__int__less__iff, fact_4785_diff__numeral__simps_I2_J, fact_476_semiring__norm_I83_J, fact_8190_floor__less__numeral, fact_189_power2__sum, fact_2741_ord__le__eq__trans, fact_3892_even__plus__one__iff, fact_9073_inverse__add, fact_5591_numeral__Bit1, fact_3188_order__le__neq__trans, fact_5407_abs__le__self__iff, fact_8833_zero__polynom__imp__zero__coeffs, fact_9650_csqrt__minus, fact_76_numeral__le__iff, fact_6327_bit__numeral__Bit0__Suc__iff, fact_1203_add__mono__thms__linordered__field_I2_J, fact_1982_mult__right__mono, fact_1059_add__left__cancel, fact_8156_cos__coeff__Suc, fact_4380_one__div__2__pow__eq, fact_7210_powr__one__eq__one, fact_6523_of__nat__less__iff, fact_1974_mult__nonneg__nonneg, fact_16_hprolist, fact_3762_infinite__super, fact_5602_cong__exp__iff__simps_I10_J, fact_1519_add__cancel__left__right, fact_2547_not__sum__power2__lt__zero, fact_6570_of__nat__power__eq__of__nat__cancel__iff, fact_4158_unit__eq__div1, fact_186_power2__sum, fact_6771_pi__half__ge__zero, fact_4318_of__bool__less__iff, fact_7211_powr__zero__eq__one, fact_4342_zero__less__of__bool__iff, fact_5725_numeral__inc, fact_4917_take__bit__nat__less__eq__self, fact_497_del__x__not__mi__newnode__not__nil, fact_6098_even__and__iff, fact_6921_norm__power__ineq, fact_5765_of__int__eq__numeral__iff, fact_2199_option_Osize_I3_J, fact_4050_dvd__div__eq__0__iff, fact_6814_sin__x__le__x, fact_4203_odd__even__add, fact_1098_mult_Oleft__commute, fact_2783_ord__less__eq__trans, fact_6316_real__sqrt__lt__0__iff, fact_4804_mult__neg__numeral__simps_I1_J, fact_9683_Complex__divide, fact_2271_add__nonneg__pos, fact_7206_sin__tan, fact_9276_pos__minus__divideR__le__eq, fact_6625_of__nat__zero__less__power__iff, fact_2082_zero__less__mult__pos2, fact_1617_mult__cancel__right1, fact_805_left__diff__distrib__numeral, fact_3081_order_Ostrict__trans1, fact_836_Nat_Odiff__cancel, fact_3677_prod__cases, fact_5577_abs__if, fact_9535_root__powr__inverse, fact_479_bits__div__by__1, fact_809_right__diff__distrib__numeral, fact_9204_scaleR__times, fact_9369_sinh__def, fact_6187_or__minus__numerals_I7_J, fact_4023_dvd__power__same, fact_7824_gauss__sum, fact_3634_finite__nat__set__iff__bounded, fact_1179_add__mono__thms__linordered__semiring_I2_J, fact_3873_even__mult__iff, fact_5676_signed__take__bit__numeral__bit1, fact_4240_even__unset__bit__iff, fact_1474_le__zero__eq, fact_1362_eq__add__iff2, fact_5928_mask__numeral, fact_579_Suc__less__eq2, fact_2317_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq, fact_6987_ceiling__add__one, fact_9142_binomial, fact_4139_dvd__div__eq__mult, fact_9434_nat__le__iff, fact_2428_mult__imp__le__div__pos, fact_7373_sum__zero__power_H, fact_5291_neg__one__power__add__eq__neg__one__power__diff, fact_5588_numeral__Bit1, fact_3316_VEBT__internal_Onaive__member_Opelims_I2_J, fact_9603_and__not__numerals_I5_J, fact_3523_cancel__div__mod__rules_I1_J, fact_4789_diff__numeral__simps_I3_J, fact_2702_antisym, fact_6043_or_Oleft__commute, fact_6957_ceiling__log__nat__eq__powr__iff, fact_2914_order__less__imp__triv, fact_6545_of__nat__1__eq__iff, fact_3953_dvd__mult2, fact_6954_norm__power__diff, fact_7803_double__arith__series, fact_8247_one__add__floor, fact_8360_pochhammer__times__pochhammer__half, fact_2025_add__nonpos__nonpos, fact_1932_power__eq__iff__eq__base, fact_1907_Zero__neq__Suc, fact_9117_power__diff__conv__inverse, fact_5154_le__minus__one__simps_I3_J, fact_5186_not__numeral__less__neg__one, fact_6732_exp__of__nat2__mult, fact_9600_atLeastLessThanSuc, fact_3912_even__power, fact_5202_mult__1s__ring__1_I1_J, fact_3799_dvd__add__triv__right__iff, fact_7256_Complex__eq__neg__1, fact_7961_sum__lessThan__telescope_H, fact_3423_Suc__mod__mult__self4, fact_5121_dvd__neg__div, fact_7779_sum__telescope_H_H, fact_3910_even__power, fact_1191_add__strict__right__mono, fact_331_numeral__One, fact_5259_power2__eq__iff, fact_6221_or__not__num__neg_Osimps_I9_J, fact_4984_minus__divide__left, fact_2200_option_Osize_I3_J, fact_3002_real__arch__pow__inv, fact_8229_floor__divide__of__int__eq, fact_1938_lambda__zero, fact_9702_complex__diff__cnj, fact_7743_sum__strict__mono2, fact_6431_int__bit__bound, fact_484_semiring__norm_I13_J, fact_1456_succ__empty, fact_8507_prod__ge__1, fact_556_Suc__numeral, fact_5512_case__prodE, fact_8416_prod_Odelta, fact_9359_cosh__field__def, fact_4504_minf_I6_J, fact_4471_minf_I3_J, fact_8002_geometric__sums, fact_1285_diff__diff__eq2, fact_2045_add__decreasing, fact_7074_powser__split__head_I3_J, fact_6576_of__nat__le__0__iff, fact_9713_card__less__Suc2, fact_2819_not__less__iff__gr__or__eq, fact_1280_diff__add__eq__diff__diff__swap, fact_8119_fact__num__eq__if, fact_924_max_Ocobounded2, fact_8646_less__1__prod2, fact_1902_vebt__buildup_Ocases, fact_5617_numeral__Bit1__div__2, fact_5931_and__int__unfold, fact_3150_dual__order_Ostrict__implies__order, fact_8332_pochhammer__same, fact_6073_AND__upper1, fact_5281_divide__less__eq__numeral_I2_J, fact_3592_product__nth, fact_9386_arctan__def, fact_6045_and_Ocommute, fact_1023_le__add__diff__inverse, fact_9307_sinh__real__le__iff, fact_3393_mod__add__self2, fact_1277_add__implies__diff, fact_6776_arctan__ubound, fact_8265_pochhammer__rec, fact_8181_pochhammer__0, fact_4499_pinf_I8_J, fact_380_power__add, fact_6532_of__nat__add, fact_1021_option_Oexhaust__sel, fact_3867_unit__div__mult__self, fact_1810_invar__vebt_Ointros_I1_J, fact_3938_dvdI, fact_6370_real__sqrt__mult, fact_2868_ord__eq__less__subst, fact_9732_nat_Odisc__eq__case_I2_J, fact_4010_dvd__div__eq__iff, fact_5335_int__bit__induct, fact_6038_bit_Oconj__disj__distrib2, fact_7766_sin__arccos__nonzero, fact_2719_linorder__wlog, fact_8837_sum_OatMost__shift, fact_4729_take__bit__numeral__1, fact_3885_even__Suc__div__two, fact_6995_ceiling__divide__eq__div__numeral, fact_8667_prod_Osubset__diff, fact_8969_choose__odd__sum, fact_9697_Im__complex__div__le__0, fact_3700_verit__sum__simplify, fact_1843_less__numeral__extra_I3_J, fact_3474_cong__exp__iff__simps_I9_J, fact_2907_order__less__subst2, fact_1783_bits__1__div__2, fact_5336_take__bit__int__less__eq, fact_7033_suminf__le, fact_6731_exp__of__nat2__mult, fact_3052_antisym__conv2, fact_578_All__less__Suc, fact_2636_all__nat__less, fact_1551_divide__cancel__right, fact_10156_hd__upt, fact_9958_ln__x__over__x__tendsto__0, fact_1294_diff__eq__eq, fact_5673_dbl__dec__simps_I4_J, fact_6513_of__nat__numeral, fact_5677_dbl__dec__simps_I3_J, fact_767_max_Oright__idem, fact_2785_less__induct, fact_7828_double__gauss__sum__from__Suc__0, fact_10206_le__prod__encode__1, fact_742_not__None__eq, fact_9666_Im__exp, fact_5020_signed__take__bit__eq__iff__take__bit__eq, fact_9339_sinh__double, fact_1915_gr0I, fact_4118_le__imp__power__dvd, fact_2423_mult__le__cancel__left2, fact_1763_mult__le__cancel2, fact_6694_of__nat__mono, fact_1952_not__numeral__le__zero, fact_1087_add__diff__cancel__right_H, fact_9624_VEBT__internal_Ovalid_H_Osimps_I1_J, fact_3501_cong__exp__iff__simps_I1_J, fact_6491_of__nat__eq__iff, fact_3826_dvd__add__times__triv__left__iff, fact_9463_modulo__int__def, fact_7462_sum__le__included, fact_7224_tan__periodic__n, fact_1823_VEBT__internal_Ovalid_H_Ocases, fact_1719_power__Suc__0, fact_6106_ln__ge__iff, help_If_2_1_If_001t__Int__Oint_T, fact_3866_unit__mult__div__div, fact_4657_case__prod__conv, fact_2163_zero__less__power, fact_2392_length__pos__if__in__set, fact_1782_bits__1__div__2, fact_4276_even__mult__exp__div__exp__iff, fact_9058_divide__real__def, fact_889_nat__less__add__iff1, fact_2118_add__neg__neg, fact_2672_order__eq__refl, fact_5860_neg__numeral__power__eq__of__int__cancel__iff, fact_3914_odd__two__times__div__two__succ, fact_2804_dual__order_Oirrefl, fact_3027_leI, fact_165_mult__2, fact_8097_fact__less__mono, fact_6777_arctan__one, fact_1888_zero__neq__one, fact_194_xmi, fact_11_bit__concat__def, fact_1000_split__option__all, fact_9802_image__minus__const__atLeastLessThan__nat, fact_1592_zero__less__double__add__iff__zero__less__single__add, fact_2523_nat__induct2, fact_9487_real__root__lt__0__iff, fact_2495_le__divide__eq__numeral_I1_J, fact_206_length__list__update, fact_9692_Re__complex__div__ge__0, fact_7935_sums__Suc__iff, fact_1066_add__le__cancel__left, fact_5087_numeral__neq__neg__one, fact_1798_sum__power2__eq__zero__iff, fact_2048_not__one__le__zero, fact_6940_norm__triangle__sub, fact_1125_add_Ocommute, fact_4670_less__eq__neg__nonpos, fact_5601_cong__exp__iff__simps_I10_J, fact_4907_take__bit__of__exp, fact_9948_tanh__real__at__bot, fact_5780_of__int__add, fact_4647_div__minus__minus, fact_2442_divide__less__eq__numeral_I1_J, fact_1118_add__left__imp__eq, fact_5636_num_Osize__gen_I3_J, fact_5775_of__int__eq__1__iff, fact_6866_sin__60, fact_5648_power2__le__iff__abs__le, fact_1716_nat__mult__less__cancel__disj, fact_4539_minf_I9_J, fact_8748_sum_OatMost__Suc__shift, fact_2446_power__Suc__less, fact_9471_powr__real__of__int, fact_8923_pochhammer__Suc__prod__rev, fact_6068_exp__ge__zero, fact_5001_concat__bit__eq__iff, fact_6641_of__nat__le__numeral__power__cancel__iff, fact_1003_split__option__ex, fact_4311_intind, fact_1352_linordered__semidom__class_Oadd__diff__inverse, fact_2358_power__inject__base, fact_9460_take__bit__nat__eq, fact_2454_power__strict__decreasing, fact_5816_of__int__less__0__iff, fact_5227_real__0__less__add__iff, fact_7652_sum__shift__lb__Suc0__0, fact_5099_group__cancel_Osub2, fact_2220_vebt__succ_Osimps_I2_J, fact_4069_unit__mult__right__cancel, fact_7114_sin__zero__norm__cos__one, fact_3420_mod__mult__self1, fact_5270_ln__le__minus__one, fact_1972_mult__nonneg__nonpos, fact_5970_bit_Oconj__one__right, fact_1859_no__zero__divisors, fact_6304_arctan__half, fact_5672_dbl__dec__simps_I4_J, fact_7555_arcsin__le__arcsin, fact_1806_VEBT__internal_OminNull_Osimps_I1_J, fact_6048_or_Ocommute, fact_9271_summable__norm__sin, fact_7321_sin__arccos__abs, fact_3841_dvd__mult__div__cancel, fact_7990_sum__less__suminf, fact_6687_of__nat__less__imp__less, fact_1600_less__add__same__cancel1, fact_2238_mult__less__cancel__right, fact_169_valid__insert__both__member__options__pres, fact_7307_arctan, fact_1607_add__less__same__cancel1, fact_6343_log__le__cancel__iff, fact_6251_finite__subset__induct, fact_8503_prod__mono, fact_139_mult__numeral__1, fact_1890_zero__neq__one, fact_8349_gbinomial__sum__up__index, fact_1206_add__mono__thms__linordered__field_I5_J, fact_6869_sin__le__zero, fact_9787_numeral__num__of__nat, fact_4246_even__flip__bit__iff, fact_5819_of__int__numeral__le__iff, fact_10069_VEBT__internal_Ovalid_H_Osimps_I2_J, fact_5008_case__prod__eta, fact_1247_mult_Ocomm__neutral, fact_5612_power__numeral__odd, fact_2575_buildup__gives__empty, fact_1256_right__diff__distrib_H, fact_8230_gbinomial__pochhammer, fact_1026_le__add__diff__inverse2, fact_3315_VEBT__internal_Onaive__member_Opelims_I3_J, fact_9011_prod__pos__nat__iff, fact_290_left__right__inverse__power, fact_2146_less__iff__diff__less__0, fact_5856_of__int__eq__neg__numeral__power__cancel__iff, fact_7118_cos__two__neq__zero, fact_9069_one__less__inverse, fact_6646_even__of__nat, fact_8878_pochhammer__Suc__prod, fact_6123_semiring__bit__operations__class_Oeven__mask__iff, fact_9061_frac__1__eq, fact_676_power__odd__eq, fact_3220_order__le__less__subst1, fact_8267_pochhammer__rec, fact_521_maxbmo, fact_1533_div__by__0, fact_4957_square__eq__iff, fact_9555_push__bit__nat__eq, fact_4438_pinf_I3_J, fact_9048_power__mult__inverse__distrib, fact_1980_mult__le__0__iff, fact_9543_xor__nat__numerals_I1_J, fact_3311_vebt__delete_Opelims, fact_2795_linorder__cases, fact_2796_dual__order_Oasym, fact_2137_le__iff__diff__le__0, fact_4579_crossproduct__eq, fact_232_power__mult__numeral, fact_9184_of__nat__id, fact_7537_sum__power__add, fact_6825_zadd__int__left, fact_3183_order__less__imp__le, fact_4566_signed__take__bit__add, fact_340_power__le__imp__le__exp, fact_8960_polyfun__diff, fact_8610_prod_Oin__pairs__0, fact_6632_of__nat__less__numeral__power__cancel__iff, fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062, fact_2187_Ex__less__Suc2, fact_246_one__add__one, fact_4003_one__dvd, fact_1462_mint__corr__help__empty, fact_3811_dvd__mult__cancel__left, fact_4750_numeral__eq__neg__one__iff, fact_637_Suc__eq__plus1__left, fact_4740_add__neg__numeral__special_I7_J, fact_4367_nth__replicate, fact_9183_exp__first__two__terms, fact_1234_distrib__left, fact_465_div__exp__eq, fact_5571_abs__if__raw, fact_4080_div__div__eq__right, fact_3886_zero__le__power__eq__numeral, fact_9497_real__root__minus, fact_2890_order__less__subst1, fact_4941_verit__negate__coefficient_I2_J, fact_2307_mult__left__le, fact_6884_norm__divide__numeral, fact_2752_le__cases3, fact_2647_ord__le__eq__subst, fact_5659_divmod__nat__def, fact_8154_fact__div__fact__le__pow, fact_9733_drop__bit__push__bit__int, fact_8937_sum_Ozero__middle, fact_5151_le__minus__one__simps_I1_J, fact_6812_sin__int__2pin, fact_949_max_OorderI, fact_6873_sin__total, fact_2609_order__refl, fact_9668_cmod__power2, fact_4597_even__set__encode__iff, fact_3672_Pair__inject, fact_7830_double__gauss__sum__from__Suc__0, fact_8380_prod_Oempty, fact_360_power__commutes, fact_8_low__inv, fact_5623_power3__eq__cube, fact_5799_dbl__inc__simps_I4_J, fact_8884_polyfun__linear__factor__root, fact_4402_of__bool__def, fact_4469_minf_I3_J, fact_5188_neg__one__less__numeral, fact_6496_of__nat__0, fact_3559_bits__stable__imp__add__self, fact_4303_unity__coeff__ex, fact_1084_add__diff__cancel__right_H, fact_4230_even__iff__mod__2__eq__zero, fact_3125_dual__order_Ostrict__trans2, fact_266_one__less__numeral__iff, fact_2469_one__less__power, fact_8364_pochhammer__code, fact_3626_length__product, fact_3934_dvdI, fact_8457_prod_Oneutral, fact_7338_sum__abs, fact_710_nat__mult__1, fact_6483_log2__of__power__le, fact_9338_sinh__double, fact_7663_sum_Onat__ivl__Suc_H, fact_5871_neg__numeral__power__less__of__int__cancel__iff, fact_702_nat__le__iff__add, fact_2499_half__gt__zero__iff, fact_5092_one__neq__neg__numeral, fact_6083_mask__nonnegative__int, fact_4020_div__div__div__same, fact_3685_surj__pair, fact_7165_cos__gt__zero, fact_4248_oddE, fact_9286_exp__def, fact_6704_of__nat__mod, fact_3079_order_Ostrict__iff__order, fact_8456_prod_Ocl__ivl__Suc, fact_9283_exp__converges, fact_673_invar__vebt_Ointros_I3_J, fact_1265_right__diff__distrib, fact_8048_fact__0, fact_7391_sum__mono, fact_201_power__one, fact_9573_sum__power2, fact_5194_nonzero__neg__divide__eq__eq2, fact_4464_minf_I2_J, fact_9635_scaleR__complex_Osimps_I1_J, fact_8177_gbinomial__0_I1_J, fact_9159_floor__add, fact_6443_real__sqrt__sum__squares__triangle__ineq, fact_3664_verit__comp__simplify1_I2_J, fact_9384_cot__less__zero, fact_7231_powr__powr, fact_1520_add__cancel__left__right, fact_5215_power__minus, fact_5130_ln__one__minus__pos__upper__bound, fact_4578_crossproduct__eq, fact_7197_cos__zero__lemma, fact_7312_lemma__tan__add1, fact_1461_maxt__corr__help__empty, fact_6246_finite__subset__induct_H, fact_4976_take__bit__diff, fact_1058_add__left__cancel, fact_49_numeral__eq__iff, fact_1101_mult_Ocommute, fact_3544_mod__eq__nat2E, fact_6345_bit__numeral__simps_I2_J, fact_6648_reals__Archimedean2, fact_4029_mod__mod__cancel, fact_6117_mask__nat__less__exp, fact_1515_add__cancel__right__left, fact_6640_of__nat__le__numeral__power__cancel__iff, fact_6363_bit__disjunctive__add__iff, fact_6622_numeral__le__real__of__nat__iff, fact_645_power__Suc2, fact_8067_fact__2, fact_9059_frac__ge__0, fact_1845_zero__neq__numeral, fact_4299_unity__coeff__ex, fact_2197_ex__least__nat__le, fact_2398_nat__diff__split, fact_6845_sin__zero__pi__iff, fact_2213_VEBT__internal_Omembermima_Ocases, fact_1571_max__nat_Oleft__neutral, fact_9337_cosh__real__ge__1, fact_3212_order__le__less__subst1, fact_2433_neg__divide__le__eq, fact_1513_add__cancel__right__right, fact_4696_add__neg__numeral__simps_I3_J, fact_5777_of__int__mult, fact_2557_odd__0__le__power__imp__0__le, fact_2515_exp__add__not__zero__imp__left, fact_166_mult__2, fact_6627_log__pow__cancel, fact_3871_pow__divides__pow__iff, fact_7157_cos__plus__cos, fact_3338_atLeastatMost__subset__iff, fact_4688_add_Oright__inverse, fact_4007_dvd__diff__commute, fact_3444_mult__mod__right, fact_9376_power2__csqrt, fact_9617_not__int__rec, fact_3893_even__plus__one__iff, fact_160_mult__2__right, fact_2872_ord__eq__less__subst, fact_7483_sum_Orelated, fact_1080_mult_Oright__neutral, fact_3457_mod__add__cong, fact_2161_divide__neg__pos, fact_4574_add__0__iff, fact_5810_of__int__le__0__iff, fact_9022_binomial__eq__0, fact_6913_norm__mult__less, fact_2806_exists__least__iff, fact_726_succ__member, fact_2269_add__nonpos__neg, fact_2403_div__eq__dividend__iff, fact_4846_add__neg__numeral__special_I9_J, fact_3967_mult__dvd__mono, fact_8187_numeral__le__floor, fact_3911_even__power, fact_4881_diff__numeral__special_I3_J, fact_459_semiring__norm_I2_J, fact_7133_Abel__lemma, fact_7892_sums__add, fact_1786_one__div__two__eq__zero, fact_9181_cos__x__cos__y, fact_3007_pos__zdiv__mult__2, fact_9195_scaleR__power, fact_964_less__max__iff__disj, fact_6831_nat__less__as__int, fact_7132_summable__power__series, fact_3214_order__le__less__subst1, fact_8933_gbinomial__Suc, fact_2740_ord__le__eq__trans, fact_9109_binomial__mono, fact_5526_abs__triangle__ineq2__sym, fact_5310_square__le__1, fact_156_left__add__twice, fact_2687_order__subst1, fact_2190_gr0__implies__Suc, fact_1376_square__diff__one__factored, fact_2886_order__less__irrefl, fact_8612_prod_Oin__pairs__0, fact_3908_even__succ__div__two, fact_7072_summable__powser__split__head, fact_5884_arctan__monotone_H, fact_5007_case__prod__eta, fact_5848_numeral__power__le__of__int__cancel__iff, fact_2123_VEBT__internal_OminNull_Oelims_I2_J, fact_8089_fact__dvd, fact_6302_log__base__10__eq1, fact_525_maxt__member, fact_1164_add__right__mono, fact_4856_minus__1__div__2__eq, fact_3998_unit__imp__dvd, fact_248_one__add__one, fact_4730_ln__one, fact_8911_sum__atLeastAtMost__code, fact_7664_sum_OatLeast__Suc__atMost, fact_8453_prod_Ocl__ivl__Suc, fact_1214_diff__eq__diff__less__eq, fact_8244_pochhammer__0__left, fact_3923_even__succ__div__exp, fact_4534_pinf_I10_J, fact_2923_order__less__imp__not__eq, fact_3878_even__add, fact_2134_less__numeral__extra_I1_J, fact_12__092_060open_062summin_A_060_A2_A_094_Am_092_060close_062, fact_999_split__option__all, fact_6078_exp__add__commuting, fact_2370_divide__diff__eq__iff, fact_9633_one__complex_Osimps_I1_J, fact_2231_mult__left__le__imp__le, fact_4060_dvd__mult__unit__iff_H, fact_4679_neg__0__less__iff__less, fact_1113_add__right__imp__eq, fact_2789_antisym__conv3, fact_6497_of__nat__0, fact_481_insert__simp__mima, fact_5245_divide__eq__eq__numeral_I2_J, fact_3181_order__less__imp__le, fact_619_lift__Suc__mono__le, fact_3566_divmod__digit__0_I1_J, fact_9138_exp__plus__inverse__exp, fact_2277_add__neg__nonpos, fact_1293_diff__eq__eq, fact_8212_pochhammer__pos, fact_7279_add__log__eq__powr, fact_7357_cos__arccos, fact_789_max_Oabsorb2, fact_5158_less__minus__one__simps_I1_J, fact_6724_not__bit__Suc__0__numeral, fact_4281_infinite__growing, fact_5585_abs__diff__less__iff, fact_1557_less__nat__zero__code, fact_382_power__add, fact_1762_nat__mult__le__cancel__disj, fact_4168_unit__div__commute, fact_6581_of__nat__Suc, fact_5868_neg__numeral__power__le__of__int__cancel__iff, fact_5920_odd__numeral__BitM, fact_2472_pos2, fact_7879_powser__sums__zero__iff, fact_8001_power__diff__sumr2, fact_8299_floor__unique, fact_4806_mult__neg__numeral__simps_I1_J, fact_8101_fact__mod, fact_8203_floor__less__neg__numeral, fact_4097_unit__div__cancel, fact_2788_antisym__conv3, fact_6446_sqrt__ge__absD, fact_5138_neg__numeral__le__zero, fact_32_newlistlength, fact_1507_zero__eq__add__iff__both__eq__0, fact_4232_odd__iff__mod__2__eq__one, fact_6016_or__minus__numerals_I2_J, fact_3905_odd__succ__div__two, fact_3469_unset__bit__less__eq, fact_7661_sum_Onat__ivl__Suc_H, fact_9148_binomial__ring, fact_2821_not__less__iff__gr__or__eq, fact_142_numeral__Bit0, fact_8587_prod__dvd__prod__subset, fact_9403_pi__def, fact_4170_unit__div__mult__swap, fact_4757_left__minus__one__mult__self, fact_5583_abs__diff__le__iff, fact_7203_ceiling__log2__div2, fact_2335_power__le__one, fact_2131_zero__less__one, fact_3890_power__less__zero__eq__numeral, fact_385_nth__equalityI, fact_7054_suminf__nonneg, fact_6452_odd__bit__iff__bit__pred, fact_9039_divide__inverse__commute, fact_8543_power__sum, fact_1079_mult_Oright__neutral, fact_6659_of__nat__less__of__int__iff, fact_3237_order__less__le__subst1, fact_3140_order_Ostrict__implies__order, fact_4585_crossproduct__noteq, fact_2321_zero__less__two, fact_667_size__neq__size__imp__neq, fact_4875_even__take__bit__eq, fact_4078_div__div__eq__right, fact_7379_norm__sum, fact_192_deg__deg__n, fact_2067_mult__strict__right__mono, fact_5267_take__bit__nat__eq__self__iff, fact_2956_subset__trans, fact_2834_dual__order_Ostrict__implies__not__eq, fact_5427_semiring__norm_I70_J, fact_6553_of__nat__1, fact_5205_mult__1s__ring__1_I2_J, fact_1137_group__cancel_Oadd2, fact_3952_dvd__mult2, fact_8084_fact__fact__dvd__fact, fact_490_semiring__norm_I75_J, fact_6589_of__nat__0__less__iff, fact_5530_abs__triangle__ineq2, fact_8763_fact__prod, fact_8549_prod__le__1, fact_8992_inverse__less__iff__less__neg, fact_6851_not__zle__0__negative, fact_185_set__n__deg__not__0, fact_7890_sums__add, fact_3629_length__product, fact_5688_le__numeral__Suc, fact_5608_numeral__code_I3_J, fact_6256_subset__insert__iff, fact_3580_mult__less__iff1, fact_6754_of__nat__less__two__power, fact_150_numeral__Bit0__div__2, fact_6050_and_Oassoc, fact_163_mult__2, fact_5211_uminus__numeral__One, fact_3906_odd__succ__div__two, fact_3594_product__nth, fact_7410_sum_Odistrib, fact_908_max_Oabsorb__iff2, fact_4079_div__div__eq__right, fact_9173_choose__alternating__sum, fact_3583_flip__bit__Suc, fact_3931_dvdE, fact_5911_dbl__inc__def, fact_5036_not__numeral__less__neg__numeral, fact_1475_le__zero__eq, fact_6844_sin__eq__0__pi, fact_5314_minus__power__mult__self, fact_7286_tan__monotone, fact_7087_cos__one__sin__zero, fact_5169_neg__numeral__le__neg__one, fact_5841_of__int__power__le__of__int__cancel__iff, fact_4535_pinf_I10_J, fact_4795_semiring__norm_I170_J, fact_4677_neg__0__less__iff__less, fact_6591_of__nat__0__less__iff, fact_8892_pochhammer__prod__rev, fact_6769_log2__of__power__eq, fact_7938_sums__zero__iff__shift, fact_2347_add__num__frac, fact_9448_nat__mult__distrib, fact_7234_powr__ge__pzero, fact_4044_not__is__unit__0, fact_1471_both__member__options__def, fact_3855_div__diff, fact_6511_of__nat__eq__0__iff, fact_471_both__member__options__equiv__member, fact_4879_diff__numeral__special_I4_J, fact_4131_dbl__def, fact_7923_sum__eq__Suc0__iff, fact_5141_not__zero__le__neg__numeral, fact_2879_ord__less__eq__subst, fact_3528_div__mult1__eq, fact_5952_or_Oright__neutral, fact_6314_real__sqrt__eq__1__iff, fact_568_nat__mult__max__right, fact_6011_or__numerals_I1_J, fact_3599_set__vebt__finite, fact_6111_and__one__eq, fact_5944_or_Oidem, fact_9800_sqr_Osimps_I3_J, fact_3582_div__mod__decomp, fact_5086_numeral__neq__neg__one, fact_4160_unit__eq__div2, fact_6800_sin__periodic__pi, fact_237_power__add__numeral, fact_4325_of__bool__eq_I2_J, fact_6505_of__nat__0__eq__iff, fact_7808_double__gauss__sum, fact_2129_zero__less__one, fact_199_power__one, fact_1574_max__0L, fact_9289_sin__minus__converges, fact_2652_ord__le__eq__subst, fact_9044_field__class_Ofield__divide__inverse, fact_824_diff__less__mono2, fact_5894_eval__nat__numeral_I2_J, fact_5110_take__bit__unset__bit__eq, fact_2264_add__pos__nonneg, fact_5249_add__divide__eq__if__simps_I3_J, fact_4937_minus__less__iff, fact_4764_minus__one__mult__self, fact_1220_diff__eq__diff__less, fact_1218_diff__strict__left__mono, fact_3844_div__add, fact_6317_real__sqrt__ge__0__iff, fact_6874_sin__pi__divide__n__gt__0, fact_5304_take__bit__nat__less__self__iff, fact_9100_ln__inverse, fact_6183_Suc__0__and__eq, fact_7888_sums__mult, fact_6916_norm__mult__ineq, fact_899_max_OcoboundedI2, fact_8541_prod_Oshift__bounds__cl__Suc__ivl, fact_5713_signed__take__bit__numeral__bit0, fact_3466_mod__Suc__Suc__eq, fact_421_all__set__conv__all__nth, fact_5864_of__int__le__neg__numeral__power__cancel__iff, fact_5581_abs__triangle__ineq4, fact_852_le__diff__conv, fact_4231_odd__iff__mod__2__eq__one, fact_2463_power__decreasing, fact_8840_sum__up__index__split, fact_1787_power2__eq__iff__nonneg, fact_3430_one__mod__two__eq__one, fact_5811_of__int__le__0__iff, fact_5703_add__neg__numeral__special_I6_J, fact_2902_order__less__subst2, fact_2844_order__less__asym, fact_2493_VEBT__internal_Omembermima_Oelims_I1_J, fact_365_power__mult__distrib, fact_7106_cos__ge__minus__one, fact_9698_complex__mod__mult__cnj, fact_7008_sin__cos__squared__add2, fact_1038_add__diff__cancel, fact_2930_order__less__imp__not__eq2, fact_9050_binomial__symmetric, fact_8891_pochhammer__prod__rev, fact_5624_power3__eq__cube, fact_5035_zero__neq__neg__numeral, fact_7309_tan__add, fact_8041_diffs__equiv, fact_8989_inverse__nonpositive__iff__nonpositive, fact_3694_verit__comp__simplify1_I3_J, fact_9807_image__Suc__lessThan, fact_3171_linorder__not__le, fact_4084_dvd__mult__imp__div, fact_9287_summable__norm__exp, fact_2232_mult__left__le__imp__le, fact_4219_dvd__power, fact_8903_prod_Oin__pairs, fact_4511_minf_I8_J, fact_4456_pinf_I7_J, fact_9112_binomial__le__pow2, fact_7116_of__int__ceiling__le__add__one, fact_505_two__realpow__ge__one, fact_9243_scaleR__nonneg__nonpos, fact_5658_power__mono__even, fact_2173_divide__eq__imp, fact_6292_Suc__0__or__eq, fact_5461_div__Suc__eq__div__add3, fact_1048_add__diff__cancel__left_H, fact_4568_subset__decode__imp__le, fact_5012_case__prodE2, fact_4966_group__cancel_Oneg1, fact_6075_AND__upper1_H, fact_6920_norm__add__less, fact_7750_member__le__sum, fact_3099_order_Ostrict__iff__not, fact_3888_power__less__zero__eq, fact_5783_of__int__power__eq__of__int__cancel__iff, fact_6543_of__nat__eq__1__iff, fact_2680_order__subst2, fact_4441_pinf_I3_J, fact_7994_lemma__termdiff1, fact_1939_VEBT__internal_Omembermima_Osimps_I3_J, fact_1891_VEBT__internal_Omembermima_Osimps_I2_J, fact_2360_power__le__imp__le__base, fact_1999_zero__le__square, fact_8524_prod_OatMost__shift, fact_5637_power__even__abs, fact_1167_less__eqE, fact_8185_zero__le__floor, fact_2002_mult__mono_H, fact_7998_diff__power__eq__sum, fact_9597_int__numeral__or__not__num__neg, fact_1272_diff__diff__eq, fact_3158_order__le__less, fact_462__092_060open_062vebt__member_A_ItreeList_A_B_Asummin_J_Alx_092_060close_062, fact_2244_mult__right__less__imp__less, fact_10072_VEBT__internal_Ovalid_H_Opelims_I2_J, fact_3560_bits__stable__imp__add__self, fact_5704_add__neg__numeral__special_I6_J, fact_9449_Suc__as__int, fact_3498_cong__exp__iff__simps_I2_J, fact_2816_order_Ostrict__trans, fact_4981_div__minus__right, fact_4860_bits__minus__1__mod__2__eq, fact_6313_real__sqrt__one, fact_8952_gbinomial__partial__sum__poly__xpos, fact_1150_ab__semigroup__add__class_Oadd__ac_I1_J, fact_4671_neg__less__eq__nonneg, fact_838_diff__add__inverse, fact_230_power__mult__numeral, fact_3398_unset__bit__negative__int__iff, fact_2769_order_Oasym, fact_5479_take__bit__minus, fact_9222_complex__scaleR, fact_1807_vebt__delete_Osimps_I2_J, fact_2348_add__num__frac, fact_3519_mod__div__decomp, fact_9659_times__complex_Osimps_I1_J, fact_2318_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq, fact_7270_powr__mult__base, fact_4983_minus__divide__left, fact_7823_arith__series, fact_2773_order_Oasym, fact_7103_cos__inj__pi, fact_9327_sinh__add, fact_2654_ord__le__eq__subst, fact_1804_VEBT__internal_OminNull_Osimps_I3_J, fact_6174_or__nat__numerals_I3_J, fact_2091_mult__pos__neg2, fact_3508_mult__div__mod__eq, fact_2125_not__one__less__zero, fact_8076_fact__gt__zero, fact_7232_powr__non__neg, fact_288_one__le__power, fact_6915_norm__mult__ineq, fact_4127_dvd__minus__self, fact_5145_not__zero__less__neg__numeral, fact_7354_of__real__neg__numeral, fact_1883_comm__monoid__add__class_Oadd__0, fact_4413_split__of__bool__asm, fact_5018_ln__less__self, fact_10143_upt__eq__Cons__conv, fact_9213_scaleR__right__distrib, fact_1929_power__eq__imp__eq__base, fact_2670_order__eq__refl, fact_2569_VEBT__internal_OminNull_Osimps_I5_J, fact_4828_eq__divide__eq__numeral1_I2_J, fact_2272_add__nonneg__pos, fact_81_numeral__less__iff, fact_164_mult__2, fact_4033_dvd__pos__nat, fact_2052_linordered__nonzero__semiring__class_Ozero__le__one, fact_7916_lessThan__Suc, fact_9591_even__not__iff__int, fact_4791_diff__numeral__simps_I3_J, fact_6395_bit__of__bool__iff, fact_8081_fact__ge__1, fact_7255_log__powr, fact_4567_signed__take__bit__diff, fact_4751_numeral__eq__neg__one__iff, fact_6887_norm__mult__numeral1, fact_3000_not__exp__less__eq__0__int, fact_4429_pinf_I1_J, fact_6763_real__of__nat__div3, fact_4377_bits__1__div__exp, fact_6044_or_Oleft__commute, fact_144_numeral__Bit0, fact_2735_order__antisym, fact_3853_unit__div__1__div__1, fact_3235_order__less__le__subst1, fact_4947_numeral__neq__neg__numeral, fact_2738_ord__le__eq__trans, fact_4263_list__decode_Ocases, fact_6519_of__nat__less__iff, fact_9494_real__root__pow__pos2, fact_4858_minus__1__mod__2__eq, fact_2869_ord__eq__less__subst, fact_9560_xor__nat__def, fact_3175_linorder__not__less, fact_2020_add__nonneg__eq__0__iff, fact_8956_polyfun__extremal__lemma, fact_2582_max__bot, fact_9502_real__root__pos__pos__le, fact_9545_xor__nat__rec, fact_3991_dvd__add__right__iff, fact_364_power__mult__distrib, fact_7254_ln__powr, fact_8287_pochhammer__eq__0__iff, fact_3051_antisym__conv2, fact_251_power__increasing__iff, fact_2912_order__less__not__sym, fact_6066_exp__gt__zero, fact_3805_nat__mult__dvd__cancel__disj, fact_6700_of__nat__dvd__iff, fact_1056_add__right__cancel, fact_6774_m2pi__less__pi, fact_2681_order__subst2, fact_5207_mult__1s__ring__1_I2_J, fact_5683_pred__numeral__inc, fact_4675_neg__less__0__iff__less, fact_5650_abs__square__le__1, fact_6306_real__sqrt__eq__iff, fact_7195_sin__expansion__lemma, fact_4314_of__bool__less__eq__iff, fact_3842_dvd__mult__div__cancel, fact_5573_abs__of__neg, fact_6717_of__nat__and__eq, fact_5771_of__int__1, fact_2668_linorder__linear, fact_7119_powser__inside, fact_2033_add__increasing2, fact_2194_option_Osize_I4_J, fact_7792_arccos__minus__abs, fact_1808_vebt__member_Osimps_I1_J, fact_2451_power__Suc__less__one, fact_848_less__diff__iff, fact_814_diff__Suc__diff__eq2, fact_4319_of__bool__less__iff, fact_3295_max__absorb2, fact_4120_le__imp__power__dvd, fact_3569_mod__double__modulus, fact_3913_odd__two__times__div__two__nat, fact_50_numeral__eq__iff, fact_6490_of__nat__eq__iff, fact_4439_pinf_I3_J, fact_4560_add__scale__eq__noteq, fact_384_nth__equalityI, fact_1910_infinite__descent0, fact_135_mult__numeral__1__right, fact_9203_scaleR__times, fact_8055_fact__Suc__0, fact_8184_pochhammer__0, fact_5861_neg__numeral__power__eq__of__int__cancel__iff, fact_10123_length__upt, fact_469_semiring__norm_I68_J, fact_3714_finite__Collect__less__nat, fact_3525_cancel__div__mod__rules_I2_J, fact_129_div__times__less__eq__dividend, fact_6770_pi__half__gt__zero, fact_5731_even__add__abs__iff, fact_7876_sum_OlessThan__Suc, fact_8091_fact__dvd, fact_1276_add__implies__diff, fact_6207_subset__singleton__iff, fact_9716_subset__card__intvl__is__intvl, fact_5107_ab__group__add__class_Oab__diff__conv__add__uminus, fact_8339_gbinomial__reduce__nat, fact_2543_sum__power2__ge__zero, fact_6567_of__nat__power__eq__of__nat__cancel__iff, fact_6685_less__imp__of__nat__less, fact_1177_add__mono__thms__linordered__semiring_I2_J, fact_4651_mod__minus__minus, fact_2040_add__increasing, fact_2061_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_5441_semiring__norm_I5_J, fact_6294_or__nat__rec, fact_6609_of__nat__power__less__of__nat__cancel__iff, fact_7237_powr__less__cancel, fact_5960_exp__le__cancel__iff, fact_1414_lambda__one, fact_3813_dvd__mult__cancel__left, fact_7148_cos__monotone__minus__pi__0, fact_6189_or__minus__numerals_I5_J, fact_6816_abs__sin__x__le__abs__x, fact_9610_and__not__numerals_I9_J, fact_7263_powr__realpow, fact_1373_less__add__iff2, fact_9313_cosh__0, fact_6670_of__nat__less__0__iff, fact_4573_signed__take__bit__int__less__self__iff, fact_1105_mult_Oassoc, fact_1128_add_Oright__cancel, fact_458_semiring__norm_I76_J, fact_6533_of__nat__mult, fact_4199_is__unit__div__mult__cancel__right, fact_4645_add__minus__cancel, fact_6535_of__nat__mult, fact_5563_eq__abs__iff_H, fact_9133_binomial__addition__formula, fact_2372_diff__divide__eq__iff, fact_2063_mult__less__cancel__right__disj, fact_7101_less__ceiling__iff, fact_526__C8_C, fact_168__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062, fact_773_max_Oidem, fact_1872_mult__not__zero, fact_5164_neg__numeral__le__one, fact_1925_diffs0__imp__equal, fact_4193_is__unitE, fact_7130_suminf__exist__split, fact_3204_order__le__less__trans, fact_7941_sum_Onat__diff__reindex, fact_9206_inverse__scaleR__times, fact_5991_or__numerals_I8_J, fact_7208_complex__unimodular__polar, fact_7355_cos__of__real__pi, fact_8240_pochhammer__nonneg, fact_4936_minus__less__iff, fact_5247_minus__divide__add__eq__iff, fact_4045_not__is__unit__0, fact_3257_order__le__imp__less__or__eq, fact_4824_not__neg__one__le__neg__numeral__iff, fact_7111_cos__diff, fact_5926_floor__exists1, fact_5332_take__bit__Suc, fact_3899_zero__less__power__eq__numeral, fact_4184_mod__greater__zero__iff__not__dvd, fact_4955_minus__mult__commute, fact_9065_le__imp__inverse__le__neg, fact_607_lift__Suc__mono__less__iff, fact_5502_verit__eq__simplify_I12_J, fact_4449_pinf_I5_J, fact_3898_even__diff__nat, fact_622_dec__induct, fact_6950_norm__triangle__ineq3, fact_2297_sum__squares__le__zero__iff, fact_1249_mult_Ocomm__neutral, fact_586_transitive__stepwise__le, fact_3255_linorder__le__less__linear, fact_7046_suminf__add, fact_5434_divide__le__0__abs__iff, fact_9486_real__root__gt__0__iff, fact_1736_less__divide__eq__1__neg, fact_1326_add__mono1, fact_9413_nat__numeral, fact_26__C112_C, fact_9720_card__sum__le__nat__sum, fact_6651_mult__of__nat__commute, fact_1394_succ__less__length__list, fact_6347_bit__numeral__simps_I3_J, fact_1545_bits__div__by__0, fact_8927_gbinomial__sum__lower__neg, fact_293_left__right__inverse__power, fact_2531_power__minus__mult, fact_5770_of__int__less__iff, fact_6807_sin__two__pi, fact_6929_norm__triangle__mono, fact_9526_sgn__power__injE, fact_8641_less__1__prod2, fact_4662_neg__0__le__iff__le, fact_4459_minf_I1_J, fact_4338_of__bool__or__iff, fact_5306_take__bit__int__greater__eq__self__iff, fact_7221_log__powr__cancel, fact_6690_of__nat__less__imp__less, fact_6449_even__bit__succ__iff, fact_7794_cos__sin__eq, fact_7921_sum__subtractf__nat, fact_9252_real__vector__eq__affinity, fact_1335_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, fact_9012_inverse__eq__divide__neg__numeral, fact_4760_left__minus__one__mult__self, fact_2103_not__square__less__zero, fact_2110_pos__add__strict, fact_5065_le__minus__one__simps_I2_J, fact_4098_unit__div__cancel, fact_9032_nonzero__inverse__mult__distrib, fact_2424_mult__le__cancel__left1, fact_1852_mult__right__cancel, fact_6811_sin__2pi__minus, fact_2649_ord__le__eq__subst, fact_6755_inverse__of__nat__le, fact_1047_add__diff__cancel__left, fact_9320_cosh__plus__sinh, fact_3223_order__le__less__subst2, fact_8910_sum__atLeastAtMost__code, fact_6674_of__nat__neq__0, fact_3538_minus__mod__eq__div__mult, fact_106_distrib__right__numeral, fact_1945_VEBT__internal_OminNull_Ocases, fact_5129_take__bit__Suc__minus__bit0, fact_3471_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend, fact_4586_signed__take__bit__int__less__eq, fact_3236_order__less__le__subst1, fact_3138_dual__order_Ostrict__iff__not, fact_4853_diff__numeral__special_I11_J, fact_1670_divide__self, fact_5600_cong__exp__iff__simps_I12_J, fact_3921_semiring__parity__class_Oeven__mask__iff, fact_6338_signed__take__bit__negative__iff, fact_8940_sum_Ozero__middle, fact_5517_abs__not__less__zero, fact_6095_mask__Suc__double, fact_1955_zero__le__numeral, fact_643_power__Suc, fact_4091_div__plus__div__distrib__dvd__left, fact_6297_of__int__round__le, fact_5781_of__int__add, fact_4592_signed__take__bit__rec, fact_4754_neg__one__eq__numeral__iff, fact_5476_signed__take__bit__Suc__bit1, fact_4265_zero__less__power__eq, fact_9546_Cauchy__iff2, fact_9085_sum__choose__upper, fact_1503_add__0, fact_2011_not__numeral__less__zero, fact_344_one__power2, fact_4122_le__imp__power__dvd, fact_5630_mod__exhaust__less__4, fact_7891_sums__add, fact_4753_neg__one__eq__numeral__iff, fact_6562_of__nat__eq__of__nat__power__cancel__iff, fact_522_power__shift, fact_1923_nat__mult__eq__cancel__disj, fact_2107_pos__add__strict, fact_8225_floor__less__iff, fact_3848_unit__div, fact_6638_numeral__power__le__of__nat__cancel__iff, fact_1451_discrete, fact_5544_abs__less__iff, fact_7983_geometric__sum, fact_10176_take__bit__concat__bit__eq, fact_2754_le__cases3, fact_4460_minf_I1_J, fact_3558_bits__stable__imp__add__self, fact_4530_pinf_I9_J, fact_8259_real__of__int__floor__add__one__gt, fact_5804_dbl__inc__simps_I5_J, fact_7558_sum__pos, fact_2571_VEBT__internal_OminNull_Osimps_I4_J, fact_4904_signed__take__bit__0, fact_2553_vebt__member_Oelims_I2_J, fact_10195_card__le__Suc__Max, fact_1488_mult__eq__0__iff, fact_4676_neg__less__0__iff__less, fact_2642_order__antisym__conv, fact_5081_less__minus__one__simps_I2_J, fact_4222_dvd__minus__add, fact_1906_Suc__neq__Zero, fact_762_option_Oinject, fact_7207_cos__tan, fact_3577_divmod__digit__1_I1_J, fact_9047_power__mult__power__inverse__commute, fact_8110_fact__numeral, fact_1835_gr__implies__not__zero, fact_27__092_060open_062high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_060_Alength_AtreeList_092_060close_062, fact_9550_xor__nonnegative__int__iff, fact_3203_order__le__less__trans, fact_5822_of__int__less__numeral__iff, fact_1095_mult_Oleft__commute, fact_8392_prod_Oinfinite, fact_2010_not__numeral__less__zero, fact_6104_even__and__iff__int, fact_2014_zero__less__numeral, fact_1998_zero__le__square, fact_5568_zero__le__power__abs, fact_9382_Arg__bounded, fact_10196_divide__nat__def, fact_1282_diff__add__eq, fact_5561_eq__abs__iff_H, fact_7801_double__arith__series, fact_6549_of__nat__1__eq__iff, fact_5543_abs__ge__minus__self, fact_2219_VEBT__internal_OminNull_Oelims_I1_J, fact_518_enat__ord__number_I2_J, fact_8835_polyfun__eq__0, fact_6597_numeral__power__eq__of__nat__cancel__iff, fact_4114_power__le__dvd, fact_8936_sum_Ozero__middle, fact_5297_ln__one__minus__pos__lower__bound, fact_2130_zero__less__one, fact_4629_minus__mult__minus, fact_381_power__add, fact_6710_of__nat__max, fact_7932_sums__Suc, fact_8982_inverse__eq__1__iff, fact_6415_signed__take__bit__eq__concat__bit, fact_6116_Suc__mask__eq__exp, fact_2016_add__nonpos__eq__0__iff, fact_3944_dvd__mult, fact_3992_dvd__add__right__iff, fact_2286_divide__nonpos__pos, fact_6392_real__sqrt__ge__one, fact_6855_neg__int__cases, fact_1815_power__0__left, fact_5736_dbl__dec__def, fact_486_semiring__norm_I12_J, fact_3116_dual__order_Ostrict__iff__order, fact_6136_mask__int__def, fact_8173_gbinomial__0_I2_J, fact_6290_round__diff__minimal, fact_9296_exp__first__term, fact_3495_unique__euclidean__semiring__numeral__class_Omod__less, fact_9569_xor__int__rec, fact_2115_add__pos__pos, fact_6592_numeral__power__eq__of__nat__cancel__iff, fact_6911_power__eq__imp__eq__norm, fact_4905_signed__take__bit__0, fact_794_max_Oabsorb1, fact_1805_VEBT__internal_OminNull_Osimps_I2_J, fact_7_high__inv, fact_9549_concat__bit__of__zero__1, fact_3036_nless__le, fact_2762_gt__ex, fact_9129_binomial__less__binomial__Suc, fact_3865_unit__mult__div__div, fact_3375_double__eq__0__iff, fact_2060_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_2143_zero__le__divide__iff, fact_6795_lemma__termdiff3, fact_5598_cong__exp__iff__simps_I13_J, fact_4943_verit__negate__coefficient_I2_J, fact_5948_zero__and__eq, fact_5137_take__bit__signed__take__bit, fact_2730_order_Otrans, fact_3216_order__le__less__subst1, fact_2112_canonically__ordered__monoid__add__class_OlessE, fact_123_div__le__dividend, fact_5246_divide__eq__eq__numeral_I2_J, fact_10113_inj__on__char__of__nat, fact_6376_bit__or__iff, fact_4021_dvd__power__same, fact_6354_bit__minus__numeral__int_I1_J, fact_3006_neg__zdiv__mult__2, fact_5131_pow_Osimps_I1_J, fact_4612_neg__le__iff__le, fact_6469_arsinh__real__aux, fact_2676_order__subst2, fact_3713_finite__Collect__le__nat, fact_6577_of__nat__le__0__iff, fact_9431_nat__mask__eq, fact_2074_mult__strict__left__mono, fact_5031_neg__numeral__le__numeral, fact_8751_sum_OatMost__Suc__shift, fact_6712_take__bit__of__nat, fact_1381_times__divide__eq__right, fact_387_nth__equalityI, fact_737_option_Ocollapse, fact_3549_unset__bit__Suc, fact_9473_arctan__inverse, fact_9347_sinh__square__eq, fact_1575_max__0R, fact_7026_summable__Suc__iff, fact_3622_length__product, fact_4133_dbl__def, fact_1817_zero__power, fact_4870_power__minus__odd, fact_6348_bit__numeral__simps_I3_J, fact_1735_less__divide__eq__1__pos, fact_779_Suc__diff__diff, fact_6227_finite__ranking__induct, fact_4946_numeral__neq__neg__numeral, fact_3696_verit__comp__simplify1_I3_J, fact_105_distrib__right__numeral, fact_3452_mod__add__right__eq, fact_5755_dbl__inc__simps_I1_J, fact_6425_bit__iff__idd__imp__stable, fact_4116_power__le__dvd, fact_1718_mult__less__cancel2, fact_2070_mult__less__cancel__left__disj, fact_5170_neg__numeral__le__neg__one, fact_3226_order__le__less__subst2, fact_2362_power__le__imp__le__base, fact_1867_divisors__zero, fact_8990_inverse__positive__iff__positive, fact_5301_take__bit__eq__0__iff, fact_9317_tanh__def, fact_358_power__commutes, fact_1281_diff__add__eq, fact_6761_pi__half__le__two, fact_7982_geometric__sum, fact_138_mult__numeral__1, fact_9250_real__vector__affinity__eq, fact_2532_power__minus__mult, fact_4381_one__mod__2__pow__eq, fact_7323_of__real__1, fact_1328_add__mono1, fact_5290_uminus__power__if, fact_7089_sin__add, fact_6321_real__sqrt__ge__1__iff, fact_4058_mult__unit__dvd__iff, fact_4374_of__bool__half__eq__0, fact_4884_diff__numeral__special_I3_J, fact_6590_of__nat__0__less__iff, fact_319_one__le__numeral, fact_8095_choose__dvd, fact_2560_VEBT__internal_Oexp__split__high__low_I1_J, fact_8838_sum_OatMost__shift, fact_8877_pochhammer__Suc__prod, fact_2995_double__diff, fact_6534_of__nat__mult, fact_2781_ord__less__eq__trans, fact_3808_dbl__simps_I2_J, fact_6377_bit__and__int__iff, fact_1341_add__le__add__imp__diff__le, fact_2813_order_Ostrict__trans, fact_8117_square__fact__le__2__fact, fact_7185_cos__double, fact_437_list__update__same__conv, fact_5735_dbl__dec__def, fact_9342_cosh__real__strict__mono, fact_8965_fact__code, fact_8003_geometric__sums, fact_6583_of__nat__Suc, fact_6529_of__nat__add, fact_4297_inf__period_I3_J, fact_4518_inf__period_I1_J, fact_9639_cmod__plus__Re__le__0__iff, fact_2003_mult__mono_H, fact_3793_dvd__add__triv__left__iff, fact_9319_cosh__plus__sinh, fact_280_le__numeral__extra_I4_J, fact_5818_of__int__numeral__le__iff, fact_7556_arcsin__minus, fact_712_invar__vebt_Ointros_I2_J, fact_3982_dvd__add, fact_4577_add__0__iff, fact_2997_Diff__subset, fact_5887_take__bit__of__int, fact_6334_log__less__one__cancel__iff, fact_3329_VEBT__internal_Omembermima_Opelims_I2_J, fact_517_enat__ord__number_I1_J, fact_126_is__num__normalize_I1_J, fact_1108_ab__semigroup__mult__class_Omult__ac_I1_J, fact_4514_exp__mod__exp, fact_1876_add_Ocomm__neutral, fact_4111_dvd__power__le, fact_1209_diff__mono, fact_9584_not__int__def, fact_8480_prod_OatMost__Suc__shift, fact_7712_cos__arccos__abs, fact_3970_dvd__mult__right, fact_5660_eq__diff__eq_H, fact_3447_mod__mult__mult2, fact_3809_dbl__simps_I2_J, fact_1161_add__le__imp__le__left, fact_1700_max__0__1_I3_J, fact_7200_sincos__total__pi__half, fact_258_one__plus__numeral, fact_4841_take__bit__of__1, fact_1072_add__less__cancel__left, fact_5260_power2__eq__iff, fact_6417_exp__eq__0__imp__not__bit, fact_4502_pinf_I8_J, fact_6955_suminf__geometric, fact_8866_prod__diff1, fact_7954_suminf__le__const, fact_191_inrg, fact_5702_add__neg__numeral__special_I6_J, fact_325_not__numeral__less__one, fact_2799_dual__order_Oasym, fact_1655_diff__add__zero, fact_870_nat__le__add__iff1, fact_277_add__One__commute, fact_8215_pochhammer__eq__0__mono, fact_1750_div__mult__self1, fact_8778_prod__mono__strict, fact_218_numeral__eq__one__iff, fact_6061_bit_Ocomplement__unique, fact_4031_mod__mod__cancel, fact_5990_or__numerals_I8_J, fact_3926_dvd__productE, fact_4603_power__numeral, fact_2047_add__decreasing, fact_3661_verit__la__disequality, fact_1039_add__diff__cancel, fact_970_max_Ostrict__boundedE, fact_9609_and__not__numerals_I6_J, fact_2797_dual__order_Oasym, fact_2015_zero__less__numeral, fact_3087_order_Ostrict__trans1, fact_2329_pos__divide__less__eq, fact_4371_odd__of__bool__self, fact_9143_choose__two, fact_1996_split__mult__pos__le, fact_71__C5_OIH_C_I2_J, fact_3555_Suc__times__mod__eq, fact_4512_minf_I8_J, fact_5762_of__int__numeral, fact_8900_summable__Cauchy__product, fact_5942_or_Oleft__idem, fact_1761_one__le__mult__iff, fact_3443_mod__mult__left__eq, fact_391_Skolem__list__nth, fact_2435_le__divide__eq, fact_9045_choose__mult__lemma, fact_6506_of__nat__0__eq__iff, fact_8906_prod_Oin__pairs, fact_6426_bit__iff__idd__imp__stable, fact_6819_int__cases, fact_5071_zero__neq__neg__one, fact_2766_less__imp__neq, fact_111_distrib__left__numeral, fact_7717_sum_Oub__add__nat, fact_3635_finite__nat__set__iff__bounded__le, fact_442_power4__eq__xxxx, fact_648_Suc__div__le__mono, fact_6956_suminf__geometric, fact_7205_tan__double, fact_6981_numeral__less__ceiling, fact_4508_minf_I8_J, fact_5698_add__neg__numeral__special_I5_J, fact_5681_Suc__eq__numeral, fact_3588_product__nth, fact_495_member__inv, fact_3601_succ__none__empty, fact_9038_inverse__unique, fact_5983_or__negative__int__iff, fact_8504_prod__pos, fact_2035_add__increasing2, fact_6714_take__bit__of__nat, fact_1455_vebt__member_Osimps_I5_J, fact_5936_and_Oleft__idem, fact_6072_AND__lower, fact_4895_neg__one__even__power, fact_5956_exp__less__mono, fact_9167_choose__alternating__linear__sum, fact_6934_norm__triangle__le__diff, fact_2216_vebt__succ_Ocases, fact_472_valid__member__both__member__options, fact_5111_take__bit__unset__bit__eq, fact_891_diff__le__diff__pow, fact_4200_is__unit__div__mult__cancel__right, fact_5959_take__bit__and, fact_5946_bit_Oconj__zero__right, fact_7818_arcsin__ubound, fact_3309_max__def, fact_6465_bit__sum__mult__2__cases, fact_9330_cosh__diff, fact_8540_prod_Oshift__bounds__cl__Suc__ivl, help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T, fact_9756_VEBT__internal_OminNull_Opelims_I1_J, fact_1946_vebt__mint_Osimps_I1_J, fact_5705_diff__numeral__special_I5_J, fact_5570_abs__if__raw, fact_580_less__antisym, fact_2826_dual__order_Ostrict__trans, fact_203_power__one__right, fact_3482_div__add1__eq, fact_655_less__not__refl3, fact_219_numeral__eq__one__iff, fact_9304_exp__two__pi__i_H, fact_9166_choose__alternating__linear__sum, fact_8729_prod_OatLeast0__atMost__Suc, fact_9268_cos__converges, fact_5922_real__of__int__div3, fact_1880_add_Ocomm__neutral, fact_3024_leD, fact_4987_minus__divide__right, fact_7217_powr__one, fact_6541_of__nat__eq__1__iff, fact_7144_le__ceiling__iff, fact_6422_stable__imp__bit__iff__odd, fact_3930_dvdE, fact_1638_div__mult__mult1__if, fact_9563_concat__bit__def, fact_1768_divide__le__eq__1__pos, fact_6371_real__sqrt__power, fact_5831_of__int__1__less__iff, fact_9103_summable__exp, fact_9151_pochhammer__binomial__sum, fact_4835_less__divide__eq__numeral1_I2_J, fact_2__C5_Ohyps_C_I8_J, fact_1311_add__less__le__mono, fact_2643_linorder__le__cases, fact_1024_le__add__diff__inverse, fact_9442_real__nat__ceiling__ge, fact_6508_of__nat__eq__0__iff, fact_6200_subset__insert, fact_7127_powser__split__head_I1_J, fact_7226_tan__periodic__int, fact_7451_Complex__mult__complex__of__real, fact_9202_norm__scaleR, fact_4223_power__dvd__imp__le, fact_1954_not__numeral__le__zero, fact_4451_pinf_I5_J, fact_6606_of__nat__less__of__nat__power__cancel__iff, fact_5075_numeral__times__minus__swap, fact_1304_max__add__distrib__left, fact_7022_summable__add, fact_6004_and__numerals_I5_J, fact_6018_and__numerals_I4_J, fact_8410_prod_Odelta_H, fact_2330_neg__less__divide__eq, fact_8077_fact__gt__zero, fact_2749_order__class_Oorder__eq__iff, fact_634_Suc__mult__less__cancel1, fact_10139_atMost__upto, fact_2671_order__eq__refl, fact_2677_order__subst2, fact_6608_of__nat__power__less__of__nat__cancel__iff, fact_5532_abs__leI, fact_6605_of__nat__less__of__nat__power__cancel__iff, fact_6397_bit__of__bool__iff, fact_292_left__right__inverse__power, fact_7342_sum_Oinsert, fact_130_div__mult2__eq, fact_4094_div__plus__div__distrib__dvd__right, fact_8297_floor__split, fact_5432_tanh__real__nonpos__iff, fact_6579_of__nat__le__0__iff, fact_9744_prod__decode__aux_Oelims, fact_4350_of__bool__not__iff, fact_4437_pinf_I3_J, fact_4215_dvd__power, fact_4692_ab__left__minus, fact_1544_bits__div__by__0, fact_1898_old_Onat_Odistinct_I2_J, fact_1740_div__mult__self4, fact_7062_ceiling__mono, fact_5764_of__int__eq__numeral__iff, fact_2820_not__less__iff__gr__or__eq, fact_7284_tan__gt__zero, fact_4634_mult__minus__left, fact_8320_gbinomial__rec, fact_5880_of__int__max, fact_7335_of__real__add, fact_1599_less__add__same__cancel1, fact_707_mult__le__mono2, fact_1956_zero__le__numeral, fact_104_distrib__right__numeral, fact_1894_power__not__zero, fact_2567_vebt__delete_Oelims, fact_2009_not__numeral__less__zero, fact_9520_real__root__pow__pos, fact_9154_pochhammer__binomial__sum, fact_2399_div__greater__zero__iff, fact_225_one__eq__numeral__iff, fact_6757_exp__divide__power__eq, fact_4837_power2__minus, fact_3108_dual__order_Oorder__iff__strict, fact_3939_dvd__def, fact_9226_scaleR__le__cancel__left__neg, fact_9097_forall__pos__mono, fact_6384_bit__numeral__simps_I1_J, fact_6857_monoseq__realpow, fact_3539_minus__div__mult__eq__mod, fact_8331_pochhammer__same, fact_6514_of__nat__numeral, fact_2188_gr0__conv__Suc, fact_4012_dvd__div__eq__iff, fact_1382_times__divide__eq__right, fact_1486_mult__eq__0__iff, fact_5986_and__numerals_I8_J, fact_3131_dual__order_Ostrict__trans2, fact_7758_convex__sum__bound__le, fact_5397_abs__1, fact_9805_image__Suc__atLeastLessThan, fact_1613_sum__squares__eq__zero__iff, fact_4604_power__numeral, fact_3137_dual__order_Ostrict__iff__not, fact_5201_mult__1s__ring__1_I1_J, fact_3541_minus__div__mult__eq__mod, fact_5684_less__numeral__Suc, fact_5102_diff__conv__add__uminus, fact_1120_add_Oleft__commute, fact_3018_Collect__subset, fact_5664_odd__mod__4__div__2, fact_5000_concat__bit__take__bit__eq, fact_9162_tan__sec, fact_2644_linorder__le__cases, fact_7972_summableI__nonneg__bounded, fact_5309_square__le__1, fact_352_Ex__list__of__length, fact_4525_vebt__buildup_Osimps_I3_J, fact_2558_odd__power__less__zero, fact_6701_pi__gt__zero, fact_4830_divide__eq__eq__numeral1_I2_J, fact_9522_odd__real__root__unique, fact_1378_square__diff__one__factored, fact_1618_mult__cancel__right1, fact_845_diff__less__Suc, fact_2192_add__is__1, fact_2825_dual__order_Ostrict__trans, fact_2698_Orderings_Oorder__eq__iff, fact_6356_bit__mod__2__iff, fact_2062_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, fact_7660_sum_Onat__ivl__Suc_H, fact_1622_mult__cancel__left2, fact_7259_powr__diff, fact_1745_div__mult__self3, fact_8938_sum_Ozero__middle, fact_2743_ord__eq__le__trans, fact_2961_Collect__mono, help_If_1_1_If_001t__Real__Oreal_T, fact_9067_inverse__le__1__iff, fact_8736_prod_Onat__ivl__Suc_H, fact_6872_sin__monotone__2pi, fact_5181_not__one__less__neg__numeral, fact_9259_neg__divideR__less__eq, fact_1851_mult__right__cancel, fact_9621_valid__eq, fact_590_Suc__n__not__le__n, fact_5346_abs__ln__one__plus__x__minus__x__bound__nonpos, fact_2829_order_Ostrict__implies__not__eq, fact_9414_nat__1, fact_10138_map__Suc__upt, fact_4207_odd__one, fact_678_nat__less__le, fact_823_VEBT__internal_Ooption__shift_Osimps_I3_J, fact_6782_less__log2__of__power, fact_4409_split__of__bool, fact_25_add__self__div__2, fact_2884_order__less__irrefl, fact_491_mi__ma__2__deg, fact_125_is__num__normalize_I1_J, fact_7302_tan__mono__le, fact_2925_order__less__imp__not__eq, fact_5949_zero__and__eq, fact_6805_powser__zero, fact_1186_add__less__imp__less__left, fact_7653_sum__shift__lb__Suc0__0, fact_1529_add_Oright__neutral, fact_4543_minf_I10_J, fact_2651_ord__le__eq__subst, fact_4233_odd__iff__mod__2__eq__one, fact_6420_bit__Suc, fact_5262_power2__eq__iff, fact_1387_times__divide__eq__left, fact_3749_finite__has__maximal2, fact_4812_mult__neg__numeral__simps_I3_J, fact_1360_square__diff__square__factored, fact_5435_abs__of__nonpos, fact_4897_neg__one__even__power, fact_5424_semiring__norm_I15_J, fact_8132_Maclaurin__zero, fact_4245_even__flip__bit__iff, fact_3425_Suc__mod__mult__self2, fact_499_xnin, fact_6015_and__minus__numerals_I6_J, fact_7993_lemma__termdiff1, fact_894_power2__diff, fact_8737_prod_Onat__ivl__Suc_H, fact_7542_arccos__le__arccos, fact_2854_order__less__asym_H, fact_8357_gbinomial__code, fact_3159_order__le__less, fact_2311_power__less__imp__less__base, fact_1196_add__strict__mono, fact_669_size__neq__size__imp__neq, fact_9495_sgn__root, fact_2041_add__increasing, fact_2441_less__divide__eq__numeral_I1_J, fact_2186_power__0, fact_7719_sum_Oub__add__nat, fact_6693_of__nat__mono, fact_6359_real__sqrt__pow2__iff, fact_2534_le__div__geq, fact_4254_parity__cases, fact_8446_prod_OlessThan__Suc, fact_3993_dvd__add__right__iff, fact_7204_tan__double, fact_4538_minf_I9_J, fact_5276_neg__minus__divide__le__eq, fact_1933_power__eq__iff__eq__base, fact_8290_pochhammer__of__nat__eq__0__lemma_H, fact_9623_valid__eq2, fact_3308_max__def, fact_9615_or__not__numerals_I8_J, fact_3384_mult__le__cancel__iff2, fact_761_minNullmin, fact_7844_lemma__termdiff2, fact_369_power__commuting__commutes, fact_153_left__add__twice, fact_3575_set__bit__Suc, fact_1826_zero__le, fact_9653_plus__complex_Osimps_I2_J, fact_9810_atLeast0__lessThan__Suc__eq__insert__0, fact_10112_inj__on__diff__nat, fact_2901_order__less__subst2, fact_2378_vebt__delete_Osimps_I5_J, fact_9454_nat__floor__neg, fact_8426_prod_Oinsert, fact_9457_floor__eq3, fact_4166_unit__div__commute, fact_4989_old_Oprod_Ocase, fact_1248_mult_Ocomm__neutral, fact_4489_of__bool__odd__eq__mod__2, fact_1452_gt__half__sum, fact_5096_square__eq__1__iff, fact_3044_antisym__conv1, fact_8093_choose__dvd, fact_5622_cong__exp__iff__simps_I3_J, fact_775_max_Oidem, fact_7304_tan__30, fact_4537_minf_I9_J, fact_335_one__plus__numeral__commute, fact_9004_right__inverse, fact_784_max_Obounded__iff, fact_4814_mult__neg__numeral__simps_I3_J, fact_3288_bot_Onot__eq__extremum, fact_4999_mod__minus__eq, fact_7952_sums__If__finite__set_H, fact_8123_fact__num__eq__if, fact_9236_zero__le__scaleR__iff, fact_6555_of__nat__1, fact_9599_numeral__or__not__num__eq, fact_5590_numeral__Bit1, fact_7807_double__gauss__sum, fact_1816_zero__power, fact_9002_inverse__le__iff__le__neg, fact_5847_of__int__power__less__of__int__cancel__iff, fact_6291_and__nat__unfold, fact_7884_sums__le, fact_489_semiring__norm_I71_J, fact_8586_prod__dvd__prod__subset, fact_811_Nat_Oadd__diff__assoc2, fact_53__C0_C, fact_3454_mod__add__left__eq, fact_4796_semiring__norm_I171_J, fact_9642_csqrt_Osimps_I2_J, fact_2380_num_Osize_I5_J, fact_1746_div__mult__self2, fact_5671_dbl__dec__simps_I4_J, fact_338_power__le__imp__le__exp, fact_3167_linorder__not__le, fact_2827_dual__order_Ostrict__trans, fact_3784_dbl__simps_I3_J, fact_4423_replicate__length__same, fact_8340_pochhammer__minus_H, fact_9006_left__inverse, fact_3524_cancel__div__mod__rules_I2_J, fact_4393_zero__less__eq__of__bool, fact_1530_add_Oright__neutral, fact_3987_dvd__add__left__iff, fact_4189_even__zero, fact_3400_mod__mult__self1__is__0, fact_1549_division__ring__divide__zero, fact_1063_add__le__cancel__right, fact_8248_floor__divide__of__nat__eq, fact_7412_sum_Odistrib, fact_8235_gbinomial__Suc__Suc, fact_5061_add__eq__0__iff, fact_5063_le__minus__one__simps_I4_J, fact_9277_neg__le__minus__divideR__eq, fact_8174_floor__numeral, fact_5136_ln__ge__zero, fact_4786_diff__numeral__simps_I2_J, fact_2817_order_Ostrict__trans, fact_1510_add__cancel__right__right, fact_3102_dense__ge__bounded, fact_9820_card__UNIV__bool, fact_5607_numeral__code_I3_J, fact_3874_even__mult__iff, fact_2855_order__less__asym_H, fact_1064_add__le__cancel__right, fact_3999_unit__imp__dvd, fact_4090_div__plus__div__distrib__dvd__left, fact_1322_less__1__mult, fact_3883_even__mod__2__iff, fact_2921_linorder__less__linear, fact_9080_nonzero__inverse__eq__divide, fact_4713_uminus__add__conv__diff, fact_5413_abs__neg__numeral, fact_373_power__mult, fact_2600_buildup__nothing__in__leaf, fact_6167_or__nat__numerals_I2_J, fact_1968_mult__nonpos__nonneg, fact_1283_diff__add__eq, fact_8245_pochhammer__0__left, fact_6797_ln__series, fact_1729_zero__le__divide__1__iff, fact_2620_div__pos__pos__trivial, fact_8739_prod_Onat__ivl__Suc_H, fact_7658_sum_OatLeast0__atMost__Suc, fact_2029_add__nonneg__nonneg, fact_6703_pi__ge__zero, fact_9343_cosh__square__eq, fact_9429_nat__one__as__int, fact_9438_and__nat__def, fact_1082_mult_Oright__neutral, fact_1973_mult__nonneg__nonpos, fact_1433_linordered__field__no__lb, fact_729_succ__corr, fact_5144_not__zero__less__neg__numeral, fact_6657_of__nat__less__of__int__iff, fact_681_less__or__eq__imp__le, fact_4762_minus__one__mult__self, fact_804_left__diff__distrib__numeral, fact_3507_mult__div__mod__eq, fact_9583_or__int__def, fact_8889_sum__power__shift, fact_3472_unique__euclidean__semiring__numeral__class_Opos__mod__bound, fact_1812_power__0__left, fact_1940_power__strict__mono, fact_3573_set__bit__Suc, fact_4087_div__mult__div__if__dvd, fact_65_Collect__mem__eq, fact_2148_zero__le__power, fact_5041_neg__numeral__less__numeral, fact_4639_minus__add__cancel, fact_2085_zero__less__mult__pos, fact_2801_dual__order_Oirrefl, fact_1554_divide__cancel__left, fact_7960_sum__lessThan__telescope_H, fact_6489_of__nat__eq__iff, fact_6907_norm__uminus__minus, fact_5592_eval__nat__numeral_I3_J, fact_650_power__gt1, fact_7455_sum_Oshift__bounds__cl__nat__ivl, fact_4180_unit__imp__mod__eq__0, fact_6033_of__int__and__eq, fact_6544_of__nat__1__eq__iff, fact_4820_neg__numeral__less__iff, fact_1818_zero__power, fact_1300_max__add__distrib__right, fact_9219_scaleR__conv__of__real, fact_6046_and_Ocommute, fact_2767_less__imp__neq, fact_8803_prod_Oinsert__remove, fact_866_VEBT__internal_Ooption__shift_Oelims, fact_6289_or__not__num__neg_Oelims, fact_1330_less__add__one, fact_6076_AND__upper2_H, fact_4064_mult__unit__dvd__iff_H, fact_3272_bot_Oextremum__unique, fact_2502_power2__le__imp__le, fact_3481_mod__eqE, fact_6039_bit_Odisj__conj__distrib, fact_694_le__add2, fact_4872_power__minus__odd, fact_1868_mult__not__zero, fact_6587_of__nat__0__less__iff, fact_1490_mult__eq__0__iff, fact_4073_dvd__div__mult, fact_4990_old_Oprod_Ocase, fact_3792_dvd__add__triv__left__iff, fact_1428_numeral__code_I2_J, fact_155_left__add__twice, fact_5566_abs__minus__le__zero, fact_1602_add__less__same__cancel2, fact_4845_add__neg__numeral__special_I9_J, fact_303_four__x__squared, fact_6986_ceiling__neg__numeral, fact_2089_mult__pos__neg2, fact_7081_suminf__pos__iff, fact_7950_sum__diff__nat, fact_3130_dual__order_Ostrict__trans2, fact_1151_ab__semigroup__add__class_Oadd__ac_I1_J, fact_9699_complex__div__gt__0, fact_2993_in__mono, fact_5280_less__divide__eq__numeral_I2_J, fact_5747_dbl__inc__simps_I3_J, fact_1521_add__cancel__left__right, fact_1091_add__diff__cancel__right, fact_2203_nat__mult__eq__cancel1, fact_759_max_Oabsorb4, fact_8895_pochhammer__prod__rev, fact_9763_infinite__nat__iff__unbounded__le, fact_9344_cosh__square__eq, fact_2313_not__sum__squares__lt__zero, fact_3974_dvd__triv__right, fact_3880_even__add, fact_7278_log__add__eq__powr, fact_5727_numeral__inc, fact_4172_is__unit__div__mult2__eq, fact_3477_mod__eq__self__iff__div__eq__0, fact_5274_pos__minus__divide__le__eq, fact_1596_less__add__same__cancel2, fact_1758_power__eq__0__iff, fact_8996_binomial__eq__0__iff, fact_2058_zero__less__one__class_Ozero__le__one, fact_1764_div__mult__self1__is__m, fact_2004_mult__mono, fact_3969_dvd__mult__right, fact_8301_less__floor__iff, fact_3230_order__le__less__subst2, fact_4300_unity__coeff__ex, fact_136_mult__numeral__1, fact_2475_power__diff, fact_5554_abs__eq__mult, fact_4821_neg__numeral__less__iff, fact_315_power__strict__increasing, fact_4022_dvd__power__same, fact_2314_not__sum__squares__lt__zero, fact_6932_norm__diff__triangle__less, fact_348_neq__if__length__neq, fact_6741_field__char__0__class_Oof__nat__div, fact_4829_eq__divide__eq__numeral1_I2_J, fact_6716_of__nat__and__eq, fact_1828_le__numeral__extra_I3_J, fact_6619_of__nat__power__le__of__nat__cancel__iff, fact_5522_abs__triangle__ineq, fact_5146_not__zero__less__neg__numeral, fact_8298_floor__eq__iff, fact_5473_divmod__algorithm__code_I7_J, fact_6204_or__not__num__neg_Osimps_I1_J, fact_3172_linorder__not__less, fact_6656_bit__of__nat__iff__bit, fact_4217_dvd__power, fact_3222_order__le__less__subst2, fact_8150_fact__less__mono__nat, fact_1725_diff__is__0__eq, fact_4057_mult__unit__dvd__iff, fact_7840_gauss__sum__from__Suc__0, fact_6832_nat__leq__as__int, fact_2416_mult__less__cancel__left1, fact_4702_mult__minus1__right, fact_2639_order__antisym__conv, fact_2837_dual__order_Ostrict__implies__not__eq, fact_4505_minf_I6_J, fact_659_linorder__neqE__nat, fact_4528_pinf_I9_J, fact_8970_choose__odd__sum, fact_5315_minus__power__mult__self, fact_267_one__less__numeral__iff, fact_6743_pi__less__4, fact_5858_of__int__eq__neg__numeral__power__cancel__iff, fact_4093_div__plus__div__distrib__dvd__right, fact_7790_sum_Oin__pairs, fact_137_mult__numeral__1, fact_8460_prod_Onot__neutral__contains__not__neutral, fact_2726_order__trans, fact_8666_prod_Osubset__diff, fact_5846_of__int__power__less__of__int__cancel__iff, fact_8553_prod__le__1, fact_6876_exp__bound__lemma, fact_1495_mult__zero__right, fact_2425_mult__le__cancel__left1, fact_5166_neg__one__le__numeral, fact_3979_dvd__add, fact_827_le__diff__iff_H, fact_713_mono__nat__linear__lb, fact_1526_double__zero__sym, fact_6602_real__of__nat__eq__numeral__power__cancel__iff, fact_1501_add__0, fact_7669_sum_OSuc__reindex__ivl, fact_8378_prod_Oempty, fact_7989_sum__less__suminf, fact_5710_diff__numeral__special_I6_J, fact_6752_of__nat__less__two__power, fact_5192_neg__numeral__less__one, fact_1260_left__diff__distrib_H, fact_7964_sum__lessThan__telescope, fact_573_less__SucE, fact_2217_vebt__insert_Osimps_I2_J, fact_4553_set__decode__Suc, fact_1928_power__eq__imp__eq__base, fact_1540_div__0, fact_1652_nonzero__mult__divide__mult__cancel__left, fact_7228_powr__numeral, fact_903_max_OcoboundedI1, fact_4838_power2__minus, fact_3617_flip__bit__nonnegative__int__iff, fact_6087_exp__gt__one, fact_6013_or__numerals_I5_J, fact_1032_double__not__eq__Suc__double, fact_6556_of__nat__power, fact_3989_dvd__add__right__iff, fact_7364_sum__zero__power, fact_2911_order__less__not__sym, fact_7810_double__gauss__sum, fact_6002_and__numerals_I1_J, fact_6037_bit_Odisj__conj__distrib2, fact_1914_not__gr0, fact_8437_Icc__subset__Iic__iff, fact_672_Suc__nat__number__of__add, fact_2607_order__refl, fact_6312_real__sqrt__le__iff, fact_1078_mult__1, fact_9132_central__binomial__odd, fact_5824_of__int__numeral__less__iff, fact_7404_sum__distrib__right, fact_1202_add__mono__thms__linordered__field_I2_J, fact_1109_ab__semigroup__mult__class_Omult__ac_I1_J, fact_1238_comm__semiring__class_Odistrib, fact_5076_less__minus__one__simps_I4_J, fact_6943_norm__triangle__ineq2, fact_2653_ord__le__eq__subst, fact_1657_diff__numeral__special_I9_J, fact_7034_suminf__le, fact_5538_abs__le__iff, fact_923_max_Ocobounded2, fact_1104_mult_Oassoc, fact_5795_zero__le__arctan__iff, fact_2629_zdiv__zmult2__eq, fact_8971_choose__odd__sum, fact_2447_frac__less__eq, fact_3786_even__succ__mod__exp, fact_892_power2__diff, fact_5548_xor__num_Ocases, fact_6293_or__Suc__0__eq, fact_9616_or__not__numerals_I9_J, fact_2221_mult__less__le__imp__less, fact_4674_neg__less__0__iff__less, fact_2093_mult__pos__pos, fact_1465_valid__tree__deg__neq__0, fact_1070_add__less__cancel__right, fact_9008_inverse__eq__divide__numeral, fact_6801_sin__periodic__pi2, fact_6686_of__nat__less__imp__less, fact_3396_minus__mod__self2, fact_5644_Suc__mod__eq__add3__mod, fact_1123_add_Ocommute, fact_9649_csqrt__of__real__nonneg, fact_2209_nat__power__less__imp__less, fact_3833_dvd__add__times__triv__right__iff, fact_10193_set__decode__div__2, fact_8479_prod_OatMost__Suc__shift, fact_2251_mult__left__less__imp__less, fact_9231_vector__fraction__eq__iff, fact_5330_power__minus1__odd, fact_3210_order__less__le__trans, fact_3832_dvd__add__times__triv__right__iff, fact_2648_ord__le__eq__subst, fact_3064_not__le__imp__less, fact_4017_dvd__div__eq__cancel, fact_5213_uminus__numeral__One, fact_6971_ceiling__add__of__int, fact_3788_even__succ__mod__exp, fact_5943_or_Oidem, fact_5029_neg__numeral__le__numeral, fact_3310_vebt__pred_Opelims, fact_7930_sums__Suc__imp, fact_5934_and_Oright__idem, fact_3074_order_Ostrict__iff__order, fact_8079_fact__ge__1, fact_5415_abs__neg__one, fact_3671_verit__comp__simplify1_I1_J, fact_2368_div__add__self1, fact_8526_lessThan__Suc__atMost, fact_1863_divisors__zero, fact_5806_dbl__dec__simps_I5_J, fact_9180_cos__x__cos__y, fact_8511_prod__ge__1, fact_441_power4__eq__xxxx, fact_9614_and__not__numerals_I8_J, fact_5935_and_Oleft__idem, fact_4898_neg__one__odd__power, fact_5232_ln__add__one__self__le__self, fact_9726_drop__bit__negative__int__iff, fact_2156_zero__less__divide__iff, fact_4176_is__unit__power__iff, fact_2524_power__eq__if, fact_316_power__increasing, fact_1995_mult__left__mono__neg, fact_3670_verit__comp__simplify1_I1_J, fact_1765_div__mult__self__is__m, fact_5886_semiring__norm_I26_J, fact_4494_pinf_I6_J, fact_3667_verit__comp__simplify1_I1_J, fact_2478_div__if, fact_6053_plus__and__or, fact_109_distrib__left__numeral, fact_6964_cos__zero, fact_616_lift__Suc__mono__le, fact_5778_of__int__mult, fact_9703_complex__div__cnj, fact_8207_floor__le__neg__numeral, fact_5460_power__even__abs__numeral, fact_562_n__not__Suc__n, fact_2660_ord__eq__le__subst, fact_4724_ln__gt__zero__iff, fact_6021_and__numerals_I6_J, fact_5876_mult__of__int__commute, fact_5774_of__int__eq__1__iff, fact_1116_add__left__imp__eq, fact_3551_unset__bit__Suc, fact_6129_one__or__eq, fact_7077_polar__Ex, fact_5689_diff__Suc__numeral, fact_3954_dvd__mult__left, fact_5870_neg__numeral__power__less__of__int__cancel__iff, fact_7454_sum_Oshift__bounds__cl__nat__ivl, fact_888_power2__commute, fact_2770_order_Oasym, fact_2338_eq__divide__eq__numeral_I1_J, fact_1543_bits__div__by__0, fact_8175_gbinomial__0_I1_J, fact_5691_max__Suc__numeral, fact_6318_real__sqrt__le__0__iff, fact_195_list__update__overwrite, fact_1163_le__iff__add, fact_6762_real__of__nat__div2, fact_1997_split__mult__pos__le, fact_4355_Ball__set__replicate, fact_2471_numeral__2__eq__2, fact_334_one__plus__numeral__commute, fact_190_power2__sum, fact_9016_power__inverse, fact_3790_dvd__add__triv__left__iff, fact_1675_divide__eq__1__iff, fact_4291_inf__period_I4_J, fact_4700_mult__minus1, fact_7394_sum__mono, fact_6888_norm__mult__numeral1, fact_4893_power__minus1__even, fact_7764_arccos__lt__bounded, fact_470_min__Null__member, fact_8348_gbinomial__sum__up__index, fact_9041_divide__inverse, fact_8329_pochhammer__absorb__comp, fact_1885_comm__monoid__add__class_Oadd__0, fact_2055_linordered__nonzero__semiring__class_Ozero__le__one, fact_1437_divide__divide__times__eq, fact_2111_canonically__ordered__monoid__add__class_OlessE, fact_3152_dual__order_Ostrict__implies__order, fact_22__C5_Ohyps_C_I7_J, fact_5641_cong__exp__iff__simps_I7_J, fact_5593_power__minus__Bit1, fact_3615_List_Ofinite__set, fact_5877_mult__of__int__commute, fact_3627_length__product, fact_6843_norm__exp, fact_5918_odd__numeral__BitM, fact_5951_and__zero__eq, fact_8908_sum__atLeastAtMost__code, fact_8058_fact__Suc__0, fact_5426_semiring__norm_I81_J, fact_9707_card__Collect__less__nat, fact_1170_add__left__mono, fact_2357_power__inject__base, fact_5485_abs__mult, fact_639_Suc__eq__plus1, fact_8221_pochhammer__fact, fact_9094_binomial__absorption, fact_3669_verit__comp__simplify1_I1_J, fact_4209_bit__eq__rec, fact_3521_cancel__div__mod__rules_I1_J, fact_1434_linordered__field__no__ub, fact_1291_eq__diff__eq, fact_5241_minus__divide__less__eq, fact_278_le__num__One__iff, fact_5924_even__of__int__iff, fact_2491_vebt__succ_Osimps_I4_J, fact_6618_of__nat__power__le__of__nat__cancel__iff, fact_7000_cos__pi__half, fact_6551_of__nat__1, fact_9126_ln__prod, fact_272_subset__code_I1_J, fact_2022_add__nonneg__eq__0__iff, fact_3565_divmod__digit__0_I1_J, fact_8251_gbinomial__absorb__comp, fact_6880_sin__zero__iff, fact_5519_abs__of__pos, fact_307_power__less__power__Suc, fact_2847_order__less__asym, fact_366_power__commuting__commutes, fact_7170_cos__double__cos, fact_3133_dual__order_Ostrict__iff__not, fact_1464_valid__0__not, fact_4559_add__scale__eq__noteq, fact_112_distrib__left__numeral, fact_3161_order__less__le, fact_3803_div__dvd__div, fact_9160_real__le__x__sinh, fact_2619_subsetI, fact_4006_dvd__diff__commute, fact_6500_of__nat__0, fact_2814_order_Ostrict__trans, fact_9480_zero__le__sgn__iff, fact_2024_add__nonpos__nonpos, fact_6760_pi__half__less__two, fact_1333_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, fact_6736_real__of__nat__div4, fact_1241_ring__class_Oring__distribs_I1_J, fact_7213_powr__nonneg__iff, fact_1287_add__diff__eq, fact_8241_pochhammer__nonneg, fact_1916_bot__nat__0_Oextremum__strict, fact_3047_antisym__conv2, fact_6070_OR__lower, fact_752_max__less__iff__conj, fact_1175_add__mono__thms__linordered__semiring_I1_J, fact_854_Nat_Odiff__add__assoc, fact_3046_antisym__conv2, fact_6996_ceiling__less__numeral, fact_3659_verit__la__disequality, fact_3540_minus__div__mult__eq__mod, fact_5919_odd__numeral__BitM, fact_5850_of__int__le__numeral__power__cancel__iff, fact_9092_inverse__diff__inverse, fact_143_numeral__Bit0, fact_9322_sinh__plus__cosh, fact_642_power__Suc, fact_2857_order__less__asym_H, fact_5198_minus__divide__eq__eq, fact_1250_mult_Ocomm__neutral, fact_1969_mult__nonpos__nonneg, fact_6861_sin__lt__zero, fact_6900_norm__ge__zero, fact_8135_Maclaurin__lemma, fact_5396_abs__1, fact_3463_mod__diff__eq, fact_6492_abs__of__nat, fact_7177_cos__times__sin, fact_2077_mult__less__cancel__left__pos, fact_6067_exp__total, fact_359_power__commutes, fact_4817_neg__numeral__le__iff, fact_3995_dvd__unit__imp__unit, fact_1550_division__ring__divide__zero, fact_7268_powr__minus__divide, fact_7102_ceiling__add__le, fact_9606_and__not__numerals_I3_J, fact_8277_pochhammer__rec_H, fact_6813_sin__3over2__pi, fact_13__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_060_A2_A_094_Adeg_092_060close_062, fact_4212_dvd__power__iff, fact_3783_dbl__simps_I3_J, fact_184_sum__squares__bound, fact_3476_mod__eq__self__iff__div__eq__0, fact_2224_mult__le__less__imp__less, fact_3688_old_Oprod_Oexhaust, fact_7230_square__powr__half, fact_9531_log__base__root, fact_3698_verit__comp__simplify1_I3_J, fact_3962_dvd__triv__left, fact_2744_ord__eq__le__trans, fact_1742_div__mult__self4, fact_3111_dual__order_Ostrict__iff__order, fact_819_add__diff__add, fact_2450_power__Suc__le__self, fact_7902_sums__iff__shift, fact_5416_abs__neg__one, fact_5017_ln__add__one__self__le__self2, fact_4301_unity__coeff__ex, fact_4861_bits__minus__1__mod__2__eq, fact_1142_group__cancel_Oadd1, fact_709_add__mult__distrib2, fact_7079_summable__rabs__comparison__test, fact_5939_or_Oright__idem, fact_5191_neg__numeral__less__one, fact_5786_of__int__eq__of__int__power__cancel__iff, fact_4935_minus__less__iff, fact_7786_sum__gp__multiplied, fact_5913_dbl__inc__def, fact_4466_minf_I2_J, fact_4944_numeral__neq__neg__numeral, fact_9155_choose__square__sum, fact_8491_prod__nonneg, fact_2381_ex__least__nat__less, fact_8986_binomial__Suc__n, fact_5225_take__bit__numeral__minus__1__eq, fact_5003_cond__case__prod__eta, fact_4894_neg__one__even__power, fact_6052_or_Oassoc, fact_1559_bot__nat__0_Onot__eq__extremum, fact_4067_unit__mult__left__cancel, fact_7084_suminf__pos2, fact_9459_nat__take__bit__eq, fact_3820_dvd__times__left__cancel__iff, fact_1361_square__diff__square__factored, fact_5038_not__numeral__less__neg__numeral, fact_2823_dual__order_Ostrict__trans, fact_5929_mask__numeral, fact_5442_semiring__norm_I4_J, fact_7214_powr__less__cancel__iff, fact_5745_dbl__inc__simps_I3_J, fact_7280_minus__log__eq__powr, fact_3503_cong__exp__iff__simps_I6_J, fact_4479_minf_I5_J, fact_5906_of__int__neg__numeral, fact_8998_binomial__n__0, fact_2928_order__less__imp__not__eq2, fact_5857_of__int__eq__neg__numeral__power__cancel__iff, fact_4306_flip__bit__0, fact_7171_cos__treble__cos, fact_6660_not__bit__Suc__0__Suc, fact_5177_not__one__le__neg__numeral, fact_3178_order__less__imp__le, fact_2247_mult__strict__mono, fact_4712_uminus__add__conv__diff, fact_8745_prod_OSuc__reindex__ivl, fact_4775_max__number__of_I2_J, fact_3173_linorder__not__less, fact_5481_abs__ge__self, fact_4234_power__mono__odd, fact_8358_gbinomial__code, fact_96_add__numeral__left, fact_5222_power__minus__Bit0, fact_9595_or__not__numerals_I2_J, fact_2510_power2__less__0, fact_5328_power__minus1__odd, fact_6766_ln__realpow, fact_379_length__induct, fact_3876_odd__add, fact_5253_add__divide__eq__if__simps_I5_J, fact_6030_or__numerals_I7_J, fact_5633_abs__square__eq__1, fact_1424_numeral__code_I2_J, fact_9561_bit__push__bit__iff__nat, fact_20_False, fact_2406_vebt__mint_Ocases, fact_247_one__add__one, fact_2432_neg__le__divide__eq, fact_5126_subset__Compl__self__eq, fact_8819_prod_Odelta__remove, fact_740_vebt__maxt_Osimps_I3_J, fact_8753_sum__telescope, fact_6476_cos__x__y__le__one, fact_835_VEBT__internal_Ooption__shift_Osimps_I1_J, fact_7610_sum_Omono__neutral__left, fact_3385_divides__aux__eq, fact_1731_eq__divide__eq__numeral1_I1_J, fact_4708_diff__minus__eq__add, fact_7293_complex__norm, fact_4368_triangle__Suc, fact_7014_neg__numeral__le__ceiling, fact_6908_norm__uminus__minus, fact_5228_real__add__less__0__iff, fact_1591_add__le__same__cancel1, fact_5937_and_Oidem, fact_2734_order__antisym, fact_40__C5_C, fact_8913_sum_Oin__pairs__0, fact_5185_not__numeral__less__neg__one, fact_7837_arcsin__le__iff, fact_3690_old_Oprod_Oexhaust, fact_5695_dbl__dec__simps_I2_J, fact_7968_sumr__diff__mult__const2, fact_3722_prod_Ofinite__Collect__op, fact_37_dele__bmo__cont__corr, fact_7023_summable__add, fact_5945_mask__nat__positive__iff, fact_2592_Diff__eq__empty__iff, fact_4194_is__unitE, fact_1407_succ__greatereq__min, fact_2026_add__nonpos__nonpos, fact_954_max_OorderE, fact_7333_of__real__power, fact_3250_order__less__le__subst2, fact_7370_arccos__0, fact_7831_double__gauss__sum__from__Suc__0, fact_4229_even__iff__mod__2__eq__zero 153.18/68.26 % No. of inferences in proof: 16512 153.18/68.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 67727 ms resp. 66590 ms w/o parsing 159.44/70.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 159.44/70.59 thf(produc5542196010084753463at_nat_type, type, produc5542196010084753463at_nat: $tType). 159.44/70.59 thf(produc5491161045314408544at_nat_type, type, produc5491161045314408544at_nat: $tType). 159.44/70.59 thf(produc1193250871479095198on_num_type, type, produc1193250871479095198on_num: $tType). 159.44/70.59 thf(produc8306885398267862888on_nat_type, type, produc8306885398267862888on_nat: $tType). 159.44/70.59 thf(produc6121120109295599847at_nat_type, type, produc6121120109295599847at_nat: $tType). 159.44/70.59 thf(produc3368934014287244435at_num_type, type, produc3368934014287244435at_num: $tType). 159.44/70.59 thf(produc4471711990508489141at_nat_type, type, produc4471711990508489141at_nat: $tType). 159.44/70.59 thf(produc7036089656553540234on_num_type, type, produc7036089656553540234on_num: $tType). 159.44/70.59 thf(produc2233624965454879586on_nat_type, type, produc2233624965454879586on_nat: $tType). 159.44/70.59 thf(set_fi4554929511873752355omplex_type, type, set_fi4554929511873752355omplex: $tType). 159.44/70.59 thf(list_P7413028617227757229T_VEBT_type, type, list_P7413028617227757229T_VEBT: $tType). 159.44/70.59 thf(produc3447558737645232053on_num_type, type, produc3447558737645232053on_num: $tType). 159.44/70.59 thf(produc4953844613479565601on_nat_type, type, produc4953844613479565601on_nat: $tType). 159.44/70.59 thf(produc2963631642982155120at_num_type, type, produc2963631642982155120at_num: $tType). 159.44/70.59 thf(produc7248412053542808358at_nat_type, type, produc7248412053542808358at_nat: $tType). 159.44/70.59 thf(set_fi7789364187291644575l_real_type, type, set_fi7789364187291644575l_real: $tType). 159.44/70.59 thf(filter6041513312241820739omplex_type, type, filter6041513312241820739omplex: $tType). 159.44/70.59 thf(list_P7037539587688870467BT_nat_type, type, list_P7037539587688870467BT_nat: $tType). 159.44/70.59 thf(list_P4547456442757143711BT_int_type, type, list_P4547456442757143711BT_int: $tType). 159.44/70.59 thf(list_P5647936690300460905T_VEBT_type, type, list_P5647936690300460905T_VEBT: $tType). 159.44/70.59 thf(produc8243902056947475879T_VEBT_type, type, produc8243902056947475879T_VEBT: $tType). 159.44/70.59 thf(set_Pr5085853215250843933omplex_type, type, set_Pr5085853215250843933omplex: $tType). 159.44/70.59 thf(produc8923325533196201883nteger_type, type, produc8923325533196201883nteger: $tType). 159.44/70.59 thf(list_P3126845725202233233VEBT_o_type, type, list_P3126845725202233233VEBT_o: $tType). 159.44/70.59 thf(list_P7495141550334521929T_VEBT_type, type, list_P7495141550334521929T_VEBT: $tType). 159.44/70.59 thf(filter2146258269922977983l_real_type, type, filter2146258269922977983l_real: $tType). 159.44/70.59 thf(list_P8526636022914148096eger_o_type, type, list_P8526636022914148096eger_o: $tType). 159.44/70.59 thf(option4927543243414619207at_nat_type, type, option4927543243414619207at_nat: $tType). 159.44/70.59 thf(filter1242075044329608583at_nat_type, type, filter1242075044329608583at_nat: $tType). 159.44/70.59 thf(set_Pr6218003697084177305l_real_type, type, set_Pr6218003697084177305l_real: $tType). 159.44/70.59 thf(list_P3744719386663036955um_num_type, type, list_P3744719386663036955um_num: $tType). 159.44/70.59 thf(list_P6011104703257516679at_nat_type, type, list_P6011104703257516679at_nat: $tType). 159.44/70.59 thf(produc9072475918466114483BT_nat_type, type, produc9072475918466114483BT_nat: $tType). 159.44/70.59 thf(produc4894624898956917775BT_int_type, type, produc4894624898956917775BT_int: $tType). 159.44/70.59 thf(set_Pr1261947904930325089at_nat_type, type, set_Pr1261947904930325089at_nat: $tType). 159.44/70.59 thf(produc4411394909380815293omplex_type, type, produc4411394909380815293omplex: $tType). 159.44/70.59 thf(list_P7333126701944960589_nat_o_type, type, list_P7333126701944960589_nat_o: $tType). 159.44/70.59 thf(list_P6285523579766656935_o_nat_type, type, list_P6285523579766656935_o_nat: $tType). 159.44/70.59 thf(list_P3795440434834930179_o_int_type, type, list_P3795440434834930179_o_int: $tType). 159.44/70.59 thf(set_list_VEBT_VEBT_type, type, set_list_VEBT_VEBT: $tType). 159.44/70.59 thf(produc334124729049499915VEBT_o_type, type, produc334124729049499915VEBT_o: $tType). 159.44/70.59 thf(produc2504756804600209347T_VEBT_type, type, produc2504756804600209347T_VEBT: $tType). 159.44/70.59 thf(produc6271795597528267376eger_o_type, type, produc6271795597528267376eger_o: $tType). 159.44/70.59 thf(produc2422161461964618553l_real_type, type, produc2422161461964618553l_real: $tType). 159.44/70.59 thf(product_prod_num_num_type, type, product_prod_num_num: $tType). 159.44/70.59 thf(product_prod_nat_num_type, type, product_prod_nat_num: $tType). 159.44/70.59 thf(product_prod_nat_nat_type, type, product_prod_nat_nat: $tType). 159.44/70.59 thf(product_prod_int_int_type, type, product_prod_int_int: $tType). 159.44/70.59 thf(list_P4002435161011370285od_o_o_type, type, list_P4002435161011370285od_o_o: $tType). 159.44/70.59 thf(set_list_complex_type, type, set_list_complex: $tType). 159.44/70.59 thf(set_set_complex_type, type, set_set_complex: $tType). 159.44/70.59 thf(set_list_real_type, type, set_list_real: $tType). 159.44/70.59 thf(list_VEBT_VEBT_type, type, list_VEBT_VEBT: $tType). 159.44/70.59 thf(set_set_real_type, type, set_set_real: $tType). 159.44/70.59 thf(set_list_nat_type, type, set_list_nat: $tType). 159.44/70.59 thf(set_list_int_type, type, set_list_int: $tType). 159.44/70.59 thf(product_prod_o_nat_type, type, product_prod_o_nat: $tType). 159.44/70.59 thf(product_prod_o_int_type, type, product_prod_o_int: $tType). 159.44/70.59 thf(list_Code_integer_type, type, list_Code_integer: $tType). 159.44/70.59 thf(set_VEBT_VEBT_type, type, set_VEBT_VEBT: $tType). 159.44/70.59 thf(set_set_nat_type, type, set_set_nat: $tType). 159.44/70.59 thf(set_Code_integer_type, type, set_Code_integer: $tType). 159.44/70.59 thf(set_Product_unit_type, type, set_Product_unit: $tType). 159.44/70.59 thf(set_Extended_enat_type, type, set_Extended_enat: $tType). 159.44/70.59 thf(list_complex_type, type, list_complex: $tType). 159.44/70.59 thf(set_list_o_type, type, set_list_o: $tType). 159.44/70.59 thf(product_prod_o_o_type, type, product_prod_o_o: $tType). 159.44/70.59 thf(set_complex_type, type, set_complex: $tType). 159.44/70.59 thf(filter_real_type, type, filter_real: $tType). 159.44/70.59 thf(option_num_type, type, option_num: $tType). 159.44/70.59 thf(option_nat_type, type, option_nat: $tType). 159.44/70.59 thf(filter_nat_type, type, filter_nat: $tType). 159.44/70.59 thf(set_char_type, type, set_char: $tType). 159.44/70.59 thf(list_real_type, type, list_real: $tType). 159.44/70.59 thf(set_real_type, type, set_real: $tType). 159.44/70.59 thf(list_num_type, type, list_num: $tType). 159.44/70.59 thf(list_nat_type, type, list_nat: $tType). 159.44/70.59 thf(list_int_type, type, list_int: $tType). 159.44/70.59 thf(vEBT_VEBT_type, type, vEBT_VEBT: $tType). 159.44/70.59 thf(set_num_type, type, set_num: $tType). 159.44/70.59 thf(set_nat_type, type, set_nat: $tType). 159.44/70.59 thf(set_int_type, type, set_int: $tType). 159.44/70.59 thf(code_integer_type, type, code_integer: $tType). 159.44/70.59 thf(extended_enat_type, type, extended_enat: $tType). 159.44/70.59 thf(list_o_type, type, list_o: $tType). 159.44/70.59 thf(complex_type, type, complex: $tType). 159.44/70.59 thf(set_o_type, type, set_o: $tType). 159.44/70.59 thf(char_type, type, char: $tType). 159.44/70.59 thf(real_type, type, real: $tType). 159.44/70.59 thf(num_type, type, num: $tType). 159.44/70.59 thf(nat_type, type, nat: $tType). 159.44/70.59 thf(int_type, type, int: $tType). 159.44/70.59 thf(archim7802044766580827645g_real_type, type, archim7802044766580827645g_real: (real > int)). 159.44/70.59 thf(archim6058952711729229775r_real_type, type, archim6058952711729229775r_real: (real > int)). 159.44/70.59 thf(archim2898591450579166408c_real_type, type, archim2898591450579166408c_real: (real > real)). 159.44/70.59 thf(archim8280529875227126926d_real_type, type, archim8280529875227126926d_real: (real > int)). 159.44/70.59 thf(binomial_type, type, binomial: (nat > (nat > nat))). 159.44/70.59 thf(gbinomial_complex_type, type, gbinomial_complex: (complex > (nat > complex))). 159.44/70.59 thf(gbinomial_int_type, type, gbinomial_int: (int > (nat > int))). 159.44/70.59 thf(gbinomial_nat_type, type, gbinomial_nat: (nat > (nat > nat))). 159.44/70.59 thf(gbinomial_real_type, type, gbinomial_real: (real > (nat > real))). 159.44/70.59 thf(bit_concat_bit_type, type, bit_concat_bit: (nat > (int > (int > int)))). 159.44/70.59 thf(bit_or_not_num_neg_type, type, bit_or_not_num_neg: (num > (num > num))). 159.44/70.59 thf(bit_ri7919022796975470100ot_int_type, type, bit_ri7919022796975470100ot_int: (int > int)). 159.44/70.59 thf(bit_ri6519982836138164636nteger_type, type, bit_ri6519982836138164636nteger: (nat > (code_integer > code_integer))). 159.44/70.59 thf(bit_ri631733984087533419it_int_type, type, bit_ri631733984087533419it_int: (nat > (int > int))). 159.44/70.59 thf(bit_se725231765392027082nd_int_type, type, bit_se725231765392027082nd_int: (int > (int > int))). 159.44/70.59 thf(bit_se727722235901077358nd_nat_type, type, bit_se727722235901077358nd_nat: (nat > (nat > nat))). 159.44/70.59 thf(bit_se8568078237143864401it_int_type, type, bit_se8568078237143864401it_int: (nat > (int > int))). 159.44/70.59 thf(bit_se8570568707652914677it_nat_type, type, bit_se8570568707652914677it_nat: (nat > (nat > nat))). 159.44/70.59 thf(bit_se1345352211410354436nteger_type, type, bit_se1345352211410354436nteger: (nat > (code_integer > code_integer))). 159.44/70.59 thf(bit_se2159334234014336723it_int_type, type, bit_se2159334234014336723it_int: (nat > (int > int))). 159.44/70.59 thf(bit_se2161824704523386999it_nat_type, type, bit_se2161824704523386999it_nat: (nat > (nat > nat))). 159.44/70.59 thf(bit_se2000444600071755411sk_int_type, type, bit_se2000444600071755411sk_int: (nat > int)). 159.44/70.59 thf(bit_se2002935070580805687sk_nat_type, type, bit_se2002935070580805687sk_nat: (nat > nat)). 159.44/70.59 thf(bit_se1080825931792720795nteger_type, type, bit_se1080825931792720795nteger: (code_integer > (code_integer > code_integer))). 159.44/70.59 thf(bit_se1409905431419307370or_int_type, type, bit_se1409905431419307370or_int: (int > (int > int))). 159.44/70.59 thf(bit_se1412395901928357646or_nat_type, type, bit_se1412395901928357646or_nat: (nat > (nat > nat))). 159.44/70.59 thf(bit_se545348938243370406it_int_type, type, bit_se545348938243370406it_int: (nat > (int > int))). 159.44/70.59 thf(bit_se547839408752420682it_nat_type, type, bit_se547839408752420682it_nat: (nat > (nat > nat))). 159.44/70.59 thf(bit_se2793503036327961859nteger_type, type, bit_se2793503036327961859nteger: (nat > (code_integer > code_integer))). 159.44/70.59 thf(bit_se7879613467334960850it_int_type, type, bit_se7879613467334960850it_int: (nat > (int > int))). 159.44/70.59 thf(bit_se7882103937844011126it_nat_type, type, bit_se7882103937844011126it_nat: (nat > (nat > nat))). 159.44/70.59 thf(bit_se1745604003318907178nteger_type, type, bit_se1745604003318907178nteger: (nat > (code_integer > code_integer))). 159.44/70.59 thf(bit_se2923211474154528505it_int_type, type, bit_se2923211474154528505it_int: (nat > (int > int))). 159.44/70.59 thf(bit_se2925701944663578781it_nat_type, type, bit_se2925701944663578781it_nat: (nat > (nat > nat))). 159.44/70.59 thf(bit_se8260200283734997820nteger_type, type, bit_se8260200283734997820nteger: (nat > (code_integer > code_integer))). 159.44/70.59 thf(bit_se4203085406695923979it_int_type, type, bit_se4203085406695923979it_int: (nat > (int > int))). 159.44/70.59 thf(bit_se4205575877204974255it_nat_type, type, bit_se4205575877204974255it_nat: (nat > (nat > nat))). 159.44/70.59 thf(bit_se6526347334894502574or_int_type, type, bit_se6526347334894502574or_int: (int > (int > int))). 159.44/70.59 thf(bit_se6528837805403552850or_nat_type, type, bit_se6528837805403552850or_nat: (nat > (nat > nat))). 159.44/70.59 thf(bit_se9216721137139052372nteger_type, type, bit_se9216721137139052372nteger: (code_integer > (nat > $o))). 159.44/70.59 thf(bit_se1146084159140164899it_int_type, type, bit_se1146084159140164899it_int: (int > (nat > $o))). 159.44/70.59 thf(bit_se1148574629649215175it_nat_type, type, bit_se1148574629649215175it_nat: (nat > (nat > $o))). 159.44/70.59 thf(code_bit_cut_integer_type, type, code_bit_cut_integer: (code_integer > produc6271795597528267376eger_o)). 159.44/70.59 thf(code_integer_of_int_type, type, code_integer_of_int: (int > code_integer)). 159.44/70.59 thf(code_integer_of_num_type, type, code_integer_of_num: (num > code_integer)). 159.44/70.59 thf(arg_type, type, arg: (complex > real)). 159.44/70.59 thf(cis_type, type, cis: (real > complex)). 159.44/70.59 thf(cnj_type, type, cnj: (complex > complex)). 159.44/70.59 thf(complex2_type, type, complex2: (real > (real > complex))). 159.44/70.59 thf(im_type, type, im: (complex > real)). 159.44/70.59 thf(re_type, type, re: (complex > real)). 159.44/70.59 thf(csqrt_type, type, csqrt: (complex > complex)). 159.44/70.59 thf(imaginary_unit_type, type, imaginary_unit: complex). 159.44/70.59 thf(divmod_nat_type, type, divmod_nat: (nat > (nat > product_prod_nat_nat))). 159.44/70.59 thf(unique6322359934112328802ux_nat_type, type, unique6322359934112328802ux_nat: (product_prod_nat_nat > $o)). 159.44/70.59 thf(unique5055182867167087721od_nat_type, type, unique5055182867167087721od_nat: (num > (num > product_prod_nat_nat))). 159.44/70.59 thf(unique5026877609467782581ep_nat_type, type, unique5026877609467782581ep_nat: (num > (product_prod_nat_nat > product_prod_nat_nat))). 159.44/70.59 thf(comm_s8582702949713902594nteger_type, type, comm_s8582702949713902594nteger: (code_integer > (nat > code_integer))). 159.44/70.59 thf(comm_s2602460028002588243omplex_type, type, comm_s2602460028002588243omplex: (complex > (nat > complex))). 159.44/70.59 thf(comm_s3181272606743183617d_enat_type, type, comm_s3181272606743183617d_enat: (extended_enat > (nat > extended_enat))). 159.44/70.59 thf(comm_s4660882817536571857er_int_type, type, comm_s4660882817536571857er_int: (int > (nat > int))). 159.44/70.59 thf(comm_s4663373288045622133er_nat_type, type, comm_s4663373288045622133er_nat: (nat > (nat > nat))). 159.44/70.59 thf(comm_s7457072308508201937r_real_type, type, comm_s7457072308508201937r_real: (real > (nat > real))). 159.44/70.59 thf(semiri3624122377584611663nteger_type, type, semiri3624122377584611663nteger: (nat > code_integer)). 159.44/70.59 thf(semiri5044797733671781792omplex_type, type, semiri5044797733671781792omplex: (nat > complex)). 159.44/70.59 thf(semiri4449623510593786356d_enat_type, type, semiri4449623510593786356d_enat: (nat > extended_enat)). 159.44/70.59 thf(semiri1406184849735516958ct_int_type, type, semiri1406184849735516958ct_int: (nat > int)). 159.44/70.59 thf(semiri1408675320244567234ct_nat_type, type, semiri1408675320244567234ct_nat: (nat > nat)). 159.44/70.59 thf(semiri2265585572941072030t_real_type, type, semiri2265585572941072030t_real: (nat > real)). 159.44/70.59 thf(invers8013647133539491842omplex_type, type, invers8013647133539491842omplex: (complex > complex)). 159.44/70.59 thf(inverse_inverse_real_type, type, inverse_inverse_real: (real > real)). 159.44/70.59 thf(at_bot_real_type, type, at_bot_real: filter_real). 159.44/70.59 thf(at_top_real_type, type, at_top_real: filter_real). 159.44/70.59 thf(filterlim_real_real_type, type, filterlim_real_real: ((real > real) > (filter_real > (filter_real > $o)))). 159.44/70.59 thf(finite_card_o_type, type, finite_card_o: (set_o > nat)). 159.44/70.59 thf(finite_card_nat_type, type, finite_card_nat: (set_nat > nat)). 159.44/70.59 thf(finite_card_char_type, type, finite_card_char: (set_char > nat)). 159.44/70.59 thf(finite_finite_list_o_type, type, finite_finite_list_o: (set_list_o > $o)). 159.44/70.59 thf(finite3922522038869484883st_int_type, type, finite3922522038869484883st_int: (set_list_int > $o)). 159.44/70.59 thf(finite3004134309566078307T_VEBT_type, type, finite3004134309566078307T_VEBT: (set_list_VEBT_VEBT > $o)). 159.44/70.59 thf(finite_finite_nat_type, type, finite_finite_nat: (set_nat > $o)). 159.44/70.59 thf(inj_on_nat_nat_type, type, inj_on_nat_nat: ((nat > nat) > (set_nat > $o))). 159.44/70.59 thf(inj_on_nat_char_type, type, inj_on_nat_char: ((nat > char) > (set_nat > $o))). 159.44/70.59 thf(abs_abs_int_type, type, abs_abs_int: (int > int)). 159.44/70.59 thf(abs_abs_real_type, type, abs_abs_real: (real > real)). 159.44/70.59 thf(minus_8373710615458151222nteger_type, type, minus_8373710615458151222nteger: (code_integer > (code_integer > code_integer))). 159.44/70.59 thf(minus_minus_complex_type, type, minus_minus_complex: (complex > (complex > complex))). 159.44/70.59 thf(minus_minus_int_type, type, minus_minus_int: (int > (int > int))). 159.44/70.59 thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))). 159.44/70.59 thf(minus_minus_real_type, type, minus_minus_real: (real > (real > real))). 159.44/70.59 thf(minus_minus_set_nat_type, type, minus_minus_set_nat: (set_nat > (set_nat > set_nat))). 159.44/70.59 thf(one_one_Code_integer_type, type, one_one_Code_integer: code_integer). 159.44/70.59 thf(one_one_complex_type, type, one_one_complex: complex). 159.44/70.59 thf(one_on7984719198319812577d_enat_type, type, one_on7984719198319812577d_enat: extended_enat). 159.44/70.59 thf(one_one_int_type, type, one_one_int: int). 159.44/70.59 thf(one_one_nat_type, type, one_one_nat: nat). 159.44/70.59 thf(one_one_real_type, type, one_one_real: real). 159.44/70.59 thf(plus_p5714425477246183910nteger_type, type, plus_p5714425477246183910nteger: (code_integer > (code_integer > code_integer))). 159.44/70.59 thf(plus_plus_complex_type, type, plus_plus_complex: (complex > (complex > complex))). 159.44/70.59 thf(plus_p3455044024723400733d_enat_type, type, plus_p3455044024723400733d_enat: (extended_enat > (extended_enat > extended_enat))). 159.44/70.59 thf(plus_plus_int_type, type, plus_plus_int: (int > (int > int))). 159.44/70.59 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 159.44/70.59 thf(plus_plus_num_type, type, plus_plus_num: (num > (num > num))). 159.44/70.59 thf(plus_plus_real_type, type, plus_plus_real: (real > (real > real))). 159.44/70.59 thf(sgn_sgn_int_type, type, sgn_sgn_int: (int > int)). 159.44/70.59 thf(sgn_sgn_real_type, type, sgn_sgn_real: (real > real)). 159.44/70.59 thf(times_3573771949741848930nteger_type, type, times_3573771949741848930nteger: (code_integer > (code_integer > code_integer))). 159.44/70.59 thf(times_times_complex_type, type, times_times_complex: (complex > (complex > complex))). 159.44/70.59 thf(times_7803423173614009249d_enat_type, type, times_7803423173614009249d_enat: (extended_enat > (extended_enat > extended_enat))). 159.44/70.59 thf(times_times_int_type, type, times_times_int: (int > (int > int))). 159.44/70.59 thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))). 159.44/70.59 thf(times_times_num_type, type, times_times_num: (num > (num > num))). 159.44/70.59 thf(times_times_real_type, type, times_times_real: (real > (real > real))). 159.44/70.59 thf(uminus1351360451143612070nteger_type, type, uminus1351360451143612070nteger: (code_integer > code_integer)). 159.44/70.59 thf(uminus1482373934393186551omplex_type, type, uminus1482373934393186551omplex: (complex > complex)). 159.44/70.59 thf(uminus_uminus_int_type, type, uminus_uminus_int: (int > int)). 159.44/70.59 thf(uminus_uminus_real_type, type, uminus_uminus_real: (real > real)). 159.44/70.59 thf(uminus5710092332889474511et_nat_type, type, uminus5710092332889474511et_nat: (set_nat > set_nat)). 159.44/70.59 thf(zero_z3403309356797280102nteger_type, type, zero_z3403309356797280102nteger: code_integer). 159.44/70.59 thf(zero_zero_complex_type, type, zero_zero_complex: complex). 159.44/70.59 thf(zero_z5237406670263579293d_enat_type, type, zero_z5237406670263579293d_enat: extended_enat). 159.44/70.59 thf(zero_zero_int_type, type, zero_zero_int: int). 159.44/70.59 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 159.44/70.59 thf(zero_zero_real_type, type, zero_zero_real: real). 159.44/70.59 thf(groups7501900531339628137nteger_type, type, groups7501900531339628137nteger: ((nat > code_integer) > (set_nat > code_integer))). 159.44/70.59 thf(groups2073611262835488442omplex_type, type, groups2073611262835488442omplex: ((nat > complex) > (set_nat > complex))). 159.44/70.59 thf(groups7108830773950497114d_enat_type, type, groups7108830773950497114d_enat: ((nat > extended_enat) > (set_nat > extended_enat))). 159.44/70.59 thf(groups3539618377306564664at_int_type, type, groups3539618377306564664at_int: ((nat > int) > (set_nat > int))). 159.44/70.59 thf(groups3542108847815614940at_nat_type, type, groups3542108847815614940at_nat: ((nat > nat) > (set_nat > nat))). 159.44/70.59 thf(groups6591440286371151544t_real_type, type, groups6591440286371151544t_real: ((nat > real) > (set_nat > real))). 159.44/70.59 thf(groups975429370522433651at_int_type, type, groups975429370522433651at_int: ((product_prod_nat_nat > int) > (set_Pr1261947904930325089at_nat > int))). 159.44/70.59 thf(groups4567486121110086003t_real_type, type, groups4567486121110086003t_real: ((product_prod_nat_nat > real) > (set_Pr1261947904930325089at_nat > real))). 159.44/70.59 thf(groups6464643781859351333omplex_type, type, groups6464643781859351333omplex: ((nat > complex) > (set_nat > complex))). 159.44/70.59 thf(groups7961826882256487087d_enat_type, type, groups7961826882256487087d_enat: ((nat > extended_enat) > (set_nat > extended_enat))). 159.44/70.59 thf(groups705719431365010083at_int_type, type, groups705719431365010083at_int: ((nat > int) > (set_nat > int))). 159.44/70.59 thf(groups708209901874060359at_nat_type, type, groups708209901874060359at_nat: ((nat > nat) > (set_nat > nat))). 159.44/70.59 thf(groups129246275422532515t_real_type, type, groups129246275422532515t_real: ((nat > real) > (set_nat > real))). 159.44/70.59 thf(groups9116527308978886569_o_int_type, type, groups9116527308978886569_o_int: (($o > int) > (int > (list_o > int)))). 159.44/70.59 thf(groups4561878855575611511st_nat_type, type, groups4561878855575611511st_nat: (list_nat > nat)). 159.44/70.59 thf(the_int_type, type, the_int: ((int > $o) > int)). 159.44/70.59 thf(the_real_type, type, the_real: ((real > $o) > real)). 159.44/70.59 thf(if_nat_nat_nat_type, type, if_nat_nat_nat: ($o > ((nat > (nat > nat)) > ((nat > (nat > nat)) > (nat > (nat > nat)))))). 159.44/70.59 thf(if_Code_integer_type, type, if_Code_integer: ($o > (code_integer > (code_integer > code_integer)))). 159.44/70.59 thf(if_complex_type, type, if_complex: ($o > (complex > (complex > complex)))). 159.44/70.59 thf(if_Extended_enat_type, type, if_Extended_enat: ($o > (extended_enat > (extended_enat > extended_enat)))). 159.44/70.59 thf(if_int_type, type, if_int: ($o > (int > (int > int)))). 159.44/70.59 thf(if_nat_type, type, if_nat: ($o > (nat > (nat > nat)))). 159.44/70.59 thf(if_option_nat_type, type, if_option_nat: ($o > (option_nat > (option_nat > option_nat)))). 159.44/70.59 thf(if_Pro6206227464963214023at_nat_type, type, if_Pro6206227464963214023at_nat: ($o > (product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)))). 159.44/70.59 thf(if_real_type, type, if_real: ($o > (real > (real > real)))). 159.44/70.59 thf(if_VEBT_VEBT_type, type, if_VEBT_VEBT: ($o > (vEBT_VEBT > (vEBT_VEBT > vEBT_VEBT)))). 159.44/70.59 thf(abs_Integ_type, type, abs_Integ: (product_prod_nat_nat > int)). 159.44/70.59 thf(nat2_type, type, nat2: (int > nat)). 159.44/70.59 thf(power_int_real_type, type, power_int_real: (real > (int > real))). 159.44/70.59 thf(ring_18347121197199848620nteger_type, type, ring_18347121197199848620nteger: (int > code_integer)). 159.44/70.59 thf(ring_17405671764205052669omplex_type, type, ring_17405671764205052669omplex: (int > complex)). 159.44/70.59 thf(ring_1_of_int_int_type, type, ring_1_of_int_int: (int > int)). 159.44/70.59 thf(ring_1_of_int_real_type, type, ring_1_of_int_real: (int > real)). 159.44/70.59 thf(semila1623282765462674594er_nat_type, type, semila1623282765462674594er_nat: ((nat > (nat > nat)) > (nat > ((nat > (nat > $o)) > ((nat > (nat > $o)) > $o))))). 159.44/70.59 thf(sup_sup_set_nat_type, type, sup_sup_set_nat: (set_nat > (set_nat > set_nat))). 159.44/70.59 thf(lattic8265883725875713057ax_nat_type, type, lattic8265883725875713057ax_nat: (set_nat > nat)). 159.44/70.59 thf(append_nat_type, type, append_nat: (list_nat > (list_nat > list_nat))). 159.44/70.59 thf(count_list_nat_type, type, count_list_nat: (list_nat > (nat > nat))). 159.44/70.59 thf(drop_nat_type, type, drop_nat: (nat > (list_nat > list_nat))). 159.44/70.59 thf(cons_nat_type, type, cons_nat: (nat > (list_nat > list_nat))). 159.44/70.59 thf(hd_nat_type, type, hd_nat: (list_nat > nat)). 159.44/70.59 thf(map_nat_nat_type, type, map_nat_nat: ((nat > nat) > (list_nat > list_nat))). 159.44/70.59 thf(set_nat2_type, type, set_nat2: (list_nat > set_nat)). 159.44/70.59 thf(set_VEBT_VEBT2_type, type, set_VEBT_VEBT2: (list_VEBT_VEBT > set_VEBT_VEBT)). 159.44/70.59 thf(tl_nat_type, type, tl_nat: (list_nat > list_nat)). 159.44/70.59 thf(list_update_o_type, type, list_update_o: (list_o > (nat > ($o > list_o)))). 159.44/70.59 thf(list_update_int_type, type, list_update_int: (list_int > (nat > (int > list_int)))). 159.44/70.59 thf(list_u1324408373059187874T_VEBT_type, type, list_u1324408373059187874T_VEBT: (list_VEBT_VEBT > (nat > (vEBT_VEBT > list_VEBT_VEBT)))). 159.44/70.59 thf(nth_o_type, type, nth_o: (list_o > (nat > $o))). 159.44/70.59 thf(nth_Code_integer_type, type, nth_Code_integer: (list_Code_integer > (nat > code_integer))). 159.44/70.59 thf(nth_int_type, type, nth_int: (list_int > (nat > int))). 159.44/70.59 thf(nth_nat_type, type, nth_nat: (list_nat > (nat > nat))). 159.44/70.59 thf(nth_num_type, type, nth_num: (list_num > (nat > num))). 159.44/70.59 thf(nth_Product_prod_o_o_type, type, nth_Product_prod_o_o: (list_P4002435161011370285od_o_o > (nat > product_prod_o_o))). 159.44/70.59 thf(nth_Pr1649062631805364268_o_int_type, type, nth_Pr1649062631805364268_o_int: (list_P3795440434834930179_o_int > (nat > product_prod_o_int))). 159.44/70.59 thf(nth_Pr6777367263587873994T_VEBT_type, type, nth_Pr6777367263587873994T_VEBT: (list_P7495141550334521929T_VEBT > (nat > produc2504756804600209347T_VEBT))). 159.44/70.59 thf(nth_Pr8522763379788166057eger_o_type, type, nth_Pr8522763379788166057eger_o: (list_P8526636022914148096eger_o > (nat > produc6271795597528267376eger_o))). 159.44/70.59 thf(nth_Pr6456567536196504476um_num_type, type, nth_Pr6456567536196504476um_num: (list_P3744719386663036955um_num > (nat > product_prod_num_num))). 159.44/70.59 thf(nth_Pr4606735188037164562VEBT_o_type, type, nth_Pr4606735188037164562VEBT_o: (list_P3126845725202233233VEBT_o > (nat > produc334124729049499915VEBT_o))). 159.44/70.59 thf(nth_Pr6837108013167703752BT_int_type, type, nth_Pr6837108013167703752BT_int: (list_P4547456442757143711BT_int > (nat > produc4894624898956917775BT_int))). 159.44/70.59 thf(nth_Pr1791586995822124652BT_nat_type, type, nth_Pr1791586995822124652BT_nat: (list_P7037539587688870467BT_nat > (nat > produc9072475918466114483BT_nat))). 159.44/70.59 thf(nth_Pr4953567300277697838T_VEBT_type, type, nth_Pr4953567300277697838T_VEBT: (list_P7413028617227757229T_VEBT > (nat > produc8243902056947475879T_VEBT))). 159.44/70.59 thf(nth_VEBT_VEBT_type, type, nth_VEBT_VEBT: (list_VEBT_VEBT > (nat > vEBT_VEBT))). 159.44/70.59 thf(product_o_o_type, type, product_o_o: (list_o > (list_o > list_P4002435161011370285od_o_o))). 159.44/70.59 thf(product_o_int_type, type, product_o_int: (list_o > (list_int > list_P3795440434834930179_o_int))). 159.44/70.59 thf(product_o_VEBT_VEBT_type, type, product_o_VEBT_VEBT: (list_o > (list_VEBT_VEBT > list_P7495141550334521929T_VEBT))). 159.44/70.59 thf(produc3607205314601156340eger_o_type, type, produc3607205314601156340eger_o: (list_Code_integer > (list_o > list_P8526636022914148096eger_o))). 159.44/70.59 thf(product_nat_o_type, type, product_nat_o: (list_nat > (list_o > list_P7333126701944960589_nat_o))). 159.44/70.59 thf(produc7156399406898700509T_VEBT_type, type, produc7156399406898700509T_VEBT: (list_nat > (list_VEBT_VEBT > list_P5647936690300460905T_VEBT))). 159.44/70.59 thf(product_num_num_type, type, product_num_num: (list_num > (list_num > list_P3744719386663036955um_num))). 159.44/70.59 thf(product_VEBT_VEBT_o_type, type, product_VEBT_VEBT_o: (list_VEBT_VEBT > (list_o > list_P3126845725202233233VEBT_o))). 159.44/70.59 thf(produc7292646706713671643BT_int_type, type, produc7292646706713671643BT_int: (list_VEBT_VEBT > (list_int > list_P4547456442757143711BT_int))). 159.44/70.59 thf(produc7295137177222721919BT_nat_type, type, produc7295137177222721919BT_nat: (list_VEBT_VEBT > (list_nat > list_P7037539587688870467BT_nat))). 159.44/70.59 thf(produc4743750530478302277T_VEBT_type, type, produc4743750530478302277T_VEBT: (list_VEBT_VEBT > (list_VEBT_VEBT > list_P7413028617227757229T_VEBT))). 159.44/70.59 thf(replicate_VEBT_VEBT_type, type, replicate_VEBT_VEBT: (nat > (vEBT_VEBT > list_VEBT_VEBT))). 159.44/70.59 thf(take_nat_type, type, take_nat: (nat > (list_nat > list_nat))). 159.44/70.59 thf(upt_type, type, upt: (nat > (nat > list_nat))). 159.44/70.59 thf(suc_type, type, suc: (nat > nat)). 159.44/70.59 thf(compow_nat_nat_type, type, compow_nat_nat: (nat > ((nat > nat) > (nat > nat)))). 159.44/70.59 thf(case_nat_o_type, type, case_nat_o: ($o > ((nat > $o) > (nat > $o)))). 159.44/70.59 thf(case_nat_nat_type, type, case_nat_nat: (nat > ((nat > nat) > (nat > nat)))). 159.44/70.59 thf(semiri4939895301339042750nteger_type, type, semiri4939895301339042750nteger: (nat > code_integer)). 159.44/70.59 thf(semiri8010041392384452111omplex_type, type, semiri8010041392384452111omplex: (nat > complex)). 159.44/70.59 thf(semiri4216267220026989637d_enat_type, type, semiri4216267220026989637d_enat: (nat > extended_enat)). 159.44/70.59 thf(semiri1314217659103216013at_int_type, type, semiri1314217659103216013at_int: (nat > int)). 159.44/70.59 thf(semiri1316708129612266289at_nat_type, type, semiri1316708129612266289at_nat: (nat > nat)). 159.44/70.59 thf(semiri5074537144036343181t_real_type, type, semiri5074537144036343181t_real: (nat > real)). 159.44/70.59 thf(semiri8422978514062236437ux_nat_type, type, semiri8422978514062236437ux_nat: ((nat > nat) > (nat > (nat > nat)))). 159.44/70.59 thf(size_size_list_o_type, type, size_size_list_o: (list_o > nat)). 159.44/70.59 thf(size_s3445333598471063425nteger_type, type, size_s3445333598471063425nteger: (list_Code_integer > nat)). 159.44/70.59 thf(size_size_list_int_type, type, size_size_list_int: (list_int > nat)). 159.44/70.59 thf(size_size_list_nat_type, type, size_size_list_nat: (list_nat > nat)). 159.44/70.59 thf(size_size_list_num_type, type, size_size_list_num: (list_num > nat)). 159.44/70.59 thf(size_s1515746228057227161od_o_o_type, type, size_s1515746228057227161od_o_o: (list_P4002435161011370285od_o_o > nat)). 159.44/70.59 thf(size_s2953683556165314199_o_int_type, type, size_s2953683556165314199_o_int: (list_P3795440434834930179_o_int > nat)). 159.44/70.59 thf(size_s4313452262239582901T_VEBT_type, type, size_s4313452262239582901T_VEBT: (list_P7495141550334521929T_VEBT > nat)). 159.44/70.59 thf(size_s6491369823275344609_nat_o_type, type, size_s6491369823275344609_nat_o: (list_P7333126701944960589_nat_o > nat)). 159.44/70.59 thf(size_s4762443039079500285T_VEBT_type, type, size_s4762443039079500285T_VEBT: (list_P5647936690300460905T_VEBT > nat)). 159.44/70.59 thf(size_s9168528473962070013VEBT_o_type, type, size_s9168528473962070013VEBT_o: (list_P3126845725202233233VEBT_o > nat)). 159.44/70.59 thf(size_s3661962791536183091BT_int_type, type, size_s3661962791536183091BT_int: (list_P4547456442757143711BT_int > nat)). 159.44/70.59 thf(size_s7466405169056248089T_VEBT_type, type, size_s7466405169056248089T_VEBT: (list_P7413028617227757229T_VEBT > nat)). 159.44/70.59 thf(size_s6755466524823107622T_VEBT_type, type, size_s6755466524823107622T_VEBT: (list_VEBT_VEBT > nat)). 159.44/70.59 thf(size_size_num_type, type, size_size_num: (num > nat)). 159.44/70.59 thf(size_size_option_nat_type, type, size_size_option_nat: (option_nat > nat)). 159.44/70.59 thf(size_s170228958280169651at_nat_type, type, size_s170228958280169651at_nat: (option4927543243414619207at_nat > nat)). 159.44/70.59 thf(nat_prod_decode_aux_type, type, nat_prod_decode_aux: (nat > (nat > product_prod_nat_nat))). 159.44/70.59 thf(nat_prod_encode_type, type, nat_prod_encode: (product_prod_nat_nat > nat)). 159.44/70.59 thf(nat_set_decode_type, type, nat_set_decode: (nat > set_nat)). 159.44/70.59 thf(nat_set_encode_type, type, nat_set_encode: (set_nat > nat)). 159.44/70.59 thf(nat_triangle_type, type, nat_triangle: (nat > nat)). 159.44/70.59 thf(root_type, type, root: (nat > (real > real))). 159.44/70.59 thf(sqrt_type, type, sqrt: (real > real)). 159.44/70.59 thf(bitM_type, type, bitM: (num > num)). 159.44/70.59 thf(inc_type, type, inc: (num > num)). 159.44/70.59 thf(neg_nu8804712462038260780nteger_type, type, neg_nu8804712462038260780nteger: (code_integer > code_integer)). 159.44/70.59 thf(neg_nu7009210354673126013omplex_type, type, neg_nu7009210354673126013omplex: (complex > complex)). 159.44/70.59 thf(neg_numeral_dbl_int_type, type, neg_numeral_dbl_int: (int > int)). 159.44/70.59 thf(neg_numeral_dbl_real_type, type, neg_numeral_dbl_real: (real > real)). 159.44/70.59 thf(neg_nu7757733837767384882nteger_type, type, neg_nu7757733837767384882nteger: (code_integer > code_integer)). 159.44/70.59 thf(neg_nu6511756317524482435omplex_type, type, neg_nu6511756317524482435omplex: (complex > complex)). 159.44/70.59 thf(neg_nu3811975205180677377ec_int_type, type, neg_nu3811975205180677377ec_int: (int > int)). 159.44/70.59 thf(neg_nu6075765906172075777c_real_type, type, neg_nu6075765906172075777c_real: (real > real)). 159.44/70.59 thf(neg_nu8557863876264182079omplex_type, type, neg_nu8557863876264182079omplex: (complex > complex)). 159.44/70.59 thf(neg_nu5851722552734809277nc_int_type, type, neg_nu5851722552734809277nc_int: (int > int)). 159.44/70.59 thf(neg_nu8295874005876285629c_real_type, type, neg_nu8295874005876285629c_real: (real > real)). 159.44/70.59 thf(neg_numeral_sub_int_type, type, neg_numeral_sub_int: (num > (num > int))). 159.44/70.59 thf(bit0_type, type, bit0: (num > num)). 159.44/70.59 thf(bit1_type, type, bit1: (num > num)). 159.44/70.59 thf(one_type, type, one: num). 159.44/70.59 thf(size_num_type, type, size_num: (num > nat)). 159.44/70.59 thf(num_of_nat_type, type, num_of_nat: (nat > num)). 159.44/70.59 thf(numera6620942414471956472nteger_type, type, numera6620942414471956472nteger: (num > code_integer)). 159.44/70.59 thf(numera6690914467698888265omplex_type, type, numera6690914467698888265omplex: (num > complex)). 159.44/70.59 thf(numera1916890842035813515d_enat_type, type, numera1916890842035813515d_enat: (num > extended_enat)). 159.44/70.59 thf(numeral_numeral_int_type, type, numeral_numeral_int: (num > int)). 159.44/70.59 thf(numeral_numeral_nat_type, type, numeral_numeral_nat: (num > nat)). 159.44/70.59 thf(numeral_numeral_real_type, type, numeral_numeral_real: (num > real)). 159.44/70.59 thf(pow_type, type, pow: (num > (num > num))). 159.44/70.59 thf(pred_numeral_type, type, pred_numeral: (num > nat)). 159.44/70.59 thf(sqr_type, type, sqr: (num > num)). 159.44/70.59 thf(none_nat_type, type, none_nat: option_nat). 159.44/70.59 thf(none_P5556105721700978146at_nat_type, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat). 159.44/70.59 thf(some_nat_type, type, some_nat: (nat > option_nat)). 159.44/70.59 thf(some_P7363390416028606310at_nat_type, type, some_P7363390416028606310at_nat: (product_prod_nat_nat > option4927543243414619207at_nat)). 159.44/70.59 thf(case_o184042715313410164at_nat_type, type, case_o184042715313410164at_nat: ($o > ((product_prod_nat_nat > $o) > (option4927543243414619207at_nat > $o)))). 159.44/70.59 thf(size_option_nat_type, type, size_option_nat: ((nat > nat) > (option_nat > nat))). 159.44/70.59 thf(size_o8335143837870341156at_nat_type, type, size_o8335143837870341156at_nat: ((product_prod_nat_nat > nat) > (option4927543243414619207at_nat > nat))). 159.44/70.59 thf(the_nat_type, type, the_nat: (option_nat > nat)). 159.44/70.59 thf(bot_bot_nat_type, type, bot_bot_nat: nat). 159.44/70.59 thf(bot_bot_set_nat_type, type, bot_bot_set_nat: set_nat). 159.44/70.59 thf(ord_le6747313008572928689nteger_type, type, ord_le6747313008572928689nteger: (code_integer > (code_integer > $o))). 159.44/70.59 thf(ord_le72135733267957522d_enat_type, type, ord_le72135733267957522d_enat: (extended_enat > (extended_enat > $o))). 159.44/70.59 thf(ord_less_int_type, type, ord_less_int: (int > (int > $o))). 159.44/70.59 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 159.44/70.59 thf(ord_less_num_type, type, ord_less_num: (num > (num > $o))). 159.44/70.59 thf(ord_less_real_type, type, ord_less_real: (real > (real > $o))). 159.44/70.59 thf(ord_le3102999989581377725nteger_type, type, ord_le3102999989581377725nteger: (code_integer > (code_integer > $o))). 159.44/70.59 thf(ord_le2932123472753598470d_enat_type, type, ord_le2932123472753598470d_enat: (extended_enat > (extended_enat > $o))). 159.44/70.59 thf(ord_less_eq_int_type, type, ord_less_eq_int: (int > (int > $o))). 159.44/70.59 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 159.44/70.59 thf(ord_less_eq_num_type, type, ord_less_eq_num: (num > (num > $o))). 159.44/70.59 thf(ord_less_eq_real_type, type, ord_less_eq_real: (real > (real > $o))). 159.44/70.59 thf(ord_less_eq_set_nat_type, type, ord_less_eq_set_nat: (set_nat > (set_nat > $o))). 159.44/70.59 thf(ord_le4337996190870823476T_VEBT_type, type, ord_le4337996190870823476T_VEBT: (set_VEBT_VEBT > (set_VEBT_VEBT > $o))). 159.44/70.59 thf(ord_max_int_type, type, ord_max_int: (int > (int > int))). 159.44/70.59 thf(ord_max_nat_type, type, ord_max_nat: (nat > (nat > nat))). 159.44/70.59 thf(ord_min_nat_type, type, ord_min_nat: (nat > (nat > nat))). 159.44/70.59 thf(order_mono_nat_nat_type, type, order_mono_nat_nat: ((nat > nat) > $o)). 159.44/70.59 thf(top_top_set_o_type, type, top_top_set_o: set_o). 159.44/70.59 thf(top_top_set_char_type, type, top_top_set_char: set_char). 159.44/70.59 thf(power_8256067586552552935nteger_type, type, power_8256067586552552935nteger: (code_integer > (nat > code_integer))). 159.44/70.59 thf(power_power_complex_type, type, power_power_complex: (complex > (nat > complex))). 159.44/70.59 thf(power_8040749407984259932d_enat_type, type, power_8040749407984259932d_enat: (extended_enat > (nat > extended_enat))). 159.44/70.59 thf(power_power_int_type, type, power_power_int: (int > (nat > int))). 159.44/70.59 thf(power_power_nat_type, type, power_power_nat: (nat > (nat > nat))). 159.44/70.59 thf(power_power_real_type, type, power_power_real: (real > (nat > real))). 159.44/70.59 thf(product_Pair_o_o_type, type, product_Pair_o_o: ($o > ($o > product_prod_o_o))). 159.44/70.59 thf(product_Pair_o_int_type, type, product_Pair_o_int: ($o > (int > product_prod_o_int))). 159.44/70.59 thf(produc2982872950893828659T_VEBT_type, type, produc2982872950893828659T_VEBT: ($o > (vEBT_VEBT > produc2504756804600209347T_VEBT))). 159.44/70.59 thf(produc6677183202524767010eger_o_type, type, produc6677183202524767010eger_o: (code_integer > ($o > produc6271795597528267376eger_o))). 159.44/70.59 thf(product_Pair_nat_nat_type, type, product_Pair_nat_nat: (nat > (nat > product_prod_nat_nat))). 159.44/70.59 thf(product_Pair_num_num_type, type, product_Pair_num_num: (num > (num > product_prod_num_num))). 159.44/70.59 thf(produc8721562602347293563VEBT_o_type, type, produc8721562602347293563VEBT_o: (vEBT_VEBT > ($o > produc334124729049499915VEBT_o))). 159.44/70.59 thf(produc736041933913180425BT_int_type, type, produc736041933913180425BT_int: (vEBT_VEBT > (int > produc4894624898956917775BT_int))). 159.44/70.59 thf(produc738532404422230701BT_nat_type, type, produc738532404422230701BT_nat: (vEBT_VEBT > (nat > produc9072475918466114483BT_nat))). 159.44/70.59 thf(produc537772716801021591T_VEBT_type, type, produc537772716801021591T_VEBT: (vEBT_VEBT > (vEBT_VEBT > produc8243902056947475879T_VEBT))). 159.44/70.59 thf(produc6081775807080527818_nat_o_type, type, produc6081775807080527818_nat_o: ((nat > (nat > $o)) > (product_prod_nat_nat > $o))). 159.44/70.59 thf(produc1830744345554046123nteger_type, type, produc1830744345554046123nteger: ((nat > (nat > code_integer)) > (product_prod_nat_nat > code_integer))). 159.44/70.59 thf(produc1917071388513777916omplex_type, type, produc1917071388513777916omplex: ((nat > (nat > complex)) > (product_prod_nat_nat > complex))). 159.44/70.59 thf(produc2676513652042109336d_enat_type, type, produc2676513652042109336d_enat: ((nat > (nat > extended_enat)) > (product_prod_nat_nat > extended_enat))). 159.44/70.59 thf(produc6840382203811409530at_int_type, type, produc6840382203811409530at_int: ((nat > (nat > int)) > (product_prod_nat_nat > int))). 159.44/70.59 thf(produc6842872674320459806at_nat_type, type, produc6842872674320459806at_nat: ((nat > (nat > nat)) > (product_prod_nat_nat > nat))). 159.44/70.59 thf(produc2626176000494625587at_nat_type, type, produc2626176000494625587at_nat: ((nat > (nat > product_prod_nat_nat)) > (product_prod_nat_nat > product_prod_nat_nat))). 159.44/70.59 thf(produc1703576794950452218t_real_type, type, produc1703576794950452218t_real: ((nat > (nat > real)) > (product_prod_nat_nat > real))). 159.44/70.59 thf(product_fst_nat_nat_type, type, product_fst_nat_nat: (product_prod_nat_nat > nat)). 159.44/70.59 thf(product_snd_nat_nat_type, type, product_snd_nat_nat: (product_prod_nat_nat > nat)). 159.44/70.59 thf(real_V1022390504157884413omplex_type, type, real_V1022390504157884413omplex: (complex > real)). 159.44/70.59 thf(real_V7735802525324610683m_real_type, type, real_V7735802525324610683m_real: (real > real)). 159.44/70.59 thf(real_V4546457046886955230omplex_type, type, real_V4546457046886955230omplex: (real > complex)). 159.44/70.59 thf(real_V1803761363581548252l_real_type, type, real_V1803761363581548252l_real: (real > real)). 159.44/70.59 thf(real_V2046097035970521341omplex_type, type, real_V2046097035970521341omplex: (real > (complex > complex))). 159.44/70.59 thf(real_V1485227260804924795R_real_type, type, real_V1485227260804924795R_real: (real > (real > real))). 159.44/70.59 thf(divide6298287555418463151nteger_type, type, divide6298287555418463151nteger: (code_integer > (code_integer > code_integer))). 159.44/70.59 thf(divide1717551699836669952omplex_type, type, divide1717551699836669952omplex: (complex > (complex > complex))). 159.44/70.59 thf(divide_divide_int_type, type, divide_divide_int: (int > (int > int))). 159.44/70.59 thf(divide_divide_nat_type, type, divide_divide_nat: (nat > (nat > nat))). 159.44/70.59 thf(divide_divide_real_type, type, divide_divide_real: (real > (real > real))). 159.44/70.59 thf(dvd_dvd_Code_integer_type, type, dvd_dvd_Code_integer: (code_integer > (code_integer > $o))). 159.44/70.59 thf(dvd_dvd_complex_type, type, dvd_dvd_complex: (complex > (complex > $o))). 159.44/70.59 thf(dvd_dv3785147216227455552d_enat_type, type, dvd_dv3785147216227455552d_enat: (extended_enat > (extended_enat > $o))). 159.44/70.59 thf(dvd_dvd_int_type, type, dvd_dvd_int: (int > (int > $o))). 159.44/70.59 thf(dvd_dvd_nat_type, type, dvd_dvd_nat: (nat > (nat > $o))). 159.44/70.59 thf(dvd_dvd_real_type, type, dvd_dvd_real: (real > (real > $o))). 159.44/70.59 thf(modulo364778990260209775nteger_type, type, modulo364778990260209775nteger: (code_integer > (code_integer > code_integer))). 159.44/70.59 thf(modulo_modulo_int_type, type, modulo_modulo_int: (int > (int > int))). 159.44/70.59 thf(modulo_modulo_nat_type, type, modulo_modulo_nat: (nat > (nat > nat))). 159.44/70.59 thf(zero_n356916108424825756nteger_type, type, zero_n356916108424825756nteger: ($o > code_integer)). 159.44/70.59 thf(zero_n2684676970156552555ol_int_type, type, zero_n2684676970156552555ol_int: ($o > int)). 159.44/70.59 thf(zero_n2687167440665602831ol_nat_type, type, zero_n2687167440665602831ol_nat: ($o > nat)). 159.44/70.59 thf(suminf_complex_type, type, suminf_complex: ((nat > complex) > complex)). 159.44/70.59 thf(suminf_nat_type, type, suminf_nat: ((nat > nat) > nat)). 159.44/70.59 thf(suminf_real_type, type, suminf_real: ((nat > real) > real)). 159.44/70.59 thf(summable_nat_type, type, summable_nat: ((nat > nat) > $o)). 159.44/70.59 thf(summable_real_type, type, summable_real: ((nat > real) > $o)). 159.44/70.59 thf(sums_complex_type, type, sums_complex: ((nat > complex) > (complex > $o))). 159.44/70.59 thf(sums_nat_type, type, sums_nat: ((nat > nat) > (nat > $o))). 159.44/70.59 thf(sums_real_type, type, sums_real: ((nat > real) > (real > $o))). 159.44/70.59 thf(collect_nat_type, type, collect_nat: ((nat > $o) > set_nat)). 159.44/70.59 thf(image_nat_nat_type, type, image_nat_nat: ((nat > nat) > (set_nat > set_nat))). 159.44/70.59 thf(image_nat_char_type, type, image_nat_char: ((nat > char) > (set_nat > set_char))). 159.44/70.59 thf(image_char_nat_type, type, image_char_nat: ((char > nat) > (set_char > set_nat))). 159.44/70.59 thf(insert_nat_type, type, insert_nat: (nat > (set_nat > set_nat))). 159.44/70.59 thf(vimage_nat_nat_type, type, vimage_nat_nat: ((nat > nat) > (set_nat > set_nat))). 159.44/70.59 thf(set_fo1517530859248394432omplex_type, type, set_fo1517530859248394432omplex: ((nat > (complex > complex)) > (nat > (nat > (complex > complex))))). 159.44/70.59 thf(set_fo2538466533108834004d_enat_type, type, set_fo2538466533108834004d_enat: ((nat > (extended_enat > extended_enat)) > (nat > (nat > (extended_enat > extended_enat))))). 159.44/70.59 thf(set_fo2584398358068434914at_nat_type, type, set_fo2584398358068434914at_nat: ((nat > (nat > nat)) > (nat > (nat > (nat > nat))))). 159.44/70.59 thf(set_fo3111899725591712190t_real_type, type, set_fo3111899725591712190t_real: ((nat > (real > real)) > (nat > (nat > (real > real))))). 159.44/70.59 thf(set_or1269000886237332187st_nat_type, type, set_or1269000886237332187st_nat: (nat > (nat > set_nat))). 159.44/70.59 thf(set_or4665077453230672383an_nat_type, type, set_or4665077453230672383an_nat: (nat > (nat > set_nat))). 159.44/70.59 thf(set_ord_atMost_nat_type, type, set_ord_atMost_nat: (nat > set_nat)). 159.44/70.59 thf(set_ord_lessThan_nat_type, type, set_ord_lessThan_nat: (nat > set_nat)). 159.44/70.59 thf(ascii_of_type, type, ascii_of: (char > char)). 159.44/70.59 thf(comm_s629917340098488124ar_nat_type, type, comm_s629917340098488124ar_nat: (char > nat)). 159.44/70.59 thf(unique3096191561947761185of_nat_type, type, unique3096191561947761185of_nat: (nat > char)). 159.44/70.59 thf(topolo6980174941875973593q_real_type, type, topolo6980174941875973593q_real: ((nat > real) > $o)). 159.44/70.59 thf(topolo2815343760600316023s_real_type, type, topolo2815343760600316023s_real: (real > filter_real)). 159.44/70.59 thf(topolo4055970368930404560y_real_type, type, topolo4055970368930404560y_real: ((nat > real) > $o)). 159.44/70.59 thf(arccos_type, type, arccos: (real > real)). 159.44/70.59 thf(arcosh_real_type, type, arcosh_real: (real > real)). 159.44/70.59 thf(arcsin_type, type, arcsin: (real > real)). 159.44/70.59 thf(arctan_type, type, arctan: (real > real)). 159.44/70.59 thf(arsinh_real_type, type, arsinh_real: (real > real)). 159.44/70.59 thf(artanh_real_type, type, artanh_real: (real > real)). 159.44/70.59 thf(cos_complex_type, type, cos_complex: (complex > complex)). 159.44/70.59 thf(cos_real_type, type, cos_real: (real > real)). 159.44/70.59 thf(cos_coeff_type, type, cos_coeff: (nat > real)). 159.44/70.59 thf(cosh_complex_type, type, cosh_complex: (complex > complex)). 159.44/70.59 thf(cosh_real_type, type, cosh_real: (real > real)). 159.44/70.59 thf(cot_real_type, type, cot_real: (real > real)). 159.44/70.59 thf(diffs_real_type, type, diffs_real: ((nat > real) > (nat > real))). 159.44/70.59 thf(exp_complex_type, type, exp_complex: (complex > complex)). 159.44/70.59 thf(exp_real_type, type, exp_real: (real > real)). 159.44/70.59 thf(ln_ln_real_type, type, ln_ln_real: (real > real)). 159.44/70.59 thf(log_type, type, log: (real > (real > real))). 159.44/70.59 thf(pi_type, type, pi: real). 159.44/70.59 thf(powr_real_type, type, powr_real: (real > (real > real))). 159.44/70.59 thf(sin_complex_type, type, sin_complex: (complex > complex)). 159.44/70.59 thf(sin_real_type, type, sin_real: (real > real)). 159.44/70.59 thf(sin_coeff_type, type, sin_coeff: (nat > real)). 159.44/70.59 thf(sinh_complex_type, type, sinh_complex: (complex > complex)). 159.44/70.59 thf(sinh_real_type, type, sinh_real: (real > real)). 159.44/70.59 thf(tan_complex_type, type, tan_complex: (complex > complex)). 159.44/70.59 thf(tan_real_type, type, tan_real: (real > real)). 159.44/70.59 thf(tanh_real_type, type, tanh_real: (real > real)). 159.44/70.59 thf(vEBT_Leaf_type, type, vEBT_Leaf: ($o > ($o > vEBT_VEBT))). 159.44/70.59 thf(vEBT_Node_type, type, vEBT_Node: (option4927543243414619207at_nat > (nat > (list_VEBT_VEBT > (vEBT_VEBT > vEBT_VEBT))))). 159.44/70.59 thf(vEBT_V8194947554948674370ptions_type, type, vEBT_V8194947554948674370ptions: (vEBT_VEBT > (nat > $o))). 159.44/70.59 thf(vEBT_VEBT_high_type, type, vEBT_VEBT_high: (nat > (nat > nat))). 159.44/70.59 thf(vEBT_V5917875025757280293ildren_type, type, vEBT_V5917875025757280293ildren: (nat > (list_VEBT_VEBT > (nat > $o)))). 159.44/70.59 thf(vEBT_VEBT_low_type, type, vEBT_VEBT_low: (nat > (nat > nat))). 159.44/70.59 thf(vEBT_VEBT_membermima_type, type, vEBT_VEBT_membermima: (vEBT_VEBT > (nat > $o))). 159.44/70.59 thf(vEBT_V4351362008482014158ma_rel_type, type, vEBT_V4351362008482014158ma_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 159.44/70.59 thf(vEBT_V5719532721284313246member_type, type, vEBT_V5719532721284313246member: (vEBT_VEBT > (nat > $o))). 159.44/70.59 thf(vEBT_V5765760719290551771er_rel_type, type, vEBT_V5765760719290551771er_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 159.44/70.59 thf(vEBT_VEBT_valid_type, type, vEBT_VEBT_valid: (vEBT_VEBT > (nat > $o))). 159.44/70.59 thf(vEBT_VEBT_valid_rel_type, type, vEBT_VEBT_valid_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 159.44/70.59 thf(vEBT_invar_vebt_type, type, vEBT_invar_vebt: (vEBT_VEBT > (nat > $o))). 159.44/70.59 thf(vEBT_set_vebt_type, type, vEBT_set_vebt: (vEBT_VEBT > set_nat)). 159.44/70.59 thf(vEBT_vebt_buildup_type, type, vEBT_vebt_buildup: (nat > vEBT_VEBT)). 159.44/70.59 thf(vEBT_v4011308405150292612up_rel_type, type, vEBT_v4011308405150292612up_rel: (nat > (nat > $o))). 159.44/70.59 thf(vEBT_vebt_delete_type, type, vEBT_vebt_delete: (vEBT_VEBT > (nat > vEBT_VEBT))). 159.44/70.59 thf(vEBT_vebt_delete_rel_type, type, vEBT_vebt_delete_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 159.44/70.59 thf(vEBT_vebt_insert_type, type, vEBT_vebt_insert: (vEBT_VEBT > (nat > vEBT_VEBT))). 159.44/70.59 thf(vEBT_vebt_insert_rel_type, type, vEBT_vebt_insert_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 159.44/70.59 thf(vEBT_VEBT_bit_concat_type, type, vEBT_VEBT_bit_concat: (nat > (nat > (nat > nat)))). 159.44/70.59 thf(vEBT_VEBT_minNull_type, type, vEBT_VEBT_minNull: (vEBT_VEBT > $o)). 159.44/70.59 thf(vEBT_V6963167321098673237ll_rel_type, type, vEBT_V6963167321098673237ll_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 159.44/70.59 thf(vEBT_VEBT_set_vebt_type, type, vEBT_VEBT_set_vebt: (vEBT_VEBT > set_nat)). 159.44/70.59 thf(vEBT_vebt_member_type, type, vEBT_vebt_member: (vEBT_VEBT > (nat > $o))). 159.44/70.59 thf(vEBT_vebt_member_rel_type, type, vEBT_vebt_member_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 159.44/70.59 thf(vEBT_VEBT_add_type, type, vEBT_VEBT_add: (option_nat > (option_nat > option_nat))). 159.44/70.59 thf(vEBT_VEBT_greater_type, type, vEBT_VEBT_greater: (option_nat > (option_nat > $o))). 159.44/70.59 thf(vEBT_VEBT_less_type, type, vEBT_VEBT_less: (option_nat > (option_nat > $o))). 159.44/70.59 thf(vEBT_VEBT_lesseq_type, type, vEBT_VEBT_lesseq: (option_nat > (option_nat > $o))). 159.44/70.59 thf(vEBT_VEBT_mul_type, type, vEBT_VEBT_mul: (option_nat > (option_nat > option_nat))). 159.44/70.59 thf(vEBT_V4262088993061758097ft_nat_type, type, vEBT_V4262088993061758097ft_nat: ((nat > (nat > nat)) > (option_nat > (option_nat > option_nat)))). 159.44/70.59 thf(vEBT_VEBT_power_type, type, vEBT_VEBT_power: (option_nat > (option_nat > option_nat))). 159.44/70.59 thf(vEBT_vebt_maxt_type, type, vEBT_vebt_maxt: (vEBT_VEBT > option_nat)). 159.44/70.59 thf(vEBT_vebt_maxt_rel_type, type, vEBT_vebt_maxt_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 159.44/70.59 thf(vEBT_vebt_mint_type, type, vEBT_vebt_mint: (vEBT_VEBT > option_nat)). 159.44/70.59 thf(vEBT_vebt_mint_rel_type, type, vEBT_vebt_mint_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 159.44/70.59 thf(vEBT_is_pred_in_set_type, type, vEBT_is_pred_in_set: (set_nat > (nat > (nat > $o)))). 159.44/70.59 thf(vEBT_vebt_pred_type, type, vEBT_vebt_pred: (vEBT_VEBT > (nat > option_nat))). 159.44/70.59 thf(vEBT_vebt_pred_rel_type, type, vEBT_vebt_pred_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 159.44/70.59 thf(vEBT_is_succ_in_set_type, type, vEBT_is_succ_in_set: (set_nat > (nat > (nat > $o)))). 159.44/70.59 thf(vEBT_vebt_succ_type, type, vEBT_vebt_succ: (vEBT_VEBT > (nat > option_nat))). 159.44/70.59 thf(vEBT_vebt_succ_rel_type, type, vEBT_vebt_succ_rel: (produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o))). 159.44/70.59 thf(accp_nat_type, type, accp_nat: ((nat > (nat > $o)) > (nat > $o))). 159.44/70.59 thf(accp_P2887432264394892906BT_nat_type, type, accp_P2887432264394892906BT_nat: ((produc9072475918466114483BT_nat > (produc9072475918466114483BT_nat > $o)) > (produc9072475918466114483BT_nat > $o))). 159.44/70.59 thf(accp_VEBT_VEBT_type, type, accp_VEBT_VEBT: ((vEBT_VEBT > (vEBT_VEBT > $o)) > (vEBT_VEBT > $o))). 159.44/70.59 thf(member_list_o_type, type, member_list_o: (list_o > (set_list_o > $o))). 159.44/70.59 thf(member_list_int_type, type, member_list_int: (list_int > (set_list_int > $o))). 159.44/70.59 thf(member2936631157270082147T_VEBT_type, type, member2936631157270082147T_VEBT: (list_VEBT_VEBT > (set_list_VEBT_VEBT > $o))). 159.44/70.59 thf(member_nat_type, type, member_nat: (nat > (set_nat > $o))). 159.44/70.59 thf(member8440522571783428010at_nat_type, type, member8440522571783428010at_nat: (product_prod_nat_nat > (set_Pr1261947904930325089at_nat > $o))). 159.44/70.59 thf(member_VEBT_VEBT_type, type, member_VEBT_VEBT: (vEBT_VEBT > (set_VEBT_VEBT > $o))). 159.44/70.59 thf(deg_type, type, deg: nat). 159.44/70.59 thf(lx_type, type, lx: nat). 159.44/70.59 thf(m_type, type, m: nat). 159.44/70.59 thf(ma_type, type, ma: nat). 159.44/70.59 thf(mi_type, type, mi: nat). 159.44/70.59 thf(na_type, type, na: nat). 159.44/70.59 thf(summary_type, type, summary: vEBT_VEBT). 159.44/70.59 thf(summin_type, type, summin: nat). 159.44/70.59 thf(treeList_type, type, treeList: list_VEBT_VEBT). 159.44/70.59 thf(xa_type, type, xa: nat). 159.44/70.59 thf(1765,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/sandbox/benchmark/theBenchmark.p',fact_5744_arctan__double)). 159.44/70.59 thf(13950,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)],[1765])). 159.44/70.59 thf(4604,axiom,((! [A:vEBT_VEBT]: (((vEBT_vebt_mint @ A) = none_nat) <= (vEBT_VEBT_minNull @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_minNullmin)). 159.44/70.59 thf(23162,plain,((! [A:vEBT_VEBT]: (((vEBT_vebt_mint @ A) = none_nat) | ~ (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4604])). 159.44/70.59 thf(3087,axiom,((! [A:int,B:int]: (((ord_less_int @ A @ B) | (A = B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3263_order__le__imp__less__or__eq)). 159.44/70.59 thf(18180,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)],[3087])). 159.44/70.59 thf(6909,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/sandbox/benchmark/theBenchmark.p',fact_5651_abs__square__less__1)). 159.44/70.59 thf(31885,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)],[6909])). 159.44/70.59 thf(7275,axiom,((! [A:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1952_not__numeral__le__zero)). 159.44/70.59 thf(33394,plain,((! [A:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7275])). 159.44/70.59 thf(6855,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/sandbox/benchmark/theBenchmark.p',fact_7778_sum__telescope_H_H)). 159.44/70.59 thf(31720,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)],[6855])). 159.44/70.59 thf(2088,axiom,((! [A:num,B:num]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4817_neg__numeral__le__iff)). 159.44/70.59 thf(14977,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)],[2088])). 159.44/70.59 thf(1127,axiom,((! [A:int,B:int]: ((A != B) => ((ord_less_int @ B @ A) <= (~ (ord_less_int @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1094_linorder__neqE__linordered__idom)). 159.44/70.59 thf(11866,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)],[1127])). 159.44/70.59 thf(1434,axiom,((bit_se2923211474154528505it_int = (^ [A:nat,B:int]: (modulo_modulo_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5282_take__bit__int__def)). 159.44/70.59 thf(12928,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)],[1434])). 159.44/70.59 thf(4162,axiom,((! [A:complex,B:nat]: ((exp_complex @ (times_times_complex @ A @ (semiri8010041392384452111omplex @ B))) = (power_power_complex @ (exp_complex @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6732_exp__of__nat2__mult)). 159.44/70.59 thf(21605,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)],[4162])). 159.44/70.59 thf(1667,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/sandbox/benchmark/theBenchmark.p',fact_5581_abs__triangle__ineq4)). 159.44/70.59 thf(13650,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)],[1667])). 159.44/70.59 thf(5276,axiom,((! [A:(nat > nat),B:nat]: (((A @ zero_zero_nat) = zero_zero_nat) => ((groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7654_sum__shift__lb__Suc0__0)). 159.44/70.59 thf(25521,plain,((! [A:(nat > nat),B:nat]: (((A @ zero_zero_nat) = zero_zero_nat) => ((groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5276])). 159.44/70.59 thf(4947,axiom,(((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4849_diff__numeral__special_I10_J)). 159.44/70.59 thf(24338,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)],[4947])). 159.44/70.59 thf(2339,axiom,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2883_order__less__irrefl)). 159.44/70.59 thf(15767,plain,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2339])). 159.44/70.59 thf(7497,axiom,((! [A:nat]: ((~ (! [B:nat]: (A != (suc @ B)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4263_list__decode_Ocases)). 159.44/70.59 thf(34178,plain,((! [A:nat]: (~ (! [B:nat]: ~ (A = (suc @ B))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7497])). 159.44/70.59 thf(5612,axiom,((! [A:num,B:(nat > num),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ A @ (B @ D)))) <= (ord_less_eq_num @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2685_order__subst1)). 159.44/70.59 thf(26820,plain,((! [A:num,B:(nat > num),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ A @ (B @ D)))) | ~ (ord_less_eq_num @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5612])). 159.44/70.59 thf(543,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ C @ B)) = ((dvd_dvd_Code_integer @ A @ C) | (B = zero_z3403309356797280102nteger))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3814_dvd__mult__cancel__right)). 159.44/70.59 thf(9982,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ C @ B)) = ((dvd_dvd_Code_integer @ A @ C) | (B = zero_z3403309356797280102nteger))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[543])). 159.44/70.59 thf(2045,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (bit0 @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1425_numeral__code_I2_J)). 159.44/70.59 thf(14852,plain,((! [A:num]: ((numera6690914467698888265omplex @ (bit0 @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2045])). 159.44/70.59 thf(4204,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 @ (plus_plus_real @ A @ B) @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2025_add__nonpos__nonpos)). 159.44/70.59 thf(21729,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 @ (plus_plus_real @ A @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4204])). 159.44/70.59 thf(2353,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2077_mult__less__cancel__left__pos)). 159.44/70.59 thf(15806,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2353])). 159.44/70.59 thf(1542,axiom,((! [A:option_nat,B:option_nat]: ((if_option_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T)). 159.44/70.59 thf(13266,plain,((! [A:option_nat,B:option_nat]: ((if_option_nat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1542])). 159.44/70.59 thf(291,axiom,((! [A:complex]: ((real_V1022390504157884413omplex @ (times_times_complex @ A @ (cnj @ A))) = (power_power_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9698_complex__mod__mult__cnj)). 159.44/70.59 thf(9131,plain,((! [A:complex]: ((real_V1022390504157884413omplex @ (times_times_complex @ A @ (cnj @ A))) = (power_power_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[291])). 159.44/70.59 thf(7637,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2202_nat__mult__less__cancel1)). 159.44/70.59 thf(34665,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7637])). 159.44/70.59 thf(827,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ C) <= (ord_less_int @ B @ C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2817_order_Ostrict__trans)). 159.44/70.59 thf(10917,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ C) | ~ (ord_less_int @ B @ C) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[827])). 159.44/70.59 thf(2295,axiom,((ord_le2932123472753598470d_enat = (^ [A:extended_enat,B:extended_enat]: ((B = A) | (ord_le72135733267957522d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3104_dual__order_Oorder__iff__strict)). 159.44/70.59 thf(15643,plain,(((ord_le2932123472753598470d_enat) = (^ [A:extended_enat,B:extended_enat]: ((B = A) | (ord_le72135733267957522d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2295])). 159.44/70.59 thf(5490,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/sandbox/benchmark/theBenchmark.p',fact_89_numeral__times__numeral)). 159.44/70.59 thf(26413,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)],[5490])). 159.44/70.59 thf(6293,axiom,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1830_le__numeral__extra_I3_J)). 159.44/70.59 thf(29473,plain,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6293])). 159.44/70.59 thf(6224,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/sandbox/benchmark/theBenchmark.p',fact_5216_power__minus)). 159.44/70.59 thf(29163,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)],[6224])). 159.44/70.59 thf(5793,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/sandbox/benchmark/theBenchmark.p',fact_3920_semiring__parity__class_Oeven__mask__iff)). 159.44/70.59 thf(27510,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)],[5793])). 159.44/70.59 thf(4679,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/sandbox/benchmark/theBenchmark.p',fact_188_power2__sum)). 159.44/70.59 thf(23428,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)],[4679])). 159.44/70.59 thf(2513,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2884_order__less__irrefl)). 159.44/70.59 thf(16340,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2513])). 159.44/70.59 thf(3019,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/sandbox/benchmark/theBenchmark.p',fact_3538_minus__mod__eq__div__mult)). 159.44/70.59 thf(17959,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)],[3019])). 159.44/70.59 thf(1462,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/sandbox/benchmark/theBenchmark.p',fact_5084_nonzero__minus__divide__right)). 159.44/70.59 thf(13024,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)],[1462])). 159.44/70.59 thf(7844,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/sandbox/benchmark/theBenchmark.p',fact_1723_nat__zero__less__power__iff)). 159.44/70.59 thf(35325,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)],[7844])). 159.44/70.59 thf(2877,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/sandbox/benchmark/theBenchmark.p',fact_4636_minus__add__distrib)). 159.44/70.59 thf(17505,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)],[2877])). 159.44/70.59 thf(730,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/sandbox/benchmark/theBenchmark.p',fact_1579_double__add__le__zero__iff__single__add__le__zero)). 159.44/70.59 thf(10609,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)],[730])). 159.44/70.59 thf(1793,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/sandbox/benchmark/theBenchmark.p',fact_5606_numeral__code_I3_J)). 159.44/70.59 thf(14038,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)],[1793])). 159.44/70.59 thf(6408,axiom,((! [A:nat,B:int]: (((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_int)) => (dvd_dvd_int @ B @ (power_power_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4218_dvd__power)). 159.44/70.59 thf(29879,plain,((! [A:nat,B:int]: (((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_int)) => (dvd_dvd_int @ B @ (power_power_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6408])). 159.44/70.59 thf(5117,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ A) => ((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/sandbox/benchmark/theBenchmark.p',fact_2001_mult__mono_H)). 159.44/70.59 thf(24963,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ A) => ((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)],[5117])). 159.44/70.59 thf(2021,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ A @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups6591440286371151544t_real @ (^ [C:nat]: (plus_plus_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/sandbox/benchmark/theBenchmark.p',fact_8915_sum_Oin__pairs__0)). 159.44/70.59 thf(14782,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (A) @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups6591440286371151544t_real @ (^ [C:nat]: (plus_plus_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)],[2021])). 159.44/70.59 thf(740,axiom,((! [A:(nat > (nat > nat)),B:(nat > (nat > nat))]: ((if_nat_nat_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T)). 159.44/70.59 thf(10647,plain,((! [A:(nat > (nat > nat)),B:(nat > (nat > nat))]: ((if_nat_nat_nat @ ($true) @ A @ B) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[740])). 159.44/70.59 thf(3559,axiom,((! [A:nat]: ((bit_se2923211474154528505it_int @ A @ one_one_int) = (zero_n2684676970156552555ol_int @ (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4842_take__bit__of__1)). 159.44/70.59 thf(19672,plain,((! [A:nat]: ((bit_se2923211474154528505it_int @ A @ one_one_int) = (zero_n2684676970156552555ol_int @ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3559])). 159.44/70.59 thf(5156,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/sandbox/benchmark/theBenchmark.p',fact_472_valid__member__both__member__options)). 159.44/70.59 thf(25098,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)],[5156])). 159.44/70.59 thf(6027,axiom,((~ (dvd_dvd_nat @ zero_zero_nat @ one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4044_not__is__unit__0)). 159.44/70.59 thf(28526,plain,((~ (dvd_dvd_nat @ zero_zero_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6027])). 159.44/70.59 thf(2966,axiom,((! [A:code_integer]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) = ((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4231_odd__iff__mod__2__eq__one)). 159.44/70.59 thf(17803,plain,((! [A:code_integer]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) = ((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2966])). 159.44/70.59 thf(5317,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/sandbox/benchmark/theBenchmark.p',fact_1429_power__numeral__even)). 159.44/70.59 thf(25705,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)],[5317])). 159.44/70.59 thf(3459,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((upt @ A @ B) = (cons_nat @ A @ (upt @ (suc @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10140_upt__conv__Cons)). 159.44/70.59 thf(19364,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((upt @ A @ B) = (cons_nat @ A @ (upt @ (suc @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3459])). 159.44/70.59 thf(4922,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6530_of__nat__add)). 159.44/70.59 thf(24265,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)],[4922])). 159.44/70.59 thf(7666,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/sandbox/benchmark/theBenchmark.p',fact_675_power__odd__eq)). 159.44/70.59 thf(34748,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)],[7666])). 159.44/70.59 thf(2726,axiom,((! [A:int]: ~ (ord_less_int @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2805_dual__order_Oirrefl)). 159.44/70.59 thf(17043,plain,((! [A:int]: ~ (ord_less_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2726])). 159.44/70.59 thf(5388,axiom,((! [A:(nat > real),B:nat,C:(nat > real)]: ((! [D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (A @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ B)) = (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (C @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ B)))) = (! [D:nat]: ((ord_less_eq_nat @ D @ B) => ((A @ D) = (C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8756_polyfun__eq__coeffs)). 159.44/70.59 thf(26016,plain,((! [A:(nat > real),B:nat,C:(nat > real)]: ((! [D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (A @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ B)) = (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (C @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ B)))) = (! [D:nat]: ((ord_less_eq_nat @ D @ B) => ((A @ D) = (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5388])). 159.44/70.59 thf(7803,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/sandbox/benchmark/theBenchmark.p',fact_676_power__odd__eq)). 159.44/70.59 thf(35193,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)],[7803])). 159.44/70.59 thf(1506,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/sandbox/benchmark/theBenchmark.p',fact_1237_comm__semiring__class_Odistrib)). 159.44/70.59 thf(13162,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)],[1506])). 159.44/70.59 thf(4549,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/sandbox/benchmark/theBenchmark.p',fact_6616_of__nat__power__le__of__nat__cancel__iff)). 159.44/70.59 thf(22966,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)],[4549])). 159.44/70.59 thf(6888,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/sandbox/benchmark/theBenchmark.p',fact_2258_add__strict__increasing2)). 159.44/70.59 thf(31818,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)],[6888])). 159.44/70.59 thf(1188,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/sandbox/benchmark/theBenchmark.p',fact_8368_gbinomial__partial__row__sum)). 159.44/70.59 thf(12055,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)],[1188])). 159.44/70.59 thf(4022,axiom,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (powr_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7234_powr__ge__pzero)). 159.44/70.59 thf(21175,plain,((! [A:real,B:real]: (ord_less_eq_real @ zero_zero_real @ (powr_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4022])). 159.44/70.59 thf(3788,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((~ (ord_less_real @ C @ A)) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4448_pinf_I5_J)). 159.44/70.59 thf(20432,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)],[3788])). 159.44/70.59 thf(7999,axiom,((! [A:nat]: ((compow_nat_nat @ A @ suc) = (plus_plus_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9770_Suc__funpow)). 159.44/70.59 thf(35813,plain,((! [A:nat]: ((compow_nat_nat @ A @ suc) = (plus_plus_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7999])). 159.44/70.59 thf(5147,axiom,((! [A:nat,B:num]: ((ord_min_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (suc @ (ord_min_nat @ A @ (pred_numeral @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10169_min__Suc__numeral)). 159.44/70.59 thf(25071,plain,((! [A:nat,B:num]: ((ord_min_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (suc @ (ord_min_nat @ A @ (pred_numeral @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5147])). 159.44/70.59 thf(6507,axiom,((! [A:num]: ((inc @ (bit0 @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5719_inc_Osimps_I2_J)). 159.44/70.59 thf(30266,plain,((! [A:num]: ((inc @ (bit0 @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6507])). 159.44/70.59 thf(629,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/sandbox/benchmark/theBenchmark.p',fact_3831_dvd__add__times__triv__right__iff)). 159.44/70.59 thf(10259,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)],[629])). 159.44/70.59 thf(6395,axiom,((! [A:nat,B:(nat > $o)]: ((ord_less_nat @ zero_zero_nat @ A) => ((B @ one_one_nat) => ((B @ A) <= (! [C:nat]: (((B @ (suc @ C)) <= (B @ C)) <= (ord_less_nat @ zero_zero_nat @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2388_nat__induct__non__zero)). 159.44/70.59 thf(29824,plain,((! [A:nat,B:(nat > $o)]: ((ord_less_nat @ zero_zero_nat @ A) => ((B @ one_one_nat) => ((B @ A) | ~ (! [C:nat]: ((B @ (suc @ C)) | ~ (B @ C) | ~ (ord_less_nat @ zero_zero_nat @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6395])). 159.44/70.59 thf(5122,axiom,((! [A:num,B:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5028_not__numeral__le__neg__numeral)). 159.44/70.59 thf(24978,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)],[5122])). 159.44/70.59 thf(8073,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/sandbox/benchmark/theBenchmark.p',fact_5267_take__bit__nat__eq__self__iff)). 159.44/70.59 thf(36066,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)],[8073])). 159.44/70.59 thf(332,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ C) = (ord_less_real @ B @ (real_V1485227260804924795R_real @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9257_pos__divideR__less__eq)). 159.44/70.59 thf(9273,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ C) = (ord_less_real @ B @ (real_V1485227260804924795R_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 159.44/70.59 thf(1312,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/sandbox/benchmark/theBenchmark.p',fact_7979_power__diff__1__eq)). 159.44/70.59 thf(12490,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)],[1312])). 159.44/70.59 thf(1735,axiom,((! [A:extended_enat,B:extended_enat]: (((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ A @ B)) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B)) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2028_add__nonneg__nonneg)). 159.44/70.59 thf(13859,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ A @ B)) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735])). 159.44/70.59 thf(7362,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_711_nat__mult__1__right)). 159.44/70.59 thf(33707,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7362])). 159.44/70.59 thf(1696,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_real @ A @ B) => ((ord_less_real @ (arcsin @ A) @ (arcsin @ B)) <= (ord_less_eq_real @ B @ one_one_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7710_arcsin__less__arcsin)). 159.44/70.59 thf(13740,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_real @ A @ B) => ((ord_less_real @ (arcsin @ A) @ (arcsin @ B)) | ~ (ord_less_eq_real @ B @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696])). 159.44/70.59 thf(482,axiom,((! [A:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ln_ln_real @ A) = (the_real @ (^ [B:real]: (($false)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9388_ln__neg__is__const)). 159.44/70.59 thf(9786,plain,((! [A:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ln_ln_real @ A) = (the_real @ (^ [B:real]: (($false)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[482])). 159.44/70.59 thf(5746,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/sandbox/benchmark/theBenchmark.p',fact_567_nat__mult__max__left)). 159.44/70.59 thf(27283,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)],[5746])). 159.44/70.59 thf(1893,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/sandbox/benchmark/theBenchmark.p',fact_5982_or__nonnegative__int__iff)). 159.44/70.59 thf(14367,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)],[1893])). 159.44/70.59 thf(2415,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/sandbox/benchmark/theBenchmark.p',fact_7300_tan__less__zero)). 159.44/70.59 thf(16013,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)],[2415])). 159.44/70.59 thf(3445,axiom,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6839_int__Suc)). 159.44/70.59 thf(19326,plain,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3445])). 159.44/70.59 thf(512,axiom,((! [A:code_integer,B:nat]: ((bit_se9216721137139052372nteger @ A @ (suc @ B)) = (bit_se9216721137139052372nteger @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6418_bit__Suc)). 159.44/70.59 thf(9886,plain,((! [A:code_integer,B:nat]: ((bit_se9216721137139052372nteger @ A @ (suc @ B)) = (bit_se9216721137139052372nteger @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[512])). 159.44/70.59 thf(785,axiom,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ one_one_int) = (plus_plus_int @ A @ (zero_n2684676970156552555ol_int @ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6125_or__one__eq)). 159.44/70.59 thf(10785,plain,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ one_one_int) = (plus_plus_int @ A @ (zero_n2684676970156552555ol_int @ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[785])). 159.44/70.59 thf(5368,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (ord_max_nat @ A @ B) @ C) = ((ord_less_nat @ B @ C) & (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_752_max__less__iff__conj)). 159.44/70.59 thf(25943,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (ord_max_nat @ A @ B) @ C) = ((ord_less_nat @ B @ C) & (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5368])). 159.44/70.59 thf(1335,axiom,((! [A:code_integer]: (dvd_dvd_Code_integer @ one_one_Code_integer @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4000_one__dvd)). 159.44/70.59 thf(12564,plain,((! [A:code_integer]: (dvd_dvd_Code_integer @ one_one_Code_integer @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335])). 159.44/70.59 thf(3588,axiom,((! [A:num]: ((code_integer_of_num @ (bit0 @ A)) = (plus_p5714425477246183910nteger @ (code_integer_of_num @ A) @ (code_integer_of_num @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9814_integer__of__num_I2_J)). 159.44/70.59 thf(19772,plain,((! [A:num]: ((code_integer_of_num @ (bit0 @ A)) = (plus_p5714425477246183910nteger @ (code_integer_of_num @ A) @ (code_integer_of_num @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3588])). 159.44/70.59 thf(3016,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/sandbox/benchmark/theBenchmark.p',fact_8318_gbinomial__factors)). 159.44/70.59 thf(17950,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)],[3016])). 159.44/70.59 thf(2737,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/sandbox/benchmark/theBenchmark.p',fact_4060_dvd__mult__unit__iff_H)). 159.44/70.59 thf(17072,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)],[2737])). 159.44/70.59 thf(5067,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) => (ord_less_eq_int @ (abs_abs_int @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5534_abs__leI)). 159.44/70.59 thf(24804,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (uminus_uminus_int @ A) @ B) => (ord_less_eq_int @ (abs_abs_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5067])). 159.44/70.59 thf(3572,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3272_bot_Oextremum__unique)). 159.44/70.59 thf(19726,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)],[3572])). 159.44/70.59 thf(7655,axiom,((! [A:nat,B:nat]: ((A != B) => ((ord_less_nat @ B @ A) <= (~ (ord_less_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_linorder__neqE__nat)). 159.44/70.59 thf(34716,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)],[7655])). 159.44/70.59 thf(5032,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1337_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc)). 159.44/70.59 thf(24659,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5032])). 159.44/70.59 thf(1680,axiom,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ (^ [C:nat]: (abs_abs_real @ (A @ C)))) <= (summable_real @ B)) <= (? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (abs_abs_real @ (A @ D)) @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7079_summable__rabs__comparison__test)). 159.44/70.59 thf(13690,plain,((! [A:(nat > real),B:(nat > real)]: ((summable_real @ (^ [C:nat]: (abs_abs_real @ (A @ C)))) | ~ (summable_real @ (B)) | ~ (? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (abs_abs_real @ (A @ D)) @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680])). 159.44/70.59 thf(5359,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/sandbox/benchmark/theBenchmark.p',fact_809_right__diff__distrib__numeral)). 159.44/70.59 thf(25916,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)],[5359])). 159.44/70.59 thf(5266,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/sandbox/benchmark/theBenchmark.p',fact_2228_mult__right__le__imp__le)). 159.44/70.59 thf(25489,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)],[5266])). 159.44/70.59 thf(5267,axiom,((! [A:num]: ((inc @ (bit1 @ A)) = (bit0 @ (inc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5720_inc_Osimps_I3_J)). 159.44/70.59 thf(25491,plain,((! [A:num]: ((inc @ (bit1 @ A)) = (bit0 @ (inc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5267])). 159.44/70.59 thf(1733,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/sandbox/benchmark/theBenchmark.p',fact_3417_mod__mult__self3)). 159.44/70.59 thf(13854,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)],[1733])). 159.44/70.59 thf(2098,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/sandbox/benchmark/theBenchmark.p',fact_3419_mod__mult__self2)). 159.44/70.59 thf(15009,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)],[2098])). 159.44/70.59 thf(12,axiom,((! [A:nat]: ~ (ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6671_of__nat__less__0__iff)). 159.44/70.59 thf(8288,plain,((! [A:nat]: ~ (ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 159.44/70.59 thf(2220,axiom,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1873_add_Ogroup__left__neutral)). 159.44/70.59 thf(15418,plain,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2220])). 159.44/70.59 thf(917,axiom,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ A @ C)) = (minus_minus_complex @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_add__diff__cancel__left)). 159.44/70.59 thf(11192,plain,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ A @ C)) = (minus_minus_complex @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[917])). 159.44/70.59 thf(2613,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((A = B) | (ord_less_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3159_order__le__less)). 159.44/70.59 thf(16676,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((A = B) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2613])). 159.44/70.59 thf(1971,axiom,((! [A:num]: ~ (ord_less_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5179_not__neg__one__less__neg__numeral)). 159.44/70.59 thf(14606,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)],[1971])). 159.44/70.59 thf(2028,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) => ((ord_le72135733267957522d_enat @ B @ (plus_p3455044024723400733d_enat @ A @ C)) <= (ord_le72135733267957522d_enat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2107_pos__add__strict)). 159.44/70.59 thf(14801,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) => ((ord_le72135733267957522d_enat @ B @ (plus_p3455044024723400733d_enat @ A @ C)) | ~ (ord_le72135733267957522d_enat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2028])). 159.44/70.59 thf(134,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/sandbox/benchmark/theBenchmark.p',fact_9678_inverse__complex_Osimps_I2_J)). 159.44/70.59 thf(8663,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)],[134])). 159.44/70.59 thf(2700,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/sandbox/benchmark/theBenchmark.p',fact_4778_ln__le__zero__iff)). 159.44/70.59 thf(16962,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)],[2700])). 159.44/70.59 thf(3662,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3878_even__add)). 159.44/70.59 thf(20014,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ 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)],[3662])). 159.44/70.59 thf(7146,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/sandbox/benchmark/theBenchmark.p',fact_2730_order_Otrans)). 159.44/70.59 thf(32927,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)],[7146])). 159.44/70.59 thf(915,axiom,((! [A:int,B:int]: (((bit_se725231765392027082nd_int @ A @ B) = (uminus_uminus_int @ one_one_int)) = ((B = (uminus_uminus_int @ one_one_int)) & (A = (uminus_uminus_int @ one_one_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6064_and__eq__minus__1__iff)). 159.44/70.59 thf(11186,plain,((! [A:int,B:int]: (((bit_se725231765392027082nd_int @ A @ B) = (uminus_uminus_int @ 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)],[915])). 159.44/70.59 thf(5558,axiom,((! [A:produc9072475918466114483BT_nat]: (((((((~ (! [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) @ (suc @ 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) @ zero_zero_nat @ C @ D) @ E)))) <= (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E)))) <= (! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ (suc @ D)))))) <= (! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ zero_zero_nat))))) <= (! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2215_vebt__pred_Ocases)). 159.44/70.59 thf(26625,plain,((! [A:produc9072475918466114483BT_nat]: (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))) | ~ (! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) | ~ (! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E))) | ~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))) | ~ (! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ (suc @ D))))) | ~ (! [B:$o,C:$o]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ zero_zero_nat)))) | ~ (! [B:$o,C:$o]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5558])). 159.44/70.59 thf(4395,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => (((modulo_modulo_int @ A @ B) = A) <= (ord_less_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3621_mod__neg__neg__trivial)). 159.44/70.59 thf(22328,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => (((modulo_modulo_int @ A @ B) = A) | ~ (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4395])). 159.44/70.59 thf(6470,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/sandbox/benchmark/theBenchmark.p',fact_4805_mult__neg__numeral__simps_I1_J)). 159.44/70.59 thf(30140,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)],[6470])). 159.44/70.59 thf(689,axiom,((! [A:complex]: ((A != zero_zero_complex) => ((invers8013647133539491842omplex @ A) = (divide1717551699836669952omplex @ one_one_complex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9080_nonzero__inverse__eq__divide)). 159.44/70.59 thf(10452,plain,((! [A:complex]: ((~ (A = zero_zero_complex)) => ((invers8013647133539491842omplex @ A) = (divide1717551699836669952omplex @ one_one_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[689])). 159.44/70.59 thf(7046,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/sandbox/benchmark/theBenchmark.p',fact_4867_Parity_Oring__1__class_Opower__minus__even)). 159.44/70.59 thf(32507,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)],[7046])). 159.44/70.59 thf(1323,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((times_times_int @ (divide_divide_int @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3838_dvd__div__mult__self)). 159.44/70.59 thf(12526,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((times_times_int @ (divide_divide_int @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323])). 159.44/70.59 thf(7193,axiom,((! [A:nat,B:nat]: (((bit_se1412395901928357646or_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6056_or__eq__0__iff)). 159.44/70.59 thf(33118,plain,((! [A:nat,B:nat]: (((bit_se1412395901928357646or_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7193])). 159.44/70.59 thf(2590,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ (sin_real @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6814_sin__x__le__x)). 159.44/70.59 thf(16576,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)],[2590])). 159.44/70.59 thf(1337,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ C @ B) <= (ord_less_int @ C @ A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3124_dual__order_Ostrict__trans1)). 159.44/70.59 thf(12570,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ C @ B) | ~ (ord_less_int @ C @ A) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337])). 159.44/70.59 thf(2334,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ (abs_abs_int @ C) @ D) => (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 @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5524_abs__mult__less)). 159.44/70.59 thf(15752,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ (abs_abs_int @ C) @ D) => (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 @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2334])). 159.44/70.59 thf(6193,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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4870_power__minus__odd)). 159.44/70.59 thf(29071,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)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6193])). 159.44/70.59 thf(4255,axiom,((invers8013647133539491842omplex = (divide1717551699836669952omplex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9052_inverse__eq__divide)). 159.44/70.59 thf(21908,plain,(((invers8013647133539491842omplex) = (divide1717551699836669952omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4255])). 159.44/70.59 thf(4159,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > num),D:num]: (((ord_less_num @ (C @ B) @ D) => ((ord_less_num @ (C @ A) @ D) <= (! [E:extended_enat,F:extended_enat]: ((ord_less_num @ (C @ E) @ (C @ F)) <= (ord_le72135733267957522d_enat @ E @ F))))) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2900_order__less__subst2)). 159.44/70.59 thf(21595,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > num),D:num]: (((ord_less_num @ (C @ B) @ D) => ((ord_less_num @ (C @ A) @ D) | ~ (! [E:extended_enat,F:extended_enat]: ((ord_less_num @ (C @ E) @ (C @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))))) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4159])). 159.44/70.59 thf(7954,axiom,((! [A:complex]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_complex @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_power2__eq__square)). 159.44/70.59 thf(35679,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)],[7954])). 159.44/70.59 thf(5407,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((! [E:nat]: ((ord_less_nat @ E @ A) => (ord_less_eq_nat @ (B @ E) @ C))) => ((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/sandbox/benchmark/theBenchmark.p',fact_8007_real__sum__nat__ivl__bounded2)). 159.44/70.59 thf(26085,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((! [E:nat]: ((ord_less_nat @ E @ A) => (ord_less_eq_nat @ (B @ E) @ C))) => ((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)],[5407])). 159.44/70.59 thf(5279,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 = C) | (B = D)))) => ((~ (! [C:nat,D:list_VEBT_VEBT]: (((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))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)))) <= (? [E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E)))))) <= (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: (((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))))))) | (B = C)) <= (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G))))))) <= (! [C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ C @ D)))) <= (! [C:$o,D:$o]: (A != (vEBT_Leaf @ C @ D)))) <= (~ (vEBT_VEBT_membermima @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2494_VEBT__internal_Omembermima_Oelims_I3_J)). 159.44/70.59 thf(25531,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:nat,D:nat]: ((? [E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F))) => ((B = C) | (B = D)))) => (~ (! [C:nat,D:list_VEBT_VEBT]: (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) & ((vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)))) | ~ (? [E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E))))) | ~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: ((B = D) | ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_VEBT_membermima @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))))) | (B = C) | ~ (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G))))))) | ~ (! [C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ C @ D))) | ~ (! [C:$o,D:$o]: ~ (A = (vEBT_Leaf @ C @ D))) | (vEBT_VEBT_membermima @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5279])). 159.44/70.59 thf(1450,axiom,((! [A:nat,B:nat,C:(nat > int)]: ((ord_less_eq_nat @ A @ B) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7669_sum_OSuc__reindex__ivl)). 159.44/70.59 thf(12975,plain,((! [A:nat,B:nat,C:(nat > int)]: ((ord_less_eq_nat @ A @ B) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450])). 159.44/70.59 thf(5991,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/sandbox/benchmark/theBenchmark.p',fact_7186_cos__double)). 159.44/70.59 thf(28409,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)],[5991])). 159.44/70.59 thf(1962,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > nat),D:nat]: ((ord_le72135733267957522d_enat @ A @ B) => (((! [E:extended_enat,F:extended_enat]: ((ord_less_nat @ (C @ E) @ (C @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_nat @ (C @ A) @ D)) <= (ord_less_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2901_order__less__subst2)). 159.44/70.59 thf(14574,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > nat),D:nat]: ((ord_le72135733267957522d_enat @ A @ B) => (((! [E:extended_enat,F:extended_enat]: ((ord_less_nat @ (C @ E) @ (C @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_nat @ (C @ A) @ D)) | ~ (ord_less_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1962])). 159.44/70.59 thf(1022,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/sandbox/benchmark/theBenchmark.p',fact_4696_add__neg__numeral__simps_I3_J)). 159.44/70.59 thf(11517,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)],[1022])). 159.44/70.59 thf(7322,axiom,((! [A:num]: ((plus_plus_num @ one @ A) = (plus_plus_num @ A @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_add__One__commute)). 159.44/70.59 thf(33575,plain,((! [A:num]: ((plus_plus_num @ one @ A) = (plus_plus_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7322])). 159.44/70.59 thf(4969,axiom,((ord_less_eq_real @ (cos_real @ (numeral_numeral_real @ (bit0 @ one))) @ zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7147_cos__two__le__zero)). 159.44/70.59 thf(24459,plain,((ord_less_eq_real @ (cos_real @ (numeral_numeral_real @ (bit0 @ one))) @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4969])). 159.44/70.59 thf(5708,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/sandbox/benchmark/theBenchmark.p',fact_808_right__diff__distrib__numeral)). 159.44/70.59 thf(27151,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)],[5708])). 159.44/70.59 thf(4976,axiom,((! [A:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one)) @ A) = (uminus1351360451143612070nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5204_mult__1s__ring__1_I1_J)). 159.44/70.59 thf(24477,plain,((! [A:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one)) @ A) = (uminus1351360451143612070nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4976])). 159.44/70.59 thf(2879,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_pred @ A @ C) = (some_nat @ D)) = (vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ A) @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_pred__corr)). 159.44/70.59 thf(17510,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_pred @ A @ C) = (some_nat @ D)) = (vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ A) @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2879])). 159.44/70.59 thf(86,axiom,((! [A:real]: ((cot_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (cot_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9385_cot__periodic)). 159.44/70.59 thf(8514,plain,((! [A:real]: ((cot_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (cot_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 159.44/70.59 thf(5396,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ zero_zero_real @ B) | (ord_less_eq_real @ B @ zero_zero_real)) & ((ord_less_eq_real @ A @ zero_zero_real) | (ord_less_eq_real @ zero_zero_real @ A))) => ((abs_abs_real @ (times_times_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5554_abs__eq__mult)). 159.44/70.59 thf(26048,plain,((! [A:real,B:real]: ((((ord_less_eq_real @ zero_zero_real @ B) | (ord_less_eq_real @ B @ zero_zero_real)) & ((ord_less_eq_real @ A @ zero_zero_real) | (ord_less_eq_real @ zero_zero_real @ A))) => ((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)],[5396])). 159.44/70.59 thf(2058,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/sandbox/benchmark/theBenchmark.p',fact_2288_divide__nonneg__pos)). 159.44/70.59 thf(14890,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)],[2058])). 159.44/70.59 thf(703,axiom,((ord_le72135733267957522d_enat = (^ [A:extended_enat,B:extended_enat]: ((A != B) & (ord_le2932123472753598470d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3160_order__less__le)). 159.44/70.59 thf(10520,plain,(((ord_le72135733267957522d_enat) = (^ [A:extended_enat,B:extended_enat]: (~ (A = B) & (ord_le2932123472753598470d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[703])). 159.44/70.59 thf(1905,axiom,(((size_num @ one) = zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5296_num_Osize__gen_I1_J)). 159.44/70.59 thf(14404,plain,(((size_num @ one) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1905])). 159.44/70.59 thf(1925,axiom,((! [A:(nat > (nat > int)),B:nat]: ((groups705719431365010083at_int @ (^ [C:nat]: (groups705719431365010083at_int @ (A @ C) @ (set_ord_lessThan_nat @ C))) @ (set_ord_atMost_nat @ B)) = (groups705719431365010083at_int @ (^ [C:nat]: (groups705719431365010083at_int @ (^ [D:nat]: (A @ D @ C)) @ (set_or1269000886237332187st_nat @ (suc @ C) @ B))) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8484_prod_Onested__swap_H)). 159.44/70.59 thf(14463,plain,((! [A:(nat > (nat > int)),B:nat]: ((groups705719431365010083at_int @ (^ [C:nat]: (groups705719431365010083at_int @ (A @ C) @ (set_ord_lessThan_nat @ C))) @ (set_ord_atMost_nat @ B)) = (groups705719431365010083at_int @ (^ [C:nat]: (groups705719431365010083at_int @ (^ [D:nat]: (A @ D @ C)) @ (set_or1269000886237332187st_nat @ (suc @ C) @ B))) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1925])). 159.44/70.59 thf(931,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/sandbox/benchmark/theBenchmark.p',fact_4177_is__unit__power__iff)). 159.44/70.59 thf(11235,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)],[931])). 159.44/70.59 thf(3980,axiom,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) = (B = (uminus1482373934393186551omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5060_add__eq__0__iff)). 159.44/70.59 thf(21050,plain,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = zero_zero_complex) = (B = (uminus1482373934393186551omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3980])). 159.44/70.59 thf(496,axiom,((! [A:real]: (ord_less_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ (plus_plus_real @ (real_V1803761363581548252l_real @ (real_V7735802525324610683m_real @ A)) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7569_norm__less__p1)). 159.44/70.59 thf(9833,plain,((! [A:real]: (ord_less_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ (plus_plus_real @ (real_V1803761363581548252l_real @ (real_V7735802525324610683m_real @ A)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[496])). 159.44/70.59 thf(5118,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2725_order__trans)). 159.44/70.59 thf(24966,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5118])). 159.44/70.59 thf(237,axiom,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (times_times_int @ (comm_s4660882817536571857er_int @ A @ B) @ (plus_plus_int @ A @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8269_pochhammer__Suc)). 159.44/70.59 thf(8976,plain,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (times_times_int @ (comm_s4660882817536571857er_int @ A @ B) @ (plus_plus_int @ A @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 159.44/70.59 thf(957,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (modulo_modulo_int @ A @ B) @ B) = (modulo_modulo_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3389_mod__mod__trivial)). 159.44/70.59 thf(11313,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)],[957])). 159.44/70.59 thf(2787,axiom,((! [A:real,B:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ B @ A)) = (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3797_dvd__add__triv__right__iff)). 159.44/70.59 thf(17226,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)],[2787])). 159.44/70.59 thf(4560,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3165_order__less__le)). 159.44/70.59 thf(22998,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4560])). 159.44/70.59 thf(7670,axiom,((! [A:nat]: ((suc @ (bit_se2002935070580805687sk_nat @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6116_Suc__mask__eq__exp)). 159.44/70.59 thf(34761,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)],[7670])). 159.44/70.59 thf(5302,axiom,((! [A:vEBT_VEBT,B:nat]: (((accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ (produc738532404422230701BT_nat @ A @ B)) => ((~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ D @ E @ F) @ B)) => (~ ((D = B) & ! [G:vEBT_VEBT]: ((vEBT_VEBT_valid @ G @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) <= (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E))) & (vEBT_VEBT_valid @ F @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) & (case_o184042715313410164at_nat @ (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)) & ! [G:vEBT_VEBT]: ((~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H))) <= (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E)))) @ (produc6081775807080527818_nat_o @ (^ [G:nat,H:nat]: ((ord_less_eq_nat @ G @ H) & (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ((! [I:vEBT_VEBT]: ((~ (? [J:nat]: (vEBT_V8194947554948674370ptions @ I @ J))) <= (member_VEBT_VEBT @ I @ (set_VEBT_VEBT2 @ E)))) <= (G = H)) & ((! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ I) => ((ord_less_nat @ G @ I) & (ord_less_eq_nat @ I @ H)))) & (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ H)) <= (G != H)) & ! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [J:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ E @ I) @ J)) = (vEBT_V8194947554948674370ptions @ F @ I)))))) @ C) & ((size_s6755466524823107622T_VEBT @ E) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))))))) <= (A = (vEBT_Node @ C @ D @ E @ F))))) <= (! [C:$o,D:$o]: (((accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (B != one_one_nat)) <= (A = (vEBT_Leaf @ C @ D)))))) <= (vEBT_VEBT_valid @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10072_VEBT__internal_Ovalid_H_Opelims_I2_J)). 159.44/70.59 thf(25622,plain,((! [A:vEBT_VEBT,B:nat]: (((accp_P2887432264394892906BT_nat @ (vEBT_VEBT_valid_rel) @ (produc738532404422230701BT_nat @ A @ B)) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((accp_P2887432264394892906BT_nat @ (vEBT_VEBT_valid_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ D @ E @ F) @ B)) => (~ ((D = B) & ! [G:vEBT_VEBT]: ((vEBT_VEBT_valid @ G @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E))) & (vEBT_VEBT_valid @ F @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) & (case_o184042715313410164at_nat @ (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)) & ! [G:vEBT_VEBT]: (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H)) | ~ (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E)))) @ (produc6081775807080527818_nat_o @ (^ [G:nat,H:nat]: ((ord_less_eq_nat @ G @ H) & (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & (! [I:vEBT_VEBT]: (~ (? [J:nat]: (vEBT_V8194947554948674370ptions @ I @ J)) | ~ (member_VEBT_VEBT @ I @ (set_VEBT_VEBT2 @ E))) | ~ (G = H)) & ((! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ I) => ((ord_less_nat @ G @ I) & (ord_less_eq_nat @ I @ H)))) & (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ H)) | (G = H)) & ! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [J:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ E @ I) @ J)) = (vEBT_V8194947554948674370ptions @ F @ I)))))) @ C) & ((size_s6755466524823107622T_VEBT @ E) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))))))) | ~ (A = (vEBT_Node @ C @ D @ E @ F)))) | ~ (! [C:$o,D:$o]: (((accp_P2887432264394892906BT_nat @ (vEBT_VEBT_valid_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (~ (B = one_one_nat))) | ~ (A = (vEBT_Leaf @ C @ D)))))) | ~ (vEBT_VEBT_valid @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5302])). 159.44/70.59 thf(4530,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4576_add__0__iff)). 159.44/70.59 thf(22893,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4530])). 159.44/70.59 thf(2266,axiom,((! [A:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ one_one_Code_integer)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3919_semiring__parity__class_Oeven__mask__iff)). 159.44/70.59 thf(15558,plain,((! [A:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ one_one_Code_integer)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2266])). 159.44/70.59 thf(3167,axiom,((! [A:extended_enat,B:extended_enat]: (((A = zero_z5237406670263579293d_enat) | (B = zero_z5237406670263579293d_enat)) <= ((times_7803423173614009249d_enat @ A @ B) = zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1863_divisors__zero)). 159.44/70.59 thf(18442,plain,((! [A:extended_enat,B:extended_enat]: ((A = zero_z5237406670263579293d_enat) | (B = zero_z5237406670263579293d_enat) | ~ ((times_7803423173614009249d_enat @ A @ B) = zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3167])). 159.44/70.59 thf(6955,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5292_neg__one__power__add__eq__neg__one__power__diff)). 159.44/70.59 thf(32058,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6955])). 159.44/70.59 thf(11,axiom,((! [A:complex]: ((ord_less_real @ (uminus_uminus_real @ pi) @ (arg @ A)) & (ord_less_eq_real @ (arg @ A) @ pi)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9382_Arg__bounded)). 159.44/70.59 thf(8283,plain,((! [A:complex]: ((ord_less_real @ (uminus_uminus_real @ pi) @ (arg @ A)) & (ord_less_eq_real @ (arg @ A) @ pi)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[11])). 159.44/70.59 thf(83,axiom,((! [A:real]: (sums_real @ (^ [B:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ zero_zero_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))) @ (sinh_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9300_sinh__converges)). 159.44/70.59 thf(8507,plain,((! [A:real]: (sums_real @ (^ [B:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ zero_zero_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))) @ (sinh_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 159.44/70.59 thf(592,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/sandbox/benchmark/theBenchmark.p',fact_7315_tan__half)). 159.44/70.59 thf(10134,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)],[592])). 159.44/70.59 thf(3312,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ (uminus_uminus_int @ one_one_int)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5968_and_Oright__neutral)). 159.44/70.59 thf(18906,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ (uminus_uminus_int @ one_one_int)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3312])). 159.44/70.59 thf(7869,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/sandbox/benchmark/theBenchmark.p',fact_335_one__plus__numeral__commute)). 159.44/70.59 thf(35400,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)],[7869])). 159.44/70.59 thf(4849,axiom,((! [A:(nat > nat),B:set_nat]: (((finite_finite_nat @ B) => ((ord_less_eq_nat @ (groups3542108847815614940at_nat @ A @ B) @ (suminf_nat @ A)) <= (! [C:nat]: ((member_nat @ C @ (uminus5710092332889474511et_nat @ B)) => (ord_less_eq_nat @ zero_zero_nat @ (A @ C)))))) <= (summable_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7721_sum__le__suminf)). 159.44/70.59 thf(24028,plain,((! [A:(nat > nat),B:set_nat]: (((finite_finite_nat @ B) => ((ord_less_eq_nat @ (groups3542108847815614940at_nat @ (A) @ B) @ (suminf_nat @ (A))) | ~ (! [C:nat]: ((member_nat @ C @ (uminus5710092332889474511et_nat @ B)) => (ord_less_eq_nat @ zero_zero_nat @ (A @ C)))))) | ~ (summable_nat @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4849])). 159.44/70.59 thf(2655,axiom,((! [A:set_nat,B:(nat > int)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_int @ zero_zero_int @ (B @ C)))) => (ord_less_int @ zero_zero_int @ (groups705719431365010083at_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8505_prod__pos)). 159.44/70.59 thf(16808,plain,((! [A:set_nat,B:(nat > int)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_int @ zero_zero_int @ (B @ C)))) => (ord_less_int @ zero_zero_int @ (groups705719431365010083at_int @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2655])). 159.44/70.59 thf(3829,axiom,((! [A:complex,B:complex,C:complex]: ((B = C) <= ((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_add__left__imp__eq)). 159.44/70.59 thf(20559,plain,((! [A:complex,B:complex,C:complex]: ((B = C) | ~ ((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3829])). 159.44/70.59 thf(3795,axiom,((dvd_dvd_int = (^ [A:int,B:int]: ? [C:int]: (B = (times_times_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3943_dvd__def)). 159.44/70.59 thf(20464,plain,(((dvd_dvd_int) = (^ [A:int,B:int]: ? [C:int]: (B = (times_times_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3795])). 159.44/70.59 thf(6291,axiom,((! [A:int,B:(int > int),C:int,D:int]: (((ord_less_eq_int @ C @ D) => ((ord_less_eq_int @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2664_ord__eq__le__subst)). 159.44/70.59 thf(29462,plain,((! [A:int,B:(int > int),C:int,D:int]: (((ord_less_eq_int @ C @ D) => ((ord_less_eq_int @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6291])). 159.44/70.59 thf(471,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((A != zero_z3403309356797280102nteger) => ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ B @ A) @ (times_3573771949741848930nteger @ C @ A)) = (dvd_dvd_Code_integer @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3821_dvd__times__right__cancel__iff)). 159.44/70.59 thf(9731,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ B @ A) @ (times_3573771949741848930nteger @ C @ A)) = (dvd_dvd_Code_integer @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[471])). 159.44/70.59 thf(6950,axiom,((! [A:int,B:num]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ B))) = (((ord_less_eq_int @ zero_zero_int @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3887_zero__le__power__eq__numeral)). 159.44/70.59 thf(32045,plain,((! [A:int,B:num]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ B))) = (((ord_less_eq_int @ zero_zero_int @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6950])). 159.44/70.59 thf(5964,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/sandbox/benchmark/theBenchmark.p',fact_4058_mult__unit__dvd__iff)). 159.44/70.59 thf(28324,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)],[5964])). 159.44/70.59 thf(6641,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2641_order__antisym__conv)). 159.44/70.59 thf(30758,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6641])). 159.44/70.59 thf(1846,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/sandbox/benchmark/theBenchmark.p',fact_2294_sum__squares__ge__zero)). 159.44/70.59 thf(14220,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)],[1846])). 159.44/70.59 thf(5599,axiom,((ord_less_num = (^ [A:num,B:num]: (~ (ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3099_order_Ostrict__iff__not)). 159.44/70.59 thf(26775,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)],[5599])). 159.44/70.59 thf(8025,axiom,((! [A:nat,B:nat]: ((ord_less_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_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2538_power2__less__imp__less)). 159.44/70.59 thf(35894,plain,((! [A:nat,B:nat]: ((ord_less_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_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8025])). 159.44/70.59 thf(3655,axiom,((! [A:int,B:int]: ((A != B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2927_order__less__imp__not__eq)). 159.44/70.59 thf(19990,plain,((! [A:int,B:int]: (~ (A = B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3655])). 159.44/70.59 thf(4331,axiom,((! [A:int,B:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_diff__add__cancel)). 159.44/70.59 thf(22133,plain,((! [A:int,B:int]: ((plus_plus_int @ (minus_minus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4331])). 159.44/70.59 thf(7577,axiom,((! [A:(nat > (nat > nat)),B:nat]: ((groups708209901874060359at_nat @ (^ [C:nat]: (groups708209901874060359at_nat @ (A @ C) @ (set_ord_lessThan_nat @ C))) @ (set_ord_atMost_nat @ B)) = (groups708209901874060359at_nat @ (^ [C:nat]: (groups708209901874060359at_nat @ (^ [D:nat]: (A @ D @ C)) @ (set_or1269000886237332187st_nat @ (suc @ C) @ B))) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8483_prod_Onested__swap_H)). 159.44/70.59 thf(34484,plain,((! [A:(nat > (nat > nat)),B:nat]: ((groups708209901874060359at_nat @ (^ [C:nat]: (groups708209901874060359at_nat @ (A @ C) @ (set_ord_lessThan_nat @ C))) @ (set_ord_atMost_nat @ B)) = (groups708209901874060359at_nat @ (^ [C:nat]: (groups708209901874060359at_nat @ (^ [D:nat]: (A @ D @ C)) @ (set_or1269000886237332187st_nat @ (suc @ C) @ B))) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7577])). 159.44/70.59 thf(5909,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/sandbox/benchmark/theBenchmark.p',fact_4845_add__neg__numeral__special_I9_J)). 159.59/70.59 thf(28097,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)],[5909])). 159.59/70.59 thf(456,axiom,((! [A:set_nat,B:(nat > real),C:nat]: ((finite_finite_nat @ A) => ((groups129246275422532515t_real @ B @ (insert_nat @ C @ A)) = (times_times_real @ (B @ C) @ (groups129246275422532515t_real @ B @ (minus_minus_set_nat @ A @ (insert_nat @ C @ bot_bot_set_nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8803_prod_Oinsert__remove)). 159.59/70.59 thf(9685,plain,((! [A:set_nat,B:(nat > real),C:nat]: ((finite_finite_nat @ A) => ((groups129246275422532515t_real @ (B) @ (insert_nat @ C @ A)) = (times_times_real @ (B @ C) @ (groups129246275422532515t_real @ (B) @ (minus_minus_set_nat @ A @ (insert_nat @ C @ bot_bot_set_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[456])). 159.59/70.59 thf(794,axiom,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ B) = (ord_less_real @ (uminus_uminus_real @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4935_minus__less__iff)). 159.59/70.59 thf(10812,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)],[794])). 159.59/70.59 thf(6673,axiom,((! [A:num]: ((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ A)) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1684_power__zero__numeral)). 159.59/70.59 thf(30866,plain,((! [A:num]: ((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6673])). 159.59/70.59 thf(1379,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > $o)]: ((finite_finite_nat @ A) => (((C @ bot_bot_set_nat) => ((C @ A) <= (! [D:nat,E:set_nat]: (((member_nat @ D @ B) => ((ord_less_eq_set_nat @ E @ B) => ((~ (member_nat @ D @ E)) => ((C @ E) => (C @ (insert_nat @ D @ E)))))) <= (finite_finite_nat @ E))))) <= (ord_less_eq_set_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6246_finite__subset__induct_H)). 159.59/70.59 thf(12731,plain,((! [A:set_nat,B:set_nat,C:(set_nat > $o)]: ((finite_finite_nat @ A) => (((C @ bot_bot_set_nat) => ((C @ A) | ~ (! [D:nat,E:set_nat]: (((member_nat @ D @ B) => ((ord_less_eq_set_nat @ E @ B) => ((~ (member_nat @ D @ E)) => ((C @ E) => (C @ (insert_nat @ D @ E)))))) | ~ (finite_finite_nat @ E))))) | ~ (ord_less_eq_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379])). 159.59/70.59 thf(5799,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_less__imp__le__nat)). 159.59/70.59 thf(27529,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5799])). 159.59/70.59 thf(6255,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/sandbox/benchmark/theBenchmark.p',fact_1702_one__eq__mult__iff)). 159.59/70.59 thf(29267,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)],[6255])). 159.59/70.59 thf(2112,axiom,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3700_verit__sum__simplify)). 159.59/70.59 thf(15055,plain,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2112])). 159.59/70.59 thf(3966,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/sandbox/benchmark/theBenchmark.p',fact_3969_dvd__mult__right)). 159.59/70.59 thf(21012,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)],[3966])). 159.59/70.59 thf(8043,axiom,((vEBT_VEBT_power = (vEBT_V4262088993061758097ft_nat @ power_power_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_local_Opower__def)). 159.59/70.59 thf(35965,plain,(((vEBT_VEBT_power) = (vEBT_V4262088993061758097ft_nat @ power_power_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8043])). 159.59/70.59 thf(272,axiom,((! [A:set_nat,B:set_nat,C:(nat > complex)]: (((finite_finite_nat @ B) => ((groups6464643781859351333omplex @ C @ B) = (times_times_complex @ (groups6464643781859351333omplex @ C @ (minus_minus_set_nat @ B @ A)) @ (groups6464643781859351333omplex @ C @ A)))) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8666_prod_Osubset__diff)). 159.59/70.59 thf(9076,plain,((! [A:set_nat,B:set_nat,C:(nat > complex)]: (((finite_finite_nat @ B) => ((groups6464643781859351333omplex @ (C) @ B) = (times_times_complex @ (groups6464643781859351333omplex @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups6464643781859351333omplex @ (C) @ A)))) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 159.59/70.59 thf(7993,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/sandbox/benchmark/theBenchmark.p',fact_364_power__mult__distrib)). 159.59/70.59 thf(35795,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)],[7993])). 159.59/70.59 thf(192,axiom,(((sin_real @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one)))) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7376_sin__of__real__pi__half)). 159.59/70.59 thf(8843,plain,(((sin_real @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one)))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 159.59/70.59 thf(7756,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((A != C) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ E @ F) @ B) = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = A) @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ A) @ (if_nat @ ((((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) <= (B = A)) & ((B = C) <= (B != A))) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (if_nat @ (B = A) @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ A) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = A) @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ A) @ (if_nat @ ((((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) <= (B = A)) & ((B != A) => (B = C))) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ E @ F))))) <= ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1400_del__in__range)). 159.59/70.59 thf(35061,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ (A = C)) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ E @ F) @ B) = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = A) @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ A) @ (if_nat @ ((((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) | ~ (B = A)) & ((B = C) | (B = A))) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (if_nat @ (B = A) @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ A) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = A) @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ A) @ (if_nat @ ((((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) | ~ (B = A)) & ((~ (B = A)) => (B = C))) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = A) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ B) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ E @ F))))) | ~ ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7756])). 159.59/70.59 thf(3848,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/sandbox/benchmark/theBenchmark.p',fact_5983_or__negative__int__iff)). 159.59/70.59 thf(20640,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)],[3848])). 159.59/70.59 thf(7630,axiom,(((semiri2265585572941072030t_real @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8068_fact__2)). 159.59/70.59 thf(34645,plain,(((semiri2265585572941072030t_real @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7630])). 159.59/70.59 thf(6309,axiom,((! [A:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5174_not__numeral__le__neg__one)). 159.59/70.59 thf(29520,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)],[6309])). 159.59/70.59 thf(7347,axiom,((! [A:product_prod_num_num]: ? [B:num,C:num]: (A = (product_Pair_num_num @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3683_surj__pair)). 159.59/70.59 thf(33658,plain,((! [A:product_prod_num_num]: ? [B:num,C:num]: (A = (product_Pair_num_num @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7347])). 159.59/70.59 thf(1436,axiom,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ B) => (~ (! [C:complex]: (B != (times_times_complex @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3930_dvdE)). 159.59/70.59 thf(12934,plain,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ B) => (~ (! [C:complex]: ~ (B = (times_times_complex @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436])). 159.59/70.59 thf(3390,axiom,((suc = (^ [A:nat]: (nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9449_Suc__as__int)). 159.59/70.59 thf(19148,plain,(((suc) = (^ [A:nat]: (nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3390])). 159.59/70.59 thf(5619,axiom,((! [A:int]: ((ord_less_eq_int @ (uminus_uminus_int @ A) @ A) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4673_neg__less__eq__nonneg)). 159.59/70.59 thf(26842,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)],[5619])). 159.59/70.59 thf(776,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ (times_times_int @ B @ C) @ (times_times_int @ A @ C)) <= (ord_less_int @ C @ zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2069_mult__strict__right__mono__neg)). 159.59/70.59 thf(10753,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ (times_times_int @ B @ C) @ (times_times_int @ A @ C)) | ~ (ord_less_int @ C @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[776])). 159.59/70.59 thf(5501,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => (((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1852_mult__right__cancel)). 159.59/70.59 thf(26461,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => (((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5501])). 159.59/70.59 thf(575,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (real_V1485227260804924795R_real @ B @ A) @ A) <= (ord_less_eq_real @ B @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9246_scaleR__left__le__one__le)). 159.59/70.59 thf(10081,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (real_V1485227260804924795R_real @ B @ A) @ A) | ~ (ord_less_eq_real @ B @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[575])). 159.59/70.59 thf(7697,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/sandbox/benchmark/theBenchmark.p',fact_1197_add__strict__mono)). 159.59/70.59 thf(34844,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)],[7697])). 159.59/70.59 thf(6781,axiom,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = B) => ((ord_less_eq_real @ zero_zero_real @ A) => ((sqrt @ B) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6438_real__sqrt__unique)). 159.59/70.59 thf(31389,plain,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = B) => ((ord_less_eq_real @ zero_zero_real @ A) => ((sqrt @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6781])). 159.59/70.59 thf(3453,axiom,((semiri2265585572941072030t_real = (comm_s7457072308508201937r_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8222_pochhammer__fact)). 159.59/70.59 thf(19350,plain,(((semiri2265585572941072030t_real) = (comm_s7457072308508201937r_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3453])). 159.59/70.59 thf(4455,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ (sqrt @ A) @ B) <= (ord_less_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6456_real__less__lsqrt)). 159.59/70.59 thf(22521,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ (sqrt @ A) @ B) | ~ (ord_less_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4455])). 159.59/70.59 thf(3814,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/sandbox/benchmark/theBenchmark.p',fact_3484_div__add1__eq)). 159.59/70.59 thf(20516,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)],[3814])). 159.59/70.59 thf(6419,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/sandbox/benchmark/theBenchmark.p',fact_5867_neg__numeral__power__le__of__int__cancel__iff)). 159.59/70.59 thf(29929,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)],[6419])). 159.59/70.59 thf(3756,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 @ C @ A) @ (divide_divide_real @ C @ B)) <= (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2427_divide__left__mono__neg)). 159.59/70.59 thf(20332,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 @ C @ A) @ (divide_divide_real @ C @ B)) | ~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3756])). 159.59/70.59 thf(4876,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/sandbox/benchmark/theBenchmark.p',fact_6608_of__nat__power__less__of__nat__cancel__iff)). 159.59/70.59 thf(24108,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)],[4876])). 159.59/70.59 thf(3227,axiom,((! [A:real,B:nat,C:(nat > (real > real))]: ((((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)) <= (B != zero_zero_nat)) <= (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8132_Maclaurin__zero)). 159.59/70.59 thf(18629,plain,((! [A:real,B:nat,C:(nat > (real > real))]: (((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)) | (B = zero_zero_nat) | ~ (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3227])). 159.59/70.59 thf(453,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/sandbox/benchmark/theBenchmark.p',fact_3617_flip__bit__nonnegative__int__iff)). 159.59/70.59 thf(9676,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)],[453])). 159.59/70.59 thf(5190,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: (B != (plus_plus_nat @ A @ C)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_less__eqE)). 159.59/70.59 thf(25214,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)],[5190])). 159.59/70.59 thf(5807,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/sandbox/benchmark/theBenchmark.p',fact_3606_old_Oprod_Oinject)). 159.59/70.59 thf(27601,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)],[5807])). 159.59/70.59 thf(6958,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/sandbox/benchmark/theBenchmark.p',fact_7191_cos__double__sin)). 159.59/70.59 thf(32066,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)],[6958])). 159.59/70.59 thf(8157,axiom,((((xa = mi) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))))) & ((xa != mi) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = xa)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_061_A_Iif_Ax_A_061_Ami_Athen_Athe_A_Ivebt__mint_Asummary_J_A_K_A2_A_094_A_Ideg_Adiv_A2_J_A_L_Athe_A_Ivebt__mint_A_ItreeList_A_B_Athe_A_Ivebt__mint_Asummary_J_J_J_Aelse_Ax_J_092_060close_062)). 159.59/70.59 thf(36340,plain,((((xa = mi) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ summary)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ (the_nat @ (vEBT_vebt_mint @ summary)))))))) & ((~ (xa = mi)) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = xa)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8157])). 159.59/70.59 thf(4290,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/sandbox/benchmark/theBenchmark.p',fact_1370_ordered__ring__class_Ole__add__iff1)). 159.59/70.59 thf(22012,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)],[4290])). 159.59/70.59 thf(7680,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2846_order__less__asym)). 159.59/70.59 thf(34797,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7680])). 159.59/70.59 thf(7441,axiom,((! [A:nat,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((power_power_real @ (sqrt @ B) @ A) = (power_power_real @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6470_real__sqrt__power__even)). 159.59/70.59 thf(33954,plain,((! [A:nat,B:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((power_power_real @ (sqrt @ B) @ A) = (power_power_real @ B @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7441])). 159.59/70.59 thf(128,axiom,((! [A:nat]: ((tan_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7223_tan__npi)). 159.59/70.59 thf(8646,plain,((! [A:nat]: ((tan_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 159.59/70.59 thf(3818,axiom,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1426_numeral__code_I2_J)). 159.59/70.59 thf(20527,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)],[3818])). 159.59/70.59 thf(7944,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/sandbox/benchmark/theBenchmark.p',fact_4513_exp__mod__exp)). 159.59/70.59 thf(35649,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)],[7944])). 159.59/70.59 thf(3553,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/sandbox/benchmark/theBenchmark.p',fact_4048_dvd__div__eq__0__iff)). 159.59/70.59 thf(19649,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)],[3553])). 159.59/70.59 thf(1998,axiom,((! [A:real,B:nat]: ((times_times_real @ (power_power_real @ A @ B) @ (inverse_inverse_real @ A)) = (times_times_real @ (inverse_inverse_real @ A) @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9048_power__mult__inverse__distrib)). 159.59/70.59 thf(14709,plain,((! [A:real,B:nat]: ((times_times_real @ (power_power_real @ A @ B) @ (inverse_inverse_real @ A)) = (times_times_real @ (inverse_inverse_real @ A) @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1998])). 159.59/70.59 thf(5289,axiom,((! [A:(nat > (nat > nat)),B:nat,C:nat]: ((produc6842872674320459806at_nat @ A @ (product_Pair_nat_nat @ B @ C)) = (A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4658_case__prod__conv)). 159.59/70.59 thf(25580,plain,((! [A:(nat > (nat > nat)),B:nat,C:nat]: ((produc6842872674320459806at_nat @ (A) @ (product_Pair_nat_nat @ B @ C)) = (A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5289])). 159.59/70.59 thf(7079,axiom,(((modulo_modulo_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3430_one__mod__two__eq__one)). 159.59/70.59 thf(32643,plain,(((modulo_modulo_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7079])). 159.59/70.59 thf(2440,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_le72135733267957522d_enat @ (semiri4216267220026989637d_enat @ A) @ (semiri4216267220026989637d_enat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6681_less__imp__of__nat__less)). 159.59/70.59 thf(16103,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_le72135733267957522d_enat @ (semiri4216267220026989637d_enat @ A) @ (semiri4216267220026989637d_enat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2440])). 159.59/70.59 thf(6438,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/sandbox/benchmark/theBenchmark.p',fact_3442_mod__mult__left__eq)). 159.59/70.59 thf(30003,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)],[6438])). 159.59/70.59 thf(55,axiom,((! [A:code_integer]: ((modulo364778990260209775nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4766_mod__minus1__right)). 159.59/70.59 thf(8415,plain,((! [A:code_integer]: ((modulo364778990260209775nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[55])). 159.59/70.59 thf(1051,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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2232_mult__left__le__imp__le)). 159.59/70.59 thf(11620,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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051])). 159.59/70.59 thf(538,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/sandbox/benchmark/theBenchmark.p',fact_9607_or__not__numerals_I7_J)). 159.59/70.59 thf(9965,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)],[538])). 159.59/70.59 thf(5609,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ zero_zero_nat @ A) => ((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 @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2002_mult__mono_H)). 159.59/70.59 thf(26810,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_eq_nat @ zero_zero_nat @ A) => ((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 @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5609])). 159.59/70.59 thf(2652,axiom,((! [A:nat,B:nat,C:(nat > real)]: (((groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_real @ (C @ (suc @ B)) @ (groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7663_sum_Onat__ivl__Suc_H)). 159.59/70.59 thf(16797,plain,((! [A:nat,B:nat,C:(nat > real)]: (((groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_real @ (C @ (suc @ B)) @ (groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ B)))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2652])). 159.59/70.59 thf(2218,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/sandbox/benchmark/theBenchmark.p',fact_5582_abs__triangle__ineq4)). 159.59/70.59 thf(15413,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)],[2218])). 159.59/70.59 thf(7511,axiom,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3660_verit__la__disequality)). 159.59/70.59 thf(34220,plain,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7511])). 159.59/70.59 thf(6787,axiom,(((neg_nu3811975205180677377ec_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5672_dbl__dec__simps_I4_J)). 159.59/70.59 thf(31408,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)],[6787])). 159.59/70.59 thf(3697,axiom,((! [A:set_nat,B:(nat > int)]: ((! [C:nat]: (((B @ C) = one_one_int) <= (member_nat @ C @ A))) => ((groups705719431365010083at_int @ B @ A) = one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8458_prod_Oneutral)). 159.59/70.59 thf(20124,plain,((! [A:set_nat,B:(nat > int)]: ((! [C:nat]: (((B @ C) = one_one_int) | ~ (member_nat @ C @ A))) => ((groups705719431365010083at_int @ (B) @ A) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3697])). 159.59/70.59 thf(983,axiom,((! [A:real]: (((powr_real @ A @ one_one_real) = A) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7217_powr__one)). 159.59/70.59 thf(11394,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)],[983])). 159.59/70.59 thf(4075,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/sandbox/benchmark/theBenchmark.p',fact_4063_mult__unit__dvd__iff_H)). 159.59/70.59 thf(21326,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)],[4075])). 159.59/70.59 thf(848,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/sandbox/benchmark/theBenchmark.p',fact_9451_nat__div__distrib)). 159.59/70.59 thf(10987,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)],[848])). 159.59/70.59 thf(980,axiom,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5952_or_Oright__neutral)). 159.59/70.59 thf(11385,plain,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[980])). 159.59/70.59 thf(4009,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/sandbox/benchmark/theBenchmark.p',fact_2285_unique__euclidean__semiring__numeral__class_Odiv__less)). 159.59/70.59 thf(21136,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)],[4009])). 159.59/70.59 thf(1305,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_eq_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B) @ A) <= (ord_less_real @ B @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_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 @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B)) <= (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5308_divide__le__eq__numeral_I2_J)). 159.59/70.59 thf(12468,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_eq_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B) @ A) | ~ (ord_less_real @ B @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ (uminus_uminus_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 @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B)) | ~ (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305])). 159.59/70.59 thf(2945,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/sandbox/benchmark/theBenchmark.p',fact_7161_cos__squared__eq)). 159.59/70.59 thf(17734,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)],[2945])). 159.59/70.59 thf(7591,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_less__not__refl)). 159.59/70.59 thf(34533,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7591])). 159.59/70.59 thf(4747,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/sandbox/benchmark/theBenchmark.p',fact_8450_prod_OatMost__Suc)). 159.59/70.59 thf(23640,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)],[4747])). 159.59/70.59 thf(7744,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_less__imp__Suc__add)). 159.59/70.59 thf(35029,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)],[7744])). 159.59/70.59 thf(3487,axiom,((! [A:num]: ((real_V4546457046886955230omplex @ (numeral_numeral_real @ A)) = (numera6690914467698888265omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7330_of__real__numeral)). 159.59/70.59 thf(19451,plain,((! [A:num]: ((real_V4546457046886955230omplex @ (numeral_numeral_real @ A)) = (numera6690914467698888265omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3487])). 159.59/70.59 thf(2073,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ one_on7984719198319812577d_enat) => ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B) => (ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ B @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2306_mult__left__le)). 159.59/70.59 thf(14932,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ one_on7984719198319812577d_enat) => ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B) => (ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ B @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2073])). 159.59/70.59 thf(163,axiom,((code_integer_of_int = (^ [A:int]: (if_Code_integer @ (ord_less_int @ A @ zero_zero_int) @ (uminus1351360451143612070nteger @ (code_integer_of_int @ (uminus_uminus_int @ A))) @ (if_Code_integer @ (A = zero_zero_int) @ zero_z3403309356797280102nteger @ (if_Code_integer @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (code_integer_of_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (code_integer_of_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_Code_integer))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9643_integer__of__int__code)). 159.59/70.59 thf(8755,plain,(((code_integer_of_int) = (^ [A:int]: (if_Code_integer @ (ord_less_int @ A @ zero_zero_int) @ (uminus1351360451143612070nteger @ (code_integer_of_int @ (uminus_uminus_int @ A))) @ (if_Code_integer @ (A = zero_zero_int) @ zero_z3403309356797280102nteger @ (if_Code_integer @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (code_integer_of_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (code_integer_of_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_Code_integer))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 159.59/70.59 thf(277,axiom,((! [A:code_integer,B:code_integer]: ((A != zero_z3403309356797280102nteger) => ((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1635_nonzero__mult__div__cancel__left)). 159.59/70.59 thf(9091,plain,((! [A:code_integer,B:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 159.59/70.59 thf(5123,axiom,((! [A:complex,B:nat,C:nat]: ((A != zero_zero_complex) => (((power_power_complex @ A @ (minus_minus_nat @ C @ B)) = (times_times_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ (invers8013647133539491842omplex @ A) @ B))) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9117_power__diff__conv__inverse)). 159.59/70.59 thf(24981,plain,((! [A:complex,B:nat,C:nat]: ((~ (A = zero_zero_complex)) => (((power_power_complex @ A @ (minus_minus_nat @ C @ B)) = (times_times_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ (invers8013647133539491842omplex @ A) @ B))) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5123])). 159.59/70.59 thf(186,axiom,((! [A:real]: (summable_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9287_summable__norm__exp)). 159.59/70.59 thf(8828,plain,((! [A:real]: (summable_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[186])). 159.59/70.59 thf(3886,axiom,((! [A:real]: (((divide_divide_real @ A @ A) = one_one_real) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1670_divide__self)). 159.59/70.59 thf(20765,plain,((! [A:real]: (((divide_divide_real @ A @ A) = one_one_real) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3886])). 159.59/70.59 thf(5833,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)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9000_prod__eq__1__iff)). 159.59/70.59 thf(27779,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)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5833])). 159.59/70.59 thf(3540,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/sandbox/benchmark/theBenchmark.p',fact_5786_of__int__eq__of__int__power__cancel__iff)). 159.59/70.59 thf(19611,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)],[3540])). 159.59/70.59 thf(1025,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ C) => (dvd_dvd_int @ A @ (modulo_modulo_int @ B @ C))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4028_dvd__mod)). 159.59/70.59 thf(11527,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ C) => (dvd_dvd_int @ A @ (modulo_modulo_int @ B @ C))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025])). 159.59/70.59 thf(4301,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/sandbox/benchmark/theBenchmark.p',fact_7160_cos__squared__eq)). 159.59/70.59 thf(22047,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)],[4301])). 159.59/70.59 thf(1317,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ B @ C) => (ord_less_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2862_order__less__trans)). 159.59/70.59 thf(12507,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ B @ C) => (ord_less_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317])). 159.59/70.59 thf(1062,axiom,((! [A:real,B:real]: (((ord_less_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/sandbox/benchmark/theBenchmark.p',fact_2286_divide__nonpos__pos)). 159.59/70.59 thf(11659,plain,((! [A:real,B:real]: (((ord_less_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)],[1062])). 159.59/70.59 thf(1303,axiom,((! [A:nat]: ((finite_card_nat @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9707_card__Collect__less__nat)). 159.59/70.59 thf(12462,plain,((! [A:nat]: ((finite_card_nat @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303])). 159.59/70.59 thf(2209,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/sandbox/benchmark/theBenchmark.p',fact_9733_drop__bit__push__bit__int)). 159.59/70.59 thf(15380,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)],[2209])). 159.59/70.59 thf(4373,axiom,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = B) <= ((plus_plus_complex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5052_add_Oinverse__unique)). 159.59/70.59 thf(22257,plain,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = B) | ~ ((plus_plus_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4373])). 159.59/70.59 thf(5823,axiom,((! [A:num]: ((semiri5074537144036343181t_real @ (numeral_numeral_nat @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6514_of__nat__numeral)). 159.59/70.59 thf(27708,plain,((! [A:num]: ((semiri5074537144036343181t_real @ (numeral_numeral_nat @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5823])). 159.59/70.59 thf(2956,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => ((ln_ln_real @ (power_power_real @ A @ B)) = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (ln_ln_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6766_ln__realpow)). 159.59/70.59 thf(17774,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => ((ln_ln_real @ (power_power_real @ A @ B)) = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (ln_ln_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2956])). 159.59/70.59 thf(2254,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) <= (ord_less_real @ zero_zero_real @ A)) <= (ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2230_mult__left__le__imp__le)). 159.59/70.59 thf(15526,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) | ~ (ord_less_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2254])). 159.59/70.59 thf(2486,axiom,((! [A:real]: (((ord_less_real @ zero_zero_real @ (ln_ln_real @ A)) = (ord_less_real @ one_one_real @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4724_ln__gt__zero__iff)). 159.59/70.59 thf(16248,plain,((! [A:real]: (((ord_less_real @ zero_zero_real @ (ln_ln_real @ A)) = (ord_less_real @ one_one_real @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2486])). 159.59/70.59 thf(3337,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/sandbox/benchmark/theBenchmark.p',fact_2371_diff__divide__eq__iff)). 159.59/70.59 thf(18985,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)],[3337])). 159.59/70.59 thf(1331,axiom,((! [A:real,B:real]: ((times_times_real @ (exp_real @ A) @ (exp_real @ B)) = (exp_real @ (plus_plus_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6080_mult__exp__exp)). 159.59/70.59 thf(12549,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)],[1331])). 159.59/70.59 thf(6377,axiom,((! [A:nat,B:nat]: (((ord_max_nat @ B @ A) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3301_max__absorb1)). 159.59/70.59 thf(29723,plain,((! [A:nat,B:nat]: (((ord_max_nat @ B @ A) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6377])). 159.59/70.59 thf(7544,axiom,((! [A:num]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5704_add__neg__numeral__special_I6_J)). 159.59/70.59 thf(34320,plain,((! [A:num]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7544])). 159.59/70.59 thf(5026,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/sandbox/benchmark/theBenchmark.p',fact_5537_abs__le__D2)). 159.59/70.59 thf(24644,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)],[5026])). 159.59/70.59 thf(5842,axiom,((! [A:num,B:num]: (((ord_less_eq_num @ A @ B) = (A = B)) <= (~ (ord_less_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3043_antisym__conv1)). 159.59/70.59 thf(27840,plain,((! [A:num,B:num]: (((ord_less_eq_num @ A @ B) = (A = B)) | (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5842])). 159.59/70.59 thf(2919,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/sandbox/benchmark/theBenchmark.p',fact_7792_arccos__minus__abs)). 159.59/70.59 thf(17656,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)],[2919])). 159.59/70.59 thf(7143,axiom,(((semiri1408675320244567234ct_nat @ (suc @ zero_zero_nat)) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8059_fact__Suc__0)). 159.59/70.59 thf(32918,plain,(((semiri1408675320244567234ct_nat @ (suc @ zero_zero_nat)) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7143])). 159.59/70.59 thf(8020,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_power__Suc)). 159.59/70.59 thf(35877,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)],[8020])). 159.59/70.59 thf(1315,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/sandbox/benchmark/theBenchmark.p',fact_334_one__plus__numeral__commute)). 159.59/70.59 thf(12500,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)],[1315])). 159.59/70.59 thf(804,axiom,((exp_complex = (^ [A:complex]: (plus_plus_complex @ one_one_complex @ (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (suc @ B))) @ (power_power_complex @ A @ (suc @ B))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9297_exp__first__term)). 159.59/70.59 thf(10844,plain,(((exp_complex) = (^ [A:complex]: (plus_plus_complex @ one_one_complex @ (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (suc @ B))) @ (power_power_complex @ A @ (suc @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[804])). 159.59/70.59 thf(2683,axiom,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1287_add__diff__eq)). 159.59/70.59 thf(16898,plain,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2683])). 159.59/70.59 thf(2822,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A) => ((ord_le2932123472753598470d_enat @ B @ C) => (ord_le2932123472753598470d_enat @ B @ (plus_p3455044024723400733d_enat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2032_add__increasing2)). 159.59/70.59 thf(17326,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A) => ((ord_le2932123472753598470d_enat @ B @ C) => (ord_le2932123472753598470d_enat @ B @ (plus_p3455044024723400733d_enat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2822])). 159.59/70.59 thf(4093,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ one_on7984719198319812577d_enat) => (((ord_le2932123472753598470d_enat @ B @ one_on7984719198319812577d_enat) => (ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ A @ B) @ one_on7984719198319812577d_enat)) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2302_mult__le__one)). 159.59/70.59 thf(21386,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ one_on7984719198319812577d_enat) => (((ord_le2932123472753598470d_enat @ B @ one_on7984719198319812577d_enat) => (ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ A @ B) @ one_on7984719198319812577d_enat)) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4093])). 159.59/70.59 thf(7000,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((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))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_869_nat__eq__add__iff2)). 159.59/70.59 thf(32356,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((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))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7000])). 159.59/70.59 thf(5532,axiom,((! [A:nat,B:nat,C:real]: ((root @ (times_times_nat @ A @ B) @ C) = (root @ A @ (root @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9500_real__root__mult__exp)). 159.59/70.59 thf(26549,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)],[5532])). 159.59/70.59 thf(668,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2274_add__nonneg__pos)). 159.59/70.59 thf(10387,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[668])). 159.59/70.59 thf(5925,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/sandbox/benchmark/theBenchmark.p',fact_6119_exp__double)). 159.59/70.59 thf(28146,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)],[5925])). 159.59/70.59 thf(5770,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/sandbox/benchmark/theBenchmark.p',fact_8270_pochhammer__Suc)). 159.59/70.59 thf(27359,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)],[5770])). 159.59/70.59 thf(2101,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3663_verit__comp__simplify1_I2_J)). 159.59/70.59 thf(15019,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2101])). 159.59/70.59 thf(4541,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4511_minf_I8_J)). 159.59/70.59 thf(22930,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)],[4541])). 159.59/70.59 thf(197,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/sandbox/benchmark/theBenchmark.p',fact_6114_tanh__altdef)). 159.59/70.59 thf(8855,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)],[197])). 159.59/70.59 thf(4326,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/sandbox/benchmark/theBenchmark.p',fact_6968_summable__cmult__iff)). 159.59/70.59 thf(22118,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)],[4326])). 159.59/70.59 thf(1302,axiom,((! [A:(nat > nat),B:(nat > nat),C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (B @ D))) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7882_sum__diff__distrib)). 159.59/70.59 thf(12458,plain,((! [A:(nat > nat),B:(nat > nat),C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (B @ D))) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302])). 159.59/70.59 thf(2203,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/sandbox/benchmark/theBenchmark.p',fact_6072_AND__lower)). 159.59/70.59 thf(15361,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)],[2203])). 159.59/70.59 thf(3295,axiom,((! [A:int,B:int]: ((ord_less_int @ (modulo_modulo_int @ B @ A) @ A) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3473_unique__euclidean__semiring__numeral__class_Opos__mod__bound)). 159.59/70.59 thf(18857,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)],[3295])). 159.59/70.59 thf(5010,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (bit_se1412395901928357646or_nat @ A @ B)) <= (! [C:nat]: (~ (bit_se1148574629649215175it_nat @ A @ C) | ~ (bit_se1148574629649215175it_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6391_disjunctive__add)). 159.59/70.59 thf(24585,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (bit_se1412395901928357646or_nat @ A @ B)) | ~ (! [C:nat]: (~ (bit_se1148574629649215175it_nat @ A @ C) | ~ (bit_se1148574629649215175it_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5010])). 159.59/70.59 thf(4138,axiom,((! [A:int]: ~ (ord_less_int @ (abs_abs_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5518_abs__not__less__zero)). 159.59/70.59 thf(21521,plain,((! [A:int]: ~ (ord_less_int @ (abs_abs_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4138])). 159.59/70.59 thf(2230,axiom,((! [A:num,B:num,C:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (plus_plus_num @ A @ B))) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4783_semiring__norm_I168_J)). 159.59/70.59 thf(15450,plain,((! [A:num,B:num,C:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B)) @ C)) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (plus_plus_num @ A @ B))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2230])). 159.59/70.60 thf(2448,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups6591440286371151544t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7974_sum_OatLeast1__atMost__eq)). 159.59/70.60 thf(16135,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups6591440286371151544t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2448])). 159.59/70.60 thf(252,axiom,((! [A:complex]: (ord_less_eq_real @ (re @ A) @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9632_complex__Re__le__cmod)). 159.59/70.60 thf(9020,plain,((! [A:complex]: (ord_less_eq_real @ (re @ A) @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[252])). 159.59/70.60 thf(4869,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1561_le0)). 159.59/70.60 thf(24087,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4869])). 159.59/70.60 thf(2405,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/sandbox/benchmark/theBenchmark.p',fact_8159_pochhammer__double)). 159.59/70.60 thf(15980,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)],[2405])). 159.59/70.60 thf(4537,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/sandbox/benchmark/theBenchmark.p',fact_4096_unit__div__cancel)). 159.59/70.60 thf(22915,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)],[4537])). 159.59/70.60 thf(5422,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/sandbox/benchmark/theBenchmark.p',fact_4826_le__divide__eq__numeral1_I2_J)). 159.59/70.60 thf(26169,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)],[5422])). 159.59/70.60 thf(6830,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/sandbox/benchmark/theBenchmark.p',fact_7666_sum_OatLeast__Suc__atMost)). 159.59/70.60 thf(31545,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)],[6830])). 159.59/70.60 thf(6084,axiom,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit1 @ B)) = (bit1 @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5421_semiring__norm_I7_J)). 159.59/70.60 thf(28701,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)],[6084])). 159.59/70.60 thf(1441,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/sandbox/benchmark/theBenchmark.p',fact_5579_abs__diff__triangle__ineq)). 159.59/70.60 thf(12949,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)],[1441])). 159.59/70.60 thf(5056,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/sandbox/benchmark/theBenchmark.p',fact_1265_right__diff__distrib)). 159.59/70.60 thf(24759,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)],[5056])). 159.59/70.60 thf(6998,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6684_less__imp__of__nat__less)). 159.59/70.60 thf(32351,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)],[6998])). 159.59/70.60 thf(6361,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/sandbox/benchmark/theBenchmark.p',fact_4758_left__minus__one__mult__self)). 159.59/70.60 thf(29676,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)],[6361])). 159.59/70.60 thf(4082,axiom,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ C @ D) => (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ C) @ (times_3573771949741848930nteger @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3964_mult__dvd__mono)). 159.59/70.60 thf(21353,plain,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ C @ D) => (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ C) @ (times_3573771949741848930nteger @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4082])). 159.59/70.60 thf(7523,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/sandbox/benchmark/theBenchmark.p',fact_3995_dvd__unit__imp__unit)). 159.59/70.60 thf(34260,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)],[7523])). 159.59/70.60 thf(5700,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/sandbox/benchmark/theBenchmark.p',fact_6763_real__of__nat__div3)). 159.59/70.60 thf(27126,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)],[5700])). 159.59/70.60 thf(4865,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/sandbox/benchmark/theBenchmark.p',fact_358_power__commutes)). 159.59/70.60 thf(24076,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)],[4865])). 159.59/70.60 thf(4826,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/sandbox/benchmark/theBenchmark.p',fact_3466_mod__Suc__Suc__eq)). 159.59/70.60 thf(23951,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)],[4826])). 159.59/70.60 thf(639,axiom,((topolo6980174941875973593q_real = (^ [A:(nat > real)]: (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_real @ (A @ B) @ (A @ C))) | ! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7860_monoseq__def)). 159.59/70.60 thf(10299,plain,(((topolo6980174941875973593q_real) = (^ [A:(nat > real)]: (! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_real @ (A @ B) @ (A @ C))) | ! [B:nat,C:nat]: ((ord_less_eq_real @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[639])). 159.59/70.60 thf(6166,axiom,((! [A:nat,B:nat]: ((bit_se1148574629649215175it_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B) = ((B = zero_zero_nat) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6358_bit__mod__2__iff)). 159.59/70.60 thf(28977,plain,((! [A:nat,B:nat]: ((bit_se1148574629649215175it_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B) = ((B = zero_zero_nat) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6166])). 159.59/70.60 thf(6914,axiom,((! [A:num]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5707_diff__numeral__special_I5_J)). 159.59/70.60 thf(31904,plain,((! [A:num]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6914])). 159.59/70.60 thf(7219,axiom,((! [A:nat,B:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B))) <= (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6782_less__log2__of__power)). 159.59/70.60 thf(33219,plain,((! [A:nat,B:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ B))) | ~ (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7219])). 159.59/70.60 thf(2060,axiom,((! [A:int]: ((plus_plus_int @ A @ (uminus_uminus_int @ A)) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4687_add_Oright__inverse)). 159.59/70.60 thf(14895,plain,((! [A:int]: ((plus_plus_int @ A @ (uminus_uminus_int @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2060])). 159.59/70.60 thf(7023,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_829_diff__le__mono)). 159.59/70.60 thf(32427,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7023])). 159.59/70.60 thf(1727,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le2932123472753598470d_enat @ B @ C) => (ord_le2932123472753598470d_enat @ (plus_p3455044024723400733d_enat @ B @ A) @ C)) <= (ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2036_add__decreasing2)). 159.59/70.60 thf(13834,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le2932123472753598470d_enat @ B @ C) => (ord_le2932123472753598470d_enat @ (plus_p3455044024723400733d_enat @ B @ A) @ C)) | ~ (ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727])). 159.59/70.60 thf(4089,axiom,((! [A:nat]: ((one_on7984719198319812577d_enat = (semiri4216267220026989637d_enat @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6544_of__nat__1__eq__iff)). 159.59/70.60 thf(21375,plain,((! [A:nat]: ((one_on7984719198319812577d_enat = (semiri4216267220026989637d_enat @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4089])). 159.59/70.60 thf(4175,axiom,((ord_less_int = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & ~ (ord_less_eq_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3061_less__le__not__le)). 159.59/70.60 thf(21645,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)],[4175])). 159.59/70.60 thf(1534,axiom,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ (minus_minus_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ (divide_divide_real @ B @ A))) @ one_one_real) @ A) @ B) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7162_ceiling__divide__lower)). 159.59/70.60 thf(13244,plain,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ (minus_minus_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ (divide_divide_real @ B @ A))) @ one_one_real) @ A) @ B) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534])). 159.59/70.60 thf(2370,axiom,((! [A:$o,B:$o]: ((ord_less_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B)) = (~ (A) & (B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4318_of__bool__less__iff)). 159.59/70.60 thf(15859,plain,((! [A:$o,B:$o]: ((ord_less_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B)) = (~ (A) & (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2370])). 159.59/70.60 thf(421,axiom,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se4203085406695923979it_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4239_even__unset__bit__iff)). 159.59/70.60 thf(9573,plain,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se4203085406695923979it_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[421])). 159.59/70.60 thf(5814,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3867_unit__div__mult__self)). 159.59/70.60 thf(27679,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5814])). 159.59/70.60 thf(2625,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((root @ A @ B) = (powr_real @ B @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ A)))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9535_root__powr__inverse)). 159.59/70.60 thf(16708,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((root @ A @ B) = (powr_real @ B @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ A)))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2625])). 159.59/70.60 thf(6155,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/sandbox/benchmark/theBenchmark.p',fact_7296_powr__half__sqrt)). 159.59/70.60 thf(28932,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)],[6155])). 159.59/70.60 thf(1196,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/sandbox/benchmark/theBenchmark.p',fact_7940_sum_Onat__diff__reindex)). 159.59/70.60 thf(12094,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)],[1196])). 159.59/70.60 thf(6694,axiom,((! [A:int,B:int]: (((A = B) <= (ord_less_eq_int @ B @ A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2736_order__antisym)). 159.59/70.60 thf(30991,plain,((! [A:int,B:int]: ((A = B) | ~ (ord_less_eq_int @ B @ A) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6694])). 159.59/70.60 thf(7921,axiom,((deg = (plus_plus_nat @ na @ m))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__C3_C)). 159.59/70.60 thf(35574,plain,((deg = (plus_plus_nat @ na @ m))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7921])). 159.59/70.60 thf(4510,axiom,((! [A:num]: (ord_less_eq_num @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2608_order__refl)). 159.59/70.60 thf(22759,plain,((! [A:num]: (ord_less_eq_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4510])). 159.59/70.60 thf(2151,axiom,((! [A:int]: ((zero_zero_int = (plus_plus_int @ A @ A)) = (A = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1527_double__zero__sym)). 159.59/70.60 thf(15190,plain,((! [A:int]: ((zero_zero_int = (plus_plus_int @ A @ A)) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2151])). 159.59/70.60 thf(5715,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBT]: ((if_VEBT_VEBT @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T)). 159.59/70.60 thf(27170,plain,((! [A:vEBT_VEBT,B:vEBT_VEBT]: ((if_VEBT_VEBT @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5715])). 159.59/70.60 thf(1262,axiom,((cos_complex = (^ [A:complex]: (sin_complex @ (minus_minus_complex @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one))) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7794_cos__sin__eq)). 159.59/70.60 thf(12334,plain,(((cos_complex) = (^ [A:complex]: (sin_complex @ (minus_minus_complex @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262])). 159.59/70.60 thf(1927,axiom,((! [A:real]: ((((log @ A @ A) = one_one_real) <= (A != one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6336_log__eq__one)). 159.59/70.60 thf(14468,plain,((! [A:real]: (((log @ A @ A) = one_one_real) | (A = one_one_real) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1927])). 159.59/70.60 thf(687,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (bit_se727722235901077358nd_nat @ A @ B)) = (bit_se725231765392027082nd_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6716_of__nat__and__eq)). 159.59/70.60 thf(10446,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (bit_se727722235901077358nd_nat @ A @ B)) = (bit_se725231765392027082nd_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[687])). 159.59/70.60 thf(5900,axiom,((? [A:real]: (! [B:real]: ((B = A) <= ((ord_less_eq_real @ B @ (numeral_numeral_real @ (bit0 @ one))) & ((cos_real @ B) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B))) & ((cos_real @ A) = zero_zero_real) & (ord_less_eq_real @ A @ (numeral_numeral_real @ (bit0 @ one))) & (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7146_cos__is__zero)). 159.59/70.60 thf(28045,plain,((? [A:real]: (! [B:real]: ((B = A) | ~ ((ord_less_eq_real @ B @ (numeral_numeral_real @ (bit0 @ one))) & ((cos_real @ B) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B))) & ((cos_real @ A) = zero_zero_real) & (ord_less_eq_real @ A @ (numeral_numeral_real @ (bit0 @ one))) & (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5900])). 159.59/70.60 thf(5435,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/sandbox/benchmark/theBenchmark.p',fact_4166_unit__div__commute)). 159.59/70.60 thf(26218,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)],[5435])). 159.59/70.60 thf(1056,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A)) <= (ord_less_real @ zero_zero_real @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9063_le__imp__inverse__le)). 159.59/70.60 thf(11635,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A)) | ~ (ord_less_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056])). 159.59/70.60 thf(3898,axiom,((! [A:nat,B:nat,C:set_nat]: (((insert_nat @ A @ bot_bot_set_nat) = (insert_nat @ B @ C)) = ((ord_less_eq_set_nat @ C @ (insert_nat @ A @ bot_bot_set_nat)) & (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6162_singleton__insert__inj__eq)). 159.59/70.60 thf(20798,plain,((! [A:nat,B:nat,C:set_nat]: (((insert_nat @ A @ bot_bot_set_nat) = (insert_nat @ B @ C)) = ((ord_less_eq_set_nat @ C @ (insert_nat @ A @ bot_bot_set_nat)) & (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3898])). 159.59/70.60 thf(620,axiom,((! [A:extended_enat,B:extended_enat]: ((zero_z5237406670263579293d_enat = (plus_p3455044024723400733d_enat @ A @ B)) = ((A = zero_z5237406670263579293d_enat) & (B = zero_z5237406670263579293d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1506_zero__eq__add__iff__both__eq__0)). 159.59/70.60 thf(10234,plain,((! [A:extended_enat,B:extended_enat]: ((zero_z5237406670263579293d_enat = (plus_p3455044024723400733d_enat @ A @ B)) = ((A = zero_z5237406670263579293d_enat) & (B = zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[620])). 159.59/70.60 thf(8202,axiom,((! [A:nat,B:nat]: (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) != zero_zero_nat) => ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2514_exp__add__not__zero__imp__left)). 159.59/70.60 thf(36478,plain,((! [A:nat,B:nat]: ((~ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) = zero_zero_nat)) => (~ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8202])). 159.59/70.60 thf(682,axiom,((! [A:real,B:real]: (((complex2 @ A @ B) = imaginary_unit) = ((A = zero_zero_real) & (B = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9350_Complex__eq__i)). 159.59/70.60 thf(10431,plain,((! [A:real,B:real]: (((complex2 @ A @ B) = imaginary_unit) = ((A = zero_zero_real) & (B = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[682])). 159.59/70.60 thf(4504,axiom,((! [A:num]: ((minus_8373710615458151222nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (numera6620942414471956472nteger @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4884_diff__numeral__special_I3_J)). 159.59/70.60 thf(22738,plain,((! [A:num]: ((minus_8373710615458151222nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (numera6620942414471956472nteger @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4504])). 159.59/70.60 thf(1687,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/sandbox/benchmark/theBenchmark.p',fact_7829_double__gauss__sum__from__Suc__0)). 159.59/70.60 thf(13712,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)],[1687])). 159.59/70.60 thf(4001,axiom,((! [A:real]: ((ord_less_real @ one_one_real @ (exp_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5994_one__less__exp__iff)). 159.59/70.60 thf(21114,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)],[4001])). 159.59/70.60 thf(3388,axiom,((! [A:real,B:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4616_neg__less__iff__less)). 159.59/70.60 thf(19142,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)],[3388])). 159.59/70.60 thf(8163,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2066_mult__strict__right__mono)). 159.59/70.60 thf(36360,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8163])). 159.59/70.60 thf(5310,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/sandbox/benchmark/theBenchmark.p',fact_2273_add__nonneg__pos)). 159.59/70.60 thf(25685,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)],[5310])). 159.59/70.60 thf(3341,axiom,((! [A:set_nat,B:nat]: ((ord_less_eq_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)) = ((A = (insert_nat @ B @ bot_bot_set_nat)) | (A = bot_bot_set_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6207_subset__singleton__iff)). 159.59/70.60 thf(18995,plain,((! [A:set_nat,B:nat]: ((ord_less_eq_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)) = ((A = (insert_nat @ B @ bot_bot_set_nat)) | (A = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3341])). 159.59/70.60 thf(1851,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/sandbox/benchmark/theBenchmark.p',fact_1442_add__divide__distrib)). 159.59/70.60 thf(14235,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)],[1851])). 159.59/70.60 thf(4181,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/sandbox/benchmark/theBenchmark.p',fact_2027_add__nonpos__nonpos)). 159.59/70.60 thf(21662,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)],[4181])). 159.59/70.60 thf(2479,axiom,((! [A:int,B:real]: ((ord_less_eq_int @ A @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (ring_1_of_int_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8224_le__floor__iff)). 159.59/70.60 thf(16228,plain,((! [A:int,B:real]: ((ord_less_eq_int @ A @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (ring_1_of_int_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2479])). 159.59/70.60 thf(1976,axiom,((! [A:int,B:int]: ((A = (uminus_uminus_int @ B)) = ((plus_plus_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5047_eq__neg__iff__add__eq__0)). 159.59/70.60 thf(14625,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)],[1976])). 159.59/70.60 thf(866,axiom,(((bit_se2000444600071755411sk_int @ (suc @ zero_zero_nat)) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5993_mask__Suc__0)). 159.59/70.60 thf(11043,plain,(((bit_se2000444600071755411sk_int @ (suc @ zero_zero_nat)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[866])). 159.59/70.60 thf(3336,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/sandbox/benchmark/theBenchmark.p',fact_7987_suminf__minus__initial__segment)). 159.59/70.60 thf(18981,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)],[3336])). 159.59/70.60 thf(7153,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/sandbox/benchmark/theBenchmark.p',fact_5848_numeral__power__le__of__int__cancel__iff)). 159.59/70.60 thf(32950,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)],[7153])). 159.59/70.60 thf(6475,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (! [C:real]: (((ord_less_real @ C @ one_one_real) => (ord_less_eq_real @ (times_times_real @ C @ A) @ B)) <= (ord_less_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2426_field__le__mult__one__interval)). 159.59/70.60 thf(30158,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (! [C:real]: (((ord_less_real @ C @ one_one_real) => (ord_less_eq_real @ (times_times_real @ C @ A) @ B)) | ~ (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6475])). 159.59/70.60 thf(2010,axiom,((! [A:real,B:(num > real),C:num,D:num]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3233_order__less__le__subst1)). 159.59/70.60 thf(14748,plain,((! [A:real,B:(num > real),C:num,D:num]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2010])). 159.59/70.60 thf(6698,axiom,((! [A:(nat > complex),B:nat]: ((! [C:complex]: ((groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ (power_power_complex @ C @ D))) @ (set_ord_atMost_nat @ B)) = zero_zero_complex)) = (! [C:nat]: (((A @ C) = zero_zero_complex) <= (ord_less_eq_nat @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8834_polyfun__eq__0)). 159.59/70.60 thf(31004,plain,((! [A:(nat > complex),B:nat]: ((! [C:complex]: ((groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ (power_power_complex @ C @ D))) @ (set_ord_atMost_nat @ B)) = zero_zero_complex)) = (! [C:nat]: (((A @ C) = zero_zero_complex) | ~ (ord_less_eq_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6698])). 159.59/70.60 thf(3939,axiom,(((neg_nu8557863876264182079omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5801_dbl__inc__simps_I4_J)). 159.59/70.60 thf(20922,plain,(((neg_nu8557863876264182079omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3939])). 159.59/70.60 thf(1132,axiom,((! [A:real,B:real]: (((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (((arctan @ B) = A) <= ((tan_real @ A) = B))) <= (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7305_arctan__unique)). 159.59/70.60 thf(11880,plain,((! [A:real,B:real]: (((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (((arctan @ B) = A) | ~ ((tan_real @ A) = B))) | ~ (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132])). 159.59/70.60 thf(2055,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ A @ B) => (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4927_le__imp__neg__le)). 159.59/70.60 thf(14880,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)],[2055])). 159.59/70.60 thf(325,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((A != zero_z3403309356797280102nteger) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ A @ B) @ C) @ A) = (plus_p5714425477246183910nteger @ B @ (divide6298287555418463151nteger @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1742_div__mult__self4)). 159.59/70.60 thf(9251,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ A @ B) @ C) @ A) = (plus_p5714425477246183910nteger @ B @ (divide6298287555418463151nteger @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 159.59/70.60 thf(4619,axiom,((! [A:nat,B:nat,C:nat]: (((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))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_le__diff__iff_H)). 159.59/70.60 thf(23219,plain,((! [A:nat,B:nat,C:nat]: (((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))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4619])). 159.59/70.60 thf(1511,axiom,((! [A:extended_enat,B:extended_enat]: ? [C:extended_enat]: ! [D:extended_enat]: (((~ (dvd_dv3785147216227455552d_enat @ A @ (plus_p3455044024723400733d_enat @ D @ B))) = (~ (dvd_dv3785147216227455552d_enat @ A @ (plus_p3455044024723400733d_enat @ D @ B)))) <= (ord_le72135733267957522d_enat @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4532_pinf_I10_J)). 159.59/70.60 thf(13177,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511])). 159.59/70.60 thf(3473,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ A @ C) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3089_order_Ostrict__trans2)). 159.59/70.60 thf(19406,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ A @ C) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3473])). 159.59/70.60 thf(5336,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((C) => (B = (some_nat @ zero_zero_nat))) & ((((~ (D)) => (B = none_nat)) & ((D) => (B = (some_nat @ one_one_nat)))) <= (~ (C))))))) => (((B != none_nat) <= (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ (! [C:nat]: ((B != (some_nat @ C)) <= (? [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)))))))) <= ((vEBT_vebt_mint @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2408_vebt__mint_Oelims)). 159.59/70.60 thf(25769,plain,((! [A:vEBT_VEBT,B:option_nat]: (((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((C) => (B = (some_nat @ zero_zero_nat))) & ((((~ (D)) => (B = none_nat)) & ((D) => (B = (some_nat @ one_one_nat)))) | (C)))))) => ((~ (B = none_nat) | ~ (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ (! [C:nat]: (~ (B = (some_nat @ C)) | ~ (? [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)))))))) | ~ ((vEBT_vebt_mint @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5336])). 159.59/70.60 thf(3732,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/sandbox/benchmark/theBenchmark.p',fact_7887_sums__mult2)). 159.59/70.60 thf(20258,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)],[3732])). 159.59/70.60 thf(427,axiom,((! [A:code_integer]: ((bit_se1080825931792720795nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5973_bit_Odisj__one__right)). 159.59/70.60 thf(9590,plain,((! [A:code_integer]: ((bit_se1080825931792720795nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])). 159.59/70.60 thf(2464,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_real @ C @ B) => ((ord_less_eq_real @ zero_zero_real @ D) => ((ord_less_eq_real @ zero_zero_real @ E) => (((plus_plus_real @ D @ E) = one_one_real) => (ord_less_real @ (plus_plus_real @ (times_times_real @ D @ A) @ (times_times_real @ E @ C)) @ B))))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2497_convex__bound__lt)). 159.59/70.60 thf(16184,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_real @ C @ B) => ((ord_less_eq_real @ zero_zero_real @ D) => ((ord_less_eq_real @ zero_zero_real @ E) => (((plus_plus_real @ D @ E) = one_one_real) => (ord_less_real @ (plus_plus_real @ (times_times_real @ D @ A) @ (times_times_real @ E @ C)) @ B))))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2464])). 159.59/70.60 thf(2176,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/sandbox/benchmark/theBenchmark.p',fact_7821_arith__series)). 159.59/70.60 thf(15267,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)],[2176])). 159.59/70.60 thf(6681,axiom,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => ((~ (member_nat @ B @ A)) => ((groups129246275422532515t_real @ C @ (insert_nat @ B @ A)) = (times_times_real @ (C @ B) @ (groups129246275422532515t_real @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8430_prod_Oinsert)). 159.59/70.60 thf(30895,plain,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => ((~ (member_nat @ B @ A)) => ((groups129246275422532515t_real @ (C) @ (insert_nat @ B @ A)) = (times_times_real @ (C @ B) @ (groups129246275422532515t_real @ (C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6681])). 159.59/70.60 thf(2305,axiom,((one_one_complex = (complex2 @ one_one_real @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7239_one__complex_Ocode)). 159.59/70.60 thf(15671,plain,((one_one_complex = (complex2 @ one_one_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2305])). 159.59/70.60 thf(5210,axiom,((! [A:int]: ((times_times_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ one))) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5206_mult__1s__ring__1_I2_J)). 159.59/70.60 thf(25304,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)],[5210])). 159.59/70.60 thf(1183,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/sandbox/benchmark/theBenchmark.p',fact_2295_sum__squares__ge__zero)). 159.59/70.60 thf(12040,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)],[1183])). 159.59/70.60 thf(3656,axiom,((! [A:(nat > real),B:real]: ((! [C:nat]: (ord_less_eq_real @ (A @ C) @ one_one_real)) => ((! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))) => (((summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) <= (ord_less_real @ B @ one_one_real)) <= (ord_less_eq_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7132_summable__power__series)). 159.59/70.60 thf(19994,plain,((! [A:(nat > real),B:real]: ((! [C:nat]: (ord_less_eq_real @ (A @ C) @ one_one_real)) => ((! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))) => ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) | ~ (ord_less_real @ B @ one_one_real) | ~ (ord_less_eq_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3656])). 159.59/70.60 thf(2806,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2832_order_Ostrict__implies__not__eq)). 159.59/70.60 thf(17278,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2806])). 159.59/70.60 thf(2642,axiom,((! [A:(nat > extended_enat),B:set_nat]: (((groups7961826882256487087d_enat @ A @ B) != one_on7984719198319812577d_enat) => (~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = one_on7984719198319812577d_enat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8460_prod_Onot__neutral__contains__not__neutral)). 159.59/70.60 thf(16765,plain,((! [A:(nat > extended_enat),B:set_nat]: ((~ ((groups7961826882256487087d_enat @ (A) @ B) = one_on7984719198319812577d_enat)) => (~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = one_on7984719198319812577d_enat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2642])). 159.59/70.60 thf(4625,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) => ((B = zero_zero_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1867_divisors__zero)). 159.59/70.60 thf(23240,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)],[4625])). 159.59/70.60 thf(3090,axiom,((! [A:real,B:(nat > real),C:nat]: ((? [D:real]: ! [E:real]: ((ord_less_eq_real @ D @ (real_V7735802525324610683m_real @ E)) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (B @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ A @ (power_power_real @ (real_V7735802525324610683m_real @ E) @ (suc @ C)))))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8957_polyfun__extremal__lemma)). 159.59/70.60 thf(18193,plain,((! [A:real,B:(nat > real),C:nat]: (? [D:real]: ! [E:real]: ((ord_less_eq_real @ D @ (real_V7735802525324610683m_real @ E)) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (B @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ A @ (power_power_real @ (real_V7735802525324610683m_real @ E) @ (suc @ C))))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3090])). 159.59/70.60 thf(4896,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/sandbox/benchmark/theBenchmark.p',fact_837_diff__cancel2)). 159.59/70.60 thf(24173,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)],[4896])). 159.59/70.60 thf(1037,axiom,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_real @ (C @ A) @ D)) <= (ord_less_real @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3228_order__le__less__subst2)). 159.59/70.60 thf(11571,plain,((! [A:nat,B:nat,C:(nat > real),D:real]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_real @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_real @ (C @ A) @ D)) | ~ (ord_less_real @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037])). 159.59/70.60 thf(432,axiom,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se1345352211410354436nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) != (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4244_even__flip__bit__iff)). 159.59/70.60 thf(9604,plain,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se1345352211410354436nteger @ A @ B)) = (~ ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) = (A = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[432])). 159.59/70.60 thf(4156,axiom,((! [A:int,B:nat]: (((bit_se725231765392027082nd_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = zero_zero_int) = (~ (bit_se1146084159140164899it_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6436_and__exp__eq__0__iff__not__bit)). 159.59/70.60 thf(21585,plain,((! [A:int,B:nat]: (((bit_se725231765392027082nd_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = zero_zero_int) = (~ (bit_se1146084159140164899it_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4156])). 159.59/70.60 thf(6282,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/sandbox/benchmark/theBenchmark.p',fact_803_diff__diff__left)). 159.59/70.60 thf(29435,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)],[6282])). 159.59/70.60 thf(1276,axiom,((! [A:extended_enat,B:extended_enat,C:num]: ((times_7803423173614009249d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ (numera1916890842035813515d_enat @ C)) = (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ A @ (numera1916890842035813515d_enat @ C)) @ (times_7803423173614009249d_enat @ B @ (numera1916890842035813515d_enat @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_distrib__right__numeral)). 159.59/70.60 thf(12376,plain,((! [A:extended_enat,B:extended_enat,C:num]: ((times_7803423173614009249d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ (numera1916890842035813515d_enat @ C)) = (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ A @ (numera1916890842035813515d_enat @ C)) @ (times_7803423173614009249d_enat @ B @ (numera1916890842035813515d_enat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276])). 159.59/70.60 thf(7472,axiom,((((=) @ int) = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & (ord_less_eq_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2698_Orderings_Oorder__eq__iff)). 159.59/70.60 thf(34071,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)],[7472])). 159.59/70.60 thf(6600,axiom,((! [A:num,B:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (times_times_complex @ B @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5074_numeral__times__minus__swap)). 159.59/70.60 thf(30603,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)],[6600])). 159.59/70.60 thf(2340,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ln_ln_real @ (inverse_inverse_real @ A)) = (uminus_uminus_real @ (ln_ln_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9100_ln__inverse)). 159.59/70.60 thf(15770,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ln_ln_real @ (inverse_inverse_real @ A)) = (uminus_uminus_real @ (ln_ln_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2340])). 159.59/70.60 thf(3103,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ A @ B)) = (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1601_less__add__same__cancel1)). 159.59/70.60 thf(18233,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)],[3103])). 159.59/70.60 thf(945,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)) | ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2145_divide__le__0__iff)). 159.59/70.60 thf(11277,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)) | ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[945])). 159.59/70.60 thf(4852,axiom,((vEBT_V8194947554948674370ptions = (^ [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_membermima @ A @ B) | (vEBT_V5719532721284313246member @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1471_both__member__options__def)). 159.59/70.60 thf(24037,plain,(((vEBT_V8194947554948674370ptions) = (^ [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_membermima @ A @ B) | (vEBT_V5719532721284313246member @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4852])). 159.59/70.60 thf(3173,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/sandbox/benchmark/theBenchmark.p',fact_7044_suminf__mult)). 159.59/70.60 thf(18459,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)],[3173])). 159.59/70.60 thf(7887,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/sandbox/benchmark/theBenchmark.p',fact_708_add__mult__distrib)). 159.59/70.60 thf(35461,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)],[7887])). 159.59/70.60 thf(3763,axiom,((! [A:real,B:nat,C:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_nat @ B @ C) <= (ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_power__less__imp__less__exp)). 159.59/70.60 thf(20354,plain,((! [A:real,B:nat,C:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_nat @ B @ C) | ~ (ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3763])). 159.59/70.60 thf(4420,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/sandbox/benchmark/theBenchmark.p',fact_7076_summable__powser__ignore__initial__segment)). 159.59/70.60 thf(22417,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)],[4420])). 159.59/70.60 thf(988,axiom,((! [A:set_nat,B:nat,C:(nat > real)]: (((member_nat @ B @ A) => (((! [D:nat]: ((ord_less_eq_real @ one_one_real @ (C @ D)) <= (member_nat @ D @ A))) => (ord_less_real @ one_one_real @ (groups129246275422532515t_real @ C @ A))) <= (ord_less_real @ one_one_real @ (C @ B)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8641_less__1__prod2)). 159.59/70.60 thf(11409,plain,((! [A:set_nat,B:nat,C:(nat > real)]: (((member_nat @ B @ A) => (((! [D:nat]: ((ord_less_eq_real @ one_one_real @ (C @ D)) | ~ (member_nat @ D @ A))) => (ord_less_real @ one_one_real @ (groups129246275422532515t_real @ (C) @ A))) | ~ (ord_less_real @ one_one_real @ (C @ B)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[988])). 159.59/70.60 thf(3143,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/sandbox/benchmark/theBenchmark.p',fact_2349_add__frac__num)). 159.59/70.60 thf(18365,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)],[3143])). 159.59/70.60 thf(5937,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ one_one_int) = (numeral_numeral_int @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6012_or__numerals_I5_J)). 159.59/70.60 thf(28205,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ one_one_int) = (numeral_numeral_int @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5937])). 159.59/70.60 thf(2916,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) = (C @ B)) <= (member_nat @ B @ A)) & (((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (B = D) @ (C @ D) @ one_one_complex)) @ A) = one_one_complex) <= (~ (member_nat @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8410_prod_Odelta_H)). 159.59/70.60 thf(17641,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) = (C @ B)) | ~ (member_nat @ B @ A)) & (((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (B = D) @ (C @ D) @ one_one_complex)) @ A) = one_one_complex) | (member_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2916])). 159.59/70.60 thf(7414,axiom,((! [A:num]: (((numera1916890842035813515d_enat @ A) = one_on7984719198319812577d_enat) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_numeral__eq__one__iff)). 159.59/70.60 thf(33870,plain,((! [A:num]: (((numera1916890842035813515d_enat @ A) = one_on7984719198319812577d_enat) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7414])). 159.59/70.60 thf(6523,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (minus_minus_nat @ A @ B) @ B) = (ord_max_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_nat__minus__add__max)). 159.59/70.60 thf(30318,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)],[6523])). 159.59/70.60 thf(825,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)) <= (ord_less_real @ C @ D)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1222_diff__strict__mono)). 159.59/70.60 thf(10912,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)) | ~ (ord_less_real @ C @ D) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[825])). 159.59/70.60 thf(347,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (real_V1485227260804924795R_real @ A @ B) @ C) = (real_V1485227260804924795R_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9187_mult__scaleR__left)). 159.59/70.60 thf(9324,plain,((! [A:real,B:real,C:real]: ((times_times_real @ (real_V1485227260804924795R_real @ A @ B) @ C) = (real_V1485227260804924795R_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 159.59/70.60 thf(3201,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ B) @ (uminus5710092332889474511et_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4608_Compl__anti__mono)). 159.59/70.60 thf(18549,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ B) @ (uminus5710092332889474511et_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3201])). 159.59/70.60 thf(8033,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/sandbox/benchmark/theBenchmark.p',fact_3911_even__power)). 159.59/70.60 thf(35928,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)],[8033])). 159.59/70.60 thf(7602,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/sandbox/benchmark/theBenchmark.p',fact_9789_num__of__nat__double)). 159.59/70.60 thf(34565,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)],[7602])). 159.59/70.60 thf(3333,axiom,((! [A:real]: ((cosh_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (plus_plus_real @ (power_power_real @ (cosh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (sinh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9353_cosh__double)). 159.59/70.60 thf(18972,plain,((! [A:real]: ((cosh_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (plus_plus_real @ (power_power_real @ (cosh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (sinh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3333])). 159.59/70.60 thf(3250,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) = (((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ B @ zero_zero_int)) | ((ord_less_int @ zero_zero_int @ B) & (ord_less_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2088_zero__less__mult__iff)). 159.59/70.60 thf(18706,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (times_times_int @ A @ B)) = (((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ B @ zero_zero_int)) | ((ord_less_int @ zero_zero_int @ B) & (ord_less_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3250])). 159.59/70.60 thf(7375,axiom,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2740_ord__le__eq__trans)). 159.59/70.60 thf(33751,plain,((! [A:nat,B:nat,C:nat]: (((B = C) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7375])). 159.59/70.60 thf(3752,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/sandbox/benchmark/theBenchmark.p',fact_8441_sum_OatMost__Suc)). 159.59/70.60 thf(20320,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)],[3752])). 159.59/70.60 thf(650,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/sandbox/benchmark/theBenchmark.p',fact_1591_add__le__same__cancel1)). 159.59/70.60 thf(10331,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)],[650])). 159.59/70.60 thf(5563,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/sandbox/benchmark/theBenchmark.p',fact_7172_cos__treble__cos)). 159.59/70.60 thf(26642,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)],[5563])). 159.59/70.60 thf(2356,axiom,((! [A:nat]: ((comm_s4663373288045622133er_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8183_pochhammer__0)). 159.59/70.60 thf(15816,plain,((! [A:nat]: ((comm_s4663373288045622133er_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2356])). 159.59/70.60 thf(6203,axiom,((ord_less_num = (^ [A:num,B:num]: (~ (ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3136_dual__order_Ostrict__iff__not)). 159.59/70.60 thf(29103,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)],[6203])). 159.59/70.60 thf(287,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/sandbox/benchmark/theBenchmark.p',fact_9663_cmod__le)). 159.59/70.60 thf(9120,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)],[287])). 159.59/70.60 thf(3910,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)) @ A) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6098_even__and__iff)). 159.59/70.60 thf(20835,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)) @ A) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3910])). 159.59/70.60 thf(7075,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/sandbox/benchmark/theBenchmark.p',fact_4267_even__mask__div__iff_H)). 159.59/70.60 thf(32631,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)],[7075])). 159.59/70.60 thf(8186,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/sandbox/benchmark/theBenchmark.p',fact_120_div__mult2__numeral__eq)). 159.59/70.60 thf(36426,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)],[8186])). 159.59/70.60 thf(4623,axiom,((! [A:nat]: (((~ (ord_less_nat @ zero_zero_nat @ A)) => ((num_of_nat @ (suc @ A)) = one)) & ((ord_less_nat @ zero_zero_nat @ A) => ((num_of_nat @ (suc @ A)) = (inc @ (num_of_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9784_num__of__nat_Osimps_I2_J)). 159.59/70.60 thf(23230,plain,((! [A:nat]: (((~ (ord_less_nat @ zero_zero_nat @ A)) => ((num_of_nat @ (suc @ A)) = one)) & ((ord_less_nat @ zero_zero_nat @ A) => ((num_of_nat @ (suc @ A)) = (inc @ (num_of_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4623])). 159.59/70.60 thf(6240,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/sandbox/benchmark/theBenchmark.p',fact_3921_semiring__parity__class_Oeven__mask__iff)). 159.59/70.60 thf(29214,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)],[6240])). 159.59/70.60 thf(3483,axiom,((! [A:nat,B:nat]: ((bot_bot_set_nat = (set_or1269000886237332187st_nat @ A @ B)) = (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3350_atLeastatMost__empty__iff2)). 159.59/70.60 thf(19438,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)],[3483])). 159.59/70.60 thf(5886,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/sandbox/benchmark/theBenchmark.p',fact_3425_Suc__mod__mult__self2)). 159.59/70.60 thf(28008,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)],[5886])). 159.59/70.60 thf(761,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3063_not__le__imp__less)). 159.59/70.60 thf(10711,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) => (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[761])). 159.59/70.60 thf(71,axiom,((! [A:int,B:int,C:int]: ((ord_max_int @ (ord_max_int @ A @ B) @ C) = (ord_max_int @ A @ (ord_max_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_max_Oassoc)). 159.59/70.60 thf(8463,plain,((! [A:int,B:int,C:int]: ((ord_max_int @ (ord_max_int @ A @ B) @ C) = (ord_max_int @ A @ (ord_max_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 159.59/70.60 thf(6875,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2038_add__decreasing2)). 159.59/70.60 thf(31780,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6875])). 159.59/70.60 thf(5112,axiom,((vEBT_invar_vebt = (^ [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:vEBT_VEBT]: ((~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) <= (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F)) & (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)) & ! [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))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((vEBT_invar_vebt @ E @ (suc @ D)) & (B = (plus_plus_nat @ D @ (suc @ 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)) @ (suc @ D)))) & ((! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))))) <= (F = G)) & ((! [H:nat]: (((((vEBT_VEBT_high @ G @ D) = H) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ G @ D))) & ! [I:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ I @ D)) & ((vEBT_VEBT_high @ I @ D) = H)) => ((ord_less_nat @ F @ I) & (ord_less_eq_nat @ I @ G)))) <= (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))))) <= (F != G)) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & (ord_less_eq_nat @ F @ G) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))) & ! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ H @ D)) & (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ B @ C @ E))) | ? [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))) & (vEBT_invar_vebt @ E @ D) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & ((! [H:nat]: ((((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ G @ D)) <= ((vEBT_VEBT_high @ G @ D) = H)) & ! [I:nat]: (((ord_less_nat @ F @ I) & (ord_less_eq_nat @ I @ G)) <= ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ I @ D)) & ((vEBT_VEBT_high @ I @ D) = H)))) <= (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)))) <= (F != G)) & (ord_less_eq_nat @ F @ G) & ((F = G) => (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)))))) & ! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ I)) = (vEBT_V8194947554948674370ptions @ E @ H))) & (B = (plus_plus_nat @ D @ D)) & (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ B @ C @ E))) | ? [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)) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [F:vEBT_VEBT]: ((~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) <= (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F)) & (B = (plus_plus_nat @ D @ D)) & (vEBT_invar_vebt @ E @ D) & (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2564_invar__vebt_Osimps)). 159.59/70.60 thf(24949,plain,(((vEBT_invar_vebt) = (^ [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:vEBT_VEBT]: (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)) | ~ (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F)) & (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)) & ! [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))) | ? [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((vEBT_invar_vebt @ E @ (suc @ D)) & (B = (plus_plus_nat @ D @ (suc @ 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)) @ (suc @ D)))) & (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)))) | ~ (F = G)) & (! [H:nat]: (((((vEBT_VEBT_high @ G @ D) = H) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ G @ D))) & ! [I:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ I @ D)) & ((vEBT_VEBT_high @ I @ D) = H)) => ((ord_less_nat @ F @ I) & (ord_less_eq_nat @ I @ G)))) | ~ (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D)))) | (F = G)) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & (ord_less_eq_nat @ F @ G) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ D))) & ! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ H @ D)) & (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ B @ C @ E))) | ? [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))) & (vEBT_invar_vebt @ E @ D) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & (! [H:nat]: ((((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ G @ D)) | ~ ((vEBT_VEBT_high @ G @ D) = H)) & ! [I:nat]: (((ord_less_nat @ F @ I) & (ord_less_eq_nat @ I @ G)) | ~ ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ (vEBT_VEBT_low @ I @ D)) & ((vEBT_VEBT_high @ I @ D) = H)))) | ~ (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) | (F = G)) & (ord_less_eq_nat @ F @ G) & ((F = G) => (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)))))) & ! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ I)) = (vEBT_V8194947554948674370ptions @ E @ H))) & (B = (plus_plus_nat @ D @ D)) & (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ B @ C @ E))) | ? [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)) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [F:vEBT_VEBT]: (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)) | ~ (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ E @ F)) & (B = (plus_plus_nat @ D @ D)) & (vEBT_invar_vebt @ E @ D) & (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5112])). 159.59/70.60 thf(1984,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/sandbox/benchmark/theBenchmark.p',fact_8167_gchoose__row__sum__weighted)). 159.59/70.60 thf(14662,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)],[1984])). 159.59/70.60 thf(630,axiom,((! [A:(nat > real),B:(nat > real)]: ((summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (A @ C)))) => ((summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (B @ C)))) => (sums_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ (suminf_real @ A) @ (suminf_real @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8930_Cauchy__product__sums)). 159.59/70.60 thf(10262,plain,((! [A:(nat > real),B:(nat > real)]: ((summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (A @ C)))) => ((summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (B @ C)))) => (sums_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ (suminf_real @ (A)) @ (suminf_real @ (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[630])). 159.59/70.60 thf(7156,axiom,((! [A:nat]: (ord_less_eq_real @ zero_zero_real @ (semiri2265585572941072030t_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8071_fact__ge__zero)). 159.59/70.60 thf(32959,plain,((! [A:nat]: (ord_less_eq_real @ zero_zero_real @ (semiri2265585572941072030t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7156])). 159.59/70.60 thf(6019,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ B)) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_int @ zero_zero_int @ A)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4258_zero__le__power__eq)). 159.59/70.60 thf(28499,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ B)) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_int @ zero_zero_int @ A)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6019])). 159.59/70.60 thf(2359,axiom,((! [A:real]: ((ord_less_real @ one_one_real @ (inverse_inverse_real @ A)) = ((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9068_one__less__inverse__iff)). 159.59/70.60 thf(15827,plain,((! [A:real]: ((ord_less_real @ one_one_real @ (inverse_inverse_real @ A)) = ((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2359])). 159.59/70.60 thf(1624,axiom,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1297_group__cancel_Osub1)). 159.59/70.60 thf(13525,plain,((! [A:real,B:real,C:real,D:real]: ((A = (plus_plus_real @ B @ C)) => ((minus_minus_real @ A @ D) = (plus_plus_real @ B @ (minus_minus_real @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624])). 159.59/70.60 thf(1465,axiom,((! [A:real]: (((divide_divide_real @ A @ (sqrt @ A)) = (sqrt @ A)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6400_real__div__sqrt)). 159.59/70.60 thf(13035,plain,((! [A:real]: (((divide_divide_real @ A @ (sqrt @ A)) = (sqrt @ A)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1465])). 159.59/70.60 thf(6410,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (times_times_nat @ A @ B)) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6535_of__nat__mult)). 159.59/70.60 thf(29888,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)],[6410])). 159.59/70.60 thf(1674,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/sandbox/benchmark/theBenchmark.p',fact_1073_add__less__cancel__left)). 159.59/70.60 thf(13672,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)],[1674])). 159.59/70.60 thf(2441,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/sandbox/benchmark/theBenchmark.p',fact_2236_mult__le__cancel__left__neg)). 159.59/70.60 thf(16105,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)],[2441])). 159.59/70.60 thf(759,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/sandbox/benchmark/theBenchmark.p',fact_8197_floor__divide__eq__div__numeral)). 159.59/70.60 thf(10705,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)],[759])). 159.59/70.60 thf(6398,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((((vEBT_vebt_succ @ A @ C) = none_nat) = ((collect_nat @ (^ [D:nat]: ((vEBT_vebt_member @ A @ D) & (ord_less_nat @ C @ D)))) = bot_bot_set_nat)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1456_succ__empty)). 159.59/70.60 thf(29844,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((((vEBT_vebt_succ @ A @ C) = none_nat) = ((collect_nat @ (^ [D:nat]: ((vEBT_vebt_member @ A @ D) & (ord_less_nat @ C @ D)))) = bot_bot_set_nat)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6398])). 159.59/70.60 thf(524,axiom,((! [A:complex,B:complex]: ((cosh_complex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ (times_times_complex @ (cosh_complex @ A) @ (cosh_complex @ B)) @ (times_times_complex @ (sinh_complex @ A) @ (sinh_complex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9329_cosh__diff)). 159.59/70.60 thf(9918,plain,((! [A:complex,B:complex]: ((cosh_complex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ (times_times_complex @ (cosh_complex @ A) @ (cosh_complex @ B)) @ (times_times_complex @ (sinh_complex @ A) @ (sinh_complex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[524])). 159.59/70.60 thf(4795,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/sandbox/benchmark/theBenchmark.p',fact_6627_log__pow__cancel)). 159.59/70.60 thf(23810,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)],[4795])). 159.59/70.60 thf(8194,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3837_dvd__div__mult__self)). 159.59/70.60 thf(36451,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ (divide_divide_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8194])). 159.59/70.60 thf(5805,axiom,((! [A:nat,B:real]: (((ord_less_eq_real @ zero_zero_real @ (root @ A @ B)) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9517_real__root__pos__pos)). 159.59/70.60 thf(27596,plain,((! [A:nat,B:real]: ((ord_less_eq_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)],[5805])). 159.59/70.60 thf(3803,axiom,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ A @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups705719431365010083at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8758_prod_OatLeast1__atMost__eq)). 159.59/70.60 thf(20484,plain,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (A) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups705719431365010083at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3803])). 159.59/70.60 thf(3988,axiom,((! [A:nat]: (((semiri4939895301339042750nteger @ A) = one_one_Code_integer) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6543_of__nat__eq__1__iff)). 159.59/70.60 thf(21072,plain,((! [A:nat]: (((semiri4939895301339042750nteger @ A) = one_one_Code_integer) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3988])). 159.59/70.60 thf(3428,axiom,((! [A:(nat > set_nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_set_nat @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_set_nat @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_lift__Suc__antimono__le)). 159.59/70.60 thf(19274,plain,((! [A:(nat > set_nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_set_nat @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_set_nat @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3428])). 159.59/70.60 thf(6962,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/sandbox/benchmark/theBenchmark.p',fact_5285_power2__eq__1__iff)). 159.59/70.60 thf(32091,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)],[6962])). 159.59/70.60 thf(2693,axiom,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5974_bit_Odisj__one__right)). 159.59/70.60 thf(16940,plain,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2693])). 159.59/70.60 thf(5950,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_nat__le__add__iff1)). 159.59/70.60 thf(28281,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5950])). 159.59/70.60 thf(4671,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/sandbox/benchmark/theBenchmark.p',fact_2540_sum__power2__le__zero__iff)). 159.59/70.60 thf(23406,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)],[4671])). 159.59/70.60 thf(4661,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ (root @ A @ C) @ (root @ B @ C)) <= (ord_less_eq_real @ C @ one_one_real))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9527_real__root__increasing)). 159.59/70.60 thf(23374,plain,((! [A:nat,B:nat,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ (root @ A @ C) @ (root @ B @ C)) | ~ (ord_less_eq_real @ C @ one_one_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4661])). 159.59/70.60 thf(7059,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/sandbox/benchmark/theBenchmark.p',fact_8636_prod_Ozero__middle)). 159.59/70.60 thf(32558,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)],[7059])). 159.59/70.60 thf(4273,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (sqrt @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6315_real__sqrt__gt__0__iff)). 159.59/70.60 thf(21961,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)],[4273])). 159.59/70.60 thf(1548,axiom,((! [A:(nat > complex),B:complex,C:complex]: ((sums_complex @ (^ [D:nat]: (divide1717551699836669952omplex @ (A @ D) @ C)) @ (divide1717551699836669952omplex @ B @ C)) <= (sums_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7895_sums__divide)). 159.59/70.60 thf(13283,plain,((! [A:(nat > complex),B:complex,C:complex]: ((sums_complex @ (^ [D:nat]: (divide1717551699836669952omplex @ (A @ D) @ C)) @ (divide1717551699836669952omplex @ B @ C)) | ~ (sums_complex @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1548])). 159.59/70.60 thf(1385,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/sandbox/benchmark/theBenchmark.p',fact_6725_ex__less__of__nat__mult)). 159.59/70.60 thf(12774,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)],[1385])). 159.59/70.60 thf(2853,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/sandbox/benchmark/theBenchmark.p',fact_5981_and__negative__int__iff)). 159.59/70.60 thf(17424,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)],[2853])). 159.59/70.60 thf(1685,axiom,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (plus_plus_nat @ A @ B)) = (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6532_of__nat__add)). 159.59/70.60 thf(13707,plain,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (plus_plus_nat @ A @ B)) = (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685])). 159.59/70.60 thf(893,axiom,((! [A:nat,B:int]: (ord_less_eq_int @ zero_zero_int @ (bit_se2923211474154528505it_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5021_take__bit__nonnegative)). 159.59/70.60 thf(11122,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)],[893])). 159.59/70.60 thf(5404,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/sandbox/benchmark/theBenchmark.p',fact_6359_real__sqrt__pow2__iff)). 159.59/70.60 thf(26076,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)],[5404])). 159.59/70.60 thf(351,axiom,((! [A:nat,B:nat,C:code_integer]: (((comm_s8582702949713902594nteger @ C @ B) = (times_3573771949741848930nteger @ (comm_s8582702949713902594nteger @ C @ A) @ (comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ C @ (semiri4939895301339042750nteger @ A)) @ (minus_minus_nat @ B @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8316_pochhammer__product)). 159.59/70.60 thf(9337,plain,((! [A:nat,B:nat,C:code_integer]: (((comm_s8582702949713902594nteger @ C @ B) = (times_3573771949741848930nteger @ (comm_s8582702949713902594nteger @ C @ A) @ (comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ C @ (semiri4939895301339042750nteger @ A)) @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[351])). 159.59/70.60 thf(5167,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 @ B @ zero_zero_real) & (ord_less_eq_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1996_split__mult__pos__le)). 159.59/70.60 thf(25140,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 @ B @ zero_zero_real) & (ord_less_eq_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5167])). 159.59/70.60 thf(802,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ pi) => ((ord_less_eq_real @ zero_zero_real @ B) => ((((cos_real @ A) = (cos_real @ B)) => (A = B)) <= (ord_less_eq_real @ B @ pi)))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7103_cos__inj__pi)). 159.59/70.60 thf(10837,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ pi) => ((ord_less_eq_real @ zero_zero_real @ B) => ((((cos_real @ A) = (cos_real @ B)) => (A = B)) | ~ (ord_less_eq_real @ B @ pi)))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[802])). 159.59/70.60 thf(4235,axiom,((! [A:int]: ~ (! [B:nat,C:nat]: (A != (abs_Integ @ (product_Pair_nat_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9773_eq__Abs__Integ)). 159.59/70.60 thf(21844,plain,((! [A:int]: ~ (! [B:nat,C:nat]: ~ (A = (abs_Integ @ (product_Pair_nat_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4235])). 159.59/70.60 thf(645,axiom,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (bit_se1409905431419307370or_int @ B @ C)) = (bit_se1409905431419307370or_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5961_take__bit__or)). 159.59/70.60 thf(10314,plain,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (bit_se1409905431419307370or_int @ B @ C)) = (bit_se1409905431419307370or_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[645])). 159.59/70.60 thf(2746,axiom,((ord_less_int @ (uminus_uminus_int @ one_one_int) @ zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5157_less__minus__one__simps_I1_J)). 159.59/70.60 thf(17104,plain,((ord_less_int @ (uminus_uminus_int @ one_one_int) @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2746])). 159.59/70.60 thf(5247,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (((? [G:nat]: (((some_nat @ G) = (vEBT_vebt_mint @ E)) & (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))))))) & (ord_less_nat @ A @ B)) <= (A != B)) <= (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_733_mintlistlength)). 159.59/70.60 thf(25425,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((? [G:nat]: (((some_nat @ G) = (vEBT_vebt_mint @ E)) & (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))))))) & (ord_less_nat @ A @ B)) | (A = B) | ~ (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)],[5247])). 159.59/70.60 thf(5634,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/sandbox/benchmark/theBenchmark.p',fact_5221_power__minus__Bit0)). 159.59/70.60 thf(26890,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)],[5634])). 159.59/70.60 thf(389,axiom,((! [A:code_integer]: ((bit_se8260200283734997820nteger @ zero_zero_nat @ A) = (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3377_unset__bit__0)). 159.59/70.60 thf(9469,plain,((! [A:code_integer]: ((bit_se8260200283734997820nteger @ zero_zero_nat @ A) = (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])). 159.59/70.60 thf(6383,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/sandbox/benchmark/theBenchmark.p',fact_1992_mult__nonpos__nonpos)). 159.59/70.60 thf(29763,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)],[6383])). 159.59/70.60 thf(7,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat)]: ((((groups3542108847815614940at_nat @ C @ B) = (plus_plus_nat @ (groups3542108847815614940at_nat @ C @ (minus_minus_set_nat @ B @ A)) @ (groups3542108847815614940at_nat @ C @ A))) <= (finite_finite_nat @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7640_sum_Osubset__diff)). 159.59/70.60 thf(8271,plain,((! [A:set_nat,B:set_nat,C:(nat > nat)]: (((groups3542108847815614940at_nat @ (C) @ B) = (plus_plus_nat @ (groups3542108847815614940at_nat @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups3542108847815614940at_nat @ (C) @ A))) | ~ (finite_finite_nat @ B) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 159.59/70.60 thf(266,axiom,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ A) = (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4672_neg__less__eq__nonneg)). 159.59/70.60 thf(9059,plain,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ A) = (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 159.59/70.60 thf(2873,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/sandbox/benchmark/theBenchmark.p',fact_1067_add__le__cancel__left)). 159.59/70.60 thf(17495,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)],[2873])). 159.59/70.60 thf(7131,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/sandbox/benchmark/theBenchmark.p',fact_1803_VEBT__internal_Onaive__member_Osimps_I2_J)). 159.59/70.60 thf(32881,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)],[7131])). 159.59/70.60 thf(3844,axiom,((! [A:real,B:nat]: ((gbinomial_real @ A @ (suc @ B)) = (divide_divide_real @ (groups129246275422532515t_real @ (^ [C:nat]: (minus_minus_real @ A @ (semiri5074537144036343181t_real @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (semiri2265585572941072030t_real @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8933_gbinomial__Suc)). 159.59/70.60 thf(20626,plain,((! [A:real,B:nat]: ((gbinomial_real @ A @ (suc @ B)) = (divide_divide_real @ (groups129246275422532515t_real @ (^ [C:nat]: (minus_minus_real @ A @ (semiri5074537144036343181t_real @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (semiri2265585572941072030t_real @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3844])). 159.59/70.60 thf(6978,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/sandbox/benchmark/theBenchmark.p',fact_7774_sum__natinterval__diff)). 159.59/70.60 thf(32257,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)],[6978])). 159.59/70.60 thf(2269,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/sandbox/benchmark/theBenchmark.p',fact_9614_and__not__numerals_I8_J)). 159.59/70.60 thf(15568,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)],[2269])). 159.59/70.60 thf(1429,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (~ (ord_less_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4486_minf_I7_J)). 159.59/70.60 thf(12911,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (~ (ord_less_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429])). 159.59/70.60 thf(304,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1485227260804924795R_real @ A @ B) @ C) @ (plus_plus_real @ (real_V1485227260804924795R_real @ D @ B) @ E)) = (ord_less_eq_real @ C @ (plus_plus_real @ (real_V1485227260804924795R_real @ (minus_minus_real @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9234_Real__Vector__Spaces_Ole__add__iff2)). 159.59/70.60 thf(9191,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1485227260804924795R_real @ A @ B) @ C) @ (plus_plus_real @ (real_V1485227260804924795R_real @ D @ B) @ E)) = (ord_less_eq_real @ C @ (plus_plus_real @ (real_V1485227260804924795R_real @ (minus_minus_real @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 159.59/70.60 thf(1227,axiom,((! [A:nat,B:nat]: ((image_nat_nat @ suc @ (set_or4665077453230672383an_nat @ A @ B)) = (set_or4665077453230672383an_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9805_image__Suc__atLeastLessThan)). 159.59/70.60 thf(12221,plain,((! [A:nat,B:nat]: ((image_nat_nat @ (suc) @ (set_or4665077453230672383an_nat @ A @ B)) = (set_or4665077453230672383an_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227])). 159.59/70.60 thf(3069,axiom,((! [A:num]: ((semiri1314217659103216013at_int @ (numeral_numeral_nat @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6817_int__ops_I3_J)). 159.59/70.60 thf(18114,plain,((! [A:num]: ((semiri1314217659103216013at_int @ (numeral_numeral_nat @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3069])). 159.59/70.60 thf(6243,axiom,((! [A:nat]: ((ord_max_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1575_max__0R)). 159.59/70.60 thf(29223,plain,((! [A:nat]: ((ord_max_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6243])). 159.59/70.60 thf(7773,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/sandbox/benchmark/theBenchmark.p',fact_4590_set__decode__def)). 159.59/70.60 thf(35110,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)],[7773])). 159.59/70.60 thf(2149,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => (((ord_less_real @ B @ C) => (ord_less_real @ (powr_real @ C @ A) @ (powr_real @ B @ A))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7233_powr__less__mono2__neg)). 159.59/70.60 thf(15185,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => (((ord_less_real @ B @ C) => (ord_less_real @ (powr_real @ C @ A) @ (powr_real @ B @ A))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2149])). 159.59/70.60 thf(2727,axiom,((! [A:(nat > complex),B:complex]: ((sums_complex @ (^ [C:nat]: (A @ (suc @ C))) @ B) = (sums_complex @ A @ (plus_plus_complex @ B @ (A @ zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7935_sums__Suc__iff)). 159.59/70.60 thf(17046,plain,((! [A:(nat > complex),B:complex]: ((sums_complex @ (^ [C:nat]: (A @ (suc @ C))) @ B) = (sums_complex @ (A) @ (plus_plus_complex @ B @ (A @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2727])). 159.59/70.60 thf(4264,axiom,((minus_minus_real = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5102_diff__conv__add__uminus)). 159.59/70.60 thf(21939,plain,(((minus_minus_real) = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4264])). 159.59/70.60 thf(1853,axiom,((! [A:int,B:int,C:int,D:int]: ((dvd_dvd_int @ A @ B) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4088_div__mult__div__if__dvd)). 159.59/70.60 thf(14241,plain,((! [A:int,B:int,C:int,D:int]: ((dvd_dvd_int @ A @ B) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1853])). 159.59/70.60 thf(5899,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3952_dvd__mult2)). 159.59/70.60 thf(28042,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)],[5899])). 159.59/70.60 thf(1949,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ one_one_int) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5966_and_Oleft__neutral)). 159.59/70.60 thf(14538,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ one_one_int) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1949])). 159.59/70.60 thf(1645,axiom,((! [A:num,B:num]: ((ord_le72135733267957522d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_numeral__less__iff)). 159.59/70.60 thf(13586,plain,((! [A:num,B:num]: ((ord_le72135733267957522d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645])). 159.59/70.60 thf(6991,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2717_dual__order_Oeq__iff)). 159.59/70.60 thf(32319,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6991])). 159.59/70.60 thf(1426,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/sandbox/benchmark/theBenchmark.p',fact_4066_unit__mult__left__cancel)). 159.59/70.60 thf(12896,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)],[1426])). 159.59/70.60 thf(6311,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/sandbox/benchmark/theBenchmark.p',fact_5527_abs__triangle__ineq3)). 159.59/70.60 thf(29525,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)],[6311])). 159.59/70.60 thf(6601,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6689_of__nat__less__imp__less)). 159.59/70.60 thf(30606,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)],[6601])). 159.59/70.60 thf(1391,axiom,((! [A:real,B:complex]: ((real_V1022390504157884413omplex @ (real_V2046097035970521341omplex @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (real_V1022390504157884413omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9202_norm__scaleR)). 159.59/70.60 thf(12789,plain,((! [A:real,B:complex]: ((real_V1022390504157884413omplex @ (real_V2046097035970521341omplex @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (real_V1022390504157884413omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391])). 159.59/70.60 thf(5361,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6590_of__nat__0__less__iff)). 159.59/70.60 thf(25921,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)],[5361])). 159.59/70.60 thf(5903,axiom,((semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat @ (^ [A:nat,B:nat]: (ord_less_eq_nat @ B @ A)) @ (^ [A:nat,B:nat]: (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9771_max__nat_Osemilattice__neutr__order__axioms)). 159.59/70.60 thf(28057,plain,((semila1623282765462674594er_nat @ (ord_max_nat) @ zero_zero_nat @ (^ [A:nat,B:nat]: (ord_less_eq_nat @ B @ A)) @ (^ [A:nat,B:nat]: (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5903])). 159.59/70.60 thf(1032,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/sandbox/benchmark/theBenchmark.p',fact_1235_distrib__left)). 159.59/70.60 thf(11556,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)],[1032])). 159.59/70.60 thf(5957,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2042_add__increasing)). 159.59/70.60 thf(28305,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5957])). 159.59/70.60 thf(2248,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ A @ (uminus1351360451143612070nteger @ B)) = (ord_le3102999989581377725nteger @ B @ (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4921_le__minus__iff)). 159.59/70.60 thf(15504,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)],[2248])). 159.59/70.60 thf(7977,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/sandbox/benchmark/theBenchmark.p',fact_9045_choose__mult__lemma)). 159.59/70.60 thf(35745,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)],[7977])). 159.59/70.60 thf(2939,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/sandbox/benchmark/theBenchmark.p',fact_7379_norm__sum)). 159.59/70.60 thf(17715,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)],[2939])). 159.59/70.60 thf(100,axiom,((ord_max_int = (^ [A:int,B:int]: (ord_max_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_880_max_Ocommute)). 159.59/70.60 thf(8563,plain,(((ord_max_int) = (^ [A:int,B:int]: (ord_max_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 159.59/70.60 thf(637,axiom,((! [A:complex]: (sums_complex @ (^ [B:nat]: (uminus1482373934393186551omplex @ (real_V2046097035970521341omplex @ (sin_coeff @ B) @ (power_power_complex @ (uminus1482373934393186551omplex @ A) @ B)))) @ (sin_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9290_sin__minus__converges)). 159.59/70.60 thf(10294,plain,((! [A:complex]: (sums_complex @ (^ [B:nat]: (uminus1482373934393186551omplex @ (real_V2046097035970521341omplex @ (sin_coeff @ B) @ (power_power_complex @ (uminus1482373934393186551omplex @ A) @ B)))) @ (sin_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[637])). 159.59/70.60 thf(7330,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/sandbox/benchmark/theBenchmark.p',fact_4243_even__set__bit__iff)). 159.59/70.60 thf(33601,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)],[7330])). 159.59/70.60 thf(6029,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = ((ord_less_num @ B @ A) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2820_not__less__iff__gr__or__eq)). 159.59/70.60 thf(28531,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)],[6029])). 159.59/70.60 thf(5034,axiom,((! [A:(real > $o),B:real,C:(real > $o)]: ((! [D:real,E:real]: ((A @ D) = (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]: (((C @ D) | (A @ D)) = ((C @ (minus_minus_real @ D @ (times_times_real @ E @ B))) | (A @ (minus_minus_real @ D @ (times_times_real @ E @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4520_inf__period_I2_J)). 159.59/70.60 thf(24666,plain,((! [A:(real > $o),B:real,C:(real > $o)]: ((! [D:real,E:real]: ((A @ D) = (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]: (((C @ D) | (A @ D)) = ((C @ (minus_minus_real @ D @ (times_times_real @ E @ B))) | (A @ (minus_minus_real @ D @ (times_times_real @ E @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5034])). 159.59/70.60 thf(792,axiom,((! [A:real,B:real,C:real]: ((((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (log @ A @ B) @ (log @ A @ C)) = (ord_less_real @ B @ C))) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6335_log__less__cancel__iff)). 159.59/70.60 thf(10805,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (log @ A @ B) @ (log @ A @ C)) = (ord_less_real @ B @ C))) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[792])). 159.59/70.60 thf(7636,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/sandbox/benchmark/theBenchmark.p',fact_3519_mod__div__decomp)). 159.59/70.60 thf(34662,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)],[7636])). 159.59/70.60 thf(6264,axiom,((~ (ord_less_eq_int @ one_one_int @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2051_not__one__le__zero)). 159.59/70.60 thf(29363,plain,((~ (ord_less_eq_int @ one_one_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6264])). 159.59/70.60 thf(6095,axiom,((! [A:nat,B:nat]: (((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (plus_plus_nat @ B @ A)) = (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5293_neg__one__power__add__eq__neg__one__power__diff)). 159.59/70.60 thf(28734,plain,((! [A:nat,B:nat]: (((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (plus_plus_nat @ B @ A)) = (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6095])). 159.59/70.60 thf(2344,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/sandbox/benchmark/theBenchmark.p',fact_3505_cong__exp__iff__simps_I8_J)). 159.59/70.60 thf(15780,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)],[2344])). 159.59/70.60 thf(6577,axiom,((! [A:num]: (((uminus_uminus_int @ one_one_int) = (uminus_uminus_int @ (numeral_numeral_int @ A))) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4754_neg__one__eq__numeral__iff)). 159.59/70.60 thf(30516,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)],[6577])). 159.59/70.60 thf(5268,axiom,((! [A:nat,B:nat,C:nat]: ((((bit_se2925701944663578781it_nat @ A @ (bit_se7882103937844011126it_nat @ B @ C)) = (bit_se2925701944663578781it_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)) & ((~ (ord_less_eq_nat @ A @ B)) => ((bit_se2925701944663578781it_nat @ A @ (bit_se7882103937844011126it_nat @ B @ C)) = (bit_se7882103937844011126it_nat @ B @ (bit_se2925701944663578781it_nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5113_take__bit__set__bit__eq)). 159.59/70.60 thf(25494,plain,((! [A:nat,B:nat,C:nat]: ((((bit_se2925701944663578781it_nat @ A @ (bit_se7882103937844011126it_nat @ B @ C)) = (bit_se2925701944663578781it_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)) & ((~ (ord_less_eq_nat @ A @ B)) => ((bit_se2925701944663578781it_nat @ A @ (bit_se7882103937844011126it_nat @ B @ C)) = (bit_se7882103937844011126it_nat @ B @ (bit_se2925701944663578781it_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5268])). 159.59/70.60 thf(6284,axiom,(((^ [A:real]: (zero_zero_real)) = (times_times_real @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1936_lambda__zero)). 159.59/70.60 thf(29441,plain,(((^ [A:real]: (zero_zero_real)) = (times_times_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6284])). 159.59/70.60 thf(692,axiom,((! [A:real,B:real]: ((real_V4546457046886955230omplex @ (plus_plus_real @ A @ B)) = (plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ (real_V4546457046886955230omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7336_of__real__add)). 159.59/70.60 thf(10463,plain,((! [A:real,B:real]: ((real_V4546457046886955230omplex @ (plus_plus_real @ A @ B)) = (plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ (real_V4546457046886955230omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[692])). 159.59/70.60 thf(3288,axiom,((! [A:nat]: ((zero_zero_int = (semiri1314217659103216013at_int @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6503_of__nat__0__eq__iff)). 159.59/70.60 thf(18837,plain,((! [A:nat]: ((zero_zero_int = (semiri1314217659103216013at_int @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3288])). 159.59/70.60 thf(5852,axiom,((! [A:num]: ~ (ord_less_eq_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5177_not__one__le__neg__numeral)). 159.59/70.60 thf(27881,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)],[5852])). 159.59/70.60 thf(7911,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: (B != (suc @ (plus_plus_nat @ A @ C))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_less__natE)). 159.59/70.60 thf(35542,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)],[7911])). 159.59/70.60 thf(5292,axiom,((! [A:num]: (((uminus_uminus_int @ (numeral_numeral_int @ A)) = (uminus_uminus_int @ one_one_int)) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4750_numeral__eq__neg__one__iff)). 159.59/70.60 thf(25591,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)],[5292])). 159.59/70.60 thf(756,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/sandbox/benchmark/theBenchmark.p',fact_7981_power__diff__1__eq)). 159.59/70.60 thf(10694,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)],[756])). 159.59/70.60 thf(7096,axiom,((bit_se2000444600071755411sk_int = (^ [A:nat]: (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6141_mask__eq__exp__minus__1)). 159.59/70.60 thf(32723,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)],[7096])). 159.59/70.60 thf(4231,axiom,((! [A:(int > $o),B:$o]: ((A @ (zero_n2684676970156552555ol_int @ B)) = (~ (((B) & ~ (A @ one_one_int)) | (~ (B) & ~ (A @ zero_zero_int))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4414_split__of__bool__asm)). 159.59/70.60 thf(21834,plain,((! [A:(int > $o),B:$o]: ((A @ (zero_n2684676970156552555ol_int @ B)) = (~ (((B) & ~ (A @ one_one_int)) | (~ (B) & ~ (A @ zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4231])). 159.59/70.60 thf(4451,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/sandbox/benchmark/theBenchmark.p',fact_5563_eq__abs__iff_H)). 159.59/70.60 thf(22508,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)],[4451])). 159.59/70.60 thf(1523,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/sandbox/benchmark/theBenchmark.p',fact_1188_add__less__imp__less__left)). 159.59/70.60 thf(13212,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)],[1523])). 159.59/70.60 thf(8015,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/sandbox/benchmark/theBenchmark.p',fact_4839_power2__minus)). 159.59/70.60 thf(35862,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)],[8015])). 159.59/70.60 thf(8137,axiom,((! [A:nat]: ((~ (! [B:nat]: (A != (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4249_oddE)). 159.59/70.60 thf(36275,plain,((! [A:nat]: (~ (! [B:nat]: ~ (A = (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8137])). 159.59/70.60 thf(6792,axiom,((zero_zero_complex != one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1887_zero__neq__one)). 159.59/70.60 thf(31421,plain,((~ (zero_zero_complex = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6792])). 159.59/70.60 thf(3831,axiom,((! [A:real,B:real]: (((real_V7735802525324610683m_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (real_V7735802525324610683m_real @ B) @ (real_V7735802525324610683m_real @ A))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6909_nonzero__norm__divide)). 159.59/70.60 thf(20566,plain,((! [A:real,B:real]: (((real_V7735802525324610683m_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (real_V7735802525324610683m_real @ B) @ (real_V7735802525324610683m_real @ A))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3831])). 159.59/70.60 thf(3683,axiom,((! [A:code_integer,B:code_integer]: ? [C:code_integer]: ! [D:code_integer]: (((~ (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ B))) = (~ (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ B)))) <= (ord_le6747313008572928689nteger @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4531_pinf_I10_J)). 159.59/70.60 thf(20081,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3683])). 159.59/70.60 thf(6668,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((dvd_dvd_nat @ B @ (minus_minus_nat @ C @ A)) => ((modulo_modulo_nat @ C @ B) = A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4224_mod__nat__eqI)). 159.59/70.60 thf(30841,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((dvd_dvd_nat @ B @ (minus_minus_nat @ C @ A)) => ((modulo_modulo_nat @ C @ B) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6668])). 159.59/70.60 thf(1679,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/sandbox/benchmark/theBenchmark.p',fact_3054_dense__le)). 159.59/70.60 thf(13687,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)],[1679])). 159.59/70.60 thf(8225,axiom,((! [A:int]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_int @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_power2__eq__square)). 159.59/70.60 thf(36551,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)],[8225])). 159.59/70.60 thf(4957,axiom,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ C @ B) <= (ord_less_eq_num @ C @ A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2706_dual__order_Otrans)). 159.59/70.60 thf(24373,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ C @ B) | ~ (ord_less_eq_num @ C @ A) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4957])). 159.59/70.60 thf(5722,axiom,((! [A:nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat,E:nat]: (((ord_less_nat @ E @ A) => (ord_less_eq_nat @ (B @ D) @ (B @ E))) <= (ord_less_eq_nat @ D @ 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/sandbox/benchmark/theBenchmark.p',fact_9618_Chebyshev__sum__upper__nat)). 159.59/70.60 thf(27195,plain,((! [A:nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat,E:nat]: (((ord_less_nat @ E @ A) => (ord_less_eq_nat @ (B @ D) @ (B @ E))) | ~ (ord_less_eq_nat @ D @ 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)],[5722])). 159.59/70.60 thf(2167,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ C) <= (ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_add__le__imp__le__right)). 159.59/70.60 thf(15239,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ C) | ~ (ord_less_eq_int @ (plus_plus_int @ A @ B) @ (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2167])). 159.59/70.60 thf(5819,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2701_antisym)). 159.59/70.60 thf(27696,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)],[5819])). 159.59/70.60 thf(7997,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/sandbox/benchmark/theBenchmark.p',fact_5304_take__bit__nat__less__self__iff)). 159.59/70.60 thf(35806,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)],[7997])). 159.59/70.60 thf(2015,axiom,((! [A:complex]: (((cos_complex @ A) != zero_zero_complex) => ((plus_plus_complex @ one_one_complex @ (power_power_complex @ (tan_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_complex @ (invers8013647133539491842omplex @ (cos_complex @ A)) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9163_tan__sec)). 159.59/70.60 thf(14765,plain,((! [A:complex]: ((~ ((cos_complex @ A) = zero_zero_complex)) => ((plus_plus_complex @ one_one_complex @ (power_power_complex @ (tan_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_complex @ (invers8013647133539491842omplex @ (cos_complex @ A)) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2015])). 159.59/70.60 thf(7500,axiom,((ord_less_eq_int = (^ [A:int,B:int]: (ord_less_eq_int @ (minus_minus_int @ A @ B) @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2137_le__iff__diff__le__0)). 159.59/70.60 thf(34188,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)],[7500])). 159.59/70.60 thf(7378,axiom,(((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = one_one_Code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4861_bits__minus__1__mod__2__eq)). 159.59/70.60 thf(33764,plain,(((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7378])). 159.59/70.60 thf(7952,axiom,((? [A:nat]: (vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_notemp)). 159.59/70.60 thf(35674,plain,((? [A:nat]: (vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7952])). 159.59/70.60 thf(3908,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/sandbox/benchmark/theBenchmark.p',fact_108_distrib__right__numeral)). 159.59/70.60 thf(20830,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)],[3908])). 159.59/70.60 thf(5548,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/sandbox/benchmark/theBenchmark.p',fact_740_vebt__maxt_Osimps_I3_J)). 159.59/70.60 thf(26598,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)],[5548])). 159.59/70.60 thf(3326,axiom,((! [A:nat,B:int,C:int,D:nat]: (((bit_se2923211474154528505it_int @ A @ B) = (bit_se2923211474154528505it_int @ A @ C)) => ((ord_less_eq_nat @ D @ A) => ((bit_se2923211474154528505it_int @ D @ B) = (bit_se2923211474154528505it_int @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4915_take__bit__tightened)). 159.59/70.60 thf(18951,plain,((! [A:nat,B:int,C:int,D:nat]: (((bit_se2923211474154528505it_int @ A @ B) = (bit_se2923211474154528505it_int @ A @ C)) => ((ord_less_eq_nat @ D @ A) => ((bit_se2923211474154528505it_int @ D @ B) = (bit_se2923211474154528505it_int @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3326])). 159.59/70.60 thf(5704,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/sandbox/benchmark/theBenchmark.p',fact_7169_cos__double__cos)). 159.59/70.60 thf(27138,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)],[5704])). 159.59/70.60 thf(3760,axiom,((! [A:nat,B:nat]: ~ (vEBT_V5719532721284313246member @ (vEBT_vebt_buildup @ A) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2600_buildup__nothing__in__leaf)). 159.59/70.60 thf(20345,plain,((! [A:nat,B:nat]: ~ (vEBT_V5719532721284313246member @ (vEBT_vebt_buildup @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3760])). 159.59/70.60 thf(6533,axiom,((! [A:num,B:num]: ((A != B) = ((ord_less_num @ B @ A) | (ord_less_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2850_linorder__neq__iff)). 159.59/70.60 thf(30375,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)],[6533])). 159.59/70.60 thf(4252,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/sandbox/benchmark/theBenchmark.p',fact_5817_of__int__less__0__iff)). 159.59/70.60 thf(21899,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)],[4252])). 159.59/70.60 thf(3835,axiom,((! [A:nat,B:complex]: (((power_power_complex @ (exp_complex @ (divide1717551699836669952omplex @ B @ (semiri8010041392384452111omplex @ A))) @ A) = (exp_complex @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6757_exp__divide__power__eq)). 159.59/70.60 thf(20598,plain,((! [A:nat,B:complex]: (((power_power_complex @ (exp_complex @ (divide1717551699836669952omplex @ B @ (semiri8010041392384452111omplex @ A))) @ A) = (exp_complex @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3835])). 159.59/70.60 thf(3714,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ B @ C)) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3949_dvd__mult2)). 159.59/70.60 thf(20198,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ B @ C)) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3714])). 159.59/70.60 thf(6375,axiom,((! [A:num,B:num,C:$o]: ((ord_less_num @ A @ B) => ((ord_less_num @ B @ A) => (C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2915_order__less__imp__triv)). 159.59/70.60 thf(29717,plain,((! [A:num,B:num,C:$o]: ((ord_less_num @ A @ B) => ((ord_less_num @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6375])). 159.59/70.60 thf(5787,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1961_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 159.59/70.60 thf(27492,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5787])). 159.59/70.60 thf(1917,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C)) <= (ord_less_eq_real @ C @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2138_divide__right__mono__neg)). 159.59/70.60 thf(14441,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (divide_divide_real @ B @ C) @ (divide_divide_real @ A @ C)) | ~ (ord_less_eq_real @ C @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1917])). 159.59/70.60 thf(7712,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2777_ord__eq__less__trans)). 159.59/70.60 thf(34911,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)],[7712])). 159.59/70.60 thf(2468,axiom,((! [A:int,B:int]: ((divide_divide_int @ A @ (uminus_uminus_int @ B)) = (divide_divide_int @ (uminus_uminus_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4981_div__minus__right)). 159.59/70.60 thf(16196,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)],[2468])). 159.59/70.60 thf(3140,axiom,((neg_numeral_dbl_int = (^ [A:int]: (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4133_dbl__def)). 159.59/70.60 thf(18356,plain,(((neg_numeral_dbl_int) = (^ [A:int]: (plus_plus_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3140])). 159.59/70.60 thf(5030,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/sandbox/benchmark/theBenchmark.p',fact_6958_summable__arctan__series)). 159.59/70.60 thf(24654,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)],[5030])). 159.59/70.60 thf(6453,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/sandbox/benchmark/theBenchmark.p',fact_6443_real__sqrt__sum__squares__triangle__ineq)). 159.59/70.60 thf(30070,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)],[6453])). 159.59/70.60 thf(4655,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)) & (((((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)) & (((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (semiri5074537144036343181t_real @ (minus_minus_nat @ (plus_plus_nat @ A @ one_one_nat) @ B))) <= (C = one_one_real))) <= (~ (ord_less_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7320_sum__gp)). 159.59/70.60 thf(23342,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)) & (((((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)) & (((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = (semiri5074537144036343181t_real @ (minus_minus_nat @ (plus_plus_nat @ A @ one_one_nat) @ B))) | ~ (C = one_one_real))) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4655])). 159.59/70.60 thf(3621,axiom,((! [A:num]: ((invers8013647133539491842omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (divide1717551699836669952omplex @ one_one_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9013_inverse__eq__divide__neg__numeral)). 159.59/70.60 thf(19883,plain,((! [A:num]: ((invers8013647133539491842omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (divide1717551699836669952omplex @ one_one_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3621])). 159.59/70.60 thf(6512,axiom,((! [A:nat,B:nat]: ((ord_min_nat @ (suc @ A) @ B) = (case_nat_nat @ zero_zero_nat @ (^ [C:nat]: (suc @ (ord_min_nat @ A @ C))) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10177_min__Suc1)). 159.59/70.60 thf(30283,plain,((! [A:nat,B:nat]: ((ord_min_nat @ (suc @ A) @ B) = (case_nat_nat @ zero_zero_nat @ (^ [C:nat]: (suc @ (ord_min_nat @ A @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6512])). 159.59/70.60 thf(4899,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/sandbox/benchmark/theBenchmark.p',fact_7402_sum__distrib__right)). 159.59/70.60 thf(24188,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)],[4899])). 159.59/70.60 thf(4633,axiom,((! [A:num]: ((plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ (numera1916890842035813515d_enat @ A)) = (numera1916890842035813515d_enat @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_one__plus__numeral)). 159.59/70.60 thf(23268,plain,((! [A:num]: ((plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ (numera1916890842035813515d_enat @ A)) = (numera1916890842035813515d_enat @ (plus_plus_num @ one @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4633])). 159.59/70.60 thf(8241,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/sandbox/benchmark/theBenchmark.p',fact_5315_minus__power__mult__self)). 159.59/70.60 thf(36749,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)],[8241])). 159.59/70.60 thf(1219,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/sandbox/benchmark/theBenchmark.p',fact_6118_exp__half__le2)). 159.59/70.60 thf(12193,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)],[1219])). 159.59/70.60 thf(3216,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/sandbox/benchmark/theBenchmark.p',fact_1064_add__le__cancel__right)). 159.59/70.60 thf(18592,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)],[3216])). 159.59/70.60 thf(2972,axiom,(((plus_plus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4737_add__neg__numeral__special_I7_J)). 159.59/70.60 thf(17820,plain,(((plus_plus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2972])). 159.59/70.60 thf(3112,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (inc @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5726_numeral__inc)). 159.59/70.60 thf(18265,plain,((! [A:num]: ((numera6690914467698888265omplex @ (inc @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3112])). 159.59/70.60 thf(6484,axiom,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (((power_power_real @ B @ A) = C) => ((root @ A @ C) = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9524_real__root__pos__unique)). 159.59/70.60 thf(30194,plain,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (((power_power_real @ B @ A) = C) => ((root @ A @ C) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6484])). 159.59/70.60 thf(1515,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ A)) = (divide_divide_real @ B @ C)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1649_nonzero__mult__divide__mult__cancel__left2)). 159.59/70.60 thf(13187,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ A)) = (divide_divide_real @ B @ C)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515])). 159.59/70.60 thf(5187,axiom,((! [A:real,B:nat]: ((abs_abs_real @ (power_power_real @ A @ B)) = (power_power_real @ (abs_abs_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5489_power__abs)). 159.59/70.60 thf(25204,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)],[5187])). 159.59/70.60 thf(5952,axiom,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (times_times_nat @ (groups708209901874060359at_nat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8730_prod_OatLeast0__atMost__Suc)). 159.59/70.60 thf(28288,plain,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (times_times_nat @ (groups708209901874060359at_nat @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5952])). 159.59/70.60 thf(444,axiom,((! [A:real,B:nat]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ pi))) = (tan_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7225_tan__periodic__nat)). 159.59/70.60 thf(9644,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)],[444])). 159.59/70.60 thf(5169,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/sandbox/benchmark/theBenchmark.p',fact_1791_power2__less__eq__zero__iff)). 159.59/70.60 thf(25147,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)],[5169])). 159.59/70.60 thf(4771,axiom,((ord_less_eq_int @ one_one_int @ one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_le__numeral__extra_I4_J)). 159.59/70.60 thf(23745,plain,((ord_less_eq_int @ one_one_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4771])). 159.59/70.60 thf(5111,axiom,((! [A:num,B:num]: (((A != B) => (ord_less_num @ A @ B)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3188_order__le__neq__trans)). 159.59/70.60 thf(24946,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)],[5111])). 159.59/70.60 thf(7404,axiom,((! [A:num,B:num]: ((ord_less_num @ (bit1 @ A) @ (bit0 @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5426_semiring__norm_I81_J)). 159.59/70.60 thf(33843,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)],[7404])). 159.59/70.60 thf(3703,axiom,((! [A:real]: ((? [B:nat]: ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B)) @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9115_ex__inverse__of__nat__less)). 159.59/70.60 thf(20145,plain,((! [A:real]: (? [B:nat]: ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B)) @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3703])). 159.59/70.60 thf(7811,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/sandbox/benchmark/theBenchmark.p',fact_3843_div__add)). 159.59/70.60 thf(35217,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)],[7811])). 159.59/70.60 thf(3302,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ C) <= (ord_less_int @ B @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3204_order__le__less__trans)). 159.59/70.60 thf(18878,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ C) | ~ (ord_less_int @ B @ C) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3302])). 159.59/70.60 thf(6426,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (modulo_modulo_nat @ A @ B)) = (modulo_modulo_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6705_of__nat__mod)). 159.59/70.60 thf(29952,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)],[6426])). 159.59/70.60 thf(3979,axiom,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2631_not__iless0)). 159.59/70.60 thf(21047,plain,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3979])). 159.59/70.60 thf(4687,axiom,((! [A:num]: ~ (ord_less_num @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3669_verit__comp__simplify1_I1_J)). 159.59/70.60 thf(23460,plain,((! [A:num]: ~ (ord_less_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4687])). 159.59/70.60 thf(7085,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_le__eq__less__or__eq)). 159.59/70.60 thf(32683,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7085])). 159.59/70.60 thf(8160,axiom,(((size_s6755466524823107622T_VEBT @ treeList) = (size_s6755466524823107622T_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24__092_060open_062length_AtreeList_A_061_Alength_A_ItreeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_J_092_060close_062)). 159.59/70.60 thf(36351,plain,(((size_s6755466524823107622T_VEBT @ treeList) = (size_s6755466524823107622T_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8160])). 159.59/70.60 thf(7590,axiom,(((modulo_modulo_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3429_one__mod__two__eq__one)). 159.59/70.60 thf(34531,plain,(((modulo_modulo_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7590])). 159.59/70.60 thf(3797,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/sandbox/benchmark/theBenchmark.p',fact_7381_norm__sum)). 159.59/70.60 thf(20469,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)],[3797])). 159.59/70.60 thf(312,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (ord_max_int @ A @ B) @ C) = ((ord_less_int @ B @ C) & (ord_less_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_max__less__iff__conj)). 159.59/70.60 thf(9212,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (ord_max_int @ A @ B) @ C) = ((ord_less_int @ B @ C) & (ord_less_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 159.59/70.60 thf(405,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3295_max__absorb2)). 159.59/70.60 thf(9526,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)],[405])). 159.59/70.60 thf(890,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ B @ (divide_divide_int @ one_one_int @ A)) = (divide_divide_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3865_unit__mult__div__div)). 159.59/70.60 thf(11112,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ B @ (divide_divide_int @ one_one_int @ A)) = (divide_divide_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[890])). 159.59/70.60 thf(27,axiom,((bit_ri6519982836138164636nteger = (^ [A:nat,B:code_integer]: (if_Code_integer @ (A = zero_zero_nat) @ (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))) @ (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_ri6519982836138164636nteger @ (minus_minus_nat @ A @ one_one_nat) @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4591_signed__take__bit__rec)). 159.59/70.60 thf(8335,plain,(((bit_ri6519982836138164636nteger) = (^ [A:nat,B:code_integer]: (if_Code_integer @ (A = zero_zero_nat) @ (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))) @ (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_ri6519982836138164636nteger @ (minus_minus_nat @ A @ one_one_nat) @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[27])). 159.59/70.60 thf(8232,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ A @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups3542108847815614940at_nat @ (^ [C:nat]: (plus_plus_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/sandbox/benchmark/theBenchmark.p',fact_8914_sum_Oin__pairs__0)). 159.59/70.60 thf(36633,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups3542108847815614940at_nat @ (^ [C:nat]: (plus_plus_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)],[8232])). 159.59/70.60 thf(5996,axiom,((! [A:nat,B:(nat > nat),C:nat,D:(nat > nat),E:nat]: ((! [F:nat]: ((ord_less_nat @ A @ F) => ((B @ F) = zero_zero_nat))) => ((! [F:nat]: ((ord_less_nat @ C @ F) => ((D @ F) = zero_zero_nat))) => ((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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8928_polynomial__product__nat)). 159.59/70.60 thf(28423,plain,((! [A:nat,B:(nat > nat),C:nat,D:(nat > nat),E:nat]: ((! [F:nat]: ((ord_less_nat @ A @ F) => ((B @ F) = zero_zero_nat))) => ((! [F:nat]: ((ord_less_nat @ C @ F) => ((D @ F) = zero_zero_nat))) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5996])). 159.59/70.60 thf(6714,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ bot_bot_nat) => (A = bot_bot_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3268_bot_Oextremum__uniqueI)). 159.59/70.60 thf(31148,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ bot_bot_nat) => (A = bot_bot_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6714])). 159.59/70.60 thf(3478,axiom,((! [A:num]: ((archim7802044766580827645g_real @ (numeral_numeral_real @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6965_ceiling__numeral)). 159.59/70.60 thf(19423,plain,((! [A:num]: ((archim7802044766580827645g_real @ (numeral_numeral_real @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3478])). 159.59/70.60 thf(7516,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBT]: ((if_VEBT_VEBT @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T)). 159.59/70.60 thf(34240,plain,((! [A:vEBT_VEBT,B:vEBT_VEBT]: ((if_VEBT_VEBT @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7516])). 159.59/70.60 thf(1121,axiom,((! [A:set_nat,B:set_nat]: (((ord_less_eq_set_nat @ B @ A) = (B = A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2639_order__antisym__conv)). 159.59/70.60 thf(11848,plain,((! [A:set_nat,B:set_nat]: (((ord_less_eq_set_nat @ B @ A) = (B = A)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121])). 159.59/70.60 thf(7719,axiom,(((semiri1408675320244567234ct_nat @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8069_fact__2)). 159.59/70.60 thf(34934,plain,(((semiri1408675320244567234ct_nat @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7719])). 159.59/70.60 thf(5335,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/sandbox/benchmark/theBenchmark.p',fact_5905_of__int__neg__numeral)). 159.59/70.60 thf(25766,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)],[5335])). 159.59/70.60 thf(2512,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/sandbox/benchmark/theBenchmark.p',fact_8352_gbinomial__absorption_H)). 159.59/70.60 thf(16336,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)],[2512])). 159.59/70.60 thf(1526,axiom,((! [A:num,B:real]: ((ord_less_int @ (numeral_numeral_int @ A) @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (numeral_numeral_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6981_numeral__less__ceiling)). 159.59/70.60 thf(13219,plain,((! [A:num,B:real]: ((ord_less_int @ (numeral_numeral_int @ A) @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (numeral_numeral_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526])). 159.59/70.60 thf(2645,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((A = B) | (ord_less_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3068_order_Oorder__iff__strict)). 159.59/70.60 thf(16777,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((A = B) | (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2645])). 159.59/70.60 thf(3129,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) => ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2252_mult__left__less__imp__less)). 159.59/70.60 thf(18316,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) => ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3129])). 159.59/70.60 thf(5836,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/sandbox/benchmark/theBenchmark.p',fact_5217_power__minus)). 159.59/70.60 thf(27789,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)],[5836])). 159.59/70.60 thf(5815,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/sandbox/benchmark/theBenchmark.p',fact_4268_even__mask__div__iff_H)). 159.59/70.60 thf(27683,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)],[5815])). 159.59/70.60 thf(875,axiom,((! [A:int,B:int,C:$o]: ((ord_less_int @ A @ B) => ((C) <= (ord_less_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2917_order__less__imp__triv)). 159.59/70.60 thf(11072,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)],[875])). 159.59/70.60 thf(1411,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C) <= (ord_less_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6917_norm__triangle__lt)). 159.59/70.60 thf(12852,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C) | ~ (ord_less_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411])). 159.59/70.60 thf(7931,axiom,((! [A:num,B:num]: ((bit_se2925701944663578781it_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (bit_se2925701944663578781it_nat @ (pred_numeral @ A) @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5738_take__bit__numeral__bit0)). 159.59/70.60 thf(35602,plain,((! [A:num,B:num]: ((bit_se2925701944663578781it_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (bit_se2925701944663578781it_nat @ (pred_numeral @ A) @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7931])). 159.59/70.60 thf(3617,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = (uminus1482373934393186551omplex @ one_one_complex)) = ((B != zero_zero_complex) & (A = (uminus1482373934393186551omplex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5210_divide__eq__minus__1__iff)). 159.59/70.60 thf(19873,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)],[3617])). 159.59/70.60 thf(7914,axiom,(((code_integer_of_num @ (bit0 @ one)) = (numera6620942414471956472nteger @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9801_integer__of__num__triv_I2_J)). 159.59/70.60 thf(35553,plain,(((code_integer_of_num @ (bit0 @ one)) = (numera6620942414471956472nteger @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7914])). 159.59/70.60 thf(542,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ C) = (ord_less_real @ (real_V1485227260804924795R_real @ A @ C) @ B)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9259_neg__divideR__less__eq)). 159.59/70.60 thf(9978,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ C) = (ord_less_real @ (real_V1485227260804924795R_real @ A @ C) @ B)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[542])). 159.59/70.60 thf(5468,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2734_order__antisym)). 159.59/70.60 thf(26333,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)],[5468])). 159.59/70.60 thf(5597,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8088_fact__mono)). 159.59/70.60 thf(26770,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)],[5597])). 159.59/70.60 thf(1559,axiom,(((neg_nu3811975205180677377ec_int @ zero_zero_int) = (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5694_dbl__dec__simps_I2_J)). 159.59/70.60 thf(13317,plain,(((neg_nu3811975205180677377ec_int @ zero_zero_int) = (uminus_uminus_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1559])). 159.59/70.60 thf(6278,axiom,((! [A:(complex > (complex > $o)),B:set_nat,C:(nat > complex),D:(nat > complex)]: (((! [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)))) => ((finite_finite_nat @ B) => ((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups6464643781859351333omplex @ C @ B) @ (groups6464643781859351333omplex @ D @ B))))) <= (A @ one_one_complex @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8561_prod_Orelated)). 159.59/70.60 thf(29403,plain,((! [A:(complex > (complex > $o)),B:set_nat,C:(nat > complex),D:(nat > complex)]: (((! [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)))) => ((finite_finite_nat @ B) => ((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups6464643781859351333omplex @ (C) @ B) @ (groups6464643781859351333omplex @ (D) @ B))))) | ~ (A @ one_one_complex @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6278])). 159.59/70.60 thf(4837,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/sandbox/benchmark/theBenchmark.p',fact_7812_double__gauss__sum)). 159.59/70.60 thf(23992,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)],[4837])). 159.59/70.60 thf(7003,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/sandbox/benchmark/theBenchmark.p',fact_3540_minus__div__mult__eq__mod)). 159.59/70.60 thf(32366,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)],[7003])). 159.59/70.60 thf(2538,axiom,((! [A:complex]: ((ord_less_real @ zero_zero_real @ (real_V1022390504157884413omplex @ A)) = (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6898_zero__less__norm__iff)). 159.59/70.60 thf(16413,plain,((! [A:complex]: ((ord_less_real @ zero_zero_real @ (real_V1022390504157884413omplex @ A)) = (~ (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2538])). 159.59/70.60 thf(5198,axiom,(((semiri1408675320244567234ct_nat @ zero_zero_nat) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8048_fact__0)). 159.59/70.60 thf(25253,plain,(((semiri1408675320244567234ct_nat @ zero_zero_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5198])). 159.59/70.60 thf(4752,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_membermima @ A @ B) => ((accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ A @ 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 @ E) @ F @ G)) => ((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 = C) | (((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)))))) => (~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((~ ((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)))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E) @ B))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E)))))) <= (! [C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ ((B = C) | (B = D))) <= (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))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3329_VEBT__internal_Omembermima_Opelims_I2_J)). 159.59/70.60 thf(23665,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_membermima @ A @ B) => ((accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ A @ 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 @ E) @ F @ G)) => ((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 = C) | (((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)))))) => (~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (~ ((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))))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E) @ B)) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E)))))) | ~ (! [C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ ((B = C) | (B = D)) | ~ (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)) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4752])). 159.59/70.60 thf(3695,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/sandbox/benchmark/theBenchmark.p',fact_96_add__numeral__left)). 159.59/70.60 thf(20117,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)],[3695])). 159.59/70.60 thf(5653,axiom,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_mult_Oright__neutral)). 159.59/70.60 thf(26950,plain,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5653])). 159.59/70.60 thf(3095,axiom,((! [A:real]: (ord_less_real @ (minus_minus_real @ A @ one_one_real) @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8261_real__of__int__floor__gt__diff__one)). 159.59/70.60 thf(18210,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)],[3095])). 159.59/70.60 thf(1658,axiom,((! [A:real]: ((summable_real @ (power_power_real @ A)) <= (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7093_summable__geometric)). 159.59/70.60 thf(13623,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)],[1658])). 159.59/70.60 thf(1675,axiom,((! [A:real]: ((ord_less_eq_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A) <= (ord_less_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5017_ln__add__one__self__le__self2)). 159.59/70.60 thf(13675,plain,((! [A:real]: ((ord_less_eq_real @ (ln_ln_real @ (plus_plus_real @ one_one_real @ A)) @ A) | ~ (ord_less_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675])). 159.59/70.60 thf(5385,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (B = (suc @ C))) <= (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_Suc__le__D)). 159.59/70.60 thf(26004,plain,((! [A:nat,B:nat]: (? [C:nat]: (B = (suc @ C)) | ~ (ord_less_eq_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5385])). 159.59/70.60 thf(4028,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/sandbox/benchmark/theBenchmark.p',fact_8447_prod_OlessThan__Suc)). 159.59/70.60 thf(21192,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)],[4028])). 159.59/70.60 thf(3239,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_real @ zero_zero_real @ B) => ((minus_minus_real @ (log @ A @ B) @ C) = (log @ A @ (times_times_real @ B @ (powr_real @ A @ (uminus_uminus_real @ C)))))) <= (A != one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7292_log__minus__eq__powr)). 159.59/70.60 thf(18667,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => (((ord_less_real @ zero_zero_real @ B) => ((minus_minus_real @ (log @ A @ B) @ C) = (log @ A @ (times_times_real @ B @ (powr_real @ A @ (uminus_uminus_real @ C)))))) | (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3239])). 159.59/70.60 thf(7189,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1249_mult_Ocomm__neutral)). 159.59/70.60 thf(33106,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7189])). 159.59/70.60 thf(5447,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2688_order__subst1)). 159.59/70.60 thf(26257,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5447])). 159.59/70.60 thf(4233,axiom,((! [A:complex]: (sums_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (sin_coeff @ B) @ (power_power_complex @ A @ B))) @ (sin_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9264_sin__converges)). 159.59/70.60 thf(21839,plain,((! [A:complex]: (sums_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (sin_coeff @ B) @ (power_power_complex @ A @ B))) @ (sin_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4233])). 159.59/70.60 thf(4345,axiom,((! [A:nat]: ((bit_se1745604003318907178nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (numera6620942414471956472nteger @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4909_take__bit__of__2)). 159.59/70.60 thf(22175,plain,((! [A:nat]: ((bit_se1745604003318907178nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (numera6620942414471956472nteger @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4345])). 159.59/70.60 thf(2298,axiom,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se2923211474154528505it_int @ A @ B) @ C) = ((ord_less_nat @ C @ A) & (bit_se1146084159140164899it_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6393_bit__take__bit__iff)). 159.59/70.60 thf(15651,plain,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se2923211474154528505it_int @ A @ B) @ C) = ((ord_less_nat @ C @ A) & (bit_se1146084159140164899it_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2298])). 159.59/70.60 thf(782,axiom,((! [A:set_nat,B:set_nat]: ((~ ((ord_less_eq_set_nat @ A @ B) => (~ (ord_less_eq_set_nat @ B @ A)))) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2981_equalityE)). 159.59/70.60 thf(10772,plain,((! [A:set_nat,B:set_nat]: (~ ((ord_less_eq_set_nat @ A @ B) => (~ (ord_less_eq_set_nat @ B @ A))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[782])). 159.59/70.60 thf(5184,axiom,(((plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat) = (numera1916890842035813515d_enat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_one__add__one)). 159.59/70.60 thf(25196,plain,(((plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat) = (numera1916890842035813515d_enat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5184])). 159.59/70.60 thf(7238,axiom,((! [A:num]: ((minus_minus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (numera6690914467698888265omplex @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4883_diff__numeral__special_I3_J)). 159.59/70.60 thf(33283,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)],[7238])). 159.59/70.60 thf(3686,axiom,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4575_add__0__iff)). 159.59/70.60 thf(20088,plain,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3686])). 159.59/70.60 thf(4359,axiom,((! [A:num]: ((neg_nu8295874005876285629c_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5804_dbl__inc__simps_I5_J)). 159.59/70.60 thf(22214,plain,((! [A:num]: ((neg_nu8295874005876285629c_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4359])). 159.59/70.60 thf(2175,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 @ B @ C)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2234_mult__le__cancel__left__pos)). 159.59/70.60 thf(15263,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 @ B @ C)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2175])). 159.59/70.60 thf(5408,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ A) = (((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ B @ one_one_real)) & ((ord_less_eq_real @ one_one_real @ B) <= (ord_less_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2422_mult__le__cancel__left2)). 159.59/70.60 thf(26089,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ A) = (((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ B @ one_one_real)) & ((ord_less_eq_real @ one_one_real @ B) | ~ (ord_less_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5408])). 159.59/70.60 thf(4962,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/sandbox/benchmark/theBenchmark.p',fact_4882_diff__numeral__special_I3_J)). 159.59/70.60 thf(24437,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)],[4962])). 159.59/70.60 thf(579,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/sandbox/benchmark/theBenchmark.p',fact_7226_tan__periodic__int)). 159.59/70.60 thf(10093,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)],[579])). 159.59/70.60 thf(6959,axiom,((divide_divide_nat = (^ [A:nat,B:nat]: (if_nat @ (B = zero_zero_nat) @ zero_zero_nat @ (lattic8265883725875713057ax_nat @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ (times_times_nat @ C @ B) @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10196_divide__nat__def)). 159.59/70.60 thf(32069,plain,(((divide_divide_nat) = (^ [A:nat,B:nat]: (if_nat @ (B = zero_zero_nat) @ zero_zero_nat @ (lattic8265883725875713057ax_nat @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ (times_times_nat @ C @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6959])). 159.59/70.60 thf(3029,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ A @ C) <= (ord_less_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2859_order__less__trans)). 159.59/70.60 thf(17988,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ A @ C) | ~ (ord_less_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3029])). 159.59/70.60 thf(3416,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => ((dvd_dvd_Code_integer @ B @ (times_3573771949741848930nteger @ C @ A)) = (dvd_dvd_Code_integer @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4054_dvd__mult__unit__iff)). 159.59/70.60 thf(19236,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => ((dvd_dvd_Code_integer @ B @ (times_3573771949741848930nteger @ C @ A)) = (dvd_dvd_Code_integer @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3416])). 159.59/70.60 thf(4426,axiom,((semiri4449623510593786356d_enat = (^ [A:nat]: (if_Extended_enat @ (A = zero_zero_nat) @ one_on7984719198319812577d_enat @ (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ A) @ (semiri4449623510593786356d_enat @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8119_fact__num__eq__if)). 159.59/70.60 thf(22434,plain,(((semiri4449623510593786356d_enat) = (^ [A:nat]: (if_Extended_enat @ (A = zero_zero_nat) @ one_on7984719198319812577d_enat @ (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ A) @ (semiri4449623510593786356d_enat @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4426])). 159.59/70.60 thf(6096,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/sandbox/benchmark/theBenchmark.p',fact_6796_sin__cos__npi)). 159.59/70.60 thf(28737,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)],[6096])). 159.59/70.60 thf(1699,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4494_pinf_I6_J)). 159.59/70.60 thf(13747,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (~ (ord_less_eq_real @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699])). 159.59/70.60 thf(2064,axiom,((! [A:nat]: ((vEBT_VEBT_set_vebt @ (vEBT_vebt_buildup @ A)) = bot_bot_set_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2575_buildup__gives__empty)). 159.59/70.60 thf(14905,plain,((! [A:nat]: ((vEBT_VEBT_set_vebt @ (vEBT_vebt_buildup @ A)) = bot_bot_set_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2064])). 159.59/70.60 thf(2140,axiom,((! [A:real,B:real,C:nat]: ((comm_s7457072308508201937r_real @ (plus_plus_real @ A @ B) @ C) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ (binomial @ C @ D)) @ (comm_s7457072308508201937r_real @ A @ D)) @ (comm_s7457072308508201937r_real @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9154_pochhammer__binomial__sum)). 159.59/70.60 thf(15158,plain,((! [A:real,B:real,C:nat]: ((comm_s7457072308508201937r_real @ (plus_plus_real @ A @ B) @ C) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ (binomial @ C @ D)) @ (comm_s7457072308508201937r_real @ A @ D)) @ (comm_s7457072308508201937r_real @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2140])). 159.59/70.60 thf(6189,axiom,((comm_s4663373288045622133er_nat = (^ [A:nat,B:nat]: (groups708209901874060359at_nat @ (^ [C:nat]: (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8894_pochhammer__prod__rev)). 159.59/70.60 thf(29059,plain,(((comm_s4663373288045622133er_nat) = (^ [A:nat,B:nat]: (groups708209901874060359at_nat @ (^ [C:nat]: (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6189])). 159.59/70.60 thf(2589,axiom,((! [A:nat,B:set_nat,C:(nat > extended_enat)]: ((((ord_le2932123472753598470d_enat @ (C @ A) @ (groups7108830773950497114d_enat @ C @ B)) <= (finite_finite_nat @ B)) <= (! [D:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (C @ D)) <= (member_nat @ D @ (minus_minus_set_nat @ B @ (insert_nat @ A @ bot_bot_set_nat)))))) <= (member_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7750_member__le__sum)). 159.59/70.60 thf(16572,plain,((! [A:nat,B:set_nat,C:(nat > extended_enat)]: ((ord_le2932123472753598470d_enat @ (C @ A) @ (groups7108830773950497114d_enat @ (C) @ B)) | ~ (finite_finite_nat @ B) | ~ (! [D:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (C @ D)) | ~ (member_nat @ D @ (minus_minus_set_nat @ B @ (insert_nat @ A @ bot_bot_set_nat))))) | ~ (member_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2589])). 159.59/70.60 thf(5781,axiom,((! [A:list_o,B:list_o]: (((size_size_list_o @ A) = (size_size_list_o @ B)) => ((A = B) <= (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_o @ A)) => ((nth_o @ A @ C) = (nth_o @ B @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_nth__equalityI)). 159.59/70.60 thf(27391,plain,((! [A:list_o,B:list_o]: (((size_size_list_o @ A) = (size_size_list_o @ B)) => ((A = B) | ~ (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_o @ A)) => ((nth_o @ A @ C) = (nth_o @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5781])). 159.59/70.60 thf(8156,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => (((power_power_nat @ A @ B) = (power_power_nat @ A @ C)) = (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_power__inject__exp)). 159.59/70.60 thf(36336,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => (((power_power_nat @ A @ B) = (power_power_nat @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8156])). 159.59/70.60 thf(659,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/sandbox/benchmark/theBenchmark.p',fact_4572_signed__take__bit__int__greater__eq__self__iff)). 159.59/70.60 thf(10358,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)],[659])). 159.59/70.60 thf(5529,axiom,((! [A:num]: (((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ one_one_Code_integer)) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4752_numeral__eq__neg__one__iff)). 159.59/70.60 thf(26542,plain,((! [A:num]: (((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ one_one_Code_integer)) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5529])). 159.59/70.60 thf(6263,axiom,((! [A:vEBT_VEBT,B:nat]: ((~ (vEBT_V5719532721284313246member @ A @ B)) => (((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (((B != zero_zero_nat) => ((B = one_one_nat) & ((B = one_one_nat) => (D)))) & ((C) <= (B = zero_zero_nat)))))) => ((! [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ C @ zero_zero_nat @ D @ E)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ zero_zero_nat @ D @ E) @ B))))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ (suc @ D) @ E @ F)) => ((((vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))) <= (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ (suc @ D) @ E @ F) @ B)))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3315_VEBT__internal_Onaive__member_Opelims_I3_J)). 159.59/70.60 thf(29339,plain,((! [A:vEBT_VEBT,B:nat]: ((~ (vEBT_V5719532721284313246member @ A @ B)) => (((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (((~ (B = zero_zero_nat)) => ((B = one_one_nat) & ((B = one_one_nat) => (D)))) & ((C) | ~ (B = zero_zero_nat)))))) => ((! [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ C @ zero_zero_nat @ D @ E)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ zero_zero_nat @ D @ E) @ B))))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ (suc @ D) @ E @ F)) => ((((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))) & (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 @ (vEBT_Node @ C @ (suc @ D) @ E @ F) @ B)))))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6263])). 159.59/70.60 thf(5586,axiom,((! [A:extended_enat]: ((power_8040749407984259932d_enat @ A @ zero_zero_nat) = one_on7984719198319812577d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2182_power__0)). 159.59/70.60 thf(26717,plain,((! [A:extended_enat]: ((power_8040749407984259932d_enat @ A @ zero_zero_nat) = one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5586])). 159.59/70.60 thf(7782,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/sandbox/benchmark/theBenchmark.p',fact_9827_range__nat__of__char)). 159.59/70.60 thf(35134,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)],[7782])). 159.59/70.60 thf(2900,axiom,((! [A:complex]: ((power_power_complex @ (cosh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_complex @ (power_power_complex @ (sinh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9344_cosh__square__eq)). 159.59/70.60 thf(17594,plain,((! [A:complex]: ((power_power_complex @ (cosh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_complex @ (power_power_complex @ (sinh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2900])). 159.59/70.60 thf(239,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/sandbox/benchmark/theBenchmark.p',fact_9609_and__not__numerals_I6_J)). 159.59/70.60 thf(8981,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)],[239])). 159.59/70.60 thf(6424,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/sandbox/benchmark/theBenchmark.p',fact_6600_real__of__nat__eq__numeral__power__cancel__iff)). 159.59/70.60 thf(29946,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)],[6424])). 159.59/70.60 thf(2291,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/sandbox/benchmark/theBenchmark.p',fact_1357_diff__less__eq)). 159.59/70.60 thf(15632,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)],[2291])). 159.59/70.60 thf(2828,axiom,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ one_one_Code_integer) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_bits__div__by__1)). 159.59/70.60 thf(17343,plain,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ one_one_Code_integer) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2828])). 159.59/70.60 thf(3817,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/sandbox/benchmark/theBenchmark.p',fact_7819_arcsin__bounded)). 159.59/70.60 thf(20524,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)],[3817])). 159.59/70.60 thf(120,axiom,(((cis @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = imaginary_unit)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9377_cis__pi__half)). 159.59/70.60 thf(8622,plain,(((cis @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = imaginary_unit)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 159.59/70.60 thf(3811,axiom,((! [A:complex,B:complex]: ((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (divide1717551699836669952omplex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4986_minus__divide__divide)). 159.59/70.60 thf(20507,plain,((! [A:complex,B:complex]: ((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (divide1717551699836669952omplex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3811])). 159.59/70.60 thf(206,axiom,((arccos = (^ [A:real]: (the_real @ (^ [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ B @ pi) & ((cos_real @ B) = A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9401_arccos__def)). 159.59/70.60 thf(8879,plain,(((arccos) = (^ [A:real]: (the_real @ (^ [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_eq_real @ B @ pi) & ((cos_real @ B) = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 159.59/70.60 thf(2617,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9030_positive__imp__inverse__positive)). 159.59/70.60 thf(16688,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2617])). 159.59/70.60 thf(6753,axiom,((! [A:nat,B:nat]: ((bit_se1412395901928357646or_nat @ (bit_se1412395901928357646or_nat @ A @ B) @ B) = (bit_se1412395901928357646or_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5940_or_Oright__idem)). 159.59/70.60 thf(31288,plain,((! [A:nat,B:nat]: ((bit_se1412395901928357646or_nat @ (bit_se1412395901928357646or_nat @ A @ B) @ B) = (bit_se1412395901928357646or_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6753])). 159.59/70.60 thf(4400,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/sandbox/benchmark/theBenchmark.p',fact_3461_mod__diff__left__eq)). 159.59/70.60 thf(22347,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)],[4400])). 159.59/70.60 thf(1985,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/sandbox/benchmark/theBenchmark.p',fact_5871_neg__numeral__power__less__of__int__cancel__iff)). 159.59/70.60 thf(14665,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)],[1985])). 159.59/70.60 thf(160,axiom,((! [A:real,B:real,C:real,D:real]: (((real_V1485227260804924795R_real @ (divide_divide_real @ A @ B) @ C) = D) = ((((real_V1485227260804924795R_real @ A @ C) = (real_V1485227260804924795R_real @ B @ D)) <= (B != zero_zero_real)) & ((D = zero_zero_real) <= (B = zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9230_vector__fraction__eq__iff)). 159.59/70.60 thf(8747,plain,((! [A:real,B:real,C:real,D:real]: (((real_V1485227260804924795R_real @ (divide_divide_real @ A @ B) @ C) = D) = ((((real_V1485227260804924795R_real @ A @ C) = (real_V1485227260804924795R_real @ B @ D)) | (B = zero_zero_real)) & ((D = zero_zero_real) | ~ (B = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 159.59/70.60 thf(3309,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/sandbox/benchmark/theBenchmark.p',fact_1192_add__strict__left__mono)). 159.59/70.60 thf(18897,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)],[3309])). 159.59/70.60 thf(328,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ zero_zero_real @ (tan_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7284_tan__gt__zero)). 159.59/70.60 thf(9261,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_real @ zero_zero_real @ (tan_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[328])). 159.59/70.60 thf(954,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = (divide_divide_real @ A @ C)) = ((B = C) | (A = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1553_divide__cancel__left)). 159.59/70.60 thf(11303,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = (divide_divide_real @ A @ C)) = ((B = C) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[954])). 159.59/70.60 thf(1197,axiom,((! [A:extended_enat,B:extended_enat]: ((A != B) => ((ord_le72135733267957522d_enat @ A @ B) <= (ord_le2932123472753598470d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3191_order__neq__le__trans)). 159.59/70.60 thf(12097,plain,((! [A:extended_enat,B:extended_enat]: ((~ (A = B)) => ((ord_le72135733267957522d_enat @ A @ B) | ~ (ord_le2932123472753598470d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197])). 159.59/70.60 thf(5872,axiom,((! [A:nat]: ((binomial @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8994_binomial__0__Suc)). 159.59/70.60 thf(27948,plain,((! [A:nat]: ((binomial @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5872])). 159.59/70.60 thf(3749,axiom,((! [A:extended_enat,B:extended_enat,C:$o]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ B @ A) => (C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2913_order__less__imp__triv)). 159.59/70.60 thf(20312,plain,((! [A:extended_enat,B:extended_enat,C:$o]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3749])). 159.59/70.60 thf(3762,axiom,((! [A:real]: (dvd_dvd_real @ one_one_real @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4003_one__dvd)). 159.59/70.60 thf(20352,plain,((! [A:real]: (dvd_dvd_real @ one_one_real @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3762])). 159.59/70.60 thf(808,axiom,((! [A:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ A) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4692_ab__left__minus)). 159.59/70.60 thf(10864,plain,((! [A:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[808])). 159.59/70.60 thf(88,axiom,((! [A:set_nat,B:set_nat,C:nat,D:set_nat]: ((ord_less_eq_set_nat @ A @ (minus_minus_set_nat @ B @ (insert_nat @ C @ D))) = (~ (member_nat @ C @ A) & (ord_less_eq_set_nat @ A @ (minus_minus_set_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6215_subset__Diff__insert)). 159.59/70.60 thf(8519,plain,((! [A:set_nat,B:set_nat,C:nat,D:set_nat]: ((ord_less_eq_set_nat @ A @ (minus_minus_set_nat @ B @ (insert_nat @ C @ D))) = (~ (member_nat @ C @ A) & (ord_less_eq_set_nat @ A @ (minus_minus_set_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 159.59/70.60 thf(6582,axiom,((! [A:nat,B:nat]: ((bit_se727722235901077358nd_nat @ (bit_se727722235901077358nd_nat @ A @ B) @ B) = (bit_se727722235901077358nd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5934_and_Oright__idem)). 159.59/70.60 thf(30531,plain,((! [A:nat,B:nat]: ((bit_se727722235901077358nd_nat @ (bit_se727722235901077358nd_nat @ A @ B) @ B) = (bit_se727722235901077358nd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6582])). 159.59/70.60 thf(3839,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((produc6081775807080527818_nat_o @ A @ (product_Pair_nat_nat @ B @ C)) => (A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5507_case__prodD)). 159.59/70.60 thf(20611,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((produc6081775807080527818_nat_o @ (A) @ (product_Pair_nat_nat @ B @ C)) => (A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3839])). 159.59/70.60 thf(3462,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (ord_le72135733267957522d_enat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2843_order__less__asym)). 159.59/70.60 thf(19374,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (ord_le72135733267957522d_enat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3462])). 159.59/70.60 thf(6152,axiom,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((A = one_one_nat) & (B = one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_nat__1__eq__mult__iff)). 159.59/70.60 thf(28922,plain,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((A = one_one_nat) & (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6152])). 159.59/70.60 thf(489,axiom,((! [A:int]: ((comm_s4660882817536571857er_int @ A @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8184_pochhammer__0)). 159.59/70.60 thf(9813,plain,((! [A:int]: ((comm_s4660882817536571857er_int @ A @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[489])). 159.59/70.60 thf(3085,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => (~ ((! [C:int]: ((C != zero_zero_int) => ((((((times_times_int @ A @ C) = one_one_int) => ((divide_divide_int @ B @ A) != (times_times_int @ B @ C))) <= ((divide_divide_int @ one_one_int @ C) = A)) <= ((divide_divide_int @ one_one_int @ A) = C)) <= (dvd_dvd_int @ C @ one_one_int)))) <= (A != zero_zero_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4194_is__unitE)). 159.59/70.60 thf(18161,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => (~ (! [C:int]: ((~ (C = zero_zero_int)) => ((((times_times_int @ A @ C) = one_one_int) => (~ ((divide_divide_int @ B @ A) = (times_times_int @ B @ C)))) | ~ ((divide_divide_int @ one_one_int @ C) = A) | ~ ((divide_divide_int @ one_one_int @ A) = C) | ~ (dvd_dvd_int @ C @ one_one_int))) | (A = zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3085])). 159.59/70.60 thf(4628,axiom,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ (suc @ zero_zero_nat)) = (zero_n2687167440665602831ol_nat @ (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4822_take__bit__of__Suc__0)). 159.59/70.60 thf(23251,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)],[4628])). 159.59/70.60 thf(8036,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) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) <= (ord_less_nat @ E @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4430_pinf_I1_J)). 159.59/70.60 thf(35938,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) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) | ~ (ord_less_nat @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8036])). 159.59/70.60 thf(3548,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/sandbox/benchmark/theBenchmark.p',fact_1071_add__less__cancel__left)). 159.59/70.60 thf(19636,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)],[3548])). 159.59/70.60 thf(5219,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => (((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2660_ord__eq__le__subst)). 159.59/70.60 thf(25328,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((A = (B @ C)) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5219])). 159.59/70.60 thf(5738,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/sandbox/benchmark/theBenchmark.p',fact_2222_mult__less__le__imp__less)). 159.59/70.60 thf(27259,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)],[5738])). 159.59/70.60 thf(876,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (exp_real @ A) @ (exp_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5956_exp__less__mono)). 159.59/70.60 thf(11075,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (exp_real @ A) @ (exp_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[876])). 159.59/70.60 thf(2658,axiom,((! [A:real]: (summable_real @ (^ [B:nat]: (times_times_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9103_summable__exp)). 159.59/70.60 thf(16817,plain,((! [A:real]: (summable_real @ (^ [B:nat]: (times_times_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2658])). 159.59/70.60 thf(15,axiom,(((real_V1803761363581548252l_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7323_of__real__1)). 159.59/70.60 thf(8298,plain,(((real_V1803761363581548252l_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 159.59/70.60 thf(3223,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/sandbox/benchmark/theBenchmark.p',fact_6940_norm__triangle__sub)). 159.59/70.60 thf(18614,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)],[3223])). 159.59/70.60 thf(4312,axiom,((! [A:nat,B:int]: ((bit_concat_bit @ A @ B @ zero_zero_int) = (bit_se2923211474154528505it_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4656_concat__bit__of__zero__2)). 159.59/70.60 thf(22076,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)],[4312])). 159.59/70.60 thf(30,axiom,((! [A:complex]: (ord_less_eq_real @ zero_zero_real @ (re @ (csqrt @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9637_Re__csqrt)). 159.59/70.60 thf(8342,plain,((! [A:complex]: (ord_less_eq_real @ zero_zero_real @ (re @ (csqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 159.59/70.60 thf(6338,axiom,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = one_one_nat) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6541_of__nat__eq__1__iff)). 159.59/70.60 thf(29604,plain,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = one_one_nat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6338])). 159.59/70.60 thf(6655,axiom,((! [A:nat]: ((? [B:nat]: (A = (suc @ B))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1909_not0__implies__Suc)). 159.59/70.60 thf(30799,plain,((! [A:nat]: (? [B:nat]: (A = (suc @ B)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6655])). 159.59/70.60 thf(7280,axiom,((! [A:(nat > (nat > nat)),B:nat,C:nat]: ((produc6842872674320459806at_nat @ A @ (product_Pair_nat_nat @ B @ C)) = (A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4990_old_Oprod_Ocase)). 159.59/70.60 thf(33409,plain,((! [A:(nat > (nat > nat)),B:nat,C:nat]: ((produc6842872674320459806at_nat @ (A) @ (product_Pair_nat_nat @ B @ C)) = (A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7280])). 159.59/70.60 thf(4942,axiom,((! [A:real,B:real,C:nat]: (((times_times_real @ A @ B) = one_one_real) => ((times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_left__right__inverse__power)). 159.59/70.60 thf(24323,plain,((! [A:real,B:real,C:nat]: (((times_times_real @ A @ B) = one_one_real) => ((times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4942])). 159.59/70.60 thf(7034,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/sandbox/benchmark/theBenchmark.p',fact_5220_power__minus__Bit0)). 159.59/70.60 thf(32458,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)],[7034])). 159.59/70.60 thf(6748,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4055_dvd__mult__unit__iff)). 159.59/70.60 thf(31271,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6748])). 159.59/70.60 thf(4556,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/sandbox/benchmark/theBenchmark.p',fact_8125_fact__reduce)). 159.59/70.60 thf(22987,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)],[4556])). 159.59/70.60 thf(6495,axiom,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_Suc__n__not__le__n)). 159.59/70.60 thf(30230,plain,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6495])). 159.59/70.60 thf(2335,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/sandbox/benchmark/theBenchmark.p',fact_5906_of__int__neg__numeral)). 159.59/70.60 thf(15755,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)],[2335])). 159.59/70.60 thf(7713,axiom,((! [A:num]: ((bit_or_not_num_neg @ (bit0 @ A) @ one) = (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6216_or__not__num__neg_Osimps_I4_J)). 159.59/70.60 thf(34916,plain,((! [A:num]: ((bit_or_not_num_neg @ (bit0 @ A) @ one) = (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7713])). 159.59/70.60 thf(1322,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((divide_divide_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) = (divide_divide_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1647_nonzero__mult__divide__mult__cancel__right)). 159.59/70.60 thf(12522,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((divide_divide_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)) = (divide_divide_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322])). 159.59/70.60 thf(6715,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ A) & (B @ C))) = (? [C:nat]: ((member_nat @ C @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) & (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9581_ex__nat__less__eq)). 159.59/70.60 thf(31151,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ A) & (B @ C))) = (? [C:nat]: ((member_nat @ C @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) & (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6715])). 159.59/70.60 thf(4115,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5946_bit_Oconj__zero__right)). 159.59/70.60 thf(21454,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4115])). 159.59/70.60 thf(5508,axiom,((! [A:num]: ~ (ord_less_eq_num @ (bit1 @ A) @ one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5427_semiring__norm_I70_J)). 159.59/70.60 thf(26483,plain,((! [A:num]: ~ (ord_less_eq_num @ (bit1 @ A) @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5508])). 159.59/70.60 thf(5231,axiom,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4654_take__bit__of__0)). 159.59/70.60 thf(25380,plain,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5231])). 159.59/70.60 thf(5326,axiom,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => (~ (! [B:int]: (A != (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4192_evenE)). 159.59/70.60 thf(25734,plain,((! [A:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => (~ (! [B:int]: ~ (A = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5326])). 159.59/70.60 thf(7813,axiom,((! [A:int]: (((power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1775_zero__eq__power2)). 159.59/70.60 thf(35222,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)],[7813])). 159.59/70.60 thf(4092,axiom,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4574_add__0__iff)). 159.59/70.60 thf(21383,plain,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4092])). 159.59/70.60 thf(2337,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/sandbox/benchmark/theBenchmark.p',fact_2165_zero__less__power)). 159.59/70.60 thf(15762,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)],[2337])). 159.59/70.60 thf(6775,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1082_mult_Oright__neutral)). 159.59/70.60 thf(31369,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6775])). 159.59/70.60 thf(2377,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/sandbox/benchmark/theBenchmark.p',fact_7007_sin__cos__squared__add2)). 159.59/70.60 thf(15885,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)],[2377])). 159.59/70.60 thf(6858,axiom,((! [A:num,B:num]: ((plus_plus_num @ (bit1 @ A) @ (bit0 @ B)) = (bit1 @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5422_semiring__norm_I9_J)). 159.59/70.60 thf(31729,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)],[6858])). 159.59/70.60 thf(6659,axiom,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ na) <= (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53__C0_C)). 159.59/70.60 thf(30814,plain,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ na) | ~ (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6659])). 159.59/70.60 thf(1377,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ A @ B)) @ C) = ((ord_less_eq_int @ (minus_minus_int @ B @ C) @ A) & (ord_less_eq_int @ A @ (plus_plus_int @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5584_abs__diff__le__iff)). 159.59/70.60 thf(12725,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ A @ B)) @ C) = ((ord_less_eq_int @ (minus_minus_int @ B @ C) @ A) & (ord_less_eq_int @ A @ (plus_plus_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377])). 159.59/70.60 thf(1669,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1040_add__diff__cancel)). 159.59/70.60 thf(13655,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669])). 159.59/70.60 thf(1490,axiom,((imaginary_unit = (complex2 @ zero_zero_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9351_imaginary__unit_Ocode)). 159.59/70.60 thf(13115,plain,((imaginary_unit = (complex2 @ zero_zero_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490])). 159.59/70.60 thf(4285,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/sandbox/benchmark/theBenchmark.p',fact_5901_of__int__pos)). 159.59/70.60 thf(21999,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)],[4285])). 159.59/70.60 thf(4909,axiom,((! [A:int,B:int,C:(int > int),D:int]: ((ord_less_eq_int @ A @ B) => (((ord_less_eq_int @ (C @ A) @ D) <= (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F))))) <= (ord_less_eq_int @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2682_order__subst2)). 159.59/70.60 thf(24220,plain,((! [A:int,B:int,C:(int > int),D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (C @ A) @ D) | ~ (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F)))) | ~ (ord_less_eq_int @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4909])). 159.59/70.60 thf(4016,axiom,((! [A:real]: ((plus_plus_real @ A @ (uminus_uminus_real @ A)) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4686_add_Oright__inverse)). 159.59/70.60 thf(21156,plain,((! [A:real]: ((plus_plus_real @ A @ (uminus_uminus_real @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4016])). 159.59/70.60 thf(6911,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/sandbox/benchmark/theBenchmark.p',fact_9467_nat__mult__distrib__neg)). 159.59/70.60 thf(31892,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)],[6911])). 159.59/70.60 thf(4819,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/sandbox/benchmark/theBenchmark.p',fact_316_power__increasing)). 159.59/70.60 thf(23929,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)],[4819])). 159.59/70.60 thf(5987,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/sandbox/benchmark/theBenchmark.p',fact_5656_divmod_H__nat__def)). 159.59/70.60 thf(28398,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)],[5987])). 159.59/70.60 thf(3654,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/sandbox/benchmark/theBenchmark.p',fact_2330_neg__less__divide__eq)). 159.59/70.60 thf(19986,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)],[3654])). 159.59/70.60 thf(2082,axiom,((! [A:real,B:real,C:complex,D:complex]: (((real_V2046097035970521341omplex @ (divide_divide_real @ A @ B) @ C) = D) = ((((real_V2046097035970521341omplex @ A @ C) = (real_V2046097035970521341omplex @ B @ D)) <= (B != zero_zero_real)) & ((D = zero_zero_complex) <= (B = zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9231_vector__fraction__eq__iff)). 159.59/70.60 thf(14959,plain,((! [A:real,B:real,C:complex,D:complex]: (((real_V2046097035970521341omplex @ (divide_divide_real @ A @ B) @ C) = D) = ((((real_V2046097035970521341omplex @ A @ C) = (real_V2046097035970521341omplex @ B @ D)) | (B = zero_zero_real)) & ((D = zero_zero_complex) | ~ (B = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2082])). 159.59/70.60 thf(7736,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_add__lessD1)). 159.59/70.60 thf(34992,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)],[7736])). 159.59/70.60 thf(3393,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ B @ A) <= (A = (times_3573771949741848930nteger @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3934_dvdI)). 159.59/70.60 thf(19159,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ B @ A) | ~ (A = (times_3573771949741848930nteger @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3393])). 159.59/70.60 thf(799,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) => (((log @ A @ (divide_divide_real @ B @ C)) = (minus_minus_real @ (log @ A @ B) @ (log @ A @ C))) <= (ord_less_real @ zero_zero_real @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6432_log__divide)). 159.59/70.60 thf(10827,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) => (((log @ A @ (divide_divide_real @ B @ C)) = (minus_minus_real @ (log @ A @ B) @ (log @ A @ C))) | ~ (ord_less_real @ zero_zero_real @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[799])). 159.59/70.60 thf(8089,axiom,((! [A:list_nat,B:list_VEBT_VEBT]: ((size_s4762443039079500285T_VEBT @ (produc7156399406898700509T_VEBT @ A @ B)) = (times_times_nat @ (size_size_list_nat @ A) @ (size_s6755466524823107622T_VEBT @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3630_length__product)). 159.59/70.60 thf(36115,plain,((! [A:list_nat,B:list_VEBT_VEBT]: ((size_s4762443039079500285T_VEBT @ (produc7156399406898700509T_VEBT @ A @ B)) = (times_times_nat @ (size_size_list_nat @ A) @ (size_s6755466524823107622T_VEBT @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8089])). 159.59/70.60 thf(6993,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/sandbox/benchmark/theBenchmark.p',fact_5557_abs__mult__pos)). 159.59/70.60 thf(32334,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)],[6993])). 159.59/70.60 thf(7395,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/sandbox/benchmark/theBenchmark.p',fact_8085_fact__fact__dvd__fact)). 159.59/70.60 thf(33818,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)],[7395])). 159.59/70.60 thf(8024,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 @ 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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_nat__less__add__iff1)). 159.59/70.60 thf(35890,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 @ 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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8024])). 159.59/70.60 thf(2794,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/sandbox/benchmark/theBenchmark.p',fact_6735_reals__Archimedean3)). 159.59/70.60 thf(17246,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)],[2794])). 159.59/70.60 thf(45,axiom,((! [A:int,B:int]: ((B = (ord_max_int @ B @ A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_max_OorderE)). 159.59/70.60 thf(8385,plain,((! [A:int,B:int]: ((B = (ord_max_int @ B @ A)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[45])). 159.59/70.60 thf(6722,axiom,((! [A:nat]: ~ (ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8075_fact__not__neg)). 159.59/70.60 thf(31171,plain,((! [A:nat]: ~ (ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6722])). 159.59/70.60 thf(3677,axiom,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ A @ C) | (bit_se1146084159140164899it_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6375_bit__or__iff)). 159.59/70.60 thf(20063,plain,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ A @ C) | (bit_se1146084159140164899it_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3677])). 159.59/70.60 thf(7947,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((C = D) & (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1200_add__mono__thms__linordered__field_I1_J)). 159.59/70.60 thf(35659,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((C = D) & (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7947])). 159.59/70.60 thf(402,axiom,((! [A:$o,B:nat]: ((bit_se9216721137139052372nteger @ (zero_n356916108424825756nteger @ A) @ B) = ((B = zero_zero_nat) & (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6395_bit__of__bool__iff)). 159.59/70.60 thf(9509,plain,((! [A:$o,B:nat]: ((bit_se9216721137139052372nteger @ (zero_n356916108424825756nteger @ A) @ B) = ((B = zero_zero_nat) & (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])). 159.59/70.60 thf(5572,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/sandbox/benchmark/theBenchmark.p',fact_855_Nat_Odiff__add__assoc2)). 159.59/70.60 thf(26670,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)],[5572])). 159.59/70.60 thf(725,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/sandbox/benchmark/theBenchmark.p',fact_7962_sum__lessThan__telescope_H)). 159.59/70.60 thf(10594,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)],[725])). 159.59/70.60 thf(4798,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/sandbox/benchmark/theBenchmark.p',fact_4809_mult__neg__numeral__simps_I2_J)). 159.59/70.60 thf(23821,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)],[4798])). 159.59/70.60 thf(7358,axiom,((! [A:code_integer,B:$o,C:code_integer,D:$o]: (((produc6677183202524767010eger_o @ A @ B) = (produc6677183202524767010eger_o @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3608_prod_Oinject)). 159.59/70.60 thf(33697,plain,((! [A:code_integer,B:$o,C:code_integer,D:$o]: (((produc6677183202524767010eger_o @ A @ B) = (produc6677183202524767010eger_o @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7358])). 159.59/70.60 thf(2110,axiom,((! [A:real,B:num]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ (numeral_numeral_int @ B)) = (ord_less_real @ A @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8190_floor__less__numeral)). 159.59/70.60 thf(15051,plain,((! [A:real,B:num]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ (numeral_numeral_int @ B)) = (ord_less_real @ A @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2110])). 159.59/70.60 thf(7849,axiom,((! [A:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1774_zero__eq__power2)). 159.59/70.60 thf(35338,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)],[7849])). 159.59/70.60 thf(601,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => (! [D:complex,E:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ D @ C)) = (dvd_dvd_complex @ A @ (plus_plus_complex @ (minus_minus_complex @ D @ (times_times_complex @ E @ B)) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4295_inf__period_I3_J)). 159.59/70.60 thf(10170,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => (! [D:complex,E:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ D @ C)) = (dvd_dvd_complex @ A @ (plus_plus_complex @ (minus_minus_complex @ D @ (times_times_complex @ E @ B)) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[601])). 159.59/70.60 thf(1167,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/sandbox/benchmark/theBenchmark.p',fact_9615_or__not__numerals_I8_J)). 159.59/70.60 thf(11994,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)],[1167])). 159.59/70.60 thf(3678,axiom,((! [A:num]: ((real_V7735802525324610683m_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6895_norm__numeral)). 159.59/70.60 thf(20066,plain,((! [A:num]: ((real_V7735802525324610683m_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3678])). 159.59/70.60 thf(8183,axiom,((! [A:nat]: ((^ [B:nat]: (times_times_nat @ B @ A)) = (times_times_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1410_mult__commute__abs)). 159.59/70.60 thf(36418,plain,((! [A:nat]: ((^ [B:nat]: (times_times_nat @ B @ A)) = (times_times_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8183])). 159.59/70.60 thf(2641,axiom,((! [A:int,B:int]: ((if_int @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Int__Oint_T)). 159.59/70.60 thf(16762,plain,((! [A:int,B:int]: ((if_int @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2641])). 159.59/70.60 thf(6649,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/sandbox/benchmark/theBenchmark.p',fact_1984_mult__right__mono)). 159.59/70.60 thf(30782,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)],[6649])). 159.59/70.60 thf(536,axiom,((! [A:set_nat,B:nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (insert_nat @ B @ C)) <= (ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6259_Diff__single__insert)). 159.59/70.60 thf(9961,plain,((! [A:set_nat,B:nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (insert_nat @ B @ C)) | ~ (ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[536])). 159.59/70.60 thf(5890,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/sandbox/benchmark/theBenchmark.p',fact_365_power__mult__distrib)). 159.59/70.60 thf(28018,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)],[5890])). 159.59/70.60 thf(2896,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/sandbox/benchmark/theBenchmark.p',fact_3018_Collect__subset)). 159.59/70.60 thf(17577,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)],[2896])). 159.59/70.60 thf(3244,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ C) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ C) @ A)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4168_unit__div__commute)). 159.59/70.60 thf(18684,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ C) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ C) @ A)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3244])). 159.59/70.60 thf(5791,axiom,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ A @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups6464643781859351333omplex @ (^ [C:nat]: (times_times_complex @ (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/sandbox/benchmark/theBenchmark.p',fact_8609_prod_Oin__pairs__0)). 159.59/70.60 thf(27505,plain,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ (A) @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups6464643781859351333omplex @ (^ [C:nat]: (times_times_complex @ (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)],[5791])). 159.59/70.60 thf(7957,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_add_Ocommute)). 159.59/70.60 thf(35688,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7957])). 159.59/70.60 thf(5324,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/sandbox/benchmark/theBenchmark.p',fact_1336_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2)). 159.59/70.60 thf(25727,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)],[5324])). 159.59/70.60 thf(207,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C))) = (ord_less_real @ (real_V1485227260804924795R_real @ A @ B) @ (uminus_uminus_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9282_pos__less__minus__divideR__eq)). 159.59/70.60 thf(8881,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C))) = (ord_less_real @ (real_V1485227260804924795R_real @ A @ B) @ (uminus_uminus_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 159.59/70.60 thf(7233,axiom,((dvd_dvd_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (times_times_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3942_dvd__def)). 159.59/70.60 thf(33266,plain,(((dvd_dvd_nat) = (^ [A:nat,B:nat]: ? [C:nat]: (B = (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7233])). 159.59/70.60 thf(1991,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ C)) <= (ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2227_mult__right__le__imp__le)). 159.59/70.60 thf(14689,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ C)) | ~ (ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1991])). 159.59/70.60 thf(2701,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/sandbox/benchmark/theBenchmark.p',fact_1052_add__shift)). 159.59/70.60 thf(16965,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)],[2701])). 159.59/70.60 thf(4930,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (ord_less_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_diff__less__mono)). 159.59/70.60 thf(24290,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (ord_less_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4930])). 159.59/70.60 thf(3885,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) <= (ord_less_real @ C @ D)) <= (ord_less_eq_real @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3215_order__le__less__subst1)). 159.59/70.60 thf(20761,plain,((! [A:real,B:(real > real),C:real,D:real]: (((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) | ~ (ord_less_real @ C @ D) | ~ (ord_less_eq_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3885])). 159.59/70.60 thf(2367,axiom,((! [A:$o]: ((semiri4939895301339042750nteger @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n356916108424825756nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6575_of__nat__of__bool)). 159.59/70.60 thf(15848,plain,((! [A:$o]: ((semiri4939895301339042750nteger @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n356916108424825756nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2367])). 159.59/70.60 thf(6536,axiom,(((power_power_complex @ imaginary_unit @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9315_power2__i)). 159.59/70.60 thf(30385,plain,(((power_power_complex @ imaginary_unit @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6536])). 159.59/70.60 thf(7147,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/sandbox/benchmark/theBenchmark.p',fact_2261_add__strict__increasing)). 159.59/70.60 thf(32930,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)],[7147])). 159.59/70.60 thf(6893,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/sandbox/benchmark/theBenchmark.p',fact_5346_abs__ln__one__plus__x__minus__x__bound__nonpos)). 159.59/70.60 thf(31835,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)],[6893])). 159.59/70.60 thf(6065,axiom,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5480_abs__ge__self)). 159.59/70.60 thf(28646,plain,((! [A:real]: (ord_less_eq_real @ A @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6065])). 159.59/70.60 thf(1873,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B)))) <= (summable_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7025_summable__ignore__initial__segment)). 159.59/70.60 thf(14301,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)],[1873])). 159.59/70.60 thf(1501,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((((divide6298287555418463151nteger @ (divide6298287555418463151nteger @ C @ A) @ (divide6298287555418463151nteger @ B @ A)) = (divide6298287555418463151nteger @ C @ B)) <= (dvd_dvd_Code_integer @ B @ C)) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4020_div__div__div__same)). 159.59/70.60 thf(13145,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (divide6298287555418463151nteger @ C @ A) @ (divide6298287555418463151nteger @ B @ A)) = (divide6298287555418463151nteger @ C @ B)) | ~ (dvd_dvd_Code_integer @ B @ C) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501])). 159.59/70.60 thf(3444,axiom,((! [A:real]: (((powr_real @ A @ one_one_real) = A) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7218_powr__one__gt__zero__iff)). 159.59/70.60 thf(19323,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)],[3444])). 159.59/70.60 thf(7851,axiom,((! [A:num]: ~ (ord_less_eq_num @ (bit0 @ A) @ one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_semiring__norm_I69_J)). 159.59/70.60 thf(35345,plain,((! [A:num]: ~ (ord_less_eq_num @ (bit0 @ A) @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7851])). 159.59/70.60 thf(4960,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ zero_zero_nat) @ C @ D) @ E) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ zero_zero_nat) @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2407_vebt__delete_Osimps_I6_J)). 159.59/70.60 thf(24430,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ zero_zero_nat) @ C @ D) @ E) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ zero_zero_nat) @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4960])). 159.59/70.60 thf(6169,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((power_power_real @ zero_zero_real @ A) = one_one_real)) & ((A != zero_zero_nat) => ((power_power_real @ zero_zero_real @ A) = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1813_power__0__left)). 159.59/70.60 thf(28987,plain,((! [A:nat]: (((A = zero_zero_nat) => ((power_power_real @ zero_zero_real @ A) = one_one_real)) & ((~ (A = zero_zero_nat)) => ((power_power_real @ zero_zero_real @ A) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6169])). 159.59/70.60 thf(849,axiom,((! [A:real,B:real]: (sums_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ (times_times_real @ (real_V1485227260804924795R_real @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C)) @ (power_power_real @ A @ D)) @ (power_power_real @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_real)) @ (set_ord_atMost_nat @ C))) @ (cos_real @ (plus_plus_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9178_sums__cos__x__plus__y)). 159.59/70.60 thf(10991,plain,((! [A:real,B:real]: (sums_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ (times_times_real @ (real_V1485227260804924795R_real @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C)) @ (power_power_real @ A @ D)) @ (power_power_real @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_real)) @ (set_ord_atMost_nat @ C))) @ (cos_real @ (plus_plus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[849])). 159.59/70.60 thf(2157,axiom,((! [A:extended_enat,B:extended_enat]: ((A != B) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2828_order_Ostrict__implies__not__eq)). 159.59/70.60 thf(15207,plain,((! [A:extended_enat,B:extended_enat]: (~ (A = B) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2157])). 159.59/70.60 thf(3996,axiom,((! [A:real]: (ord_less_eq_real @ (cos_real @ A) @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7065_cos__le__one)). 159.59/70.60 thf(21096,plain,((! [A:real]: (ord_less_eq_real @ (cos_real @ A) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3996])). 159.59/70.60 thf(770,axiom,((! [A:real]: (ord_less_eq_real @ A @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7063_le__of__int__ceiling)). 159.59/70.60 thf(10737,plain,((! [A:real]: (ord_less_eq_real @ A @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[770])). 159.59/70.60 thf(2842,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/sandbox/benchmark/theBenchmark.p',fact_7999_power__diff__sumr2)). 159.59/70.60 thf(17390,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)],[2842])). 159.59/70.60 thf(1510,axiom,((! [A:real]: ((ord_less_real @ (sqrt @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6316_real__sqrt__lt__0__iff)). 159.59/70.60 thf(13174,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)],[1510])). 159.59/70.60 thf(4385,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/sandbox/benchmark/theBenchmark.p',fact_6928_norm__triangle__ineq)). 159.59/70.60 thf(22300,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)],[4385])). 159.59/70.60 thf(6508,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1839_gr__zeroI)). 159.59/70.60 thf(30269,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6508])). 159.59/70.60 thf(6024,axiom,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ A @ B)) => ((bit_se2925701944663578781it_nat @ A @ (bit_se2161824704523386999it_nat @ B @ C)) = (bit_se2161824704523386999it_nat @ B @ (bit_se2925701944663578781it_nat @ A @ C)))) & (((bit_se2925701944663578781it_nat @ A @ (bit_se2161824704523386999it_nat @ B @ C)) = (bit_se2925701944663578781it_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5115_take__bit__flip__bit__eq)). 159.59/70.60 thf(28514,plain,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ A @ B)) => ((bit_se2925701944663578781it_nat @ A @ (bit_se2161824704523386999it_nat @ B @ C)) = (bit_se2161824704523386999it_nat @ B @ (bit_se2925701944663578781it_nat @ A @ C)))) & (((bit_se2925701944663578781it_nat @ A @ (bit_se2161824704523386999it_nat @ B @ C)) = (bit_se2925701944663578781it_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6024])). 159.59/70.60 thf(3638,axiom,((! [A:real,B:real]: ((ord_less_real @ (sqrt @ A) @ (sqrt @ B)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6367_real__sqrt__less__mono)). 159.59/70.60 thf(19932,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)],[3638])). 159.59/70.60 thf(5975,axiom,((vEBT_is_succ_in_set = (^ [A:set_nat,B:nat,C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ B @ C) & ! [D:nat]: (((ord_less_nat @ B @ D) => (ord_less_eq_nat @ C @ D)) <= (member_nat @ D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1449_is__succ__in__set__def)). 159.59/70.60 thf(28366,plain,(((vEBT_is_succ_in_set) = (^ [A:set_nat,B:nat,C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ B @ C) & ! [D:nat]: (((ord_less_nat @ B @ D) => (ord_less_eq_nat @ C @ D)) | ~ (member_nat @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5975])). 159.59/70.60 thf(3872,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_add__diff__cancel__right_H)). 159.59/70.60 thf(20722,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3872])). 159.59/70.60 thf(7174,axiom,((! [A:nat,B:(nat > ($o > $o))]: ((! [C:nat]: ((? [D:$o]: (B @ C @ D)) <= (ord_less_nat @ C @ A))) = (? [C:list_o]: (! [D:nat]: ((B @ D @ (nth_o @ C @ D)) <= (ord_less_nat @ D @ A)) & ((size_size_list_o @ C) = A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_Skolem__list__nth)). 159.59/70.60 thf(33036,plain,((! [A:nat,B:(nat > ($o > $o))]: ((! [C:nat]: (? [D:$o]: (B @ C @ D) | ~ (ord_less_nat @ C @ A))) = (? [C:list_o]: (! [D:nat]: ((B @ D @ (nth_o @ C @ D)) | ~ (ord_less_nat @ D @ A)) & ((size_size_list_o @ C) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7174])). 159.59/70.60 thf(6358,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/sandbox/benchmark/theBenchmark.p',fact_9094_binomial__absorption)). 159.59/70.60 thf(29668,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)],[6358])). 159.59/70.60 thf(6267,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6483_log2__of__power__le)). 159.59/70.60 thf(29371,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6267])). 159.59/70.60 thf(1101,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/sandbox/benchmark/theBenchmark.p',fact_7168_cos__one__2pi__int)). 159.59/70.60 thf(11786,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)],[1101])). 159.59/70.60 thf(2808,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (sqrt @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6387_real__sqrt__gt__zero)). 159.59/70.60 thf(17285,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2808])). 159.59/70.60 thf(1109,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/sandbox/benchmark/theBenchmark.p',fact_6103_exp__ge__add__one__self__aux)). 159.59/70.60 thf(11816,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)],[1109])). 159.59/70.60 thf(7287,axiom,((! [A:(nat > complex),B:nat,C:nat]: ((! [D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (A @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ B)) = zero_zero_complex)) => ((ord_less_eq_nat @ C @ B) => ((A @ C) = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8832_zero__polynom__imp__zero__coeffs)). 159.59/70.60 thf(33431,plain,((! [A:(nat > complex),B:nat,C:nat]: ((! [D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (A @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ B)) = zero_zero_complex)) => ((ord_less_eq_nat @ C @ B) => ((A @ C) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7287])). 159.59/70.60 thf(4217,axiom,((! [A:$o,B:$o]: ((zero_n2684676970156552555ol_int @ ((A) & (B))) = (times_times_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4388_of__bool__conj)). 159.59/70.60 thf(21781,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)],[4217])). 159.59/70.60 thf(8097,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/sandbox/benchmark/theBenchmark.p',fact_3528_div__mult1__eq)). 159.59/70.60 thf(36137,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)],[8097])). 159.59/70.60 thf(4715,axiom,((! [A:nat,B:nat,C:(nat > int),D:(nat > int)]: (((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)))))) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8637_prod_Ozero__middle)). 159.59/70.60 thf(23547,plain,((! [A:nat,B:nat,C:(nat > int),D:(nat > int)]: (((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)))))) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4715])). 159.59/70.60 thf(4894,axiom,((! [A:nat]: ((ord_max_nat @ bot_bot_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2582_max__bot)). 159.59/70.60 thf(24166,plain,((! [A:nat]: ((ord_max_nat @ bot_bot_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4894])). 159.59/70.60 thf(1889,axiom,((! [A:real,B:real]: ((real_V4546457046886955230omplex @ (divide_divide_real @ A @ B)) = (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ A) @ (real_V4546457046886955230omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7332_of__real__divide)). 159.59/70.60 thf(14354,plain,((! [A:real,B:real]: ((real_V4546457046886955230omplex @ (divide_divide_real @ A @ B)) = (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ A) @ (real_V4546457046886955230omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1889])). 159.59/70.60 thf(162,axiom,((! [A:nat]: (((semiri4939895301339042750nteger @ A) = zero_z3403309356797280102nteger) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6512_of__nat__eq__0__iff)). 159.59/70.60 thf(8752,plain,((! [A:nat]: (((semiri4939895301339042750nteger @ A) = zero_z3403309356797280102nteger) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[162])). 159.59/70.60 thf(6906,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((power_power_nat @ A @ B) != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1892_power__not__zero)). 159.59/70.60 thf(31875,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => (~ ((power_power_nat @ A @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6906])). 159.59/70.60 thf(2605,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/sandbox/benchmark/theBenchmark.p',fact_1047_add__diff__cancel__left)). 159.59/70.60 thf(16630,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)],[2605])). 159.59/70.60 thf(3217,axiom,((! [A:(int > $o),B:int]: (((A @ B) <= (! [C:nat]: (A @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ C)))))) <= (! [C:nat]: (A @ (semiri1314217659103216013at_int @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6820_int__of__nat__induct)). 159.59/70.60 thf(18595,plain,((! [A:(int > $o),B:int]: ((A @ B) | ~ (! [C:nat]: (A @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ C))))) | ~ (! [C:nat]: (A @ (semiri1314217659103216013at_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3217])). 159.59/70.60 thf(3927,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/sandbox/benchmark/theBenchmark.p',fact_6969_summable__divide__iff)). 159.59/70.60 thf(20885,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)],[3927])). 159.59/70.60 thf(410,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/sandbox/benchmark/theBenchmark.p',fact_8249_gbinomial__addition__formula)). 159.59/70.60 thf(9540,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)],[410])). 159.59/70.60 thf(7002,axiom,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (groups708209901874060359at_nat @ (^ [C:nat]: (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8922_pochhammer__Suc__prod__rev)). 159.59/70.60 thf(32363,plain,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (groups708209901874060359at_nat @ (^ [C:nat]: (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7002])). 159.59/70.60 thf(3661,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/sandbox/benchmark/theBenchmark.p',fact_5839_of__int__eq__numeral__power__cancel__iff)). 159.59/70.60 thf(20011,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)],[3661])). 159.59/70.60 thf(5415,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((((? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))) => (C)) => (((~ (! [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 = (~ ((B != D) => ((B != E) => (((~ (ord_less_nat @ B @ D)) => (~ (ord_less_nat @ E @ B) & ((((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 @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G))) <= (~ (ord_less_nat @ E @ B))))) & ~ (ord_less_nat @ B @ D))))))))) <= ((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))))) <= ((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:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (C = (~ ((((B = one_one_nat) & ((B = one_one_nat) => (E))) <= (B != zero_zero_nat)) & ((B = zero_zero_nat) => (D)))))))) <= ((vEBT_vebt_member @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2554_vebt__member_Oelims_I1_J)). 159.59/70.60 thf(26108,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: ((((? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))) => (C)) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT]: ((? [H:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H))) => (C = (~ ((~ (B = D)) => ((~ (B = E)) => (((~ (ord_less_nat @ B @ D)) => (~ (ord_less_nat @ E @ B) & ((((vEBT_vebt_member @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G))) | (ord_less_nat @ E @ B)))) & ~ (ord_less_nat @ B @ D)))))))) | ~ ((C) | ~ (? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F)))) | ~ ((C) | ~ (? [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F)))))) | ~ (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (C = (~ ((((B = one_one_nat) & ((B = one_one_nat) => (E))) | (B = zero_zero_nat)) & ((B = zero_zero_nat) => (D))))))) | ~ ((vEBT_vebt_member @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5415])). 159.59/70.60 thf(7255,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_nat @ B @ C)) <= (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2251_mult__left__less__imp__less)). 159.59/70.60 thf(33337,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_nat @ B @ C)) | ~ (ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7255])). 159.59/70.60 thf(8248,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((A @ C) <= (! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2785_less__induct)). 159.59/70.60 thf(36771,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)],[8248])). 159.59/70.60 thf(17,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B)) @ C) = (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ (uminus_uminus_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9278_neg__minus__divideR__le__eq)). 159.59/70.60 thf(8303,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B)) @ C) = (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ (uminus_uminus_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 159.59/70.60 thf(5252,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((ord_less_eq_nat @ D @ C) <= (A @ D))) => (~ (! [D:nat]: ((~ (! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E)))) <= (A @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3365_bounded__Max__nat)). 159.59/70.60 thf(25444,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (A @ D))) => (~ (! [D:nat]: (~ (! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E))) | ~ (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5252])). 159.59/70.60 thf(6839,axiom,((! [A:num]: ((bit_se2000444600071755411sk_int @ (numeral_numeral_nat @ A)) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2000444600071755411sk_int @ (pred_numeral @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5929_mask__numeral)). 159.59/70.60 thf(31573,plain,((! [A:num]: ((bit_se2000444600071755411sk_int @ (numeral_numeral_nat @ A)) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2000444600071755411sk_int @ (pred_numeral @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6839])). 159.59/70.60 thf(3651,axiom,((! [A:real,B:real]: ((A != zero_zero_real) => ((B != zero_zero_real) => ((plus_plus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (times_times_real @ (times_times_real @ (inverse_inverse_real @ A) @ (plus_plus_real @ A @ B)) @ (inverse_inverse_real @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9070_division__ring__inverse__add)). 159.59/70.60 thf(19975,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real)) => ((~ (B = zero_zero_real)) => ((plus_plus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (times_times_real @ (times_times_real @ (inverse_inverse_real @ A) @ (plus_plus_real @ A @ B)) @ (inverse_inverse_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3651])). 159.59/70.60 thf(8172,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/sandbox/benchmark/theBenchmark.p',fact_1311_add__less__le__mono)). 159.59/70.60 thf(36386,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)],[8172])). 159.59/70.60 thf(657,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/sandbox/benchmark/theBenchmark.p',fact_3206_order__less__le__trans)). 159.59/70.60 thf(10351,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)],[657])). 159.59/70.60 thf(1870,axiom,((! [A:nat]: ((semiri4939895301339042750nteger @ (suc @ A)) = (plus_p5714425477246183910nteger @ one_one_Code_integer @ (semiri4939895301339042750nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6586_of__nat__Suc)). 159.59/70.60 thf(14292,plain,((! [A:nat]: ((semiri4939895301339042750nteger @ (suc @ A)) = (plus_p5714425477246183910nteger @ one_one_Code_integer @ (semiri4939895301339042750nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1870])). 159.59/70.60 thf(1071,axiom,((! [A:real,B:real,C:num]: (((divide_divide_real @ A @ B) = (numeral_numeral_real @ C)) = (((B = zero_zero_real) => ((numeral_numeral_real @ C) = zero_zero_real)) & ((A = (times_times_real @ (numeral_numeral_real @ C) @ B)) <= (B != zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2339_divide__eq__eq__numeral_I1_J)). 159.59/70.60 thf(11684,plain,((! [A:real,B:real,C:num]: (((divide_divide_real @ A @ B) = (numeral_numeral_real @ C)) = (((B = zero_zero_real) => ((numeral_numeral_real @ C) = zero_zero_real)) & ((A = (times_times_real @ (numeral_numeral_real @ C) @ B)) | (B = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071])). 159.59/70.60 thf(5510,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))) = ((ord_less_nat @ C @ B) | ((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4276_even__mult__exp__div__exp__iff)). 159.59/70.60 thf(26488,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))) = ((ord_less_nat @ C @ B) | ((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5510])). 159.59/70.60 thf(3383,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ (sin_real @ A)) <= (ord_less_eq_real @ A @ pi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6835_sin__ge__zero)). 159.59/70.60 thf(19123,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ (sin_real @ A)) | ~ (ord_less_eq_real @ A @ pi))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3383])). 159.59/70.60 thf(5659,axiom,((! [A:nat,B:list_VEBT_VEBT,C:list_nat]: (((nth_Pr1791586995822124652BT_nat @ (produc7295137177222721919BT_nat @ B @ C) @ A) = (produc738532404422230701BT_nat @ (nth_VEBT_VEBT @ B @ (divide_divide_nat @ A @ (size_size_list_nat @ C))) @ (nth_nat @ C @ (modulo_modulo_nat @ A @ (size_size_list_nat @ C))))) <= (ord_less_nat @ A @ (times_times_nat @ (size_s6755466524823107622T_VEBT @ B) @ (size_size_list_nat @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3591_product__nth)). 159.59/70.60 thf(26979,plain,((! [A:nat,B:list_VEBT_VEBT,C:list_nat]: (((nth_Pr1791586995822124652BT_nat @ (produc7295137177222721919BT_nat @ B @ C) @ A) = (produc738532404422230701BT_nat @ (nth_VEBT_VEBT @ B @ (divide_divide_nat @ A @ (size_size_list_nat @ C))) @ (nth_nat @ C @ (modulo_modulo_nat @ A @ (size_size_list_nat @ C))))) | ~ (ord_less_nat @ A @ (times_times_nat @ (size_s6755466524823107622T_VEBT @ B) @ (size_size_list_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5659])). 159.59/70.60 thf(3007,axiom,((! [A:real]: (((abs_abs_real @ (cos_real @ A)) = one_one_real) <= ((sin_real @ A) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7125_sin__zero__abs__cos__one)). 159.59/70.60 thf(17924,plain,((! [A:real]: (((abs_abs_real @ (cos_real @ A)) = one_one_real) | ~ ((sin_real @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3007])). 159.59/70.60 thf(3241,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ (plus_plus_int @ A @ C)) <= (ord_less_int @ B @ C)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2259_add__strict__increasing2)). 159.59/70.60 thf(18674,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ B @ (plus_plus_int @ A @ C)) | ~ (ord_less_int @ B @ C) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3241])). 159.59/70.60 thf(7652,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_nat__1__add__1)). 159.59/70.60 thf(34709,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7652])). 159.59/70.60 thf(2310,axiom,(((arccos @ (uminus_uminus_real @ one_one_real)) = pi)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7350_arccos__minus__1)). 159.59/70.60 thf(15683,plain,(((arccos @ (uminus_uminus_real @ one_one_real)) = pi)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2310])). 159.59/70.60 thf(2793,axiom,((! [A:real,B:num]: ((real_V1022390504157884413omplex @ (plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ (numera6690914467698888265omplex @ B))) = (abs_abs_real @ (plus_plus_real @ A @ (numeral_numeral_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7369_norm__of__real__addn)). 159.59/70.60 thf(17243,plain,((! [A:real,B:num]: ((real_V1022390504157884413omplex @ (plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ (numera6690914467698888265omplex @ B))) = (abs_abs_real @ (plus_plus_real @ A @ (numeral_numeral_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2793])). 159.59/70.60 thf(2638,axiom,((! [A:real,B:real]: ((B != A) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2834_dual__order_Ostrict__implies__not__eq)). 159.59/70.60 thf(16752,plain,((! [A:real,B:real]: (~ (B = A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2638])). 159.59/70.60 thf(745,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ A @ C) <= (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3211_order__less__le__trans)). 159.59/70.60 thf(10662,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ A @ C) | ~ (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[745])). 159.59/70.60 thf(4097,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((times_times_real @ A @ (powr_real @ A @ B)) = (powr_real @ A @ (plus_plus_real @ one_one_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7270_powr__mult__base)). 159.59/70.60 thf(21398,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((times_times_real @ A @ (powr_real @ A @ B)) = (powr_real @ A @ (plus_plus_real @ one_one_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4097])). 159.59/70.60 thf(217,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (~ ((A != zero_z3403309356797280102nteger) => (! [C:code_integer]: (B != (times_3573771949741848930nteger @ A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4136_unit__dvdE)). 159.59/70.60 thf(8911,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (~ ((~ (A = zero_z3403309356797280102nteger)) => (! [C:code_integer]: ~ (B = (times_3573771949741848930nteger @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 159.59/70.60 thf(4342,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/sandbox/benchmark/theBenchmark.p',fact_2154_divide__strict__right__mono__neg)). 159.59/70.60 thf(22165,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)],[4342])). 159.59/70.60 thf(4137,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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1651_nonzero__mult__divide__mult__cancel__left)). 159.59/70.60 thf(21517,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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4137])). 159.59/70.60 thf(1000,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/sandbox/benchmark/theBenchmark.p',fact_9562_concat__bit__eq)). 159.59/70.60 thf(11449,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)],[1000])). 159.59/70.60 thf(3161,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/sandbox/benchmark/theBenchmark.p',fact_7183_cos__diff__cos)). 159.59/70.60 thf(18425,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)],[3161])). 159.59/70.60 thf(4582,axiom,((ord_less_eq_nat @ mi @ ma)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__C5_Ohyps_C_I7_J)). 159.59/70.60 thf(23061,plain,((ord_less_eq_nat @ mi @ ma)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4582])). 159.59/70.60 thf(2610,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/sandbox/benchmark/theBenchmark.p',fact_6937_norm__triangle__ineq4)). 159.59/70.60 thf(16668,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)],[2610])). 159.59/70.60 thf(3237,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/sandbox/benchmark/theBenchmark.p',fact_8264_pochhammer__rec)). 159.59/70.60 thf(18661,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)],[3237])). 159.59/70.60 thf(6737,axiom,((! [A:num]: ((pred_numeral @ (inc @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5683_pred__numeral__inc)). 159.59/70.60 thf(31220,plain,((! [A:num]: ((pred_numeral @ (inc @ A)) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6737])). 159.59/70.60 thf(7738,axiom,((! [A:nat,B:nat,C:nat]: ((drop_nat @ A @ (upt @ B @ C)) = (upt @ (plus_plus_nat @ B @ A) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10182_drop__upt)). 159.59/70.60 thf(35012,plain,((! [A:nat,B:nat,C:nat]: ((drop_nat @ A @ (upt @ B @ C)) = (upt @ (plus_plus_nat @ B @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7738])). 159.59/70.60 thf(3668,axiom,((! [A:nat,B:nat]: (((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ B) = zero_zero_complex) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8280_pochhammer__of__nat__eq__0__lemma)). 159.59/70.60 thf(20034,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)],[3668])). 159.59/70.60 thf(8255,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 @ A @ F) & (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)))))))) <= (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_member__inv)). 159.59/70.60 thf(36796,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 @ A @ F) & (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)))))))) | ~ (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)],[8255])). 159.59/70.60 thf(6966,axiom,((! [A:set_nat,B:(set_nat > $o)]: ((finite_finite_nat @ A) => (((B @ A) <= (! [C:nat,D:set_nat]: ((finite_finite_nat @ D) => ((! [E:nat]: ((member_nat @ E @ D) => (ord_less_nat @ E @ C))) => ((B @ (insert_nat @ C @ D)) <= (B @ D)))))) <= (B @ bot_bot_set_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6235_finite__linorder__max__induct)). 159.59/70.60 thf(32101,plain,((! [A:set_nat,B:(set_nat > $o)]: ((finite_finite_nat @ A) => ((B @ A) | ~ (! [C:nat,D:set_nat]: ((finite_finite_nat @ D) => ((! [E:nat]: ((member_nat @ E @ D) => (ord_less_nat @ E @ C))) => ((B @ (insert_nat @ C @ D)) | ~ (B @ D))))) | ~ (B @ bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6966])). 159.59/70.60 thf(7308,axiom,((! [A:vEBT_VEBT,B:nat]: (((((((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((((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))))))) | (B = D) | (B = C)) <= (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G) @ B))) <= (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]: (((((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))) <= (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E) @ B))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E)))))) <= (! [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 = D) | (B = C)))))) <= (! [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))))) <= (! [C:$o,D:$o]: ((~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B))) <= (A = (vEBT_Leaf @ C @ D))))) <= (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ A @ B))) <= (~ (vEBT_VEBT_membermima @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3328_VEBT__internal_Omembermima_Opelims_I3_J)). 159.59/70.60 thf(33511,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((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))))))) | (B = D) | (B = C) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ E) @ F @ G) @ B)) | ~ (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]: ((((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))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E) @ B)) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E)))))) | ~ (! [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 = D) | (B = C))))) | ~ (! [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)))) | ~ (! [C:$o,D:$o]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) | ~ (A = (vEBT_Leaf @ C @ D)))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ A @ B)) | (vEBT_VEBT_membermima @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7308])). 159.59/70.60 thf(5531,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ B) @ (minus_minus_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5336_take__bit__int__less__eq)). 159.59/70.60 thf(26547,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ B) @ (minus_minus_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5531])). 159.59/70.60 thf(7676,axiom,((bit_se2002935070580805687sk_nat = (^ [A:nat]: (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6132_mask__nat__def)). 159.59/70.60 thf(34784,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)],[7676])). 159.59/70.60 thf(7580,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_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/sandbox/benchmark/theBenchmark.p',fact_1980_mult__le__0__iff)). 159.59/70.60 thf(34494,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_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)],[7580])). 159.59/70.60 thf(652,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/sandbox/benchmark/theBenchmark.p',fact_7166_cos__60)). 159.59/70.60 thf(10336,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)],[652])). 159.59/70.60 thf(4362,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/sandbox/benchmark/theBenchmark.p',fact_7006_ceiling__minus__divide__eq__div__numeral)). 159.59/70.60 thf(22223,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)],[4362])). 159.59/70.60 thf(7367,axiom,((! [A:real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2184_power__0)). 159.59/70.60 thf(33722,plain,((! [A:real]: ((power_power_real @ A @ zero_zero_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7367])). 159.59/70.60 thf(1828,axiom,((! [A:complex,B:complex]: (sums_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (if_complex @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (times_times_complex @ (real_V2046097035970521341omplex @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C)) @ (power_power_complex @ A @ D)) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_complex)) @ (set_ord_atMost_nat @ C))) @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9181_cos__x__cos__y)). 159.59/70.60 thf(14168,plain,((! [A:complex,B:complex]: (sums_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (if_complex @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (times_times_complex @ (real_V2046097035970521341omplex @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C)) @ (power_power_complex @ A @ D)) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_complex)) @ (set_ord_atMost_nat @ C))) @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1828])). 159.59/70.60 thf(1660,axiom,((! [A:nat,B:nat,C:(nat > real)]: (((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)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7671_sum_OSuc__reindex__ivl)). 159.59/70.60 thf(13628,plain,((! [A:nat,B:nat,C:(nat > real)]: (((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)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660])). 159.59/70.60 thf(3828,axiom,((! [A:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) = (A = zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1474_le__zero__eq)). 159.59/70.60 thf(20556,plain,((! [A:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) = (A = zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3828])). 159.59/70.60 thf(7879,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) <= ((vEBT_vebt_succ @ A @ C) = (some_nat @ D))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_helpyd)). 159.59/70.60 thf(35437,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ ((vEBT_vebt_succ @ A @ C) = (some_nat @ D)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7879])). 159.59/70.60 thf(5008,axiom,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2050_not__one__le__zero)). 159.59/70.60 thf(24581,plain,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5008])). 159.59/70.60 thf(5040,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/sandbox/benchmark/theBenchmark.p',fact_3680_prod__cases)). 159.59/70.60 thf(24686,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)],[5040])). 159.59/70.60 thf(2872,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6827_int__ops_I5_J)). 159.59/70.60 thf(17492,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)],[2872])). 159.59/70.60 thf(6869,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/sandbox/benchmark/theBenchmark.p',fact_5597_cong__exp__iff__simps_I13_J)). 159.59/70.60 thf(31761,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)],[6869])). 159.59/70.60 thf(2358,axiom,((! [A:extended_enat,B:(extended_enat > extended_enat),C:extended_enat,D:extended_enat]: (((ord_le72135733267957522d_enat @ C @ D) => ((ord_le72135733267957522d_enat @ A @ (B @ D)) <= (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) <= (ord_le72135733267957522d_enat @ E @ F))))) <= (ord_le72135733267957522d_enat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2888_order__less__subst1)). 159.59/70.60 thf(15823,plain,((! [A:extended_enat,B:(extended_enat > extended_enat),C:extended_enat,D:extended_enat]: (((ord_le72135733267957522d_enat @ C @ D) => ((ord_le72135733267957522d_enat @ A @ (B @ D)) | ~ (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))))) | ~ (ord_le72135733267957522d_enat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2358])). 159.59/70.60 thf(4227,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A)) <= (ord_less_real @ B @ zero_zero_real)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9065_le__imp__inverse__le__neg)). 159.59/70.60 thf(21824,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A)) | ~ (ord_less_real @ B @ zero_zero_real) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4227])). 159.59/70.60 thf(5735,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/sandbox/benchmark/theBenchmark.p',fact_5295_realpow__square__minus__le)). 159.59/70.60 thf(27244,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)],[5735])). 159.59/70.60 thf(2810,axiom,((! [A:nat]: ~ (bit_se1146084159140164899it_int @ one_one_int @ (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6381_not__bit__1__Suc)). 159.59/70.60 thf(17290,plain,((! [A:nat]: ~ (bit_se1146084159140164899it_int @ one_one_int @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2810])). 159.59/70.60 thf(5573,axiom,((! [A:num,B:num]: ((numera6620942414471956472nteger @ A) != (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4947_numeral__neq__neg__numeral)). 159.59/70.60 thf(26674,plain,((! [A:num,B:num]: ~ ((numera6620942414471956472nteger @ A) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5573])). 159.59/70.60 thf(7463,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/sandbox/benchmark/theBenchmark.p',fact_77_numeral__le__iff)). 159.59/70.60 thf(34039,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)],[7463])). 159.59/70.60 thf(7061,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((real_V4546457046886955230omplex @ (sqrt @ A)) = (csqrt @ (real_V4546457046886955230omplex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9381_of__real__sqrt)). 159.59/70.60 thf(32565,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)],[7061])). 159.59/70.60 thf(8124,axiom,(((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2458_zero__power2)). 159.59/70.60 thf(36226,plain,(((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8124])). 159.59/70.60 thf(6555,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_nat__le__linear)). 159.59/70.60 thf(30446,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6555])). 159.59/70.60 thf(7428,axiom,((! [A:real,B:real,C:real]: ((((minus_minus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (uminus_uminus_real @ C)) <= (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)) <= (A != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5255_add__divide__eq__if__simps_I6_J)). 159.59/70.60 thf(33912,plain,((! [A:real,B:real,C:real]: ((((minus_minus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (uminus_uminus_real @ C)) | ~ (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)) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7428])). 159.59/70.60 thf(5691,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => ((~ (! [D:nat]: (A != (plus_plus_nat @ C @ (times_times_nat @ B @ D))))) <= (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3545_mod__eq__nat1E)). 159.59/70.60 thf(27098,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => (~ (! [D:nat]: ~ (A = (plus_plus_nat @ C @ (times_times_nat @ B @ D)))) | ~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5691])). 159.59/70.60 thf(7966,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2789_antisym__conv3)). 159.59/70.60 thf(35713,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((~ (ord_less_nat @ B @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7966])). 159.59/70.60 thf(829,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1038_add__diff__cancel)). 159.59/70.60 thf(10923,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[829])). 159.59/70.60 thf(5956,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/sandbox/benchmark/theBenchmark.p',fact_5692_max__numeral__Suc)). 159.59/70.60 thf(28302,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)],[5956])). 159.59/70.60 thf(3148,axiom,((((=) @ code_integer) = (^ [A:code_integer,B:code_integer]: (((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))) & ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4210_bit__eq__rec)). 159.59/70.60 thf(18384,plain,((((=) @ code_integer) = (^ [A:code_integer,B:code_integer]: (((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))) & ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3148])). 159.59/70.60 thf(1740,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/sandbox/benchmark/theBenchmark.p',fact_7056_suminf__eq__zero__iff)). 159.59/70.60 thf(13874,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)],[1740])). 159.59/70.60 thf(3061,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ A) => (ord_less_eq_set_nat @ C @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2705_dual__order_Otrans)). 159.59/70.60 thf(18090,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ C @ A) => (ord_less_eq_set_nat @ C @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3061])). 159.59/70.60 thf(1769,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/sandbox/benchmark/theBenchmark.p',fact_6469_arsinh__real__aux)). 159.59/70.60 thf(13965,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)],[1769])). 159.59/70.60 thf(4898,axiom,((! [A:nat,B:$o,C:$o]: ((((((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ C)) <= (A != one_one_nat)) & (((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ ($true))) <= (A = one_one_nat))) <= (A != zero_zero_nat)) & ((A = zero_zero_nat) => ((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ ($true) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1824_vebt__insert_Osimps_I1_J)). 159.59/70.60 thf(24178,plain,((! [A:nat,B:$o,C:$o]: ((((((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ C)) | (A = one_one_nat)) & (((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ ($true))) | ~ (A = one_one_nat))) | (A = zero_zero_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)],[4898])). 159.59/70.60 thf(501,axiom,((! [A:code_integer]: (((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = A) => ((plus_p5714425477246183910nteger @ A @ (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))) = zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3558_bits__stable__imp__add__self)). 159.59/70.60 thf(9845,plain,((! [A:code_integer]: (((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = A) => ((plus_p5714425477246183910nteger @ A @ (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))) = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])). 159.59/70.60 thf(7284,axiom,((! [A:nat,B:nat,C:real]: ((((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)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2462_power__decreasing)). 159.59/70.60 thf(33421,plain,((! [A:nat,B:nat,C:real]: (((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) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7284])). 159.59/70.60 thf(3206,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/sandbox/benchmark/theBenchmark.p',fact_3511_mod__mult__div__eq)). 159.59/70.60 thf(18563,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)],[3206])). 159.59/70.60 thf(1431,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/sandbox/benchmark/theBenchmark.p',fact_6838_int__cases4)). 159.59/70.60 thf(12916,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)],[1431])). 159.59/70.60 thf(3527,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/sandbox/benchmark/theBenchmark.p',fact_9725_drop__bit__nonnegative__int__iff)). 159.59/70.60 thf(19575,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)],[3527])). 159.59/70.60 thf(1206,axiom,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: ((? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F))))) <= (? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => ((C @ F) = (D @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4458_minf_I1_J)). 159.59/70.60 thf(12141,plain,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: ((? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => ((A @ F) = (B @ F)))) => (? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F)))) | ~ (? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => ((C @ F) = (D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206])). 159.59/70.60 thf(5941,axiom,((! [A:(nat > (nat > $o)),B:set_nat,C:(nat > nat),D:(nat > nat)]: ((A @ zero_zero_nat @ zero_zero_nat) => ((((A @ (groups3542108847815614940at_nat @ C @ B) @ (groups3542108847815614940at_nat @ D @ B)) <= (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E))))) <= (finite_finite_nat @ B)) <= (! [E:nat,F:nat,G:nat,H:nat]: (((A @ F @ H) & (A @ E @ G)) => (A @ (plus_plus_nat @ E @ F) @ (plus_plus_nat @ G @ H)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7490_sum_Orelated)). 159.59/70.60 thf(28231,plain,((! [A:(nat > (nat > $o)),B:set_nat,C:(nat > nat),D:(nat > nat)]: ((A @ zero_zero_nat @ zero_zero_nat) => ((A @ (groups3542108847815614940at_nat @ (C) @ B) @ (groups3542108847815614940at_nat @ (D) @ B)) | ~ (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) | ~ (finite_finite_nat @ B) | ~ (! [E:nat,F:nat,G:nat,H:nat]: (((A @ F @ H) & (A @ E @ G)) => (A @ (plus_plus_nat @ E @ F) @ (plus_plus_nat @ G @ H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5941])). 159.59/70.60 thf(556,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/sandbox/benchmark/theBenchmark.p',fact_8911_sum__atLeastAtMost__code)). 159.59/70.60 thf(10022,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)],[556])). 159.59/70.60 thf(2667,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ A @ B) => (ord_less_real @ (cosh_real @ A) @ (cosh_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9342_cosh__real__strict__mono)). 159.59/70.60 thf(16849,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ A @ B) => (ord_less_real @ (cosh_real @ A) @ (cosh_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2667])). 159.59/70.60 thf(5616,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/sandbox/benchmark/theBenchmark.p',fact_7662_sum_Onat__ivl__Suc_H)). 159.59/70.60 thf(26833,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)],[5616])). 159.59/70.60 thf(1029,axiom,((! [A:$o,B:$o]: ((ord_le3102999989581377725nteger @ (zero_n356916108424825756nteger @ A) @ (zero_n356916108424825756nteger @ B)) = ((A) => (B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4314_of__bool__less__eq__iff)). 159.59/70.60 thf(11542,plain,((! [A:$o,B:$o]: ((ord_le3102999989581377725nteger @ (zero_n356916108424825756nteger @ A) @ (zero_n356916108424825756nteger @ B)) = ((A) => (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029])). 159.59/70.60 thf(4267,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/sandbox/benchmark/theBenchmark.p',fact_6859_sin__45)). 159.59/70.60 thf(21948,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)],[4267])). 159.59/70.60 thf(3520,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/sandbox/benchmark/theBenchmark.p',fact_4041_subset__divisors__dvd)). 159.59/70.60 thf(19553,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)],[3520])). 159.59/70.60 thf(7538,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) | (B = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1488_mult__eq__0__iff)). 159.59/70.60 thf(34303,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)],[7538])). 159.59/70.60 thf(7633,axiom,((! [A:nat,B:list_VEBT_VEBT,C:list_o]: (((nth_Pr4606735188037164562VEBT_o @ (product_VEBT_VEBT_o @ B @ C) @ A) = (produc8721562602347293563VEBT_o @ (nth_VEBT_VEBT @ B @ (divide_divide_nat @ A @ (size_size_list_o @ C))) @ (nth_o @ C @ (modulo_modulo_nat @ A @ (size_size_list_o @ C))))) <= (ord_less_nat @ A @ (times_times_nat @ (size_s6755466524823107622T_VEBT @ B) @ (size_size_list_o @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3590_product__nth)). 159.59/70.60 thf(34653,plain,((! [A:nat,B:list_VEBT_VEBT,C:list_o]: (((nth_Pr4606735188037164562VEBT_o @ (product_VEBT_VEBT_o @ B @ C) @ A) = (produc8721562602347293563VEBT_o @ (nth_VEBT_VEBT @ B @ (divide_divide_nat @ A @ (size_size_list_o @ C))) @ (nth_o @ C @ (modulo_modulo_nat @ A @ (size_size_list_o @ C))))) | ~ (ord_less_nat @ A @ (times_times_nat @ (size_s6755466524823107622T_VEBT @ B) @ (size_size_list_o @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7633])). 159.59/70.60 thf(7572,axiom,(((vEBT_vebt_buildup @ (suc @ zero_zero_nat)) = (vEBT_Leaf @ ($false) @ ($false)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3003_vebt__buildup_Osimps_I2_J)). 159.59/70.60 thf(34467,plain,(((vEBT_vebt_buildup @ (suc @ zero_zero_nat)) = (vEBT_Leaf @ ($false) @ ($false)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7572])). 159.59/70.60 thf(1771,axiom,((! [A:int,B:real]: (((archim6058952711729229775r_real @ (divide_divide_real @ B @ (ring_1_of_int_real @ A))) = (divide_divide_int @ (archim6058952711729229775r_real @ B) @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8309_floor__divide__real__eq__div)). 159.59/70.60 thf(13970,plain,((! [A:int,B:real]: (((archim6058952711729229775r_real @ (divide_divide_real @ B @ (ring_1_of_int_real @ A))) = (divide_divide_int @ (archim6058952711729229775r_real @ B) @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771])). 159.59/70.60 thf(727,axiom,((! [A:nat,B:int]: ((ord_less_nat @ zero_zero_nat @ A) => (((divide_divide_int @ (power_power_int @ B @ A) @ B) = (power_power_int @ B @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)))) <= (ord_less_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3019_int__power__div__base)). 159.59/70.60 thf(10599,plain,((! [A:nat,B:int]: ((ord_less_nat @ zero_zero_nat @ A) => (((divide_divide_int @ (power_power_int @ B @ A) @ B) = (power_power_int @ B @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)))) | ~ (ord_less_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[727])). 159.59/70.60 thf(7797,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4236_odd__pos)). 159.59/70.60 thf(35175,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7797])). 159.59/70.60 thf(2938,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (? [D:real]: (! [E:real]: ((ord_less_real @ (abs_abs_real @ (minus_minus_real @ B @ E)) @ D) => ((ord_less_real @ A @ E) & (ord_less_real @ E @ C))) & (ord_less_real @ zero_zero_real @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5603_lemma__interval__lt)). 159.59/70.60 thf(17710,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (? [D:real]: (! [E:real]: ((ord_less_real @ (abs_abs_real @ (minus_minus_real @ B @ E)) @ D) => ((ord_less_real @ A @ E) & (ord_less_real @ E @ C))) & (ord_less_real @ zero_zero_real @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2938])). 159.59/70.60 thf(3882,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (modulo_modulo_nat @ A @ B)) = (modulo_modulo_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6704_of__nat__mod)). 159.59/70.60 thf(20752,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)],[3882])). 159.59/70.60 thf(5730,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/sandbox/benchmark/theBenchmark.p',fact_5810_of__int__le__0__iff)). 159.59/70.60 thf(27230,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)],[5730])). 159.59/70.60 thf(4105,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ A @ C) <= (ord_less_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2814_order_Ostrict__trans)). 159.59/70.60 thf(21422,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ A @ C) | ~ (ord_less_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4105])). 159.59/70.60 thf(7211,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_Nat_Ole__imp__diff__is__add)). 159.59/70.60 thf(33177,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7211])). 159.59/70.60 thf(6650,axiom,((! [A:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4700_mult__minus1)). 159.59/70.60 thf(30785,plain,((! [A:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6650])). 159.59/70.60 thf(7985,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/sandbox/benchmark/theBenchmark.p',fact_5312_minus__power__mult__self)). 159.59/70.60 thf(35767,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)],[7985])). 159.59/70.60 thf(3274,axiom,(((arctan @ one_one_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6777_arctan__one)). 159.59/70.60 thf(18793,plain,(((arctan @ one_one_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3274])). 159.59/70.60 thf(2603,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/sandbox/benchmark/theBenchmark.p',fact_1735_less__divide__eq__1__pos)). 159.59/70.60 thf(16623,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)],[2603])). 159.59/70.60 thf(2324,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/sandbox/benchmark/theBenchmark.p',fact_3535_minus__mod__eq__mult__div)). 159.59/70.60 thf(15723,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)],[2324])). 159.59/70.60 thf(3174,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/sandbox/benchmark/theBenchmark.p',fact_7049_suminf__divide)). 159.59/70.60 thf(18463,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)],[3174])). 159.59/70.60 thf(1036,axiom,((! [A:set_nat,B:set_nat]: (((A = B) <= (ord_less_eq_set_nat @ B @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2612_subset__antisym)). 159.59/70.60 thf(11568,plain,((! [A:set_nat,B:set_nat]: ((A = B) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036])). 159.59/70.60 thf(4251,axiom,((! [A:real]: ~ (ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2103_not__square__less__zero)). 159.59/70.60 thf(21896,plain,((! [A:real]: ~ (ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4251])). 159.59/70.60 thf(6743,axiom,((! [A:num,B:num]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4815_mult__neg__numeral__simps_I3_J)). 159.59/70.60 thf(31239,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)],[6743])). 159.59/70.60 thf(5055,axiom,((! [A:int,B:(num > int),C:num,D:num]: ((ord_less_eq_int @ A @ (B @ C)) => (((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))) => (ord_less_eq_int @ A @ (B @ D))) <= (ord_less_eq_num @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2690_order__subst1)). 159.59/70.60 thf(24755,plain,((! [A:int,B:(num > int),C:num,D:num]: ((ord_less_eq_int @ A @ (B @ C)) => (((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))) => (ord_less_eq_int @ A @ (B @ D))) | ~ (ord_less_eq_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5055])). 159.59/70.60 thf(6689,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_le__Suc__ex)). 159.59/70.60 thf(30972,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6689])). 159.59/70.60 thf(7266,axiom,((! [A:num]: ~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5143_not__zero__le__neg__numeral)). 159.59/70.60 thf(33367,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)],[7266])). 159.59/70.60 thf(6260,axiom,((! [A:num,B:(num > num),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F))))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2656_ord__eq__le__subst)). 159.59/70.60 thf(29324,plain,((! [A:num,B:(num > num),C:num,D:num]: (((ord_less_eq_num @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6260])). 159.59/70.60 thf(2740,axiom,((! [A:$o]: (((zero_n2684676970156552555ol_int @ A) = one_one_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4330_of__bool__eq__1__iff)). 159.59/70.60 thf(17081,plain,((! [A:$o]: (((zero_n2684676970156552555ol_int @ A) = one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2740])). 159.59/70.60 thf(182,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/sandbox/benchmark/theBenchmark.p',fact_9642_csqrt_Osimps_I2_J)). 159.59/70.60 thf(8816,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)],[182])). 159.59/70.60 thf(4493,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less_nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_Suc__less__eq2)). 159.59/70.60 thf(22704,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)],[4493])). 159.59/70.60 thf(4893,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/sandbox/benchmark/theBenchmark.p',fact_3446_mod__mult__mult2)). 159.59/70.60 thf(24163,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)],[4893])). 159.59/70.60 thf(106,axiom,((filterlim_real_real @ arctan @ (topolo2815343760600316023s_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ at_top_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9963_tendsto__arctan__at__top)). 159.59/70.60 thf(8578,plain,((filterlim_real_real @ (arctan) @ (topolo2815343760600316023s_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ at_top_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[106])). 159.59/70.60 thf(3131,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ A) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_add__diff__cancel__left_H)). 159.59/70.60 thf(18321,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3131])). 159.59/70.60 thf(3046,axiom,((! [A:real,B:int]: (((archim7802044766580827645g_real @ A) = B) = ((ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ B) @ one_one_real) @ A) & (ord_less_eq_real @ A @ (ring_1_of_int_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7138_ceiling__eq__iff)). 159.59/70.60 thf(18040,plain,((! [A:real,B:int]: (((archim7802044766580827645g_real @ A) = B) = ((ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ B) @ one_one_real) @ A) & (ord_less_eq_real @ A @ (ring_1_of_int_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3046])). 159.59/70.60 thf(1049,axiom,((! [A:$o]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (zero_n356916108424825756nteger @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4371_odd__of__bool__self)). 159.59/70.60 thf(11613,plain,((! [A:$o]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (zero_n356916108424825756nteger @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049])). 159.59/70.60 thf(5170,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/sandbox/benchmark/theBenchmark.p',fact_6615_of__nat__le__of__nat__power__cancel__iff)). 159.59/70.60 thf(25150,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)],[5170])). 159.59/70.60 thf(1382,axiom,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ one_one_Code_integer) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4269_even__mask__div__iff_H)). 159.59/70.60 thf(12763,plain,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ one_one_Code_integer) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382])). 159.59/70.60 thf(6205,axiom,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_mult__numeral__1__right)). 159.59/70.60 thf(29108,plain,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6205])). 159.59/70.60 thf(472,axiom,((! [A:set_nat,B:(set_nat > $o)]: (((B @ bot_bot_set_nat) => ((! [C:set_nat]: ((finite_finite_nat @ C) => ((C != bot_bot_set_nat) => (((! [D:nat]: ((member_nat @ D @ C) => (B @ (minus_minus_set_nat @ C @ (insert_nat @ D @ bot_bot_set_nat))))) => (B @ C)) <= (ord_less_eq_set_nat @ C @ A))))) => (B @ A))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6275_finite__remove__induct)). 159.59/70.60 thf(9735,plain,((! [A:set_nat,B:(set_nat > $o)]: (((B @ bot_bot_set_nat) => ((! [C:set_nat]: ((finite_finite_nat @ C) => ((~ (C = bot_bot_set_nat)) => (((! [D:nat]: ((member_nat @ D @ C) => (B @ (minus_minus_set_nat @ C @ (insert_nat @ D @ bot_bot_set_nat))))) => (B @ C)) | ~ (ord_less_eq_set_nat @ C @ A))))) => (B @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])). 159.59/70.60 thf(5884,axiom,((! [A:option4927543243414619207at_nat]: ((~ (! [B:product_prod_nat_nat]: (A != (some_P7363390416028606310at_nat @ B)))) <= (A != none_P5556105721700978146at_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_option_Oexhaust)). 159.59/70.60 thf(28001,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)],[5884])). 159.59/70.60 thf(3346,axiom,((! [A:num]: ((plus_plus_complex @ one_one_complex @ (numera6690914467698888265omplex @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_one__plus__numeral__commute)). 159.59/70.60 thf(19012,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)],[3346])). 159.59/70.60 thf(6905,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 @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1963_zero__le__mult__iff)). 159.59/70.60 thf(31872,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 @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6905])). 159.59/70.60 thf(5902,axiom,((! [A:$o]: (ord_less_eq_nat @ (zero_n2687167440665602831ol_nat @ A) @ one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4395_of__bool__less__eq__one)). 159.59/70.60 thf(28054,plain,((! [A:$o]: (ord_less_eq_nat @ (zero_n2687167440665602831ol_nat @ A) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5902])). 159.59/70.60 thf(7339,axiom,((! [A:nat,B:nat]: (((binomial @ B @ A) = (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9118_binomial__altdef__nat)). 159.59/70.60 thf(33631,plain,((! [A:nat,B:nat]: (((binomial @ B @ A) = (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7339])). 159.59/70.60 thf(5477,axiom,((! [A:nat,B:list_int,C:nat,D:int]: (((((nth_int @ (list_update_int @ B @ A @ D) @ C) = (nth_int @ B @ C)) <= (A != C)) & ((A = C) => ((nth_int @ (list_update_int @ B @ A @ D) @ C) = D))) <= (ord_less_nat @ A @ (size_size_list_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_nth__list__update)). 159.59/70.60 thf(26361,plain,((! [A:nat,B:list_int,C:nat,D:int]: (((((nth_int @ (list_update_int @ B @ A @ D) @ C) = (nth_int @ B @ C)) | (A = C)) & ((A = C) => ((nth_int @ (list_update_int @ B @ A @ D) @ C) = D))) | ~ (ord_less_nat @ A @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5477])). 159.59/70.60 thf(5391,axiom,((! [A:$o,B:$o]: ((zero_n2687167440665602831ol_nat @ ((A) | (B))) = (ord_max_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4337_of__bool__or__iff)). 159.59/70.60 thf(26024,plain,((! [A:$o,B:$o]: ((zero_n2687167440665602831ol_nat @ ((A) | (B))) = (ord_max_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5391])). 159.59/70.60 thf(3125,axiom,((! [A:real,B:real]: (((plus_plus_real @ (minus_minus_real @ B @ A) @ A) = B) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1026_le__add__diff__inverse2)). 159.59/70.60 thf(18304,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)],[3125])). 159.59/70.60 thf(255,axiom,((! [A:nat]: ((A != one_one_nat) => ((groups7501900531339628137nteger @ (^ [B:nat]: (times_3573771949741848930nteger @ (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (semiri4939895301339042750nteger @ B)) @ (semiri4939895301339042750nteger @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9166_choose__alternating__linear__sum)). 159.59/70.60 thf(9027,plain,((! [A:nat]: ((~ (A = one_one_nat)) => ((groups7501900531339628137nteger @ (^ [B:nat]: (times_3573771949741848930nteger @ (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (semiri4939895301339042750nteger @ B)) @ (semiri4939895301339042750nteger @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 159.59/70.60 thf(1253,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ A @ (modulo_modulo_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3648_neg__mod__bound)). 159.59/70.60 thf(12303,plain,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_int @ A @ (modulo_modulo_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253])). 159.59/70.60 thf(362,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/sandbox/benchmark/theBenchmark.p',fact_9604_and__not__numerals_I7_J)). 159.59/70.60 thf(9379,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)],[362])). 159.59/70.60 thf(1380,axiom,((! [A:int]: (((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = A) <= (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4226_even__two__times__div__two)). 159.59/70.60 thf(12757,plain,((! [A:int]: (((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) = A) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380])). 159.59/70.60 thf(3574,axiom,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2695_Orderings_Oorder__eq__iff)). 159.59/70.60 thf(19732,plain,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) & (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3574])). 159.59/70.60 thf(279,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ (real_V1485227260804924795R_real @ A @ C)) = (ord_less_eq_real @ B @ C)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9227_scaleR__le__cancel__left__pos)). 159.59/70.60 thf(9096,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ (real_V1485227260804924795R_real @ A @ C)) = (ord_less_eq_real @ B @ C)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 159.59/70.60 thf(574,axiom,((! [A:complex]: ((plus_plus_complex @ (sinh_complex @ A) @ (cosh_complex @ A)) = (exp_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9321_sinh__plus__cosh)). 159.59/70.60 thf(10078,plain,((! [A:complex]: ((plus_plus_complex @ (sinh_complex @ A) @ (cosh_complex @ A)) = (exp_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[574])). 159.59/70.60 thf(3339,axiom,((ord_less_real @ zero_zero_real @ pi)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6701_pi__gt__zero)). 159.59/70.60 thf(18992,plain,((ord_less_real @ zero_zero_real @ pi)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3339])). 159.59/70.60 thf(7054,axiom,((! [A:$o,B:$o]: ((ord_less_eq_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B)) = ((B) <= (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4312_of__bool__less__eq__iff)). 159.59/70.60 thf(32533,plain,((! [A:$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)],[7054])). 159.59/70.60 thf(547,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = ((A = zero_z3403309356797280102nteger) | (dvd_dvd_Code_integer @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3810_dvd__mult__cancel__left)). 159.59/70.60 thf(9994,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = ((A = zero_z3403309356797280102nteger) | (dvd_dvd_Code_integer @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[547])). 159.59/70.60 thf(6138,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/sandbox/benchmark/theBenchmark.p',fact_1098_mult_Oleft__commute)). 159.59/70.60 thf(28879,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)],[6138])). 159.59/70.60 thf(1360,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/sandbox/benchmark/theBenchmark.p',fact_5910_int__less__real__le)). 159.59/70.60 thf(12646,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)],[1360])). 159.59/70.60 thf(7136,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ A) @ B) = (times_times_complex @ A @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4954_minus__mult__commute)). 159.59/70.60 thf(32898,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)],[7136])). 159.59/70.60 thf(6889,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/sandbox/benchmark/theBenchmark.p',fact_8442_sum_OatMost__Suc)). 159.59/70.60 thf(31821,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)],[6889])). 159.59/70.60 thf(3366,axiom,((! [A:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ zero_zero_int) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4675_neg__less__0__iff__less)). 159.59/70.60 thf(19069,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)],[3366])). 159.59/70.60 thf(4325,axiom,((! [A:num]: ((neg_nu7009210354673126013omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu7009210354673126013omplex @ (numera6690914467698888265omplex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4735_dbl__simps_I1_J)). 159.59/70.60 thf(22115,plain,((! [A:num]: ((neg_nu7009210354673126013omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu7009210354673126013omplex @ (numera6690914467698888265omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4325])). 159.59/70.60 thf(3691,axiom,((! [A:(nat > int),B:nat,C:nat]: ((groups705719431365010083at_int @ A @ (set_or1269000886237332187st_nat @ (suc @ B) @ (suc @ C))) = (groups705719431365010083at_int @ (^ [D:nat]: (A @ (suc @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8541_prod_Oshift__bounds__cl__Suc__ivl)). 159.59/70.60 thf(20107,plain,((! [A:(nat > int),B:nat,C:nat]: ((groups705719431365010083at_int @ (A) @ (set_or1269000886237332187st_nat @ (suc @ B) @ (suc @ C))) = (groups705719431365010083at_int @ (^ [D:nat]: (A @ (suc @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3691])). 159.59/70.60 thf(6797,axiom,((! [A:int]: ((times_times_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_mult__2__right)). 159.59/70.60 thf(31436,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)],[6797])). 159.59/70.60 thf(1042,axiom,((! [A:extended_enat,B:(real > extended_enat),C:real,D:real]: ((A = (B @ C)) => (((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) <= (ord_less_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2868_ord__eq__less__subst)). 159.59/70.60 thf(11588,plain,((! [A:extended_enat,B:(real > extended_enat),C:real,D:real]: ((A = (B @ C)) => (((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) | ~ (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042])). 159.59/70.60 thf(7208,axiom,((! [A:num]: ((numeral_numeral_int @ A) != (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5087_numeral__neq__neg__one)). 159.59/70.60 thf(33167,plain,((! [A:num]: ~ ((numeral_numeral_int @ A) = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7208])). 159.59/70.60 thf(3904,axiom,((! [A:int,B:int,C:int]: (((times_times_int @ C @ (divide_divide_int @ B @ A)) = (divide_divide_int @ (times_times_int @ C @ B) @ A)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4076_div__mult__swap)). 159.59/70.60 thf(20818,plain,((! [A:int,B:int,C:int]: (((times_times_int @ C @ (divide_divide_int @ B @ A)) = (divide_divide_int @ (times_times_int @ C @ B) @ A)) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3904])). 159.59/70.60 thf(5397,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/sandbox/benchmark/theBenchmark.p',fact_276_L2__set__mult__ineq__lemma)). 159.59/70.60 thf(26057,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)],[5397])). 159.59/70.60 thf(1445,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => ((dvd_dvd_complex @ A @ (plus_plus_complex @ C @ B)) = (dvd_dvd_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3985_dvd__add__left__iff)). 159.59/70.60 thf(12960,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => ((dvd_dvd_complex @ A @ (plus_plus_complex @ C @ B)) = (dvd_dvd_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1445])). 159.59/70.60 thf(6134,axiom,((! [A:int,B:nat,C:nat]: ((((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)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1772_power__strict__decreasing__iff)). 159.59/70.60 thf(28862,plain,((! [A:int,B:nat,C:nat]: (((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) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6134])). 159.59/70.60 thf(860,axiom,((! [A:real]: (ord_less_eq_real @ (plus_plus_real @ one_one_real @ A) @ (exp_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6088_exp__ge__add__one__self)). 159.59/70.60 thf(11024,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)],[860])). 159.59/70.60 thf(3327,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/sandbox/benchmark/theBenchmark.p',fact_2968_subset__iff)). 159.59/70.60 thf(18955,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)],[3327])). 159.59/70.60 thf(1126,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4227_even__two__times__div__two)). 159.59/70.60 thf(11863,plain,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126])). 159.59/70.60 thf(6120,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (ord_max_nat @ A @ C) @ B) <= (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_max_OboundedI)). 159.59/70.60 thf(28818,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (ord_max_nat @ A @ C) @ B) | ~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6120])). 159.59/70.60 thf(3322,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/sandbox/benchmark/theBenchmark.p',fact_3782_concat__bit__Suc)). 159.59/70.60 thf(18938,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)],[3322])). 159.59/70.60 thf(5393,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/sandbox/benchmark/theBenchmark.p',fact_6622_numeral__le__real__of__nat__iff)). 159.59/70.60 thf(26040,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)],[5393])). 159.59/70.60 thf(1238,axiom,((! [A:(real > $o),B:real]: ((! [C:real,D:real]: ((ord_less_real @ C @ D) => ((A @ D) <= (A @ C)))) => (((A @ B) <= (ord_less_real @ zero_zero_real @ B)) <= (! [C:nat]: (A @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ (suc @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9096_forall__pos__mono__1)). 159.59/70.60 thf(12257,plain,((! [A:(real > $o),B:real]: ((! [C:real,D:real]: ((ord_less_real @ C @ D) => ((A @ D) | ~ (A @ C)))) => ((A @ B) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (! [C:nat]: (A @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ (suc @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238])). 159.59/70.60 thf(7430,axiom,((! [A:nat]: ((groups708209901874060359at_nat @ suc @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) = (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9601_prod__Suc__fact)). 159.59/70.60 thf(33922,plain,((! [A:nat]: ((groups708209901874060359at_nat @ (suc) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)) = (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7430])). 159.59/70.60 thf(1934,axiom,((! [A:(extended_enat > $o),B:(extended_enat > $o),C:(extended_enat > $o),D:(extended_enat > $o)]: ((? [E:extended_enat]: ! [F:extended_enat]: (((A @ F) = (B @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => ((? [E:extended_enat]: ! [F:extended_enat]: (((C @ F) = (D @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => (? [E:extended_enat]: ! [F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4432_pinf_I2_J)). 159.59/70.60 thf(14488,plain,((! [A:(extended_enat > $o),B:(extended_enat > $o),C:(extended_enat > $o),D:(extended_enat > $o)]: ((? [E:extended_enat]: ! [F:extended_enat]: (((A @ F) = (B @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => ((? [E:extended_enat]: ! [F:extended_enat]: (((C @ F) = (D @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => (? [E:extended_enat]: ! [F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1934])). 159.59/70.60 thf(6320,axiom,((! [A:num]: (ord_less_eq_num @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3664_verit__comp__simplify1_I2_J)). 159.59/70.60 thf(29557,plain,((! [A:num]: (ord_less_eq_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6320])). 159.59/70.60 thf(2729,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/sandbox/benchmark/theBenchmark.p',fact_6922_norm__power__ineq)). 159.59/70.60 thf(17053,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)],[2729])). 159.59/70.60 thf(6372,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (suc @ (numeral_numeral_nat @ (bitM @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5894_eval__nat__numeral_I2_J)). 159.59/70.60 thf(29708,plain,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (suc @ (numeral_numeral_nat @ (bitM @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6372])). 159.59/70.60 thf(7772,axiom,((~ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_False)). 159.59/70.60 thf(35108,plain,((~ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7772])). 159.59/70.60 thf(2491,axiom,((! [A:num,B:extended_enat,C:extended_enat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ (plus_p3455044024723400733d_enat @ B @ C)) = (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ B) @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_distrib__left__numeral)). 159.59/70.60 thf(16268,plain,((! [A:num,B:extended_enat,C:extended_enat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ (plus_p3455044024723400733d_enat @ B @ C)) = (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ B) @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2491])). 159.59/70.60 thf(7972,axiom,((ord_less_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__092_060open_062summin_A_060_A2_A_094_Am_092_060close_062)). 159.59/70.60 thf(35730,plain,((ord_less_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7972])). 159.59/70.60 thf(5140,axiom,((! [A:nat,B:nat,C:nat]: ((((A = C) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ A)) <= ((power_power_nat @ A @ (suc @ B)) = (power_power_nat @ C @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2358_power__inject__base)). 159.59/70.60 thf(25035,plain,((! [A:nat,B:nat,C:nat]: ((A = C) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ A) | ~ ((power_power_nat @ A @ (suc @ B)) = (power_power_nat @ C @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5140])). 159.59/70.60 thf(6498,axiom,((! [A:nat]: ((set_ord_atMost_nat @ (suc @ A)) = (insert_nat @ zero_zero_nat @ (image_nat_nat @ suc @ (set_ord_atMost_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9812_atMost__Suc__eq__insert__0)). 159.59/70.60 thf(30241,plain,((! [A:nat]: ((set_ord_atMost_nat @ (suc @ A)) = (insert_nat @ zero_zero_nat @ (image_nat_nat @ (suc) @ (set_ord_atMost_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6498])). 159.59/70.60 thf(5255,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((ord_less_eq_nat @ D @ C) <= (vEBT_vebt_member @ A @ D)) <= ((vEBT_vebt_maxt @ A) = (some_nat @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_maxt__corr__help)). 159.59/70.60 thf(25457,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_eq_nat @ D @ C) | ~ (vEBT_vebt_member @ A @ D) | ~ ((vEBT_vebt_maxt @ A) = (some_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5255])). 159.59/70.60 thf(6513,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/sandbox/benchmark/theBenchmark.p',fact_3537_minus__mod__eq__div__mult)). 159.59/70.60 thf(30286,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)],[6513])). 159.59/70.60 thf(540,axiom,((! [A:int,B:nat,C:nat]: ((comm_s4660882817536571857er_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (comm_s4660882817536571857er_int @ A @ B) @ (comm_s4660882817536571857er_int @ (plus_plus_int @ A @ (semiri1314217659103216013at_int @ B)) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8293_pochhammer__product_H)). 159.59/70.60 thf(9971,plain,((! [A:int,B:nat,C:nat]: ((comm_s4660882817536571857er_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (comm_s4660882817536571857er_int @ A @ B) @ (comm_s4660882817536571857er_int @ (plus_plus_int @ A @ (semiri1314217659103216013at_int @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[540])). 159.59/70.60 thf(1701,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/sandbox/benchmark/theBenchmark.p',fact_8342_pochhammer__minus_H)). 159.59/70.60 thf(13751,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)],[1701])). 159.59/70.60 thf(2575,axiom,((! [A:(nat > real)]: (summable_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7067_summable__zero__power_H)). 159.59/70.60 thf(16530,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)],[2575])). 159.59/70.60 thf(1280,axiom,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ one_one_Code_integer) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1037_div__by__1)). 159.59/70.60 thf(12388,plain,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ one_one_Code_integer) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280])). 159.59/70.60 thf(388,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ A) @ (times_3573771949741848930nteger @ C @ A)) = (divide6298287555418463151nteger @ B @ C)) <= (A != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1641_div__mult__mult2)). 159.59/70.60 thf(9465,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ A) @ (times_3573771949741848930nteger @ C @ A)) = (divide6298287555418463151nteger @ B @ C)) | (A = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])). 159.59/70.60 thf(3108,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ A) => (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2710_dual__order_Oantisym)). 159.59/70.60 thf(18252,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ A) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3108])). 159.59/70.60 thf(2312,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/sandbox/benchmark/theBenchmark.p',fact_1348_le__diff__eq)). 159.59/70.60 thf(15688,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)],[2312])). 159.59/70.60 thf(2556,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/sandbox/benchmark/theBenchmark.p',fact_2089_mult__pos__neg2)). 159.59/70.60 thf(16469,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)],[2556])). 159.59/70.60 thf(2744,axiom,((! [A:real,B:real]: (sums_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (if_real @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (times_times_real @ (real_V1485227260804924795R_real @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C)) @ (power_power_real @ A @ D)) @ (power_power_real @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_real)) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ (cos_real @ A) @ (cos_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9180_cos__x__cos__y)). 159.59/70.60 thf(17100,plain,((! [A:real,B:real]: (sums_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (if_real @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (times_times_real @ (real_V1485227260804924795R_real @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C)) @ (power_power_real @ A @ D)) @ (power_power_real @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_real)) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ (cos_real @ A) @ (cos_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2744])). 159.59/70.60 thf(2532,axiom,((! [A:real]: (((ord_less_eq_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) => (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 @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6143_real__exp__bound__lemma)). 159.59/70.60 thf(16398,plain,((! [A:real]: (((ord_less_eq_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) => (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 @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2532])). 159.59/70.60 thf(6908,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/sandbox/benchmark/theBenchmark.p',fact_6602_real__of__nat__eq__numeral__power__cancel__iff)). 159.59/70.60 thf(31882,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)],[6908])). 159.59/70.60 thf(8208,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 @ C @ D) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1320_add__mono__thms__linordered__field_I4_J)). 159.59/70.60 thf(36505,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 @ C @ D) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8208])). 159.59/70.60 thf(5229,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/sandbox/benchmark/theBenchmark.p',fact_9531_log__base__root)). 159.59/70.60 thf(25374,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)],[5229])). 159.59/70.60 thf(3849,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/sandbox/benchmark/theBenchmark.p',fact_1640_div__mult__mult2)). 159.59/70.60 thf(20643,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)],[3849])). 159.59/70.60 thf(3780,axiom,((log = (^ [A:real,B:real]: (divide_divide_real @ (ln_ln_real @ B) @ (ln_ln_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6398_log__def)). 159.59/70.60 thf(20409,plain,(((log) = (^ [A:real,B:real]: (divide_divide_real @ (ln_ln_real @ B) @ (ln_ln_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3780])). 159.59/70.60 thf(4699,axiom,((! [A:nat]: (((root @ A @ one_one_real) = one_one_real) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9484_real__root__one)). 159.59/70.60 thf(23500,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)],[4699])). 159.59/70.60 thf(4032,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/sandbox/benchmark/theBenchmark.p',fact_4960_add_Oinverse__distrib__swap)). 159.59/70.60 thf(21203,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)],[4032])). 159.59/70.60 thf(3071,axiom,((! [A:nat,B:int]: ((bit_concat_bit @ A @ zero_zero_int @ B) = (bit_se545348938243370406it_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9549_concat__bit__of__zero__1)). 159.59/70.60 thf(18120,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)],[3071])). 159.59/70.60 thf(6198,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ (modulo_modulo_nat @ A @ B) @ B) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3409_bits__mod__div__trivial)). 159.59/70.60 thf(29086,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)],[6198])). 159.59/70.60 thf(368,axiom,((! [A:code_integer,B:code_integer]: ((if_Code_integer @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Code____Numeral__Ointeger_T)). 159.59/70.60 thf(9396,plain,((! [A:code_integer,B:code_integer]: ((if_Code_integer @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])). 159.59/70.60 thf(6070,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5404_abs__le__zero__iff)). 159.59/70.60 thf(28659,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6070])). 159.59/70.60 thf(6915,axiom,((! [A:$o,B:$o]: ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = none_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1825_vebt__pred_Osimps_I1_J)). 159.59/70.60 thf(31907,plain,((! [A:$o,B:$o]: ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6915])). 159.59/70.60 thf(3466,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1310_add__less__le__mono)). 159.59/70.60 thf(19387,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3466])). 159.59/70.60 thf(140,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/sandbox/benchmark/theBenchmark.p',fact_9659_times__complex_Osimps_I1_J)). 159.59/70.60 thf(8678,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)],[140])). 159.59/70.60 thf(4441,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/sandbox/benchmark/theBenchmark.p',fact_7098_suminf__split__head)). 159.59/70.60 thf(22476,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)],[4441])). 159.59/70.60 thf(4408,axiom,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (bit_se725231765392027082nd_int @ B @ C)) = (bit_se725231765392027082nd_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5958_take__bit__and)). 159.59/70.60 thf(22370,plain,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (bit_se725231765392027082nd_int @ B @ C)) = (bit_se725231765392027082nd_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4408])). 159.59/70.60 thf(5803,axiom,(((neg_numeral_dbl_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3784_dbl__simps_I3_J)). 159.59/70.60 thf(27592,plain,(((neg_numeral_dbl_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5803])). 159.59/70.60 thf(25,axiom,((sinh_real = (^ [A:real]: (divide_divide_real @ (minus_minus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9360_sinh__field__def)). 159.59/70.60 thf(8330,plain,(((sinh_real) = (^ [A:real]: (divide_divide_real @ (minus_minus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 159.59/70.60 thf(4440,axiom,((vEBT_set_vebt = (^ [A:vEBT_VEBT]: (collect_nat @ (vEBT_V8194947554948674370ptions @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1423_set__vebt__def)). 159.59/70.60 thf(22474,plain,(((vEBT_set_vebt) = (^ [A:vEBT_VEBT]: (collect_nat @ (vEBT_V8194947554948674370ptions @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4440])). 159.59/70.60 thf(148,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C))) = (ord_less_eq_real @ (uminus_uminus_real @ C) @ (real_V1485227260804924795R_real @ A @ B))) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9277_neg__le__minus__divideR__eq)). 159.59/70.60 thf(8699,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C))) = (ord_less_eq_real @ (uminus_uminus_real @ C) @ (real_V1485227260804924795R_real @ A @ B))) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[148])). 159.59/70.60 thf(6844,axiom,((! [A:num,B:num]: (((numera6690914467698888265omplex @ A) = (numera6690914467698888265omplex @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_numeral__eq__iff)). 159.59/70.60 thf(31684,plain,((! [A:num,B:num]: (((numera6690914467698888265omplex @ A) = (numera6690914467698888265omplex @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6844])). 159.59/70.60 thf(4693,axiom,(((semiri5044797733671781792omplex @ zero_zero_nat) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8045_fact__0)). 159.59/70.60 thf(23479,plain,(((semiri5044797733671781792omplex @ zero_zero_nat) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4693])). 159.59/70.60 thf(6648,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ B) @ A) = (modulo_modulo_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3394_mod__add__self1)). 159.59/70.60 thf(30779,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)],[6648])). 159.59/70.60 thf(6235,axiom,((! [A:num,B:nat]: ((archim7802044766580827645g_real @ (power_power_real @ (numeral_numeral_real @ A) @ B)) = (power_power_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6990_ceiling__numeral__power)). 159.59/70.60 thf(29199,plain,((! [A:num,B:nat]: ((archim7802044766580827645g_real @ (power_power_real @ (numeral_numeral_real @ A) @ B)) = (power_power_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6235])). 159.59/70.60 thf(82,axiom,((! [A:complex,B:complex]: ((ord_less_eq_real @ zero_zero_real @ (re @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_eq_real @ zero_zero_real @ (re @ (times_times_complex @ A @ (cnj @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9692_Re__complex__div__ge__0)). 159.59/70.60 thf(8504,plain,((! [A:complex,B:complex]: ((ord_less_eq_real @ zero_zero_real @ (re @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_eq_real @ zero_zero_real @ (re @ (times_times_complex @ A @ (cnj @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 159.59/70.60 thf(7389,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_nat @ A @ B) => ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (some_nat @ B))) & (((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_option_nat @ ((vEBT_VEBT_less @ (some_nat @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (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 @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_succ @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)) <= (~ (ord_less_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1447_vebt__succ_Osimps_I6_J)). 159.59/70.60 thf(33796,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_nat @ A @ B) => ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (some_nat @ B))) & (((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_option_nat @ ((vEBT_VEBT_less @ (some_nat @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ~ ((vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (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 @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (some_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_succ @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7389])). 159.59/70.60 thf(2749,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_add__diff__cancel__left_H)). 159.59/70.60 thf(17111,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2749])). 159.59/70.60 thf(6215,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_less__Suc__eq)). 159.59/70.60 thf(29140,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)],[6215])). 159.59/70.60 thf(2932,axiom,((ord_less_real @ zero_zero_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6770_pi__half__gt__zero)). 159.59/70.60 thf(17697,plain,((ord_less_real @ zero_zero_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2932])). 159.59/70.60 thf(6526,axiom,((! [A:(nat > real),B:nat,C:nat]: ((((A @ C) = zero_zero_real) <= (ord_less_eq_nat @ C @ B)) <= (! [D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (A @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ B)) = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8833_zero__polynom__imp__zero__coeffs)). 159.59/70.60 thf(30343,plain,((! [A:(nat > real),B:nat,C:nat]: (((A @ C) = zero_zero_real) | ~ (ord_less_eq_nat @ C @ B) | ~ (! [D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (A @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ B)) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6526])). 159.59/70.60 thf(448,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/sandbox/benchmark/theBenchmark.p',fact_9611_or__not__numerals_I6_J)). 159.59/70.60 thf(9657,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)],[448])). 159.59/70.60 thf(1142,axiom,((! [A:real]: ((ord_less_eq_real @ (exp_real @ A) @ one_one_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5997_exp__le__one__iff)). 159.59/70.60 thf(11912,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)],[1142])). 159.59/70.60 thf(7024,axiom,((ord_max_nat = (^ [A:nat,B:nat]: (if_nat @ (ord_less_eq_nat @ A @ B) @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3308_max__def)). 159.59/70.60 thf(32430,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)],[7024])). 159.59/70.60 thf(5039,axiom,((! [A:num]: ((ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ (numera1916890842035813515d_enat @ A)) = (ord_less_num @ one @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_one__less__numeral__iff)). 159.59/70.60 thf(24683,plain,((! [A:num]: ((ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ (numera1916890842035813515d_enat @ A)) = (ord_less_num @ one @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5039])). 159.59/70.60 thf(6476,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/sandbox/benchmark/theBenchmark.p',fact_8095_choose__dvd)). 159.59/70.60 thf(30162,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)],[6476])). 159.59/70.60 thf(1010,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) => (ord_le2932123472753598470d_enat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3027_leI)). 159.59/70.60 thf(11481,plain,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) => (ord_le2932123472753598470d_enat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010])). 159.59/70.60 thf(7840,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/sandbox/benchmark/theBenchmark.p',fact_4862_Power_Oring__1__class_Opower__minus__even)). 159.59/70.60 thf(35314,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)],[7840])). 159.59/70.60 thf(4571,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/sandbox/benchmark/theBenchmark.p',fact_2405_vebt__insert_Osimps_I3_J)). 159.59/70.60 thf(23030,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)],[4571])). 159.59/70.60 thf(3407,axiom,((! [A:(nat > complex),B:(nat > complex)]: (((sums_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))) @ (times_times_complex @ (suminf_complex @ A) @ (suminf_complex @ B))) <= (summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (B @ C))))) <= (summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8929_Cauchy__product__sums)). 159.59/70.60 thf(19209,plain,((! [A:(nat > complex),B:(nat > complex)]: ((sums_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))) @ (times_times_complex @ (suminf_complex @ (A)) @ (suminf_complex @ (B)))) | ~ (summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (B @ C)))) | ~ (summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3407])). 159.59/70.60 thf(6755,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/sandbox/benchmark/theBenchmark.p',fact_75_numeral__le__iff)). 159.59/70.60 thf(31293,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)],[6755])). 159.59/70.60 thf(7709,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/sandbox/benchmark/theBenchmark.p',fact_3913_odd__two__times__div__two__nat)). 159.59/70.60 thf(34880,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)],[7709])). 159.59/70.60 thf(1717,axiom,((! [A:real]: ? [B:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ B) @ A) & ! [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_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ B @ one_one_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5926_floor__exists1)). 159.59/70.60 thf(13800,plain,((! [A:real]: ? [B:int]: ((ord_less_eq_real @ (ring_1_of_int_real @ B) @ A) & ! [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_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ B @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1717])). 159.59/70.60 thf(5751,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/sandbox/benchmark/theBenchmark.p',fact_9105_choose__rising__sum_I1_J)). 159.59/70.60 thf(27298,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)],[5751])). 159.59/70.60 thf(2051,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (ord_less_eq_int @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4502_pinf_I8_J)). 159.59/70.60 thf(14871,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)],[2051])). 159.59/70.60 thf(1115,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2764_less__imp__neq)). 159.59/70.60 thf(11831,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115])). 159.59/70.60 thf(1854,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (plus_plus_real @ B @ A) @ C)) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2037_add__decreasing2)). 159.59/70.60 thf(14245,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (plus_plus_real @ B @ A) @ C)) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1854])). 159.59/70.60 thf(5759,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/sandbox/benchmark/theBenchmark.p',fact_836_Nat_Odiff__cancel)). 159.59/70.60 thf(27323,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)],[5759])). 159.59/70.60 thf(4260,axiom,((! [A:code_integer,B:code_integer,C:nat]: ((dvd_dvd_Code_integer @ A @ B) => ((power_8256067586552552935nteger @ (divide6298287555418463151nteger @ B @ A) @ C) = (divide6298287555418463151nteger @ (power_8256067586552552935nteger @ B @ C) @ (power_8256067586552552935nteger @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4107_div__power)). 159.59/70.60 thf(21921,plain,((! [A:code_integer,B:code_integer,C:nat]: ((dvd_dvd_Code_integer @ A @ B) => ((power_8256067586552552935nteger @ (divide6298287555418463151nteger @ B @ A) @ C) = (divide6298287555418463151nteger @ (power_8256067586552552935nteger @ B @ C) @ (power_8256067586552552935nteger @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4260])). 159.59/70.60 thf(6032,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1489_mult__eq__0__iff)). 159.59/70.60 thf(28541,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)],[6032])). 159.59/70.60 thf(1654,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/sandbox/benchmark/theBenchmark.p',fact_7404_sum__distrib__right)). 159.59/70.60 thf(13611,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)],[1654])). 159.59/70.60 thf(5463,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) | (A = zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1490_mult__eq__0__iff)). 159.59/70.60 thf(26318,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)],[5463])). 159.59/70.60 thf(903,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/sandbox/benchmark/theBenchmark.p',fact_1217_diff__strict__right__mono)). 159.59/70.60 thf(11151,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)],[903])). 159.59/70.60 thf(6088,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3665_verit__comp__simplify1_I2_J)). 159.59/70.60 thf(28714,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6088])). 159.59/70.60 thf(3726,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/sandbox/benchmark/theBenchmark.p',fact_5783_of__int__power__eq__of__int__cancel__iff)). 159.59/70.60 thf(20239,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)],[3726])). 159.59/70.60 thf(5442,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/sandbox/benchmark/theBenchmark.p',fact_2467_self__le__power)). 159.59/70.60 thf(26240,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)],[5442])). 159.59/70.60 thf(2866,axiom,((! [A:int,B:int]: (((~ (ord_less_int @ A @ B)) => (ord_less_int @ B @ A)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2842_linorder__neqE)). 159.59/70.60 thf(17475,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)],[2866])). 159.59/70.60 thf(7534,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/sandbox/benchmark/theBenchmark.p',fact_9743_Suc__0__mod__numeral)). 159.59/70.60 thf(34292,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)],[7534])). 159.59/70.60 thf(5521,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (((suc @ A) != B) => (ord_less_nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_Suc__lessI)). 159.59/70.60 thf(26520,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((~ ((suc @ A) = B)) => (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5521])). 159.59/70.60 thf(7821,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F)) <= ((ord_less_nat @ C @ A) | (ord_less_nat @ A @ B))) & (((((A = C) & (A = B)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F))) & ((~ ((A = C) & (A = B))) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (A = B) @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ B) @ (if_nat @ (((A != B) => (A = C)) & (((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) <= (A = B))) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (if_nat @ (A = B) @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ C))) @ (suc @ (suc @ D)) @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (A = B) @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ B) @ (if_nat @ (((A = C) <= (A != B)) & (((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) <= (A = B))) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ C))) @ (suc @ (suc @ D)) @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F))))) <= (~ ((ord_less_nat @ C @ A) | (ord_less_nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1454_vebt__delete_Osimps_I7_J)). 159.59/70.60 thf(35249,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F)) | ~ ((ord_less_nat @ C @ A) | (ord_less_nat @ A @ B))) & (((((A = C) & (A = B)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F))) & ((~ ((A = C) & (A = B))) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ A) = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (A = B) @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ B) @ (if_nat @ (((~ (A = B)) => (A = C)) & (((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) | ~ (A = B))) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (if_nat @ (A = B) @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ B) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ C))) @ (suc @ (suc @ D)) @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (A = B) @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ B) @ (if_nat @ (((A = C) | (A = B)) & (((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) | ~ (A = B))) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ C))) @ (suc @ (suc @ D)) @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (A = B) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ A) @ (divide_divide_nat @ (suc @ (suc @ D)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F))))) | (ord_less_nat @ C @ A) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7821])). 159.59/70.60 thf(6121,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/sandbox/benchmark/theBenchmark.p',fact_9730_drop__bit__Suc__minus__bit1)). 159.59/70.60 thf(28821,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)],[6121])). 159.59/70.60 thf(2607,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((cos_real @ (arccos @ A)) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7357_cos__arccos)). 159.59/70.60 thf(16636,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((cos_real @ (arccos @ A)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2607])). 159.59/70.60 thf(5224,axiom,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: (((B @ A @ C) <= (A = none_P5556105721700978146at_nat)) => (((B @ A @ C) <= (! [D:product_prod_nat_nat,E:product_prod_nat_nat]: ((A = (some_P7363390416028606310at_nat @ D)) => ((B @ A @ C) <= (C = (some_P7363390416028606310at_nat @ E)))))) <= ((C = none_P5556105721700978146at_nat) => (B @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_combine__options__cases)). 159.59/70.60 thf(25348,plain,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: (((B @ A @ C) | ~ (A = none_P5556105721700978146at_nat)) => ((B @ A @ C) | ~ (! [D:product_prod_nat_nat,E:product_prod_nat_nat]: ((A = (some_P7363390416028606310at_nat @ D)) => ((B @ A @ C) | ~ (C = (some_P7363390416028606310at_nat @ E))))) | ~ ((C = none_P5556105721700978146at_nat) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5224])). 159.59/70.60 thf(8151,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_nat @ B @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_self__le__ge2__pow)). 159.59/70.60 thf(36319,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_nat @ B @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8151])). 159.59/70.60 thf(3607,axiom,((plus_plus_int = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_add_Ocommute)). 159.59/70.60 thf(19836,plain,(((plus_plus_int) = (^ [A:int,B:int]: (plus_plus_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3607])). 159.59/70.60 thf(5107,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/sandbox/benchmark/theBenchmark.p',fact_4109_dvd__power__le)). 159.59/70.60 thf(24934,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)],[5107])). 159.59/70.60 thf(4710,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = ((A = zero_zero_complex) | (B = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1487_mult__eq__0__iff)). 159.59/70.60 thf(23532,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = ((A = zero_zero_complex) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4710])). 159.59/70.60 thf(5766,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ A @ (set_ord_atMost_nat @ (plus_plus_nat @ B @ C))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ A @ (set_ord_atMost_nat @ B)) @ (groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ B) @ (plus_plus_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8842_sum__up__index__split)). 159.59/70.60 thf(27344,plain,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_ord_atMost_nat @ (plus_plus_nat @ B @ C))) = (plus_plus_nat @ (groups3542108847815614940at_nat @ (A) @ (set_ord_atMost_nat @ B)) @ (groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ (suc @ B) @ (plus_plus_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5766])). 159.59/70.60 thf(5162,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/sandbox/benchmark/theBenchmark.p',fact_7185_cos__double)). 159.59/70.60 thf(25126,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)],[5162])). 159.59/70.60 thf(3682,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/sandbox/benchmark/theBenchmark.p',fact_3443_mod__mult__left__eq)). 159.59/70.60 thf(20078,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)],[3682])). 159.59/70.60 thf(3791,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ (cosh_real @ A) @ (cosh_real @ B)) = (ord_less_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9341_cosh__real__nonneg__less__iff)). 159.59/70.60 thf(20441,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_real @ (cosh_real @ A) @ (cosh_real @ B)) = (ord_less_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3791])). 159.59/70.60 thf(6409,axiom,((! [A:nat,B:nat,C:complex]: ((ord_less_eq_nat @ A @ B) => ((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_complex @ (power_power_complex @ C @ A) @ (groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_ord_atMost_nat @ (minus_minus_nat @ B @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8888_sum__power__shift)). 159.59/70.60 thf(29884,plain,((! [A:nat,B:nat,C:complex]: ((ord_less_eq_nat @ A @ B) => ((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_complex @ (power_power_complex @ C @ A) @ (groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_ord_atMost_nat @ (minus_minus_nat @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6409])). 159.59/70.60 thf(6436,axiom,((! [A:num,B:real]: ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8202_neg__numeral__le__floor)). 159.59/70.60 thf(29997,plain,((! [A:num,B:real]: ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6436])). 159.59/70.60 thf(737,axiom,((! [A:real,B:real,C:real]: (((A = zero_zero_real) => ((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = B)) & (((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ B @ A) @ C) @ A)) <= (A != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2375_add__divide__eq__if__simps_I4_J)). 159.59/70.60 thf(10633,plain,((! [A:real,B:real,C:real]: (((A = zero_zero_real) => ((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = B)) & (((minus_minus_real @ B @ (divide_divide_real @ C @ A)) = (divide_divide_real @ (minus_minus_real @ (times_times_real @ B @ A) @ C) @ A)) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[737])). 159.59/70.60 thf(3969,axiom,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) = (the_real @ (^ [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ A @ (numeral_numeral_real @ (bit0 @ one))) & ((cos_real @ A) = zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9402_pi__half)). 159.59/70.60 thf(21021,plain,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) = (the_real @ (^ [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ A @ (numeral_numeral_real @ (bit0 @ one))) & ((cos_real @ A) = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3969])). 159.59/70.60 thf(625,axiom,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5943_or_Oidem)). 159.59/70.60 thf(10248,plain,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[625])). 159.59/70.60 thf(6583,axiom,((! [A:num,B:num,C:num,D:num]: (((product_Pair_num_num @ A @ B) = (product_Pair_num_num @ C @ D)) => (~ ((A = C) => (B != D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3673_Pair__inject)). 159.59/70.60 thf(30534,plain,((! [A:num,B:num,C:num,D:num]: (((product_Pair_num_num @ A @ B) = (product_Pair_num_num @ C @ D)) => (~ ((A = C) => (~ (B = D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6583])). 159.59/70.60 thf(723,axiom,((! [A:complex,B:complex,C:complex]: ((A = (minus_minus_complex @ C @ B)) <= ((plus_plus_complex @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1274_add__implies__diff)). 159.59/70.60 thf(10584,plain,((! [A:complex,B:complex,C:complex]: ((A = (minus_minus_complex @ C @ B)) | ~ ((plus_plus_complex @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[723])). 159.59/70.60 thf(8069,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ (divide_divide_nat @ B @ A) @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2484_dividend__less__div__times)). 159.59/70.60 thf(36055,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ (divide_divide_nat @ B @ A) @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8069])). 159.59/70.60 thf(6854,axiom,((! [A:nat]: ((~ (! [B:nat]: (A != (suc @ B)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1901_old_Onat_Oexhaust)). 159.59/70.60 thf(31716,plain,((! [A:nat]: (~ (! [B:nat]: ~ (A = (suc @ B))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6854])). 159.59/70.60 thf(1843,axiom,((! [A:complex]: (summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9288_summable__norm__exp)). 159.59/70.60 thf(14213,plain,((! [A:complex]: (summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1843])). 159.59/70.60 thf(4860,axiom,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = (ord_less_num @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3696_verit__comp__simplify1_I3_J)). 159.59/70.60 thf(24060,plain,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = (ord_less_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4860])). 159.59/70.60 thf(6058,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/sandbox/benchmark/theBenchmark.p',fact_6360_real__sqrt__pow2)). 159.59/70.60 thf(28627,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)],[6058])). 159.59/70.60 thf(3860,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/sandbox/benchmark/theBenchmark.p',fact_6941_norm__diff__ineq)). 159.59/70.60 thf(20679,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)],[3860])). 159.59/70.60 thf(6522,axiom,((! [A:num]: ((minus_minus_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ one_one_int)) = (numeral_numeral_int @ (inc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5710_diff__numeral__special_I6_J)). 159.59/70.60 thf(30315,plain,((! [A:num]: ((minus_minus_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ one_one_int)) = (numeral_numeral_int @ (inc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6522])). 159.59/70.60 thf(5813,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_VEBT_membermima @ A @ B) = C) => ((accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ A @ B)) => ((! [D:$o,E:$o]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B))) <= (~ (C))) <= (A = (vEBT_Leaf @ D @ E)))) => ((! [D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E)) => ((~ (C)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E) @ B)))))) => (((! [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 @ F) @ G @ H)) => ((C = ((B = D) | (((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))))) <= (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))) | (B = E))) => (~ (accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H) @ B)))))) => (~ (! [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: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))) => (~ (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))))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3327_VEBT__internal_Omembermima_Opelims_I1_J)). 159.59/70.60 thf(27624,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_VEBT_membermima @ A @ B) = C) => ((accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ A @ B)) => ((! [D:$o,E:$o]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)) | (C) | ~ (A = (vEBT_Leaf @ D @ E)))) => ((! [D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E)) => ((~ (C)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E) @ B)))))) => (((! [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 @ F) @ G @ H)) => ((C = ((B = D) | (((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))))) | ~ (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))) | (B = E))) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_V4351362008482014158ma_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H) @ B)))))) => (~ (! [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: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))) => (~ (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))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5813])). 159.59/70.60 thf(108,axiom,((sin_real = (^ [A:real]: (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (sin_coeff @ B) @ (power_power_real @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9265_sin__def)). 159.59/70.60 thf(8583,plain,(((sin_real) = (^ [A:real]: (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (sin_coeff @ B) @ (power_power_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 159.59/70.60 thf(6083,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((((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_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6957_ceiling__log__nat__eq__powr__iff)). 159.59/70.60 thf(28697,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((((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_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6083])). 159.59/70.60 thf(7242,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/sandbox/benchmark/theBenchmark.p',fact_779_Suc__diff__diff)). 159.59/70.60 thf(33294,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)],[7242])). 159.59/70.60 thf(1420,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/sandbox/benchmark/theBenchmark.p',fact_5847_of__int__power__less__of__int__cancel__iff)). 159.59/70.60 thf(12879,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)],[1420])). 159.59/70.60 thf(5726,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((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)))) <= (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_mi__eq__ma__no__ch)). 159.59/70.60 thf(27212,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((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)))) | ~ (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)],[5726])). 159.59/70.60 thf(1539,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/sandbox/benchmark/theBenchmark.p',fact_5229_real__0__le__add__iff)). 159.59/70.60 thf(13258,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)],[1539])). 159.59/70.60 thf(3165,axiom,((! [A:(nat > complex)]: ((groups6464643781859351333omplex @ A @ bot_bot_set_nat) = one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8379_prod_Oempty)). 159.59/70.60 thf(18437,plain,((! [A:(nat > complex)]: ((groups6464643781859351333omplex @ (A) @ bot_bot_set_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3165])). 159.59/70.60 thf(7332,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/sandbox/benchmark/theBenchmark.p',fact_5644_Suc__mod__eq__add3__mod)). 159.59/70.60 thf(33608,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)],[7332])). 159.59/70.60 thf(6081,axiom,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit1 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6018_and__numerals_I4_J)). 159.59/70.60 thf(28691,plain,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit1 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6081])). 159.59/70.60 thf(4418,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/sandbox/benchmark/theBenchmark.p',fact_9745_prod__decode__aux_Osimps)). 159.59/70.60 thf(22412,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)],[4418])). 159.59/70.60 thf(1408,axiom,((! [A:real,B:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ B) = (minus_minus_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4710_uminus__add__conv__diff)). 159.59/70.60 thf(12843,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)],[1408])). 159.59/70.60 thf(3298,axiom,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ (insert_nat @ C @ A) @ (insert_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6203_insert__mono)). 159.59/70.60 thf(18866,plain,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ (insert_nat @ C @ A) @ (insert_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3298])). 159.59/70.60 thf(1237,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/sandbox/benchmark/theBenchmark.p',fact_3563_div__exp__mod__exp__eq)). 159.59/70.60 thf(12254,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)],[1237])). 159.59/70.60 thf(6528,axiom,((! [A:nat,B:(nat > complex),C:complex,D:complex]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_complex @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (B @ E) @ (power_power_complex @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (B @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_complex @ (minus_minus_complex @ C @ D) @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (B @ F) @ (power_power_complex @ D @ (minus_minus_nat @ (minus_minus_nat @ F @ E) @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ E) @ A)) @ (power_power_complex @ C @ E))) @ (set_ord_lessThan_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8958_polyfun__diff)). 159.59/70.60 thf(30350,plain,((! [A:nat,B:(nat > complex),C:complex,D:complex]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_complex @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (B @ E) @ (power_power_complex @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (B @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_complex @ (minus_minus_complex @ C @ D) @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (B @ F) @ (power_power_complex @ D @ (minus_minus_nat @ (minus_minus_nat @ F @ E) @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ E) @ A)) @ (power_power_complex @ C @ E))) @ (set_ord_lessThan_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6528])). 159.59/70.60 thf(6184,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5309_square__le__1)). 159.59/70.60 thf(29044,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6184])). 159.59/70.60 thf(3931,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ B) <= (ord_less_eq_int @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3131_dual__order_Ostrict__trans2)). 159.59/70.60 thf(20894,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ B) | ~ (ord_less_eq_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3931])). 159.59/70.60 thf(7115,axiom,((! [A:nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1686_power__Suc0__right)). 159.59/70.60 thf(32791,plain,((! [A:nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7115])). 159.59/70.60 thf(3263,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/sandbox/benchmark/theBenchmark.p',fact_2499_half__gt__zero__iff)). 159.59/70.60 thf(18754,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)],[3263])). 159.59/70.60 thf(3963,axiom,((ord_less_int = (^ [A:int,B:int]: (~ (ord_less_eq_int @ B @ A) & (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3138_dual__order_Ostrict__iff__not)). 159.59/70.60 thf(21004,plain,(((ord_less_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)],[3963])). 159.59/70.60 thf(4447,axiom,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (numeral_numeral_int @ (bit1 @ A)) @ (suc @ B)) = (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6328_bit__numeral__Bit1__Suc__iff)). 159.59/70.60 thf(22493,plain,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (numeral_numeral_int @ (bit1 @ A)) @ (suc @ B)) = (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4447])). 159.59/70.60 thf(1516,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/sandbox/benchmark/theBenchmark.p',fact_4124_mod__eq__dvd__iff)). 159.59/70.60 thf(13191,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)],[1516])). 159.59/70.60 thf(7103,axiom,((! [A:num]: ((semiri1316708129612266289at_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6516_of__nat__numeral)). 159.59/70.60 thf(32742,plain,((! [A:num]: ((semiri1316708129612266289at_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7103])). 159.59/70.60 thf(993,axiom,((neg_nu6075765906172075777c_real = (^ [A:real]: (minus_minus_real @ (plus_plus_real @ A @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5735_dbl__dec__def)). 159.59/70.60 thf(11426,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)],[993])). 159.59/70.60 thf(339,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)) = (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ C)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9255_pos__le__divideR__eq)). 159.59/70.60 thf(9300,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)) = (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ C)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 159.59/70.60 thf(265,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/sandbox/benchmark/theBenchmark.p',fact_9592_and__not__numerals_I4_J)). 159.59/70.60 thf(9056,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)],[265])). 159.59/70.60 thf(5103,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6166_and__nat__numerals_I1_J)). 159.59/70.60 thf(24922,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)],[5103])). 159.59/70.60 thf(5226,axiom,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8086_fact__mono)). 159.59/70.60 thf(25367,plain,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5226])). 159.59/70.60 thf(8231,axiom,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: ((((! [D:$o]: ((? [E:$o]: (A = (vEBT_Leaf @ D @ E))) => ((C != (vEBT_Leaf @ D @ ($false))) <= (B = (suc @ zero_zero_nat))))) => ((((! [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((C != (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G)) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G)))) => ((~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: ((~ (((C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)) <= ((ord_less_nat @ B @ D) | (ord_less_nat @ E @ B))) & ((((C = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ F)) @ G @ H)) <= ((B = E) & (B = D))) & ((~ ((B = E) & (B = D))) => (C = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (if_nat @ (((B != D) => (B = E)) & ((B = D) => ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) = E))) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (if_nat @ (((B != D) => (B = E)) & ((B = D) => ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) = E))) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ 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))))) <= (~ ((ord_less_nat @ E @ B) | (ord_less_nat @ B @ D)))))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H))))) <= (! [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((C != (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ zero_zero_nat) @ F @ G)) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ zero_zero_nat) @ F @ G)))))) <= (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((C != (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))))) <= (! [D:$o,E:$o]: (((C != (vEBT_Leaf @ D @ E)) <= (? [F:nat]: (B = (suc @ (suc @ F))))) <= (A = (vEBT_Leaf @ D @ E)))))) <= (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((B = zero_zero_nat) => (C != (vEBT_Leaf @ ($false) @ E)))))) <= ((vEBT_vebt_delete @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2567_vebt__delete_Oelims)). 159.59/70.60 thf(36569,plain,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((! [D:$o]: ((? [E:$o]: (A = (vEBT_Leaf @ D @ E))) => (~ (C = (vEBT_Leaf @ D @ ($false))) | ~ (B = (suc @ zero_zero_nat))))) => (((! [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (~ (C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G)) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G)))) => (~ (! [D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (~ (((C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)) | ~ ((ord_less_nat @ B @ D) | (ord_less_nat @ E @ B))) & ((((C = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ F)) @ G @ H)) | ~ ((B = E) & (B = D))) & ((~ ((B = E) & (B = D))) => (C = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (if_nat @ (((~ (B = D)) => (B = E)) & ((B = D) => ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) = E))) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (if_nat @ (((~ (B = D)) => (B = E)) & ((B = D) => ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) = E))) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ 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))))) | (ord_less_nat @ E @ B) | (ord_less_nat @ B @ D))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))) | ~ (! [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (~ (C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ zero_zero_nat) @ F @ G)) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ zero_zero_nat) @ F @ G)))))) | ~ (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ (C = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)))) | ~ (! [D:$o,E:$o]: (~ (C = (vEBT_Leaf @ D @ E)) | ~ (? [F:nat]: (B = (suc @ (suc @ F)))) | ~ (A = (vEBT_Leaf @ D @ E)))))) | ~ (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((B = zero_zero_nat) => (~ (C = (vEBT_Leaf @ ($false) @ E)))))) | ~ ((vEBT_vebt_delete @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8231])). 159.59/70.60 thf(2583,axiom,((! [A:complex,B:complex,C:complex]: ((A = C) <= ((plus_plus_complex @ A @ B) = (plus_plus_complex @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1111_add__right__imp__eq)). 159.59/70.60 thf(16552,plain,((! [A:complex,B:complex,C:complex]: ((A = C) | ~ ((plus_plus_complex @ A @ B) = (plus_plus_complex @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2583])). 159.59/70.60 thf(5930,axiom,((! [A:nat]: (((semiri5044797733671781792omplex @ A) = (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ A @ one_one_nat)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8126_fact__reduce)). 159.59/70.60 thf(28160,plain,((! [A:nat]: (((semiri5044797733671781792omplex @ A) = (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ A @ one_one_nat)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5930])). 159.59/70.60 thf(2850,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/sandbox/benchmark/theBenchmark.p',fact_5819_of__int__numeral__le__iff)). 159.59/70.60 thf(17415,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)],[2850])). 159.59/70.60 thf(1670,axiom,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ A) = B) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3869_unit__div__mult__self)). 159.59/70.60 thf(13658,plain,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ A) = B) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670])). 159.59/70.60 thf(2389,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) = (ord_le2932123472753598470d_enat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3172_linorder__not__less)). 159.59/70.60 thf(15922,plain,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) = (ord_le2932123472753598470d_enat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2389])). 159.59/70.60 thf(3712,axiom,((! [A:complex,B:complex]: ((((invers8013647133539491842omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers8013647133539491842omplex @ B) @ (invers8013647133539491842omplex @ A))) <= (B != zero_zero_complex)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9032_nonzero__inverse__mult__distrib)). 159.59/70.60 thf(20191,plain,((! [A:complex,B:complex]: (((invers8013647133539491842omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers8013647133539491842omplex @ B) @ (invers8013647133539491842omplex @ A))) | (B = zero_zero_complex) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3712])). 159.59/70.60 thf(7135,axiom,((! [A:num,B:num,C:num,D:num]: (((product_Pair_num_num @ A @ B) = (product_Pair_num_num @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3609_prod_Oinject)). 159.59/70.60 thf(32895,plain,((! [A:num,B:num,C:num,D:num]: (((product_Pair_num_num @ A @ B) = (product_Pair_num_num @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7135])). 159.59/70.60 thf(7082,axiom,((! [A:set_nat,B:(set_nat > $o)]: ((finite_finite_nat @ A) => ((B @ bot_bot_set_nat) => ((B @ A) <= (! [C:nat,D:set_nat]: ((((B @ D) => (B @ (insert_nat @ C @ D))) <= (! [E:nat]: ((ord_less_nat @ C @ E) <= (member_nat @ E @ D)))) <= (finite_finite_nat @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6240_finite__linorder__min__induct)). 159.59/70.60 thf(32651,plain,((! [A:set_nat,B:(set_nat > $o)]: ((finite_finite_nat @ A) => ((B @ bot_bot_set_nat) => ((B @ A) | ~ (! [C:nat,D:set_nat]: (((B @ D) => (B @ (insert_nat @ C @ D))) | ~ (! [E:nat]: ((ord_less_nat @ C @ E) | ~ (member_nat @ E @ D))) | ~ (finite_finite_nat @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7082])). 159.59/70.60 thf(2541,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/sandbox/benchmark/theBenchmark.p',fact_1840_field__lbound__gt__zero)). 159.59/70.60 thf(16420,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)],[2541])). 159.59/70.60 thf(4258,axiom,(((arcsin @ one_one_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7371_arcsin__1)). 159.59/70.60 thf(21916,plain,(((arcsin @ one_one_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4258])). 159.59/70.60 thf(3968,axiom,((! [A:real,B:real,C:real]: (((uminus_uminus_real @ A) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ C))) <= (A = (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4964_group__cancel_Oneg1)). 159.59/70.60 thf(21017,plain,((! [A:real,B:real,C:real]: (((uminus_uminus_real @ A) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ C))) | ~ (A = (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3968])). 159.59/70.60 thf(1954,axiom,((! [A:int,B:real]: ((ord_less_int @ A @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (ring_1_of_int_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7101_less__ceiling__iff)). 159.59/70.60 thf(14552,plain,((! [A:int,B:real]: ((ord_less_int @ A @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (ring_1_of_int_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1954])). 159.59/70.60 thf(2200,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (ord_le3102999989581377725nteger @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4612_neg__le__iff__le)). 159.59/70.60 thf(15353,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)],[2200])). 159.59/70.60 thf(1307,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = (times_times_real @ B @ A)) => ((exp_real @ (plus_plus_real @ A @ B)) = (times_times_real @ (exp_real @ A) @ (exp_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6078_exp__add__commuting)). 159.59/70.60 thf(12475,plain,((! [A:real,B:real]: (((times_times_real @ A @ B) = (times_times_real @ B @ A)) => ((exp_real @ (plus_plus_real @ A @ B)) = (times_times_real @ (exp_real @ A) @ (exp_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307])). 159.59/70.60 thf(5211,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/sandbox/benchmark/theBenchmark.p',fact_1430_power__numeral__even)). 159.59/70.60 thf(25307,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)],[5211])). 159.59/70.60 thf(6124,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/sandbox/benchmark/theBenchmark.p',fact_362_power__mult__distrib)). 159.59/70.60 thf(28830,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)],[6124])). 159.59/70.60 thf(6828,axiom,((! [A:num]: ~ (ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5175_not__one__le__neg__numeral)). 159.59/70.60 thf(31539,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)],[6828])). 159.59/70.60 thf(1929,axiom,((! [A:complex]: ((real_V2046097035970521341omplex @ (uminus_uminus_real @ one_one_real) @ A) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9198_scaleR__minus1__left)). 159.59/70.60 thf(14474,plain,((! [A:complex]: ((real_V2046097035970521341omplex @ (uminus_uminus_real @ one_one_real) @ A) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1929])). 159.59/70.60 thf(6692,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/sandbox/benchmark/theBenchmark.p',fact_5601_cong__exp__iff__simps_I10_J)). 159.59/70.60 thf(30984,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)],[6692])). 159.59/70.60 thf(8132,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat,G:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => (((~ (ord_less_nat @ 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)) <= (B != A))) <= (F = (suc @ (suc @ G))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_nested__mint)). 159.59/70.60 thf(36251,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat,G:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => (((~ (ord_less_nat @ 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)) | (B = A))) | ~ (F = (suc @ (suc @ G))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8132])). 159.59/70.60 thf(1221,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/sandbox/benchmark/theBenchmark.p',fact_2619_subsetI)). 159.59/70.60 thf(12197,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)],[1221])). 159.59/70.60 thf(1995,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/sandbox/benchmark/theBenchmark.p',fact_1280_diff__add__eq__diff__diff__swap)). 159.59/70.60 thf(14701,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)],[1995])). 159.59/70.60 thf(4402,axiom,((! [A:num,B:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5039_neg__numeral__less__numeral)). 159.59/70.60 thf(22353,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)],[4402])). 159.59/70.60 thf(1573,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ B @ A)) <= (ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9023_inverse__less__imp__less)). 159.59/70.60 thf(13360,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ B @ A)) | ~ (ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1573])). 159.59/70.60 thf(4626,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/sandbox/benchmark/theBenchmark.p',fact_830_Nat_Odiff__diff__eq)). 159.59/70.60 thf(23243,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)],[4626])). 159.59/70.60 thf(7394,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/sandbox/benchmark/theBenchmark.p',fact_8480_prod_OatMost__Suc__shift)). 159.59/70.60 thf(33815,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)],[7394])). 159.59/70.60 thf(6559,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/sandbox/benchmark/theBenchmark.p',fact_853_Nat_Ole__diff__conv2)). 159.59/70.60 thf(30456,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)],[6559])). 159.59/70.60 thf(2906,axiom,((! [A:(nat > complex),B:complex,C:complex]: ((sums_complex @ A @ B) => (sums_complex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ C)) @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7886_sums__mult2)). 159.59/70.60 thf(17610,plain,((! [A:(nat > complex),B:complex,C:complex]: ((sums_complex @ (A) @ B) => (sums_complex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ C)) @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2906])). 159.59/70.60 thf(7751,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/sandbox/benchmark/theBenchmark.p',fact_672_Suc__nat__number__of__add)). 159.59/70.60 thf(35044,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)],[7751])). 159.59/70.60 thf(2105,axiom,((! [A:int]: (((divide_divide_int @ A @ A) = one_one_int) <= (A != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1661_div__self)). 159.59/70.60 thf(15033,plain,((! [A:int]: (((divide_divide_int @ A @ A) = one_one_int) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2105])). 159.59/70.60 thf(2487,axiom,((~ (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5160_less__minus__one__simps_I3_J)). 159.59/70.60 thf(16251,plain,((~ (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2487])). 159.59/70.60 thf(1439,axiom,((! [A:nat,B:nat,C:nat]: (((power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B) = (semiri4939895301339042750nteger @ C)) = ((power_power_nat @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6565_of__nat__eq__of__nat__power__cancel__iff)). 159.59/70.60 thf(12943,plain,((! [A:nat,B:nat,C:nat]: (((power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B) = (semiri4939895301339042750nteger @ C)) = ((power_power_nat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1439])). 159.59/70.60 thf(3389,axiom,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6054_bit_Odisj__zero__right)). 159.59/70.60 thf(19145,plain,((! [A:int]: ((bit_se1409905431419307370or_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3389])). 159.59/70.60 thf(5159,axiom,((! [A:nat,B:nat]: ((bit_se1148574629649215175it_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (bit_se1148574629649215175it_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6656_bit__of__nat__iff__bit)). 159.59/70.60 thf(25117,plain,((! [A:nat,B:nat]: ((bit_se1148574629649215175it_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (bit_se1148574629649215175it_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5159])). 159.59/70.60 thf(234,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A) => ((divide6298287555418463151nteger @ B @ (times_3573771949741848930nteger @ C @ A)) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ B @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2317_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq)). 159.59/70.60 thf(8967,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A) => ((divide6298287555418463151nteger @ B @ (times_3573771949741848930nteger @ C @ A)) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 159.59/70.60 thf(7884,axiom,((! [A:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3438_add__self__mod__2)). 159.59/70.60 thf(35452,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)],[7884])). 159.59/70.60 thf(5148,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/sandbox/benchmark/theBenchmark.p',fact_2311_power__less__imp__less__base)). 159.59/70.60 thf(25074,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)],[5148])). 159.59/70.60 thf(6092,axiom,((! [A:set_nat]: ((groups708209901874060359at_nat @ (^ [B:nat]: (one_one_nat)) @ A) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8375_prod_Oneutral__const)). 159.59/70.60 thf(28726,plain,((! [A:set_nat]: ((groups708209901874060359at_nat @ (^ [B:nat]: (one_one_nat)) @ A) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6092])). 159.59/70.60 thf(6183,axiom,((! [A:$o,B:$o]: (((~ (A)) => ((((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = none_nat) <= (~ (B))) & ((B) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ zero_zero_nat))))) & ((A) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ one_one_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1947_vebt__maxt_Osimps_I1_J)). 159.59/70.60 thf(29031,plain,((! [A:$o,B:$o]: (((~ (A)) => ((((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = none_nat) | (B)) & ((B) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ zero_zero_nat))))) & ((A) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6183])). 159.59/70.60 thf(3240,axiom,((! [A:nat]: ((bit_se2923211474154528505it_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = (times_times_int @ (zero_n2684676970156552555ol_int @ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4910_take__bit__of__2)). 159.59/70.60 thf(18671,plain,((! [A:nat]: ((bit_se2923211474154528505it_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = (times_times_int @ (zero_n2684676970156552555ol_int @ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3240])). 159.59/70.60 thf(3585,axiom,((! [A:extended_enat]: ((plus_p3455044024723400733d_enat @ A @ zero_z5237406670263579293d_enat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1876_add_Ocomm__neutral)). 159.59/70.60 thf(19763,plain,((! [A:extended_enat]: ((plus_p3455044024723400733d_enat @ A @ zero_z5237406670263579293d_enat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3585])). 159.59/70.60 thf(3277,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/sandbox/benchmark/theBenchmark.p',fact_8320_gbinomial__rec)). 159.59/70.60 thf(18801,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)],[3277])). 159.59/70.60 thf(7320,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/sandbox/benchmark/theBenchmark.p',fact_4762_minus__one__mult__self)). 159.59/70.60 thf(33568,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)],[7320])). 159.59/70.60 thf(921,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (vEBT_VEBT_less @ (some_nat @ A) @ (some_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_less__shift)). 159.59/70.60 thf(11203,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)],[921])). 159.59/70.60 thf(2408,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/sandbox/benchmark/theBenchmark.p',fact_1383_divide__divide__eq__right)). 159.59/70.60 thf(15990,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)],[2408])). 159.59/70.60 thf(4218,axiom,((! [A:nat]: (((A != zero_zero_nat) => ((comm_s2602460028002588243omplex @ zero_zero_complex @ A) = zero_zero_complex)) & (((comm_s2602460028002588243omplex @ zero_zero_complex @ A) = one_one_complex) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8243_pochhammer__0__left)). 159.59/70.60 thf(21794,plain,((! [A:nat]: (((~ (A = zero_zero_nat)) => ((comm_s2602460028002588243omplex @ zero_zero_complex @ A) = zero_zero_complex)) & (((comm_s2602460028002588243omplex @ zero_zero_complex @ A) = one_one_complex) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4218])). 159.59/70.60 thf(4469,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_delete @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2568_vebt__delete_Osimps_I4_J)). 159.59/70.60 thf(22621,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_delete @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4469])). 159.59/70.60 thf(5144,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/sandbox/benchmark/theBenchmark.p',fact_1987_mult__right__mono__neg)). 159.59/70.60 thf(25054,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)],[5144])). 159.59/70.60 thf(8083,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/sandbox/benchmark/theBenchmark.p',fact_4308_flip__bit__0)). 159.59/70.60 thf(36097,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)],[8083])). 159.59/70.60 thf(7049,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_n__not__Suc__n)). 159.59/70.60 thf(32516,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7049])). 159.59/70.60 thf(5771,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/sandbox/benchmark/theBenchmark.p',fact_1046_add__diff__cancel__left)). 159.59/70.60 thf(27362,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)],[5771])). 159.59/70.60 thf(7584,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/sandbox/benchmark/theBenchmark.p',fact_410_in__set__conv__nth)). 159.59/70.60 thf(34506,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)],[7584])). 159.59/70.60 thf(851,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/sandbox/benchmark/theBenchmark.p',fact_3002_real__arch__pow__inv)). 159.59/70.60 thf(10997,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)],[851])). 159.59/70.60 thf(2164,axiom,((! [A:(nat > complex),B:nat,C:complex]: ((sums_complex @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ B))) @ (minus_minus_complex @ C @ (groups2073611262835488442omplex @ A @ (set_ord_lessThan_nat @ B)))) = (sums_complex @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7905_sums__iff__shift_H)). 159.59/70.60 thf(15229,plain,((! [A:(nat > complex),B:nat,C:complex]: ((sums_complex @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ B))) @ (minus_minus_complex @ C @ (groups2073611262835488442omplex @ (A) @ (set_ord_lessThan_nat @ B)))) = (sums_complex @ (A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2164])). 159.59/70.60 thf(1595,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/sandbox/benchmark/theBenchmark.p',fact_6070_OR__lower)). 159.59/70.60 thf(13429,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)],[1595])). 159.59/70.60 thf(3450,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/sandbox/benchmark/theBenchmark.p',fact_9547_push__bit__nonnegative__int__iff)). 159.59/70.60 thf(19342,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)],[3450])). 159.59/70.60 thf(775,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/sandbox/benchmark/theBenchmark.p',fact_1185_add__less__imp__less__right)). 159.59/70.60 thf(10751,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)],[775])). 159.59/70.60 thf(3262,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/sandbox/benchmark/theBenchmark.p',fact_3988_dvd__add__left__iff)). 159.59/70.60 thf(18750,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)],[3262])). 159.59/70.60 thf(6113,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se4205575877204974255it_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ C) & (A != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6379_bit__unset__bit__iff)). 159.59/70.60 thf(28794,plain,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se4205575877204974255it_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ C) & ~ (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6113])). 159.59/70.60 thf(2974,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/sandbox/benchmark/theBenchmark.p',fact_7846_geometric__deriv__sums)). 159.59/70.60 thf(17824,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)],[2974])). 159.59/70.60 thf(4961,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/sandbox/benchmark/theBenchmark.p',fact_5599_cong__exp__iff__simps_I12_J)). 159.59/70.60 thf(24433,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)],[4961])). 159.59/70.60 thf(1246,axiom,(((neg_numeral_dbl_int @ zero_zero_int) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3809_dbl__simps_I2_J)). 159.59/70.60 thf(12286,plain,(((neg_numeral_dbl_int @ zero_zero_int) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246])). 159.59/70.60 thf(4728,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (sqrt @ A) @ B) => (ord_less_eq_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6429_sqrt__le__D)). 159.59/70.60 thf(23587,plain,((! [A:real,B:real]: ((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)],[4728])). 159.59/70.60 thf(4327,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/sandbox/benchmark/theBenchmark.p',fact_8627_prod_OatLeastAtMost__rev)). 159.59/70.60 thf(22121,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)],[4327])). 159.59/70.60 thf(2985,axiom,((! [A:complex]: ((plus_plus_complex @ A @ (uminus1482373934393186551omplex @ A)) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4688_add_Oright__inverse)). 159.59/70.60 thf(17857,plain,((! [A:complex]: ((plus_plus_complex @ A @ (uminus1482373934393186551omplex @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2985])). 159.59/70.60 thf(3728,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (uminus_uminus_real @ B)) = (ord_less_real @ B @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4938_less__minus__iff)). 159.59/70.60 thf(20245,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)],[3728])). 159.59/70.60 thf(545,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/sandbox/benchmark/theBenchmark.p',fact_3397_unset__bit__nonnegative__int__iff)). 159.59/70.60 thf(9988,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)],[545])). 159.59/70.60 thf(274,axiom,(((cos_real @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one)))) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7374_cos__of__real__pi__half)). 159.59/70.60 thf(9084,plain,(((cos_real @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one)))) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 159.59/70.60 thf(5614,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/sandbox/benchmark/theBenchmark.p',fact_5466_Suc__mod__eq__add3__mod__numeral)). 159.59/70.60 thf(26827,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)],[5614])). 159.59/70.60 thf(2495,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/sandbox/benchmark/theBenchmark.p',fact_7167_cos__30)). 159.59/70.60 thf(16287,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)],[2495])). 159.59/70.60 thf(5352,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) <= (ord_less_eq_int @ zero_zero_int @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1991_mult__left__mono)). 159.59/70.60 thf(25861,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5352])). 159.59/70.60 thf(6221,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/sandbox/benchmark/theBenchmark.p',fact_859_vebt__mint_Osimps_I2_J)). 159.59/70.60 thf(29155,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)],[6221])). 159.59/70.60 thf(1888,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1513_add__cancel__right__right)). 159.59/70.60 thf(14351,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1888])). 159.59/70.60 thf(7781,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2926_order__less__imp__not__eq)). 159.59/70.60 thf(35130,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7781])). 159.59/70.60 thf(36,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/sandbox/benchmark/theBenchmark.p',fact_9550_xor__nonnegative__int__iff)). 159.59/70.60 thf(8357,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)],[36])). 159.59/70.60 thf(6776,axiom,((! [A:nat]: ((set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ A)) = (insert_nat @ (suc @ A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6405_atLeast0__atMost__Suc)). 159.59/70.60 thf(31372,plain,((! [A:nat]: ((set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ A)) = (insert_nat @ (suc @ A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6776])). 159.59/70.60 thf(626,axiom,((! [A:(nat > int),B:nat,C:nat]: ((groups3539618377306564664at_int @ A @ (set_ord_atMost_nat @ (plus_plus_nat @ B @ C))) = (plus_plus_int @ (groups3539618377306564664at_int @ A @ (set_ord_atMost_nat @ B)) @ (groups3539618377306564664at_int @ A @ (set_or1269000886237332187st_nat @ (suc @ B) @ (plus_plus_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8841_sum__up__index__split)). 159.59/70.60 thf(10251,plain,((! [A:(nat > int),B:nat,C:nat]: ((groups3539618377306564664at_int @ (A) @ (set_ord_atMost_nat @ (plus_plus_nat @ B @ C))) = (plus_plus_int @ (groups3539618377306564664at_int @ (A) @ (set_ord_atMost_nat @ B)) @ (groups3539618377306564664at_int @ (A) @ (set_or1269000886237332187st_nat @ (suc @ B) @ (plus_plus_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[626])). 159.59/70.60 thf(4939,axiom,(((numeral_numeral_nat @ one) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2379_numeral__1__eq__Suc__0)). 159.59/70.60 thf(24316,plain,(((numeral_numeral_nat @ one) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4939])). 159.59/70.60 thf(7004,axiom,((! [A:(nat > nat),B:nat]: (((summable_nat @ A) <= (! [C:nat]: (ord_less_eq_nat @ (groups3542108847815614940at_nat @ A @ (set_ord_lessThan_nat @ C)) @ B))) <= (! [C:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7971_summableI__nonneg__bounded)). 159.59/70.60 thf(32369,plain,((! [A:(nat > nat),B:nat]: ((summable_nat @ (A)) | ~ (! [C:nat]: (ord_less_eq_nat @ (groups3542108847815614940at_nat @ (A) @ (set_ord_lessThan_nat @ C)) @ B)) | ~ (! [C:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7004])). 159.59/70.60 thf(5829,axiom,(((minus_minus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = (numeral_numeral_int @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4853_diff__numeral__special_I11_J)). 159.59/70.60 thf(27725,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)],[5829])). 159.59/70.60 thf(995,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (arctan @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5792_zero__less__arctan__iff)). 159.59/70.60 thf(11431,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (arctan @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[995])). 159.59/70.60 thf(180,axiom,((! [A:num,B:num]: ((((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ B)) <= (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)) = (uminus_uminus_int @ (numeral_numeral_int @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4772_max__number__of_I3_J)). 159.59/70.60 thf(8806,plain,((! [A:num,B:num]: ((((ord_max_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)) = (numeral_numeral_int @ B)) | ~ (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)) = (uminus_uminus_int @ (numeral_numeral_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 159.59/70.60 thf(5076,axiom,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2729_order_Otrans)). 159.59/70.60 thf(24839,plain,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C)) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5076])). 159.59/70.60 thf(6504,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ A @ B) @ C) => ((ord_less_eq_nat @ C @ (power_power_nat @ A @ (plus_plus_nat @ B @ one_one_nat))) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7202_ceiling__log__nat__eq__if)). 159.59/70.60 thf(30258,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ A @ B) @ C) => ((ord_less_eq_nat @ C @ (power_power_nat @ A @ (plus_plus_nat @ B @ one_one_nat))) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6504])). 159.59/70.60 thf(3083,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/sandbox/benchmark/theBenchmark.p',fact_8233_gbinomial__pochhammer_H)). 159.59/70.60 thf(18155,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)],[3083])). 159.59/70.60 thf(5626,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2022_add__nonneg__eq__0__iff)). 159.59/70.60 thf(26866,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5626])). 159.59/70.60 thf(4189,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/sandbox/benchmark/theBenchmark.p',fact_5479_take__bit__minus)). 159.59/70.60 thf(21684,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)],[4189])). 159.59/70.60 thf(949,axiom,((! [A:real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1539_div__0)). 159.59/70.60 thf(11289,plain,((! [A:real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[949])). 159.59/70.60 thf(7556,axiom,((! [A:real]: ? [B:nat]: (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6647_real__arch__simple)). 159.59/70.60 thf(34360,plain,((! [A:real]: ? [B:nat]: (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7556])). 159.59/70.60 thf(952,axiom,((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2052_linordered__nonzero__semiring__class_Ozero__le__one)). 159.59/70.60 thf(11299,plain,((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[952])). 159.59/70.60 thf(7365,axiom,((! [A:product_prod_num_num]: (((! [B:num]: (A != (product_Pair_num_num @ one @ (bit0 @ B)))) => (((((! [B:num,C:num]: (A != (product_Pair_num_num @ (bit0 @ B) @ (bit1 @ C)))) => ((! [B:num]: (A != (product_Pair_num_num @ (bit1 @ B) @ one))) => ((! [B:num,C:num]: (A != (product_Pair_num_num @ (bit1 @ B) @ (bit0 @ C)))) => (~ (! [B:num,C:num]: (A != (product_Pair_num_num @ (bit1 @ B) @ (bit1 @ C)))))))) <= (! [B:num,C:num]: (A != (product_Pair_num_num @ (bit0 @ B) @ (bit0 @ C))))) <= (! [B:num]: (A != (product_Pair_num_num @ (bit0 @ B) @ one)))) <= (! [B:num]: (A != (product_Pair_num_num @ one @ (bit1 @ B)))))) <= (A != (product_Pair_num_num @ one @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5548_xor__num_Ocases)). 159.59/70.60 thf(33715,plain,((! [A:product_prod_num_num]: (((! [B:num]: ~ (A = (product_Pair_num_num @ one @ (bit0 @ B)))) => (((! [B:num,C:num]: ~ (A = (product_Pair_num_num @ (bit0 @ B) @ (bit1 @ C)))) => ((! [B:num]: ~ (A = (product_Pair_num_num @ (bit1 @ B) @ one))) => ((! [B:num,C:num]: ~ (A = (product_Pair_num_num @ (bit1 @ B) @ (bit0 @ C)))) => (~ (! [B:num,C:num]: ~ (A = (product_Pair_num_num @ (bit1 @ B) @ (bit1 @ C)))))))) | ~ (! [B:num,C:num]: ~ (A = (product_Pair_num_num @ (bit0 @ B) @ (bit0 @ C)))) | ~ (! [B:num]: ~ (A = (product_Pair_num_num @ (bit0 @ B) @ one))) | ~ (! [B:num]: ~ (A = (product_Pair_num_num @ one @ (bit1 @ B)))))) | (A = (product_Pair_num_num @ one @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7365])). 159.59/70.60 thf(855,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (inverse_inverse_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8988_inverse__nonnegative__iff__nonnegative)). 159.59/70.60 thf(11010,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (inverse_inverse_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[855])). 159.59/70.60 thf(3663,axiom,((~ (ord_less_real @ one_one_real @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2125_not__one__less__zero)). 159.59/70.60 thf(20017,plain,((~ (ord_less_real @ one_one_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3663])). 159.59/70.60 thf(4495,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2299_mult__left__le__one__le)). 159.59/70.60 thf(22710,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4495])). 159.59/70.60 thf(7416,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (minus_minus_nat @ A @ (suc @ B)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2385_diff__Suc__less)). 159.59/70.60 thf(33876,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ (minus_minus_nat @ A @ (suc @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7416])). 159.59/70.60 thf(1808,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4441_pinf_I3_J)). 159.59/70.60 thf(14088,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1808])). 159.59/70.60 thf(6608,axiom,((! [A:nat,B:nat,C:real]: ((root @ A @ (root @ B @ C)) = (root @ B @ (root @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9498_real__root__commute)). 159.59/70.60 thf(30630,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)],[6608])). 159.59/70.60 thf(4596,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_succ @ (vEBT_Leaf @ A @ B) @ (suc @ C)) = none_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2220_vebt__succ_Osimps_I2_J)). 159.59/70.60 thf(23123,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_succ @ (vEBT_Leaf @ A @ B) @ (suc @ C)) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4596])). 159.59/70.60 thf(6082,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ C) => ((ord_less_eq_nat @ D @ B) => (dvd_dvd_nat @ (power_power_nat @ A @ D) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4114_power__le__dvd)). 159.59/70.60 thf(28694,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ C) => ((ord_less_eq_nat @ D @ B) => (dvd_dvd_nat @ (power_power_nat @ A @ D) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6082])). 159.59/70.60 thf(6051,axiom,((! [A:nat,B:nat,C:(nat > real)]: ((ord_less_eq_nat @ A @ B) => ((groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_real @ (C @ A) @ (groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8733_prod_OatLeast__Suc__atMost)). 159.59/70.60 thf(28602,plain,((! [A:nat,B:nat,C:(nat > real)]: ((ord_less_eq_nat @ A @ B) => ((groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_real @ (C @ A) @ (groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6051])). 159.59/70.60 thf(4844,axiom,((! [A:int,B:int]: ((times_times_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (times_times_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4628_minus__mult__minus)). 159.59/70.60 thf(24013,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)],[4844])). 159.59/70.60 thf(2718,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ (times_times_complex @ A @ A) @ (times_times_complex @ B @ B)) = (times_times_complex @ (plus_plus_complex @ A @ B) @ (minus_minus_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1359_square__diff__square__factored)). 159.59/70.60 thf(17017,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ (times_times_complex @ A @ A) @ (times_times_complex @ B @ B)) = (times_times_complex @ (plus_plus_complex @ A @ B) @ (minus_minus_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2718])). 159.59/70.60 thf(2297,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2276_add__neg__nonpos)). 159.59/70.60 thf(15648,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2297])). 159.59/70.60 thf(290,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_se6526347334894502574or_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/sandbox/benchmark/theBenchmark.p',fact_9568_XOR__upper)). 159.59/70.60 thf(9128,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_se6526347334894502574or_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)],[290])). 159.59/70.60 thf(7400,axiom,((~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5155_le__minus__one__simps_I3_J)). 159.59/70.60 thf(33832,plain,((~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7400])). 159.59/70.60 thf(5721,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/sandbox/benchmark/theBenchmark.p',fact_8969_choose__odd__sum)). 159.59/70.60 thf(27192,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)],[5721])). 159.59/70.60 thf(1830,axiom,((! [A:nat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ A) @ (plus_p3455044024723400733d_enat @ (semiri4216267220026989637d_enat @ A) @ one_on7984719198319812577d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7827_double__gauss__sum__from__Suc__0)). 159.59/70.60 thf(14173,plain,((! [A:nat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (groups7108830773950497114d_enat @ (semiri4216267220026989637d_enat) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ A) @ (plus_p3455044024723400733d_enat @ (semiri4216267220026989637d_enat @ A) @ one_on7984719198319812577d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1830])). 159.59/70.60 thf(7727,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/sandbox/benchmark/theBenchmark.p',fact_1150_ab__semigroup__add__class_Oadd__ac_I1_J)). 159.59/70.60 thf(34965,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)],[7727])). 159.59/70.60 thf(7874,axiom,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_mult__numeral__1__right)). 159.59/70.60 thf(35424,plain,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7874])). 159.59/70.60 thf(5650,axiom,((! [A:set_nat,B:nat,C:(nat > complex)]: ((((member_nat @ B @ A) => ((groups6464643781859351333omplex @ C @ (insert_nat @ B @ A)) = (groups6464643781859351333omplex @ C @ A))) & (((groups6464643781859351333omplex @ C @ (insert_nat @ B @ A)) = (times_times_complex @ (C @ B) @ (groups6464643781859351333omplex @ C @ A))) <= (~ (member_nat @ B @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8571_prod_Oinsert__if)). 159.59/70.60 thf(26934,plain,((! [A:set_nat,B:nat,C:(nat > complex)]: ((((member_nat @ B @ A) => ((groups6464643781859351333omplex @ (C) @ (insert_nat @ B @ A)) = (groups6464643781859351333omplex @ (C) @ A))) & (((groups6464643781859351333omplex @ (C) @ (insert_nat @ B @ A)) = (times_times_complex @ (C @ B) @ (groups6464643781859351333omplex @ (C) @ A))) | (member_nat @ B @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5650])). 159.59/70.60 thf(8146,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F))))) <= (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4460_minf_I1_J)). 159.59/70.60 thf(36300,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F)))) | ~ (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8146])). 159.59/70.60 thf(3625,axiom,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (times_times_complex @ A @ B)) = (times_times_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6902_norm__mult)). 159.59/70.60 thf(19895,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)],[3625])). 159.59/70.60 thf(2427,axiom,(((csqrt @ imaginary_unit) = (divide1717551699836669952omplex @ (plus_plus_complex @ one_one_complex @ imaginary_unit) @ (real_V4546457046886955230omplex @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9372_csqrt__ii)). 159.59/70.60 thf(16067,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)],[2427])). 159.59/70.60 thf(1160,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ C) <= (B = C)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2783_ord__less__eq__trans)). 159.59/70.60 thf(11966,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ C) | ~ (B = C) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160])). 159.59/70.60 thf(6592,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/sandbox/benchmark/theBenchmark.p',fact_6594_numeral__power__eq__of__nat__cancel__iff)). 159.59/70.60 thf(30579,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)],[6592])). 159.59/70.60 thf(1153,axiom,((! [A:(nat > real)]: ((groups129246275422532515t_real @ A @ bot_bot_set_nat) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8380_prod_Oempty)). 159.59/70.60 thf(11944,plain,((! [A:(nat > real)]: ((groups129246275422532515t_real @ (A) @ bot_bot_set_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153])). 159.59/70.60 thf(3926,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/sandbox/benchmark/theBenchmark.p',fact_6334_log__less__one__cancel__iff)). 159.59/70.60 thf(20881,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)],[3926])). 159.59/70.60 thf(595,axiom,((! [A:nat,B:nat]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6690_of__nat__less__imp__less)). 159.59/70.60 thf(10142,plain,((! [A:nat,B:nat]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) => (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[595])). 159.59/70.60 thf(2508,axiom,((! [A:real]: ((ord_less_eq_real @ (arctan @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5794_arctan__le__zero__iff)). 159.59/70.60 thf(16325,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)],[2508])). 159.59/70.60 thf(6813,axiom,((! [A:set_nat]: ((~ (finite_finite_nat @ A)) = (! [B:nat]: ? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9765_infinite__nat__iff__unbounded)). 159.59/70.60 thf(31487,plain,((! [A:set_nat]: ((~ (finite_finite_nat @ A)) = (! [B:nat]: ? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6813])). 159.59/70.60 thf(2680,axiom,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = B) = ((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5324_take__bit__int__eq__self__iff)). 159.59/70.60 thf(16890,plain,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = B) = ((ord_less_eq_int @ zero_zero_int @ B) & (ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2680])). 159.59/70.60 thf(1503,axiom,((! [A:nat,B:nat,C:complex]: ((ord_less_eq_nat @ A @ B) => ((comm_s2602460028002588243omplex @ C @ B) = (times_times_complex @ (comm_s2602460028002588243omplex @ C @ A) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ C @ (semiri8010041392384452111omplex @ A)) @ (minus_minus_nat @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8315_pochhammer__product)). 159.59/70.60 thf(13151,plain,((! [A:nat,B:nat,C:complex]: ((ord_less_eq_nat @ A @ B) => ((comm_s2602460028002588243omplex @ C @ B) = (times_times_complex @ (comm_s2602460028002588243omplex @ C @ A) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ C @ (semiri8010041392384452111omplex @ A)) @ (minus_minus_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503])). 159.59/70.60 thf(4241,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > num),D:num]: ((((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))) => (ord_less_num @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2875_ord__less__eq__subst)). 159.59/70.60 thf(21861,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > num),D:num]: (((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))) => (ord_less_num @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4241])). 159.59/70.60 thf(4211,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => ((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2344_divide__add__eq__iff)). 159.59/70.60 thf(21755,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => ((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4211])). 159.59/70.60 thf(4973,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2845_order__less__asym)). 159.59/70.60 thf(24469,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4973])). 159.59/70.60 thf(4246,axiom,((! [A:complex,B:real,C:complex,D:real]: (((ord_less_real @ (real_V1022390504157884413omplex @ C) @ D) => (ord_less_real @ (real_V1022390504157884413omplex @ (times_times_complex @ A @ C)) @ (times_times_real @ B @ D))) <= (ord_less_real @ (real_V1022390504157884413omplex @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6914_norm__mult__less)). 159.59/70.60 thf(21880,plain,((! [A:complex,B:real,C:complex,D:real]: (((ord_less_real @ (real_V1022390504157884413omplex @ C) @ D) => (ord_less_real @ (real_V1022390504157884413omplex @ (times_times_complex @ A @ C)) @ (times_times_real @ B @ D))) | ~ (ord_less_real @ (real_V1022390504157884413omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4246])). 159.59/70.60 thf(617,axiom,((~ (ord_less_real @ zero_zero_real @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1842_less__numeral__extra_I3_J)). 159.59/70.60 thf(10221,plain,((~ (ord_less_real @ zero_zero_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[617])). 159.59/70.60 thf(1533,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/sandbox/benchmark/theBenchmark.p',fact_9737_diff__Suc)). 159.59/70.60 thf(13241,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)],[1533])). 159.59/70.60 thf(5527,axiom,((times_times_real = (^ [A:real,B:real]: (times_times_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_mult_Ocommute)). 159.59/70.60 thf(26538,plain,(((times_times_real) = (^ [A:real,B:real]: (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5527])). 159.59/70.60 thf(7057,axiom,((! [A:$o]: (((zero_n2687167440665602831ol_nat @ A) = one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4329_of__bool__eq__1__iff)). 159.59/70.60 thf(32548,plain,((! [A:$o]: (((zero_n2687167440665602831ol_nat @ A) = one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7057])). 159.59/70.60 thf(6273,axiom,((! [A:int]: ((power_power_int @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_int @ (times_times_int @ A @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5626_power3__eq__cube)). 159.59/70.60 thf(29388,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)],[6273])). 159.59/70.60 thf(5922,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1516_add__cancel__right__left)). 159.59/70.60 thf(28138,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5922])). 159.59/70.60 thf(5533,axiom,((! [A:nat,B:nat]: (((binomial @ B @ A) = (binomial @ B @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9050_binomial__symmetric)). 159.59/70.60 thf(26552,plain,((! [A:nat,B:nat]: (((binomial @ B @ A) = (binomial @ B @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5533])). 159.59/70.60 thf(7469,axiom,((! [A:real,B:real,C:real,D:real]: (((((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 @ zero_zero_real @ B)) <= (ord_less_eq_real @ C @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2005_mult__mono)). 159.59/70.60 thf(34057,plain,((! [A:real,B:real,C:real,D:real]: (((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 @ zero_zero_real @ B) | ~ (ord_less_eq_real @ C @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7469])). 159.59/70.60 thf(2144,axiom,((! [A:int,B:int]: (((modulo_modulo_int @ A @ B) = A) = ((divide_divide_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3478_mod__eq__self__iff__div__eq__0)). 159.59/70.60 thf(15171,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)],[2144])). 159.59/70.60 thf(6852,axiom,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5169_neg__numeral__le__neg__one)). 159.59/70.60 thf(31711,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)],[6852])). 159.59/70.60 thf(8049,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((((list_u1324408373059187874T_VEBT @ B @ A @ C) = B) = ((nth_VEBT_VEBT @ B @ A) = C)) <= (ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_list__update__same__conv)). 159.59/70.60 thf(35987,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((((list_u1324408373059187874T_VEBT @ B @ A @ C) = B) = ((nth_VEBT_VEBT @ B @ A) = C)) | ~ (ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8049])). 159.59/70.60 thf(4460,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/sandbox/benchmark/theBenchmark.p',fact_1851_mult__right__cancel)). 159.59/70.60 thf(22536,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)],[4460])). 159.59/70.60 thf(764,axiom,((! [A:nat,B:nat]: ((dvd_dvd_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8091_fact__dvd)). 159.59/70.60 thf(10719,plain,((! [A:nat,B:nat]: ((dvd_dvd_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[764])). 159.59/70.60 thf(5423,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6693_of__nat__mono)). 159.59/70.60 thf(26172,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)],[5423])). 159.59/70.60 thf(6835,axiom,((! [A:num]: ((plus_plus_num @ one @ (bitM @ A)) = (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5896_one__plus__BitM)). 159.59/70.60 thf(31561,plain,((! [A:num]: ((plus_plus_num @ one @ (bitM @ A)) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6835])). 159.59/70.60 thf(7547,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2766_less__imp__neq)). 159.59/70.60 thf(34328,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7547])). 159.59/70.60 thf(6348,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((insert_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (set_or1269000886237332187st_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6406_atLeastAtMost__insertL)). 159.59/70.60 thf(29636,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((insert_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (set_or1269000886237332187st_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6348])). 159.59/70.60 thf(174,axiom,((! [A:code_integer,B:nat,C:nat]: ((A != zero_z3403309356797280102nteger) => ((ord_less_eq_nat @ B @ C) => ((power_8256067586552552935nteger @ A @ (minus_minus_nat @ C @ B)) = (divide6298287555418463151nteger @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2477_power__diff)). 159.59/70.60 thf(8785,plain,((! [A:code_integer,B:nat,C:nat]: ((~ (A = zero_z3403309356797280102nteger)) => ((ord_less_eq_nat @ B @ C) => ((power_8256067586552552935nteger @ A @ (minus_minus_nat @ C @ B)) = (divide6298287555418463151nteger @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 159.59/70.60 thf(6575,axiom,(((xa != mi) | (xa != ma))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196__092_060open_062x_A_092_060noteq_062_Ami_A_092_060or_062_Ax_A_092_060noteq_062_Ama_092_060close_062)). 159.59/70.60 thf(30506,plain,((~ (xa = mi) | ~ (xa = ma))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6575])). 159.59/70.60 thf(7925,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/sandbox/benchmark/theBenchmark.p',fact_3507_mult__div__mod__eq)). 159.59/70.60 thf(35584,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)],[7925])). 159.59/70.60 thf(4901,axiom,((! [A:nat]: ((set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ A)) = (insert_nat @ zero_zero_nat @ (image_nat_nat @ suc @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9809_atLeast0__atMost__Suc__eq__insert__0)). 159.59/70.60 thf(24194,plain,((! [A:nat]: ((set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ A)) = (insert_nat @ zero_zero_nat @ (image_nat_nat @ (suc) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4901])). 159.59/70.60 thf(4170,axiom,((neg_numeral_dbl_real = (^ [A:real]: (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4132_dbl__def)). 159.59/70.60 thf(21631,plain,(((neg_numeral_dbl_real) = (^ [A:real]: (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4170])). 159.59/70.60 thf(4563,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/sandbox/benchmark/theBenchmark.p',fact_741_vebt__mint_Osimps_I3_J)). 159.59/70.60 thf(23006,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)],[4563])). 159.59/70.60 thf(189,axiom,((! [A:complex]: ((minus_minus_complex @ A @ (cnj @ A)) = (times_times_complex @ (real_V4546457046886955230omplex @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (im @ A))) @ imaginary_unit)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9702_complex__diff__cnj)). 159.59/70.60 thf(8834,plain,((! [A:complex]: ((minus_minus_complex @ A @ (cnj @ A)) = (times_times_complex @ (real_V4546457046886955230omplex @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (im @ A))) @ imaginary_unit)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 159.59/70.60 thf(3139,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3173_linorder__not__less)). 159.59/70.60 thf(18353,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3139])). 159.59/70.60 thf(5785,axiom,((! [A:nat]: (vEBT_invar_vebt @ (vEBT_vebt_delete @ summary @ A) @ m))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71__C5_OIH_C_I2_J)). 159.59/70.60 thf(27487,plain,((! [A:nat]: (vEBT_invar_vebt @ (vEBT_vebt_delete @ summary @ A) @ m))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5785])). 159.59/70.60 thf(2560,axiom,((! [A:int]: ((sin_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6804_sin__npi__int)). 159.59/70.60 thf(16480,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)],[2560])). 159.59/70.60 thf(1722,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/sandbox/benchmark/theBenchmark.p',fact_8631_Iic__subset__Iio__iff)). 159.59/70.60 thf(13820,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)],[1722])). 159.59/70.60 thf(1004,axiom,((! [A:nat,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ B) => (((bit_ri631733984087533419it_int @ A @ B) = B) <= (ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5321_signed__take__bit__int__eq__self)). 159.59/70.60 thf(11458,plain,((! [A:nat,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ B) => (((bit_ri631733984087533419it_int @ A @ B) = B) | ~ (ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004])). 159.59/70.60 thf(6829,axiom,((! [A:nat,B:nat]: (((times_times_nat @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (binomial @ B @ A)) = (semiri1408675320244567234ct_nat @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9095_binomial__fact__lemma)). 159.59/70.60 thf(31542,plain,((! [A:nat,B:nat]: (((times_times_nat @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (binomial @ B @ A)) = (semiri1408675320244567234ct_nat @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6829])). 159.59/70.60 thf(5489,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((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))) & ((~ (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) = (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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1446_vebt__pred_Osimps_I7_J)). 159.59/70.60 thf(26406,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((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))) & ((~ (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) = (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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5489])). 159.59/70.60 thf(6158,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ (uminus_uminus_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5535_abs__le__D2)). 159.59/70.60 thf(28942,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ (uminus_uminus_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6158])). 159.59/70.60 thf(359,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/sandbox/benchmark/theBenchmark.p',fact_9674_complex__neq__0)). 159.59/70.60 thf(9360,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)],[359])). 159.59/70.60 thf(2452,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) & (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)) => (((arccos @ A) = (arccos @ B)) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7543_arccos__eq__iff)). 159.59/70.60 thf(16146,plain,((! [A:real,B:real]: (((ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real) & (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)) => (((arccos @ A) = (arccos @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2452])). 159.59/70.60 thf(2868,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (B != zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1834_gr__implies__not__zero)). 159.59/70.60 thf(17481,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (B = zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2868])). 159.59/70.60 thf(3494,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/sandbox/benchmark/theBenchmark.p',fact_5600_cong__exp__iff__simps_I12_J)). 159.59/70.60 thf(19472,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)],[3494])). 159.59/70.60 thf(6887,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/sandbox/benchmark/theBenchmark.p',fact_4764_minus__one__mult__self)). 159.59/70.60 thf(31815,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)],[6887])). 159.59/70.60 thf(8164,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2205_mult__less__mono1)). 159.59/70.60 thf(36363,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8164])). 159.59/70.60 thf(7955,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/sandbox/benchmark/theBenchmark.p',fact_3585_flip__bit__Suc)). 159.59/70.60 thf(35682,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)],[7955])). 159.59/70.60 thf(2803,axiom,((! [A:nat]: ((semiri4216267220026989637d_enat @ (suc @ A)) != zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6672_of__nat__neq__0)). 159.59/70.60 thf(17270,plain,((! [A:nat]: ~ ((semiri4216267220026989637d_enat @ (suc @ A)) = zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2803])). 159.59/70.60 thf(5865,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/sandbox/benchmark/theBenchmark.p',fact_4597_even__set__encode__iff)). 159.59/70.60 thf(27920,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)],[5865])). 159.59/70.60 thf(4100,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/sandbox/benchmark/theBenchmark.p',fact_1767_le__divide__eq__1__neg)). 159.59/70.60 thf(21407,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)],[4100])). 159.59/70.60 thf(920,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1128_add_Oright__cancel)). 159.59/70.60 thf(11200,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)],[920])). 159.59/70.60 thf(89,axiom,((! [A:(nat > extended_enat),B:nat,C:nat]: ((groups7961826882256487087d_enat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo2538466533108834004d_enat @ (^ [D:nat]: (times_7803423173614009249d_enat @ (A @ D))) @ B @ C @ one_on7984719198319812577d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8517_prod__atLeastAtMost__code)). 159.59/70.60 thf(8522,plain,((! [A:(nat > extended_enat),B:nat,C:nat]: ((groups7961826882256487087d_enat @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo2538466533108834004d_enat @ (^ [D:nat]: (times_7803423173614009249d_enat @ (A @ D))) @ B @ C @ one_on7984719198319812577d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 159.59/70.60 thf(5677,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1837_not__less__zero)). 159.59/70.60 thf(27060,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5677])). 159.59/70.60 thf(2302,axiom,((! [A:int,B:int]: (((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ A @ one_one_int)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3996_dvd__unit__imp__unit)). 159.59/70.60 thf(15663,plain,((! [A:int,B:int]: (((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ A @ one_one_int)) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2302])). 159.59/70.60 thf(6912,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/sandbox/benchmark/theBenchmark.p',fact_4260_zero__le__odd__power)). 159.59/70.60 thf(31896,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)],[6912])). 159.59/70.60 thf(1455,axiom,((! [A:real]: (((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (sin_real @ A) @ zero_zero_real)) <= (ord_less_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6870_sin__less__zero)). 159.59/70.60 thf(12993,plain,((! [A:real]: (((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (sin_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)],[1455])). 159.59/70.60 thf(2907,axiom,((! [A:int,B:nat]: ((gbinomial_int @ A @ (suc @ B)) = (divide_divide_int @ (groups705719431365010083at_int @ (^ [C:nat]: (minus_minus_int @ A @ (semiri1314217659103216013at_int @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (semiri1406184849735516958ct_int @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8935_gbinomial__Suc)). 159.59/70.60 thf(17613,plain,((! [A:int,B:nat]: ((gbinomial_int @ A @ (suc @ B)) = (divide_divide_int @ (groups705719431365010083at_int @ (^ [C:nat]: (minus_minus_int @ A @ (semiri1314217659103216013at_int @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (semiri1406184849735516958ct_int @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2907])). 159.59/70.60 thf(8075,axiom,((! [A:nat]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_nat @ (times_times_nat @ A @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5625_power3__eq__cube)). 159.59/70.60 thf(36073,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)],[8075])). 159.59/70.60 thf(5077,axiom,(((num_of_nat @ zero_zero_nat) = one)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9786_num__of__nat_Osimps_I1_J)). 159.59/70.61 thf(24842,plain,(((num_of_nat @ zero_zero_nat) = one)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5077])). 159.59/70.61 thf(4059,axiom,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ B @ A) = bot_bot_set_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3332_atLeastatMost__empty)). 159.59/70.61 thf(21281,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)],[4059])). 159.59/70.61 thf(1282,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > real),D:real]: ((((! [E:extended_enat,F:extended_enat]: ((ord_less_real @ (C @ E) @ (C @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_real @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2874_ord__less__eq__subst)). 159.59/70.61 thf(12394,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > real),D:real]: (((! [E:extended_enat,F:extended_enat]: ((ord_less_real @ (C @ E) @ (C @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_real @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282])). 159.59/70.61 thf(6254,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/sandbox/benchmark/theBenchmark.p',fact_4896_neg__one__even__power)). 159.59/70.61 thf(29264,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)],[6254])). 159.59/70.61 thf(1941,axiom,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5190_neg__numeral__less__one)). 159.59/70.61 thf(14515,plain,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1941])). 159.59/70.61 thf(5038,axiom,((! [A:nat]: ((modulo364778990260209775nteger @ one_one_Code_integer @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) = (zero_n356916108424825756nteger @ (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4383_one__mod__2__pow__eq)). 159.59/70.61 thf(24680,plain,((! [A:nat]: ((modulo364778990260209775nteger @ one_one_Code_integer @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) = (zero_n356916108424825756nteger @ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5038])). 159.59/70.61 thf(3918,axiom,((! [A:int,B:real]: ((cos_complex @ (times_times_complex @ (ring_17405671764205052669omplex @ A) @ (real_V4546457046886955230omplex @ B))) = (real_V4546457046886955230omplex @ (cos_real @ (times_times_real @ (ring_1_of_int_real @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7768_cos__int__times__real)). 159.59/70.61 thf(20858,plain,((! [A:int,B:real]: ((cos_complex @ (times_times_complex @ (ring_17405671764205052669omplex @ A) @ (real_V4546457046886955230omplex @ B))) = (real_V4546457046886955230omplex @ (cos_real @ (times_times_real @ (ring_1_of_int_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3918])). 159.59/70.61 thf(4364,axiom,((! [A:num]: ~ (ord_le72135733267957522d_enat @ (numera1916890842035813515d_enat @ A) @ zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2008_not__numeral__less__zero)). 159.59/70.61 thf(22229,plain,((! [A:num]: ~ (ord_le72135733267957522d_enat @ (numera1916890842035813515d_enat @ A) @ zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4364])). 159.59/70.61 thf(4108,axiom,(((semiri8010041392384452111omplex @ zero_zero_nat) = zero_zero_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6499_of__nat__0)). 159.59/70.61 thf(21430,plain,(((semiri8010041392384452111omplex @ zero_zero_nat) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4108])). 159.59/70.61 thf(8152,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (B = C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2782_ord__less__eq__trans)). 159.59/70.61 thf(36322,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (B = C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8152])). 159.59/70.61 thf(5000,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/sandbox/benchmark/theBenchmark.p',fact_1479_mult__cancel__right)). 159.59/70.61 thf(24558,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)],[5000])). 159.59/70.61 thf(2649,axiom,((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6779_minus__pi__half__less__zero)). 159.59/70.61 thf(16789,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)],[2649])). 159.59/70.61 thf(520,axiom,((cos_real = (^ [A:real]: (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (cos_coeff @ B) @ (power_power_real @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9269_cos__def)). 159.59/70.61 thf(9909,plain,(((cos_real) = (^ [A:real]: (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (cos_coeff @ B) @ (power_power_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[520])). 159.59/70.61 thf(552,axiom,(((divide6298287555418463151nteger @ one_one_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1786_one__div__two__eq__zero)). 159.59/70.61 thf(10010,plain,(((divide6298287555418463151nteger @ one_one_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[552])). 159.59/70.61 thf(5940,axiom,((! [A:set_nat,B:(set_nat > $o),C:(nat > nat)]: ((finite_finite_nat @ A) => ((B @ bot_bot_set_nat) => ((B @ A) <= (! [D:nat,E:set_nat]: (((! [F:nat]: ((member_nat @ F @ E) => (ord_less_eq_nat @ (C @ F) @ (C @ D)))) => ((B @ E) => (B @ (insert_nat @ D @ E)))) <= (finite_finite_nat @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6227_finite__ranking__induct)). 159.59/70.61 thf(28213,plain,((! [A:set_nat,B:(set_nat > $o),C:(nat > nat)]: ((finite_finite_nat @ A) => ((B @ bot_bot_set_nat) => ((B @ A) | ~ (! [D:nat,E:set_nat]: (((! [F:nat]: ((member_nat @ F @ E) => (ord_less_eq_nat @ (C @ F) @ (C @ D)))) => ((B @ E) => (B @ (insert_nat @ D @ E)))) | ~ (finite_finite_nat @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5940])). 159.59/70.61 thf(4910,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_real @ (power_power_real @ C @ A) @ (groups6591440286371151544t_real @ (power_power_real @ C) @ (set_ord_atMost_nat @ (minus_minus_nat @ B @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8890_sum__power__shift)). 159.59/70.61 thf(24224,plain,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((groups6591440286371151544t_real @ (power_power_real @ C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_real @ (power_power_real @ C @ A) @ (groups6591440286371151544t_real @ (power_power_real @ C) @ (set_ord_atMost_nat @ (minus_minus_nat @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4910])). 159.59/70.61 thf(2626,axiom,((! [A:nat]: ((bit_se2000444600071755411sk_int @ (suc @ A)) = (bit_se1409905431419307370or_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (bit_se2000444600071755411sk_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6086_mask__Suc__exp)). 159.59/70.61 thf(16712,plain,((! [A:nat]: ((bit_se2000444600071755411sk_int @ (suc @ A)) = (bit_se1409905431419307370or_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (bit_se2000444600071755411sk_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2626])). 159.59/70.61 thf(2070,axiom,((! [A:complex]: ((real_V2046097035970521341omplex @ one_one_real @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9190_scaleR__one)). 159.59/70.61 thf(14923,plain,((! [A:complex]: ((real_V2046097035970521341omplex @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2070])). 159.59/70.61 thf(3043,axiom,((! [A:real,B:(nat > real),C:real]: (((sums_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ (times_times_real @ A @ C)) = (sums_real @ B @ C)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7915_sums__mult__iff)). 159.59/70.61 thf(18030,plain,((! [A:real,B:(nat > real),C:real]: (((sums_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ (times_times_real @ A @ C)) = (sums_real @ (B) @ C)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3043])). 159.59/70.61 thf(2837,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ A) <= (A = (times_times_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3938_dvdI)). 159.59/70.61 thf(17371,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ B @ A) | ~ (A = (times_times_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2837])). 159.59/70.61 thf(2761,axiom,((minus_minus_real = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5128_minus__real__def)). 159.59/70.61 thf(17149,plain,(((minus_minus_real) = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2761])). 159.59/70.61 thf(1343,axiom,((~ (ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2124_not__one__less__zero)). 159.59/70.61 thf(12589,plain,((~ (ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343])). 159.59/70.61 thf(6619,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) != zero_zero_nat) => ((A != zero_zero_nat) & (B != zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1871_mult__not__zero)). 159.59/70.61 thf(30667,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)],[6619])). 159.59/70.61 thf(6803,axiom,((! [A:(product_prod_nat_nat > nat)]: ((produc6842872674320459806at_nat @ (^ [B:nat,C:nat]: (A @ (product_Pair_nat_nat @ B @ C)))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5008_case__prod__eta)). 159.59/70.61 thf(31453,plain,((! [A:(product_prod_nat_nat > nat)]: ((produc6842872674320459806at_nat @ (^ [B:nat,C:nat]: (A @ (product_Pair_nat_nat @ B @ C)))) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6803])). 159.59/70.61 thf(6907,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/sandbox/benchmark/theBenchmark.p',fact_3130_dual__order_Ostrict__trans2)). 159.59/70.61 thf(31879,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)],[6907])). 159.59/70.61 thf(729,axiom,((! [A:int,B:real]: ((plus_plus_int @ A @ (archim6058952711729229775r_real @ B)) = (archim6058952711729229775r_real @ (plus_plus_real @ (ring_1_of_int_real @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8228_int__add__floor)). 159.59/70.61 thf(10606,plain,((! [A:int,B:real]: ((plus_plus_int @ A @ (archim6058952711729229775r_real @ B)) = (archim6058952711729229775r_real @ (plus_plus_real @ (ring_1_of_int_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[729])). 159.59/70.61 thf(5082,axiom,((! [A:nat]: ((modulo_modulo_nat @ A @ one_one_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3404_mod__by__1)). 159.59/70.61 thf(24857,plain,((! [A:nat]: ((modulo_modulo_nat @ A @ one_one_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5082])). 159.59/70.61 thf(6139,axiom,((! [A:num]: ((abs_abs_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5389_abs__numeral)). 159.59/70.61 thf(28882,plain,((! [A:num]: ((abs_abs_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6139])). 159.59/70.61 thf(41,axiom,((! [A:real]: (((real_V1803761363581548252l_real @ A) = one_one_real) = (A = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7325_of__real__eq__1__iff)). 159.59/70.61 thf(8374,plain,((! [A:real]: (((real_V1803761363581548252l_real @ A) = one_one_real) = (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[41])). 159.59/70.61 thf(3392,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_nat @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2906_order__less__subst2)). 159.59/70.61 thf(19155,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_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3392])). 159.59/70.61 thf(1349,axiom,((! [A:nat]: ((groups7501900531339628137nteger @ semiri4939895301339042750nteger @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ one_one_Code_integer)) @ (numera6620942414471956472nteger @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7841_gauss__sum__from__Suc__0)). 159.59/70.61 thf(12606,plain,((! [A:nat]: ((groups7501900531339628137nteger @ (semiri4939895301339042750nteger) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ one_one_Code_integer)) @ (numera6620942414471956472nteger @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349])). 159.59/70.61 thf(8000,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1113_add__right__imp__eq)). 159.59/70.61 thf(35816,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)],[8000])). 159.59/70.61 thf(6758,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) | (A = B)) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_less__or__eq__imp__le)). 159.59/70.61 thf(31302,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)],[6758])). 159.59/70.61 thf(8251,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_mult__numeral__1)). 159.59/70.61 thf(36781,plain,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8251])). 159.59/70.61 thf(4836,axiom,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o),C:nat]: ((! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)) => (B @ D))) => ((B @ (nth_VEBT_VEBT @ A @ C)) <= (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_inthall)). 159.59/70.61 thf(23988,plain,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o),C:nat]: ((! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)) => (B @ D))) => ((B @ (nth_VEBT_VEBT @ A @ C)) | ~ (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4836])). 159.59/70.61 thf(2318,axiom,((ord_less_int = (^ [A:int,B:int]: (ord_less_int @ (minus_minus_int @ A @ B) @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2147_less__iff__diff__less__0)). 159.59/70.61 thf(15706,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)],[2318])). 159.59/70.61 thf(602,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/sandbox/benchmark/theBenchmark.p',fact_9563_concat__bit__def)). 159.59/70.61 thf(10174,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)],[602])). 159.59/70.61 thf(4372,axiom,((! [A:int]: (((plus_plus_int @ A @ A) = zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3376_double__eq__0__iff)). 159.59/70.61 thf(22254,plain,((! [A:int]: (((plus_plus_int @ A @ A) = zero_zero_int) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4372])). 159.59/70.61 thf(5073,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]: ((ord_less_num @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:num]: ! [F:num]: ((ord_less_num @ F @ E) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4464_minf_I2_J)). 159.59/70.61 thf(24823,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]: ((ord_less_num @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:num]: ! [F:num]: ((ord_less_num @ F @ E) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5073])). 159.59/70.61 thf(2346,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/sandbox/benchmark/theBenchmark.p',fact_7184_cos__diff__cos)). 159.59/70.61 thf(15787,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)],[2346])). 159.59/70.61 thf(869,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & ((power_power_real @ C @ (suc @ B)) = A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3001_realpow__pos__nth2)). 159.59/70.61 thf(11051,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & ((power_power_real @ C @ (suc @ B)) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[869])). 159.59/70.61 thf(530,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((ord_less_eq_set_nat @ A @ B) => ((finite_finite_nat @ B) => ((groups3539618377306564664at_int @ C @ B) = (plus_plus_int @ (groups3539618377306564664at_int @ C @ (minus_minus_set_nat @ B @ A)) @ (groups3539618377306564664at_int @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7639_sum_Osubset__diff)). 159.59/70.61 thf(9938,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((ord_less_eq_set_nat @ A @ B) => ((finite_finite_nat @ B) => ((groups3539618377306564664at_int @ (C) @ B) = (plus_plus_int @ (groups3539618377306564664at_int @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups3539618377306564664at_int @ (C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[530])). 159.59/70.61 thf(3543,axiom,((! [A:real,B:real]: ((((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)))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6872_sin__monotone__2pi)). 159.59/70.61 thf(19621,plain,((! [A:real,B:real]: (((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)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3543])). 159.59/70.61 thf(4914,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((((vEBT_vebt_pred @ A @ C) = none_nat) = ((collect_nat @ (^ [D:nat]: ((vEBT_vebt_member @ A @ D) & (ord_less_nat @ D @ C)))) = bot_bot_set_nat)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1457_pred__empty)). 159.59/70.61 thf(24237,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((((vEBT_vebt_pred @ A @ C) = none_nat) = ((collect_nat @ (^ [D:nat]: ((vEBT_vebt_member @ A @ D) & (ord_less_nat @ D @ C)))) = bot_bot_set_nat)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4914])). 159.59/70.61 thf(2227,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((times_times_int @ A @ (divide_divide_int @ B @ A)) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3841_dvd__mult__div__cancel)). 159.59/70.61 thf(15441,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ B) => ((times_times_int @ A @ (divide_divide_int @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2227])). 159.59/70.61 thf(990,axiom,((! [A:num]: ((numera1916890842035813515d_enat @ (bit1 @ A)) = (plus_p3455044024723400733d_enat @ (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ A)) @ one_on7984719198319812577d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5587_numeral__Bit1)). 159.59/70.61 thf(11416,plain,((! [A:num]: ((numera1916890842035813515d_enat @ (bit1 @ A)) = (plus_p3455044024723400733d_enat @ (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ A)) @ one_on7984719198319812577d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[990])). 159.59/70.61 thf(6440,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = ((B != A) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2756_nle__le)). 159.59/70.61 thf(30013,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)],[6440])). 159.59/70.61 thf(1545,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/sandbox/benchmark/theBenchmark.p',fact_2282_div__positive)). 159.59/70.61 thf(13275,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)],[1545])). 159.59/70.61 thf(4762,axiom,((! [A:nat]: ((bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6661_bit__Suc__0__iff)). 159.59/70.61 thf(23713,plain,((! [A:nat]: ((bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4762])). 159.59/70.61 thf(1170,axiom,((! [A:complex,B:complex]: (dvd_dvd_complex @ A @ (times_times_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3960_dvd__triv__left)). 159.59/70.61 thf(12003,plain,((! [A:complex,B:complex]: (dvd_dvd_complex @ A @ (times_times_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170])). 159.59/70.61 thf(5689,axiom,((! [A:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ one)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3500_cong__exp__iff__simps_I1_J)). 159.59/70.61 thf(27092,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)],[5689])). 159.59/70.61 thf(4716,axiom,(((size_size_option_nat @ none_nat) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2200_option_Osize_I3_J)). 159.59/70.61 thf(23551,plain,(((size_size_option_nat @ none_nat) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4716])). 159.59/70.61 thf(7749,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ bot_bot_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3283_bot_Oextremum__strict)). 159.59/70.61 thf(35039,plain,((! [A:nat]: ~ (ord_less_nat @ A @ bot_bot_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7749])). 159.59/70.61 thf(4598,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_802_diff__diff__cancel)). 159.59/70.61 thf(23140,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)],[4598])). 159.59/70.61 thf(6696,axiom,((! [A:num,B:num]: (~ (ord_less_eq_num @ B @ A) | ~ (ord_less_eq_num @ A @ B) | (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3659_verit__la__disequality)). 159.59/70.61 thf(30997,plain,((! [A:num,B:num]: (~ (ord_less_eq_num @ B @ A) | ~ (ord_less_eq_num @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6696])). 159.59/70.61 thf(6119,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ A @ B @ C @ D) @ E) => (B = E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_deg__deg__n)). 159.59/70.61 thf(28815,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ A @ B @ C @ D) @ E) => (B = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6119])). 159.59/70.61 thf(5305,axiom,((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4205_odd__one)). 159.59/70.61 thf(25644,plain,((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5305])). 159.59/70.61 thf(7433,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C))) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1209_diff__mono)). 159.59/70.61 thf(33930,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C))) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7433])). 159.59/70.61 thf(1373,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/sandbox/benchmark/theBenchmark.p',fact_8083_fact__fact__dvd__fact)). 159.59/70.61 thf(12713,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)],[1373])). 159.59/70.61 thf(4545,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_num @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3261_order__le__imp__less__or__eq)). 159.59/70.61 thf(22955,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)],[4545])). 159.59/70.61 thf(7905,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/sandbox/benchmark/theBenchmark.p',fact_155_left__add__twice)). 159.59/70.61 thf(35525,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)],[7905])). 159.59/70.61 thf(4823,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D))) => (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_full__nat__induct)). 159.59/70.61 thf(23941,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4823])). 159.59/70.61 thf(3413,axiom,((! [A:complex,B:complex,C:complex]: (((B = (times_times_complex @ C @ A)) => ((divide1717551699836669952omplex @ B @ A) = C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2173_divide__eq__imp)). 159.59/70.61 thf(19226,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)],[3413])). 159.59/70.61 thf(3245,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4437_pinf_I3_J)). 159.59/70.61 thf(18688,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3245])). 159.59/70.61 thf(4943,axiom,(((('?') @ option_nat) = (^ [A:(option_nat > $o)]: (? [B:nat]: (A @ (some_nat @ B)) | (A @ none_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_split__option__ex)). 159.59/70.61 thf(24327,plain,(((('?') @ option_nat) = (^ [A:(option_nat > $o)]: (? [B:nat]: (A @ (some_nat @ B)) | (A @ none_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4943])). 159.59/70.61 thf(3104,axiom,((! [A:set_nat,B:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((((groups7108830773950497114d_enat @ B @ A) = zero_z5237406670263579293d_enat) = (! [C:nat]: ((member_nat @ C @ A) => ((B @ C) = zero_z5237406670263579293d_enat)))) <= (! [C:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ C)) <= (member_nat @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7468_sum__nonneg__eq__0__iff)). 159.59/70.61 thf(18236,plain,((! [A:set_nat,B:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((((groups7108830773950497114d_enat @ (B) @ A) = zero_z5237406670263579293d_enat) = (! [C:nat]: ((member_nat @ C @ A) => ((B @ C) = zero_z5237406670263579293d_enat)))) | ~ (! [C:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ C)) | ~ (member_nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3104])). 159.59/70.61 thf(1095,axiom,((! [A:complex,B:(nat > complex),C:complex]: (((sums_complex @ (^ [D:nat]: (times_times_complex @ A @ (B @ D))) @ (times_times_complex @ A @ C)) = (sums_complex @ B @ C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7914_sums__mult__iff)). 159.59/70.61 thf(11760,plain,((! [A:complex,B:(nat > complex),C:complex]: (((sums_complex @ (^ [D:nat]: (times_times_complex @ A @ (B @ D))) @ (times_times_complex @ A @ C)) = (sums_complex @ (B) @ C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095])). 159.59/70.61 thf(7235,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) <= (A = (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1900_nat_OdiscI)). 159.59/70.61 thf(33270,plain,((! [A:nat,B:nat]: (~ (A = zero_zero_nat) | ~ (A = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7235])). 159.59/70.61 thf(4809,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/sandbox/benchmark/theBenchmark.p',fact_6120_exp__double)). 159.59/70.61 thf(23864,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)],[4809])). 159.59/70.61 thf(7683,axiom,(((divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))) = na)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__C9_C)). 159.59/70.61 thf(34805,plain,(((divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))) = na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7683])). 159.59/70.61 thf(2038,axiom,(((sin_complex @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one)))) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7377_sin__of__real__pi__half)). 159.59/70.61 thf(14830,plain,(((sin_complex @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one)))) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2038])). 159.59/70.61 thf(1,conjecture,((ord_less_nat @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)). 159.59/70.61 thf(2,negated_conjecture,((~ (ord_less_nat @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)))),inference(neg_conjecture,[status(cth)],[1])). 159.59/70.61 thf(8257,plain,((~ (ord_less_nat @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 159.59/70.61 thf(5906,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ B) = (((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ A @ one_one_int)) & ((ord_less_int @ B @ zero_zero_int) => (ord_less_eq_int @ one_one_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2419_mult__le__cancel__right2)). 159.59/70.61 thf(28089,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ B) = (((ord_less_int @ zero_zero_int @ B) => (ord_less_eq_int @ A @ one_one_int)) & ((ord_less_int @ B @ zero_zero_int) => (ord_less_eq_int @ one_one_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5906])). 159.59/70.61 thf(7989,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1603_add__less__same__cancel2)). 159.59/70.61 thf(35778,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)],[7989])). 159.59/70.61 thf(5885,axiom,((! [A:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5172_not__numeral__le__neg__one)). 159.59/70.61 thf(28005,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)],[5885])). 159.59/70.61 thf(4462,axiom,((! [A:num,B:num]: ((ord_less_num @ B @ A) <= (~ (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3064_not__le__imp__less)). 159.59/70.61 thf(22585,plain,((! [A:num,B:num]: ((ord_less_num @ B @ A) | (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4462])). 159.59/70.61 thf(377,axiom,((! [A:real]: (summable_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (real_V1485227260804924795R_real @ (sin_coeff @ B) @ (power_power_real @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9271_summable__norm__sin)). 159.59/70.61 thf(9420,plain,((! [A:real]: (summable_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (real_V1485227260804924795R_real @ (sin_coeff @ B) @ (power_power_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])). 159.59/70.61 thf(5300,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/sandbox/benchmark/theBenchmark.p',fact_1259_right__diff__distrib_H)). 159.59/70.61 thf(25615,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)],[5300])). 159.59/70.61 thf(7674,axiom,((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_060_A2_A_094_Adeg_092_060close_062)). 159.59/70.61 thf(34780,plain,((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7674])). 159.59/70.61 thf(195,axiom,((! [A:code_integer,B:code_integer]: ((divide6298287555418463151nteger @ (modulo364778990260209775nteger @ A @ B) @ B) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3408_bits__mod__div__trivial)). 159.59/70.61 thf(8849,plain,((! [A:code_integer,B:code_integer]: ((divide6298287555418463151nteger @ (modulo364778990260209775nteger @ A @ B) @ B) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 159.59/70.61 thf(2763,axiom,((! [A:(nat > real)]: ((summable_real @ A) => ((! [B:nat]: (ord_less_real @ zero_zero_real @ (A @ B))) => (ord_less_real @ zero_zero_real @ (suminf_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7059_suminf__pos)). 159.59/70.61 thf(17154,plain,((! [A:(nat > real)]: ((summable_real @ (A)) => ((! [B:nat]: (ord_less_real @ zero_zero_real @ (A @ B))) => (ord_less_real @ zero_zero_real @ (suminf_real @ (A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2763])). 159.59/70.61 thf(3595,axiom,((! [A:code_integer,B:nat,C:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C))) = (((ord_less_eq_nat @ B @ C) & (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (minus_minus_nat @ C @ B))))) | ((power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C) = zero_z3403309356797280102nteger) | (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4277_even__mult__exp__div__exp__iff)). 159.59/70.61 thf(19795,plain,((! [A:code_integer,B:nat,C:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C))) = (((ord_less_eq_nat @ B @ C) & (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (minus_minus_nat @ C @ B))))) | ((power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C) = zero_z3403309356797280102nteger) | (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3595])). 159.59/70.61 thf(2148,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/sandbox/benchmark/theBenchmark.p',fact_5768_of__int__le__iff)). 159.59/70.61 thf(15182,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)],[2148])). 159.59/70.61 thf(7250,axiom,((! [A:nat]: ((power_power_nat @ one_one_nat @ A) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_power__one)). 159.59/70.61 thf(33322,plain,((! [A:nat]: ((power_power_nat @ one_one_nat @ A) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7250])). 159.59/70.61 thf(7971,axiom,((! [A:num]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bitM @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5919_odd__numeral__BitM)). 159.59/70.61 thf(35727,plain,((! [A:num]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7971])). 159.59/70.61 thf(439,axiom,((zero_z3403309356797280102nteger != (uminus1351360451143612070nteger @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5071_zero__neq__neg__one)). 159.59/70.61 thf(9629,plain,((~ (zero_z3403309356797280102nteger = (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[439])). 159.59/70.61 thf(1684,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)) & ((ord_less_eq_int @ B @ C) <= (ord_less_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2256_mult__le__cancel__left)). 159.59/70.61 thf(13704,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)) & ((ord_less_eq_int @ B @ C) | ~ (ord_less_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684])). 159.59/70.61 thf(5663,axiom,((! [A:nat,B:nat]: (((((bit_se2925701944663578781it_nat @ B @ A) = (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((bit_se2925701944663578781it_nat @ B @ A) = zero_zero_nat))) <= ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5340_stable__imp__take__bit__eq)). 159.59/70.61 thf(26991,plain,((! [A:nat,B:nat]: (((((bit_se2925701944663578781it_nat @ B @ A) = (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ one_one_nat)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((bit_se2925701944663578781it_nat @ B @ A) = zero_zero_nat))) | ~ ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5663])). 159.59/70.61 thf(3792,axiom,((! [A:real,B:real,C:(real > (real > $o))]: ((((C @ A @ B) <= (! [D:real]: ((ord_less_eq_real @ A @ D) => ((? [E:real]: (! [F:real,G:real]: ((C @ F @ G) <= ((ord_less_eq_real @ F @ D) & (ord_less_eq_real @ D @ G) & (ord_less_real @ (minus_minus_real @ G @ F) @ E))) & (ord_less_real @ zero_zero_real @ E))) <= (ord_less_eq_real @ D @ B))))) <= (! [D:real,E:real,F:real]: ((C @ D @ E) => ((((C @ D @ F) <= (ord_less_eq_real @ E @ F)) <= (ord_less_eq_real @ D @ E)) <= (C @ E @ F))))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3380_Bolzano)). 159.59/70.61 thf(20445,plain,((! [A:real,B:real,C:(real > (real > $o))]: ((C @ A @ B) | ~ (! [D:real]: ((ord_less_eq_real @ A @ D) => (? [E:real]: (! [F:real,G:real]: ((C @ F @ G) | ~ ((ord_less_eq_real @ F @ D) & (ord_less_eq_real @ D @ G) & (ord_less_real @ (minus_minus_real @ G @ F) @ E))) & (ord_less_real @ zero_zero_real @ E)) | ~ (ord_less_eq_real @ D @ B)))) | ~ (! [D:real,E:real,F:real]: ((C @ D @ E) => ((C @ D @ F) | ~ (ord_less_eq_real @ E @ F) | ~ (ord_less_eq_real @ D @ E) | ~ (C @ E @ F)))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3792])). 159.59/70.61 thf(2634,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ A @ (uminus1482373934393186551omplex @ B)) = (plus_plus_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4708_diff__minus__eq__add)). 159.59/70.61 thf(16740,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ A @ (uminus1482373934393186551omplex @ B)) = (plus_plus_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2634])). 159.59/70.61 thf(3360,axiom,((! [A:int,B:int,C:nat,D:nat]: ((dvd_dvd_int @ A @ B) => ((ord_less_eq_nat @ C @ D) => (dvd_dvd_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4111_dvd__power__le)). 159.59/70.61 thf(19052,plain,((! [A:int,B:int,C:nat,D:nat]: ((dvd_dvd_int @ A @ B) => ((ord_less_eq_nat @ C @ D) => (dvd_dvd_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3360])). 159.59/70.61 thf(914,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (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) @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6030_or__numerals_I7_J)). 159.59/70.61 thf(11183,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (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) @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[914])). 159.59/70.61 thf(4525,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/sandbox/benchmark/theBenchmark.p',fact_1181_add__mono__thms__linordered__semiring_I3_J)). 159.59/70.61 thf(22827,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)],[4525])). 159.59/70.61 thf(1724,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/sandbox/benchmark/theBenchmark.p',fact_5121_dvd__neg__div)). 159.59/70.61 thf(13826,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)],[1724])). 159.59/70.61 thf(7128,axiom,((ord_less_eq_num = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3071_order_Oorder__iff__strict)). 159.59/70.61 thf(32863,plain,(((ord_less_eq_num) = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7128])). 159.59/70.61 thf(1702,axiom,((! [A:real]: ((ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ (plus_plus_real @ A @ (inverse_inverse_real @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9144_plus__inverse__ge__2)). 159.59/70.61 thf(13754,plain,((! [A:real]: ((ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ (plus_plus_real @ A @ (inverse_inverse_real @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702])). 159.59/70.61 thf(2357,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((divide_divide_int @ B @ A) = C) = (B = (times_times_int @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4158_unit__eq__div1)). 159.59/70.61 thf(15819,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((divide_divide_int @ B @ A) = C) = (B = (times_times_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2357])). 159.59/70.61 thf(1058,axiom,(((plus_plus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ one_one_complex)) = zero_zero_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4739_add__neg__numeral__special_I7_J)). 159.59/70.61 thf(11641,plain,(((plus_plus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ one_one_complex)) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058])). 159.59/70.61 thf(9,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/sandbox/benchmark/theBenchmark.p',fact_3320_set__bit__nonnegative__int__iff)). 159.59/70.61 thf(8278,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)],[9])). 159.59/70.61 thf(3681,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ A @ (plus_plus_real @ C @ B)) = (dvd_dvd_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3986_dvd__add__left__iff)). 159.59/70.61 thf(20074,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ A @ (plus_plus_real @ C @ B)) = (dvd_dvd_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3681])). 159.59/70.61 thf(3079,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/sandbox/benchmark/theBenchmark.p',fact_1374_less__add__iff1)). 159.59/70.61 thf(18143,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)],[3079])). 159.59/70.61 thf(930,axiom,((! [A:int,B:int]: (((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) <= (ord_less_int @ zero_zero_int @ B)) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2100_mult__neg__pos)). 159.59/70.61 thf(11232,plain,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) | ~ (ord_less_int @ zero_zero_int @ B) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[930])). 159.59/70.61 thf(7650,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/sandbox/benchmark/theBenchmark.p',fact_4864_Power_Oring__1__class_Opower__minus__even)). 159.59/70.61 thf(34705,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)],[7650])). 159.59/70.61 thf(1883,axiom,((! [A:real]: ((((ord_less_eq_real @ zero_zero_real @ (arccos @ A)) & (ord_less_eq_real @ (arccos @ A) @ pi) & ((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/sandbox/benchmark/theBenchmark.p',fact_7791_arccos)). 159.59/70.61 thf(14331,plain,((! [A:real]: (((ord_less_eq_real @ zero_zero_real @ (arccos @ A)) & (ord_less_eq_real @ (arccos @ A) @ pi) & ((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)],[1883])). 159.59/70.61 thf(2386,axiom,((! [A:real,B:real,C:(real > extended_enat),D:extended_enat]: ((ord_less_real @ A @ B) => ((ord_le2932123472753598470d_enat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3244_order__less__le__subst2)). 159.59/70.61 thf(15911,plain,((! [A:real,B:real,C:(real > extended_enat),D:extended_enat]: ((ord_less_real @ A @ B) => ((ord_le2932123472753598470d_enat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2386])). 159.59/70.61 thf(6934,axiom,((! [A:(product_prod_num_num > $o),B:product_prod_num_num]: ((A @ B) <= (! [C:num,D:num]: (A @ (product_Pair_num_num @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3678_prod__cases)). 159.59/70.61 thf(31981,plain,((! [A:(product_prod_num_num > $o),B:product_prod_num_num]: ((A @ B) | ~ (! [C:num,D:num]: (A @ (product_Pair_num_num @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6934])). 159.59/70.61 thf(5955,axiom,((! [A:complex,B:nat,C:nat]: ((A != zero_zero_complex) => (((power_power_complex @ A @ (minus_minus_nat @ C @ B)) = (divide1717551699836669952omplex @ (power_power_complex @ A @ C) @ (power_power_complex @ A @ B))) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2476_power__diff)). 159.59/70.61 thf(28298,plain,((! [A:complex,B:nat,C:nat]: ((~ (A = zero_zero_complex)) => (((power_power_complex @ A @ (minus_minus_nat @ C @ B)) = (divide1717551699836669952omplex @ (power_power_complex @ A @ C) @ (power_power_complex @ A @ B))) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5955])). 159.59/70.61 thf(3147,axiom,((! [A:int,B:int]: (((((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)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3570_mod__double__modulus)). 159.59/70.61 thf(18380,plain,((! [A:int,B:int]: (((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) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3147])). 159.59/70.61 thf(4872,axiom,((! [A:real,B:nat,C:nat]: ((A != zero_zero_real) => (((power_power_real @ A @ (minus_minus_nat @ C @ B)) = (times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ (inverse_inverse_real @ A) @ B))) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9116_power__diff__conv__inverse)). 159.59/70.61 thf(24095,plain,((! [A:real,B:nat,C:nat]: ((~ (A = zero_zero_real)) => (((power_power_real @ A @ (minus_minus_nat @ C @ B)) = (times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ (inverse_inverse_real @ A) @ B))) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4872])). 159.59/70.61 thf(5049,axiom,((! [A:int,B:int]: ((A = (times_times_int @ A @ B)) = ((A = zero_zero_int) | (B = one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1625_mult__cancel__left1)). 159.59/70.61 thf(24740,plain,((! [A:int,B:int]: ((A = (times_times_int @ A @ B)) = ((A = zero_zero_int) | (B = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5049])). 159.59/70.61 thf(2997,axiom,(((neg_nu5851722552734809277nc_int @ zero_zero_int) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5798_dbl__inc__simps_I2_J)). 159.59/70.61 thf(17894,plain,(((neg_nu5851722552734809277nc_int @ zero_zero_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2997])). 159.59/70.61 thf(7694,axiom,((! [A:nat]: (((divide_divide_nat @ (suc @ 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/sandbox/benchmark/theBenchmark.p',fact_3885_even__Suc__div__two)). 159.59/70.61 thf(34837,plain,((! [A:nat]: (((divide_divide_nat @ (suc @ 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)],[7694])). 159.59/70.61 thf(5403,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1721_zero__less__diff)). 159.59/70.61 thf(26073,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)],[5403])). 159.59/70.61 thf(1406,axiom,((! [A:num]: ((semiri4939895301339042750nteger @ (numeral_numeral_nat @ A)) = (numera6620942414471956472nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6518_of__nat__numeral)). 159.59/70.61 thf(12837,plain,((! [A:num]: ((semiri4939895301339042750nteger @ (numeral_numeral_nat @ A)) = (numera6620942414471956472nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406])). 159.59/70.61 thf(6144,axiom,((! [A:num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ one_one_real)) = (A != one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4832_neg__numeral__less__neg__one__iff)). 159.59/70.61 thf(28897,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)],[6144])). 159.59/70.61 thf(3871,axiom,((! [A:int,B:int,C:int,D:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) <= (dvd_dvd_int @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3968_mult__dvd__mono)). 159.59/70.61 thf(20719,plain,((! [A:int,B:int,C:int,D:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) | ~ (dvd_dvd_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3871])). 159.59/70.61 thf(111,axiom,((! [A:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ A) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4693_ab__left__minus)). 159.59/70.61 thf(8590,plain,((! [A:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ A) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 159.59/70.61 thf(5551,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5949_zero__and__eq)). 159.59/70.61 thf(26606,plain,((! [A:nat]: ((bit_se727722235901077358nd_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5551])). 159.59/70.61 thf(708,axiom,((! [A:extended_enat,B:extended_enat]: ((B != A) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2833_dual__order_Ostrict__implies__not__eq)). 159.59/70.61 thf(10534,plain,((! [A:extended_enat,B:extended_enat]: (~ (B = A) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[708])). 159.59/70.61 thf(4784,axiom,(((neg_nu7009210354673126013omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4888_dbl__simps_I4_J)). 159.59/70.61 thf(23781,plain,(((neg_nu7009210354673126013omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4784])). 159.59/70.61 thf(1006,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/sandbox/benchmark/theBenchmark.p',fact_1461_maxt__corr__help__empty)). 159.59/70.61 thf(11463,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)],[1006])). 159.59/70.61 thf(2743,axiom,((! [A:nat,B:nat,C:nat]: (((semiri4939895301339042750nteger @ A) = (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ B) @ C)) = (A = (power_power_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6570_of__nat__power__eq__of__nat__cancel__iff)). 159.59/70.61 thf(17097,plain,((! [A:nat,B:nat,C:nat]: (((semiri4939895301339042750nteger @ A) = (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ B) @ C)) = (A = (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2743])). 159.59/70.61 thf(3089,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/sandbox/benchmark/theBenchmark.p',fact_507_field__sum__of__halves)). 159.59/70.61 thf(18190,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)],[3089])). 159.59/70.61 thf(7934,axiom,(((power_8040749407984259932d_enat @ one_on7984719198319812577d_enat @ (numeral_numeral_nat @ (bit0 @ one))) = one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_one__power2)). 159.59/70.61 thf(35611,plain,(((power_8040749407984259932d_enat @ one_on7984719198319812577d_enat @ (numeral_numeral_nat @ (bit0 @ one))) = one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7934])). 159.59/70.61 thf(5505,axiom,((! [A:nat,B:nat]: ((B = zero_zero_nat) <= ((plus_plus_nat @ A @ B) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1921_add__eq__self__zero)). 159.59/70.61 thf(26474,plain,((! [A:nat,B:nat]: ((B = zero_zero_nat) | ~ ((plus_plus_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5505])). 159.59/70.61 thf(5464,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2210_diff__add__0)). 159.59/70.61 thf(26321,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)],[5464])). 159.59/70.61 thf(1788,axiom,((! [A:int,B:int]: ((minus_minus_int @ A @ (uminus_uminus_int @ B)) = (plus_plus_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4707_diff__minus__eq__add)). 159.59/70.61 thf(14024,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)],[1788])). 159.59/70.61 thf(4824,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) @ B) & (ord_less_eq_nat @ (suc @ zero_zero_nat) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1761_one__le__mult__iff)). 159.59/70.61 thf(23945,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) @ B) & (ord_less_eq_nat @ (suc @ zero_zero_nat) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4824])). 159.59/70.61 thf(4592,axiom,((! [A:nat]: ((dvd_dvd_nat @ A @ (suc @ zero_zero_nat)) = (A = (suc @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3800_dvd__1__iff__1)). 159.59/70.61 thf(23108,plain,((! [A:nat]: ((dvd_dvd_nat @ A @ (suc @ zero_zero_nat)) = (A = (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4592])). 159.59/70.61 thf(393,axiom,((! [A:real]: (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (tanh_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5552_tanh__real__gt__neg1)). 159.59/70.61 thf(9480,plain,((! [A:real]: (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (tanh_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[393])). 159.59/70.61 thf(6656,axiom,((! [A:num]: ((size_num @ (bit0 @ A)) = (plus_plus_nat @ (size_num @ A) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4601_num_Osize__gen_I2_J)). 159.59/70.61 thf(30802,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)],[6656])). 159.59/70.61 thf(4128,axiom,((ord_le72135733267957522d_enat = (^ [A:extended_enat,B:extended_enat]: (~ (ord_le2932123472753598470d_enat @ B @ A) & (ord_le2932123472753598470d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3132_dual__order_Ostrict__iff__not)). 159.59/70.61 thf(21491,plain,(((ord_le72135733267957522d_enat) = (^ [A:extended_enat,B:extended_enat]: (~ (ord_le2932123472753598470d_enat @ B @ A) & (ord_le2932123472753598470d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4128])). 159.59/70.61 thf(4855,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/sandbox/benchmark/theBenchmark.p',fact_1564_mult__cancel2)). 159.59/70.61 thf(24045,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)],[4855])). 159.59/70.61 thf(6767,axiom,((! [A:nat]: (((A != zero_zero_nat) => ((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ A) = zero_z5237406670263579293d_enat)) & ((A = zero_zero_nat) => ((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ A) = one_on7984719198319812577d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1811_power__0__left)). 159.59/70.61 thf(31340,plain,((! [A:nat]: (((~ (A = zero_zero_nat)) => ((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ A) = zero_z5237406670263579293d_enat)) & ((A = zero_zero_nat) => ((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ A) = one_on7984719198319812577d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6767])). 159.59/70.61 thf(8054,axiom,((! [A:nat,B:nat,C:(vEBT_VEBT > $o),D:vEBT_VEBT]: ((ord_less_nat @ A @ B) => ((C @ (nth_VEBT_VEBT @ (replicate_VEBT_VEBT @ B @ D) @ A)) <= (C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4311_intind)). 159.59/70.61 thf(36002,plain,((! [A:nat,B:nat,C:(vEBT_VEBT > $o),D:vEBT_VEBT]: ((ord_less_nat @ A @ B) => ((C @ (nth_VEBT_VEBT @ (replicate_VEBT_VEBT @ B @ D) @ A)) | ~ (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8054])). 159.59/70.61 thf(940,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ one_one_int) => ((divide_divide_int @ C @ (times_times_int @ A @ B)) = (divide_divide_int @ (divide_divide_int @ C @ A) @ B))) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4173_is__unit__div__mult2__eq)). 159.59/70.61 thf(11264,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ one_one_int) => ((divide_divide_int @ C @ (times_times_int @ A @ B)) = (divide_divide_int @ (divide_divide_int @ C @ A) @ B))) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[940])). 159.59/70.61 thf(2500,axiom,((! [A:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ A) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5056_ab__group__add__class_Oab__left__minus)). 159.59/70.61 thf(16300,plain,((! [A:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2500])). 159.59/70.61 thf(1922,axiom,((! [A:complex,B:complex]: ((sin_complex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ (times_times_complex @ (sin_complex @ A) @ (cos_complex @ B)) @ (times_times_complex @ (cos_complex @ A) @ (sin_complex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7091_sin__diff)). 159.59/70.61 thf(14455,plain,((! [A:complex,B:complex]: ((sin_complex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ (times_times_complex @ (sin_complex @ A) @ (cos_complex @ B)) @ (times_times_complex @ (cos_complex @ A) @ (sin_complex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1922])). 159.59/70.61 thf(6892,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (times_times_int @ A @ B)) = (((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ B @ one_one_int)) & ((ord_less_eq_int @ one_one_int @ B) <= (ord_less_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2425_mult__le__cancel__left1)). 159.59/70.61 thf(31832,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (times_times_int @ A @ B)) = (((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ B @ one_one_int)) & ((ord_less_eq_int @ one_one_int @ B) | ~ (ord_less_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6892])). 159.59/70.61 thf(6780,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((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)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_nat__diff__add__eq1)). 159.59/70.61 thf(31385,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((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)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6780])). 159.59/70.61 thf(7092,axiom,((! [A:vEBT_VEBT]: ((~ (! [B:$o,C:$o]: (A != (vEBT_Leaf @ B @ C)))) <= (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ B @ C @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1822_VEBT_Oexhaust)). 159.59/70.61 thf(32710,plain,((! [A:vEBT_VEBT]: (~ (! [B:$o,C:$o]: ~ (A = (vEBT_Leaf @ B @ C))) | ~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ B @ C @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7092])). 159.59/70.61 thf(702,axiom,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_complex @ (groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_complex @ (C @ A) @ (groups2073611262835488442omplex @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7668_sum_OSuc__reindex__ivl)). 159.59/70.61 thf(10516,plain,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_complex @ (groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (plus_plus_complex @ (C @ A) @ (groups2073611262835488442omplex @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[702])). 159.59/70.61 thf(3121,axiom,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2011_not__numeral__less__zero)). 159.59/70.61 thf(18292,plain,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3121])). 159.59/70.61 thf(7215,axiom,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ A @ C) <= (B = C)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2739_ord__le__eq__trans)). 159.59/70.61 thf(33206,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ C) | ~ (B = C) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7215])). 159.59/70.61 thf(1528,axiom,((! [A:nat]: (exp_complex = (^ [B:complex]: (plus_plus_complex @ (groups2073611262835488442omplex @ (^ [C:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ C)) @ (power_power_complex @ B @ C))) @ (set_ord_lessThan_nat @ A)) @ (suminf_complex @ (^ [C:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (plus_plus_nat @ C @ A))) @ (power_power_complex @ B @ (plus_plus_nat @ C @ A)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9299_exp__first__terms)). 159.59/70.61 thf(13226,plain,((! [A:nat]: ((exp_complex) = (^ [B:complex]: (plus_plus_complex @ (groups2073611262835488442omplex @ (^ [C:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ C)) @ (power_power_complex @ B @ C))) @ (set_ord_lessThan_nat @ A)) @ (suminf_complex @ (^ [C:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (plus_plus_nat @ C @ A))) @ (power_power_complex @ B @ (plus_plus_nat @ C @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528])). 159.59/70.61 thf(3628,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ (plus_plus_int @ B @ C)) <= (dvd_dvd_int @ A @ C)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3983_dvd__add)). 159.59/70.61 thf(19905,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ C)) | ~ (dvd_dvd_int @ A @ C) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3628])). 159.59/70.61 thf(4114,axiom,((! [A:code_integer,B:nat]: (((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = A) => ((((bit_se1745604003318907178nteger @ B @ A) = zero_z3403309356797280102nteger) <= (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) & (((bit_se1745604003318907178nteger @ B @ A) = (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) @ one_one_Code_integer)) <= (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5338_stable__imp__take__bit__eq)). 159.59/70.61 thf(21447,plain,((! [A:code_integer,B:nat]: (((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = A) => ((((bit_se1745604003318907178nteger @ B @ A) = zero_z3403309356797280102nteger) | ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) & (((bit_se1745604003318907178nteger @ B @ A) = (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) @ one_one_Code_integer)) | (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4114])). 159.59/70.61 thf(2728,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((B = (divide6298287555418463151nteger @ C @ A)) = ((times_3573771949741848930nteger @ B @ A) = C)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4162_unit__eq__div2)). 159.59/70.61 thf(17049,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((B = (divide6298287555418463151nteger @ C @ A)) = ((times_3573771949741848930nteger @ B @ A) = C)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2728])). 159.59/70.61 thf(585,axiom,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (groups705719431365010083at_int @ (^ [C:nat]: (plus_plus_int @ A @ (semiri1314217659103216013at_int @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8881_pochhammer__Suc__prod)). 159.59/70.61 thf(10110,plain,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (groups705719431365010083at_int @ (^ [C:nat]: (plus_plus_int @ A @ (semiri1314217659103216013at_int @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[585])). 159.59/70.61 thf(19,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (((divide6298287555418463151nteger @ B @ A) = zero_z3403309356797280102nteger) = (B = zero_z3403309356797280102nteger))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4156_unit__div__eq__0__iff)). 159.59/70.61 thf(8310,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (((divide6298287555418463151nteger @ B @ A) = zero_z3403309356797280102nteger) = (B = zero_z3403309356797280102nteger))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[19])). 159.59/70.61 thf(5692,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) <= (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8099_fact__less__mono)). 159.59/70.61 thf(27102,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) | ~ (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5692])). 159.59/70.61 thf(1035,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ B @ pi) => ((ord_less_real @ (cos_real @ A) @ (cos_real @ B)) = (ord_less_real @ B @ A)))) <= (ord_less_eq_real @ A @ pi)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7122_cos__mono__less__eq)). 159.59/70.61 thf(11564,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ B @ pi) => ((ord_less_real @ (cos_real @ A) @ (cos_real @ B)) = (ord_less_real @ B @ A)))) | ~ (ord_less_eq_real @ A @ pi) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035])). 159.59/70.61 thf(1973,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5950_and__zero__eq)). 159.59/70.61 thf(14616,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1973])). 159.59/70.61 thf(2881,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int) <= (ord_less_int @ B @ zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2270_add__nonpos__neg)). 159.59/70.61 thf(17517,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int) | ~ (ord_less_int @ B @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2881])). 159.59/70.61 thf(183,axiom,((semiri3624122377584611663nteger = (^ [A:nat]: (if_Code_integer @ (A = zero_zero_nat) @ one_one_Code_integer @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (semiri3624122377584611663nteger @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8122_fact__num__eq__if)). 159.59/70.61 thf(8819,plain,(((semiri3624122377584611663nteger) = (^ [A:nat]: (if_Code_integer @ (A = zero_zero_nat) @ one_one_Code_integer @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (semiri3624122377584611663nteger @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[183])). 159.59/70.61 thf(5494,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2750_order__class_Oorder__eq__iff)). 159.59/70.61 thf(26425,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5494])). 159.59/70.61 thf(6861,axiom,((ord_less_eq_real = (^ [A:real,B:real]: (ord_less_eq_real @ (minus_minus_real @ A @ B) @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2136_le__iff__diff__le__0)). 159.59/70.61 thf(31738,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)],[6861])). 159.59/70.61 thf(2331,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) = ((B = zero_zero_int) & (A = zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2297_sum__squares__le__zero__iff)). 159.59/70.61 thf(15742,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) = ((B = zero_zero_int) & (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2331])). 159.59/70.61 thf(2565,axiom,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5164_neg__numeral__le__one)). 159.59/70.61 thf(16495,plain,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2565])). 159.59/70.61 thf(2891,axiom,((ord_less_real = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3161_order__less__le)). 159.59/70.61 thf(17562,plain,(((ord_less_real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2891])). 159.59/70.61 thf(2382,axiom,((! [A: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))))))) <= ((cos_complex @ A) != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7205_tan__double)). 159.59/70.61 thf(15900,plain,((! [A: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))))))) | ((cos_complex @ A) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2382])). 159.59/70.61 thf(5093,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/sandbox/benchmark/theBenchmark.p',fact_1165_add__right__mono)). 159.59/70.61 thf(24890,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)],[5093])). 159.59/70.61 thf(2018,axiom,((! [A:num,B:real,C:real]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (divide_divide_real @ B @ C)) = (((((ord_less_eq_real @ (numeral_numeral_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 @ (numeral_numeral_real @ A) @ C)))) <= (~ (ord_less_real @ zero_zero_real @ C))) & ((ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ A) @ C) @ B) <= (ord_less_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2495_le__divide__eq__numeral_I1_J)). 159.59/70.61 thf(14773,plain,((! [A:num,B:real,C:real]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ (divide_divide_real @ B @ C)) = (((((ord_less_eq_real @ (numeral_numeral_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 @ (numeral_numeral_real @ A) @ C)))) | (ord_less_real @ zero_zero_real @ C)) & ((ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ A) @ C) @ B) | ~ (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2018])). 159.59/70.61 thf(3476,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))) & (((minus_minus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = B) <= (A = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2376_add__divide__eq__if__simps_I4_J)). 159.59/70.61 thf(19414,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))) & (((minus_minus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = B) | ~ (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3476])). 159.59/70.61 thf(1205,axiom,((! [A:complex,B:complex,C:complex]: (((uminus1482373934393186551omplex @ A) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ C))) <= (A = (plus_plus_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4966_group__cancel_Oneg1)). 159.59/70.61 thf(12137,plain,((! [A:complex,B:complex,C:complex]: (((uminus1482373934393186551omplex @ A) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ C))) | ~ (A = (plus_plus_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205])). 159.59/70.61 thf(7313,axiom,((bit_se2000444600071755411sk_int = (^ [A:nat]: (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6136_mask__int__def)). 159.59/70.61 thf(33549,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)],[7313])). 159.59/70.61 thf(7520,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/sandbox/benchmark/theBenchmark.p',fact_6189_or__minus__numerals_I5_J)). 159.59/70.61 thf(34252,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)],[7520])). 159.59/70.61 thf(7377,axiom,((! [A:nat]: ((bit_se1412395901928357646or_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5953_or_Oright__neutral)). 159.59/70.61 thf(33761,plain,((! [A:nat]: ((bit_se1412395901928357646or_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7377])). 159.59/70.61 thf(4533,axiom,((! [A:int,B:int]: ((times_times_int @ (uminus_uminus_int @ A) @ B) = (times_times_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4953_minus__mult__commute)). 159.59/70.61 thf(22902,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)],[4533])). 159.59/70.61 thf(4445,axiom,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_int @ (A @ zero_zero_nat) @ (groups705719431365010083at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8743_prod_OlessThan__Suc__shift)). 159.59/70.61 thf(22488,plain,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (A) @ (set_ord_lessThan_nat @ (suc @ 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)],[4445])). 159.59/70.61 thf(7705,axiom,((! [A:num,B:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6027_or__numerals_I4_J)). 159.59/70.61 thf(34869,plain,((! [A:num,B:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7705])). 159.59/70.61 thf(3666,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/sandbox/benchmark/theBenchmark.p',fact_2337_eq__divide__eq__numeral_I1_J)). 159.59/70.61 thf(20027,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)],[3666])). 159.59/70.61 thf(6524,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/sandbox/benchmark/theBenchmark.p',fact_5477_divmod__algorithm__code_I6_J)). 159.59/70.61 thf(30321,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)],[6524])). 159.59/70.61 thf(4921,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/sandbox/benchmark/theBenchmark.p',fact_9746_Suc__0__div__numeral)). 159.59/70.61 thf(24262,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)],[4921])). 159.59/70.61 thf(4792,axiom,(((neg_nu8557863876264182079omplex @ one_one_complex) = (numera6690914467698888265omplex @ (bit1 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5745_dbl__inc__simps_I3_J)). 159.59/70.61 thf(23803,plain,(((neg_nu8557863876264182079omplex @ one_one_complex) = (numera6690914467698888265omplex @ (bit1 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4792])). 159.59/70.61 thf(5878,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/sandbox/benchmark/theBenchmark.p',fact_4878_diff__numeral__special_I4_J)). 159.59/70.61 thf(27964,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)],[5878])). 159.59/70.61 thf(4471,axiom,((! [A:num,B:(int > num),C:int,D:int]: ((A = (B @ C)) => (((! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))) <= (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2662_ord__eq__le__subst)). 159.59/70.61 thf(22627,plain,((! [A:num,B:(int > num),C:int,D:int]: ((A = (B @ C)) => (((! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_num @ (B @ E) @ (B @ F)))) => (ord_less_eq_num @ A @ (B @ D))) | ~ (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4471])). 159.59/70.61 thf(3291,axiom,((! [A:num]: ~ (ord_less_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5181_not__one__less__neg__numeral)). 159.59/70.61 thf(18846,plain,((! [A:num]: ~ (ord_less_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3291])). 159.59/70.61 thf(7125,axiom,((! [A:nat,B:real,C:real]: ((((power_power_real @ B @ A) = C) = ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (if_real @ (D = zero_zero_nat) @ (uminus_uminus_real @ C) @ (if_real @ (D = A) @ one_one_real @ zero_zero_real)) @ (power_power_real @ B @ D))) @ (set_ord_atMost_nat @ A)) = zero_zero_real)) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8946_root__polyfun)). 159.59/70.61 thf(32848,plain,((! [A:nat,B:real,C:real]: ((((power_power_real @ B @ A) = C) = ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (if_real @ (D = zero_zero_nat) @ (uminus_uminus_real @ C) @ (if_real @ (D = A) @ one_one_real @ zero_zero_real)) @ (power_power_real @ B @ D))) @ (set_ord_atMost_nat @ A)) = zero_zero_real)) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7125])). 159.59/70.61 thf(8103,axiom,((! [A:nat]: ((nat_set_decode @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (vimage_nat_nat @ suc @ (nat_set_decode @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10193_set__decode__div__2)). 159.59/70.61 thf(36156,plain,((! [A:nat]: ((nat_set_decode @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (vimage_nat_nat @ (suc) @ (nat_set_decode @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8103])). 159.59/70.61 thf(4980,axiom,((! [A:nat,B:real]: ((root @ A @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (root @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9497_real__root__minus)). 159.59/70.61 thf(24490,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)],[4980])). 159.59/70.61 thf(1958,axiom,((! [A:real]: ((? [B:real]: ((exp_real @ B) = A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6067_exp__total)). 159.59/70.61 thf(14564,plain,((! [A:real]: (? [B:real]: ((exp_real @ B) = A) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1958])). 159.59/70.61 thf(1230,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/sandbox/benchmark/theBenchmark.p',fact_7280_minus__log__eq__powr)). 159.59/70.61 thf(12229,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)],[1230])). 159.59/70.61 thf(6872,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/sandbox/benchmark/theBenchmark.p',fact_8623_atMost__nat__numeral)). 159.59/70.61 thf(31770,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)],[6872])). 159.59/70.61 thf(3184,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/sandbox/benchmark/theBenchmark.p',fact_9161_real__le__abs__sinh)). 159.59/70.61 thf(18492,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)],[3184])). 159.59/70.61 thf(3020,axiom,((! [A:real]: (((cos_real @ A) = zero_zero_real) = (? [B:nat]: (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = (uminus_uminus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))) | ? [B:nat]: (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7198_cos__zero__iff)). 159.59/70.61 thf(17962,plain,((! [A:real]: (((cos_real @ A) = zero_zero_real) = (? [B:nat]: (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = (uminus_uminus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))) | ? [B:nat]: (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3020])). 159.59/70.61 thf(7210,axiom,((! [A:nat]: ((modulo_modulo_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3390_bits__mod__0)). 159.59/70.61 thf(33174,plain,((! [A:nat]: ((modulo_modulo_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7210])). 159.59/70.61 thf(5136,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) => (((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ E)) @ A @ D @ F) @ C) = (if_option_nat @ (((vEBT_vebt_maxt @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_nat) & (vEBT_VEBT_less @ (some_nat @ (vEBT_VEBT_low @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ C @ (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 @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_succ @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ D @ (the_nat @ (vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) <= (ord_less_nat @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1394_succ__less__length__list)). 159.59/70.61 thf(25022,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) => (((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ E)) @ A @ D @ F) @ C) = (if_option_nat @ (~ ((vEBT_vebt_maxt @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) & (vEBT_VEBT_less @ (some_nat @ (vEBT_VEBT_low @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ C @ (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 @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_succ @ (nth_VEBT_VEBT @ D @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ D @ (the_nat @ (vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5136])). 159.59/70.61 thf(5321,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/sandbox/benchmark/theBenchmark.p',fact_3531_minus__mult__div__eq__mod)). 159.59/70.61 thf(25717,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)],[5321])). 159.59/70.61 thf(7495,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/sandbox/benchmark/theBenchmark.p',fact_6221_or__not__num__neg_Osimps_I9_J)). 159.59/70.61 thf(34172,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)],[7495])). 159.59/70.61 thf(406,axiom,((filterlim_real_real @ tanh_real @ (topolo2815343760600316023s_real @ one_one_real) @ at_top_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9955_tanh__real__at__top)). 159.59/70.61 thf(9529,plain,((filterlim_real_real @ (tanh_real) @ (topolo2815343760600316023s_real @ one_one_real) @ at_top_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])). 159.59/70.61 thf(1088,axiom,((! [A:int]: ((bit_se1409905431419307370or_int @ one_one_int @ A) = (plus_plus_int @ A @ (zero_n2684676970156552555ol_int @ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6128_one__or__eq)). 159.59/70.61 thf(11741,plain,((! [A:int]: ((bit_se1409905431419307370or_int @ one_one_int @ A) = (plus_plus_int @ A @ (zero_n2684676970156552555ol_int @ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088])). 159.59/70.61 thf(5299,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/sandbox/benchmark/theBenchmark.p',fact_7171_cos__treble__cos)). 159.59/70.61 thf(25612,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)],[5299])). 159.59/70.61 thf(5583,axiom,(((sqrt @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6330_real__sqrt__four)). 159.59/70.61 thf(26705,plain,(((sqrt @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5583])). 159.59/70.61 thf(3640,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/sandbox/benchmark/theBenchmark.p',fact_2431_pos__divide__le__eq)). 159.59/70.61 thf(19937,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)],[3640])). 159.59/70.61 thf(897,axiom,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B) @ (modulo364778990260209775nteger @ A @ B)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3515_div__mult__mod__eq)). 159.59/70.61 thf(11132,plain,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B) @ (modulo364778990260209775nteger @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[897])). 159.59/70.61 thf(7593,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/sandbox/benchmark/theBenchmark.p',fact_3513_mod__div__mult__eq)). 159.59/70.61 thf(34538,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)],[7593])). 159.59/70.61 thf(6728,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) <= (ord_less_eq_nat @ B @ zero_zero_nat)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2026_add__nonpos__nonpos)). 159.59/70.61 thf(31193,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_eq_nat @ B @ zero_zero_nat) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6728])). 159.59/70.61 thf(741,axiom,((! [A:real,B:real]: ((A = B) | (ord_less_real @ B @ A) | (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2919_linorder__less__linear)). 159.59/70.61 thf(10650,plain,((! [A:real,B:real]: ((A = B) | (ord_less_real @ B @ A) | (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[741])). 159.59/70.61 thf(1584,axiom,((! [A:code_integer]: ((bit_se2793503036327961859nteger @ zero_zero_nat @ A) = (plus_p5714425477246183910nteger @ one_one_Code_integer @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2576_set__bit__0)). 159.59/70.61 thf(13393,plain,((! [A:code_integer]: ((bit_se2793503036327961859nteger @ zero_zero_nat @ A) = (plus_p5714425477246183910nteger @ one_one_Code_integer @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584])). 159.59/70.61 thf(5295,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => ((~ (! [D:nat]: (C != (plus_plus_nat @ A @ (times_times_nat @ B @ D))))) <= (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3544_mod__eq__nat2E)). 159.59/70.61 thf(25599,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => (~ (! [D:nat]: ~ (C = (plus_plus_nat @ A @ (times_times_nat @ B @ D)))) | ~ (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5295])). 159.59/70.61 thf(2477,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/sandbox/benchmark/theBenchmark.p',fact_5580_abs__diff__triangle__ineq)). 159.59/70.61 thf(16223,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)],[2477])). 159.59/70.61 thf(4478,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/sandbox/benchmark/theBenchmark.p',fact_6461_real__sqrt__ge__abs1)). 159.59/70.61 thf(22659,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)],[4478])). 159.59/70.61 thf(3850,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/sandbox/benchmark/theBenchmark.p',fact_1576_zero__le__double__add__iff__zero__le__single__add)). 159.59/70.61 thf(20647,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)],[3850])). 159.59/70.61 thf(7150,axiom,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2183_power__0)). 159.59/70.61 thf(32940,plain,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7150])). 159.59/70.61 thf(4449,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ one_one_nat @ A) => (ord_less_eq_nat @ one_one_nat @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_one__le__power)). 159.59/70.61 thf(22498,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ one_one_nat @ A) => (ord_less_eq_nat @ one_one_nat @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4449])). 159.59/70.61 thf(95,axiom,((ord_max_int = (^ [A:int,B:int]: (if_int @ (ord_less_eq_int @ A @ B) @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3712_max__def__raw)). 159.59/70.61 thf(8543,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)],[95])). 159.59/70.61 thf(5429,axiom,((! [A:(num > $o),B:num]: (((! [C:num]: ((A @ (inc @ C)) <= (A @ C))) => (A @ B)) <= (A @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5715_num__induct)). 159.59/70.61 thf(26190,plain,((! [A:(num > $o),B:num]: (((! [C:num]: ((A @ (inc @ C)) | ~ (A @ C))) => (A @ B)) | ~ (A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5429])). 159.59/70.61 thf(321,axiom,((! [A:$o]: (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (zero_n356916108424825756nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4393_zero__less__eq__of__bool)). 159.59/70.61 thf(9240,plain,((! [A:$o]: (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (zero_n356916108424825756nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 159.59/70.61 thf(2141,axiom,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se545348938243370406it_int @ A @ B) @ C) = ((ord_less_eq_nat @ A @ C) & (bit_se1146084159140164899it_int @ B @ (minus_minus_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9559_bit__push__bit__iff__int)). 159.59/70.61 thf(15161,plain,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se545348938243370406it_int @ A @ B) @ C) = ((ord_less_eq_nat @ A @ C) & (bit_se1146084159140164899it_int @ B @ (minus_minus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2141])). 159.59/70.61 thf(138,axiom,((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ zero_z3403309356797280102nteger)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5151_le__minus__one__simps_I1_J)). 159.59/70.61 thf(8674,plain,((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ zero_z3403309356797280102nteger)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 159.59/70.61 thf(6468,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/sandbox/benchmark/theBenchmark.p',fact_2444_power__Suc__less)). 159.59/70.61 thf(30134,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)],[6468])). 159.59/70.61 thf(3097,axiom,((! [A:num]: ((neg_nu6511756317524482435omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bitM @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5806_dbl__dec__simps_I5_J)). 159.59/70.61 thf(18215,plain,((! [A:num]: ((neg_nu6511756317524482435omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3097])). 159.59/70.61 thf(7876,axiom,((bit_se547839408752420682it_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9565_push__bit__nat__def)). 159.59/70.61 thf(35429,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)],[7876])). 159.59/70.61 thf(5087,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4917_take__bit__nat__less__eq__self)). 159.59/70.61 thf(24871,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5087])). 159.59/70.61 thf(123,axiom,(((cos_real @ (real_V1803761363581548252l_real @ pi)) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7355_cos__of__real__pi)). 159.59/70.61 thf(8632,plain,(((cos_real @ (real_V1803761363581548252l_real @ pi)) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 159.59/70.61 thf(149,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B)) @ C) = (ord_less_real @ (real_V1485227260804924795R_real @ A @ C) @ (uminus_uminus_real @ B))) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9279_neg__minus__divideR__less__eq)). 159.59/70.61 thf(8703,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B)) @ C) = (ord_less_real @ (real_V1485227260804924795R_real @ A @ C) @ (uminus_uminus_real @ B))) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[149])). 159.59/70.61 thf(4423,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/sandbox/benchmark/theBenchmark.p',fact_6956_suminf__geometric)). 159.59/70.61 thf(22425,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)],[4423])). 159.59/70.61 thf(1493,axiom,((! [A:nat]: (((semiri4216267220026989637d_enat @ A) = one_on7984719198319812577d_enat) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6538_of__nat__eq__1__iff)). 159.59/70.61 thf(13123,plain,((! [A:nat]: (((semiri4216267220026989637d_enat @ A) = one_on7984719198319812577d_enat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493])). 159.59/70.61 thf(3190,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)) & (((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = zero_zero_complex) <= (A = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1654_mult__divide__mult__cancel__left__if)). 159.59/70.61 thf(18511,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)) & (((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C)) = zero_zero_complex) | ~ (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3190])). 159.59/70.61 thf(2079,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ A @ B) @ C) = (plus_p5714425477246183910nteger @ (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ A @ C) @ (divide6298287555418463151nteger @ B @ C)) @ (divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ A @ C) @ (modulo364778990260209775nteger @ B @ C)) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3482_div__add1__eq)). 159.59/70.61 thf(14949,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ A @ B) @ C) = (plus_p5714425477246183910nteger @ (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ A @ C) @ (divide6298287555418463151nteger @ B @ C)) @ (divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ A @ C) @ (modulo364778990260209775nteger @ B @ C)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2079])). 159.59/70.61 thf(2234,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_complex @ (groups2073611262835488442omplex @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7875_sum_OlessThan__Suc)). 159.59/70.61 thf(15462,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_complex @ (groups2073611262835488442omplex @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2234])). 159.59/70.61 thf(3905,axiom,((! [A:int,B:int,C:int]: ((B = C) <= ((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1118_add__left__imp__eq)). 159.59/70.61 thf(20822,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)],[3905])). 159.59/70.61 thf(720,axiom,((! [A:real,B:nat,C:nat]: ((((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)) & ((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/sandbox/benchmark/theBenchmark.p',fact_7834_sum__gp__offset)). 159.59/70.61 thf(10570,plain,((! [A:real,B:nat,C:nat]: ((((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)) & ((~ (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)],[720])). 159.59/70.61 thf(746,axiom,((! [A:num,B:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5041_neg__numeral__less__numeral)). 159.59/70.61 thf(10665,plain,((! [A:num,B:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[746])). 159.59/70.61 thf(8149,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ C) => (((divide_divide_nat @ C @ A) = B) <= (ord_less_nat @ C @ (times_times_nat @ A @ (suc @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_div__nat__eqI)). 159.59/70.61 thf(36315,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ C) => (((divide_divide_nat @ C @ A) = B) | ~ (ord_less_nat @ C @ (times_times_nat @ A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8149])). 159.59/70.61 thf(6514,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_le__add__diff__inverse2)). 159.59/70.61 thf(30289,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6514])). 159.59/70.61 thf(835,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = ((plus_plus_real @ A @ C) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1291_eq__diff__eq)). 159.59/70.61 thf(10945,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)],[835])). 159.59/70.61 thf(3330,axiom,((comm_s7457072308508201937r_real = (^ [A:real,B:nat]: (groups129246275422532515t_real @ (^ [C:nat]: (plus_plus_real @ A @ (semiri5074537144036343181t_real @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8891_pochhammer__prod__rev)). 159.59/70.61 thf(18964,plain,(((comm_s7457072308508201937r_real) = (^ [A:real,B:nat]: (groups129246275422532515t_real @ (^ [C:nat]: (plus_plus_real @ A @ (semiri5074537144036343181t_real @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3330])). 159.59/70.61 thf(8055,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/sandbox/benchmark/theBenchmark.p',fact_5643_Suc__div__eq__add3__div)). 159.59/70.61 thf(36008,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)],[8055])). 159.59/70.61 thf(4570,axiom,((! [A:set_nat,B:(nat > nat)]: (((ord_less_nat @ zero_zero_nat @ (groups708209901874060359at_nat @ B @ A)) = (! [C:nat]: ((member_nat @ C @ A) => (ord_less_nat @ zero_zero_nat @ (B @ C))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9011_prod__pos__nat__iff)). 159.59/70.61 thf(23026,plain,((! [A:set_nat,B:(nat > nat)]: (((ord_less_nat @ zero_zero_nat @ (groups708209901874060359at_nat @ (B) @ A)) = (! [C:nat]: ((member_nat @ C @ A) => (ord_less_nat @ zero_zero_nat @ (B @ C))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4570])). 159.59/70.61 thf(6953,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/sandbox/benchmark/theBenchmark.p',fact_612_lift__Suc__antimono__le)). 159.59/70.61 thf(32052,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)],[6953])). 159.59/70.61 thf(2903,axiom,((! [A:real]: (ord_less_real @ zero_zero_real @ (exp_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6066_exp__gt__zero)). 159.59/70.61 thf(17603,plain,((! [A:real]: (ord_less_real @ zero_zero_real @ (exp_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2903])). 159.59/70.61 thf(3646,axiom,((! [A:set_nat,B:nat,C:(nat > extended_enat)]: (((((groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (D = B) @ (C @ D) @ one_on7984719198319812577d_enat)) @ A) = one_on7984719198319812577d_enat) <= (~ (member_nat @ B @ A))) & ((member_nat @ B @ A) => ((groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (D = B) @ (C @ D) @ one_on7984719198319812577d_enat)) @ A) = (C @ B)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8416_prod_Odelta)). 159.59/70.61 thf(19956,plain,((! [A:set_nat,B:nat,C:(nat > extended_enat)]: (((((groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (D = B) @ (C @ D) @ one_on7984719198319812577d_enat)) @ A) = one_on7984719198319812577d_enat) | (member_nat @ B @ A)) & ((member_nat @ B @ A) => ((groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (D = B) @ (C @ D) @ one_on7984719198319812577d_enat)) @ A) = (C @ B)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3646])). 159.59/70.61 thf(7721,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/sandbox/benchmark/theBenchmark.p',fact_5269_take__bit__nat__eq__self)). 159.59/70.61 thf(34939,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)],[7721])). 159.59/70.61 thf(1486,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ B @ A)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2933_order__less__imp__not__less)). 159.59/70.61 thf(13102,plain,((! [A:extended_enat,B:extended_enat]: (~ (ord_le72135733267957522d_enat @ B @ A) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486])). 159.59/70.61 thf(1617,axiom,((~ (ord_less_int @ one_one_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_less__numeral__extra_I4_J)). 159.59/70.61 thf(13506,plain,((~ (ord_less_int @ one_one_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617])). 159.59/70.61 thf(758,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/sandbox/benchmark/theBenchmark.p',fact_5758_dbl__dec__simps_I1_J)). 159.59/70.61 thf(10702,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)],[758])). 159.59/70.61 thf(6210,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((groups6591440286371151544t_real @ (^ [B:nat]: (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (semiri5074537144036343181t_real @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9173_choose__alternating__sum)). 159.59/70.61 thf(29123,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((groups6591440286371151544t_real @ (^ [B:nat]: (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (semiri5074537144036343181t_real @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6210])). 159.59/70.61 thf(2504,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/sandbox/benchmark/theBenchmark.p',fact_5591_numeral__Bit1)). 159.59/70.61 thf(16315,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)],[2504])). 159.59/70.61 thf(5001,axiom,((! [A:int]: ((times_times_int @ A @ (numeral_numeral_int @ one)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_mult__numeral__1__right)). 159.59/70.61 thf(24561,plain,((! [A:int]: ((times_times_int @ A @ (numeral_numeral_int @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5001])). 159.59/70.61 thf(7938,axiom,((! [A:nat,B:nat]: ((if_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Nat__Onat_T)). 159.59/70.61 thf(35623,plain,((! [A:nat,B:nat]: ((if_nat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7938])). 159.59/70.61 thf(5419,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ C) & (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6394_bit__take__bit__iff)). 159.59/70.61 thf(26160,plain,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ C) & (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5419])). 159.59/70.61 thf(1468,axiom,((! [A:(nat > complex),B:set_nat]: (((groups6464643781859351333omplex @ A @ B) != one_one_complex) => (~ (! [C:nat]: (((A @ C) = one_one_complex) <= (member_nat @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8464_prod_Onot__neutral__contains__not__neutral)). 159.59/70.61 thf(13044,plain,((! [A:(nat > complex),B:set_nat]: ((~ ((groups6464643781859351333omplex @ (A) @ B) = one_one_complex)) => (~ (! [C:nat]: (((A @ C) = one_one_complex) | ~ (member_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1468])). 159.59/70.61 thf(5471,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/sandbox/benchmark/theBenchmark.p',fact_9033_Suc__times__binomial)). 159.59/70.61 thf(26343,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)],[5471])). 159.59/70.61 thf(2143,axiom,((! [A:complex,B:complex]: ((((cos_complex @ 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 @ (minus_minus_complex @ A @ B)) != zero_zero_complex))) <= ((cos_complex @ A) != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7311_tan__diff)). 159.59/70.61 thf(15167,plain,((! [A:complex,B:complex]: (((~ ((cos_complex @ 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 @ (minus_minus_complex @ A @ B)) = zero_zero_complex))) | ((cos_complex @ A) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2143])). 159.59/70.61 thf(7451,axiom,((! [A:num]: ((numeral_numeral_real @ (bitM @ A)) = (minus_minus_real @ (numeral_numeral_real @ (bit0 @ A)) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5916_numeral__BitM)). 159.59/70.61 thf(33993,plain,((! [A:num]: ((numeral_numeral_real @ (bitM @ A)) = (minus_minus_real @ (numeral_numeral_real @ (bit0 @ A)) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7451])). 159.59/70.61 thf(6685,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1691_zero__less__Suc)). 159.59/70.61 thf(30920,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6685])). 159.59/70.61 thf(1079,axiom,((! [A:real,B:real,C:num]: (((complex2 @ A @ B) = (numera6690914467698888265omplex @ C)) = ((B = zero_zero_real) & (A = (numeral_numeral_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7241_Complex__eq__numeral)). 159.59/70.61 thf(11716,plain,((! [A:real,B:real,C:num]: (((complex2 @ A @ B) = (numera6690914467698888265omplex @ C)) = ((B = zero_zero_real) & (A = (numeral_numeral_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079])). 159.59/70.61 thf(6328,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/sandbox/benchmark/theBenchmark.p',fact_1066_add__le__cancel__left)). 159.59/70.61 thf(29576,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)],[6328])). 159.59/70.61 thf(6970,axiom,((! [A:num,B:num]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4621_neg__numeral__eq__iff)). 159.59/70.61 thf(32129,plain,((! [A:num,B:num]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6970])). 159.59/70.61 thf(2152,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/sandbox/benchmark/theBenchmark.p',fact_1164_add__right__mono)). 159.59/70.61 thf(15193,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)],[2152])). 159.59/70.61 thf(2118,axiom,((! [A:int,B:int]: (((bit_se1409905431419307370or_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6055_or__eq__0__iff)). 159.59/70.61 thf(15073,plain,((! [A:int,B:int]: (((bit_se1409905431419307370or_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2118])). 159.59/70.61 thf(7579,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ C) => (((divide_divide_nat @ B @ A) = (divide_divide_nat @ C @ A)) = (B = C))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4008_dvd__div__eq__iff)). 159.59/70.61 thf(34490,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ C) => (((divide_divide_nat @ B @ A) = (divide_divide_nat @ C @ A)) = (B = C))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7579])). 159.59/70.61 thf(4337,axiom,((! [A:real,B:real]: (((divide_divide_real @ (times_times_real @ B @ A) @ A) = B) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1627_nonzero__mult__div__cancel__right)). 159.59/70.61 thf(22150,plain,((! [A:real,B:real]: (((divide_divide_real @ (times_times_real @ B @ A) @ A) = B) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4337])). 159.59/70.61 thf(6478,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq_nat @ A @ B) => ((((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B)) <= (! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F))))) <= (! [D:nat]: (C @ D @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_transitive__stepwise__le)). 159.59/70.61 thf(30166,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((ord_less_eq_nat @ A @ B) => (((! [D:nat]: (C @ D @ (suc @ D))) => (C @ A @ B)) | ~ (! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) | ~ (! [D:nat]: (C @ D @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6478])). 159.59/70.61 thf(8166,axiom,(((numeral_numeral_nat @ (bit0 @ one)) = (suc @ (suc @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2471_numeral__2__eq__2)). 159.59/70.61 thf(36368,plain,(((numeral_numeral_nat @ (bit0 @ one)) = (suc @ (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8166])). 159.59/70.61 thf(2909,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) => ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ A @ B)) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2263_add__pos__nonneg)). 159.59/70.61 thf(17620,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) => ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ A @ B)) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2909])). 159.59/70.61 thf(1570,axiom,((bit_se1146084159140164899it_int = (^ [A:int,B:nat]: (((B = zero_zero_nat) => (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) & ((B != zero_zero_nat) => (bit_se1146084159140164899it_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6467_bit__rec)). 159.59/70.61 thf(13350,plain,(((bit_se1146084159140164899it_int) = (^ [A:int,B:nat]: (((B = zero_zero_nat) => (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) & ((~ (B = zero_zero_nat)) => (bit_se1146084159140164899it_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570])). 159.59/70.61 thf(4692,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => ((divide_divide_nat @ A @ B) = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2284_unique__euclidean__semiring__numeral__class_Odiv__less)). 159.59/70.61 thf(23475,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => ((divide_divide_nat @ A @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4692])). 159.59/70.61 thf(5258,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/sandbox/benchmark/theBenchmark.p',fact_5561_eq__abs__iff_H)). 159.59/70.61 thf(25467,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)],[5258])). 159.59/70.61 thf(3833,axiom,((! [A:complex,B:complex]: ((cos_complex @ (minus_minus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B)) @ (times_times_complex @ (sin_complex @ A) @ (sin_complex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7110_cos__diff)). 159.59/70.61 thf(20592,plain,((! [A:complex,B:complex]: ((cos_complex @ (minus_minus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B)) @ (times_times_complex @ (sin_complex @ A) @ (sin_complex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3833])). 159.59/70.61 thf(5220,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/sandbox/benchmark/theBenchmark.p',fact_6755_inverse__of__nat__le)). 159.59/70.61 thf(25336,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)],[5220])). 159.59/70.61 thf(5488,axiom,((! [A:num]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6724_not__bit__Suc__0__numeral)). 159.59/70.61 thf(26403,plain,((! [A:num]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5488])). 159.59/70.61 thf(6292,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (bit_se1412395901928357646or_nat @ A @ B)) = (bit_se1412395901928357646or_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6720_of__nat__or__eq)). 159.59/70.61 thf(29470,plain,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (bit_se1412395901928357646or_nat @ A @ B)) = (bit_se1412395901928357646or_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6292])). 159.59/70.61 thf(34,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_max_Oabsorb1)). 159.59/70.61 thf(8352,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)],[34])). 159.59/70.61 thf(5596,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/sandbox/benchmark/theBenchmark.p',fact_4796_semiring__norm_I171_J)). 159.59/70.61 thf(26767,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)],[5596])). 159.59/70.61 thf(99,axiom,((! [A:$o]: ((ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (zero_n356916108424825756nteger @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4343_zero__less__of__bool__iff)). 159.59/70.61 thf(8558,plain,((! [A:$o]: ((ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (zero_n356916108424825756nteger @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[99])). 159.59/70.61 thf(6574,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 @ A @ C) @ (times_times_real @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1983_mult__right__mono)). 159.59/70.61 thf(30503,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 @ A @ C) @ (times_times_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6574])). 159.59/70.61 thf(2154,axiom,((! [A:complex]: (ord_less_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ (plus_plus_complex @ (real_V4546457046886955230omplex @ (real_V1022390504157884413omplex @ A)) @ one_one_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7570_norm__less__p1)). 159.59/70.61 thf(15199,plain,((! [A:complex]: (ord_less_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ (plus_plus_complex @ (real_V4546457046886955230omplex @ (real_V1022390504157884413omplex @ A)) @ one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2154])). 159.59/70.61 thf(391,axiom,((! [A:complex,B:nat]: ((re @ (divide1717551699836669952omplex @ A @ (semiri8010041392384452111omplex @ B))) = (divide_divide_real @ (re @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9628_Re__divide__of__nat)). 159.59/70.61 thf(9475,plain,((! [A:complex,B:nat]: ((re @ (divide1717551699836669952omplex @ A @ (semiri8010041392384452111omplex @ B))) = (divide_divide_real @ (re @ A) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[391])). 159.59/70.61 thf(4157,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/sandbox/benchmark/theBenchmark.p',fact_4961_add_Oinverse__distrib__swap)). 159.59/70.61 thf(21588,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)],[4157])). 159.59/70.61 thf(2757,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => (! [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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4296_inf__period_I3_J)). 159.59/70.61 thf(17136,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => (! [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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2757])). 159.59/70.61 thf(3895,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ C) => (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3979_dvd__add)). 159.59/70.61 thf(20790,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ C) => (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3895])). 159.59/70.61 thf(6671,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/sandbox/benchmark/theBenchmark.p',fact_9490_real__root__gt__1__iff)). 159.59/70.61 thf(30859,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)],[6671])). 159.59/70.61 thf(5399,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_eq_nat @ C @ A))) = (! [C:nat]: ((member_nat @ C @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) => (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2636_all__nat__less)). 159.59/70.61 thf(26061,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_eq_nat @ C @ A))) = (! [C:nat]: ((member_nat @ C @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5399])). 159.59/70.61 thf(4006,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/sandbox/benchmark/theBenchmark.p',fact_7072_summable__powser__split__head)). 159.59/70.61 thf(21128,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)],[4006])). 159.59/70.61 thf(6380,axiom,((! [A:real,B:num]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_eq_real @ A @ (minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7013_ceiling__less__neg__numeral)). 159.59/70.61 thf(29756,plain,((! [A:real,B:num]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_eq_real @ A @ (minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6380])). 159.59/70.61 thf(6920,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (times_times_real @ B @ A)) = (((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/sandbox/benchmark/theBenchmark.p',fact_2420_mult__le__cancel__right1)). 159.59/70.61 thf(31928,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (times_times_real @ B @ A)) = (((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)],[6920])). 159.59/70.61 thf(1688,axiom,((! [A:real,B:real]: ((plus_plus_real @ A @ (plus_plus_real @ (uminus_uminus_real @ A) @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4643_add__minus__cancel)). 159.59/70.61 thf(13715,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)],[1688])). 159.59/70.61 thf(3989,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/sandbox/benchmark/theBenchmark.p',fact_3532_minus__mult__div__eq__mod)). 159.59/70.61 thf(21075,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)],[3989])). 159.59/70.61 thf(6047,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_le__add2)). 159.59/70.61 thf(28591,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6047])). 159.59/70.61 thf(1321,axiom,((! [A:real,B:real,C:real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2775_ord__eq__less__trans)). 159.59/70.61 thf(12517,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)],[1321])). 159.59/70.61 thf(3047,axiom,((! [A:set_nat,B:(nat > real),C:nat]: ((finite_finite_nat @ A) => ((((~ (member_nat @ C @ A)) => ((groups129246275422532515t_real @ B @ (minus_minus_set_nat @ A @ (insert_nat @ C @ bot_bot_set_nat))) = (groups129246275422532515t_real @ B @ A))) & ((member_nat @ C @ A) => ((groups129246275422532515t_real @ B @ (minus_minus_set_nat @ A @ (insert_nat @ C @ bot_bot_set_nat))) = (divide_divide_real @ (groups129246275422532515t_real @ B @ A) @ (B @ C))))) <= ((B @ C) != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8866_prod__diff1)). 159.59/70.61 thf(18043,plain,((! [A:set_nat,B:(nat > real),C:nat]: ((finite_finite_nat @ A) => ((((~ (member_nat @ C @ A)) => ((groups129246275422532515t_real @ (B) @ (minus_minus_set_nat @ A @ (insert_nat @ C @ bot_bot_set_nat))) = (groups129246275422532515t_real @ (B) @ A))) & ((member_nat @ C @ A) => ((groups129246275422532515t_real @ (B) @ (minus_minus_set_nat @ A @ (insert_nat @ C @ bot_bot_set_nat))) = (divide_divide_real @ (groups129246275422532515t_real @ (B) @ A) @ (B @ C))))) | ((B @ C) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3047])). 159.59/70.61 thf(6201,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1920_le__0__eq)). 159.59/70.61 thf(29095,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6201])). 159.59/70.61 thf(465,axiom,((! [A:real,B:real]: (((cos_real @ A) != zero_zero_real) => (((cos_real @ B) != zero_zero_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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7308_tan__add)). 159.59/70.61 thf(9712,plain,((! [A:real,B:real]: ((~ ((cos_real @ A) = zero_zero_real)) => ((~ ((cos_real @ B) = zero_zero_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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])). 159.59/70.61 thf(4238,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/sandbox/benchmark/theBenchmark.p',fact_1578_double__add__le__zero__iff__single__add__le__zero)). 159.59/70.61 thf(21852,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)],[4238])). 159.59/70.61 thf(3883,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/sandbox/benchmark/theBenchmark.p',fact_3445_mult__mod__right)). 159.59/70.61 thf(20755,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)],[3883])). 159.59/70.61 thf(7346,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/sandbox/benchmark/theBenchmark.p',fact_8973_choose__even__sum)). 159.59/70.61 thf(33655,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)],[7346])). 159.59/70.61 thf(330,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/sandbox/benchmark/theBenchmark.p',fact_9436_sgn__mod)). 159.59/70.61 thf(9266,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)],[330])). 159.59/70.61 thf(3870,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ A @ B) = (divide6298287555418463151nteger @ C @ B)) => ((dvd_dvd_Code_integer @ B @ A) => ((dvd_dvd_Code_integer @ B @ C) => (A = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4017_dvd__div__eq__cancel)). 159.59/70.61 thf(20716,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ A @ B) = (divide6298287555418463151nteger @ C @ B)) => ((dvd_dvd_Code_integer @ B @ A) => ((dvd_dvd_Code_integer @ B @ C) => (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3870])). 159.59/70.61 thf(3179,axiom,((! [A:set_nat,B:nat]: (ord_less_eq_set_nat @ A @ (insert_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6195_subset__insertI)). 159.59/70.61 thf(18479,plain,((! [A:set_nat,B:nat]: (ord_less_eq_set_nat @ A @ (insert_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3179])). 159.59/70.61 thf(5967,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3182_order__less__imp__le)). 159.59/70.61 thf(28334,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5967])). 159.59/70.61 thf(1748,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_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/sandbox/benchmark/theBenchmark.p',fact_2896_order__less__subst1)). 159.59/70.61 thf(13895,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_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)],[1748])). 159.59/70.61 thf(4048,axiom,(((neg_nu8295874005876285629c_real @ zero_zero_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5797_dbl__inc__simps_I2_J)). 159.59/70.61 thf(21249,plain,(((neg_nu8295874005876285629c_real @ zero_zero_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4048])). 159.59/70.61 thf(2942,axiom,((! [A:real,B:real,C:real]: (((dvd_dvd_real @ B @ A) => ((dvd_dvd_real @ B @ C) => (A = C))) <= ((divide_divide_real @ A @ B) = (divide_divide_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4014_dvd__div__eq__cancel)). 159.59/70.61 thf(17723,plain,((! [A:real,B:real,C:real]: (((dvd_dvd_real @ B @ A) => ((dvd_dvd_real @ B @ C) => (A = C))) | ~ ((divide_divide_real @ A @ B) = (divide_divide_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2942])). 159.59/70.61 thf(557,axiom,((! [A:int]: ((ord_max_int @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_max_Oidem)). 159.59/70.61 thf(10025,plain,((! [A:int]: ((ord_max_int @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[557])). 159.59/70.61 thf(6108,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1968_mult__nonpos__nonneg)). 159.59/70.61 thf(28779,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6108])). 159.59/70.61 thf(7528,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) <= (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3189_order__le__neq__trans)). 159.59/70.61 thf(34274,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)],[7528])). 159.59/70.61 thf(1027,axiom,((! [A:int,B:nat]: ((((bit_se2923211474154528505it_int @ B @ A) = A) <= (ord_less_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5325_take__bit__int__eq__self)). 159.59/70.61 thf(11533,plain,((! [A:int,B:nat]: (((bit_se2923211474154528505it_int @ B @ A) = A) | ~ (ord_less_int @ A @ (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)],[1027])). 159.59/70.61 thf(1608,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 @ C @ D) & (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1179_add__mono__thms__linordered__semiring_I2_J)). 159.59/70.61 thf(13474,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 @ C @ D) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608])). 159.59/70.61 thf(2397,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ A @ B) & (C = D)) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1199_add__mono__thms__linordered__field_I1_J)). 159.59/70.61 thf(15954,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ A @ B) & (C = D)) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2397])). 159.59/70.61 thf(3609,axiom,(((cos_real @ pi) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6972_cos__pi)). 159.59/70.61 thf(19840,plain,(((cos_real @ pi) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3609])). 159.59/70.61 thf(706,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/sandbox/benchmark/theBenchmark.p',fact_7839_arccos__cos__eq__abs__2pi)). 159.59/70.61 thf(10527,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)],[706])). 159.59/70.61 thf(6873,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) <= (dvd_dvd_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3982_dvd__add)). 159.59/70.61 thf(31773,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) | ~ (dvd_dvd_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6873])). 159.59/70.61 thf(1641,axiom,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = C) = (((A = (times_times_real @ C @ B)) <= (B != zero_zero_real)) & ((B = zero_zero_real) => (C = zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2176_divide__eq__eq)). 159.59/70.61 thf(13575,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ A @ B) = C) = (((A = (times_times_real @ C @ B)) | (B = zero_zero_real)) & ((B = zero_zero_real) => (C = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641])). 159.59/70.61 thf(3528,axiom,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1530_add_Oright__neutral)). 159.59/70.61 thf(19578,plain,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3528])). 159.59/70.61 thf(5280,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/sandbox/benchmark/theBenchmark.p',fact_5528_abs__triangle__ineq3)). 159.59/70.61 thf(25555,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)],[5280])). 159.59/70.61 thf(4779,axiom,((ord_less_num = (^ [A:num,B:num]: ((A != B) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3164_order__less__le)). 159.59/70.61 thf(23768,plain,(((ord_less_num) = (^ [A:num,B:num]: (~ (A = B) & (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4779])). 159.59/70.61 thf(5515,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/sandbox/benchmark/theBenchmark.p',fact_1482_mult__cancel__left)). 159.59/70.61 thf(26502,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)],[5515])). 159.59/70.61 thf(7891,axiom,((! [A:nat]: (((divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3884_odd__Suc__div__two)). 159.59/70.61 thf(35478,plain,((! [A:nat]: (((divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (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)],[7891])). 159.59/70.61 thf(6933,axiom,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: (((? [E:num]: ! [F:num]: (((C @ F) = (D @ F)) <= (ord_less_num @ E @ F))) => (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F)))))) <= (? [E:num]: ! [F:num]: (((A @ F) = (B @ F)) <= (ord_less_num @ E @ F)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4429_pinf_I1_J)). 159.59/70.61 thf(31971,plain,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: (((? [E:num]: ! [F:num]: (((C @ F) = (D @ F)) | ~ (ord_less_num @ E @ F))) => (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F)))))) | ~ (? [E:num]: ! [F:num]: (((A @ F) = (B @ F)) | ~ (ord_less_num @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6933])). 159.59/70.61 thf(4736,axiom,((! [A:num]: ((bitM @ (inc @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5891_BitM__inc__eq)). 159.59/70.61 thf(23611,plain,((! [A:num]: ((bitM @ (inc @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4736])). 159.59/70.61 thf(7162,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/sandbox/benchmark/theBenchmark.p',fact_3452_mod__add__right__eq)). 159.59/70.61 thf(32977,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)],[7162])). 159.59/70.61 thf(2923,axiom,((archim8280529875227126926d_real = (^ [A:real]: (if_int @ (ord_less_eq_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (archim2898591450579166408c_real @ A)) @ (archim7802044766580827645g_real @ A) @ (archim6058952711729229775r_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8976_round__altdef)). 159.59/70.61 thf(17667,plain,(((archim8280529875227126926d_real) = (^ [A:real]: (if_int @ (ord_less_eq_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (archim2898591450579166408c_real @ A)) @ (archim7802044766580827645g_real @ A) @ (archim6058952711729229775r_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2923])). 159.59/70.61 thf(3624,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/sandbox/benchmark/theBenchmark.p',fact_5731_even__add__abs__iff)). 159.59/70.61 thf(19892,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)],[3624])). 159.59/70.61 thf(643,axiom,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ B) = (minus_minus_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4711_uminus__add__conv__diff)). 159.59/70.61 thf(10309,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)],[643])). 159.59/70.61 thf(2918,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ C @ (log @ A @ B)) = (ord_less_real @ (powr_real @ A @ C) @ B))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7267_less__log__iff)). 159.59/70.61 thf(17652,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ C @ (log @ A @ B)) = (ord_less_real @ (powr_real @ A @ C) @ B))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2918])). 159.59/70.61 thf(4519,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (times_times_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4629_minus__mult__minus)). 159.59/70.61 thf(22784,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)],[4519])). 159.59/70.61 thf(908,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/sandbox/benchmark/theBenchmark.p',fact_8142_cos__paired)). 159.59/70.61 thf(11163,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)],[908])). 159.59/70.61 thf(5380,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/sandbox/benchmark/theBenchmark.p',fact_5073_numeral__times__minus__swap)). 159.59/70.61 thf(25989,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)],[5380])). 159.59/70.61 thf(6331,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5663_abs__ln__one__plus__x__minus__x__bound__nonneg)). 159.59/70.61 thf(29585,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6331])). 159.59/70.61 thf(8016,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((groups708209901874060359at_nat @ A @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups708209901874060359at_nat @ (^ [D:nat]: (times_times_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/sandbox/benchmark/theBenchmark.p',fact_8905_prod_Oin__pairs)). 159.59/70.61 thf(35865,plain,((! [A:(nat > nat),B:nat,C:nat]: ((groups708209901874060359at_nat @ (A) @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups708209901874060359at_nat @ (^ [D:nat]: (times_times_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)],[8016])). 159.59/70.61 thf(7261,axiom,((! [A:nat]: ((A != one_one_nat) => ((groups3539618377306564664at_int @ (^ [B:nat]: (times_times_int @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (semiri1314217659103216013at_int @ B)) @ (semiri1314217659103216013at_int @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9164_choose__alternating__linear__sum)). 159.59/70.61 thf(33353,plain,((! [A:nat]: ((~ (A = one_one_nat)) => ((groups3539618377306564664at_int @ (^ [B:nat]: (times_times_int @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (semiri1314217659103216013at_int @ B)) @ (semiri1314217659103216013at_int @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7261])). 159.59/70.61 thf(2374,axiom,((! [A:real]: ((ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real) => (sums_real @ (power_power_real @ A) @ (divide_divide_real @ one_one_real @ (minus_minus_real @ one_one_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8002_geometric__sums)). 159.59/70.61 thf(15878,plain,((! [A:real]: ((ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real) => (sums_real @ (power_power_real @ A) @ (divide_divide_real @ one_one_real @ (minus_minus_real @ one_one_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2374])). 159.59/70.61 thf(5014,axiom,((! [A:nat,B:complex]: (((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (power_power_complex @ B @ A))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4872_power__minus__odd)). 159.59/70.61 thf(24599,plain,((! [A:nat,B:complex]: (((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)],[5014])). 159.59/70.61 thf(309,axiom,((! [A:nat,B:int]: (ord_less_eq_int @ (bit_se4203085406695923979it_int @ A @ B) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3469_unset__bit__less__eq)). 159.59/70.61 thf(9204,plain,((! [A:nat,B:int]: (ord_less_eq_int @ (bit_se4203085406695923979it_int @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 159.59/70.61 thf(6448,axiom,((! [A:num]: ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5618_odd__numeral)). 159.59/70.61 thf(30049,plain,((! [A:num]: ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6448])). 159.59/70.61 thf(5565,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/sandbox/benchmark/theBenchmark.p',fact_3490_mod__if)). 159.59/70.61 thf(26649,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)],[5565])). 159.59/70.61 thf(48,axiom,((! [A:real,B:real]: ((real_V1803761363581548252l_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (real_V1803761363581548252l_real @ A) @ (real_V1803761363581548252l_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7335_of__real__add)). 159.59/70.61 thf(8394,plain,((! [A:real,B:real]: ((real_V1803761363581548252l_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (real_V1803761363581548252l_real @ A) @ (real_V1803761363581548252l_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 159.59/70.61 thf(1947,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3140_order_Ostrict__implies__order)). 159.59/70.61 thf(14533,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1947])). 159.59/70.61 thf(340,axiom,((! [A:int,B:int]: (((ord_max_int @ A @ B) = B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_max_Oabsorb4)). 159.59/70.61 thf(9304,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])). 159.59/70.61 thf(7858,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/sandbox/benchmark/theBenchmark.p',fact_3502_cong__exp__iff__simps_I6_J)). 159.59/70.61 thf(35364,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)],[7858])). 159.59/70.61 thf(7331,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/sandbox/benchmark/theBenchmark.p',fact_5556_abs__mult__pos)). 159.59/70.61 thf(33604,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)],[7331])). 159.59/70.61 thf(4155,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/sandbox/benchmark/theBenchmark.p',fact_1349_le__diff__eq)). 159.59/70.61 thf(21582,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)],[4155])). 159.59/70.61 thf(5559,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) <= (A = (ord_max_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_max_OorderI)). 159.59/70.61 thf(26629,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)],[5559])). 159.59/70.61 thf(8094,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) => (ord_less_eq_nat @ (binomial @ C @ A) @ (binomial @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9109_binomial__mono)). 159.59/70.61 thf(36129,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) => (ord_less_eq_nat @ (binomial @ C @ A) @ (binomial @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8094])). 159.59/70.61 thf(768,axiom,((! [A:real,B:nat,C:(nat > (extended_enat > real))]: ((A = zero_zero_real) => ((B != zero_zero_nat) => ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_z5237406670263579293d_enat) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_z5237406670263579293d_enat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8130_Maclaurin__zero)). 159.59/70.61 thf(10729,plain,((! [A:real,B:nat,C:(nat > (extended_enat > real))]: ((A = zero_zero_real) => ((~ (B = zero_zero_nat)) => ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (divide_divide_real @ (C @ D @ zero_z5237406670263579293d_enat) @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D))) @ (set_ord_lessThan_nat @ B)) = (C @ zero_zero_nat @ zero_z5237406670263579293d_enat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[768])). 159.59/70.61 thf(5866,axiom,((! [A:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6579_of__nat__le__0__iff)). 159.59/70.61 thf(27923,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)],[5866])). 159.59/70.61 thf(5110,axiom,((! [A:int]: ((times_times_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4699_mult__minus1)). 159.59/70.61 thf(24943,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)],[5110])). 159.59/70.61 thf(230,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ A @ zero_zero_real) & (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 @ (real_V1485227260804924795R_real @ A @ B) @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9240_split__scaleR__neg__le)). 159.59/70.61 thf(8956,plain,((! [A:real,B:real]: ((((ord_less_eq_real @ A @ zero_zero_real) & (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 @ (real_V1485227260804924795R_real @ A @ B) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[230])). 159.59/70.61 thf(428,axiom,((arcosh_real = (^ [A:real]: (ln_ln_real @ (plus_plus_real @ A @ (powr_real @ (minus_minus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) @ (real_V1803761363581548252l_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7317_arcosh__def)). 159.59/70.61 thf(9593,plain,(((arcosh_real) = (^ [A:real]: (ln_ln_real @ (plus_plus_real @ A @ (powr_real @ (minus_minus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) @ (real_V1803761363581548252l_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])). 159.59/70.61 thf(8239,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1353_linordered__semidom__class_Oadd__diff__inverse)). 159.59/70.61 thf(36743,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)],[8239])). 159.59/70.61 thf(5351,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se727722235901077358nd_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ C) & (bit_se1148574629649215175it_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6374_bit__and__iff)). 159.59/70.61 thf(25858,plain,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se727722235901077358nd_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ C) & (bit_se1148574629649215175it_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5351])). 159.59/70.61 thf(7465,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/sandbox/benchmark/theBenchmark.p',fact_5439_semiring__norm_I10_J)). 159.59/70.61 thf(34045,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)],[7465])). 159.59/70.61 thf(7272,axiom,((! [A:nat,B:nat]: ((ord_less_eq_real @ (power_power_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A)) @ A) @ (semiri5074537144036343181t_real @ (binomial @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9107_binomial__ge__n__over__k__pow__k)). 159.59/70.61 thf(33385,plain,((! [A:nat,B:nat]: ((ord_less_eq_real @ (power_power_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A)) @ A) @ (semiri5074537144036343181t_real @ (binomial @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7272])). 159.59/70.61 thf(5412,axiom,(((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1785_one__div__two__eq__zero)). 159.59/70.61 thf(26100,plain,(((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5412])). 159.59/70.61 thf(5223,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/sandbox/benchmark/theBenchmark.p',fact_4800_semiring__norm_I172_J)). 159.59/70.61 thf(25345,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)],[5223])). 159.59/70.61 thf(1267,axiom,((! [A:$o]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (zero_n2684676970156552555ol_int @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4370_odd__of__bool__self)). 159.59/70.61 thf(12347,plain,((! [A:$o]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (zero_n2684676970156552555ol_int @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267])). 159.59/70.61 thf(677,axiom,((! [A:nat]: ((divide6298287555418463151nteger @ one_one_Code_integer @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) = (zero_n356916108424825756nteger @ (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4377_bits__1__div__exp)). 159.59/70.61 thf(10419,plain,((! [A:nat]: ((divide6298287555418463151nteger @ one_one_Code_integer @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) = (zero_n356916108424825756nteger @ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[677])). 159.59/70.61 thf(6428,axiom,((! [A:nat,B:(nat > int),C:nat,D:(nat > int),E:int]: (((! [F:nat]: (((D @ F) = zero_zero_int) <= (ord_less_nat @ C @ F))) => ((times_times_int @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (B @ F) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ A)) @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (D @ F) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ C))) = (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (groups3539618377306564664at_int @ (^ [G:nat]: (times_times_int @ (B @ G) @ (D @ (minus_minus_nat @ F @ G)))) @ (set_ord_atMost_nat @ F)) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ (plus_plus_nat @ A @ C))))) <= (! [F:nat]: ((ord_less_nat @ A @ F) => ((B @ F) = zero_zero_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8917_polynomial__product)). 159.59/70.61 thf(29958,plain,((! [A:nat,B:(nat > int),C:nat,D:(nat > int),E:int]: (((! [F:nat]: (((D @ F) = zero_zero_int) | ~ (ord_less_nat @ C @ F))) => ((times_times_int @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (B @ F) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ A)) @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (D @ F) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ C))) = (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (groups3539618377306564664at_int @ (^ [G:nat]: (times_times_int @ (B @ G) @ (D @ (minus_minus_nat @ F @ G)))) @ (set_ord_atMost_nat @ F)) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ (plus_plus_nat @ A @ C))))) | ~ (! [F:nat]: ((ord_less_nat @ A @ F) => ((B @ F) = zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6428])). 159.59/70.61 thf(8088,axiom,((ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (size_s6755466524823107622T_VEBT @ treeList))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27__092_060open_062high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_060_Alength_AtreeList_092_060close_062)). 159.59/70.61 thf(36114,plain,((ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (size_s6755466524823107622T_VEBT @ treeList))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8088])). 159.59/70.61 thf(7814,axiom,((! [A:nat,B:nat]: ((vEBT_VEBT_bit_concat @ (vEBT_VEBT_high @ A @ B) @ (vEBT_VEBT_low @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_bit__split__inv)). 159.59/70.61 thf(35225,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)],[7814])). 159.59/70.61 thf(4465,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_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ A @ E @ F) @ B) = (some_nat @ C)) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_721_succ__min)). 159.59/70.61 thf(22608,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_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ A @ E @ F) @ B) = (some_nat @ C)) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4465])). 159.59/70.61 thf(2450,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = ((dvd_dvd_real @ A @ C) | (B = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3816_dvd__mult__cancel__right)). 159.59/70.61 thf(16141,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ (times_times_real @ C @ B)) = ((dvd_dvd_real @ A @ C) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2450])). 159.59/70.61 thf(796,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((ord_less_real @ A @ zero_zero_real) & (ord_less_real @ B @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2087_zero__less__mult__iff)). 159.59/70.61 thf(10818,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((ord_less_real @ A @ zero_zero_real) & (ord_less_real @ B @ 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)],[796])). 159.59/70.61 thf(1175,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6534_of__nat__mult)). 159.59/70.61 thf(12018,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)],[1175])). 159.59/70.61 thf(7296,axiom,(((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ one_one_real)) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4745_diff__numeral__special_I12_J)). 159.59/70.61 thf(33468,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)],[7296])). 159.59/70.61 thf(738,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ (divide_divide_real @ A @ B)) = (((ord_less_real @ B @ A) & (ord_less_real @ zero_zero_real @ B)) | ((ord_less_real @ A @ B) & (ord_less_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2341_less__divide__eq__1)). 159.59/70.61 thf(10641,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ (divide_divide_real @ A @ B)) = (((ord_less_real @ B @ A) & (ord_less_real @ zero_zero_real @ B)) | ((ord_less_real @ A @ B) & (ord_less_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[738])). 159.59/70.61 thf(335,axiom,((! [A:nat]: ((cot_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9387_cot__npi)). 159.59/70.61 thf(9283,plain,((! [A:nat]: ((cot_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 159.59/70.61 thf(6308,axiom,((! [A:complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1492_mult__zero__right)). 159.59/70.61 thf(29517,plain,((! [A:complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6308])). 159.59/70.61 thf(997,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 @ (divide6298287555418463151nteger @ A @ B) @ one_one_Code_integer))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3848_unit__div)). 159.59/70.61 thf(11441,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 @ (divide6298287555418463151nteger @ A @ B) @ one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[997])). 159.59/70.61 thf(2454,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) => (ord_less_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8098_fact__less__mono)). 159.59/70.61 thf(16151,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) => (ord_less_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2454])). 159.59/70.61 thf(7539,axiom,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5163_neg__numeral__le__one)). 159.59/70.61 thf(34306,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)],[7539])). 159.59/70.61 thf(4513,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/sandbox/benchmark/theBenchmark.p',fact_2543_sum__power2__ge__zero)). 159.59/70.61 thf(22767,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)],[4513])). 159.59/70.61 thf(6068,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/sandbox/benchmark/theBenchmark.p',fact_8968_choose__odd__sum)). 159.59/70.61 thf(28654,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)],[6068])). 159.59/70.61 thf(3551,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/sandbox/benchmark/theBenchmark.p',fact_7015_cos__3over2__pi)). 159.59/70.61 thf(19643,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)],[3551])). 159.59/70.61 thf(6407,axiom,((! [A:num]: ((bit1 @ A) != one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5387_semiring__norm_I86_J)). 159.59/70.61 thf(29875,plain,((! [A:num]: ~ ((bit1 @ A) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6407])). 159.59/70.61 thf(2832,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((A = B) | (ord_less_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_less__eq__real__def)). 159.59/70.61 thf(17354,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((A = B) | (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2832])). 159.59/70.61 thf(6050,axiom,((! [A:num]: ((ring_17405671764205052669omplex @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5907_of__int__neg__numeral)). 159.59/70.61 thf(28599,plain,((! [A:num]: ((ring_17405671764205052669omplex @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6050])). 159.59/70.61 thf(8171,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/sandbox/benchmark/theBenchmark.p',fact_5453_power2__abs)). 159.59/70.61 thf(36383,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)],[8171])). 159.59/70.61 thf(3209,axiom,((! [A:real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1664_zero__eq__1__divide__iff)). 159.59/70.61 thf(18571,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)],[3209])). 159.59/70.61 thf(8148,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/sandbox/benchmark/theBenchmark.p',fact_4375_bits__1__div__exp)). 159.59/70.61 thf(36312,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)],[8148])). 159.59/70.61 thf(5539,axiom,((! [A:num,B:num,C:num]: (((ord_less_num @ C @ B) <= (ord_less_num @ C @ A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3122_dual__order_Ostrict__trans1)). 159.59/70.61 thf(26571,plain,((! [A:num,B:num,C:num]: ((ord_less_num @ C @ B) | ~ (ord_less_num @ C @ A) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5539])). 159.59/70.61 thf(1245,axiom,((! [A:set_nat]: ((finite_finite_nat @ A) => ((? [B:nat]: ((member_nat @ B @ A) & ! [C:nat]: (((B = C) <= (ord_less_eq_nat @ B @ C)) <= (member_nat @ C @ A)))) <= (A != bot_bot_set_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3770_finite__has__maximal)). 159.59/70.61 thf(12281,plain,((! [A:set_nat]: ((finite_finite_nat @ A) => (? [B:nat]: ((member_nat @ B @ A) & ! [C:nat]: ((B = C) | ~ (ord_less_eq_nat @ B @ C) | ~ (member_nat @ C @ A))) | (A = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245])). 159.59/70.61 thf(1061,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/sandbox/benchmark/theBenchmark.p',fact_3459_mod__add__eq)). 159.59/70.61 thf(11656,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)],[1061])). 159.59/70.61 thf(2322,axiom,((! [A:nat,B:int]: ~ (ord_less_int @ (bit_se2923211474154528505it_int @ A @ B) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5023_not__take__bit__negative)). 159.59/70.61 thf(15716,plain,((! [A:nat,B:int]: ~ (ord_less_int @ (bit_se2923211474154528505it_int @ A @ B) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2322])). 159.59/70.61 thf(3769,axiom,((! [A:int,B:int,C:nat]: ((! [D:nat]: (~ (bit_se1146084159140164899it_int @ A @ D) | ~ (bit_se1146084159140164899it_int @ B @ D))) => ((bit_se1146084159140164899it_int @ (plus_plus_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ A @ C) | (bit_se1146084159140164899it_int @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6363_bit__disjunctive__add__iff)). 159.59/70.61 thf(20373,plain,((! [A:int,B:int,C:nat]: ((! [D:nat]: (~ (bit_se1146084159140164899it_int @ A @ D) | ~ (bit_se1146084159140164899it_int @ B @ D))) => ((bit_se1146084159140164899it_int @ (plus_plus_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ A @ C) | (bit_se1146084159140164899it_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3769])). 159.59/70.61 thf(3421,axiom,((! [A:$o]: ((zero_n2684676970156552555ol_int @ (~ (A))) = (minus_minus_int @ one_one_int @ (zero_n2684676970156552555ol_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4350_of__bool__not__iff)). 159.59/70.61 thf(19250,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)],[3421])). 159.59/70.61 thf(4429,axiom,((! [A:extended_enat,B:(int > extended_enat),C:int,D:int]: ((ord_le72135733267957522d_enat @ A @ (B @ C)) => (((ord_le72135733267957522d_enat @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_int @ E @ F) => (ord_le72135733267957522d_enat @ (B @ E) @ (B @ F))))) <= (ord_less_int @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2892_order__less__subst1)). 159.59/70.61 thf(22442,plain,((! [A:extended_enat,B:(int > extended_enat),C:int,D:int]: ((ord_le72135733267957522d_enat @ A @ (B @ C)) => ((ord_le72135733267957522d_enat @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_int @ E @ F) => (ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)))) | ~ (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4429])). 159.59/70.61 thf(1775,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/sandbox/benchmark/theBenchmark.p',fact_3883_even__mod__2__iff)). 159.59/70.61 thf(13987,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)],[1775])). 159.59/70.61 thf(8111,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/sandbox/benchmark/theBenchmark.p',fact_887_power2__commute)). 159.59/70.61 thf(36180,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)],[8111])). 159.59/70.61 thf(967,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/sandbox/benchmark/theBenchmark.p',fact_1360_square__diff__square__factored)). 159.59/70.61 thf(11344,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)],[967])). 159.59/70.61 thf(7359,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (~ (ord_less_num @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4484_minf_I7_J)). 159.59/70.61 thf(33700,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)],[7359])). 159.59/70.61 thf(7180,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_real @ (root @ A @ B) @ one_one_real) = (ord_less_real @ B @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9491_real__root__lt__1__iff)). 159.59/70.61 thf(33055,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_real @ (root @ A @ B) @ one_one_real) = (ord_less_real @ B @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7180])). 159.59/70.61 thf(7366,axiom,((! [A:code_integer,B:$o,C:code_integer,D:$o]: (((produc6677183202524767010eger_o @ A @ B) = (produc6677183202524767010eger_o @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3603_old_Oprod_Oinject)). 159.59/70.61 thf(33719,plain,((! [A:code_integer,B:$o,C:code_integer,D:$o]: (((produc6677183202524767010eger_o @ A @ B) = (produc6677183202524767010eger_o @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7366])). 159.59/70.61 thf(1177,axiom,(((cos_complex @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one)))) = zero_zero_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7375_cos__of__real__pi__half)). 159.59/70.61 thf(12023,plain,(((cos_complex @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one)))) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177])). 159.59/70.61 thf(6431,axiom,((! [A:nat]: ((power_power_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1677_power__0__Suc)). 159.59/70.61 thf(29980,plain,((! [A:nat]: ((power_power_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6431])). 159.59/70.61 thf(2689,axiom,((! [A:real]: (((real_V7735802525324610683m_real @ (cos_real @ A)) = one_one_real) <= ((sin_real @ A) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7114_sin__zero__norm__cos__one)). 159.59/70.61 thf(16929,plain,((! [A:real]: (((real_V7735802525324610683m_real @ (cos_real @ A)) = one_one_real) | ~ ((sin_real @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2689])). 159.59/70.61 thf(5810,axiom,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5168_neg__one__le__numeral)). 159.59/70.61 thf(27615,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)],[5810])). 159.59/70.61 thf(7742,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/sandbox/benchmark/theBenchmark.p',fact_4580_crossproduct__eq)). 159.59/70.61 thf(35024,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)],[7742])). 159.59/70.61 thf(1994,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/sandbox/benchmark/theBenchmark.p',fact_9456_nat__mod__distrib)). 159.59/70.61 thf(14697,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)],[1994])). 159.59/70.61 thf(4229,axiom,((! [A:nat]: ((semiri5044797733671781792omplex @ (suc @ A)) = (times_times_complex @ (semiri8010041392384452111omplex @ (suc @ A)) @ (semiri5044797733671781792omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8061_fact__Suc)). 159.59/70.61 thf(21829,plain,((! [A:nat]: ((semiri5044797733671781792omplex @ (suc @ A)) = (times_times_complex @ (semiri8010041392384452111omplex @ (suc @ A)) @ (semiri5044797733671781792omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4229])). 159.59/70.61 thf(7134,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (((vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ A @ D @ E) @ F) => ((F = C) | (F = B) | (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))))))) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_both__member__options__from__complete__tree__to__child)). 159.59/70.61 thf(32891,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (((vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ A @ D @ E) @ F) => ((F = C) | (F = B) | (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))))))) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7134])). 159.59/70.61 thf(5446,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1562_Nat_Oadd__0__right)). 159.59/70.61 thf(26254,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5446])). 159.59/70.61 thf(4269,axiom,((! [A:real,B:real]: ? [C:real]: ! [D:real]: ((ord_less_real @ D @ C) => ((dvd_dvd_real @ A @ (plus_plus_real @ D @ B)) = (dvd_dvd_real @ A @ (plus_plus_real @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4538_minf_I9_J)). 159.59/70.61 thf(21953,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4269])). 159.59/70.61 thf(4594,axiom,((! [A:nat,B:nat,C:nat]: ((? [D:nat,E:nat]: ((A = (times_times_nat @ D @ E)) & (dvd_dvd_nat @ E @ C) & (dvd_dvd_nat @ D @ B))) <= (dvd_dvd_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3927_division__decomp)). 159.59/70.61 thf(23115,plain,((! [A:nat,B:nat,C:nat]: (? [D:nat,E:nat]: ((A = (times_times_nat @ D @ E)) & (dvd_dvd_nat @ E @ C) & (dvd_dvd_nat @ D @ B)) | ~ (dvd_dvd_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4594])). 159.59/70.61 thf(7529,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((times_times_nat @ B @ (divide_divide_nat @ one_one_nat @ A)) = (divide_divide_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3864_unit__mult__div__div)). 159.59/70.61 thf(34277,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((times_times_nat @ B @ (divide_divide_nat @ one_one_nat @ A)) = (divide_divide_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7529])). 159.59/70.61 thf(349,axiom,((! [A:code_integer,B:code_integer]: ((A != zero_z3403309356797280102nteger) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ A @ B) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ B @ A) @ one_one_Code_integer))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2368_div__add__self1)). 159.59/70.61 thf(9330,plain,((! [A:code_integer,B:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ A @ B) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ B @ A) @ one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 159.59/70.61 thf(4346,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/sandbox/benchmark/theBenchmark.p',fact_5394_abs__add__abs)). 159.59/70.61 thf(22178,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)],[4346])). 159.59/70.61 thf(3972,axiom,((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2132_less__numeral__extra_I1_J)). 159.59/70.61 thf(21029,plain,((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3972])). 159.59/70.61 thf(7710,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => ((A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) <= (ord_less_nat @ zero_zero_nat @ C)))) => ((! [C:nat]: ((A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) <= (A @ C))) => (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2550_nat__bit__induct)). 159.59/70.61 thf(34883,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((A @ C) => ((A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) | ~ (ord_less_nat @ zero_zero_nat @ C)))) => ((! [C:nat]: ((A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) | ~ (A @ C))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7710])). 159.59/70.61 thf(3243,axiom,((! [A:nat,B:nat]: (((semiri4939895301339042750nteger @ A) = (semiri4939895301339042750nteger @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6491_of__nat__eq__iff)). 159.59/70.61 thf(18681,plain,((! [A:nat,B:nat]: (((semiri4939895301339042750nteger @ A) = (semiri4939895301339042750nteger @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3243])). 159.59/70.61 thf(6502,axiom,(((neg_nu8295874005876285629c_real @ one_one_real) = (numeral_numeral_real @ (bit1 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5746_dbl__inc__simps_I3_J)). 159.59/70.61 thf(30253,plain,(((neg_nu8295874005876285629c_real @ one_one_real) = (numeral_numeral_real @ (bit1 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6502])). 159.59/70.61 thf(7423,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/sandbox/benchmark/theBenchmark.p',fact_3857_concat__bit__nonnegative__iff)). 159.59/70.61 thf(33898,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)],[7423])). 159.59/70.61 thf(4885,axiom,((! [A:nat]: ((zero_zero_nat = (semiri1316708129612266289at_nat @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6504_of__nat__0__eq__iff)). 159.59/70.61 thf(24137,plain,((! [A:nat]: ((zero_zero_nat = (semiri1316708129612266289at_nat @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4885])). 159.59/70.61 thf(6974,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_VEBT_membermima @ A @ B) = C) => (((? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E))) => (C)) => (((? [D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E))) => (C)) => (((~ (! [D:nat,E:list_VEBT_VEBT]: ((? [F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ D) @ E @ F))) => (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]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H))) => (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))))))) <= (! [D:nat,E:nat]: ((C = (~ ((B = E) | (B = D)))) <= (? [F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2493_VEBT__internal_Omembermima_Oelims_I1_J)). 159.59/70.61 thf(32202,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_VEBT_membermima @ A @ B) = C) => (((? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E))) => (C)) => (((? [D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ D @ E))) => (C)) => (~ (! [D:nat,E:list_VEBT_VEBT]: ((? [F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ D) @ E @ F))) => (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]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ F) @ G @ H))) => (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)))))) | ~ (! [D:nat,E:nat]: ((C = (~ ((B = E) | (B = D)))) | ~ (? [F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6974])). 159.59/70.61 thf(4329,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((B != zero_zero_complex) => ((plus_plus_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B)) = (times_times_complex @ (times_times_complex @ (plus_plus_complex @ A @ B) @ (invers8013647133539491842omplex @ A)) @ (invers8013647133539491842omplex @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9073_inverse__add)). 159.59/70.61 thf(22127,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => ((~ (B = zero_zero_complex)) => ((plus_plus_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B)) = (times_times_complex @ (times_times_complex @ (plus_plus_complex @ A @ B) @ (invers8013647133539491842omplex @ A)) @ (invers8013647133539491842omplex @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4329])). 159.59/70.61 thf(5033,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/sandbox/benchmark/theBenchmark.p',fact_4818_neg__numeral__le__iff)). 159.59/70.61 thf(24663,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)],[5033])). 159.59/70.61 thf(3349,axiom,((! [A:extended_enat,B:extended_enat]: ((if_Extended_enat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Extended____Nat__Oenat_T)). 159.59/70.61 thf(19020,plain,((! [A:extended_enat,B:extended_enat]: ((if_Extended_enat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3349])). 159.59/70.61 thf(2768,axiom,((! [A:int,B:int]: ((ring_17405671764205052669omplex @ (plus_plus_int @ A @ B)) = (plus_plus_complex @ (ring_17405671764205052669omplex @ A) @ (ring_17405671764205052669omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5780_of__int__add)). 159.59/70.61 thf(17171,plain,((! [A:int,B:int]: ((ring_17405671764205052669omplex @ (plus_plus_int @ A @ B)) = (plus_plus_complex @ (ring_17405671764205052669omplex @ A) @ (ring_17405671764205052669omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2768])). 159.59/70.61 thf(2914,axiom,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (sin_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6836_sin__ge__minus__one)). 159.59/70.61 thf(17635,plain,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (sin_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2914])). 159.59/70.61 thf(3115,axiom,((! [A:complex,B:complex,C:complex]: (((dvd_dvd_complex @ A @ C) => (dvd_dvd_complex @ A @ (plus_plus_complex @ B @ C))) <= (dvd_dvd_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3980_dvd__add)). 159.59/70.61 thf(18273,plain,((! [A:complex,B:complex,C:complex]: (((dvd_dvd_complex @ A @ C) => (dvd_dvd_complex @ A @ (plus_plus_complex @ B @ C))) | ~ (dvd_dvd_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3115])). 159.59/70.61 thf(8101,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_nat @ A @ B) | (ord_less_nat @ C @ A)) => (((vEBT_vebt_delete @ (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/sandbox/benchmark/theBenchmark.p',fact_487_delt__out__of__range)). 159.59/70.61 thf(36146,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_nat @ A @ B) | (ord_less_nat @ C @ A)) => (((vEBT_vebt_delete @ (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)],[8101])). 159.59/70.61 thf(6434,axiom,((! [A:complex,B:nat]: (((power_power_complex @ A @ B) != zero_zero_complex) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1895_power__not__zero)). 159.59/70.61 thf(29990,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)],[6434])). 159.59/70.61 thf(6901,axiom,((! [A:int,B:num]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ zero_zero_int) = ((((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))) & (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3918_power__le__zero__eq__numeral)). 159.59/70.61 thf(31860,plain,((! [A:int,B:num]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ B)) @ zero_zero_int) = ((((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))) & (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6901])). 159.59/70.61 thf(6067,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A)))) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6014_and__minus__numerals_I2_J)). 159.59/70.61 thf(28651,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)],[6067])). 159.59/70.61 thf(4987,axiom,((! [A:nat,B:nat]: ((ord_less_eq_real @ (semiri2265585572941072030t_real @ A) @ (semiri2265585572941072030t_real @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8087_fact__mono)). 159.59/70.61 thf(24509,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)],[4987])). 159.59/70.61 thf(5121,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_real @ zero_zero_real @ A) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1818_zero__power)). 159.59/70.61 thf(24975,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_real @ zero_zero_real @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5121])). 159.59/70.61 thf(1580,axiom,((! [A:nat,B:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6683_less__imp__of__nat__less)). 159.59/70.61 thf(13382,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)],[1580])). 159.59/70.61 thf(1403,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/sandbox/benchmark/theBenchmark.p',fact_6113_take__bit__eq__mask__iff)). 159.59/70.61 thf(12828,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)],[1403])). 159.59/70.61 thf(6411,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2745_ord__eq__le__trans)). 159.59/70.61 thf(29891,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6411])). 159.59/70.61 thf(270,axiom,((cot_real = (^ [A:real]: (divide_divide_real @ (cos_real @ A) @ (sin_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9399_cot__def)). 159.59/70.61 thf(9071,plain,(((cot_real) = (^ [A:real]: (divide_divide_real @ (cos_real @ A) @ (sin_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 159.59/70.61 thf(5644,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/sandbox/benchmark/theBenchmark.p',fact_338_power__le__imp__le__exp)). 159.59/70.61 thf(26916,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)],[5644])). 159.59/70.61 thf(1666,axiom,((! [A:nat,B:nat]: ((modulo364778990260209775nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ (ord_less_nat @ A @ B)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4515_exp__mod__exp)). 159.59/70.61 thf(13647,plain,((! [A:nat,B:nat]: ((modulo364778990260209775nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ (ord_less_nat @ A @ B)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666])). 159.59/70.61 thf(3508,axiom,((! [A:num,B:num,C:extended_enat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ B) @ C)) = (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (times_times_num @ A @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_mult__numeral__left__semiring__numeral)). 159.59/70.61 thf(19514,plain,((! [A:num,B:num,C:extended_enat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ B) @ C)) = (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (times_times_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3508])). 159.59/70.61 thf(5718,axiom,((! [A:int,B:nat]: (((ord_less_eq_int @ (power_power_int @ A @ B) @ one_one_int) <= (ord_less_eq_int @ A @ one_one_int)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2336_power__le__one)). 159.59/70.61 thf(27179,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ (power_power_int @ A @ B) @ one_one_int) | ~ (ord_less_eq_int @ A @ one_one_int) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5718])). 159.59/70.61 thf(1628,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/sandbox/benchmark/theBenchmark.p',fact_110_distrib__left__numeral)). 159.59/70.61 thf(13538,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)],[1628])). 159.59/70.61 thf(6695,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((((vEBT_VEBT_membermima @ A @ C) | (vEBT_V5719532721284313246member @ A @ C)) <= (vEBT_vebt_member @ A @ C)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1472_member__valid__both__member__options)). 159.59/70.61 thf(30994,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_VEBT_membermima @ A @ C) | (vEBT_V5719532721284313246member @ A @ C) | ~ (vEBT_vebt_member @ A @ C) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6695])). 159.59/70.61 thf(6140,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/sandbox/benchmark/theBenchmark.p',fact_706_mult__le__mono1)). 159.59/70.61 thf(28885,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)],[6140])). 159.59/70.61 thf(7390,axiom,((! [A:$o,B:$o]: (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1810_invar__vebt_Ointros_I1_J)). 159.59/70.61 thf(33803,plain,((! [A:$o,B:$o]: (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7390])). 159.59/70.61 thf(2999,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ A @ (set_ord_atMost_nat @ B)) = (plus_plus_int @ (A @ zero_zero_nat) @ (groups3539618377306564664at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8837_sum_OatMost__shift)). 159.59/70.61 thf(17899,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (A) @ (set_ord_atMost_nat @ 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)],[2999])). 159.59/70.61 thf(8066,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2861_order__less__trans)). 159.59/70.61 thf(36046,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8066])). 159.59/70.61 thf(7228,axiom,((! [A:num,B:nat,C:nat]: ((((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)))) <= (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 @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1391_divmod__step__eq)). 159.59/70.61 thf(33246,plain,((! [A:num,B:nat,C:nat]: ((((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)))) | ~ (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 @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7228])). 159.59/70.61 thf(2550,axiom,((! [A:num]: ((numeral_numeral_int @ (inc @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5729_numeral__inc)). 159.59/70.61 thf(16448,plain,((! [A:num]: ((numeral_numeral_int @ (inc @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2550])). 159.59/70.61 thf(6702,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/sandbox/benchmark/theBenchmark.p',fact_6762_real__of__nat__div2)). 159.59/70.61 thf(31016,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)],[6702])). 159.59/70.61 thf(3498,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/sandbox/benchmark/theBenchmark.p',fact_5602_cong__exp__iff__simps_I10_J)). 159.59/70.61 thf(19485,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)],[3498])). 159.59/70.61 thf(2252,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/sandbox/benchmark/theBenchmark.p',fact_1738_divide__less__eq__1__neg)). 159.59/70.61 thf(15515,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)],[2252])). 159.59/70.61 thf(6521,axiom,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ B)) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_int @ zero_zero_int @ A)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A != zero_zero_int)) | (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4265_zero__less__power__eq)). 159.59/70.61 thf(30312,plain,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ A @ B)) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_int @ zero_zero_int @ A)) | ((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)],[6521])). 159.59/70.61 thf(4160,axiom,((! [A:nat,B:int]: ((times_times_int @ (semiri1314217659103216013at_int @ A) @ B) = (times_times_int @ B @ (semiri1314217659103216013at_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6650_mult__of__nat__commute)). 159.59/70.61 thf(21599,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)],[4160])). 159.59/70.61 thf(7448,axiom,((! [A:(int > $o),B:nat,C:nat]: ((A @ (semiri1314217659103216013at_int @ (minus_minus_nat @ B @ C))) = (((A @ zero_zero_int) <= (ord_less_nat @ B @ C)) & ((ord_less_eq_nat @ C @ B) => (A @ (minus_minus_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6856_zdiff__int__split)). 159.59/70.61 thf(33986,plain,((! [A:(int > $o),B:nat,C:nat]: ((A @ (semiri1314217659103216013at_int @ (minus_minus_nat @ B @ C))) = (((A @ zero_zero_int) | ~ (ord_less_nat @ B @ C)) & ((ord_less_eq_nat @ C @ B) => (A @ (minus_minus_int @ (semiri1314217659103216013at_int @ B) @ (semiri1314217659103216013at_int @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7448])). 159.59/70.61 thf(6352,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/sandbox/benchmark/theBenchmark.p',fact_4918_take__bit__tightened__less__eq__nat)). 159.59/70.61 thf(29648,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)],[6352])). 159.59/70.61 thf(1345,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/sandbox/benchmark/theBenchmark.p',fact_1283_diff__add__eq)). 159.59/70.61 thf(12593,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)],[1345])). 159.59/70.61 thf(7998,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ A) @ B) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_low__inv)). 159.59/70.61 thf(35809,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ A) @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7998])). 159.59/70.61 thf(1965,axiom,((! [A:num]: ((modulo_modulo_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ one)) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3501_cong__exp__iff__simps_I1_J)). 159.59/70.61 thf(14584,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)],[1965])). 159.59/70.61 thf(2950,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ A @ B)) @ C) = (((((ord_less_real @ (times_times_real @ C @ B) @ (uminus_uminus_real @ 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 @ (uminus_uminus_real @ A) @ (times_times_real @ C @ B)) <= (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5241_minus__divide__less__eq)). 159.59/70.61 thf(17747,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ A @ B)) @ C) = (((((ord_less_real @ (times_times_real @ C @ B) @ (uminus_uminus_real @ 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 @ (uminus_uminus_real @ A) @ (times_times_real @ C @ B)) | ~ (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2950])). 159.59/70.61 thf(5171,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/sandbox/benchmark/theBenchmark.p',fact_6951_square__norm__one)). 159.59/70.61 thf(25153,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)],[5171])). 159.59/70.61 thf(7514,axiom,((! [A:num,B:num,C:num]: (((ord_less_eq_num @ A @ C) <= (ord_less_eq_num @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2744_ord__eq__le__trans)). 159.59/70.61 thf(34232,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)],[7514])). 159.59/70.61 thf(7309,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/sandbox/benchmark/theBenchmark.p',fact_1104_mult_Oassoc)). 159.59/70.61 thf(33539,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)],[7309])). 159.59/70.61 thf(1822,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/sandbox/benchmark/theBenchmark.p',fact_9423_nat__less__numeral__power__cancel__iff)). 159.59/70.61 thf(14132,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)],[1822])). 159.59/70.61 thf(179,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ (times_3573771949741848930nteger @ A @ C)) @ A) = (plus_p5714425477246183910nteger @ C @ (divide6298287555418463151nteger @ B @ A))) <= (A != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1748_div__mult__self2)). 159.59/70.61 thf(8802,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ (times_3573771949741848930nteger @ A @ C)) @ A) = (plus_p5714425477246183910nteger @ C @ (divide6298287555418463151nteger @ B @ A))) | (A = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[179])). 159.59/70.61 thf(199,axiom,((! [A:code_integer,B:code_integer]: ((divide6298287555418463151nteger @ (modulo364778990260209775nteger @ A @ B) @ B) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3411_mod__div__trivial)). 159.59/70.61 thf(8860,plain,((! [A:code_integer,B:code_integer]: ((divide6298287555418463151nteger @ (modulo364778990260209775nteger @ A @ B) @ B) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 159.59/70.61 thf(4324,axiom,((! [A:int,B:int]: ((ord_less_int @ (abs_abs_int @ (ring_1_of_int_int @ A)) @ B) => ((A = zero_zero_int) | (ord_less_int @ one_one_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5904_of__int__lessD)). 159.59/70.61 thf(22112,plain,((! [A:int,B:int]: ((ord_less_int @ (abs_abs_int @ (ring_1_of_int_int @ A)) @ B) => ((A = zero_zero_int) | (ord_less_int @ one_one_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4324])). 159.59/70.61 thf(6832,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/sandbox/benchmark/theBenchmark.p',fact_3632_zmod__numeral__Bit0)). 159.59/70.61 thf(31552,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)],[6832])). 159.59/70.61 thf(8050,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_trans__less__add2)). 159.59/70.61 thf(35991,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)],[8050])). 159.59/70.61 thf(7918,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/sandbox/benchmark/theBenchmark.p',fact_6610_of__nat__power__less__of__nat__cancel__iff)). 159.59/70.61 thf(35564,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)],[7918])). 159.59/70.61 thf(5750,axiom,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1464_valid__0__not)). 159.59/70.61 thf(27295,plain,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5750])). 159.59/70.61 thf(4528,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sqrt @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6317_real__sqrt__ge__0__iff)). 159.59/70.61 thf(22887,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)],[4528])). 159.59/70.61 thf(7145,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: (((vEBT_vebt_member @ A @ C) = (member_nat @ C @ (vEBT_set_vebt @ A))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_member__correct)). 159.59/70.61 thf(32923,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: (((vEBT_vebt_member @ A @ C) = (member_nat @ C @ (vEBT_set_vebt @ A))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7145])). 159.59/70.61 thf(904,axiom,((ord_less_real @ (uminus_uminus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) @ pi)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6774_m2pi__less__pi)). 159.59/70.61 thf(11154,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)],[904])). 159.59/70.61 thf(2599,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/sandbox/benchmark/theBenchmark.p',fact_9466_nat__less__iff)). 159.59/70.61 thf(16608,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)],[2599])). 159.59/70.61 thf(1039,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/sandbox/benchmark/theBenchmark.p',fact_8262_real__of__int__floor__ge__diff__one)). 159.59/70.61 thf(11577,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)],[1039])). 159.59/70.61 thf(7477,axiom,((! [A:num,B:num]: (((A != B) => (ord_less_num @ B @ A)) <= (~ (ord_less_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2793_linorder__cases)). 159.59/70.61 thf(34084,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)],[7477])). 159.59/70.61 thf(4171,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/sandbox/benchmark/theBenchmark.p',fact_9569_xor__int__rec)). 159.59/70.61 thf(21633,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)],[4171])). 159.59/70.61 thf(1862,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/sandbox/benchmark/theBenchmark.p',fact_3503_cong__exp__iff__simps_I6_J)). 159.59/70.61 thf(14267,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)],[1862])). 159.59/70.61 thf(2236,axiom,((! [A:(nat > real),B:(nat > real)]: ((? [C:nat]: ! [D:nat]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (A @ D)) @ (B @ D)) <= (ord_less_eq_nat @ C @ D))) => ((summable_real @ A) <= (summable_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7017_summable__comparison__test)). 159.59/70.61 thf(15468,plain,((! [A:(nat > real),B:(nat > real)]: ((? [C:nat]: ! [D:nat]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (A @ D)) @ (B @ D)) | ~ (ord_less_eq_nat @ C @ D))) => ((summable_real @ (A)) | ~ (summable_real @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2236])). 159.59/70.61 thf(3501,axiom,((! [A:nat,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ (semiri1314217659103216013at_int @ A) @ B)) = ((B = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6624_of__nat__zero__less__power__iff)). 159.59/70.61 thf(19495,plain,((! [A:nat,B:nat]: ((ord_less_int @ zero_zero_int @ (power_power_int @ (semiri1314217659103216013at_int @ A) @ B)) = ((B = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3501])). 159.59/70.61 thf(5843,axiom,((! [A:$o,B:nat]: ((bit_se1148574629649215175it_nat @ (zero_n2687167440665602831ol_nat @ A) @ B) = ((B = zero_zero_nat) & (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6397_bit__of__bool__iff)). 159.59/70.61 thf(27843,plain,((! [A:$o,B:nat]: ((bit_se1148574629649215175it_nat @ (zero_n2687167440665602831ol_nat @ A) @ B) = ((B = zero_zero_nat) & (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5843])). 159.59/70.61 thf(5013,axiom,((! [A:nat,B:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6524_of__nat__le__iff)). 159.59/70.61 thf(24596,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)],[5013])). 159.59/70.61 thf(498,axiom,((! [A:nat]: (filterlim_real_real @ (^ [B:real]: (divide_divide_real @ (power_power_real @ B @ A) @ (exp_real @ B))) @ (topolo2815343760600316023s_real @ zero_zero_real) @ at_top_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9959_tendsto__power__div__exp__0)). 159.59/70.61 thf(9837,plain,((! [A:nat]: (filterlim_real_real @ (^ [B:real]: (divide_divide_real @ (power_power_real @ B @ A) @ (exp_real @ B))) @ (topolo2815343760600316023s_real @ zero_zero_real) @ at_top_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])). 159.59/70.61 thf(7929,axiom,(((semiri4449623510593786356d_enat @ (numeral_numeral_nat @ (bit0 @ one))) = (numera1916890842035813515d_enat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8065_fact__2)). 159.59/70.61 thf(35596,plain,(((semiri4449623510593786356d_enat @ (numeral_numeral_nat @ (bit0 @ one))) = (numera1916890842035813515d_enat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7929])). 159.59/70.61 thf(3536,axiom,((! [A:num,B:num,C:(num > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_real @ (C @ E) @ (C @ F)) <= (ord_less_num @ E @ F))))) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3247_order__less__le__subst2)). 159.59/70.61 thf(19598,plain,((! [A:num,B:num,C:(num > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_real @ (C @ E) @ (C @ F)) | ~ (ord_less_num @ E @ F))))) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3536])). 159.59/70.61 thf(7726,axiom,((! [A:nat,B:nat]: ((((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))) <= (ord_less_nat @ zero_zero_nat @ B)) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3922_even__succ__div__exp)). 159.59/70.61 thf(34961,plain,((! [A:nat,B:nat]: (((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))) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7726])). 159.59/70.61 thf(5043,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/sandbox/benchmark/theBenchmark.p',fact_5654_divmod__def)). 159.59/70.61 thf(24695,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)],[5043])). 159.59/70.61 thf(5645,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/sandbox/benchmark/theBenchmark.p',fact_3819_dvd__times__left__cancel__iff)). 159.59/70.61 thf(26919,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)],[5645])). 159.59/70.61 thf(4840,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/sandbox/benchmark/theBenchmark.p',fact_5219_power__minus__Bit0)). 159.59/70.61 thf(24001,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)],[4840])). 159.59/70.61 thf(7618,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/sandbox/benchmark/theBenchmark.p',fact_3483_div__add1__eq)). 159.59/70.61 thf(34607,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)],[7618])). 159.59/70.61 thf(22,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/sandbox/benchmark/theBenchmark.p',fact_971_max_Ostrict__boundedE)). 159.59/70.61 thf(8321,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)],[22])). 159.59/70.61 thf(3746,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (ln_ln_real @ A) @ zero_zero_real) <= (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5134_ln__less__zero)). 159.59/70.61 thf(20304,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (ln_ln_real @ A) @ zero_zero_real) | ~ (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3746])). 159.59/70.61 thf(2742,axiom,((! [A:real]: ((((powr_real @ A @ zero_zero_real) = one_one_real) <= (A != zero_zero_real)) & ((A = zero_zero_real) => ((powr_real @ A @ zero_zero_real) = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7211_powr__zero__eq__one)). 159.59/70.61 thf(17090,plain,((! [A:real]: ((((powr_real @ A @ zero_zero_real) = one_one_real) | (A = zero_zero_real)) & ((A = zero_zero_real) => ((powr_real @ A @ zero_zero_real) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2742])). 159.59/70.61 thf(6750,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/sandbox/benchmark/theBenchmark.p',fact_5713_signed__take__bit__numeral__bit0)). 159.59/70.61 thf(31279,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)],[6750])). 159.59/70.61 thf(505,axiom,((! [A:real,B:num]: ((real_V7735802525324610683m_real @ (plus_plus_real @ (real_V1803761363581548252l_real @ A) @ (numeral_numeral_real @ B))) = (abs_abs_real @ (plus_plus_real @ A @ (numeral_numeral_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7368_norm__of__real__addn)). 159.59/70.61 thf(9860,plain,((! [A:real,B:num]: ((real_V7735802525324610683m_real @ (plus_plus_real @ (real_V1803761363581548252l_real @ A) @ (numeral_numeral_real @ B))) = (abs_abs_real @ (plus_plus_real @ A @ (numeral_numeral_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])). 159.59/70.61 thf(6534,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ one_one_nat) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6111_and__one__eq)). 159.59/70.61 thf(30378,plain,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ one_one_nat) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6534])). 159.59/70.61 thf(1458,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/sandbox/benchmark/theBenchmark.p',fact_6130_OR__upper)). 159.59/70.61 thf(13013,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)],[1458])). 159.59/70.61 thf(2137,axiom,((ord_less_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2135_less__numeral__extra_I1_J)). 159.59/70.61 thf(15150,plain,((ord_less_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2137])). 159.59/70.61 thf(3955,axiom,((! [A:complex,B:complex,C:complex,D:complex]: (((plus_plus_complex @ A @ D) = (plus_plus_complex @ B @ (plus_plus_complex @ C @ D))) <= (A = (plus_plus_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_group__cancel_Oadd1)). 159.59/70.61 thf(20978,plain,((! [A:complex,B:complex,C:complex,D:complex]: (((plus_plus_complex @ A @ D) = (plus_plus_complex @ B @ (plus_plus_complex @ C @ D))) | ~ (A = (plus_plus_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3955])). 159.59/70.61 thf(3031,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/sandbox/benchmark/theBenchmark.p',fact_7957_sum_OlessThan__Suc__shift)). 159.59/70.61 thf(17994,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)],[3031])). 159.59/70.61 thf(4850,axiom,((! [A:real,B:real]: ((sqrt @ (times_times_real @ A @ B)) = (times_times_real @ (sqrt @ A) @ (sqrt @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6370_real__sqrt__mult)). 159.59/70.61 thf(24032,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)],[4850])). 159.59/70.61 thf(2845,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/sandbox/benchmark/theBenchmark.p',fact_7889_sums__mult)). 159.59/70.61 thf(17398,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)],[2845])). 159.59/70.61 thf(6457,axiom,((! [A:(real > $o),B:nat,C:real]: ((A @ (root @ B @ C)) = (((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)))) & ((B = zero_zero_nat) => (A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9506_split__root)). 159.59/70.61 thf(30081,plain,((! [A:(real > $o),B:nat,C:real]: ((A @ (root @ B @ C)) = (((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)))) & ((B = zero_zero_nat) => (A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6457])). 159.59/70.61 thf(7679,axiom,((! [A:set_nat,B:nat]: ((((nat_set_encode @ (insert_nat @ B @ A)) = (plus_plus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (nat_set_encode @ A))) <= (~ (member_nat @ B @ A))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6362_set__encode__insert)). 159.59/70.61 thf(34793,plain,((! [A:set_nat,B:nat]: (((nat_set_encode @ (insert_nat @ B @ A)) = (plus_plus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (nat_set_encode @ A))) | (member_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7679])). 159.59/70.61 thf(1590,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => (dvd_dvd_complex @ A @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3950_dvd__mult2)). 159.59/70.61 thf(13414,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => (dvd_dvd_complex @ A @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1590])). 159.59/70.61 thf(1091,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ zero_z5237406670263579293d_enat @ A) = zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1496_mult__zero__left)). 159.59/70.61 thf(11748,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ zero_z5237406670263579293d_enat @ A) = zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091])). 159.59/70.61 thf(3073,axiom,((ord_less_int = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3080_order_Ostrict__iff__order)). 159.59/70.61 thf(18126,plain,(((ord_less_int) = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3073])). 159.59/70.61 thf(2869,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ C @ B) => (ord_le72135733267957522d_enat @ C @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4477_minf_I5_J)). 159.59/70.61 thf(17485,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ C @ B) => (ord_le72135733267957522d_enat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2869])). 159.59/70.61 thf(5731,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/sandbox/benchmark/theBenchmark.p',fact_2527_power__eq__if)). 159.59/70.61 thf(27233,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)],[5731])). 159.59/70.61 thf(8144,axiom,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4911_take__bit__of__2)). 159.59/70.61 thf(36294,plain,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8144])). 159.59/70.61 thf(7321,axiom,((! [A:complex,B:complex]: ((((minus_minus_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B)) = (uminus1482373934393186551omplex @ (times_times_complex @ (times_times_complex @ (invers8013647133539491842omplex @ A) @ (minus_minus_complex @ A @ B)) @ (invers8013647133539491842omplex @ B)))) <= (B != zero_zero_complex)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9092_inverse__diff__inverse)). 159.59/70.61 thf(33571,plain,((! [A:complex,B:complex]: (((minus_minus_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B)) = (uminus1482373934393186551omplex @ (times_times_complex @ (times_times_complex @ (invers8013647133539491842omplex @ A) @ (minus_minus_complex @ A @ B)) @ (invers8013647133539491842omplex @ B)))) | (B = zero_zero_complex) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7321])). 159.59/70.61 thf(2497,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_eq_real @ (powr_real @ (ln_ln_real @ A) @ B) @ (times_times_real @ (powr_real @ B @ B) @ A)) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7276_ln__powr__bound2)). 159.59/70.61 thf(16293,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_eq_real @ (powr_real @ (ln_ln_real @ A) @ B) @ (times_times_real @ (powr_real @ B @ B) @ A)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2497])). 159.59/70.61 thf(7120,axiom,((! [A:num,B:num]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4811_mult__neg__numeral__simps_I2_J)). 159.59/70.61 thf(32831,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)],[7120])). 159.59/70.61 thf(5772,axiom,((! [A:nat,B:nat,C:real]: ((((ord_less_eq_real @ one_one_real @ C) => (ord_less_eq_real @ (root @ B @ C) @ (root @ A @ C))) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9519_real__root__decreasing)). 159.59/70.61 thf(27365,plain,((! [A:nat,B:nat,C:real]: (((ord_less_eq_real @ one_one_real @ C) => (ord_less_eq_real @ (root @ B @ C) @ (root @ A @ C))) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5772])). 159.59/70.61 thf(6341,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/sandbox/benchmark/theBenchmark.p',fact_5322_minus__1__div__exp__eq__int)). 159.59/70.61 thf(29612,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)],[6341])). 159.59/70.61 thf(4179,axiom,((! [A:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (semiri4939895301339042750nteger @ A)) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6646_even__of__nat)). 159.59/70.61 thf(21656,plain,((! [A:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (semiri4939895301339042750nteger @ A)) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4179])). 159.59/70.61 thf(5707,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((((power_power_nat @ B @ A) = (power_power_nat @ C @ A)) = (B = C)) <= (ord_less_eq_nat @ zero_zero_nat @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1932_power__eq__iff__eq__base)). 159.59/70.61 thf(27147,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((((power_power_nat @ B @ A) = (power_power_nat @ C @ A)) = (B = C)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5707])). 159.59/70.61 thf(879,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1243_ring__class_Oring__distribs_I2_J)). 159.59/70.61 thf(11083,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[879])). 159.59/70.61 thf(844,axiom,((! [A:num]: ~ (ord_le72135733267957522d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_not__numeral__less__one)). 159.59/70.61 thf(10972,plain,((! [A:num]: ~ (ord_le72135733267957522d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[844])). 159.59/70.61 thf(7141,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/sandbox/benchmark/theBenchmark.p',fact_5331_power__minus1__odd)). 159.59/70.61 thf(32912,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)],[7141])). 159.59/70.61 thf(7300,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/sandbox/benchmark/theBenchmark.p',fact_698_add__le__mono)). 159.59/70.61 thf(33485,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)],[7300])). 159.59/70.61 thf(126,axiom,((semiri4939895301339042750nteger = (^ [A:nat]: (if_Code_integer @ (A = zero_zero_nat) @ zero_z3403309356797280102nteger @ (produc1830744345554046123nteger @ (^ [B:nat,C:nat]: (if_Code_integer @ (C = zero_zero_nat) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (semiri4939895301339042750nteger @ B)) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (semiri4939895301339042750nteger @ B)) @ one_one_Code_integer))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6791_of__nat__code__if)). 159.59/70.61 thf(8642,plain,(((semiri4939895301339042750nteger) = (^ [A:nat]: (if_Code_integer @ (A = zero_zero_nat) @ zero_z3403309356797280102nteger @ (produc1830744345554046123nteger @ (^ [B:nat,C:nat]: (if_Code_integer @ (C = zero_zero_nat) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (semiri4939895301339042750nteger @ B)) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (semiri4939895301339042750nteger @ B)) @ one_one_Code_integer))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 159.59/70.61 thf(4165,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2934_order__less__imp__not__less)). 159.59/70.61 thf(21614,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4165])). 159.59/70.61 thf(3124,axiom,((! [A:nat,B:nat]: ((bit_se1745604003318907178nteger @ A @ (semiri4939895301339042750nteger @ B)) = (semiri4939895301339042750nteger @ (bit_se2925701944663578781it_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6712_take__bit__of__nat)). 159.59/70.61 thf(18301,plain,((! [A:nat,B:nat]: ((bit_se1745604003318907178nteger @ A @ (semiri4939895301339042750nteger @ B)) = (semiri4939895301339042750nteger @ (bit_se2925701944663578781it_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3124])). 159.59/70.61 thf(7775,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2936_order__less__imp__not__less)). 159.59/70.61 thf(35115,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7775])). 159.59/70.61 thf(375,axiom,((! [A:complex]: (sums_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (cos_coeff @ B) @ (power_power_complex @ A @ B))) @ (cos_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9268_cos__converges)). 159.59/70.61 thf(9415,plain,((! [A:complex]: (sums_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (cos_coeff @ B) @ (power_power_complex @ A @ B))) @ (cos_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])). 159.59/70.61 thf(4959,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat,F:nat,G:nat]: (((((((! [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) => (((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ E @ A @ C) @ E) <= ((F != G) => (! [H:nat]: ((((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ G @ B)) <= ((vEBT_VEBT_high @ G @ B) = H)) & ! [I:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ I @ B)) & ((vEBT_VEBT_high @ I @ B) = H)) => ((ord_less_eq_nat @ I @ G) & (ord_less_nat @ F @ I)))) <= (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)))))) <= (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)))))) <= (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)) <= (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ H @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_invar__vebt_Ointros_I4_J)). 159.59/70.61 thf(24390,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat,F:nat,G:nat]: (((! [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) => ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ E @ A @ C) @ E) | ~ ((~ (F = G)) => (! [H:nat]: ((((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ G @ B)) | ~ ((vEBT_VEBT_high @ G @ B) = H)) & ! [I:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ I @ B)) & ((vEBT_VEBT_high @ I @ B) = H)) => ((ord_less_eq_nat @ I @ G) & (ord_less_nat @ F @ I)))) | ~ (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) | ~ (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)))))) | ~ (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) | ~ (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ H @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4959])). 159.59/70.61 thf(1802,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/sandbox/benchmark/theBenchmark.p',fact_1439_divide__divide__eq__left_H)). 159.59/70.61 thf(14066,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)],[1802])). 159.59/70.61 thf(2695,axiom,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) = ((plus_plus_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5042_neg__eq__iff__add__eq__0)). 159.59/70.61 thf(16946,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)],[2695])). 159.59/70.61 thf(2874,axiom,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_add__right__cancel)). 159.59/70.61 thf(17498,plain,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2874])). 159.59/70.61 thf(1103,axiom,((! [A:real,B:real]: ((((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 @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5235_ln__div)). 159.59/70.61 thf(11793,plain,((! [A:real,B:real]: (((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 @ B) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103])). 159.59/70.61 thf(6932,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (uminus1351360451143612070nteger @ A)) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5258_even__minus)). 159.59/70.61 thf(31968,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)],[6932])). 159.59/70.61 thf(1243,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/sandbox/benchmark/theBenchmark.p',fact_3902_even__succ__div__2)). 159.59/70.61 thf(12276,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)],[1243])). 159.59/70.61 thf(6691,axiom,((! [A:nat,B:(nat > $o),C:nat]: ((! [D:nat]: ((B @ D) <= (ord_less_nat @ A @ D))) => ((B @ C) <= (! [D:nat]: (((! [E:nat]: ((B @ E) <= (ord_less_nat @ D @ E))) => (B @ D)) <= (ord_less_eq_nat @ D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9762_nat__descend__induct)). 159.59/70.61 thf(30977,plain,((! [A:nat,B:(nat > $o),C:nat]: ((! [D:nat]: ((B @ D) | ~ (ord_less_nat @ A @ D))) => ((B @ C) | ~ (! [D:nat]: (((! [E:nat]: ((B @ E) | ~ (ord_less_nat @ D @ E))) => (B @ D)) | ~ (ord_less_eq_nat @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6691])). 159.59/70.61 thf(2308,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1536_div__by__0)). 159.59/70.61 thf(15678,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2308])). 159.59/70.61 thf(999,axiom,((! [A:real,B:complex,C:nat]: ((power_power_complex @ (real_V2046097035970521341omplex @ A @ B) @ C) = (real_V2046097035970521341omplex @ (power_power_real @ A @ C) @ (power_power_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9196_scaleR__power)). 159.59/70.61 thf(11446,plain,((! [A:real,B:complex,C:nat]: ((power_power_complex @ (real_V2046097035970521341omplex @ A @ B) @ C) = (real_V2046097035970521341omplex @ (power_power_real @ A @ C) @ (power_power_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[999])). 159.59/70.61 thf(665,axiom,((! [A:nat]: ((bit_ri631733984087533419it_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4561_signed__take__bit__of__0)). 159.59/70.61 thf(10378,plain,((! [A:nat]: ((bit_ri631733984087533419it_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[665])). 159.59/70.61 thf(365,axiom,(((cis @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9378_cis__2pi)). 159.59/70.61 thf(9388,plain,(((cis @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])). 159.59/70.61 thf(165,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C))) = (ord_less_real @ (uminus_uminus_real @ C) @ (real_V1485227260804924795R_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9280_neg__less__minus__divideR__eq)). 159.59/70.61 thf(8759,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C))) = (ord_less_real @ (uminus_uminus_real @ C) @ (real_V1485227260804924795R_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[165])). 159.59/70.61 thf(2987,axiom,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1133_add_Oassoc)). 159.59/70.61 thf(17862,plain,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2987])). 159.59/70.61 thf(1161,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/sandbox/benchmark/theBenchmark.p',fact_1754_nonzero__divide__mult__cancel__left)). 159.59/70.61 thf(11971,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)],[1161])). 159.59/70.61 thf(7062,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_vebt_member @ A @ B) => ((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ ((((B = one_one_nat) & ((D) <= (B = one_one_nat))) <= (B != zero_zero_nat)) & ((C) <= (B = zero_zero_nat)))))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: ((~ (((((~ (ord_less_nat @ D @ B) & (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))))) <= (~ (ord_less_nat @ D @ B)))) <= (~ (ord_less_nat @ B @ C))) & ~ (ord_less_nat @ B @ C)) <= (B != D)) <= (B != C))) <= (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2553_vebt__member_Oelims_I2_J)). 159.59/70.61 thf(32568,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_vebt_member @ A @ B) => ((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ ((((B = one_one_nat) & ((D) | ~ (B = one_one_nat))) | (B = zero_zero_nat)) & ((C) | ~ (B = zero_zero_nat)))))) => (~ (! [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)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7062])). 159.59/70.61 thf(4996,axiom,((! [A:real]: ((ord_less_eq_int @ zero_zero_int @ (archim6058952711729229775r_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8185_zero__le__floor)). 159.59/70.61 thf(24546,plain,((! [A:real]: ((ord_less_eq_int @ zero_zero_int @ (archim6058952711729229775r_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4996])). 159.59/70.61 thf(4394,axiom,((! [A:complex]: ((minus_minus_complex @ (power_power_complex @ (cosh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (sinh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9345_hyperbolic__pythagoras)). 159.59/70.61 thf(22325,plain,((! [A:complex]: ((minus_minus_complex @ (power_power_complex @ (cosh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (sinh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4394])). 159.59/70.61 thf(2544,axiom,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2748_order__class_Oorder__eq__iff)). 159.59/70.61 thf(16431,plain,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2544])). 159.59/70.61 thf(1852,axiom,((! [A:real]: (((exp_real @ A) = one_one_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5979_exp__eq__one__iff)). 159.59/70.61 thf(14238,plain,((! [A:real]: (((exp_real @ A) = one_one_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1852])). 159.59/70.61 thf(6846,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) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2507_power2__eq__imp__eq)). 159.59/70.61 thf(31689,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) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6846])). 159.59/70.61 thf(4067,axiom,((! [A:nat,B:nat]: (((semiri8010041392384452111omplex @ A) = (semiri8010041392384452111omplex @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6490_of__nat__eq__iff)). 159.59/70.61 thf(21303,plain,((! [A:nat,B:nat]: (((semiri8010041392384452111omplex @ A) = (semiri8010041392384452111omplex @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4067])). 159.59/70.61 thf(3132,axiom,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ one_one_real) => (? [B:real]: (((tan_real @ B) = A) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) & (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7314_tan__total__pi4)). 159.59/70.61 thf(18324,plain,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ one_one_real) => (? [B:real]: (((tan_real @ B) = A) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) & (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3132])). 159.59/70.61 thf(7183,axiom,((! [A:num,B:num]: ((ord_less_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_semiring__norm_I78_J)). 159.59/70.61 thf(33091,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)],[7183])). 159.59/70.61 thf(5028,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1267_left__diff__distrib)). 159.59/70.61 thf(24648,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5028])). 159.59/70.61 thf(7986,axiom,((! [A:nat]: (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_less__exp)). 159.59/70.61 thf(35770,plain,((! [A:nat]: (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7986])). 159.59/70.61 thf(4989,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ (divide_divide_nat @ A @ B) @ one_one_nat) <= (dvd_dvd_nat @ B @ one_one_nat)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3846_unit__div)). 159.59/70.61 thf(24514,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (divide_divide_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)],[4989])). 159.59/70.61 thf(3611,axiom,((! [A:real,B:nat,C:real]: (((log @ (power_power_real @ A @ B) @ C) = (divide_divide_real @ (log @ A @ C) @ (semiri5074537144036343181t_real @ B))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6765_log__base__pow)). 159.59/70.61 thf(19845,plain,((! [A:real,B:nat,C:real]: (((log @ (power_power_real @ A @ B) @ C) = (divide_divide_real @ (log @ A @ C) @ (semiri5074537144036343181t_real @ B))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3611])). 159.59/70.61 thf(5476,axiom,((! [A:num]: ((plus_plus_num @ one @ (bit1 @ A)) = (bit0 @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5442_semiring__norm_I4_J)). 159.59/70.61 thf(26358,plain,((! [A:num]: ((plus_plus_num @ one @ (bit1 @ A)) = (bit0 @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5476])). 159.59/70.61 thf(1277,axiom,((! [A:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) = (A = zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2634_ile0__eq)). 159.59/70.61 thf(12379,plain,((! [A:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) = (A = zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277])). 159.59/70.61 thf(1850,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/sandbox/benchmark/theBenchmark.p',fact_127_is__num__normalize_I1_J)). 159.59/70.61 thf(14232,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)],[1850])). 159.59/70.61 thf(769,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/sandbox/benchmark/theBenchmark.p',fact_9479_sgn__le__0__iff)). 159.59/70.61 thf(10734,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)],[769])). 159.59/70.61 thf(7545,axiom,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2749_order__class_Oorder__eq__iff)). 159.59/70.61 thf(34323,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)],[7545])). 159.59/70.61 thf(345,axiom,((! [A:nat]: ((gbinomial_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8173_gbinomial__0_I2_J)). 159.59/70.61 thf(9319,plain,((! [A:nat]: ((gbinomial_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])). 159.59/70.61 thf(1232,axiom,((! [A:real]: ((sin_real @ (plus_plus_real @ pi @ A)) = (uminus_uminus_real @ (sin_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6801_sin__periodic__pi2)). 159.59/70.61 thf(12236,plain,((! [A:real]: ((sin_real @ (plus_plus_real @ pi @ A)) = (uminus_uminus_real @ (sin_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232])). 159.59/70.61 thf(3687,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/sandbox/benchmark/theBenchmark.p',fact_336_one__plus__numeral__commute)). 159.59/70.61 thf(20091,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)],[3687])). 159.59/70.61 thf(6923,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/sandbox/benchmark/theBenchmark.p',fact_86_mult__numeral__left__semiring__numeral)). 159.59/70.61 thf(31936,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)],[6923])). 159.59/70.61 thf(5114,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_int @ (archim7802044766580827645g_real @ (times_times_real @ A @ B)) @ (times_times_int @ (archim7802044766580827645g_real @ A) @ (archim7802044766580827645g_real @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7142_mult__ceiling__le)). 159.59/70.61 thf(24954,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_int @ (archim7802044766580827645g_real @ (times_times_real @ A @ B)) @ (times_times_int @ (archim7802044766580827645g_real @ A) @ (archim7802044766580827645g_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5114])). 159.59/70.61 thf(2369,axiom,((! [A:(nat > real),B:nat,C:nat]: (((ord_less_real @ (A @ B) @ (A @ C)) <= (ord_less_nat @ B @ C)) <= (! [D:nat]: (ord_less_real @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_lift__Suc__mono__less)). 159.59/70.61 thf(15856,plain,((! [A:(nat > real),B:nat,C:nat]: ((ord_less_real @ (A @ B) @ (A @ C)) | ~ (ord_less_nat @ B @ C) | ~ (! [D:nat]: (ord_less_real @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2369])). 159.59/70.61 thf(1626,axiom,((! [A:real]: (((ord_less_real @ A @ one_one_real) => (ord_less_real @ one_one_real @ (inverse_inverse_real @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9069_one__less__inverse)). 159.59/70.61 thf(13533,plain,((! [A:real]: (((ord_less_real @ A @ one_one_real) => (ord_less_real @ one_one_real @ (inverse_inverse_real @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626])). 159.59/70.61 thf(7392,axiom,((bit_se1412395901928357646or_nat = (^ [A:nat,B:nat]: (bit_se1412395901928357646or_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6048_or_Ocommute)). 159.59/70.61 thf(33810,plain,(((bit_se1412395901928357646or_nat) = (^ [A:nat,B:nat]: (bit_se1412395901928357646or_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7392])). 159.59/70.61 thf(6295,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => (((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2003_mult__mono_H)). 159.59/70.61 thf(29477,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => (((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6295])). 159.59/70.61 thf(2739,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/sandbox/benchmark/theBenchmark.p',fact_3896_even__diff)). 159.59/70.61 thf(17078,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)],[2739])). 159.59/70.61 thf(8065,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((plus_plus_nat @ B @ (times_times_nat @ A @ D)) != (plus_plus_nat @ C @ (times_times_nat @ A @ E))) <= ((D != E) & (B = C))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4559_add__scale__eq__noteq)). 159.59/70.61 thf(36041,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (~ ((plus_plus_nat @ B @ (times_times_nat @ A @ D)) = (plus_plus_nat @ C @ (times_times_nat @ A @ E))) | ~ (~ (D = E) & (B = C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8065])). 159.59/70.61 thf(4808,axiom,((! [A:vEBT_VEBT]: ((((! [B:$o]: (A != (vEBT_Leaf @ B @ ($true)))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E))))) <= (! [B:$o]: (A != (vEBT_Leaf @ ($true) @ B)))) <= (~ (vEBT_VEBT_minNull @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1949_VEBT__internal_OminNull_Oelims_I3_J)). 159.59/70.61 thf(23860,plain,((! [A:vEBT_VEBT]: (((! [B:$o]: ~ (A = (vEBT_Leaf @ B @ ($true)))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E))))) | ~ (! [B:$o]: ~ (A = (vEBT_Leaf @ ($true) @ B))) | (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4808])). 159.59/70.61 thf(864,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/sandbox/benchmark/theBenchmark.p',fact_8250_gbinomial__addition__formula)). 159.59/70.61 thf(11036,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)],[864])). 159.59/70.61 thf(2380,axiom,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_complex @ (A @ zero_zero_nat) @ (groups6464643781859351333omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8740_prod_OlessThan__Suc__shift)). 159.59/70.61 thf(15893,plain,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_complex @ (A @ zero_zero_nat) @ (groups6464643781859351333omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2380])). 159.59/70.61 thf(4644,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/sandbox/benchmark/theBenchmark.p',fact_4229_even__iff__mod__2__eq__zero)). 159.59/70.61 thf(23301,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)],[4644])). 159.59/70.61 thf(4527,axiom,((! [A:vEBT_VEBT,B:nat,C:option_nat]: (((vEBT_vebt_succ @ A @ B) = C) => ((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((B = zero_zero_nat) => (~ (((~ (E)) => (C = none_nat)) & ((C = (some_nat @ one_one_nat)) <= (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))) => (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)) => (~ (((C = (some_nat @ D)) <= (ord_less_nat @ B @ D)) & ((~ (ord_less_nat @ B @ D)) => (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_less @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((vEBT_vebt_maxt @ (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_succ @ (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_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)))))))) <= ((? [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)))) <= ((C != none_nat) <= (? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))))) <= ((? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E))) => ((? [D:nat]: (B = (suc @ D))) => (C != none_nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2572_vebt__succ_Oelims)). 159.59/70.61 thf(22838,plain,((! [A:vEBT_VEBT,B:nat,C:option_nat]: (((vEBT_vebt_succ @ A @ B) = C) => ((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((B = zero_zero_nat) => (~ (((~ (E)) => (C = none_nat)) & ((C = (some_nat @ one_one_nat)) | ~ (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))) => (~ (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)) => (~ (((C = (some_nat @ D)) | ~ (ord_less_nat @ B @ D)) & ((~ (ord_less_nat @ B @ D)) => (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_less @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ~ ((vEBT_vebt_maxt @ (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_succ @ (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_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat))))))) | ~ ((? [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))))) | ~ (~ (C = none_nat) | ~ (? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)))) | ~ ((? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E))) => ((? [D:nat]: (B = (suc @ D))) => (~ (C = none_nat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4527])). 159.59/70.61 thf(3205,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1883_comm__monoid__add__class_Oadd__0)). 159.59/70.61 thf(18560,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3205])). 159.59/70.61 thf(5825,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_add__leD2)). 159.59/70.61 thf(27714,plain,((! [A:nat,B:nat,C: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)],[5825])). 159.59/70.61 thf(7641,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_div__times__less__eq__dividend)). 159.59/70.61 thf(34677,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)],[7641])). 159.59/70.61 thf(8045,axiom,((! [A:nat]: ((the_nat @ (some_nat @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_option_Osel)). 159.59/70.61 thf(35970,plain,((! [A:nat]: ((the_nat @ (some_nat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8045])). 159.59/70.61 thf(1024,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_eq_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2235_mult__le__cancel__left__neg)). 159.59/70.61 thf(11523,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_eq_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024])). 159.59/70.61 thf(910,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ B @ one_one_Code_integer) => (dvd_dvd_Code_integer @ A @ one_one_Code_integer))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3994_dvd__unit__imp__unit)). 159.59/70.61 thf(11168,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((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)],[910])). 159.59/70.61 thf(3045,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => (dvd_dvd_int @ (groups705719431365010083at_int @ C @ B) @ (groups705719431365010083at_int @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8587_prod__dvd__prod__subset)). 159.59/70.61 thf(18037,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => (dvd_dvd_int @ (groups705719431365010083at_int @ (C) @ B) @ (groups705719431365010083at_int @ (C) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3045])). 159.59/70.61 thf(8005,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 != A) => ((F != B) => (((~ (ord_less_nat @ B @ F) & (((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 @ F @ A))) & ~ (ord_less_nat @ F @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1455_vebt__member_Osimps_I5_J)). 159.59/70.61 thf(35831,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 = A)) => ((~ (F = B)) => (((~ (ord_less_nat @ B @ F) & (((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 @ F @ A)) & ~ (ord_less_nat @ F @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8005])). 159.59/70.61 thf(2781,axiom,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_diff__add__cancel)). 159.59/70.61 thf(17210,plain,((! [A:real,B:real]: ((plus_plus_real @ (minus_minus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2781])). 159.59/70.61 thf(5687,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/sandbox/benchmark/theBenchmark.p',fact_5257_even__minus)). 159.59/70.61 thf(27087,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)],[5687])). 159.59/70.61 thf(2978,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/sandbox/benchmark/theBenchmark.p',fact_1551_divide__cancel__right)). 159.59/70.61 thf(17835,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)],[2978])). 159.59/70.61 thf(4496,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/sandbox/benchmark/theBenchmark.p',fact_9728_drop__bit__Suc__minus__bit0)). 159.59/70.61 thf(22713,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)],[4496])). 159.59/70.61 thf(6831,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (ord_max_nat @ B @ C)) = ((ord_less_nat @ A @ C) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_less__max__iff__disj)). 159.59/70.61 thf(31549,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (ord_max_nat @ B @ C)) = ((ord_less_nat @ A @ C) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6831])). 159.59/70.61 thf(2286,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => (((arcsin @ (sin_real @ A)) = A) <= (ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7820_arcsin__sin)). 159.59/70.61 thf(15618,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => (((arcsin @ (sin_real @ A)) = A) | ~ (ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2286])). 159.59/70.61 thf(2447,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((C != A) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4438_pinf_I3_J)). 159.59/70.61 thf(16131,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (C = A) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2447])). 159.59/70.61 thf(5606,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/sandbox/benchmark/theBenchmark.p',fact_9486_real__root__gt__0__iff)). 159.59/70.61 thf(26799,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)],[5606])). 159.59/70.61 thf(1457,axiom,((! [A:int,B:int,C:nat,D:nat]: ((((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) = zero_zero_int) | (C = zero_zero_nat) | ((sgn_sgn_int @ A) = zero_zero_int))) & ((~ ((C = zero_zero_nat) | ((sgn_sgn_int @ B) = zero_zero_int) | ((sgn_sgn_int @ A) = 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))))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9409_divide__int__unfold)). 159.59/70.61 thf(12998,plain,((! [A:int,B:int,C:nat,D:nat]: ((((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) = zero_zero_int) | (C = zero_zero_nat) | ((sgn_sgn_int @ A) = zero_zero_int))) & ((~ ((C = zero_zero_nat) | ((sgn_sgn_int @ B) = zero_zero_int) | ((sgn_sgn_int @ A) = 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))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457])). 159.59/70.61 thf(6672,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/sandbox/benchmark/theBenchmark.p',fact_5607_numeral__code_I3_J)). 159.59/70.61 thf(30863,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)],[6672])). 159.59/70.61 thf(8063,axiom,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4203_odd__even__add)). 159.59/70.61 thf(36034,plain,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8063])). 159.59/70.61 thf(62,axiom,(((ord_max_int @ zero_zero_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1708_max__0__1_I1_J)). 159.59/70.61 thf(8438,plain,(((ord_max_int @ zero_zero_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[62])). 159.59/70.61 thf(3751,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/sandbox/benchmark/theBenchmark.p',fact_29_divide__less__eq__numeral1_I1_J)). 159.59/70.61 thf(20317,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)],[3751])). 159.59/70.61 thf(7518,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/sandbox/benchmark/theBenchmark.p',fact_4825_not__neg__one__le__neg__numeral__iff)). 159.59/70.61 thf(34245,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)],[7518])). 159.59/70.61 thf(4421,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3176_linorder__not__less)). 159.59/70.61 thf(22420,plain,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = (ord_less_eq_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4421])). 159.59/70.61 thf(1867,axiom,((! [A:(nat > real)]: ((! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_real @ (A @ C) @ (A @ B)))) => (topolo6980174941875973593q_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7854_monoI2)). 159.59/70.61 thf(14284,plain,((! [A:(nat > real)]: ((! [B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_eq_real @ (A @ C) @ (A @ B)))) => (topolo6980174941875973593q_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1867])). 159.59/70.61 thf(7418,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/sandbox/benchmark/theBenchmark.p',fact_6188_or__minus__numerals_I3_J)). 159.59/70.61 thf(33881,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)],[7418])). 159.59/70.61 thf(790,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/sandbox/benchmark/theBenchmark.p',fact_4108_dvd__power__le)). 159.59/70.61 thf(10799,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)],[790])). 159.59/70.61 thf(3560,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) <= (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2045_add__decreasing)). 159.59/70.61 thf(19675,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) | ~ (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3560])). 159.59/70.61 thf(2320,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/sandbox/benchmark/theBenchmark.p',fact_4780_semiring__norm_I168_J)). 159.59/70.61 thf(15710,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)],[2320])). 159.59/70.61 thf(4828,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (^ [C:nat]: (minus_minus_int @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_atMost_nat @ B)) = (minus_minus_int @ (A @ zero_zero_nat) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8753_sum__telescope)). 159.59/70.61 thf(23964,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (^ [C:nat]: (minus_minus_int @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_atMost_nat @ B)) = (minus_minus_int @ (A @ zero_zero_nat) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4828])). 159.59/70.61 thf(5664,axiom,((! [A:complex,B:complex]: ((A = (times_times_complex @ A @ B)) = ((B = one_one_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1623_mult__cancel__left1)). 159.59/70.61 thf(26998,plain,((! [A:complex,B:complex]: ((A = (times_times_complex @ A @ B)) = ((B = one_one_complex) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5664])). 159.59/70.61 thf(1009,axiom,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (numeral_numeral_int @ (bit0 @ A)) @ (suc @ B)) = (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6326_bit__numeral__Bit0__Suc__iff)). 159.59/70.61 thf(11478,plain,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (numeral_numeral_int @ (bit0 @ A)) @ (suc @ B)) = (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009])). 159.59/70.61 thf(3987,axiom,((! [A:int]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5972_bit_Odisj__one__left)). 159.59/70.61 thf(21069,plain,((! [A:int]: ((bit_se1409905431419307370or_int @ (uminus_uminus_int @ one_one_int) @ A) = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3987])). 159.59/70.61 thf(1358,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/sandbox/benchmark/theBenchmark.p',fact_2108_pos__add__strict)). 159.59/70.61 thf(12638,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)],[1358])). 159.59/70.61 thf(8216,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/sandbox/benchmark/theBenchmark.p',fact_3879_even__add)). 159.59/70.61 thf(36526,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)],[8216])). 159.59/70.61 thf(5296,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/sandbox/benchmark/theBenchmark.p',fact_5838_of__int__eq__numeral__power__cancel__iff)). 159.59/70.61 thf(25603,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)],[5296])). 159.59/70.61 thf(5896,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/sandbox/benchmark/theBenchmark.p',fact_5341_divmod__step__nat__def)). 159.59/70.61 thf(28033,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)],[5896])). 159.59/70.61 thf(3533,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((~ (ord_le2932123472753598470d_enat @ A @ C)) <= (ord_le72135733267957522d_enat @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4508_minf_I8_J)). 159.59/70.61 thf(19591,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: (~ (ord_le2932123472753598470d_enat @ A @ C) | ~ (ord_le72135733267957522d_enat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3533])). 159.59/70.61 thf(6603,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/sandbox/benchmark/theBenchmark.p',fact_1853_mult__right__cancel)). 159.59/70.61 thf(30615,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)],[6603])). 159.59/70.61 thf(3072,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((sin_real @ (arcsin @ A)) = A) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7358_sin__arcsin)). 159.59/70.61 thf(18123,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((sin_real @ (arcsin @ A)) = A) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3072])). 159.59/70.61 thf(4360,axiom,((! [A:complex,B:complex]: ((invers8013647133539491842omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8985_inverse__divide)). 159.59/70.61 thf(22217,plain,((! [A:complex,B:complex]: ((invers8013647133539491842omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4360])). 159.59/70.61 thf(5370,axiom,((! [A:num]: ~ (ord_less_num @ A @ one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_semiring__norm_I75_J)). 159.59/70.61 thf(25948,plain,((! [A:num]: ~ (ord_less_num @ A @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5370])). 159.59/70.61 thf(7973,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ B) | (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1704_add__gr__0)). 159.59/70.61 thf(35731,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_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)],[7973])). 159.59/70.61 thf(961,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/sandbox/benchmark/theBenchmark.p',fact_7803_double__arith__series)). 159.59/70.61 thf(11325,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)],[961])). 159.59/70.61 thf(3053,axiom,((! [A:(nat > complex),B:complex,C:complex]: ((sums_complex @ A @ B) => (sums_complex @ (^ [D:nat]: (times_times_complex @ C @ (A @ D))) @ (times_times_complex @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7888_sums__mult)). 159.59/70.61 thf(18065,plain,((! [A:(nat > complex),B:complex,C:complex]: ((sums_complex @ (A) @ B) => (sums_complex @ (^ [D:nat]: (times_times_complex @ C @ (A @ D))) @ (times_times_complex @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3053])). 159.59/70.61 thf(3690,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/sandbox/benchmark/theBenchmark.p',fact_6738_mod__mult2__eq_H)). 159.59/70.61 thf(20104,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)],[3690])). 159.59/70.61 thf(3518,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/sandbox/benchmark/theBenchmark.p',fact_7177_cos__times__sin)). 159.59/70.61 thf(19546,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)],[3518])). 159.59/70.61 thf(3943,axiom,(((exp_complex @ (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (real_V4546457046886955230omplex @ pi)) @ imaginary_unit)) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9305_exp__two__pi__i)). 159.59/70.61 thf(20934,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)],[3943])). 159.59/70.61 thf(7460,axiom,((! [A:num,B:nat]: ((ord_min_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (suc @ (ord_min_nat @ (pred_numeral @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10170_min__numeral__Suc)). 159.59/70.61 thf(34020,plain,((! [A:num,B:nat]: ((ord_min_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (suc @ (ord_min_nat @ (pred_numeral @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7460])). 159.59/70.61 thf(7982,axiom,(((power_power_complex @ one_one_complex @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_one__power2)). 159.59/70.61 thf(35759,plain,(((power_power_complex @ one_one_complex @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7982])). 159.59/70.61 thf(436,axiom,((! [A:complex,B:complex]: ((im @ (plus_plus_complex @ A @ B)) = (plus_plus_real @ (im @ A) @ (im @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9653_plus__complex_Osimps_I2_J)). 159.59/70.61 thf(9616,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)],[436])). 159.59/70.61 thf(4637,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3181_order__less__imp__le)). 159.59/70.61 thf(23280,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4637])). 159.59/70.61 thf(2580,axiom,((! [A:real]: ((ord_less_real @ (ln_ln_real @ A) @ A) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5018_ln__less__self)). 159.59/70.61 thf(16544,plain,((! [A:real]: ((ord_less_real @ (ln_ln_real @ A) @ A) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2580])). 159.59/70.61 thf(2091,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri8010041392384452111omplex @ (minus_minus_nat @ B @ A)) = (minus_minus_complex @ (semiri8010041392384452111omplex @ B) @ (semiri8010041392384452111omplex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6729_of__nat__diff)). 159.59/70.61 thf(14987,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri8010041392384452111omplex @ (minus_minus_nat @ B @ A)) = (minus_minus_complex @ (semiri8010041392384452111omplex @ B) @ (semiri8010041392384452111omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2091])). 159.59/70.61 thf(6417,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => (ord_less_real @ (power_power_real @ A @ (suc @ B)) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2451_power__Suc__less__one)). 159.59/70.61 thf(29923,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => (ord_less_real @ (power_power_real @ A @ (suc @ B)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6417])). 159.59/70.61 thf(5698,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/sandbox/benchmark/theBenchmark.p',fact_9509_real__root__power)). 159.59/70.61 thf(27119,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)],[5698])). 159.59/70.61 thf(1737,axiom,((! [A:(nat > extended_enat)]: ((groups7961826882256487087d_enat @ A @ bot_bot_set_nat) = one_on7984719198319812577d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8378_prod_Oempty)). 159.59/70.61 thf(13865,plain,((! [A:(nat > extended_enat)]: ((groups7961826882256487087d_enat @ (A) @ bot_bot_set_nat) = one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737])). 159.59/70.61 thf(5923,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/sandbox/benchmark/theBenchmark.p',fact_1257_right__diff__distrib_H)). 159.59/70.61 thf(28141,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)],[5923])). 159.59/70.61 thf(2678,axiom,((! [A:nat,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B) => ((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_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6786_exp__ge__one__plus__x__over__n__power__n)). 159.59/70.61 thf(16885,plain,((! [A:nat,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B) => ((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_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2678])). 159.59/70.61 thf(2664,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ A @ B) = (ord_less_int @ C @ D)) <= ((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1221_diff__eq__diff__less)). 159.59/70.61 thf(16841,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ A @ B) = (ord_less_int @ C @ D)) | ~ ((minus_minus_int @ A @ B) = (minus_minus_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2664])). 159.59/70.61 thf(7015,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/sandbox/benchmark/theBenchmark.p',fact_635_Suc__mult__le__cancel1)). 159.59/70.61 thf(32401,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)],[7015])). 159.59/70.61 thf(7920,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (divide_divide_nat @ B @ A) @ C) = (ord_less_nat @ B @ (times_times_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2402_div__less__iff__less__mult)). 159.59/70.61 thf(35570,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (divide_divide_nat @ B @ A) @ C) = (ord_less_nat @ B @ (times_times_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7920])). 159.59/70.61 thf(1555,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/sandbox/benchmark/theBenchmark.p',fact_6413_bit__imp__take__bit__positive)). 159.59/70.61 thf(13305,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)],[1555])). 159.59/70.61 thf(2345,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/sandbox/benchmark/theBenchmark.p',fact_8014_one__diff__power__eq_H)). 159.59/70.61 thf(15784,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)],[2345])). 159.59/70.61 thf(7661,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/sandbox/benchmark/theBenchmark.p',fact_100_numeral__plus__numeral)). 159.59/70.61 thf(34733,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)],[7661])). 159.59/70.61 thf(1293,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((((divide6298287555418463151nteger @ C @ (times_3573771949741848930nteger @ A @ B)) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ C @ A) @ B)) <= (dvd_dvd_Code_integer @ B @ one_one_Code_integer)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4174_is__unit__div__mult2__eq)). 159.59/70.61 thf(12430,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ C @ (times_3573771949741848930nteger @ A @ B)) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ C @ A) @ B)) | ~ (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)],[1293])). 159.59/70.61 thf(3530,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/sandbox/benchmark/theBenchmark.p',fact_7204_tan__double)). 159.59/70.61 thf(19585,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)],[3530])). 159.59/70.61 thf(68,axiom,((! [A:real,B:real]: ((ord_less_real @ (sinh_real @ A) @ (sinh_real @ B)) = (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9306_sinh__real__less__iff)). 159.59/70.61 thf(8454,plain,((! [A:real,B:real]: ((ord_less_real @ (sinh_real @ A) @ (sinh_real @ B)) = (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 159.59/70.61 thf(3842,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/sandbox/benchmark/theBenchmark.p',fact_4565_signed__take__bit__mult)). 159.59/70.61 thf(20619,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)],[3842])). 159.59/70.61 thf(7278,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (power_power_real @ A @ B) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2334_power__le__one)). 159.59/70.61 thf(33404,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (power_power_real @ A @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7278])). 159.59/70.61 thf(3539,axiom,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = B) = (A = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1522_add__cancel__left__left)). 159.59/70.61 thf(19608,plain,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = B) = (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3539])). 159.59/70.61 thf(3258,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (bit1 @ A)) = (plus_plus_complex @ (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A)) @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5605_numeral__code_I3_J)). 159.59/70.61 thf(18737,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)],[3258])). 159.59/70.61 thf(6474,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ one_one_nat) => ((divide_divide_nat @ C @ (times_times_nat @ A @ B)) = (divide_divide_nat @ (divide_divide_nat @ C @ A) @ B))) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4172_is__unit__div__mult2__eq)). 159.59/70.61 thf(30154,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ B @ one_one_nat) => ((divide_divide_nat @ C @ (times_times_nat @ A @ B)) = (divide_divide_nat @ (divide_divide_nat @ C @ A) @ B))) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6474])). 159.59/70.61 thf(105,axiom,((! [A:int,B:num]: ((bit_se6526347334894502574or_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (bit_ri7919022796975470100ot_int @ (bit_se6526347334894502574or_int @ A @ (neg_numeral_sub_int @ B @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9767_xor__minus__numerals_I2_J)). 159.59/70.61 thf(8575,plain,((! [A:int,B:num]: ((bit_se6526347334894502574or_int @ A @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (bit_ri7919022796975470100ot_int @ (bit_se6526347334894502574or_int @ A @ (neg_numeral_sub_int @ B @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[105])). 159.59/70.61 thf(892,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (times_times_int @ A @ B) @ B) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3403_mod__mult__self2__is__0)). 159.59/70.61 thf(11119,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)],[892])). 159.59/70.61 thf(5801,axiom,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((vEBT_vebt_insert @ A @ B) = C) => (((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((((C = (vEBT_Leaf @ ($true) @ E)) <= (B = zero_zero_nat)) & ((((C = (vEBT_Leaf @ D @ ($true))) <= (B = one_one_nat)) & ((B != one_one_nat) => (C = (vEBT_Leaf @ D @ E)))) <= (B != zero_zero_nat))) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)))))) => ((! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ (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))) <= (A = (vEBT_Node @ D @ zero_zero_nat @ 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)) => ((~ (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 @ (~ ((B = E) | (B = D)) & (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))) @ (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: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)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F) @ B)))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F))))) <= (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F) @ B))) <= (C = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F))) <= (A = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ (produc738532404422230701BT_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3312_vebt__insert_Opelims)). 159.59/70.61 thf(27537,plain,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((vEBT_vebt_insert @ A @ B) = C) => (((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((((C = (vEBT_Leaf @ ($true) @ E)) | ~ (B = zero_zero_nat)) & ((((C = (vEBT_Leaf @ D @ ($true))) | ~ (B = one_one_nat)) & ((~ (B = one_one_nat)) => (C = (vEBT_Leaf @ D @ E)))) | (B = zero_zero_nat))) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)))))) => ((! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ (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)) | ~ (A = (vEBT_Node @ D @ zero_zero_nat @ 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)) => (~ (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 @ (~ ((B = E) | (B = D)) & (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))) @ (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: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)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F) @ B)))) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F)))) | ~ (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F) @ B)) | ~ (C = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)) | ~ (A = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F))))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_insert_rel) @ (produc738532404422230701BT_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5801])). 159.59/70.61 thf(4748,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/sandbox/benchmark/theBenchmark.p',fact_1960_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 159.59/70.61 thf(23643,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)],[4748])). 159.59/70.61 thf(6924,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2668_linorder__linear)). 159.59/70.61 thf(31939,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)],[6924])). 159.59/70.61 thf(326,axiom,((! [A:complex,B:complex]: ((sinh_complex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ (times_times_complex @ (sinh_complex @ A) @ (cosh_complex @ B)) @ (times_times_complex @ (cosh_complex @ A) @ (sinh_complex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9331_sinh__diff)). 159.59/70.61 thf(9255,plain,((! [A:complex,B:complex]: ((sinh_complex @ (minus_minus_complex @ A @ B)) = (minus_minus_complex @ (times_times_complex @ (sinh_complex @ A) @ (cosh_complex @ B)) @ (times_times_complex @ (cosh_complex @ A) @ (sinh_complex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 159.59/70.61 thf(4215,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/sandbox/benchmark/theBenchmark.p',fact_5274_pos__minus__divide__le__eq)). 159.59/70.61 thf(21774,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)],[4215])). 159.59/70.61 thf(8226,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/sandbox/benchmark/theBenchmark.p',fact_492_summaxma)). 159.59/70.61 thf(36554,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)],[8226])). 159.59/70.61 thf(4928,axiom,((! [A:int,B:int,C:nat]: ((((ord_less_nat @ zero_zero_nat @ C) => (ord_less_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))) <= (ord_less_eq_int @ zero_zero_int @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1942_power__strict__mono)). 159.59/70.61 thf(24284,plain,((! [A:int,B:int,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4928])). 159.59/70.61 thf(527,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/sandbox/benchmark/theBenchmark.p',fact_7312_lemma__tan__add1)). 159.59/70.61 thf(9928,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)],[527])). 159.59/70.61 thf(801,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ C) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ C @ A))) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4092_div__plus__div__distrib__dvd__left)). 159.59/70.61 thf(10833,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ C) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ C @ A))) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[801])). 159.59/70.61 thf(7596,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/sandbox/benchmark/theBenchmark.p',fact_6601_real__of__nat__eq__numeral__power__cancel__iff)). 159.59/70.61 thf(34548,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)],[7596])). 159.59/70.61 thf(714,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) => (((ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_int @ zero_zero_int @ B))) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2249_mult__strict__mono)). 159.59/70.61 thf(10551,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) => ((ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ D)) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_int @ zero_zero_int @ B))) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[714])). 159.59/70.61 thf(6814,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2193_one__is__add)). 159.59/70.61 thf(31490,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6814])). 159.59/70.61 thf(6945,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/sandbox/benchmark/theBenchmark.p',fact_5465_mod__Suc__eq__mod__add3)). 159.59/70.61 thf(32030,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)],[6945])). 159.59/70.61 thf(3767,axiom,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = (ord_less_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3698_verit__comp__simplify1_I3_J)). 159.59/70.61 thf(20368,plain,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = (ord_less_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3767])). 159.59/70.61 thf(5671,axiom,((! [A:nat]: (((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ A) = zero_z5237406670263579293d_enat) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1816_zero__power)). 159.59/70.61 thf(27019,plain,((! [A:nat]: (((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ A) = zero_z5237406670263579293d_enat) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5671])). 159.59/70.61 thf(6680,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ C) @ D @ E) @ F)))) <= (! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1809_VEBT__internal_Onaive__member_Ocases)). 159.59/70.61 thf(30891,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$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 @ (suc @ C) @ D @ E) @ F))) | ~ (! [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)],[6680])). 159.59/70.61 thf(4307,axiom,(((neg_nu6075765906172075777c_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5678_dbl__dec__simps_I3_J)). 159.59/70.61 thf(22065,plain,(((neg_nu6075765906172075777c_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4307])). 159.59/70.61 thf(709,axiom,((! [A:nat]: ((sin_real @ (times_times_real @ pi @ (semiri5074537144036343181t_real @ A))) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6802_sin__npi2)). 159.59/70.61 thf(10538,plain,((! [A:nat]: ((sin_real @ (times_times_real @ pi @ (semiri5074537144036343181t_real @ A))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[709])). 159.59/70.61 thf(6774,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/sandbox/benchmark/theBenchmark.p',fact_2563_arith__geo__mean)). 159.59/70.61 thf(31366,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)],[6774])). 159.59/70.61 thf(1386,axiom,((! [A:num]: ((neg_nu5851722552734809277nc_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5805_dbl__inc__simps_I5_J)). 159.59/70.61 thf(12777,plain,((! [A:num]: ((neg_nu5851722552734809277nc_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386])). 159.59/70.61 thf(384,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/sandbox/benchmark/theBenchmark.p',fact_9577_and__minus__minus__numerals)). 159.59/70.61 thf(9452,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)],[384])). 159.59/70.61 thf(4858,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ B @ A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3024_leD)). 159.59/70.61 thf(24055,plain,((! [A:num,B:num]: (~ (ord_less_num @ B @ A) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4858])). 159.59/70.61 thf(52,axiom,((! [A:code_integer,B:nat,C:nat]: ((A != zero_z3403309356797280102nteger) => ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ B) @ (power_8256067586552552935nteger @ A @ C)) = ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) | (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4211_dvd__power__iff)). 159.59/70.61 thf(8406,plain,((! [A:code_integer,B:nat,C:nat]: ((~ (A = zero_z3403309356797280102nteger)) => ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ B) @ (power_8256067586552552935nteger @ A @ C)) = ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) | (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 159.59/70.61 thf(2830,axiom,((! [A:(nat > real),B:real]: ((summable_real @ A) => (summable_real @ (^ [C:nat]: (divide_divide_real @ (A @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7027_summable__divide)). 159.59/70.61 thf(17349,plain,((! [A:(nat > real),B:real]: ((summable_real @ (A)) => (summable_real @ (^ [C:nat]: (divide_divide_real @ (A @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2830])). 159.59/70.61 thf(6170,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/sandbox/benchmark/theBenchmark.p',fact_8275_pochhammer__rec_H)). 159.59/70.61 thf(28995,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)],[6170])). 159.59/70.61 thf(2350,axiom,(((neg_nu3811975205180677377ec_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5679_dbl__dec__simps_I3_J)). 159.59/70.61 thf(15799,plain,(((neg_nu3811975205180677377ec_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2350])). 159.59/70.61 thf(3220,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/sandbox/benchmark/theBenchmark.p',fact_2157_divide__less__cancel)). 159.59/70.61 thf(18604,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)],[3220])). 159.59/70.61 thf(8047,axiom,((! [A:nat,B:nat]: ((if_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Nat__Onat_T)). 159.59/70.61 thf(35981,plain,((! [A:nat,B:nat]: ((if_nat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8047])). 159.59/70.61 thf(3819,axiom,((! [A:complex,B:complex]: ((cos_complex @ (plus_plus_complex @ A @ B)) = (minus_minus_complex @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B)) @ (times_times_complex @ (sin_complex @ A) @ (sin_complex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7112_cos__add)). 159.59/70.61 thf(20530,plain,((! [A:complex,B:complex]: ((cos_complex @ (plus_plus_complex @ A @ B)) = (minus_minus_complex @ (times_times_complex @ (cos_complex @ A) @ (cos_complex @ B)) @ (times_times_complex @ (sin_complex @ A) @ (sin_complex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3819])). 159.59/70.61 thf(887,axiom,((! [A:real,B:real]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) => (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8211_floor__less__cancel)). 159.59/70.61 thf(11104,plain,((! [A:real,B:real]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) => (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[887])). 159.59/70.61 thf(1107,axiom,((! [A:complex]: ((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))))) <= (ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7847_geometric__deriv__sums)). 159.59/70.61 thf(11806,plain,((! [A:complex]: ((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))))) | ~ (ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107])). 159.59/70.61 thf(294,axiom,((! [A:int,B:int]: ((ring_1_of_int_int @ (ord_max_int @ A @ B)) = (ord_max_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5880_of__int__max)). 159.59/70.61 thf(9140,plain,((! [A:int,B:int]: ((ring_1_of_int_int @ (ord_max_int @ A @ B)) = (ord_max_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[294])). 159.59/70.61 thf(2629,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B)) => (((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3462_mod__diff__cong)). 159.59/70.61 thf(16725,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((modulo_modulo_int @ A @ B) = (modulo_modulo_int @ C @ B)) => (((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2629])). 159.59/70.61 thf(2935,axiom,((! [A:real,B:nat]: ((real_V4546457046886955230omplex @ (power_power_real @ A @ B)) = (power_power_complex @ (real_V4546457046886955230omplex @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7334_of__real__power)). 159.59/70.61 thf(17702,plain,((! [A:real,B:nat]: ((real_V4546457046886955230omplex @ (power_power_real @ A @ B)) = (power_power_complex @ (real_V4546457046886955230omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2935])). 159.59/70.61 thf(6016,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ B @ A))) <= (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2384_one__less__mult)). 159.59/70.61 thf(28490,plain,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ B @ A))) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6016])). 159.59/70.61 thf(6370,axiom,((! [A:nat,B:nat]: ((A != B) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3196_order__neq__le__trans)). 159.59/70.61 thf(29703,plain,((! [A:nat,B:nat]: ((~ (A = B)) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6370])). 159.59/70.61 thf(6768,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/sandbox/benchmark/theBenchmark.p',fact_7879_powser__sums__zero__iff)). 159.59/70.61 thf(31347,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)],[6768])). 159.59/70.61 thf(5441,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/sandbox/benchmark/theBenchmark.p',fact_2626_half__nonnegative__int__iff)). 159.59/70.61 thf(26237,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)],[5441])). 159.59/70.61 thf(4062,axiom,((! [A:int,B:real]: ((ord_less_eq_int @ A @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ A) @ one_one_real) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7144_le__ceiling__iff)). 159.59/70.61 thf(21290,plain,((! [A:int,B:real]: ((ord_less_eq_int @ A @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ A) @ one_one_real) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4062])). 159.59/70.61 thf(5633,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/sandbox/benchmark/theBenchmark.p',fact_6741_field__char__0__class_Oof__nat__div)). 159.59/70.61 thf(26887,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)],[5633])). 159.59/70.61 thf(7001,axiom,((! [A:num]: ((semiri4449623510593786356d_enat @ (numeral_numeral_nat @ A)) = (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ (semiri4449623510593786356d_enat @ (pred_numeral @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8110_fact__numeral)). 159.59/70.61 thf(32360,plain,((! [A:num]: ((semiri4449623510593786356d_enat @ (numeral_numeral_nat @ A)) = (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ (semiri4449623510593786356d_enat @ (pred_numeral @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7001])). 159.59/70.61 thf(989,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C) => (ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ C @ A) @ (times_7803423173614009249d_enat @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1959_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 159.59/70.61 thf(11413,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C) => (ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ C @ A) @ (times_7803423173614009249d_enat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[989])). 159.59/70.61 thf(6116,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ B)) = (times_times_real @ A @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_power__Suc)). 159.59/70.61 thf(28804,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)],[6116])). 159.59/70.61 thf(4982,axiom,(((neg_numeral_dbl_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4887_dbl__simps_I4_J)). 159.59/70.61 thf(24496,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)],[4982])). 159.59/70.61 thf(7254,axiom,((! [A:nat,B:nat]: ((bit_se1412395901928357646or_nat @ A @ (bit_se1412395901928357646or_nat @ A @ B)) = (bit_se1412395901928357646or_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5942_or_Oleft__idem)). 159.59/70.61 thf(33334,plain,((! [A:nat,B:nat]: ((bit_se1412395901928357646or_nat @ A @ (bit_se1412395901928357646or_nat @ A @ B)) = (bit_se1412395901928357646or_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7254])). 159.59/70.61 thf(1082,axiom,((! [A:nat,B:nat]: ((semiri8010041392384452111omplex @ (power_power_nat @ A @ B)) = (power_power_complex @ (semiri8010041392384452111omplex @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6559_of__nat__power)). 159.59/70.61 thf(11723,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)],[1082])). 159.59/70.61 thf(4796,axiom,((! [A:nat,B:list_int,C:int]: ((((list_update_int @ B @ A @ C) = B) = ((nth_int @ B @ A) = C)) <= (ord_less_nat @ A @ (size_size_list_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_list__update__same__conv)). 159.59/70.61 thf(23814,plain,((! [A:nat,B:list_int,C:int]: ((((list_update_int @ B @ A @ C) = B) = ((nth_int @ B @ A) = C)) | ~ (ord_less_nat @ A @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4796])). 159.59/70.61 thf(6437,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1531_add_Oright__neutral)). 159.59/70.61 thf(30000,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6437])). 159.59/70.61 thf(3110,axiom,((! [A:extended_enat,B:extended_enat]: (((~ (ord_le72135733267957522d_enat @ B @ A)) = (B = A)) <= (~ (ord_le72135733267957522d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2786_antisym__conv3)). 159.59/70.61 thf(18260,plain,((! [A:extended_enat,B:extended_enat]: (((~ (ord_le72135733267957522d_enat @ B @ A)) = (B = A)) | (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3110])). 159.59/70.61 thf(673,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/sandbox/benchmark/theBenchmark.p',fact_8443_sum_OatMost__Suc)). 159.59/70.61 thf(10405,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)],[673])). 159.59/70.61 thf(7927,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C))))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_infinite__descent)). 159.59/70.61 thf(35589,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7927])). 159.59/70.61 thf(4892,axiom,((! [A:(nat > real),B:nat,C:nat]: ((groups129246275422532515t_real @ A @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups129246275422532515t_real @ (^ [D:nat]: (times_times_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/sandbox/benchmark/theBenchmark.p',fact_8904_prod_Oin__pairs)). 159.59/70.61 thf(24160,plain,((! [A:(nat > real),B:nat,C:nat]: ((groups129246275422532515t_real @ (A) @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups129246275422532515t_real @ (^ [D:nat]: (times_times_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)],[4892])). 159.59/70.61 thf(7621,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/sandbox/benchmark/theBenchmark.p',fact_3525_cancel__div__mod__rules_I2_J)). 159.59/70.61 thf(34617,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)],[7621])). 159.59/70.61 thf(2196,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/sandbox/benchmark/theBenchmark.p',fact_5749_of__int__code__if)). 159.59/70.61 thf(15343,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)],[2196])). 159.59/70.61 thf(1476,axiom,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ A) = (ord_less_int @ B @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1607_add__less__same__cancel1)). 159.59/70.61 thf(13072,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)],[1476])). 159.59/70.61 thf(2313,axiom,((! [A:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ zero_zero_int) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6580_of__nat__le__0__iff)). 159.59/70.61 thf(15691,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)],[2313])). 159.59/70.61 thf(6570,axiom,((! [A:num,B:num]: ((plus_plus_num @ A @ (inc @ B)) = (inc @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5716_add__inc)). 159.59/70.61 thf(30491,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)],[6570])). 159.59/70.61 thf(3151,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/sandbox/benchmark/theBenchmark.p',fact_9495_sgn__root)). 159.59/70.61 thf(18392,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)],[3151])). 159.59/70.61 thf(5221,axiom,((! [A:nat]: ((groups708209901874060359at_nat @ suc @ (set_or4665077453230672383an_nat @ (suc @ zero_zero_nat) @ A)) = (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9602_prod__Suc__Suc__fact)). 159.59/70.61 thf(25339,plain,((! [A:nat]: ((groups708209901874060359at_nat @ (suc) @ (set_or4665077453230672383an_nat @ (suc @ zero_zero_nat) @ A)) = (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5221])). 159.59/70.61 thf(32,axiom,((! [A:complex,B:nat]: ((times_times_complex @ (gbinomial_complex @ A @ B) @ A) = (plus_plus_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ B) @ (gbinomial_complex @ A @ B)) @ (times_times_complex @ (semiri8010041392384452111omplex @ (suc @ B)) @ (gbinomial_complex @ A @ (suc @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8257_gbinomial__mult__1_H)). 159.59/70.61 thf(8347,plain,((! [A:complex,B:nat]: ((times_times_complex @ (gbinomial_complex @ A @ B) @ A) = (plus_plus_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ B) @ (gbinomial_complex @ A @ B)) @ (times_times_complex @ (semiri8010041392384452111omplex @ (suc @ B)) @ (gbinomial_complex @ A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 159.59/70.61 thf(4620,axiom,((! [A:num]: ((minus_8373710615458151222nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (numera6620942414471956472nteger @ (inc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5712_diff__numeral__special_I6_J)). 159.59/70.61 thf(23223,plain,((! [A:num]: ((minus_8373710615458151222nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (numera6620942414471956472nteger @ (inc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4620])). 159.59/70.61 thf(2821,axiom,((! [A:nat,B:real,C:real]: (((ord_less_real @ (root @ A @ B) @ (root @ A @ C)) = (ord_less_real @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9482_real__root__less__iff)). 159.59/70.61 thf(17322,plain,((! [A:nat,B:real,C:real]: (((ord_less_real @ (root @ A @ B) @ (root @ A @ C)) = (ord_less_real @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2821])). 159.59/70.61 thf(4621,axiom,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ A) @ (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5541_abs__ge__minus__self)). 159.59/70.61 thf(23226,plain,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ A) @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4621])). 159.59/70.61 thf(3906,axiom,((! [A:real]: (((ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one))) => (ord_less_real @ (cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) @ one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7164_cos__double__less__one)). 159.59/70.61 thf(20826,plain,((! [A:real]: (((ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one))) => (ord_less_real @ (cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) @ one_one_real)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3906])). 159.59/70.61 thf(6418,axiom,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1543_bits__div__by__0)). 159.59/70.61 thf(29926,plain,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6418])). 159.59/70.61 thf(2006,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => (((times_times_complex @ B @ A) = C) => (B = (divide1717551699836669952omplex @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2171_eq__divide__imp)). 159.59/70.61 thf(14733,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)],[2006])). 159.59/70.61 thf(143,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/sandbox/benchmark/theBenchmark.p',fact_8252_gbinomial__absorb__comp)). 159.59/70.61 thf(8686,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)],[143])). 159.59/70.61 thf(6987,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/sandbox/benchmark/theBenchmark.p',fact_4176_is__unit__power__iff)). 159.59/70.61 thf(32288,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)],[6987])). 159.59/70.61 thf(4759,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/sandbox/benchmark/theBenchmark.p',fact_1962_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 159.59/70.61 thf(23700,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)],[4759])). 159.59/70.61 thf(522,axiom,((! [A:real]: (summable_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9261_summable__exp__generic)). 159.59/70.61 thf(9914,plain,((! [A:real]: (summable_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[522])). 159.59/70.61 thf(1133,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/sandbox/benchmark/theBenchmark.p',fact_9138_exp__plus__inverse__exp)). 159.59/70.61 thf(11885,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)],[1133])). 159.59/70.61 thf(3299,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4988_minus__divide__right)). 159.59/70.61 thf(18869,plain,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3299])). 159.59/70.61 thf(1592,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = (times_times_real @ B @ A)) => ((times_times_real @ (inverse_inverse_real @ A) @ B) = (times_times_real @ B @ (inverse_inverse_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9017_mult__commute__imp__mult__inverse__commute)). 159.59/70.61 thf(13420,plain,((! [A:real,B:real]: (((times_times_real @ A @ B) = (times_times_real @ B @ A)) => ((times_times_real @ (inverse_inverse_real @ A) @ B) = (times_times_real @ B @ (inverse_inverse_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1592])). 159.59/70.61 thf(5081,axiom,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ one_one_nat) = (zero_n2687167440665602831ol_nat @ (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4843_take__bit__of__1)). 159.59/70.61 thf(24854,plain,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ one_one_nat) = (zero_n2687167440665602831ol_nat @ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5081])). 159.59/70.61 thf(7753,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4445_pinf_I4_J)). 159.59/70.61 thf(35051,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7753])). 159.59/70.61 thf(4895,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/sandbox/benchmark/theBenchmark.p',fact_6794_lemma__termdiff3)). 159.59/70.61 thf(24169,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)],[4895])). 159.59/70.61 thf(5588,axiom,(((semiri5074537144036343181t_real @ zero_zero_nat) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6496_of__nat__0)). 159.59/70.61 thf(26724,plain,(((semiri5074537144036343181t_real @ zero_zero_nat) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5588])). 159.59/70.61 thf(1287,axiom,((! [A:real,B:real]: (((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A) <= (~ (ord_less_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1352_linordered__semidom__class_Oadd__diff__inverse)). 159.59/70.61 thf(12411,plain,((! [A:real,B:real]: (((plus_plus_real @ B @ (minus_minus_real @ A @ B)) = A) | (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287])). 159.59/70.61 thf(352,axiom,((! [A:code_integer,B:nat]: ((bit_se9216721137139052372nteger @ (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ B) = ((B = zero_zero_nat) & ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6356_bit__mod__2__iff)). 159.59/70.61 thf(9341,plain,((! [A:code_integer,B:nat]: ((bit_se9216721137139052372nteger @ (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ B) = ((B = zero_zero_nat) & ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 159.59/70.61 thf(2586,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/sandbox/benchmark/theBenchmark.p',fact_7996_diff__power__eq__sum)). 159.59/70.61 thf(16562,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)],[2586])). 159.59/70.61 thf(2418,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/sandbox/benchmark/theBenchmark.p',fact_7964_sum__lessThan__telescope)). 159.59/70.61 thf(16028,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)],[2418])). 159.59/70.61 thf(1013,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/sandbox/benchmark/theBenchmark.p',fact_1582_le__add__same__cancel2)). 159.59/70.61 thf(11490,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)],[1013])). 159.59/70.61 thf(1975,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat,D:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ C) @ (plus_p3455044024723400733d_enat @ B @ D)) <= (ord_le72135733267957522d_enat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1195_add__strict__mono)). 159.59/70.61 thf(14622,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat,D:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ C) @ (plus_p3455044024723400733d_enat @ B @ D)) | ~ (ord_le72135733267957522d_enat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1975])). 159.59/70.61 thf(669,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ (times_times_complex @ A @ B)) = (divide1717551699836669952omplex @ one_one_complex @ B)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1755_nonzero__divide__mult__cancel__left)). 159.59/70.61 thf(10390,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ (times_times_complex @ A @ B)) = (divide1717551699836669952omplex @ one_one_complex @ B)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[669])). 159.59/70.61 thf(5540,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/sandbox/benchmark/theBenchmark.p',fact_5252_minus__divide__diff__eq__iff)). 159.59/70.61 thf(26574,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)],[5540])). 159.59/70.61 thf(5472,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit0 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_semiring__norm_I71_J)). 159.59/70.61 thf(26346,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)],[5472])). 159.59/70.61 thf(3133,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) => (A = bot_bot_set_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3267_bot_Oextremum__uniqueI)). 159.59/70.61 thf(18329,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)],[3133])). 159.59/70.61 thf(5951,axiom,((! [A:real]: ((times_times_real @ A @ (numeral_numeral_real @ (bit0 @ one))) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_mult__2__right)). 159.59/70.61 thf(28285,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)],[5951])). 159.59/70.61 thf(4707,axiom,((! [A:real,B:real]: (((sqrt @ A) = (sqrt @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6306_real__sqrt__eq__iff)). 159.59/70.61 thf(23524,plain,((! [A:real,B:real]: (((sqrt @ A) = (sqrt @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4707])). 159.59/70.61 thf(7779,axiom,(((modulo_modulo_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3427_bits__one__mod__two__eq__one)). 159.59/70.61 thf(35125,plain,(((modulo_modulo_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7779])). 159.59/70.61 thf(3371,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((((ord_less_real @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_real @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3238_order__less__le__subst1)). 159.59/70.61 thf(19085,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_real @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_real @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3371])). 159.59/70.61 thf(4787,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/sandbox/benchmark/theBenchmark.p',fact_1263_left__diff__distrib_H)). 159.59/70.61 thf(23788,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)],[4787])). 159.59/70.61 thf(1650,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/sandbox/benchmark/theBenchmark.p',fact_4905_signed__take__bit__0)). 159.59/70.61 thf(13600,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)],[1650])). 159.59/70.61 thf(7764,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_numeral__Bit0)). 159.59/70.61 thf(35083,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)],[7764])). 159.59/70.61 thf(4031,axiom,((! [A:real]: ((cos_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (cos_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7002_cos__periodic)). 159.59/70.61 thf(21200,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)],[4031])). 159.59/70.61 thf(3777,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (vEBT_VEBT_greater @ (some_nat @ B) @ (some_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_greater__shift)). 159.59/70.61 thf(20401,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)],[3777])). 159.59/70.61 thf(6678,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ A @ (times_times_nat @ A @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2382_n__less__n__mult__m)). 159.59/70.61 thf(30885,plain,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ A @ (times_times_nat @ A @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6678])). 159.59/70.61 thf(7047,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/sandbox/benchmark/theBenchmark.p',fact_6460_real__sqrt__ge__abs2)). 159.59/70.61 thf(32511,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)],[7047])). 159.59/70.61 thf(2027,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1875_add_Ogroup__left__neutral)). 159.59/70.61 thf(14798,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2027])). 159.59/70.61 thf(2407,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)) = (ord_less_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4649_ln__less__cancel__iff)). 159.59/70.61 thf(15986,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)) = (ord_less_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2407])). 159.59/70.61 thf(6367,axiom,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1465_valid__tree__deg__neq__0)). 159.59/70.61 thf(29695,plain,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6367])). 159.59/70.61 thf(4685,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/sandbox/benchmark/theBenchmark.p',fact_7454_sum_Oshift__bounds__cl__nat__ivl)). 159.59/70.61 thf(23451,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)],[4685])). 159.59/70.61 thf(1084,axiom,((! [A:set_nat,B:set_nat]: ((A = B) => (ord_less_eq_set_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2972_equalityD2)). 159.59/70.61 thf(11728,plain,((! [A:set_nat,B:set_nat]: ((A = B) => (ord_less_eq_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084])). 159.59/70.61 thf(3901,axiom,((! [A:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5054_ab__group__add__class_Oab__left__minus)). 159.59/70.61 thf(20809,plain,((! [A:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3901])). 159.59/70.61 thf(8092,axiom,(((power_power_real @ zero_zero_real @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2459_zero__power2)). 159.59/70.61 thf(36124,plain,(((power_power_real @ zero_zero_real @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8092])). 159.59/70.61 thf(6404,axiom,((! [A:(nat > complex),B:nat,C:complex]: ((! [D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (A @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ B)) = C)) = (! [D:nat]: (((A @ D) = zero_zero_complex) <= (member_nat @ D @ (set_or1269000886237332187st_nat @ one_one_nat @ B))) & ((A @ zero_zero_nat) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8924_polyfun__eq__const)). 159.59/70.61 thf(29865,plain,((! [A:(nat > complex),B:nat,C:complex]: ((! [D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (A @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ B)) = C)) = (! [D:nat]: (((A @ D) = zero_zero_complex) | ~ (member_nat @ D @ (set_or1269000886237332187st_nat @ one_one_nat @ B))) & ((A @ zero_zero_nat) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6404])). 159.59/70.61 thf(8006,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/sandbox/benchmark/theBenchmark.p',fact_5268_take__bit__nat__less__exp)). 159.59/70.61 thf(35834,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)],[8006])). 159.59/70.61 thf(5421,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/sandbox/benchmark/theBenchmark.p',fact_4813_mult__neg__numeral__simps_I3_J)). 159.59/70.61 thf(26166,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)],[5421])). 159.59/70.61 thf(1414,axiom,((! [A:nat]: ~ (ord_less_int @ (semiri1314217659103216013at_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6669_of__nat__less__0__iff)). 159.59/70.61 thf(12860,plain,((! [A:nat]: ~ (ord_less_int @ (semiri1314217659103216013at_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414])). 159.59/70.61 thf(1100,axiom,((! [A:(int > $o),B:real]: ((A @ (archim7802044766580827645g_real @ B)) = (! [C:int]: ((A @ C) <= ((ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ C) @ one_one_real) @ B) & (ord_less_eq_real @ B @ (ring_1_of_int_real @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7139_ceiling__split)). 159.59/70.61 thf(11783,plain,((! [A:(int > $o),B:real]: ((A @ (archim7802044766580827645g_real @ B)) = (! [C:int]: ((A @ C) | ~ ((ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ C) @ one_one_real) @ B) & (ord_less_eq_real @ B @ (ring_1_of_int_real @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100])). 159.59/70.61 thf(7975,axiom,((! [A:list_o,B:list_o]: ((size_s1515746228057227161od_o_o @ (product_o_o @ A @ B)) = (times_times_nat @ (size_size_list_o @ A) @ (size_size_list_o @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3627_length__product)). 159.59/70.61 thf(35738,plain,((! [A:list_o,B:list_o]: ((size_s1515746228057227161od_o_o @ (product_o_o @ A @ B)) = (times_times_nat @ (size_size_list_o @ A) @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7975])). 159.59/70.61 thf(7098,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/sandbox/benchmark/theBenchmark.p',fact_3888_power__less__zero__eq)). 159.59/70.61 thf(32727,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)],[7098])). 159.59/70.61 thf(3010,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (times_times_int @ A @ B) @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3401_mod__mult__self1__is__0)). 159.59/70.61 thf(17933,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)],[3010])). 159.59/70.61 thf(3561,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9062_inverse__le__imp__le)). 159.59/70.61 thf(19678,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3561])). 159.59/70.61 thf(5291,axiom,((! [A:nat,B:(num > nat),C:num,D:num]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_num @ C @ D) => ((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))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2687_order__subst1)). 159.59/70.61 thf(25587,plain,((! [A:nat,B:(num > nat),C:num,D:num]: ((ord_less_eq_nat @ A @ (B @ C)) => ((ord_less_eq_num @ C @ D) => ((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))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5291])). 159.59/70.61 thf(7573,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/sandbox/benchmark/theBenchmark.p',fact_9537_xor__Suc__0__eq)). 159.59/70.61 thf(34469,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)],[7573])). 159.59/70.61 thf(678,axiom,((! [A:int,B:int]: (((~ (ord_less_int @ B @ A)) = (B = A)) <= (~ (ord_less_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2790_antisym__conv3)). 159.59/70.61 thf(10422,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)],[678])). 159.59/70.61 thf(5249,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2308_mult__left__le)). 159.59/70.61 thf(25435,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ one_one_nat) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5249])). 159.59/70.61 thf(5593,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/sandbox/benchmark/theBenchmark.p',fact_8096_choose__dvd)). 159.59/70.61 thf(26737,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)],[5593])). 159.59/70.61 thf(5132,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_nat__mult__1)). 159.59/70.61 thf(25010,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5132])). 159.59/70.61 thf(2199,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1085_add__diff__cancel__right_H)). 159.59/70.61 thf(15350,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2199])). 159.59/70.61 thf(5487,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/sandbox/benchmark/theBenchmark.p',fact_3675_Pair__inject)). 159.59/70.61 thf(26396,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)],[5487])). 159.59/70.61 thf(3837,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3999_unit__imp__dvd)). 159.59/70.61 thf(20605,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3837])). 159.59/70.61 thf(5316,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9543_xor__nat__numerals_I1_J)). 159.59/70.61 thf(25702,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)],[5316])). 159.59/70.61 thf(4926,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/sandbox/benchmark/theBenchmark.p',fact_9493_real__root__le__1__iff)). 159.59/70.61 thf(24277,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)],[4926])). 159.59/70.61 thf(8011,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/sandbox/benchmark/theBenchmark.p',fact_1234_distrib__left)). 159.59/70.61 thf(35850,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)],[8011])). 159.59/70.61 thf(4298,axiom,((! [A:(nat > (nat > nat)),B:(nat > (nat > nat))]: ((if_nat_nat_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T)). 159.59/70.61 thf(22038,plain,((! [A:(nat > (nat > nat)),B:(nat > (nat > nat))]: ((if_nat_nat_nat @ ($false) @ A @ B) = (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4298])). 159.59/70.61 thf(5180,axiom,((! [A:num]: ((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ A)) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1685_power__zero__numeral)). 159.59/70.61 thf(25185,plain,((! [A:num]: ((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5180])). 159.59/70.61 thf(7531,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/sandbox/benchmark/theBenchmark.p',fact_6783_le__log2__of__power)). 159.59/70.61 thf(34284,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)],[7531])). 159.59/70.61 thf(1043,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ zero_zero_int @ (plus_plus_int @ A @ B)) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2031_add__nonneg__nonneg)). 159.59/70.61 thf(11596,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_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)],[1043])). 159.59/70.61 thf(2108,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/sandbox/benchmark/theBenchmark.p',fact_6939_norm__triangle__sub)). 159.59/70.61 thf(15041,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)],[2108])). 159.59/70.61 thf(3354,axiom,((! [A:nat]: (exp_real = (^ [B:real]: (plus_plus_real @ (groups6591440286371151544t_real @ (^ [C:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ C)) @ (power_power_real @ B @ C))) @ (set_ord_lessThan_nat @ A)) @ (suminf_real @ (^ [C:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (plus_plus_nat @ C @ A))) @ (power_power_real @ B @ (plus_plus_nat @ C @ A)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9298_exp__first__terms)). 159.59/70.61 thf(19033,plain,((! [A:nat]: ((exp_real) = (^ [B:real]: (plus_plus_real @ (groups6591440286371151544t_real @ (^ [C:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ C)) @ (power_power_real @ B @ C))) @ (set_ord_lessThan_nat @ A)) @ (suminf_real @ (^ [C:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (plus_plus_nat @ C @ A))) @ (power_power_real @ B @ (plus_plus_nat @ C @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3354])). 159.59/70.61 thf(7732,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/sandbox/benchmark/theBenchmark.p',fact_560_div2__Suc__Suc)). 159.59/70.61 thf(34982,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)],[7732])). 159.59/70.61 thf(64,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/sandbox/benchmark/theBenchmark.p',fact_9597_int__numeral__or__not__num__neg)). 159.59/70.61 thf(8443,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)],[64])). 159.59/70.61 thf(4236,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/sandbox/benchmark/theBenchmark.p',fact_5921_real__of__int__div2)). 159.59/70.61 thf(21848,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)],[4236])). 159.59/70.61 thf(974,axiom,((! [A:complex]: ((A != zero_zero_complex) => ((times_times_complex @ A @ (invers8013647133539491842omplex @ A)) = one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9004_right__inverse)). 159.59/70.61 thf(11367,plain,((! [A:complex]: ((~ (A = zero_zero_complex)) => ((times_times_complex @ A @ (invers8013647133539491842omplex @ A)) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[974])). 159.59/70.61 thf(7467,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/sandbox/benchmark/theBenchmark.p',fact_9425_numeral__power__le__nat__cancel__iff)). 159.59/70.61 thf(34052,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)],[7467])). 159.59/70.61 thf(5308,axiom,((! [A:int,B:int]: ((bit_concat_bit @ zero_zero_nat @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3806_concat__bit__0)). 159.59/70.61 thf(25666,plain,((! [A:int,B:int]: ((bit_concat_bit @ zero_zero_nat @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5308])). 159.59/70.61 thf(3306,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/sandbox/benchmark/theBenchmark.p',fact_7959_sum_OlessThan__Suc__shift)). 159.59/70.61 thf(18888,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)],[3306])). 159.59/70.61 thf(5365,axiom,((! [A:nat]: ? [B:list_VEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_Ex__list__of__length)). 159.59/70.61 thf(25933,plain,((! [A:nat]: ? [B:list_VEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5365])). 159.59/70.61 thf(4903,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2231_mult__left__le__imp__le)). 159.59/70.61 thf(24201,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4903])). 159.59/70.61 thf(3281,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/sandbox/benchmark/theBenchmark.p',fact_4569_signed__take__bit__int__less__exp)). 159.59/70.61 thf(18814,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)],[3281])). 159.59/70.61 thf(2545,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/sandbox/benchmark/theBenchmark.p',fact_9625_csqrt_Osimps_I1_J)). 159.59/70.61 thf(16433,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)],[2545])). 159.59/70.61 thf(4437,axiom,((! [A:(nat > real)]: ((summable_real @ (^ [B:nat]: (A @ (suc @ B)))) = (summable_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7026_summable__Suc__iff)). 159.59/70.61 thf(22466,plain,((! [A:(nat > real)]: ((summable_real @ (^ [B:nat]: (A @ (suc @ B)))) = (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4437])). 159.59/70.61 thf(4956,axiom,((! [A:product_prod_nat_nat]: ~ (! [B:nat,C:nat]: (A != (product_Pair_nat_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3690_old_Oprod_Oexhaust)). 159.59/70.61 thf(24369,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)],[4956])). 159.59/70.61 thf(8182,axiom,((! [A:(nat > nat),B:nat,C:(nat > nat),D:nat]: ((sums_nat @ A @ B) => ((sums_nat @ (^ [E:nat]: (plus_plus_nat @ (A @ E) @ (C @ E))) @ (plus_plus_nat @ B @ D)) <= (sums_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7892_sums__add)). 159.59/70.61 thf(36415,plain,((! [A:(nat > nat),B:nat,C:(nat > nat),D:nat]: ((sums_nat @ (A) @ B) => ((sums_nat @ (^ [E:nat]: (plus_plus_nat @ (A @ E) @ (C @ E))) @ (plus_plus_nat @ B @ D)) | ~ (sums_nat @ (C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8182])). 159.59/70.61 thf(3890,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4468_minf_I3_J)). 159.59/70.61 thf(20775,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3890])). 159.59/70.61 thf(2670,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))) = ((A != zero_zero_real) | (B != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2315_sum__squares__gt__zero__iff)). 159.59/70.61 thf(16858,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (times_times_real @ A @ A) @ (times_times_real @ B @ B))) = (~ (A = zero_zero_real) | ~ (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2670])). 159.59/70.61 thf(5131,axiom,((! [A:num]: ((unique5055182867167087721od_nat @ one @ (bit0 @ A)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5463_divmod__algorithm__code_I3_J)). 159.59/70.61 thf(25007,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)],[5131])). 159.59/70.61 thf(4182,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/sandbox/benchmark/theBenchmark.p',fact_6736_real__of__nat__div4)). 159.59/70.61 thf(21665,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)],[4182])). 159.59/70.61 thf(8141,axiom,((bit_se8570568707652914677it_nat = (^ [A:nat,B:nat]: (divide_divide_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9742_drop__bit__nat__def)). 159.59/70.61 thf(36287,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)],[8141])). 159.59/70.61 thf(6954,axiom,((! [A:int,B:int]: ((A = (times_times_int @ B @ A)) = ((A = zero_zero_int) | (B = one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1619_mult__cancel__right1)). 159.59/70.61 thf(32055,plain,((! [A:int,B:int]: ((A = (times_times_int @ B @ A)) = ((A = zero_zero_int) | (B = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6954])). 159.59/70.61 thf(2277,axiom,((! [A:complex,B:complex,C:complex,D:complex]: (((A != B) & (C != D)) = ((plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ D)) != (plus_plus_complex @ (times_times_complex @ A @ D) @ (times_times_complex @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4582_crossproduct__noteq)). 159.59/70.61 thf(15591,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((~ (A = B) & ~ (C = D)) = (~ ((plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ D)) = (plus_plus_complex @ (times_times_complex @ A @ D) @ (times_times_complex @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2277])). 159.59/70.61 thf(3475,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/sandbox/benchmark/theBenchmark.p',fact_6929_norm__triangle__mono)). 159.59/70.61 thf(19411,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)],[3475])). 159.59/70.61 thf(7831,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ B) <= (ord_less_nat @ C @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2826_dual__order_Ostrict__trans)). 159.59/70.61 thf(35289,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ C @ B) | ~ (ord_less_nat @ C @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7831])). 159.59/70.61 thf(4487,axiom,((! [A:nat]: (ord_less_eq_real @ one_one_real @ (semiri2265585572941072030t_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8080_fact__ge__1)). 159.59/70.61 thf(22685,plain,((! [A:nat]: (ord_less_eq_real @ one_one_real @ (semiri2265585572941072030t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4487])). 159.59/70.61 thf(4742,axiom,((! [A:num]: ((ord_max_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_max__0__1_I6_J)). 159.59/70.61 thf(23628,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)],[4742])). 159.59/70.61 thf(5328,axiom,((! [A:real,B:num]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ (numeral_numeral_int @ B)) = (ord_less_eq_real @ A @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6979_ceiling__le__numeral)). 159.59/70.61 thf(25741,plain,((! [A:real,B:num]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ (numeral_numeral_int @ B)) = (ord_less_eq_real @ A @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5328])). 159.59/70.61 thf(628,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ B @ (times_3573771949741848930nteger @ C @ A))) = (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3829_dvd__add__times__triv__right__iff)). 159.59/70.61 thf(10256,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ B @ (times_3573771949741848930nteger @ C @ A))) = (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[628])). 159.59/70.61 thf(918,axiom,((vEBT_VEBT_set_vebt = (^ [A:vEBT_VEBT]: (collect_nat @ (vEBT_vebt_member @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1395_set__vebt_H__def)). 159.59/70.61 thf(11195,plain,(((vEBT_VEBT_set_vebt) = (^ [A:vEBT_VEBT]: (collect_nat @ (vEBT_vebt_member @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[918])). 159.59/70.61 thf(2062,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/sandbox/benchmark/theBenchmark.p',fact_6959_cos__pi__eq__zero)). 159.59/70.61 thf(14900,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)],[2062])). 159.59/70.61 thf(4697,axiom,((! [A:num]: ((numera6690914467698888265omplex @ A) != (uminus1482373934393186551omplex @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5088_numeral__neq__neg__one)). 159.59/70.61 thf(23492,plain,((! [A:num]: ~ ((numera6690914467698888265omplex @ A) = (uminus1482373934393186551omplex @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4697])). 159.59/70.61 thf(1254,axiom,((! [A:real,B:real,C:(real > int),D:int]: ((ord_less_real @ A @ B) => ((ord_less_int @ (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/sandbox/benchmark/theBenchmark.p',fact_2907_order__less__subst2)). 159.59/70.61 thf(12306,plain,((! [A:real,B:real,C:(real > int),D:int]: ((ord_less_real @ A @ B) => ((ord_less_int @ (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)],[1254])). 159.59/70.61 thf(1504,axiom,((! [A:real,B:nat,C:(nat > (nat > real))]: (((B != zero_zero_nat) => ((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))) <= (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8133_Maclaurin__zero)). 159.59/70.61 thf(13155,plain,((! [A:real,B:nat,C:(nat > (nat > real))]: (((~ (B = zero_zero_nat)) => ((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))) | ~ (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504])). 159.59/70.61 thf(243,axiom,((! [A:real,B:real]: ((real_V1803761363581548252l_real @ (times_times_real @ A @ B)) = (times_times_real @ (real_V1803761363581548252l_real @ A) @ (real_V1803761363581548252l_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7327_of__real__mult)). 159.59/70.61 thf(8992,plain,((! [A:real,B:real]: ((real_V1803761363581548252l_real @ (times_times_real @ A @ B)) = (times_times_real @ (real_V1803761363581548252l_real @ A) @ (real_V1803761363581548252l_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 159.59/70.61 thf(4224,axiom,((! [A:(nat > real)]: (summable_real @ (^ [B:nat]: (times_times_real @ (A @ B) @ (power_power_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7070_summable__0__powser)). 159.59/70.61 thf(21816,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)],[4224])). 159.59/70.61 thf(3080,axiom,((divide1717551699836669952omplex = (^ [A:complex,B:complex]: (times_times_complex @ (invers8013647133539491842omplex @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9040_divide__inverse__commute)). 159.59/70.61 thf(18146,plain,(((divide1717551699836669952omplex) = (^ [A:complex,B:complex]: (times_times_complex @ (invers8013647133539491842omplex @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3080])). 159.59/70.61 thf(5005,axiom,((! [A:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one))) = (uminus1351360451143612070nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5208_mult__1s__ring__1_I2_J)). 159.59/70.61 thf(24573,plain,((! [A:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one))) = (uminus1351360451143612070nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5005])). 159.59/70.61 thf(7107,axiom,((! [A:nat,B:nat,C:nat,D:list_nat]: (((upt @ A @ B) = (cons_nat @ C @ D)) = ((A = C) & ((upt @ (plus_plus_nat @ A @ one_one_nat) @ B) = D) & (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10143_upt__eq__Cons__conv)). 159.59/70.61 thf(32759,plain,((! [A:nat,B:nat,C:nat,D:list_nat]: (((upt @ A @ B) = (cons_nat @ C @ D)) = ((A = C) & ((upt @ (plus_plus_nat @ A @ one_one_nat) @ B) = D) & (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7107])). 159.59/70.61 thf(5090,axiom,((! [A:nat]: ((semiri1316708129612266289at_nat @ (suc @ A)) = (plus_plus_nat @ one_one_nat @ (semiri1316708129612266289at_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6584_of__nat__Suc)). 159.59/70.61 thf(24881,plain,((! [A:nat]: ((semiri1316708129612266289at_nat @ (suc @ A)) = (plus_plus_nat @ one_one_nat @ (semiri1316708129612266289at_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5090])). 159.59/70.61 thf(3081,axiom,((semiri3624122377584611663nteger = (^ [A:nat]: (semiri4939895301339042750nteger @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8963_fact__code)). 159.59/70.61 thf(18148,plain,(((semiri3624122377584611663nteger) = (^ [A:nat]: (semiri4939895301339042750nteger @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3081])). 159.59/70.61 thf(7908,axiom,((! [A:nat,B:nat]: ((B != A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_less__not__refl2)). 159.59/70.61 thf(35533,plain,((! [A:nat,B:nat]: (~ (B = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7908])). 159.59/70.61 thf(586,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/sandbox/benchmark/theBenchmark.p',fact_1305_max__add__distrib__left)). 159.59/70.61 thf(10113,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)],[586])). 159.59/70.61 thf(3440,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/sandbox/benchmark/theBenchmark.p',fact_1369_ordered__ring__class_Ole__add__iff2)). 159.59/70.61 thf(19310,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)],[3440])). 159.59/70.61 thf(1825,axiom,((exp_complex = (^ [A:complex]: (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9286_exp__def)). 159.59/70.61 thf(14160,plain,(((exp_complex) = (^ [A:complex]: (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1825])). 159.59/70.61 thf(7243,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ one_one_int @ B) | (A = zero_zero_int)) <= (ord_less_eq_int @ (abs_abs_int @ (ring_1_of_int_int @ A)) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5900_of__int__leD)). 159.59/70.61 thf(33297,plain,((! [A:int,B:int]: ((ord_less_eq_int @ one_one_int @ B) | (A = zero_zero_int) | ~ (ord_less_eq_int @ (abs_abs_int @ (ring_1_of_int_int @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7243])). 159.59/70.61 thf(5443,axiom,((! [A:list_VEBT_VEBT,B:nat,C:nat]: ((! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ D @ B))) => ((ord_less_eq_nat @ one_one_nat @ B) <= ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_set__n__deg__not__0)). 159.59/70.61 thf(26243,plain,((! [A:list_VEBT_VEBT,B:nat,C:nat]: ((! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ D @ B))) => ((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)],[5443])). 159.59/70.61 thf(3221,axiom,((! [A:nat,B:list_nat,C:(nat > $o)]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((C @ (nth_nat @ B @ A)) <= (! [D:nat]: ((member_nat @ D @ (set_nat2 @ B)) => (C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_list__ball__nth)). 159.59/70.61 thf(18607,plain,((! [A:nat,B:list_nat,C:(nat > $o)]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((C @ (nth_nat @ B @ A)) | ~ (! [D:nat]: ((member_nat @ D @ (set_nat2 @ B)) => (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3221])). 159.59/70.61 thf(516,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ C))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9224_scaleR__right__mono)). 159.59/70.61 thf(9896,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ C))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[516])). 159.59/70.61 thf(7802,axiom,((! [A:num]: ((plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_numeral__plus__one)). 159.59/70.61 thf(35190,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)],[7802])). 159.59/70.61 thf(2587,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ C @ (divide_divide_int @ B @ A)) = (dvd_dvd_int @ (times_times_int @ C @ A) @ B))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4146_dvd__div__iff__mult)). 159.59/70.61 thf(16565,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ C @ (divide_divide_int @ B @ A)) = (dvd_dvd_int @ (times_times_int @ C @ A) @ B))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2587])). 159.59/70.61 thf(3877,axiom,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5185_not__numeral__less__neg__one)). 159.59/70.61 thf(20736,plain,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3877])). 159.59/70.61 thf(3573,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/sandbox/benchmark/theBenchmark.p',fact_1376_square__diff__one__factored)). 159.59/70.61 thf(19729,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)],[3573])). 159.59/70.61 thf(2398,axiom,((! [A:real]: (((ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one))) => (ord_less_real @ zero_zero_real @ (sin_real @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6854_sin__gt__zero__02)). 159.59/70.61 thf(15958,plain,((! [A:real]: (((ord_less_real @ A @ (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)],[2398])). 159.59/70.61 thf(6683,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ A @ B) => (~ (ord_less_eq_int @ B @ C))) => ((((((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 @ B @ A)))) <= ((~ (ord_less_eq_int @ C @ B)) <= (ord_less_eq_int @ A @ C))) <= ((~ (ord_less_eq_int @ A @ C)) <= (ord_less_eq_int @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2754_le__cases3)). 159.59/70.61 thf(30902,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ A @ B) => (~ (ord_less_eq_int @ B @ C))) => ((((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 @ B @ A))) | ~ (~ (ord_less_eq_int @ C @ B) | ~ (ord_less_eq_int @ A @ C)) | ~ (~ (ord_less_eq_int @ A @ C) | ~ (ord_less_eq_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6683])). 159.59/70.61 thf(5613,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int) = (((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ A)) | ((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1981_mult__le__0__iff)). 159.59/70.61 thf(26824,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int) = (((ord_less_eq_int @ B @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ A)) | ((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5613])). 159.59/70.61 thf(3156,axiom,((! [A:set_nat,B:(nat > extended_enat)]: ((! [C:nat]: ((member_nat @ C @ A) => ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ C)) & (ord_le2932123472753598470d_enat @ (B @ C) @ one_on7984719198319812577d_enat)))) => (ord_le2932123472753598470d_enat @ (groups7961826882256487087d_enat @ B @ A) @ one_on7984719198319812577d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8549_prod__le__1)). 159.59/70.61 thf(18412,plain,((! [A:set_nat,B:(nat > extended_enat)]: ((! [C:nat]: ((member_nat @ C @ A) => ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ C)) & (ord_le2932123472753598470d_enat @ (B @ C) @ one_on7984719198319812577d_enat)))) => (ord_le2932123472753598470d_enat @ (groups7961826882256487087d_enat @ (B) @ A) @ one_on7984719198319812577d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3156])). 159.59/70.61 thf(2442,axiom,((! [A:real,B:real]: (((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))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5272_ln__diff__le)). 159.59/70.61 thf(16109,plain,((! [A:real,B:real]: (((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))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2442])). 159.59/70.61 thf(2969,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/sandbox/benchmark/theBenchmark.p',fact_5875_of__int__less__neg__numeral__power__cancel__iff)). 159.59/70.61 thf(17811,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)],[2969])). 159.59/70.61 thf(5057,axiom,((! [A:num]: ((plus_plus_num @ (bitM @ A) @ one) = (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5895_BitM__plus__one)). 159.59/70.61 thf(24762,plain,((! [A:num]: ((plus_plus_num @ (bitM @ A) @ one) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5057])). 159.59/70.61 thf(1838,axiom,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => ((! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C)))) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_nth__equalityI)). 159.59/70.61 thf(14196,plain,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => ((! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C)))) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1838])). 159.59/70.61 thf(492,axiom,((ord_less_int = (^ [A:int,B:int]: ((B != A) & (B = (ord_max_int @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_max_Ostrict__order__iff)). 159.59/70.61 thf(9822,plain,(((ord_less_int) = (^ [A:int,B:int]: (~ (B = A) & (B = (ord_max_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[492])). 159.59/70.61 thf(220,axiom,((! [A:nat,B:real]: ((cos_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ B)) = (re @ (power_power_complex @ (cis @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9640_cos__n__Re__cis__pow__n)). 159.59/70.61 thf(8924,plain,((! [A:nat,B:real]: ((cos_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ B)) = (re @ (power_power_complex @ (cis @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[220])). 159.59/70.61 thf(1678,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > $o)]: ((finite_finite_nat @ A) => ((groups6464643781859351333omplex @ B @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & (C @ D))))) = (groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (C @ D) @ (B @ D) @ one_one_complex)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8534_prod_Ointer__filter)). 159.59/70.61 thf(13683,plain,((! [A:set_nat,B:(nat > complex),C:(nat > $o)]: ((finite_finite_nat @ A) => ((groups6464643781859351333omplex @ (B) @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & (C @ D))))) = (groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (C @ D) @ (B @ D) @ one_one_complex)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1678])). 159.59/70.61 thf(7812,axiom,((vEBT_invar_vebt @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ na)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_nnvalid)). 159.59/70.61 thf(35221,plain,((vEBT_invar_vebt @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7812])). 159.59/70.61 thf(4934,axiom,((! [A:nat,B:nat]: (((ord_less_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6784_log2__of__power__less)). 159.59/70.61 thf(24302,plain,((! [A:nat,B:nat]: ((ord_less_real @ (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4934])). 159.59/70.61 thf(5998,axiom,((! [A:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((abs_abs_real @ A) = (uminus_uminus_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5435_abs__of__nonpos)). 159.59/70.61 thf(28435,plain,((! [A:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((abs_abs_real @ A) = (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5998])). 159.59/70.61 thf(4977,axiom,((! [A:num]: (zero_zero_real != (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5032_zero__neq__neg__numeral)). 159.59/70.61 thf(24480,plain,((! [A:num]: ~ (zero_zero_real = (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4977])). 159.59/70.61 thf(5392,axiom,((! [A:nat]: ((minus_minus_nat @ (suc @ A) @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_diff__Suc__1)). 159.59/70.61 thf(26037,plain,((! [A:nat]: ((minus_minus_nat @ (suc @ A) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5392])). 159.59/70.61 thf(2066,axiom,((! [A:real]: ((~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ A))) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2625_not__real__square__gt__zero)). 159.59/70.61 thf(14911,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)],[2066])). 159.59/70.61 thf(5848,axiom,((! [A:(list_VEBT_VEBT > $o),B:list_VEBT_VEBT]: ((A @ B) <= (! [C:list_VEBT_VEBT]: ((A @ C) <= (! [D:list_VEBT_VEBT]: ((A @ D) <= (ord_less_nat @ (size_s6755466524823107622T_VEBT @ D) @ (size_s6755466524823107622T_VEBT @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_length__induct)). 159.59/70.61 thf(27865,plain,((! [A:(list_VEBT_VEBT > $o),B:list_VEBT_VEBT]: ((A @ B) | ~ (! [C:list_VEBT_VEBT]: ((A @ C) | ~ (! [D:list_VEBT_VEBT]: ((A @ D) | ~ (ord_less_nat @ (size_s6755466524823107622T_VEBT @ D) @ (size_s6755466524823107622T_VEBT @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5848])). 159.59/70.61 thf(4390,axiom,((! [A:list_nat,B:(nat > $o)]: ((! [C:nat]: ((member_nat @ C @ (set_nat2 @ A)) => (B @ C))) = (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (B @ (nth_nat @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_all__set__conv__all__nth)). 159.59/70.61 thf(22314,plain,((! [A:list_nat,B:(nat > $o)]: ((! [C:nat]: ((member_nat @ C @ (set_nat2 @ A)) => (B @ C))) = (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => (B @ (nth_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4390])). 159.59/70.61 thf(7397,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/sandbox/benchmark/theBenchmark.p',fact_784_max_Obounded__iff)). 159.59/70.61 thf(33823,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)],[7397])). 159.59/70.61 thf(262,axiom,((! [A:real]: (sums_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (cos_coeff @ B) @ (power_power_real @ (uminus_uminus_real @ A) @ B))) @ (cos_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9291_cos__minus__converges)). 159.59/70.61 thf(9048,plain,((! [A:real]: (sums_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (cos_coeff @ B) @ (power_power_real @ (uminus_uminus_real @ A) @ B))) @ (cos_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 159.59/70.61 thf(4558,axiom,((! [A:nat]: ((ord_max_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1574_max__0L)). 159.59/70.61 thf(22992,plain,((! [A:nat]: ((ord_max_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4558])). 159.59/70.61 thf(7718,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/sandbox/benchmark/theBenchmark.p',fact_4191_evenE)). 159.59/70.61 thf(34930,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)],[7718])). 159.59/70.61 thf(3549,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/sandbox/benchmark/theBenchmark.p',fact_1207_add__mono__thms__linordered__field_I5_J)). 159.59/70.61 thf(19639,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)],[3549])). 159.59/70.61 thf(783,axiom,((! [A:num]: ((numera1916890842035813515d_enat @ (bit1 @ A)) = (plus_p3455044024723400733d_enat @ (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ A)) @ one_on7984719198319812577d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5604_numeral__code_I3_J)). 159.59/70.61 thf(10779,plain,((! [A:num]: ((numera1916890842035813515d_enat @ (bit1 @ A)) = (plus_p3455044024723400733d_enat @ (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ A)) @ one_on7984719198319812577d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[783])). 159.59/70.61 thf(1960,axiom,((! [A:complex,B:nat,C:complex,D:nat]: ((dvd_dvd_complex @ (power_power_complex @ A @ B) @ C) => ((dvd_dvd_complex @ (power_power_complex @ A @ D) @ C) <= (ord_less_eq_nat @ D @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4117_power__le__dvd)). 159.59/70.61 thf(14569,plain,((! [A:complex,B:nat,C:complex,D:nat]: ((dvd_dvd_complex @ (power_power_complex @ A @ B) @ C) => ((dvd_dvd_complex @ (power_power_complex @ A @ D) @ C) | ~ (ord_less_eq_nat @ D @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1960])). 159.59/70.61 thf(3744,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2239_mult__strict__mono_H)). 159.59/70.61 thf(20299,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3744])). 159.59/70.61 thf(462,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit1 @ A)))) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9606_and__not__numerals_I3_J)). 159.59/70.61 thf(9703,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)],[462])). 159.59/70.61 thf(3136,axiom,((! [A:int,B:nat]: ((ord_less_int @ A @ (bit_se2923211474154528505it_int @ B @ A)) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5024_take__bit__int__greater__self__iff)). 159.59/70.61 thf(18344,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)],[3136])). 159.59/70.61 thf(1956,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/sandbox/benchmark/theBenchmark.p',fact_2083_zero__less__mult__pos2)). 159.59/70.61 thf(14558,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)],[1956])). 159.59/70.61 thf(390,axiom,((! [A:complex,B:real]: ((im @ (divide1717551699836669952omplex @ A @ (real_V4546457046886955230omplex @ B))) = (divide_divide_real @ (im @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9644_Im__divide__of__real)). 159.59/70.61 thf(9472,plain,((! [A:complex,B:real]: ((im @ (divide1717551699836669952omplex @ A @ (real_V4546457046886955230omplex @ B))) = (divide_divide_real @ (im @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])). 159.59/70.61 thf(2543,axiom,((! [A:real]: (((((sin_real @ A) = zero_zero_real) => (A = zero_zero_real)) <= (ord_less_real @ A @ pi)) <= (ord_less_real @ (uminus_uminus_real @ pi) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6844_sin__eq__0__pi)). 159.59/70.61 thf(16428,plain,((! [A:real]: ((((sin_real @ A) = zero_zero_real) => (A = zero_zero_real)) | ~ (ord_less_real @ A @ pi) | ~ (ord_less_real @ (uminus_uminus_real @ pi) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2543])). 159.59/70.61 thf(4531,axiom,((! [A:num,B:nat]: ((bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ B) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6366_bit__numeral__iff)). 159.59/70.61 thf(22896,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4531])). 159.59/70.61 thf(4645,axiom,((! [A:(nat > nat)]: ((size_option_nat @ A @ none_nat) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4588_option_Osize__gen_I1_J)). 159.59/70.61 thf(23304,plain,((! [A:(nat > nat)]: ((size_option_nat @ (A) @ none_nat) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4645])). 159.59/70.61 thf(6746,axiom,((! [A:nat,B:complex]: (((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (power_power_complex @ B @ A)) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4868_Parity_Oring__1__class_Opower__minus__even)). 159.59/70.61 thf(31249,plain,((! [A:nat,B:complex]: (((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (power_power_complex @ B @ A)) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6746])). 159.59/70.61 thf(6265,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (times_times_complex @ B @ C)) = (times_times_complex @ B @ (times_times_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_mult_Oleft__commute)). 159.59/70.61 thf(29365,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (times_times_complex @ B @ C)) = (times_times_complex @ B @ (times_times_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6265])). 159.59/70.61 thf(3965,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/sandbox/benchmark/theBenchmark.p',fact_3499_cong__exp__iff__simps_I2_J)). 159.59/70.61 thf(21009,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)],[3965])). 159.59/70.61 thf(415,axiom,((! [A:real]: ((plus_plus_real @ (sinh_real @ A) @ (cosh_real @ A)) = (exp_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9322_sinh__plus__cosh)). 159.59/70.61 thf(9556,plain,((! [A:real]: ((plus_plus_real @ (sinh_real @ A) @ (cosh_real @ A)) = (exp_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])). 159.59/70.61 thf(1834,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le72135733267957522d_enat @ C @ B) <= (ord_le72135733267957522d_enat @ C @ A)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2823_dual__order_Ostrict__trans)). 159.59/70.61 thf(14184,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ C @ B) | ~ (ord_le72135733267957522d_enat @ C @ A) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1834])). 159.59/70.61 thf(548,axiom,((! [A:nat]: ((semiri4939895301339042750nteger @ (suc @ A)) != zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6677_of__nat__neq__0)). 159.59/70.61 thf(9997,plain,((! [A:nat]: ~ ((semiri4939895301339042750nteger @ (suc @ A)) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[548])). 159.59/70.61 thf(6849,axiom,(((neg_nu7757733837767384882nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (bit1 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5674_dbl__dec__simps_I4_J)). 159.59/70.61 thf(31698,plain,(((neg_nu7757733837767384882nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (bit1 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6849])). 159.59/70.61 thf(5345,axiom,((! [A:vEBT_VEBT]: (((~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D)))) <= (A != (vEBT_Leaf @ ($false) @ ($false)))) <= (vEBT_VEBT_minNull @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2123_VEBT__internal_OminNull_Oelims_I2_J)). 159.59/70.61 thf(25834,plain,((! [A:vEBT_VEBT]: (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) | (A = (vEBT_Leaf @ ($false) @ ($false))) | ~ (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5345])). 159.59/70.61 thf(6363,axiom,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ (root @ A @ B) @ (root @ A @ C)) = (ord_less_eq_real @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9483_real__root__le__iff)). 159.59/70.61 thf(29682,plain,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ (root @ A @ B) @ (root @ A @ C)) = (ord_less_eq_real @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6363])). 159.59/70.61 thf(3040,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/sandbox/benchmark/theBenchmark.p',fact_3574_set__bit__Suc)). 159.59/70.61 thf(18022,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)],[3040])). 159.59/70.61 thf(3961,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/sandbox/benchmark/theBenchmark.p',fact_7174_sin__times__sin)). 159.59/70.61 thf(20998,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)],[3961])). 159.59/70.61 thf(7281,axiom,((! [A:num]: (((uminus1482373934393186551omplex @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4755_neg__one__eq__numeral__iff)). 159.59/70.61 thf(33412,plain,((! [A:num]: (((uminus1482373934393186551omplex @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7281])). 159.59/70.61 thf(6244,axiom,((! [A:nat,B:num]: ((bit_se2925701944663578781it_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ (times_times_nat @ (bit_se2925701944663578781it_nat @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5662_take__bit__Suc__bit1)). 159.59/70.61 thf(29226,plain,((! [A:nat,B:num]: ((bit_se2925701944663578781it_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ (times_times_nat @ (bit_se2925701944663578781it_nat @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6244])). 159.59/70.61 thf(5428,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/sandbox/benchmark/theBenchmark.p',fact_6621_real__of__nat__less__numeral__iff)). 159.59/70.61 thf(26187,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)],[5428])). 159.59/70.61 thf(3820,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/sandbox/benchmark/theBenchmark.p',fact_5823_of__int__less__numeral__iff)). 159.59/70.61 thf(20533,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)],[3820])). 159.59/70.61 thf(468,axiom,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ zero_zero_int @ (comm_s4660882817536571857er_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8214_pochhammer__pos)). 159.59/70.61 thf(9720,plain,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ zero_zero_int @ (comm_s4660882817536571857er_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])). 159.59/70.61 thf(4652,axiom,((! [A:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1954_not__numeral__le__zero)). 159.59/70.61 thf(23332,plain,((! [A:num]: ~ (ord_less_eq_int @ (numeral_numeral_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4652])). 159.59/70.61 thf(4726,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/sandbox/benchmark/theBenchmark.p',fact_6593_numeral__power__eq__of__nat__cancel__iff)). 159.59/70.61 thf(23581,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)],[4726])). 159.59/70.61 thf(1549,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => ((ord_less_eq_real @ zero_zero_real @ (arccos @ A)) & (ord_less_eq_real @ (arccos @ A) @ pi))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7765_arccos__bounded)). 159.59/70.61 thf(13286,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => ((ord_less_eq_real @ zero_zero_real @ (arccos @ A)) & (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)],[1549])). 159.59/70.61 thf(5678,axiom,((! [A:vEBT_VEBT,B:nat]: ((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))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2574_inrange)). 159.59/70.61 thf(27063,plain,((! [A:vEBT_VEBT,B:nat]: ((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))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5678])). 159.59/70.61 thf(1571,axiom,((! [A:set_nat,B:set_nat,C:(nat > real)]: (((ord_less_eq_set_nat @ B @ A) => (((! [D:nat]: ((member_nat @ D @ B) => (ord_less_eq_real @ zero_zero_real @ (C @ D)))) => (ord_less_eq_real @ (groups129246275422532515t_real @ C @ B) @ (groups129246275422532515t_real @ C @ A))) <= (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => (ord_less_eq_real @ one_one_real @ (C @ D)))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8857_prod__mono2)). 159.59/70.61 thf(13352,plain,((! [A:set_nat,B:set_nat,C:(nat > real)]: (((ord_less_eq_set_nat @ B @ A) => (((! [D:nat]: ((member_nat @ D @ B) => (ord_less_eq_real @ zero_zero_real @ (C @ D)))) => (ord_less_eq_real @ (groups129246275422532515t_real @ (C) @ B) @ (groups129246275422532515t_real @ (C) @ A))) | ~ (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => (ord_less_eq_real @ one_one_real @ (C @ D)))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571])). 159.59/70.61 thf(3619,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/sandbox/benchmark/theBenchmark.p',fact_4695_add__neg__numeral__simps_I3_J)). 159.59/70.61 thf(19877,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)],[3619])). 159.59/70.61 thf(6642,axiom,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ A) = (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_int @ one_one_int @ B)) & ((ord_less_int @ B @ one_one_int) <= (ord_less_eq_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2415_mult__less__cancel__left2)). 159.59/70.61 thf(30761,plain,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ A) = (((ord_less_eq_int @ A @ zero_zero_int) => (ord_less_int @ one_one_int @ B)) & ((ord_less_int @ B @ one_one_int) | ~ (ord_less_eq_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6642])). 159.59/70.61 thf(2005,axiom,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1535_div__by__0)). 159.59/70.61 thf(14730,plain,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2005])). 159.59/70.61 thf(4365,axiom,((! [A:real]: ((sqrt @ (inverse_inverse_real @ A)) = (inverse_inverse_real @ (sqrt @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9014_real__sqrt__inverse)). 159.59/70.61 thf(22232,plain,((! [A:real]: ((sqrt @ (inverse_inverse_real @ A)) = (inverse_inverse_real @ (sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4365])). 159.59/70.61 thf(6532,axiom,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3240_order__less__le__subst1)). 159.59/70.61 thf(30371,plain,((! [A:nat,B:(nat > nat),C:nat,D:nat]: ((ord_less_nat @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((ord_less_nat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6532])). 159.59/70.61 thf(4606,axiom,((! [A:num,B:num]: ((pow @ A @ (bit1 @ B)) = (times_times_num @ (sqr @ (pow @ A @ B)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9795_pow_Osimps_I3_J)). 159.59/70.61 thf(23175,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)],[4606])). 159.59/70.61 thf(5602,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/sandbox/benchmark/theBenchmark.p',fact_1762_nat__mult__le__cancel__disj)). 159.59/70.61 thf(26788,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)],[5602])). 159.59/70.61 thf(77,axiom,((! [A:code_integer,B:code_integer]: (((modulo364778990260209775nteger @ A @ B) = A) = ((divide6298287555418463151nteger @ A @ B) = zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3476_mod__eq__self__iff__div__eq__0)). 159.59/70.61 thf(8486,plain,((! [A:code_integer,B:code_integer]: (((modulo364778990260209775nteger @ A @ B) = A) = ((divide6298287555418463151nteger @ A @ B) = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 159.59/70.61 thf(1826,axiom,((! [A:code_integer,B:code_integer]: ((uminus1351360451143612070nteger @ (plus_p5714425477246183910nteger @ A @ B)) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4971_is__num__normalize_I8_J)). 159.59/70.61 thf(14162,plain,((! [A:code_integer,B:code_integer]: ((uminus1351360451143612070nteger @ (plus_p5714425477246183910nteger @ A @ B)) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1826])). 159.59/70.61 thf(4281,axiom,((! [A:nat,B:int]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (ring_18347121197199848620nteger @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6659_of__nat__less__of__int__iff)). 159.59/70.61 thf(21983,plain,((! [A:nat,B:int]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (ring_18347121197199848620nteger @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4281])). 159.59/70.61 thf(4755,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_nat__le__iff__add)). 159.59/70.61 thf(23688,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)],[4755])). 159.59/70.61 thf(3168,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/sandbox/benchmark/theBenchmark.p',fact_5909_int__le__real__less)). 159.59/70.61 thf(18445,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)],[3168])). 159.59/70.61 thf(3192,axiom,((! [A:int]: ((? [B:nat]: (A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ B))))) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6853_negD)). 159.59/70.61 thf(18520,plain,((! [A:int]: (? [B:nat]: (A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ B)))) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3192])). 159.59/70.61 thf(5179,axiom,((! [A:(nat > real),B:real]: ((sums_real @ A @ B) => (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)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8015_sums__if_H)). 159.59/70.61 thf(25183,plain,((! [A:(nat > real),B:real]: ((sums_real @ (A) @ B) => (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)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5179])). 159.59/70.61 thf(3313,axiom,((! [A:nat]: (((semiri8010041392384452111omplex @ A) = one_one_complex) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6542_of__nat__eq__1__iff)). 159.59/70.61 thf(18909,plain,((! [A:nat]: (((semiri8010041392384452111omplex @ A) = one_one_complex) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3313])). 159.59/70.61 thf(5958,axiom,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = (ord_less_num @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3169_linorder__not__le)). 159.59/70.61 thf(28308,plain,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = (ord_less_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5958])). 159.59/70.61 thf(245,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/sandbox/benchmark/theBenchmark.p',fact_9671_complex__eq__0)). 159.59/70.61 thf(8999,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)],[245])). 159.59/70.61 thf(4535,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/sandbox/benchmark/theBenchmark.p',fact_1212_diff__right__mono)). 159.59/70.61 thf(22909,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)],[4535])). 159.59/70.61 thf(6299,axiom,((! [A:list_int,B:list_int]: (((size_size_list_int @ A) != (size_size_list_int @ B)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_size__neq__size__imp__neq)). 159.59/70.61 thf(29489,plain,((! [A:list_int,B:list_int]: ((~ ((size_size_list_int @ A) = (size_size_list_int @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6299])). 159.59/70.61 thf(3836,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((modulo364778990260209775nteger @ A @ B) = (modulo364778990260209775nteger @ C @ B)) = (dvd_dvd_Code_integer @ B @ (minus_8373710615458151222nteger @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4123_mod__eq__dvd__iff)). 159.59/70.61 thf(20602,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((modulo364778990260209775nteger @ A @ B) = (modulo364778990260209775nteger @ C @ B)) = (dvd_dvd_Code_integer @ B @ (minus_8373710615458151222nteger @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3836])). 159.59/70.61 thf(4738,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9541_xor__nat__numerals_I3_J)). 159.59/70.61 thf(23617,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)],[4738])). 159.59/70.61 thf(455,axiom,((! [A:real,B:real,C:real,D:real]: ((A = (real_V1485227260804924795R_real @ (divide_divide_real @ B @ C) @ D)) = (((A = zero_zero_real) <= (C = zero_zero_real)) & (((real_V1485227260804924795R_real @ C @ A) = (real_V1485227260804924795R_real @ B @ D)) <= (C != zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9232_eq__vector__fraction__iff)). 159.59/70.61 thf(9682,plain,((! [A:real,B:real,C:real,D:real]: ((A = (real_V1485227260804924795R_real @ (divide_divide_real @ B @ C) @ D)) = (((A = zero_zero_real) | ~ (C = zero_zero_real)) & (((real_V1485227260804924795R_real @ C @ A) = (real_V1485227260804924795R_real @ B @ D)) | (C = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])). 159.59/70.61 thf(4735,axiom,((! [A:set_nat,B:(nat > nat)]: ((((groups3542108847815614940at_nat @ B @ A) = (suc @ zero_zero_nat)) = (? [C:nat]: ((member_nat @ C @ A) & ! [D:nat]: ((member_nat @ D @ A) => ((C != D) => ((B @ D) = zero_zero_nat))) & ((B @ C) = (suc @ zero_zero_nat))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7923_sum__eq__Suc0__iff)). 159.59/70.61 thf(23607,plain,((! [A:set_nat,B:(nat > nat)]: ((((groups3542108847815614940at_nat @ (B) @ A) = (suc @ zero_zero_nat)) = (? [C:nat]: ((member_nat @ C @ A) & ! [D:nat]: ((member_nat @ D @ A) => ((~ (C = D)) => ((B @ D) = zero_zero_nat))) & ((B @ C) = (suc @ zero_zero_nat))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4735])). 159.59/70.61 thf(5015,axiom,((! [A:nat,B:(int > nat),C:int,D:int]: ((A = (B @ C)) => ((ord_less_eq_int @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2663_ord__eq__le__subst)). 159.59/70.61 thf(24603,plain,((! [A:nat,B:(int > nat),C:int,D:int]: ((A = (B @ C)) => ((ord_less_eq_int @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5015])). 159.59/70.61 thf(2890,axiom,((! [A:real,B:int]: ((((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)) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ (nat2 @ (uminus_uminus_int @ B))))) <= (~ (ord_less_eq_int @ zero_zero_int @ B)))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9408_powr__int)). 159.59/70.61 thf(17555,plain,((! [A:real,B:int]: ((((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)) = (divide_divide_real @ one_one_real @ (power_power_real @ A @ (nat2 @ (uminus_uminus_int @ B))))) | (ord_less_eq_int @ zero_zero_int @ B))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2890])). 159.59/70.61 thf(1137,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/sandbox/benchmark/theBenchmark.p',fact_9415_zless__nat__conj)). 159.59/70.61 thf(11897,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)],[1137])). 159.59/70.61 thf(7434,axiom,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1569_diff__0__eq__0)). 159.59/70.61 thf(33933,plain,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7434])). 159.59/70.61 thf(4572,axiom,((semiri1408675320244567234ct_nat = (^ [A:nat]: (semiri1316708129612266289at_nat @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8766_fact__prod)). 159.59/70.61 thf(23033,plain,(((semiri1408675320244567234ct_nat) = (^ [A:nat]: (semiri1316708129612266289at_nat @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4572])). 159.59/70.61 thf(5046,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: ((ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C)) => ((ord_less_nat @ D @ A) => (((D != E) => ((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)))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_insert__simp__excp)). 159.59/70.61 thf(24702,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: ((ord_less_nat @ (vEBT_VEBT_high @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C)) => ((ord_less_nat @ D @ A) => (((~ (D = E)) => ((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)))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5046])). 159.59/70.61 thf(6802,axiom,((! [A:num]: ((abs_abs_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5390_abs__numeral)). 159.59/70.61 thf(31450,plain,((! [A:num]: ((abs_abs_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6802])). 159.59/70.61 thf(4593,axiom,((! [A:nat,B:nat,C:(nat > complex),D:(nat > complex)]: (((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)))))) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8634_prod_Ozero__middle)). 159.59/70.61 thf(23111,plain,((! [A:nat,B:nat,C:(nat > complex),D:(nat > complex)]: (((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)))))) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4593])). 159.59/70.61 thf(1342,axiom,((! [A:complex]: ((real_V2046097035970521341omplex @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (plus_plus_complex @ A @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9210_scaleR__half__double)). 159.59/70.61 thf(12586,plain,((! [A:complex]: ((real_V2046097035970521341omplex @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (plus_plus_complex @ A @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342])). 159.59/70.61 thf(131,axiom,((! [A:real]: (ord_less_real @ (archim2898591450579166408c_real @ A) @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9060_frac__lt__1)). 159.59/70.61 thf(8655,plain,((! [A:real]: (ord_less_real @ (archim2898591450579166408c_real @ A) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 159.59/70.61 thf(2883,axiom,((! [A:nat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ A) @ (plus_p3455044024723400733d_enat @ (semiri4216267220026989637d_enat @ A) @ one_on7984719198319812577d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7807_double__gauss__sum)). 159.59/70.61 thf(17523,plain,((! [A:nat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (groups7108830773950497114d_enat @ (semiri4216267220026989637d_enat) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ A) @ (plus_p3455044024723400733d_enat @ (semiri4216267220026989637d_enat @ A) @ one_on7984719198319812577d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2883])). 159.59/70.61 thf(1720,axiom,((! [A:real,B:real,C:real]: (((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)))))) <= (ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ B @ (sqrt @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6477_real__sqrt__sum__squares__less)). 159.59/70.61 thf(13814,plain,((! [A:real,B:real,C:real]: ((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))))) | ~ (ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ B @ (sqrt @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720])). 159.59/70.61 thf(7530,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/sandbox/benchmark/theBenchmark.p',fact_8470_prod_Odistrib)). 159.59/70.61 thf(34281,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)],[7530])). 159.59/70.61 thf(6804,axiom,((! [A:complex,B:complex,C:nat]: (((times_times_complex @ A @ B) = (times_times_complex @ B @ A)) => ((times_times_complex @ (power_power_complex @ A @ C) @ B) = (times_times_complex @ B @ (power_power_complex @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_power__commuting__commutes)). 159.59/70.61 thf(31456,plain,((! [A:complex,B:complex,C:nat]: (((times_times_complex @ A @ B) = (times_times_complex @ B @ A)) => ((times_times_complex @ (power_power_complex @ A @ C) @ B) = (times_times_complex @ B @ (power_power_complex @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6804])). 159.59/70.61 thf(6214,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/sandbox/benchmark/theBenchmark.p',fact_9776_uminus__int_Oabs__eq)). 159.59/70.61 thf(29137,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)],[6214])). 159.59/70.61 thf(4416,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = ((A = B) | (ord_less_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2819_not__less__iff__gr__or__eq)). 159.59/70.61 thf(22406,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = ((A = B) | (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4416])). 159.59/70.61 thf(5811,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)) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1789_power2__eq__iff__nonneg)). 159.59/70.61 thf(27617,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)) | ~ (ord_less_eq_int @ zero_zero_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5811])). 159.59/70.61 thf(937,axiom,((! [A:nat]: ((gbinomial_real @ zero_zero_real @ (suc @ A)) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8171_gbinomial__0_I2_J)). 159.59/70.61 thf(11255,plain,((! [A:nat]: ((gbinomial_real @ zero_zero_real @ (suc @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[937])). 159.59/70.61 thf(2430,axiom,((! [A:int,B:int]: ((divide_divide_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (divide_divide_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4647_div__minus__minus)). 159.59/70.61 thf(16076,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)],[2430])). 159.59/70.61 thf(6562,axiom,((! [A:num,B:num]: (((ord_less_num @ B @ A) <= (~ (ord_less_num @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2840_linorder__neqE)). 159.59/70.61 thf(30466,plain,((! [A:num,B:num]: ((ord_less_num @ B @ A) | (ord_less_num @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6562])). 159.59/70.61 thf(5150,axiom,((! [A:nat,B:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6691_of__nat__mono)). 159.59/70.61 thf(25079,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)],[5150])). 159.59/70.61 thf(2197,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/sandbox/benchmark/theBenchmark.p',fact_7316_tan__half)). 159.59/70.61 thf(15345,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)],[2197])). 159.59/70.61 thf(3990,axiom,((! [A:real]: (((ord_less_eq_real @ (uminus_uminus_real @ pi) @ A) => ((arccos @ (cos_real @ A)) = (uminus_uminus_real @ A))) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7771_arccos__cos2)). 159.59/70.61 thf(21078,plain,((! [A:real]: (((ord_less_eq_real @ (uminus_uminus_real @ pi) @ A) => ((arccos @ (cos_real @ A)) = (uminus_uminus_real @ A))) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3990])). 159.59/70.61 thf(772,axiom,((! [A:nat]: ((semiri5074537144036343181t_real @ (suc @ A)) = (plus_plus_real @ one_one_real @ (semiri5074537144036343181t_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6582_of__nat__Suc)). 159.59/70.61 thf(10742,plain,((! [A:nat]: ((semiri5074537144036343181t_real @ (suc @ A)) = (plus_plus_real @ one_one_real @ (semiri5074537144036343181t_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[772])). 159.59/70.61 thf(838,axiom,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (numeral_numeral_real @ C)) = (((((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)) <= (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2496_divide__le__eq__numeral_I1_J)). 159.59/70.61 thf(10954,plain,((! [A:real,B:real,C:num]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (numeral_numeral_real @ C)) = (((((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)) | ~ (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[838])). 159.59/70.61 thf(221,axiom,((! [A:real,B:real,C:real,D:real]: ((((plus_plus_real @ (real_V1485227260804924795R_real @ A @ B) @ C) = D) = (B = (minus_minus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ D) @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9249_real__vector__affinity__eq)). 159.59/70.61 thf(8927,plain,((! [A:real,B:real,C:real,D:real]: ((((plus_plus_real @ (real_V1485227260804924795R_real @ A @ B) @ C) = D) = (B = (minus_minus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ D) @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 159.59/70.61 thf(812,axiom,((! [A:complex,B:complex,C:nat]: (((real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ C)) @ (power_power_complex @ (plus_plus_complex @ A @ B) @ C)) = (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ D)) @ (power_power_complex @ A @ D)) @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (minus_minus_nat @ C @ D))) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D))))) @ (set_ord_atMost_nat @ C))) <= ((times_times_complex @ A @ B) = (times_times_complex @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9295_exp__series__add__commuting)). 159.59/70.61 thf(10875,plain,((! [A:complex,B:complex,C:nat]: (((real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ C)) @ (power_power_complex @ (plus_plus_complex @ A @ B) @ C)) = (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ D)) @ (power_power_complex @ A @ D)) @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (minus_minus_nat @ C @ D))) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D))))) @ (set_ord_atMost_nat @ C))) | ~ ((times_times_complex @ A @ B) = (times_times_complex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[812])). 159.59/70.61 thf(3873,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = C) = (((C = zero_zero_complex) <= (B = zero_zero_complex)) & ((B != zero_zero_complex) => (A = (times_times_complex @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2177_divide__eq__eq)). 159.59/70.61 thf(20725,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = C) = (((C = zero_zero_complex) | ~ (B = zero_zero_complex)) & ((~ (B = zero_zero_complex)) => (A = (times_times_complex @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3873])). 159.59/70.61 thf(2798,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/sandbox/benchmark/theBenchmark.p',fact_6790_of__nat__code__if)). 159.59/70.61 thf(17257,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)],[2798])). 159.59/70.61 thf(6106,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (? [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 @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5629_lemma__interval)). 159.59/70.61 thf(28772,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ C) => (? [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 @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6106])). 159.59/70.61 thf(3761,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((B != zero_zero_complex) => ((plus_plus_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B)) = (times_times_complex @ (times_times_complex @ (invers8013647133539491842omplex @ A) @ (plus_plus_complex @ A @ B)) @ (invers8013647133539491842omplex @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9071_division__ring__inverse__add)). 159.59/70.61 thf(20348,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => ((~ (B = zero_zero_complex)) => ((plus_plus_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B)) = (times_times_complex @ (times_times_complex @ (invers8013647133539491842omplex @ A) @ (plus_plus_complex @ A @ B)) @ (invers8013647133539491842omplex @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3761])). 159.59/70.61 thf(6788,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: ((((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))))) => (vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ B @ C @ F) @ A)) <= (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/sandbox/benchmark/theBenchmark.p',fact_496_both__member__options__from__chilf__to__complete__tree)). 159.59/70.61 thf(31410,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:nat,E:nat,F:vEBT_VEBT]: (((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))))) => (vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ B @ C @ F) @ A)) | ~ (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)],[6788])). 159.59/70.61 thf(3096,axiom,((! [A:nat]: ((bit_se8568078237143864401it_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9727_drop__bit__minus__one)). 159.59/70.61 thf(18212,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)],[3096])). 159.59/70.61 thf(6122,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (ord_max_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1572_max__nat_Oneutr__eq__iff)). 159.59/70.61 thf(28824,plain,((! [A:nat,B:nat]: ((zero_zero_nat = (ord_max_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6122])). 159.59/70.61 thf(6302,axiom,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1255_comm__monoid__mult__class_Omult__1)). 159.59/70.61 thf(29499,plain,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6302])). 159.59/70.61 thf(3128,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ A)) = (divide1717551699836669952omplex @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5083_nonzero__minus__divide__divide)). 159.59/70.61 thf(18312,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)],[3128])). 159.59/70.61 thf(3323,axiom,((! [A:num,B:num]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (uminus1351360451143612070nteger @ (plus_p5714425477246183910nteger @ (numera6620942414471956472nteger @ A) @ (numera6620942414471956472nteger @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4697_add__neg__numeral__simps_I3_J)). 159.59/70.61 thf(18941,plain,((! [A:num,B:num]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (uminus1351360451143612070nteger @ (plus_p5714425477246183910nteger @ (numera6620942414471956472nteger @ A) @ (numera6620942414471956472nteger @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3323])). 159.59/70.61 thf(8129,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/sandbox/benchmark/theBenchmark.p',fact_442_power4__eq__xxxx)). 159.59/70.61 thf(36242,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)],[8129])). 159.59/70.61 thf(539,axiom,((! [A:nat,B:nat]: ((bit_se9216721137139052372nteger @ (semiri4939895301339042750nteger @ A) @ B) = (bit_se1148574629649215175it_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6654_bit__of__nat__iff__bit)). 159.59/70.61 thf(9968,plain,((! [A:nat,B:nat]: ((bit_se9216721137139052372nteger @ (semiri4939895301339042750nteger @ A) @ B) = (bit_se1148574629649215175it_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[539])). 159.59/70.61 thf(8192,axiom,((! [A:nat,B:list_Code_integer,C:list_o]: (((nth_Pr8522763379788166057eger_o @ (produc3607205314601156340eger_o @ B @ C) @ A) = (produc6677183202524767010eger_o @ (nth_Code_integer @ B @ (divide_divide_nat @ A @ (size_size_list_o @ C))) @ (nth_o @ C @ (modulo_modulo_nat @ A @ (size_size_list_o @ C))))) <= (ord_less_nat @ A @ (times_times_nat @ (size_s3445333598471063425nteger @ B) @ (size_size_list_o @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3588_product__nth)). 159.59/70.61 thf(36445,plain,((! [A:nat,B:list_Code_integer,C:list_o]: (((nth_Pr8522763379788166057eger_o @ (produc3607205314601156340eger_o @ B @ C) @ A) = (produc6677183202524767010eger_o @ (nth_Code_integer @ B @ (divide_divide_nat @ A @ (size_size_list_o @ C))) @ (nth_o @ C @ (modulo_modulo_nat @ A @ (size_size_list_o @ C))))) | ~ (ord_less_nat @ A @ (times_times_nat @ (size_s3445333598471063425nteger @ B) @ (size_size_list_o @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8192])). 159.59/70.61 thf(6631,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1560_bot__nat__0_Oextremum)). 159.59/70.61 thf(30712,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6631])). 159.59/70.61 thf(8221,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/sandbox/benchmark/theBenchmark.p',fact_5_high__bound__aux)). 159.59/70.61 thf(36541,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)],[8221])). 159.59/70.61 thf(1466,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/sandbox/benchmark/theBenchmark.p',fact_5228_real__add__less__0__iff)). 159.59/70.61 thf(13038,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)],[1466])). 159.59/70.61 thf(3503,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ one_one_real @ (times_times_real @ A @ B)) <= (ord_less_real @ one_one_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1322_less__1__mult)). 159.59/70.61 thf(19502,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ one_one_real @ (times_times_real @ A @ B)) | ~ (ord_less_real @ one_one_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3503])). 159.59/70.61 thf(2436,axiom,((! [A:real,B:real,C:nat]: ((power_power_real @ (plus_plus_real @ A @ B) @ C) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ (binomial @ C @ D)) @ (power_power_real @ A @ D)) @ (power_power_real @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9149_binomial__ring)). 159.59/70.61 thf(16091,plain,((! [A:real,B:real,C:nat]: ((power_power_real @ (plus_plus_real @ A @ B) @ C) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ (binomial @ C @ D)) @ (power_power_real @ A @ D)) @ (power_power_real @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2436])). 159.59/70.61 thf(7543,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((groups4561878855575611511st_nat @ (upt @ A @ B)) = (groups3542108847815614940at_nat @ (^ [C:nat]: (C)) @ (set_or4665077453230672383an_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10147_sum__list__upt)). 159.59/70.61 thf(34317,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((groups4561878855575611511st_nat @ (upt @ A @ B)) = (groups3542108847815614940at_nat @ (^ [C:nat]: (C)) @ (set_or4665077453230672383an_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7543])). 159.59/70.61 thf(1999,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (arcsin @ A) @ (arcsin @ B)) <= (ord_less_eq_real @ B @ one_one_real))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7555_arcsin__le__arcsin)). 159.59/70.61 thf(14712,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (arcsin @ A) @ (arcsin @ B)) | ~ (ord_less_eq_real @ B @ one_one_real))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1999])). 159.59/70.61 thf(594,axiom,((! [A:(int > $o),B:real]: ((A @ (archim6058952711729229775r_real @ B)) = (! [C:int]: ((A @ C) <= ((ord_less_eq_real @ (ring_1_of_int_real @ C) @ B) & (ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ C) @ one_one_real)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8297_floor__split)). 159.59/70.61 thf(10139,plain,((! [A:(int > $o),B:real]: ((A @ (archim6058952711729229775r_real @ B)) = (! [C:int]: ((A @ C) | ~ ((ord_less_eq_real @ (ring_1_of_int_real @ C) @ B) & (ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ C) @ one_one_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[594])). 159.59/70.61 thf(2022,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) <= (ord_less_real @ zero_zero_real @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2072_mult__strict__left__mono)). 159.59/70.61 thf(14785,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) | ~ (ord_less_real @ zero_zero_real @ C) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2022])). 159.59/70.61 thf(5582,axiom,((finite_finite_nat = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) <= (member_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3634_finite__nat__set__iff__bounded)). 159.59/70.61 thf(26703,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)],[5582])). 159.59/70.61 thf(7978,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/sandbox/benchmark/theBenchmark.p',fact_1184_add__less__imp__less__right)). 159.59/70.61 thf(35748,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)],[7978])). 159.59/70.61 thf(7904,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/sandbox/benchmark/theBenchmark.p',fact_1121_add_Oleft__commute)). 159.59/70.61 thf(35522,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)],[7904])). 159.59/70.61 thf(44,axiom,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ zero_z3403309356797280102nteger) = (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4676_neg__less__0__iff__less)). 159.59/70.61 thf(8382,plain,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ zero_z3403309356797280102nteger) = (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 159.59/70.61 thf(911,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/sandbox/benchmark/theBenchmark.p',fact_7451_Complex__mult__complex__of__real)). 159.59/70.61 thf(11170,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)],[911])). 159.59/70.61 thf(2422,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/sandbox/benchmark/theBenchmark.p',fact_5082_nonzero__minus__divide__divide)). 159.59/70.61 thf(16044,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)],[2422])). 159.59/70.61 thf(5969,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6168_or__nat__numerals_I4_J)). 159.59/70.61 thf(28340,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)],[5969])). 159.59/70.61 thf(3268,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (ord_le72135733267957522d_enat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2769_order_Oasym)). 159.59/70.61 thf(18774,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (ord_le72135733267957522d_enat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3268])). 159.59/70.61 thf(3086,axiom,((! [A:real]: ((cos_real @ (plus_plus_real @ A @ pi)) = (uminus_uminus_real @ (cos_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6973_cos__periodic__pi)). 159.59/70.61 thf(18177,plain,((! [A:real]: ((cos_real @ (plus_plus_real @ A @ pi)) = (uminus_uminus_real @ (cos_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3086])). 159.59/70.61 thf(7201,axiom,((! [A:nat,B:nat]: ((map_nat_nat @ (^ [C:nat]: (plus_plus_nat @ C @ A)) @ (upt @ zero_zero_nat @ B)) = (upt @ A @ (plus_plus_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10137_map__add__upt)). 159.59/70.61 thf(33146,plain,((! [A:nat,B:nat]: ((map_nat_nat @ (^ [C:nat]: (plus_plus_nat @ C @ A)) @ (upt @ zero_zero_nat @ B)) = (upt @ A @ (plus_plus_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7201])). 159.59/70.61 thf(6226,axiom,((! [A:nat,B:real]: (((ord_less_real @ (root @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ zero_zero_real)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9487_real__root__lt__0__iff)). 159.59/70.61 thf(29169,plain,((! [A:nat,B:real]: (((ord_less_real @ (root @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ zero_zero_real)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6226])). 159.59/70.61 thf(7102,axiom,((! [A:nat,B:nat]: ((ord_max_nat @ A @ (ord_max_nat @ A @ B)) = (ord_max_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_max_Oleft__idem)). 159.59/70.61 thf(32739,plain,((! [A:nat,B:nat]: ((ord_max_nat @ A @ (ord_max_nat @ A @ B)) = (ord_max_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7102])). 159.59/70.61 thf(6251,axiom,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ A) @ B) = (uminus1351360451143612070nteger @ (times_3573771949741848930nteger @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4634_mult__minus__left)). 159.59/70.61 thf(29256,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)],[6251])). 159.59/70.61 thf(3293,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/sandbox/benchmark/theBenchmark.p',fact_4723_ln__less__zero__iff)). 159.59/70.61 thf(18852,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)],[3293])). 159.59/70.61 thf(1222,axiom,((! [A:real,B:complex]: ((ord_less_eq_real @ A @ (real_V1022390504157884413omplex @ B)) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (invers8013647133539491842omplex @ B)) @ (inverse_inverse_real @ A)) <= (ord_less_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9021_norm__inverse__le__norm)). 159.59/70.61 thf(12200,plain,((! [A:real,B:complex]: ((ord_less_eq_real @ A @ (real_V1022390504157884413omplex @ B)) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (invers8013647133539491842omplex @ B)) @ (inverse_inverse_real @ A)) | ~ (ord_less_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222])). 159.59/70.61 thf(5574,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/sandbox/benchmark/theBenchmark.p',fact_6407_atLeastAtMostSuc__conv)). 159.59/70.61 thf(26678,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)],[5574])). 159.59/70.61 thf(4813,axiom,(((minus_minus_int @ one_one_int @ one_one_int) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1658_diff__numeral__special_I9_J)). 159.59/70.61 thf(23881,plain,(((minus_minus_int @ one_one_int @ one_one_int) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4813])). 159.59/70.61 thf(7549,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)) <= (ord_less_eq_num @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2684_order__subst1)). 159.59/70.61 thf(34336,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) | ~ (ord_less_eq_num @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7549])). 159.59/70.61 thf(3236,axiom,((! [A:real]: ((sin_real @ (plus_plus_real @ A @ pi)) = (uminus_uminus_real @ (sin_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6800_sin__periodic__pi)). 159.59/70.61 thf(18658,plain,((! [A:real]: ((sin_real @ (plus_plus_real @ A @ pi)) = (uminus_uminus_real @ (sin_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3236])). 159.59/70.61 thf(3238,axiom,((! [A:list_nat,B:set_nat]: ((ord_less_eq_set_nat @ (set_nat2 @ A) @ B) = (! [C:nat]: ((member_nat @ C @ B) <= (member_nat @ C @ (set_nat2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_subset__code_I1_J)). 159.59/70.61 thf(18664,plain,((! [A:list_nat,B:set_nat]: ((ord_less_eq_set_nat @ (set_nat2 @ A) @ B) = (! [C:nat]: ((member_nat @ C @ B) | ~ (member_nat @ C @ (set_nat2 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3238])). 159.59/70.61 thf(1111,axiom,((! [A:nat,B:nat]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6523_of__nat__less__iff)). 159.59/70.61 thf(11820,plain,((! [A:nat,B:nat]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111])). 159.59/70.61 thf(5327,axiom,((! [A:num,B:num]: (((~ (ord_less_num @ A @ B)) = (A = B)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3050_antisym__conv2)). 159.59/70.61 thf(25738,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)],[5327])). 159.59/70.61 thf(2204,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/sandbox/benchmark/theBenchmark.p',fact_7090_sin__add)). 159.59/70.61 thf(15364,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)],[2204])). 159.59/70.61 thf(56,axiom,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => (((groups129246275422532515t_real @ C @ A) = (times_times_real @ (C @ B) @ (groups129246275422532515t_real @ C @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))) <= (member_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8793_prod_Oremove)). 159.59/70.61 thf(8418,plain,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => (((groups129246275422532515t_real @ (C) @ A) = (times_times_real @ (C @ B) @ (groups129246275422532515t_real @ (C) @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))) | ~ (member_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 159.59/70.61 thf(8081,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/sandbox/benchmark/theBenchmark.p',fact_4208_bit__eq__rec)). 159.59/70.61 thf(36092,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)],[8081])). 159.59/70.61 thf(1871,axiom,((! [A:int,B:int]: ((bit_se725231765392027082nd_int @ (bit_se725231765392027082nd_int @ A @ B) @ B) = (bit_se725231765392027082nd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5933_and_Oright__idem)). 159.59/70.61 thf(14295,plain,((! [A:int,B:int]: ((bit_se725231765392027082nd_int @ (bit_se725231765392027082nd_int @ A @ B) @ B) = (bit_se725231765392027082nd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1871])). 159.59/70.61 thf(4499,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 = B) | (E = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1939_VEBT__internal_Omembermima_Osimps_I3_J)). 159.59/70.61 thf(22722,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 = B) | (E = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4499])). 159.59/70.61 thf(4829,axiom,((! [A:nat]: ((ord_max_nat @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_773_max_Oidem)). 159.59/70.61 thf(23967,plain,((! [A:nat]: ((ord_max_nat @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4829])). 159.59/70.61 thf(610,axiom,((! [A:set_nat,B:set_nat,C:nat]: (((member_nat @ C @ A) => (member_nat @ C @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2988_subsetD)). 159.59/70.61 thf(10197,plain,((! [A:set_nat,B:set_nat,C:nat]: (((member_nat @ C @ A) => (member_nat @ C @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[610])). 159.59/70.61 thf(5740,axiom,((! [A:real]: ((root @ (suc @ zero_zero_nat) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9476_real__root__Suc__0)). 159.59/70.61 thf(27265,plain,((! [A:real]: ((root @ (suc @ zero_zero_nat) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5740])). 159.59/70.61 thf(2315,axiom,((! [A:real,B:real]: ((((divide_divide_real @ B @ A) = zero_zero_real) = (B = zero_zero_real)) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4047_dvd__div__eq__0__iff)). 159.59/70.61 thf(15697,plain,((! [A:real,B:real]: ((((divide_divide_real @ B @ A) = zero_zero_real) = (B = zero_zero_real)) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2315])). 159.59/70.61 thf(5379,axiom,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups708209901874060359at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8757_prod_OatLeast1__atMost__eq)). 159.59/70.61 thf(25986,plain,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (A) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups708209901874060359at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5379])). 159.59/70.61 thf(1487,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 @ (times_times_real @ B @ C)) = (plus_plus_real @ (log @ A @ B) @ (log @ A @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6430_log__mult)). 159.59/70.61 thf(13104,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 @ (times_times_real @ B @ C)) = (plus_plus_real @ (log @ A @ B) @ (log @ A @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487])). 159.59/70.61 thf(7445,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3109_dual__order_Oorder__iff__strict)). 159.59/70.61 thf(33972,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7445])). 159.59/70.61 thf(3315,axiom,((! [A:nat,B:nat,C:(nat > int)]: ((ord_less_eq_nat @ A @ B) => ((groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_int @ (C @ A) @ (groups3539618377306564664at_int @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7665_sum_OatLeast__Suc__atMost)). 159.59/70.61 thf(18915,plain,((! [A:nat,B:nat,C:(nat > int)]: ((ord_less_eq_nat @ A @ B) => ((groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_int @ (C @ A) @ (groups3539618377306564664at_int @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3315])). 159.59/70.61 thf(5945,axiom,(((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ one_one_int)) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4746_diff__numeral__special_I12_J)). 159.59/70.61 thf(28267,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)],[5945])). 159.59/70.61 thf(7983,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/sandbox/benchmark/theBenchmark.p',fact_451_power__even__eq)). 159.59/70.61 thf(35761,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)],[7983])). 159.59/70.61 thf(4008,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat)]: ((finite_finite_nat @ A) => ((dvd_dvd_nat @ (groups708209901874060359at_nat @ C @ B) @ (groups708209901874060359at_nat @ C @ A)) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8586_prod__dvd__prod__subset)). 159.59/70.61 thf(21133,plain,((! [A:set_nat,B:set_nat,C:(nat > nat)]: ((finite_finite_nat @ A) => ((dvd_dvd_nat @ (groups708209901874060359at_nat @ (C) @ B) @ (groups708209901874060359at_nat @ (C) @ A)) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4008])). 159.59/70.61 thf(231,axiom,((bit_se4205575877204974255it_nat = (^ [A:nat,B:nat]: (nat2 @ (bit_se4203085406695923979it_int @ A @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9430_unset__bit__nat__def)). 159.59/70.61 thf(8959,plain,(((bit_se4205575877204974255it_nat) = (^ [A:nat,B:nat]: (nat2 @ (bit_se4203085406695923979it_int @ A @ (semiri1314217659103216013at_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 159.59/70.61 thf(6623,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/sandbox/benchmark/theBenchmark.p',fact_4667_neg__le__0__iff__le)). 159.59/70.61 thf(30685,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)],[6623])). 159.59/70.61 thf(5517,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6175_or__nat__numerals_I1_J)). 159.59/70.61 thf(26509,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)],[5517])). 159.59/70.61 thf(5568,axiom,((! [A:nat,B:nat,C:(nat > complex),D:(nat > complex)]: (((ord_less_eq_nat @ B @ A) => ((groups2073611262835488442omplex @ (^ [E:nat]: (if_complex @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_complex @ (E = B) @ zero_zero_complex @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups2073611262835488442omplex @ (^ [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)))))) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8937_sum_Ozero__middle)). 159.59/70.61 thf(26658,plain,((! [A:nat,B:nat,C:(nat > complex),D:(nat > complex)]: (((ord_less_eq_nat @ B @ A) => ((groups2073611262835488442omplex @ (^ [E:nat]: (if_complex @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_complex @ (E = B) @ zero_zero_complex @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups2073611262835488442omplex @ (^ [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)))))) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5568])). 159.59/70.61 thf(311,axiom,((! [A:num]: ((real_V1803761363581548252l_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7353_of__real__neg__numeral)). 159.59/70.61 thf(9209,plain,((! [A:num]: ((real_V1803761363581548252l_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 159.59/70.61 thf(49,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 @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9239_scaleR__mono_H)). 159.59/70.61 thf(8397,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 @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 159.59/70.61 thf(1470,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((arccos @ (uminus_uminus_real @ A)) = (minus_minus_real @ pi @ (arccos @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7772_arccos__minus)). 159.59/70.61 thf(13051,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((arccos @ (uminus_uminus_real @ A)) = (minus_minus_real @ pi @ (arccos @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1470])). 159.59/70.61 thf(1072,axiom,(((neg_numeral_dbl_real @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3808_dbl__simps_I2_J)). 159.59/70.61 thf(11687,plain,(((neg_numeral_dbl_real @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072])). 159.59/70.61 thf(5467,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/sandbox/benchmark/theBenchmark.p',fact_2707_dual__order_Otrans)). 159.59/70.61 thf(26330,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)],[5467])). 159.59/70.61 thf(7990,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:nat,J:vEBT_VEBT,K:list_VEBT_VEBT]: (((B != C) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => (((((((((~ (vEBT_VEBT_minNull @ J)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (plus_plus_nat @ (times_times_nat @ F @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ F)))) @ C))) @ D @ K @ G))) & ((vEBT_VEBT_minNull @ J) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)) = none_nat) @ E @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)))))))) @ C))) @ D @ K @ (vEBT_vebt_delete @ G @ F))))) <= (K = (list_u1324408373059187874T_VEBT @ H @ F @ J))) <= (J = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I))) <= (ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H))) <= ((vEBT_VEBT_low @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = I)) <= (E = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ G)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ H @ (the_nat @ (vEBT_vebt_mint @ G)))))))) <= ((vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F)))) <= ((A = B) & (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1402_del__x__mi__lets__in)). 159.59/70.61 thf(35781,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:nat,J:vEBT_VEBT,K:list_VEBT_VEBT]: (((~ (B = C)) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((((~ (vEBT_VEBT_minNull @ J)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (plus_plus_nat @ (times_times_nat @ F @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ F)))) @ C))) @ D @ K @ G))) & ((vEBT_VEBT_minNull @ J) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)) = none_nat) @ E @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)))))))) @ C))) @ D @ K @ (vEBT_vebt_delete @ G @ F))))) | ~ (K = (list_u1324408373059187874T_VEBT @ H @ F @ J)) | ~ (J = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) | ~ (ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)) | ~ ((vEBT_VEBT_low @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = I) | ~ (E = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ G)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ H @ (the_nat @ (vEBT_vebt_mint @ G))))))) | ~ ((vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F)))) | ~ ((A = B) & (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7990])). 159.59/70.61 thf(1469,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C) <= (ord_less_eq_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6933_norm__triangle__le__diff)). 159.59/70.61 thf(13049,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C) | ~ (ord_less_eq_real @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ (real_V7735802525324610683m_real @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1469])). 159.59/70.61 thf(7403,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/sandbox/benchmark/theBenchmark.p',fact_5418_abs__power__minus)). 159.59/70.61 thf(33840,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)],[7403])). 159.59/70.61 thf(1767,axiom,((! [A:int,B:real]: ((ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ A) @ one_one_real) @ B) => (((archim7802044766580827645g_real @ B) = A) <= (ord_less_eq_real @ B @ (ring_1_of_int_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7137_ceiling__unique)). 159.59/70.61 thf(13956,plain,((! [A:int,B:real]: ((ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ A) @ one_one_real) @ B) => (((archim7802044766580827645g_real @ B) = A) | ~ (ord_less_eq_real @ B @ (ring_1_of_int_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1767])). 159.59/70.61 thf(1003,axiom,((! [A:real]: ? [B:int]: (ord_less_eq_real @ A @ (ring_1_of_int_real @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6137_ex__le__of__int)). 159.59/70.61 thf(11456,plain,((! [A:real]: ? [B:int]: (ord_less_eq_real @ A @ (ring_1_of_int_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003])). 159.59/70.61 thf(4448,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_eq_num @ C @ A) <= (ord_less_num @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4505_minf_I6_J)). 159.59/70.61 thf(22496,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)],[4448])). 159.59/70.61 thf(3929,axiom,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3961_dvd__triv__left)). 159.59/70.61 thf(20889,plain,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3929])). 159.59/70.61 thf(7167,axiom,((! [A:nat,B:nat]: (((B != zero_zero_nat) => ((times_times_nat @ A @ B) != zero_zero_nat)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1861_no__zero__divisors)). 159.59/70.61 thf(33014,plain,((! [A:nat,B:nat]: (((~ (B = zero_zero_nat)) => (~ ((times_times_nat @ A @ B) = zero_zero_nat))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7167])). 159.59/70.61 thf(2511,axiom,((! [A:real,B:real,C:real]: (((minus_minus_real @ A @ B) = C) = (A = (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1294_diff__eq__eq)). 159.59/70.61 thf(16333,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)],[2511])). 159.59/70.61 thf(874,axiom,((! [A:complex]: ((comm_s2602460028002588243omplex @ A @ zero_zero_nat) = one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8181_pochhammer__0)). 159.59/70.61 thf(11069,plain,((! [A:complex]: ((comm_s2602460028002588243omplex @ A @ zero_zero_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[874])). 159.59/70.61 thf(7703,axiom,((! [A:nat]: (((ord_less_nat @ (vEBT_VEBT_high @ A @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => ((ord_less_eq_nat @ A @ ma) & (ord_less_nat @ (vEBT_VEBT_low @ A @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) & (ord_less_nat @ mi @ A))) <= (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ A @ na)) @ (vEBT_VEBT_low @ A @ na))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_yhelper)). 159.59/70.61 thf(34862,plain,((! [A:nat]: (((ord_less_nat @ (vEBT_VEBT_high @ A @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => ((ord_less_eq_nat @ A @ ma) & (ord_less_nat @ (vEBT_VEBT_low @ A @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) & (ord_less_nat @ mi @ A))) | ~ (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ A @ na)) @ (vEBT_VEBT_low @ A @ na))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7703])). 159.59/70.61 thf(6977,axiom,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ A) = (semiri5074537144036343181t_real @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6487_of__nat__eq__iff)). 159.59/70.61 thf(32254,plain,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ A) = (semiri5074537144036343181t_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6977])). 159.59/70.61 thf(8105,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/sandbox/benchmark/theBenchmark.p',fact_368_power__commuting__commutes)). 159.59/70.61 thf(36163,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)],[8105])). 159.59/70.61 thf(6506,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/sandbox/benchmark/theBenchmark.p',fact_2301_mult__right__le__one__le)). 159.59/70.61 thf(30263,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)],[6506])). 159.59/70.61 thf(1594,axiom,((! [A:complex,B:real,C:complex,D:real]: ((ord_less_real @ (real_V1022390504157884413omplex @ A) @ B) => ((ord_less_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ C)) @ (plus_plus_real @ B @ D)) <= (ord_less_real @ (real_V1022390504157884413omplex @ C) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6920_norm__add__less)). 159.59/70.61 thf(13426,plain,((! [A:complex,B:real,C:complex,D:real]: ((ord_less_real @ (real_V1022390504157884413omplex @ A) @ B) => ((ord_less_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ C)) @ (plus_plus_real @ B @ D)) | ~ (ord_less_real @ (real_V1022390504157884413omplex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594])). 159.59/70.61 thf(6117,axiom,((! [A:real,B:nat,C:real,D:real]: (((C = (times_times_real @ (sgn_sgn_real @ D) @ (power_power_real @ (abs_abs_real @ D) @ B))) => ((ord_less_nat @ zero_zero_nat @ B) => (A = D))) <= ((times_times_real @ (sgn_sgn_real @ A) @ (power_power_real @ (abs_abs_real @ A) @ B)) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9526_sgn__power__injE)). 159.59/70.61 thf(28807,plain,((! [A:real,B:nat,C:real,D:real]: (((C = (times_times_real @ (sgn_sgn_real @ D) @ (power_power_real @ (abs_abs_real @ D) @ B))) => ((ord_less_nat @ zero_zero_nat @ B) => (A = D))) | ~ ((times_times_real @ (sgn_sgn_real @ A) @ (power_power_real @ (abs_abs_real @ A) @ B)) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6117])). 159.59/70.61 thf(3505,axiom,((divide1717551699836669952omplex = (^ [A:complex,B:complex]: (times_times_complex @ A @ (invers8013647133539491842omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9042_divide__inverse)). 159.59/70.61 thf(19507,plain,(((divide1717551699836669952omplex) = (^ [A:complex,B:complex]: (times_times_complex @ A @ (invers8013647133539491842omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3505])). 159.59/70.61 thf(1370,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/sandbox/benchmark/theBenchmark.p',fact_7220_numeral__powr__numeral__real)). 159.59/70.61 thf(12705,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)],[1370])). 159.59/70.61 thf(6515,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/sandbox/benchmark/theBenchmark.p',fact_294_left__right__inverse__power)). 159.59/70.61 thf(30292,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)],[6515])). 159.59/70.61 thf(4776,axiom,(((neg_nu6075765906172075777c_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit1 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5671_dbl__dec__simps_I4_J)). 159.59/70.61 thf(23757,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)],[4776])). 159.59/70.61 thf(4113,axiom,((! [A:set_nat,B:(nat > extended_enat)]: ((ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ (groups7961826882256487087d_enat @ B @ A)) <= (! [C:nat]: ((member_nat @ C @ A) => (ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ (B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8507_prod__ge__1)). 159.59/70.61 thf(21444,plain,((! [A:set_nat,B:(nat > extended_enat)]: ((ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ (groups7961826882256487087d_enat @ (B) @ A)) | ~ (! [C:nat]: ((member_nat @ C @ A) => (ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ (B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4113])). 159.59/70.61 thf(4603,axiom,((! [A:real,B:nat]: ((((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_atMost_nat @ B)) = (divide_divide_real @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (suc @ B))) @ (minus_minus_real @ one_one_real @ A))) <= (A != one_one_real)) & ((A = one_one_real) => ((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_atMost_nat @ B)) = (semiri5074537144036343181t_real @ (plus_plus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8948_sum__gp0)). 159.59/70.61 thf(23155,plain,((! [A:real,B:nat]: ((((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_atMost_nat @ B)) = (divide_divide_real @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (suc @ B))) @ (minus_minus_real @ one_one_real @ A))) | (A = one_one_real)) & ((A = one_one_real) => ((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_atMost_nat @ B)) = (semiri5074537144036343181t_real @ (plus_plus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4603])). 159.59/70.61 thf(3446,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/sandbox/benchmark/theBenchmark.p',fact_1122_add_Oleft__commute)). 159.59/70.61 thf(19329,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)],[3446])). 159.59/70.61 thf(800,axiom,((! [A:nat]: (ord_less_eq_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1314217659103216013at_int @ (power_power_nat @ A @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8103_fact__le__power)). 159.59/70.61 thf(10831,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)],[800])). 159.59/70.61 thf(4838,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1260_left__diff__distrib_H)). 159.59/70.61 thf(23995,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4838])). 159.59/70.61 thf(6699,axiom,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => (((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_num @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3224_order__le__less__subst2)). 159.59/70.61 thf(31007,plain,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => ((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_num @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6699])). 159.59/70.61 thf(5622,axiom,((! [A:int]: ~ (! [B:nat]: ((~ ((ord_less_nat @ zero_zero_nat @ B) => ((bit_se1146084159140164899it_int @ A @ (minus_minus_nat @ B @ one_one_nat)) = (~ (bit_se1146084159140164899it_int @ A @ B))))) <= (! [C:nat]: (((bit_se1146084159140164899it_int @ A @ C) = (bit_se1146084159140164899it_int @ A @ B)) <= (ord_less_eq_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6431_int__bit__bound)). 159.59/70.61 thf(26851,plain,((! [A:int]: ~ (! [B:nat]: (~ ((ord_less_nat @ zero_zero_nat @ B) => ((bit_se1146084159140164899it_int @ A @ (minus_minus_nat @ B @ one_one_nat)) = (~ (bit_se1146084159140164899it_int @ A @ B)))) | ~ (! [C:nat]: (((bit_se1146084159140164899it_int @ A @ C) = (bit_se1146084159140164899it_int @ A @ B)) | ~ (ord_less_eq_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5622])). 159.59/70.61 thf(8038,axiom,((! [A:nat]: ((order_mono_nat_nat @ (times_times_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10076_mono__times__nat)). 159.59/70.61 thf(35949,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)],[8038])). 159.59/70.61 thf(8162,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/sandbox/benchmark/theBenchmark.p',fact_90_numeral__times__numeral)). 159.59/70.61 thf(36357,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)],[8162])). 159.59/70.61 thf(3881,axiom,((! [A:(nat > real),B:real]: (((summable_real @ A) <= (! [C:nat]: (ord_less_eq_real @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ C)) @ B))) <= (! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7972_summableI__nonneg__bounded)). 159.59/70.61 thf(20749,plain,((! [A:(nat > real),B:real]: ((summable_real @ (A)) | ~ (! [C:nat]: (ord_less_eq_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ C)) @ B)) | ~ (! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3881])). 159.59/70.61 thf(2571,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))) & ((B = zero_zero_real) => (C = zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5197_minus__divide__eq__eq)). 159.59/70.61 thf(16516,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))) & ((B = zero_zero_real) => (C = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2571])). 159.59/70.61 thf(6863,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (modulo_modulo_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3496_unique__euclidean__semiring__numeral__class_Opos__mod__sign)). 159.59/70.61 thf(31743,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (modulo_modulo_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6863])). 159.59/70.61 thf(6772,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/sandbox/benchmark/theBenchmark.p',fact_230_power__mult__numeral)). 159.59/70.61 thf(31360,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)],[6772])). 159.59/70.61 thf(4731,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/sandbox/benchmark/theBenchmark.p',fact_602_lift__Suc__mono__less)). 159.59/70.61 thf(23594,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)],[4731])). 159.59/70.61 thf(75,axiom,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (comm_s4660882817536571857er_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8241_pochhammer__nonneg)). 159.59/70.61 thf(8481,plain,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (comm_s4660882817536571857er_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 159.59/70.61 thf(4766,axiom,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_mult__2)). 159.59/70.61 thf(23731,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)],[4766])). 159.59/70.61 thf(2499,axiom,((! [A:num]: ((numeral_numeral_int @ (bit0 @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_numeral__Bit0)). 159.59/70.61 thf(16297,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)],[2499])). 159.59/70.61 thf(3997,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ B @ C) => (ord_le2932123472753598470d_enat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4498_pinf_I8_J)). 159.59/70.61 thf(21098,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ B @ C) => (ord_le2932123472753598470d_enat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3997])). 159.59/70.61 thf(1224,axiom,((! [A:int,B:int,C:int]: ((((dvd_dvd_int @ B @ C) => (A = C)) <= (dvd_dvd_int @ B @ A)) <= ((divide_divide_int @ A @ B) = (divide_divide_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4015_dvd__div__eq__cancel)). 159.59/70.61 thf(12205,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ C) => (A = C)) | ~ (dvd_dvd_int @ B @ A) | ~ ((divide_divide_int @ A @ B) = (divide_divide_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224])). 159.59/70.61 thf(7767,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/sandbox/benchmark/theBenchmark.p',fact_3416_mod__mult__self3)). 159.59/70.61 thf(35094,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)],[7767])). 159.59/70.61 thf(6917,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/sandbox/benchmark/theBenchmark.p',fact_5097_square__eq__1__iff)). 159.59/70.61 thf(31918,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)],[6917])). 159.59/70.61 thf(5938,axiom,(((semiri1316708129612266289at_nat @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6498_of__nat__0)). 159.59/70.61 thf(28208,plain,(((semiri1316708129612266289at_nat @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5938])). 159.59/70.61 thf(1202,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/sandbox/benchmark/theBenchmark.p',fact_5825_of__int__numeral__less__iff)). 159.59/70.61 thf(12127,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)],[1202])). 159.59/70.61 thf(5409,axiom,((! [A:option_nat]: ((A = (some_nat @ (the_nat @ A))) <= (A != none_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_option_Oexhaust__sel)). 159.59/70.61 thf(26092,plain,((! [A:option_nat]: ((A = (some_nat @ (the_nat @ A))) | (A = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5409])). 159.59/70.61 thf(2835,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => (((dvd_dvd_int @ (divide_divide_int @ B @ A) @ C) = (dvd_dvd_int @ B @ (times_times_int @ C @ A))) <= (dvd_dvd_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4143_div__dvd__iff__mult)). 159.59/70.61 thf(17363,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => (((dvd_dvd_int @ (divide_divide_int @ B @ A) @ C) = (dvd_dvd_int @ B @ (times_times_int @ C @ A))) | ~ (dvd_dvd_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2835])). 159.59/70.61 thf(3754,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/sandbox/benchmark/theBenchmark.p',fact_8305_Suc__times__gbinomial)). 159.59/70.61 thf(20326,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)],[3754])). 159.59/70.61 thf(5585,axiom,((! [A:nat,B:int]: ((((power_power_int @ (uminus_uminus_int @ B) @ A) = (power_power_int @ B @ A)) <= (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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5288_uminus__power__if)). 159.59/70.61 thf(26710,plain,((! [A:nat,B:int]: ((((power_power_int @ (uminus_uminus_int @ B) @ A) = (power_power_int @ B @ A)) | ~ (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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5585])). 159.59/70.61 thf(1993,axiom,((! [A:int,B:int,C:nat]: ((dvd_dvd_int @ A @ B) => ((power_power_int @ (divide_divide_int @ B @ A) @ C) = (divide_divide_int @ (power_power_int @ B @ C) @ (power_power_int @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4106_div__power)). 159.59/70.61 thf(14693,plain,((! [A:int,B:int,C:nat]: ((dvd_dvd_int @ A @ B) => ((power_power_int @ (divide_divide_int @ B @ A) @ C) = (divide_divide_int @ (power_power_int @ B @ C) @ (power_power_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1993])). 159.59/70.61 thf(5920,axiom,((! [A:produc9072475918466114483BT_nat]: (((((~ (! [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)))) <= (! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2214_vebt__insert_Ocases)). 159.59/70.62 thf(28130,plain,((! [A:produc9072475918466114483BT_nat]: (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))) | ~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ B)) @ C @ D) @ E))) | ~ (! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ zero_zero_nat) @ C @ D) @ E))) | ~ (! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))) | ~ (! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5920])). 159.59/70.62 thf(3068,axiom,((set_or4665077453230672383an_nat = (^ [A:nat,B:nat]: (set_nat2 @ (upt @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10132_atLeastLessThan__upt)). 159.59/70.62 thf(18112,plain,(((set_or4665077453230672383an_nat) = (^ [A:nat,B:nat]: (set_nat2 @ (upt @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3068])). 159.59/70.62 thf(2030,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/sandbox/benchmark/theBenchmark.p',fact_7303_tan__bound__pi2)). 159.59/70.62 thf(14808,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)],[2030])). 159.59/70.62 thf(4981,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/sandbox/benchmark/theBenchmark.p',fact_5812_of__int__0__le__iff)). 159.59/70.62 thf(24493,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)],[4981])). 159.59/70.62 thf(5646,axiom,(((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ one_one_complex)) = zero_zero_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4747_diff__numeral__special_I12_J)). 159.59/70.62 thf(26923,plain,(((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ one_one_complex)) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5646])). 159.59/70.62 thf(6204,axiom,((! [A:num,B:num]: (((uminus_uminus_int @ (numeral_numeral_int @ A)) = (uminus_uminus_int @ (numeral_numeral_int @ B))) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4620_neg__numeral__eq__iff)). 159.59/70.62 thf(29105,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)],[6204])). 159.59/70.62 thf(136,axiom,((! [A:complex]: (ord_less_eq_real @ (abs_abs_real @ (im @ A)) @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9655_abs__Im__le__cmod)). 159.59/70.62 thf(8668,plain,((! [A:complex]: (ord_less_eq_real @ (abs_abs_real @ (im @ A)) @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 159.59/70.62 thf(260,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/sandbox/benchmark/theBenchmark.p',fact_3618_flip__bit__negative__int__iff)). 159.59/70.62 thf(9043,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)],[260])). 159.59/70.62 thf(3410,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((times_3573771949741848930nteger @ A @ (divide6298287555418463151nteger @ B @ A)) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3842_dvd__mult__div__cancel)). 159.59/70.62 thf(19218,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((times_3573771949741848930nteger @ A @ (divide6298287555418463151nteger @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3410])). 159.59/70.62 thf(5270,axiom,((! [A:nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ A @ B) => ((times_times_nat @ (groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (times_times_nat @ (C @ A) @ (groups708209901874060359at_nat @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8746_prod_OSuc__reindex__ivl)). 159.59/70.62 thf(25505,plain,((! [A:nat,B:nat,C:(nat > nat)]: ((ord_less_eq_nat @ A @ B) => ((times_times_nat @ (groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (times_times_nat @ (C @ A) @ (groups708209901874060359at_nat @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5270])). 159.59/70.62 thf(4073,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B)) <= (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8097_fact__less__mono)). 159.59/70.62 thf(21320,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B)) | ~ (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4073])). 159.59/70.62 thf(1016,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 @ B @ D) & (ord_less_eq_nat @ C @ A)) | ~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3338_atLeastatMost__subset__iff)). 159.59/70.62 thf(11499,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 @ B @ D) & (ord_less_eq_nat @ C @ A)) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016])). 159.59/70.62 thf(4642,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_not__less__eq)). 159.59/70.62 thf(23295,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4642])). 159.59/70.62 thf(6615,axiom,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((((power_power_real @ B @ A) = (power_power_real @ C @ A)) = (B = C)) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1931_power__eq__iff__eq__base)). 159.59/70.62 thf(30652,plain,((! [A:nat,B:real,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((((power_power_real @ B @ A) = (power_power_real @ C @ A)) = (B = C)) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6615])). 159.59/70.62 thf(6880,axiom,((! [A:nat]: (ord_less_eq_int @ one_one_int @ (semiri1406184849735516958ct_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8079_fact__ge__1)). 159.59/70.62 thf(31794,plain,((! [A:nat]: (ord_less_eq_int @ one_one_int @ (semiri1406184849735516958ct_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6880])). 159.59/70.62 thf(4411,axiom,((! [A:real,B:real]: (((((plus_plus_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) & (B = zero_zero_real))) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2021_add__nonneg__eq__0__iff)). 159.59/70.62 thf(22386,plain,((! [A:real,B:real]: ((((plus_plus_real @ A @ B) = zero_zero_real) = ((A = zero_zero_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)],[4411])). 159.59/70.62 thf(6223,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((sin_real @ (arccos @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7322_sin__arccos)). 159.59/70.62 thf(29160,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((sin_real @ (arccos @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6223])). 159.59/70.62 thf(5871,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6165_and__nat__numerals_I3_J)). 159.59/70.62 thf(27945,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)],[5871])). 159.59/70.62 thf(7505,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1916_bot__nat__0_Oextremum__strict)). 159.59/70.62 thf(34204,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7505])). 159.59/70.62 thf(7160,axiom,((! [A:num]: ((semiri2265585572941072030t_real @ (numeral_numeral_nat @ A)) = (times_times_real @ (numeral_numeral_real @ A) @ (semiri2265585572941072030t_real @ (pred_numeral @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8113_fact__numeral)). 159.59/70.62 thf(32971,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)],[7160])). 159.59/70.62 thf(4111,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/sandbox/benchmark/theBenchmark.p',fact_7568_arcsin__le__mono)). 159.59/70.62 thf(21438,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)],[4111])). 159.59/70.62 thf(1665,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/sandbox/benchmark/theBenchmark.p',fact_3460_mod__diff__right__eq)). 159.59/70.62 thf(13644,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)],[1665])). 159.59/70.62 thf(7317,axiom,((! [A:code_integer]: (((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_Code_integer) <= (ord_le3102999989581377725nteger @ A @ one_one_Code_integer)) <= (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5310_square__le__1)). 159.59/70.62 thf(33559,plain,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_Code_integer) | ~ (ord_le3102999989581377725nteger @ A @ one_one_Code_integer) | ~ (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7317])). 159.59/70.62 thf(5172,axiom,((! [A:num,B:num]: ((B != A) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2930_order__less__imp__not__eq2)). 159.59/70.62 thf(25156,plain,((! [A:num,B:num]: (~ (B = A) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5172])). 159.59/70.62 thf(4319,axiom,((! [A:real]: (((sin_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/sandbox/benchmark/theBenchmark.p',fact_6878_sin__zero__iff__int)). 159.59/70.62 thf(22097,plain,((! [A:real]: (((sin_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)],[4319])). 159.59/70.62 thf(152,axiom,((! [A:code_integer,B:nat,C:nat]: ((comm_s8582702949713902594nteger @ A @ (plus_plus_nat @ B @ C)) = (times_3573771949741848930nteger @ (comm_s8582702949713902594nteger @ A @ B) @ (comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ A @ (semiri4939895301339042750nteger @ B)) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8296_pochhammer__product_H)). 159.59/70.62 thf(8712,plain,((! [A:code_integer,B:nat,C:nat]: ((comm_s8582702949713902594nteger @ A @ (plus_plus_nat @ B @ C)) = (times_3573771949741848930nteger @ (comm_s8582702949713902594nteger @ A @ B) @ (comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ A @ (semiri4939895301339042750nteger @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[152])). 159.59/70.62 thf(4492,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1332_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add)). 159.59/70.62 thf(22699,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ B) => (((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4492])). 159.59/70.62 thf(6525,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: ((((! [D:$o,E:$o]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B))) <= (C = (B = one_one_nat))) <= (A = (vEBT_Leaf @ D @ E)))) => (~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ E @ F @ G) @ B))) <= (C = (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ F)) => (vEBT_VEBT_valid @ H @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))))) & (case_o184042715313410164at_nat @ (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ F)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)))) & ~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H))) @ (produc6081775807080527818_nat_o @ (^ [H:nat,I:nat]: (((H = I) => (! [J:vEBT_VEBT]: ((~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K))) <= (member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ F))))) & ((! [J:nat]: ((((ord_less_nat @ H @ J) & (ord_less_eq_nat @ J @ I)) <= (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))) @ F @ J)) <= (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E))) & (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))) @ F @ I)) <= (H != I)) & ! [J:nat]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [K:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ F @ J) @ K)) = (vEBT_V8194947554948674370ptions @ G @ J))) & (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)) & (ord_less_eq_nat @ H @ I)))) @ D) & ((size_s6755466524823107622T_VEBT @ F) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))))) & (vEBT_VEBT_valid @ G @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))))) & (E = B)))) <= (A = (vEBT_Node @ D @ E @ F @ G)))))) <= (accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ (produc738532404422230701BT_nat @ A @ B))) <= ((vEBT_VEBT_valid @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10073_VEBT__internal_Ovalid_H_Opelims_I1_J)). 159.59/70.62 thf(30324,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((! [D:$o,E:$o]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_VEBT_valid_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)) | ~ (C = (B = one_one_nat)) | ~ (A = (vEBT_Leaf @ D @ E)))) => (~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_VEBT_valid_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ D @ E @ F @ G) @ B)) | ~ (C = (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ F)) => (vEBT_VEBT_valid @ H @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))))) & (case_o184042715313410164at_nat @ (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ F)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)))) & ~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H))) @ (produc6081775807080527818_nat_o @ (^ [H:nat,I:nat]: (((H = I) => (! [J:vEBT_VEBT]: (~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K)) | ~ (member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ F))))) & ((! [J:nat]: (((ord_less_nat @ H @ J) & (ord_less_eq_nat @ J @ I)) | ~ (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))) @ F @ J) | ~ (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E))) & (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))) @ F @ I)) | (H = I)) & ! [J:nat]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [K:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ F @ J) @ K)) = (vEBT_V8194947554948674370ptions @ G @ J))) & (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)) & (ord_less_eq_nat @ H @ I)))) @ D) & ((size_s6755466524823107622T_VEBT @ F) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))))) & (vEBT_VEBT_valid @ G @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))))) & (E = B))) | ~ (A = (vEBT_Node @ D @ E @ F @ G)))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_VEBT_valid_rel) @ (produc738532404422230701BT_nat @ A @ B)) | ~ ((vEBT_VEBT_valid @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6525])). 159.59/70.62 thf(655,axiom,((! [A:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ A) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4681_neg__less__pos)). 159.59/70.62 thf(10345,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)],[655])). 159.59/70.62 thf(2884,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/sandbox/benchmark/theBenchmark.p',fact_1186_add__less__imp__less__left)). 159.59/70.62 thf(17526,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)],[2884])). 159.59/70.62 thf(7356,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2265_add__pos__nonneg)). 159.59/70.62 thf(33691,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7356])). 159.59/70.62 thf(950,axiom,((! [A:num,B:num]: ~ (ord_le6747313008572928689nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5038_not__numeral__less__neg__numeral)). 159.59/70.62 thf(11292,plain,((! [A:num,B:num]: ~ (ord_le6747313008572928689nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[950])). 159.59/70.62 thf(5651,axiom,((! [A:(nat > (nat > nat)),B:nat,C:nat]: ((vEBT_V4262088993061758097ft_nat @ A @ (some_nat @ B) @ (some_nat @ C)) = (some_nat @ (A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_VEBT__internal_Ooption__shift_Osimps_I3_J)). 159.59/70.62 thf(26941,plain,((! [A:(nat > (nat > nat)),B:nat,C:nat]: ((vEBT_V4262088993061758097ft_nat @ (A) @ (some_nat @ B) @ (some_nat @ C)) = (some_nat @ (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5651])). 159.59/70.62 thf(5564,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/sandbox/benchmark/theBenchmark.p',fact_3235_order__less__le__subst1)). 159.59/70.62 thf(26645,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)],[5564])). 159.59/70.62 thf(3026,axiom,((semiri1408675320244567234ct_nat = (comm_s4663373288045622133er_nat @ one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8223_pochhammer__fact)). 159.59/70.62 thf(17980,plain,(((semiri1408675320244567234ct_nat) = (comm_s4663373288045622133er_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3026])). 159.59/70.62 thf(1198,axiom,((! [A:code_integer,B:code_integer]: ((modulo364778990260209775nteger @ (minus_8373710615458151222nteger @ A @ B) @ A) = (modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4719_minus__mod__self1)). 159.59/70.62 thf(12100,plain,((! [A:code_integer,B:code_integer]: ((modulo364778990260209775nteger @ (minus_8373710615458151222nteger @ A @ B) @ A) = (modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198])). 159.59/70.62 thf(2621,axiom,((! [A:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4563_signed__take__bit__numeral__of__1)). 159.59/70.62 thf(16697,plain,((! [A:num]: ((bit_ri631733984087533419it_int @ (numeral_numeral_nat @ A) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2621])). 159.59/70.62 thf(1631,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/sandbox/benchmark/theBenchmark.p',fact_8977_Maclaurin__sin__bound)). 159.59/70.62 thf(13547,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)],[1631])). 159.59/70.62 thf(2121,axiom,((! [A:code_integer,B:code_integer]: ((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ A @ B)) @ B) = (modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4999_mod__minus__eq)). 159.59/70.62 thf(15082,plain,((! [A:code_integer,B:code_integer]: ((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ A @ B)) @ B) = (modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2121])). 159.59/70.62 thf(4219,axiom,((! [A:nat,B:nat]: ((semiri8010041392384452111omplex @ (times_times_nat @ A @ B)) = (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (semiri8010041392384452111omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6536_of__nat__mult)). 159.59/70.62 thf(21801,plain,((! [A:nat,B:nat]: ((semiri8010041392384452111omplex @ (times_times_nat @ A @ B)) = (times_times_complex @ (semiri8010041392384452111omplex @ A) @ (semiri8010041392384452111omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4219])). 159.59/70.62 thf(7181,axiom,((! [A:vEBT_VEBT,B:nat]: (((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (((((B = one_one_nat) => (D)) & (B = one_one_nat)) <= (B != zero_zero_nat)) & ((C) <= (B = zero_zero_nat))))) => ((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) => (((! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ (suc @ zero_zero_nat) @ D @ E))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: (((B != C) => ((~ (ord_less_nat @ B @ C) & ((~ (ord_less_nat @ B @ C)) => (~ (ord_less_nat @ D @ B) & (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)))) <= (~ (ord_less_nat @ D @ B)))))) <= (B != D))) <= (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G))))))) <= (! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ zero_zero_nat @ D @ E)))))) <= (~ (vEBT_vebt_member @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2555_vebt__member_Oelims_I3_J)). 159.59/70.62 thf(33059,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (((((B = one_one_nat) => (D)) & (B = one_one_nat)) | (B = zero_zero_nat)) & ((C) | ~ (B = zero_zero_nat))))) => ((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ 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]: (((~ (B = C)) => ((~ (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 = D))) | ~ (? [G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G))))))) | ~ (! [C:product_prod_nat_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ zero_zero_nat @ D @ E)))))) | (vEBT_vebt_member @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7181])). 159.59/70.62 thf(2981,axiom,((! [A:code_integer,B:nat]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) => ((bit_se9216721137139052372nteger @ A @ B) = ((bit_se9216721137139052372nteger @ (minus_8373710615458151222nteger @ A @ one_one_Code_integer) @ B) | (B = zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6452_odd__bit__iff__bit__pred)). 159.59/70.62 thf(17844,plain,((! [A:code_integer,B:nat]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) => ((bit_se9216721137139052372nteger @ A @ B) = ((bit_se9216721137139052372nteger @ (minus_8373710615458151222nteger @ A @ one_one_Code_integer) @ B) | (B = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2981])). 159.59/70.62 thf(4134,axiom,((! [A:list_nat,B:(nat > $o),C:nat]: (((B @ C) <= (member_nat @ C @ (set_nat2 @ A))) <= (! [D:nat]: ((B @ (nth_nat @ A @ D)) <= (ord_less_nat @ D @ (size_size_list_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_all__nth__imp__all__set)). 159.59/70.62 thf(21507,plain,((! [A:list_nat,B:(nat > $o),C:nat]: ((B @ C) | ~ (member_nat @ C @ (set_nat2 @ A)) | ~ (! [D:nat]: ((B @ (nth_nat @ A @ D)) | ~ (ord_less_nat @ D @ (size_size_list_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4134])). 159.59/70.62 thf(1599,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/sandbox/benchmark/theBenchmark.p',fact_7108_summable__norm)). 159.59/70.62 thf(13448,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)],[1599])). 159.59/70.62 thf(2562,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1061_add__left__cancel)). 159.59/70.62 thf(16487,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)],[2562])). 159.59/70.62 thf(5934,axiom,((! [A:num]: ((ord_less_int @ one_one_int @ (numeral_numeral_int @ A)) = (ord_less_num @ one @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_one__less__numeral__iff)). 159.59/70.62 thf(28187,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)],[5934])). 159.59/70.62 thf(7519,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2034_add__increasing2)). 159.59/70.62 thf(34249,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7519])). 159.59/70.62 thf(3535,axiom,((! [A:code_integer]: (((divide6298287555418463151nteger @ one_one_Code_integer @ (divide6298287555418463151nteger @ one_one_Code_integer @ A)) = A) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3854_unit__div__1__div__1)). 159.59/70.62 thf(19595,plain,((! [A:code_integer]: (((divide6298287555418463151nteger @ one_one_Code_integer @ (divide6298287555418463151nteger @ one_one_Code_integer @ A)) = A) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3535])). 159.59/70.62 thf(7923,axiom,((! [A:nat]: ((bit_se2002935070580805687sk_nat @ (suc @ A)) = (bit_se1412395901928357646or_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (bit_se2002935070580805687sk_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6085_mask__Suc__exp)). 159.59/70.62 thf(35579,plain,((! [A:nat]: ((bit_se2002935070580805687sk_nat @ (suc @ A)) = (bit_se1412395901928357646or_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (bit_se2002935070580805687sk_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7923])). 159.59/70.62 thf(5713,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/sandbox/benchmark/theBenchmark.p',fact_8123_fact__num__eq__if)). 159.59/70.62 thf(27165,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)],[5713])). 159.59/70.62 thf(2242,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/sandbox/benchmark/theBenchmark.p',fact_9450_nat__abs__triangle__ineq)). 159.59/70.62 thf(15486,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)],[2242])). 159.59/70.62 thf(4332,axiom,((! [A:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ A @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ one_one_Code_integer)) <= (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3906_odd__succ__div__two)). 159.59/70.62 thf(22136,plain,((! [A:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ A @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ one_one_Code_integer)) | (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4332])). 159.59/70.62 thf(1295,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2768_less__imp__neq)). 159.59/70.62 thf(12437,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295])). 159.59/70.62 thf(902,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 @ B @ C)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3384_mult__le__cancel__iff2)). 159.59/70.62 thf(11147,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 @ B @ C)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[902])). 159.59/70.62 thf(6604,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2605_dual__order_Orefl)). 159.59/70.62 thf(30619,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6604])). 159.59/70.62 thf(4261,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/sandbox/benchmark/theBenchmark.p',fact_5250_add__divide__eq__if__simps_I3_J)). 159.59/70.62 thf(21925,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)],[4261])). 159.59/70.62 thf(1023,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/sandbox/benchmark/theBenchmark.p',fact_5872_neg__numeral__power__less__of__int__cancel__iff)). 159.59/70.62 thf(11520,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)],[1023])). 159.59/70.62 thf(581,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) = ((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4228_even__iff__mod__2__eq__zero)). 159.59/70.62 thf(10099,plain,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) = ((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[581])). 159.59/70.62 thf(7576,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) = ((B = zero_zero_real) & (A = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1797_sum__power2__eq__zero__iff)). 159.59/70.62 thf(34481,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) = ((B = zero_zero_real) & (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7576])). 159.59/70.62 thf(1092,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (minus_minus_int @ A @ B)) = (ord_less_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1611_diff__gt__0__iff__gt)). 159.59/70.62 thf(11751,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)],[1092])). 159.59/70.62 thf(1279,axiom,((! [A:nat]: ((semiri1314217659103216013at_int @ (bit_se2002935070580805687sk_nat @ A)) = (bit_se2000444600071755411sk_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6723_of__nat__mask__eq)). 159.59/70.62 thf(12385,plain,((! [A:nat]: ((semiri1314217659103216013at_int @ (bit_se2002935070580805687sk_nat @ A)) = (bit_se2000444600071755411sk_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279])). 159.59/70.62 thf(4098,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))))) = ((B != zero_zero_int) | (A != zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2545_sum__power2__gt__zero__iff)). 159.59/70.62 thf(21402,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))))) = (~ (B = zero_zero_int) | ~ (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4098])). 159.59/70.62 thf(8147,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2761_gt__ex)). 159.59/70.62 thf(36310,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8147])). 159.59/70.62 thf(7800,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ B) = (plus_plus_nat @ B @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_mult__Suc)). 159.59/70.62 thf(35184,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)],[7800])). 159.59/70.62 thf(965,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/sandbox/benchmark/theBenchmark.p',fact_9465_Suc__nat__eq__nat__zadd1)). 159.59/70.62 thf(11339,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)],[965])). 159.59/70.62 thf(2271,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/sandbox/benchmark/theBenchmark.p',fact_2144_divide__right__mono)). 159.59/70.62 thf(15574,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)],[2271])). 159.59/70.62 thf(2283,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ A @ B) => (ord_less_int @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3197_order__neq__le__trans)). 159.59/70.62 thf(15610,plain,((! [A:int,B:int]: (((ord_less_eq_int @ A @ B) => (ord_less_int @ A @ B)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2283])). 159.59/70.62 thf(6097,axiom,((! [A:int,B:int]: ((((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ B)) | ((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/sandbox/benchmark/theBenchmark.p',fact_1979_split__mult__neg__le)). 159.59/70.62 thf(28740,plain,((! [A:int,B:int]: ((((ord_less_eq_int @ A @ zero_zero_int) & (ord_less_eq_int @ zero_zero_int @ B)) | ((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)],[6097])). 159.59/70.62 thf(4760,axiom,((! [A:nat,B:num]: (((~ (ord_less_eq_nat @ A @ (pred_numeral @ B))) => ((set_or4665077453230672383an_nat @ A @ (numeral_numeral_nat @ B)) = bot_bot_set_nat)) & ((ord_less_eq_nat @ A @ (pred_numeral @ B)) => ((set_or4665077453230672383an_nat @ A @ (numeral_numeral_nat @ B)) = (insert_nat @ (pred_numeral @ B) @ (set_or4665077453230672383an_nat @ A @ (pred_numeral @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9608_atLeastLessThan__nat__numeral)). 159.59/70.62 thf(23703,plain,((! [A:nat,B:num]: (((~ (ord_less_eq_nat @ A @ (pred_numeral @ B))) => ((set_or4665077453230672383an_nat @ A @ (numeral_numeral_nat @ B)) = bot_bot_set_nat)) & ((ord_less_eq_nat @ A @ (pred_numeral @ B)) => ((set_or4665077453230672383an_nat @ A @ (numeral_numeral_nat @ B)) = (insert_nat @ (pred_numeral @ B) @ (set_or4665077453230672383an_nat @ A @ (pred_numeral @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4760])). 159.59/70.62 thf(3862,axiom,((! [A:int]: (dvd_dvd_int @ one_one_int @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4005_one__dvd)). 159.59/70.62 thf(20684,plain,((! [A:int]: (dvd_dvd_int @ one_one_int @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3862])). 159.59/70.62 thf(173,axiom,((semiri1406184849735516958ct_int = (comm_s4660882817536571857er_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8221_pochhammer__fact)). 159.59/70.62 thf(8783,plain,(((semiri1406184849735516958ct_int) = (comm_s4660882817536571857er_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[173])). 159.59/70.62 thf(1593,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (exp_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5996_one__le__exp__iff)). 159.59/70.62 thf(13423,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)],[1593])). 159.59/70.62 thf(2243,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/sandbox/benchmark/theBenchmark.p',fact_6848_pos__int__cases)). 159.59/70.62 thf(15488,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)],[2243])). 159.59/70.62 thf(1494,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ B @ C)) = (B = (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5660_eq__diff__eq_H)). 159.59/70.62 thf(13126,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)],[1494])). 159.59/70.62 thf(3011,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/sandbox/benchmark/theBenchmark.p',fact_2094_mult__pos__pos)). 159.59/70.62 thf(17936,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)],[3011])). 159.59/70.62 thf(6055,axiom,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_num @ A @ C) <= (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2781_ord__less__eq__trans)). 159.59/70.62 thf(28615,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)],[6055])). 159.59/70.62 thf(6079,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/sandbox/benchmark/theBenchmark.p',fact_5858_of__int__eq__neg__numeral__power__cancel__iff)). 159.59/70.62 thf(28685,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)],[6079])). 159.59/70.62 thf(4902,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ (times_times_nat @ C @ D)) => ((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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4222_dvd__minus__add)). 159.59/70.62 thf(24197,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ (times_times_nat @ C @ D)) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4902])). 159.59/70.62 thf(3134,axiom,((! [A:extended_enat,B:(extended_enat > extended_enat),C:extended_enat,D:extended_enat]: (((ord_le72135733267957522d_enat @ C @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)))) => (ord_le72135733267957522d_enat @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2863_ord__eq__less__subst)). 159.59/70.62 thf(18332,plain,((! [A:extended_enat,B:(extended_enat > extended_enat),C:extended_enat,D:extended_enat]: (((ord_le72135733267957522d_enat @ C @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)))) => (ord_le72135733267957522d_enat @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3134])). 159.59/70.62 thf(171,axiom,((! [A:code_integer,B:nat]: ((times_3573771949741848930nteger @ (minus_8373710615458151222nteger @ A @ (semiri4939895301339042750nteger @ B)) @ (comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ A) @ B)) = (times_3573771949741848930nteger @ A @ (comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ one_one_Code_integer) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8329_pochhammer__absorb__comp)). 159.59/70.62 thf(8778,plain,((! [A:code_integer,B:nat]: ((times_3573771949741848930nteger @ (minus_8373710615458151222nteger @ A @ (semiri4939895301339042750nteger @ B)) @ (comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ A) @ B)) = (times_3573771949741848930nteger @ A @ (comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ one_one_Code_integer) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 159.59/70.62 thf(2671,axiom,((! [A:num]: ((numera1916890842035813515d_enat @ (bit0 @ A)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_numeral__Bit0)). 159.59/70.62 thf(16861,plain,((! [A:num]: ((numera1916890842035813515d_enat @ (bit0 @ A)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2671])). 159.59/70.62 thf(404,axiom,((! [A:code_integer,B:code_integer]: (((dvd_dvd_Code_integer @ B @ one_one_Code_integer) => ((divide6298287555418463151nteger @ A @ (times_3573771949741848930nteger @ B @ A)) = (divide6298287555418463151nteger @ one_one_Code_integer @ B))) <= (A != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4201_is__unit__div__mult__cancel__right)). 159.59/70.62 thf(9522,plain,((! [A:code_integer,B:code_integer]: (((dvd_dvd_Code_integer @ B @ one_one_Code_integer) => ((divide6298287555418463151nteger @ A @ (times_3573771949741848930nteger @ B @ A)) = (divide6298287555418463151nteger @ one_one_Code_integer @ B))) | (A = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])). 159.59/70.62 thf(7968,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/sandbox/benchmark/theBenchmark.p',fact_4837_power2__minus)). 159.59/70.62 thf(35719,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)],[7968])). 159.59/70.62 thf(7277,axiom,((! [A:nat]: (((~ (! [B:nat]: (A != (suc @ (suc @ B))))) <= (A != (suc @ zero_zero_nat))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1902_vebt__buildup_Ocases)). 159.59/70.62 thf(33400,plain,((! [A:nat]: (~ (! [B:nat]: ~ (A = (suc @ (suc @ B)))) | (A = (suc @ zero_zero_nat)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7277])). 159.59/70.62 thf(8142,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/sandbox/benchmark/theBenchmark.p',fact_1105_mult_Oassoc)). 159.59/70.62 thf(36289,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)],[8142])). 159.59/70.62 thf(932,axiom,((! [A:real]: ((summable_real @ (power_power_real @ A)) = (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6991_summable__geometric__iff)). 159.59/70.62 thf(11238,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)],[932])). 159.59/70.62 thf(3092,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/sandbox/benchmark/theBenchmark.p',fact_1089_add__diff__cancel__right)). 159.59/70.62 thf(18200,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)],[3092])). 159.59/70.62 thf(2630,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (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 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6472_arith__geo__mean__sqrt)). 159.59/70.62 thf(16729,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (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 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2630])). 159.59/70.62 thf(2472,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/sandbox/benchmark/theBenchmark.p',fact_3480_cong__exp__iff__simps_I4_J)). 159.59/70.62 thf(16210,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)],[2472])). 159.59/70.62 thf(7151,axiom,((! [A:nat,B:nat]: ((A = B) <= ((suc @ A) = (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_Suc__inject)). 159.59/70.62 thf(32943,plain,((! [A:nat,B:nat]: ((A = B) | ~ ((suc @ A) = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7151])). 159.59/70.62 thf(3631,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/sandbox/benchmark/theBenchmark.p',fact_4167_unit__div__commute)). 159.59/70.62 thf(19914,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)],[3631])). 159.59/70.62 thf(7293,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_Suc__leD)). 159.59/70.62 thf(33459,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)],[7293])). 159.59/70.62 thf(7091,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/sandbox/benchmark/theBenchmark.p',fact_5740_take__bit__numeral__minus__bit0)). 159.59/70.62 thf(32707,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)],[7091])). 159.59/70.62 thf(4481,axiom,((! [A:nat]: ((bit_se1148574629649215175it_nat @ one_one_nat @ A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6386_bit__1__iff)). 159.59/70.62 thf(22667,plain,((! [A:nat]: ((bit_se1148574629649215175it_nat @ one_one_nat @ A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4481])). 159.59/70.62 thf(6756,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit1 @ A))) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6015_and__minus__numerals_I6_J)). 159.59/70.62 thf(31296,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)],[6756])). 159.59/70.62 thf(981,axiom,((! [A:list_VEBT_VEBT,B:set_VEBT_VEBT]: ((ord_le4337996190870823476T_VEBT @ (set_VEBT_VEBT2 @ A) @ B) = (! [C:vEBT_VEBT]: ((member_VEBT_VEBT @ C @ B) <= (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_subset__code_I1_J)). 159.59/70.62 thf(11388,plain,((! [A:list_VEBT_VEBT,B:set_VEBT_VEBT]: ((ord_le4337996190870823476T_VEBT @ (set_VEBT_VEBT2 @ A) @ B) = (! [C:vEBT_VEBT]: ((member_VEBT_VEBT @ C @ B) | ~ (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[981])). 159.59/70.62 thf(3610,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4970_is__num__normalize_I8_J)). 159.59/70.62 thf(19842,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)],[3610])). 159.59/70.62 thf(2760,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (powr_real @ A @ B) @ zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7213_powr__nonneg__iff)). 159.59/70.62 thf(17146,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)],[2760])). 159.59/70.62 thf(4821,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3870_pow__divides__pow__iff)). 159.59/70.62 thf(23935,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (power_power_nat @ B @ A) @ (power_power_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4821])). 159.59/70.62 thf(2365,axiom,((archim6058952711729229775r_real = (^ [A:real]: (the_int @ (^ [B:int]: ((ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ B @ one_one_int))) & (ord_less_eq_real @ (ring_1_of_int_real @ B) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9723_floor__real__def)). 159.59/70.62 thf(15843,plain,(((archim6058952711729229775r_real) = (^ [A:real]: (the_int @ (^ [B:int]: ((ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ B @ one_one_int))) & (ord_less_eq_real @ (ring_1_of_int_real @ B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2365])). 159.59/70.62 thf(2606,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ one_one_real @ C) => (ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7238_powr__mono)). 159.59/70.62 thf(16633,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ one_one_real @ C) => (ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2606])). 159.59/70.62 thf(3439,axiom,((! [A:real,B:real,C:real]: ((((divide_divide_real @ B @ A) = C) <= (B = (times_times_real @ C @ A))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2172_divide__eq__imp)). 159.59/70.62 thf(19305,plain,((! [A:real,B:real,C:real]: (((divide_divide_real @ B @ A) = C) | ~ (B = (times_times_real @ C @ A)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3439])). 159.59/70.62 thf(5640,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_704_le__square)). 159.59/70.62 thf(26906,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5640])). 159.59/70.62 thf(1554,axiom,((! [A:real,B:(int > real),C:int,D:int]: ((ord_less_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/sandbox/benchmark/theBenchmark.p',fact_2897_order__less__subst1)). 159.59/70.62 thf(13301,plain,((! [A:real,B:(int > real),C:int,D:int]: ((ord_less_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)],[1554])). 159.59/70.62 thf(4456,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 @ B @ C)) @ D @ E @ F)))) <= (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D)))) <= (! [B:$o,C:$o]: (A != (vEBT_Leaf @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2406_vebt__mint_Ocases)). 159.59/70.62 thf(22524,plain,((! [A:vEBT_VEBT]: (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F))) | ~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) | ~ (! [B:$o,C:$o]: ~ (A = (vEBT_Leaf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4456])). 159.59/70.62 thf(6836,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) <= (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2556_odd__0__le__power__imp__0__le)). 159.59/70.62 thf(31564,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6836])). 159.59/70.62 thf(5675,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/sandbox/benchmark/theBenchmark.p',fact_241_power__add__numeral2)). 159.59/70.62 thf(27054,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)],[5675])). 159.59/70.62 thf(1732,axiom,((! [A:extended_enat,B:extended_enat]: (((((plus_p3455044024723400733d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((B = zero_z5237406670263579293d_enat) & (A = zero_z5237406670263579293d_enat))) <= (ord_le2932123472753598470d_enat @ B @ zero_z5237406670263579293d_enat)) <= (ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2016_add__nonpos__eq__0__iff)). 159.59/70.62 thf(13850,plain,((! [A:extended_enat,B:extended_enat]: ((((plus_p3455044024723400733d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((B = zero_z5237406670263579293d_enat) & (A = zero_z5237406670263579293d_enat))) | ~ (ord_le2932123472753598470d_enat @ B @ zero_z5237406670263579293d_enat) | ~ (ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732])). 159.59/70.62 thf(1890,axiom,((! [A:num,B:real]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (minus_minus_real @ (numeral_numeral_real @ A) @ one_one_real) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6997_numeral__le__ceiling)). 159.59/70.62 thf(14357,plain,((! [A:num,B:real]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (minus_minus_real @ (numeral_numeral_real @ A) @ one_one_real) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1890])). 159.59/70.62 thf(6786,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2277_add__neg__nonpos)). 159.59/70.62 thf(31405,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6786])). 159.59/70.62 thf(3375,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/sandbox/benchmark/theBenchmark.p',fact_2430_pos__le__divide__eq)). 159.59/70.62 thf(19099,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)],[3375])). 159.59/70.62 thf(1880,axiom,((! [A:(extended_enat > $o),B:extended_enat]: ((? [C:extended_enat]: (A @ (times_7803423173614009249d_enat @ B @ C))) = (? [C:extended_enat]: ((dvd_dv3785147216227455552d_enat @ B @ (plus_p3455044024723400733d_enat @ C @ zero_z5237406670263579293d_enat)) & (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4299_unity__coeff__ex)). 159.59/70.62 thf(14323,plain,((! [A:(extended_enat > $o),B:extended_enat]: ((? [C:extended_enat]: (A @ (times_7803423173614009249d_enat @ B @ C))) = (? [C:extended_enat]: ((dvd_dv3785147216227455552d_enat @ B @ (plus_p3455044024723400733d_enat @ C @ zero_z5237406670263579293d_enat)) & (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1880])). 159.59/70.62 thf(845,axiom,((! [A:real,B:nat,C:(nat > real)]: (((summable_real @ C) <= (! [D:nat]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (C @ (suc @ D))) @ (times_times_real @ A @ (real_V7735802525324610683m_real @ (C @ D)))) <= (ord_less_eq_nat @ B @ D)))) <= (ord_less_real @ A @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7140_summable__ratio__test)). 159.59/70.62 thf(10975,plain,((! [A:real,B:nat,C:(nat > real)]: ((summable_real @ (C)) | ~ (! [D:nat]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (C @ (suc @ D))) @ (times_times_real @ A @ (real_V7735802525324610683m_real @ (C @ D)))) | ~ (ord_less_eq_nat @ B @ D))) | ~ (ord_less_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[845])). 159.59/70.62 thf(3526,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_eq_real @ B @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9001_inverse__le__iff__le)). 159.59/70.62 thf(19571,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_eq_real @ B @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3526])). 159.59/70.62 thf(5431,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((B != A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3116_dual__order_Ostrict__iff__order)). 159.59/70.62 thf(26202,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (B = A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5431])). 159.59/70.62 thf(4584,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/sandbox/benchmark/theBenchmark.p',fact_91_numeral__times__numeral)). 159.59/70.62 thf(23081,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)],[4584])). 159.59/70.62 thf(4830,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3150_dual__order_Ostrict__implies__order)). 159.59/70.62 thf(23970,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4830])). 159.59/70.62 thf(5458,axiom,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: (((some_P7363390416028606310at_nat @ A) = (some_P7363390416028606310at_nat @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_762_option_Oinject)). 159.59/70.62 thf(26302,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)],[5458])). 159.59/70.62 thf(5486,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/sandbox/benchmark/theBenchmark.p',fact_847_Suc__diff__le)). 159.59/70.62 thf(26393,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)],[5486])). 159.59/70.62 thf(3514,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/sandbox/benchmark/theBenchmark.p',fact_5853_numeral__power__less__of__int__cancel__iff)). 159.59/70.62 thf(19534,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)],[3514])). 159.59/70.62 thf(373,axiom,((! [A:nat]: (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (semiri4939895301339042750nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6664_of__nat__0__le__iff)). 159.59/70.62 thf(9412,plain,((! [A:nat]: (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (semiri4939895301339042750nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[373])). 159.59/70.62 thf(6865,axiom,((times_times_int = (^ [A:int,B:int]: (times_times_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1102_mult_Ocommute)). 159.59/70.62 thf(31749,plain,(((times_times_int) = (^ [A:int,B:int]: (times_times_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6865])). 159.59/70.62 thf(5939,axiom,((! [A:nat,B:nat,C:nat]: ((ord_max_nat @ A @ (ord_max_nat @ B @ C)) = (ord_max_nat @ B @ (ord_max_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_max_Oleft__commute)). 159.59/70.62 thf(28210,plain,((! [A:nat,B:nat,C:nat]: ((ord_max_nat @ A @ (ord_max_nat @ B @ C)) = (ord_max_nat @ B @ (ord_max_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5939])). 159.59/70.62 thf(5285,axiom,((! [A:(nat > nat),B:nat]: ((sums_nat @ A @ (plus_plus_nat @ B @ (A @ zero_zero_nat))) <= (sums_nat @ (^ [C:nat]: (A @ (suc @ C))) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7933_sums__Suc)). 159.59/70.62 thf(25569,plain,((! [A:(nat > nat),B:nat]: ((sums_nat @ (A) @ (plus_plus_nat @ B @ (A @ zero_zero_nat))) | ~ (sums_nat @ (^ [C:nat]: (A @ (suc @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5285])). 159.59/70.62 thf(5542,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2697_Orderings_Oorder__eq__iff)). 159.59/70.62 thf(26582,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)],[5542])). 159.59/70.62 thf(7708,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/sandbox/benchmark/theBenchmark.p',fact_1460_VEBT__internal_Omembermima_Osimps_I5_J)). 159.59/70.62 thf(34877,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)],[7708])). 159.59/70.62 thf(1318,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((divide6298287555418463151nteger @ B @ (uminus1351360451143612070nteger @ A)) = (uminus1351360451143612070nteger @ (divide6298287555418463151nteger @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5119_dvd__div__neg)). 159.59/70.62 thf(12510,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((divide6298287555418463151nteger @ B @ (uminus1351360451143612070nteger @ A)) = (uminus1351360451143612070nteger @ (divide6298287555418463151nteger @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318])). 159.59/70.62 thf(4486,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/sandbox/benchmark/theBenchmark.p',fact_9763_infinite__nat__iff__unbounded__le)). 159.59/70.62 thf(22682,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)],[4486])). 159.59/70.62 thf(3942,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/sandbox/benchmark/theBenchmark.p',fact_5785_of__int__power__eq__of__int__cancel__iff)). 159.59/70.62 thf(20931,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)],[3942])). 159.59/70.62 thf(3600,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1634_nonzero__mult__div__cancel__left)). 159.59/70.62 thf(19813,plain,((! [A:complex,B:complex]: ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3600])). 159.59/70.62 thf(7207,axiom,((! [A:num,B:real]: (((power_power_real @ (abs_abs_real @ B) @ (numeral_numeral_nat @ A)) = (power_power_real @ B @ (numeral_numeral_nat @ A))) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5459_power__even__abs__numeral)). 159.59/70.62 thf(33163,plain,((! [A:num,B:real]: (((power_power_real @ (abs_abs_real @ B) @ (numeral_numeral_nat @ A)) = (power_power_real @ B @ (numeral_numeral_nat @ A))) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7207])). 159.59/70.62 thf(2077,axiom,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (plus_plus_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))) = (bit_se2923211474154528505it_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4913_take__bit__add)). 159.59/70.62 thf(14943,plain,((! [A:nat,B:int,C:int]: ((bit_se2923211474154528505it_int @ A @ (plus_plus_int @ (bit_se2923211474154528505it_int @ A @ B) @ (bit_se2923211474154528505it_int @ A @ C))) = (bit_se2923211474154528505it_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2077])). 159.59/70.62 thf(3219,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/sandbox/benchmark/theBenchmark.p',fact_9529_ln__root)). 159.59/70.62 thf(18600,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)],[3219])). 159.59/70.62 thf(4221,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ C) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4074_dvd__div__mult)). 159.59/70.62 thf(21806,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ C) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4221])). 159.59/70.62 thf(4472,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9542_xor__nat__numerals_I2_J)). 159.59/70.62 thf(22635,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)],[4472])). 159.59/70.62 thf(1747,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (abs_abs_int @ A)) = (A != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5411_zero__less__abs__iff)). 159.59/70.62 thf(13892,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)],[1747])). 159.59/70.62 thf(7792,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/sandbox/benchmark/theBenchmark.p',fact_6455_set__decode__plus__power__2)). 159.59/70.62 thf(35162,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)],[7792])). 159.59/70.62 thf(4044,axiom,((! [A:real,B:real]: (((uminus_uminus_real @ A) = B) <= ((plus_plus_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5050_add_Oinverse__unique)). 159.59/70.62 thf(21238,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)],[4044])). 159.59/70.62 thf(5151,axiom,((! [A:nat,B:(nat > int),C:int,D:int]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_int @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (B @ E) @ (power_power_int @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (B @ E) @ (power_power_int @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_int @ (minus_minus_int @ C @ D) @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (B @ F) @ (power_power_int @ D @ (minus_minus_nat @ (minus_minus_nat @ F @ E) @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ E) @ A)) @ (power_power_int @ C @ E))) @ (set_ord_lessThan_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8959_polyfun__diff)). 159.59/70.62 thf(25081,plain,((! [A:nat,B:(nat > int),C:int,D:int]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_int @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (B @ E) @ (power_power_int @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (B @ E) @ (power_power_int @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_int @ (minus_minus_int @ C @ D) @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (B @ F) @ (power_power_int @ D @ (minus_minus_nat @ (minus_minus_nat @ F @ E) @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ E) @ A)) @ (power_power_int @ C @ E))) @ (set_ord_lessThan_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5151])). 159.59/70.62 thf(7675,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) => (ord_less_nat @ (binomial @ C @ A) @ (binomial @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9131_binomial__strict__mono)). 159.59/70.62 thf(34781,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) => (ord_less_nat @ (binomial @ C @ A) @ (binomial @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7675])). 159.59/70.62 thf(6005,axiom,(((uminus_uminus_int @ (numeral_numeral_int @ one)) = (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5212_uminus__numeral__One)). 159.59/70.62 thf(28458,plain,(((uminus_uminus_int @ (numeral_numeral_int @ one)) = (uminus_uminus_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6005])). 159.59/70.62 thf(209,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ (bit_ri7919022796975470100ot_int @ A)) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9574_not__nonnegative__int__iff)). 159.59/70.62 thf(8888,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)],[209])). 159.59/70.62 thf(5293,axiom,((! [A:nat]: (((groups3539618377306564664at_int @ (^ [B:nat]: (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (semiri1314217659103216013at_int @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_int) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9170_choose__alternating__sum)). 159.59/70.62 thf(25594,plain,((! [A:nat]: (((groups3539618377306564664at_int @ (^ [B:nat]: (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (semiri1314217659103216013at_int @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_int) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5293])). 159.59/70.62 thf(3958,axiom,((! [A:nat,B:code_integer]: ((bit_ri6519982836138164636nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_ri6519982836138164636nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4550_signed__take__bit__Suc)). 159.59/70.62 thf(20989,plain,((! [A:nat,B:code_integer]: ((bit_ri6519982836138164636nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_ri6519982836138164636nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3958])). 159.59/70.62 thf(3578,axiom,((! [A:int,B:nat]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ (plus_plus_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (bit_se2923211474154528505it_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5337_take__bit__int__greater__eq)). 159.59/70.62 thf(19744,plain,((! [A:int,B:nat]: ((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ (plus_plus_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ (bit_se2923211474154528505it_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3578])). 159.59/70.62 thf(7305,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/sandbox/benchmark/theBenchmark.p',fact_2635_ex__nat__less)). 159.59/70.62 thf(33503,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)],[7305])). 159.59/70.62 thf(2814,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/sandbox/benchmark/theBenchmark.p',fact_8474_prod__power__distrib)). 159.59/70.62 thf(17303,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)],[2814])). 159.59/70.62 thf(1640,axiom,((! [A:num,B:num]: ((ord_le2932123472753598470d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_numeral__le__iff)). 159.59/70.62 thf(13572,plain,((! [A:num,B:num]: ((ord_le2932123472753598470d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640])). 159.59/70.62 thf(806,axiom,((! [A:nat,B:int]: ((bit_se2923211474154528505it_int @ A @ (ring_1_of_int_int @ B)) = (ring_1_of_int_int @ (bit_se2923211474154528505it_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5887_take__bit__of__int)). 159.59/70.62 thf(10858,plain,((! [A:nat,B:int]: ((bit_se2923211474154528505it_int @ A @ (ring_1_of_int_int @ B)) = (ring_1_of_int_int @ (bit_se2923211474154528505it_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[806])). 159.59/70.62 thf(1080,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/sandbox/benchmark/theBenchmark.p',fact_3451_mod__mult__eq)). 159.59/70.62 thf(11719,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)],[1080])). 159.59/70.62 thf(7188,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => (ord_less_eq_real @ one_one_real @ (sqrt @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6392_real__sqrt__ge__one)). 159.59/70.62 thf(33104,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => (ord_less_eq_real @ one_one_real @ (sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7188])). 159.59/70.62 thf(2528,axiom,((! [A:real,B:num]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ (numeral_numeral_int @ B)) = (ord_less_real @ A @ (plus_plus_real @ (numeral_numeral_real @ B) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8199_floor__le__numeral)). 159.59/70.62 thf(16386,plain,((! [A:real,B:num]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ (numeral_numeral_int @ B)) = (ord_less_real @ A @ (plus_plus_real @ (numeral_numeral_real @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2528])). 159.59/70.62 thf(8181,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1716_nat__mult__less__cancel__disj)). 159.59/70.62 thf(36412,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8181])). 159.59/70.62 thf(3648,axiom,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ (times_times_real @ A @ (power_power_real @ A @ B))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_power__gt1__lemma)). 159.59/70.62 thf(19967,plain,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ (times_times_real @ A @ (power_power_real @ A @ B))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3648])). 159.59/70.62 thf(4913,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6167_or__nat__numerals_I2_J)). 159.59/70.62 thf(24234,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)],[4913])). 159.59/70.62 thf(4750,axiom,((! [A:nat,B:nat]: ((? [C:nat,D:nat,E:nat]: (((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C)) & (dvd_dvd_nat @ C @ B) & (dvd_dvd_nat @ C @ A))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4125_bezout__add__strong__nat)). 159.59/70.62 thf(23649,plain,((! [A:nat,B:nat]: (? [C:nat,D:nat,E:nat]: (((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C)) & (dvd_dvd_nat @ C @ B) & (dvd_dvd_nat @ C @ A)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4750])). 159.59/70.62 thf(4374,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/sandbox/benchmark/theBenchmark.p',fact_4566_signed__take__bit__add)). 159.59/70.62 thf(22260,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)],[4374])). 159.59/70.62 thf(7974,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_pred @ A @ C) = (some_nat @ D)) => (ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_helpypredd)). 159.59/70.62 thf(35734,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_pred @ A @ C) = (some_nat @ D)) => (ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7974])). 159.59/70.62 thf(2474,axiom,((! [A:complex]: (sums_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B))) @ (exp_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9284_exp__converges)). 159.59/70.62 thf(16215,plain,((! [A:complex]: (sums_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B))) @ (exp_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2474])). 159.59/70.62 thf(927,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/sandbox/benchmark/theBenchmark.p',fact_3471_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend)). 159.59/70.62 thf(11223,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)],[927])). 159.59/70.62 thf(1218,axiom,((! [A:nat,B:num]: (((semiri1314217659103216013at_int @ A) = (numeral_numeral_int @ B)) = (A = (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6798_int__eq__iff__numeral)). 159.59/70.62 thf(12190,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)],[1218])). 159.59/70.62 thf(6733,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ A) = (B = A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2642_order__antisym__conv)). 159.59/70.62 thf(31208,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ A) = (B = A)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6733])). 159.59/70.62 thf(3271,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/sandbox/benchmark/theBenchmark.p',fact_7134_sin__double)). 159.59/70.62 thf(18784,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)],[3271])). 159.59/70.62 thf(1847,axiom,((! [A:real,B:complex,C:complex,D:complex]: ((((plus_plus_complex @ (real_V2046097035970521341omplex @ A @ B) @ C) = D) = (B = (minus_minus_complex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ A) @ D) @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ A) @ C)))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9250_real__vector__affinity__eq)). 159.59/70.62 thf(14222,plain,((! [A:real,B:complex,C:complex,D:complex]: ((((plus_plus_complex @ (real_V2046097035970521341omplex @ A @ B) @ C) = D) = (B = (minus_minus_complex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ A) @ D) @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ A) @ C)))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1847])). 159.59/70.62 thf(6021,axiom,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ C @ A)) @ (set_ord_atMost_nat @ B)) = (binomial @ (suc @ B) @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9085_sum__choose__upper)). 159.59/70.62 thf(28505,plain,((! [A:nat,B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (binomial @ C @ A)) @ (set_ord_atMost_nat @ B)) = (binomial @ (suc @ B) @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6021])). 159.59/70.62 thf(6485,axiom,((! [A:option_nat]: (((some_nat @ (the_nat @ A)) = A) <= (A != none_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_737_option_Ocollapse)). 159.59/70.62 thf(30199,plain,((! [A:option_nat]: (((some_nat @ (the_nat @ A)) = A) | (A = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6485])). 159.59/70.62 thf(5506,axiom,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ B)) = (uminus1351360451143612070nteger @ (times_3573771949741848930nteger @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4626_mult__minus__right)). 159.59/70.62 thf(26477,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)],[5506])). 159.59/70.62 thf(5372,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ B @ A)) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2771_order_Oasym)). 159.59/70.62 thf(25954,plain,((! [A:num,B:num]: (~ (ord_less_num @ B @ A) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5372])). 159.59/70.62 thf(3215,axiom,((! [A:num,B:num]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (numera1916890842035813515d_enat @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_numeral__times__numeral)). 159.59/70.62 thf(18589,plain,((! [A:num,B:num]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (numera1916890842035813515d_enat @ (times_times_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3215])). 159.59/70.62 thf(2555,axiom,((! [A:int,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((bit_se1146084159140164899it_int @ (plus_plus_int @ one_one_int @ A) @ B) = ((bit_se1146084159140164899it_int @ A @ B) | (B = zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6450_even__bit__succ__iff)). 159.59/70.62 thf(16465,plain,((! [A:int,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((bit_se1146084159140164899it_int @ (plus_plus_int @ one_one_int @ A) @ B) = ((bit_se1146084159140164899it_int @ A @ B) | (B = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2555])). 159.59/70.62 thf(1339,axiom,((! [A:int,B: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)) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ B @ A)))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3704_pos__zmod__mult__2)). 159.59/70.62 thf(12576,plain,((! [A:int,B: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)) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (modulo_modulo_int @ B @ A)))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339])). 159.59/70.62 thf(7466,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8314_pochhammer__product)). 159.59/70.62 thf(34048,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7466])). 159.59/70.62 thf(1448,axiom,((! [A:real]: (((inverse_inverse_real @ A) = (divide_divide_real @ one_one_real @ A)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9079_nonzero__inverse__eq__divide)). 159.59/70.62 thf(12970,plain,((! [A:real]: (((inverse_inverse_real @ A) = (divide_divide_real @ one_one_real @ A)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448])). 159.59/70.62 thf(5762,axiom,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ one_one_real @ (power_power_real @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2468_one__less__power)). 159.59/70.62 thf(27332,plain,((! [A:real,B:nat]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ one_one_real @ (power_power_real @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5762])). 159.59/70.62 thf(3414,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => ((abs_abs_int @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5520_abs__of__pos)). 159.59/70.62 thf(19231,plain,((! [A:int]: ((ord_less_int @ zero_zero_int @ A) => ((abs_abs_int @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3414])). 159.59/70.62 thf(4599,axiom,((! [A:nat]: ~ (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6670_of__nat__less__0__iff)). 159.59/70.62 thf(23143,plain,((! [A:nat]: ~ (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4599])). 159.59/70.62 thf(5867,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3701_verit__sum__simplify)). 159.59/70.62 thf(27926,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5867])). 159.59/70.62 thf(2893,axiom,((! [A:num]: ((semiri1314217659103216013at_int @ (numeral_numeral_nat @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6515_of__nat__numeral)). 159.59/70.62 thf(17567,plain,((! [A:num]: ((semiri1314217659103216013at_int @ (numeral_numeral_nat @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2893])). 159.59/70.62 thf(6098,axiom,((! [A:nat]: ((one_one_real = (semiri5074537144036343181t_real @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6545_of__nat__1__eq__iff)). 159.59/70.62 thf(28743,plain,((! [A:nat]: ((one_one_real = (semiri5074537144036343181t_real @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6098])). 159.59/70.62 thf(4154,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/sandbox/benchmark/theBenchmark.p',fact_7936_sums__Suc__iff)). 159.59/70.62 thf(21579,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)],[4154])). 159.59/70.62 thf(7665,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/sandbox/benchmark/theBenchmark.p',fact_4890_power__minus1__even)). 159.59/70.62 thf(34745,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)],[7665])). 159.59/70.62 thf(2979,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le72135733267957522d_enat @ A @ C) <= (ord_le72135733267957522d_enat @ B @ C)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2858_order__less__trans)). 159.59/70.62 thf(17838,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ C) | ~ (ord_le72135733267957522d_enat @ B @ C) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2979])). 159.59/70.62 thf(8104,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => (((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) => (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_less__add__eq__less)). 159.59/70.62 thf(36159,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => (((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) => (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8104])). 159.59/70.62 thf(743,axiom,((~ (ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2048_not__one__le__zero)). 159.59/70.62 thf(10657,plain,((~ (ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[743])). 159.59/70.62 thf(3344,axiom,((! [A:set_nat,B:(nat > int)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_int @ zero_zero_int @ (B @ C)))) => (ord_less_eq_int @ zero_zero_int @ (groups705719431365010083at_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8492_prod__nonneg)). 159.59/70.62 thf(19006,plain,((! [A:set_nat,B:(nat > int)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_int @ zero_zero_int @ (B @ C)))) => (ord_less_eq_int @ zero_zero_int @ (groups705719431365010083at_int @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3344])). 159.59/70.62 thf(2928,axiom,((! [A:real,B:real]: ((one_one_real = (divide_divide_real @ A @ B)) = ((A = B) & (B != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1672_one__eq__divide__iff)). 159.59/70.62 thf(17683,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)],[2928])). 159.59/70.62 thf(5384,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (((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 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1787_power2__eq__iff__nonneg)). 159.59/70.62 thf(26000,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (((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 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5384])). 159.59/70.62 thf(4063,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => (ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B))) <= (ord_less_real @ C @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2324_divide__strict__left__mono__neg)). 159.59/70.62 thf(21293,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => (ord_less_real @ (divide_divide_real @ C @ A) @ (divide_divide_real @ C @ B))) | ~ (ord_less_real @ C @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4063])). 159.59/70.62 thf(3711,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/sandbox/benchmark/theBenchmark.p',fact_649_power__gt1)). 159.59/70.62 thf(20188,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)],[3711])). 159.59/70.62 thf(6606,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (((C = zero_zero_nat) & (A @ zero_zero_nat)) | ? [D:nat]: ((ord_less_eq_nat @ (times_times_nat @ C @ D) @ B) & (ord_less_nat @ B @ (times_times_nat @ C @ (suc @ D))) & (A @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2533_split__div_H)). 159.59/70.62 thf(30624,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (((C = zero_zero_nat) & (A @ zero_zero_nat)) | ? [D:nat]: ((ord_less_eq_nat @ (times_times_nat @ C @ D) @ B) & (ord_less_nat @ B @ (times_times_nat @ C @ (suc @ D))) & (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6606])). 159.59/70.62 thf(4720,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se1412395901928357646or_nat @ A @ (bit_se1412395901928357646or_nat @ B @ C)) = (bit_se1412395901928357646or_nat @ B @ (bit_se1412395901928357646or_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6044_or_Oleft__commute)). 159.59/70.62 thf(23562,plain,((! [A:nat,B:nat,C:nat]: ((bit_se1412395901928357646or_nat @ A @ (bit_se1412395901928357646or_nat @ B @ C)) = (bit_se1412395901928357646or_nat @ B @ (bit_se1412395901928357646or_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4720])). 159.59/70.62 thf(3054,axiom,((! [A:complex,B:complex,C:num]: ((A = (divide1717551699836669952omplex @ B @ (numera6690914467698888265omplex @ C))) = ((((numera6690914467698888265omplex @ C) != zero_zero_complex) => ((times_times_complex @ A @ (numera6690914467698888265omplex @ C)) = B)) & ((A = zero_zero_complex) <= ((numera6690914467698888265omplex @ C) = zero_zero_complex)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1731_eq__divide__eq__numeral1_I1_J)). 159.59/70.62 thf(18068,plain,((! [A:complex,B:complex,C:num]: ((A = (divide1717551699836669952omplex @ B @ (numera6690914467698888265omplex @ C))) = (((~ ((numera6690914467698888265omplex @ C) = zero_zero_complex)) => ((times_times_complex @ A @ (numera6690914467698888265omplex @ C)) = B)) & ((A = zero_zero_complex) | ~ ((numera6690914467698888265omplex @ C) = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3054])). 159.59/70.62 thf(1008,axiom,((! [A:nat,B:nat,C:(nat > int)]: (((ord_less_nat @ (suc @ A) @ B) => ((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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7361_sum_Ocl__ivl__Suc)). 159.59/70.62 thf(11471,plain,((! [A:nat,B:nat,C:(nat > int)]: (((ord_less_nat @ (suc @ A) @ B) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008])). 159.59/70.62 thf(731,axiom,((! [A:int]: ((modulo_modulo_int @ A @ one_one_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3405_mod__by__1)). 159.59/70.62 thf(10612,plain,((! [A:int]: ((modulo_modulo_int @ A @ one_one_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[731])). 159.59/70.62 thf(5161,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((set_or1269000886237332187st_nat @ A @ B) = (insert_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6408_Icc__eq__insert__lb__nat)). 159.59/70.62 thf(25123,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((set_or1269000886237332187st_nat @ A @ B) = (insert_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5161])). 159.59/70.62 thf(3266,axiom,((! [A:real,B:real,C:real]: ((A != zero_zero_real) => ((B = (divide_divide_real @ C @ A)) = ((times_times_real @ B @ A) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2166_nonzero__eq__divide__eq)). 159.59/70.62 thf(18767,plain,((! [A:real,B:real,C:real]: ((~ (A = zero_zero_real)) => ((B = (divide_divide_real @ C @ A)) = ((times_times_real @ B @ A) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3266])). 159.59/70.62 thf(7370,axiom,(((neg_nu5851722552734809277nc_int @ one_one_int) = (numeral_numeral_int @ (bit1 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5747_dbl__inc__simps_I3_J)). 159.59/70.62 thf(33735,plain,(((neg_nu5851722552734809277nc_int @ one_one_int) = (numeral_numeral_int @ (bit1 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7370])). 159.59/70.62 thf(7424,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/sandbox/benchmark/theBenchmark.p',fact_8251_gbinomial__absorb__comp)). 159.59/70.62 thf(33901,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)],[7424])). 159.59/70.62 thf(6688,axiom,((! [A:num,B:num]: (((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))) & ((~ (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 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_max__number__of_I1_J)). 159.59/70.62 thf(30965,plain,((! [A:num,B:num]: (((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))) & ((~ (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 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6688])). 159.59/70.62 thf(156,axiom,((! [A:code_integer,B:code_integer]: ((~ ((! [C:code_integer]: (((dvd_dvd_Code_integer @ C @ one_one_Code_integer) => (((((times_3573771949741848930nteger @ A @ C) = one_one_Code_integer) => ((divide6298287555418463151nteger @ B @ A) != (times_3573771949741848930nteger @ B @ C))) <= ((divide6298287555418463151nteger @ one_one_Code_integer @ C) = A)) <= ((divide6298287555418463151nteger @ one_one_Code_integer @ A) = C))) <= (C != zero_z3403309356797280102nteger))) <= (A != zero_z3403309356797280102nteger))) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4195_is__unitE)). 159.59/70.62 thf(8724,plain,((! [A:code_integer,B:code_integer]: (~ (! [C:code_integer]: (((dvd_dvd_Code_integer @ C @ one_one_Code_integer) => ((((times_3573771949741848930nteger @ A @ C) = one_one_Code_integer) => (~ ((divide6298287555418463151nteger @ B @ A) = (times_3573771949741848930nteger @ B @ C)))) | ~ ((divide6298287555418463151nteger @ one_one_Code_integer @ C) = A) | ~ ((divide6298287555418463151nteger @ one_one_Code_integer @ A) = C))) | (C = zero_z3403309356797280102nteger)) | (A = zero_z3403309356797280102nteger)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 159.59/70.62 thf(3434,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_add__mono)). 159.59/70.62 thf(19290,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ C @ D) => (ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3434])). 159.59/70.62 thf(4773,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/sandbox/benchmark/theBenchmark.p',fact_4784_diff__numeral__simps_I2_J)). 159.59/70.62 thf(23748,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)],[4773])). 159.59/70.62 thf(1344,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/sandbox/benchmark/theBenchmark.p',fact_8232_gbinomial__pochhammer_H)). 159.59/70.62 thf(12591,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)],[1344])). 159.59/70.62 thf(6167,axiom,((! [A:nat,B:nat,C:nat]: ((ord_max_nat @ (ord_max_nat @ A @ B) @ C) = (ord_max_nat @ A @ (ord_max_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_max_Oassoc)). 159.59/70.62 thf(28980,plain,((! [A:nat,B:nat,C:nat]: ((ord_max_nat @ (ord_max_nat @ A @ B) @ C) = (ord_max_nat @ A @ (ord_max_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6167])). 159.59/70.62 thf(2126,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ A) => ((ord_less_real @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ B)) @ (suminf_real @ A)) <= (! [C:nat]: ((ord_less_real @ zero_zero_real @ (A @ C)) <= (ord_less_eq_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7990_sum__less__suminf)). 159.59/70.62 thf(15097,plain,((! [A:(nat > real),B:nat]: ((summable_real @ (A)) => ((ord_less_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ B)) @ (suminf_real @ (A))) | ~ (! [C:nat]: ((ord_less_real @ zero_zero_real @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2126])). 159.59/70.62 thf(8179,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/sandbox/benchmark/theBenchmark.p',fact_4225_even__two__times__div__two)). 159.59/70.62 thf(36406,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)],[8179])). 159.59/70.62 thf(6778,axiom,((! [A:set_nat,B:(nat > extended_enat),C:(nat > extended_enat)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((B @ D) != one_on7984719198319812577d_enat))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((C @ D) != one_on7984719198319812577d_enat))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((times_7803423173614009249d_enat @ (B @ D) @ (C @ D)) != one_on7984719198319812577d_enat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3722_prod_Ofinite__Collect__op)). 159.59/70.62 thf(31378,plain,((! [A:set_nat,B:(nat > extended_enat),C:(nat > extended_enat)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((B @ D) = one_on7984719198319812577d_enat))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((C @ D) = one_on7984719198319812577d_enat))))) => (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((times_7803423173614009249d_enat @ (B @ D) @ (C @ D)) = one_on7984719198319812577d_enat))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6778])). 159.59/70.62 thf(1725,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (~ (ord_less_eq_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4509_minf_I8_J)). 159.59/70.62 thf(13829,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (~ (ord_less_eq_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725])). 159.59/70.62 thf(98,axiom,((! [A:real]: ? [B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) & ! [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)))))) & ((tan_real @ B) = A) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7285_tan__total)). 159.59/70.62 thf(8550,plain,((! [A:real]: ? [B:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) & ! [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)))))) & ((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)],[98])). 159.59/70.62 thf(5672,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ one_one_real) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ one_one_real) <= (ord_less_eq_real @ B @ one_one_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2303_mult__le__one)). 159.59/70.62 thf(27022,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ one_one_real) => ((ord_less_eq_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (times_times_real @ A @ B) @ one_one_real) | ~ (ord_less_eq_real @ B @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5672])). 159.59/70.62 thf(2114,axiom,((! [A:num]: ((archim6058952711729229775r_real @ (numeral_numeral_real @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8174_floor__numeral)). 159.59/70.62 thf(15061,plain,((! [A:num]: ((archim6058952711729229775r_real @ (numeral_numeral_real @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2114])). 159.59/70.62 thf(5341,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/sandbox/benchmark/theBenchmark.p',fact_9538_Suc__0__xor__eq)). 159.59/70.62 thf(25812,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)],[5341])). 159.59/70.62 thf(1409,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/sandbox/benchmark/theBenchmark.p',fact_4551_signed__take__bit__Suc)). 159.59/70.62 thf(12846,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)],[1409])). 159.59/70.62 thf(5052,axiom,((ord_less_eq_num = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3108_dual__order_Oorder__iff__strict)). 159.59/70.62 thf(24748,plain,(((ord_less_eq_num) = (^ [A:num,B:num]: ((ord_less_num @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5052])). 159.59/70.62 thf(4704,axiom,((! [A:nat,B:nat,C:(nat > nat)]: (((groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_nat @ (C @ A) @ (groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8734_prod_OatLeast__Suc__atMost)). 159.59/70.62 thf(23514,plain,((! [A:nat,B:nat,C:(nat > nat)]: (((groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_nat @ (C @ A) @ (groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4704])). 159.59/70.62 thf(3864,axiom,((! [A:extended_enat]: ((plus_p3455044024723400733d_enat @ zero_z5237406670263579293d_enat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1881_comm__monoid__add__class_Oadd__0)). 159.59/70.62 thf(20689,plain,((! [A:extended_enat]: ((plus_p3455044024723400733d_enat @ zero_z5237406670263579293d_enat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3864])). 159.59/70.62 thf(5448,axiom,((! [A:num,B:num]: (((B = A) <= (ord_less_eq_num @ B @ A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2711_dual__order_Oantisym)). 159.59/70.62 thf(26261,plain,((! [A:num,B:num]: ((B = A) | ~ (ord_less_eq_num @ B @ A) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5448])). 159.59/70.62 thf(5155,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/sandbox/benchmark/theBenchmark.p',fact_2452_power__Suc__less__one)). 159.59/70.62 thf(25095,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)],[5155])). 159.59/70.62 thf(853,axiom,((! [A:extended_enat,B:(num > extended_enat),C:num,D:num]: ((ord_le72135733267957522d_enat @ A @ (B @ C)) => (((! [E:num,F:num]: ((ord_le2932123472753598470d_enat @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) <= (ord_less_eq_num @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3232_order__less__le__subst1)). 159.59/70.62 thf(11003,plain,((! [A:extended_enat,B:(num > extended_enat),C:num,D:num]: ((ord_le72135733267957522d_enat @ A @ (B @ C)) => (((! [E:num,F:num]: ((ord_le2932123472753598470d_enat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) | ~ (ord_less_eq_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[853])). 159.59/70.62 thf(7285,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) @ ($false)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1945_VEBT__internal_OminNull_Ocases)). 159.59/70.62 thf(33424,plain,((! [A:vEBT_VEBT]: (((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E))))) | ~ (! [B:$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)],[7285])). 159.59/70.62 thf(582,axiom,((! [A:real]: ((real_V1485227260804924795R_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (plus_plus_real @ A @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9209_scaleR__half__double)). 159.59/70.62 thf(10102,plain,((! [A:real]: ((real_V1485227260804924795R_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))) @ (plus_plus_real @ A @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[582])). 159.59/70.62 thf(888,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/sandbox/benchmark/theBenchmark.p',fact_7536_sum__power__add)). 159.59/70.62 thf(11106,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)],[888])). 159.59/70.62 thf(6651,axiom,((! [A:real]: ((power_power_real @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1687_power__Suc0__right)). 159.59/70.62 thf(30788,plain,((! [A:real]: ((power_power_real @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6651])). 159.59/70.62 thf(7839,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/sandbox/benchmark/theBenchmark.p',fact_2207_Euclidean__Division_Odiv__eq__0__iff)). 159.59/70.62 thf(35311,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)],[7839])). 159.59/70.62 thf(4891,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/sandbox/benchmark/theBenchmark.p',fact_4240_even__unset__bit__iff)). 159.59/70.62 thf(24157,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)],[4891])). 159.59/70.62 thf(2596,axiom,((! [A:set_nat,B:set_nat]: (((ord_less_eq_set_nat @ B @ A) => (A = B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2733_order__antisym)). 159.59/70.62 thf(16597,plain,((! [A:set_nat,B:set_nat]: (((ord_less_eq_set_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2596])). 159.59/70.62 thf(1374,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/sandbox/benchmark/theBenchmark.p',fact_8131_Maclaurin__zero)). 159.59/70.62 thf(12715,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)],[1374])). 159.59/70.62 thf(6647,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B)) = ((B = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6625_of__nat__zero__less__power__iff)). 159.59/70.62 thf(30776,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B)) = ((B = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6647])). 159.59/70.62 thf(670,axiom,((! [A:real,B:real]: (((ord_less_real @ B @ A) <= (~ (ord_less_real @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2839_linorder__neqE)). 159.59/70.62 thf(10394,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)],[670])). 159.59/70.62 thf(5993,axiom,(((semiri4449623510593786356d_enat @ (suc @ zero_zero_nat)) = one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8055_fact__Suc__0)). 159.59/70.62 thf(28414,plain,(((semiri4449623510593786356d_enat @ (suc @ zero_zero_nat)) = one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5993])). 159.59/70.62 thf(1478,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/sandbox/benchmark/theBenchmark.p',fact_7011_cos__2npi)). 159.59/70.62 thf(13078,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)],[1478])). 159.59/70.62 thf(576,axiom,((! [A:complex]: (((im @ A) = zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ (re @ A)) => ((csqrt @ A) = (real_V4546457046886955230omplex @ (sqrt @ (re @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9649_csqrt__of__real__nonneg)). 159.59/70.62 thf(10084,plain,((! [A:complex]: (((im @ A) = zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ (re @ A)) => ((csqrt @ A) = (real_V4546457046886955230omplex @ (sqrt @ (re @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[576])). 159.59/70.62 thf(3826,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (minus_minus_complex @ (A @ (suc @ C)) @ (A @ C))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_complex @ (A @ B) @ (A @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7963_sum__lessThan__telescope)). 159.59/70.62 thf(20550,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (minus_minus_complex @ (A @ (suc @ C)) @ (A @ C))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_complex @ (A @ B) @ (A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3826])). 159.59/70.62 thf(4314,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat,D:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => (((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A) => ((ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ A @ C) @ (times_7803423173614009249d_enat @ B @ D)) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C))) <= (ord_le2932123472753598470d_enat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2000_mult__mono_H)). 159.59/70.62 thf(22082,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat,D:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => (((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A) => ((ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ A @ C) @ (times_7803423173614009249d_enat @ B @ D)) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C))) | ~ (ord_le2932123472753598470d_enat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4314])). 159.59/70.62 thf(4916,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3072_order_Oorder__iff__strict)). 159.59/70.62 thf(24244,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4916])). 159.59/70.62 thf(6670,axiom,((! [A:vEBT_VEBT,B:nat]: (((~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ D @ E @ F)) => ((D = B) & (vEBT_VEBT_valid @ F @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) & (case_o184042715313410164at_nat @ (! [G:vEBT_VEBT]: ((member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E)) => (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H)))) & ~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) @ (produc6081775807080527818_nat_o @ (^ [G:nat,H:nat]: ((ord_less_eq_nat @ G @ H) & (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [I:nat]: (((? [J:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ E @ I) @ J)) = (vEBT_V8194947554948674370ptions @ F @ I)) <= (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((G = H) => (! [I:vEBT_VEBT]: ((member_VEBT_VEBT @ I @ (set_VEBT_VEBT2 @ E)) => (~ (? [J:nat]: (vEBT_V8194947554948674370ptions @ I @ J)))))) & (((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ H) & ! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => (((ord_less_eq_nat @ I @ H) & (ord_less_nat @ G @ I)) <= (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ I)))) <= (G != H))))) @ C) & ((size_s6755466524823107622T_VEBT @ E) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) & ! [G:vEBT_VEBT]: ((vEBT_VEBT_valid @ G @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) <= (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E))))))) <= ((B = one_one_nat) <= (? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))))) <= (~ (vEBT_VEBT_valid @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10070_VEBT__internal_Ovalid_H_Oelims_I3_J)). 159.59/70.62 thf(30847,plain,((! [A:vEBT_VEBT,B:nat]: (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ D @ E @ F)) => ((D = B) & (vEBT_VEBT_valid @ F @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) & (case_o184042715313410164at_nat @ (! [G:vEBT_VEBT]: ((member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E)) => (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H)))) & ~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) @ (produc6081775807080527818_nat_o @ (^ [G:nat,H:nat]: ((ord_less_eq_nat @ G @ H) & (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [I:nat]: (((? [J:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ E @ I) @ J)) = (vEBT_V8194947554948674370ptions @ F @ I)) | ~ (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((G = H) => (! [I:vEBT_VEBT]: ((member_VEBT_VEBT @ I @ (set_VEBT_VEBT2 @ E)) => (~ (? [J:nat]: (vEBT_V8194947554948674370ptions @ I @ J)))))) & (((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ H) & ! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => (((ord_less_eq_nat @ I @ H) & (ord_less_nat @ G @ I)) | ~ (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ I)))) | (G = H))))) @ C) & ((size_s6755466524823107622T_VEBT @ E) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) & ! [G:vEBT_VEBT]: ((vEBT_VEBT_valid @ G @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E)))))) | ~ ((B = one_one_nat) | ~ (? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D)))) | (vEBT_VEBT_valid @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6670])). 159.59/70.62 thf(7752,axiom,((! [A:nat,B:nat]: ((~ (bit_se1148574629649215175it_nat @ B @ A)) <= ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6417_exp__eq__0__imp__not__bit)). 159.59/70.62 thf(35047,plain,((! [A:nat,B:nat]: (~ (bit_se1148574629649215175it_nat @ B @ A) | ~ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7752])). 159.59/70.62 thf(6446,axiom,(((abs_abs_real @ (uminus_uminus_real @ one_one_real)) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5415_abs__neg__one)). 159.59/70.62 thf(30044,plain,(((abs_abs_real @ (uminus_uminus_real @ one_one_real)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6446])). 159.59/70.62 thf(2323,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((ord_less_real @ (abs_abs_real @ B) @ one_one_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))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5925_arctan__add)). 159.59/70.62 thf(15719,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((ord_less_real @ (abs_abs_real @ B) @ one_one_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))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2323])). 159.59/70.62 thf(3973,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/sandbox/benchmark/theBenchmark.p',fact_1328_add__mono1)). 159.59/70.62 thf(21030,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)],[3973])). 159.59/70.62 thf(4820,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/sandbox/benchmark/theBenchmark.p',fact_9083_binomial__absorb__comp)). 159.59/70.62 thf(23932,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)],[4820])). 159.59/70.62 thf(4399,axiom,((ord_less_real @ zero_zero_real @ one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2133_less__numeral__extra_I1_J)). 159.59/70.62 thf(22346,plain,((ord_less_real @ zero_zero_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4399])). 159.59/70.62 thf(1587,axiom,((! [A:complex]: (ord_less_eq_real @ zero_zero_real @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6900_norm__ge__zero)). 159.59/70.62 thf(13401,plain,((! [A:complex]: (ord_less_eq_real @ zero_zero_real @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587])). 159.59/70.62 thf(4250,axiom,((! [A:nat,B:int]: ((ord_less_int @ (bit_ri631733984087533419it_int @ A @ B) @ zero_zero_int) = (bit_se1146084159140164899it_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6338_signed__take__bit__negative__iff)). 159.59/70.62 thf(21893,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)],[4250])). 159.59/70.62 thf(6554,axiom,((! [A:nat,B:num]: ((minus_minus_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (minus_minus_nat @ A @ (pred_numeral @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5689_diff__Suc__numeral)). 159.59/70.62 thf(30443,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)],[6554])). 159.59/70.62 thf(1141,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => (((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_real @ B @ A)) <= (ord_less_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8992_inverse__less__iff__less__neg)). 159.59/70.62 thf(11908,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => (((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_real @ B @ A)) | ~ (ord_less_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141])). 159.59/70.62 thf(4927,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/sandbox/benchmark/theBenchmark.p',fact_4789_diff__numeral__simps_I3_J)). 159.59/70.62 thf(24281,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)],[4927])). 159.59/70.62 thf(4272,axiom,((! [A:extended_enat,B:extended_enat]: ((A != B) => ((ord_le72135733267957522d_enat @ B @ A) <= (~ (ord_le72135733267957522d_enat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2838_linorder__neqE)). 159.59/70.62 thf(21958,plain,((! [A:extended_enat,B:extended_enat]: ((~ (A = B)) => ((ord_le72135733267957522d_enat @ B @ A) | (ord_le72135733267957522d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4272])). 159.59/70.62 thf(924,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/sandbox/benchmark/theBenchmark.p',fact_7265_less__powr__iff)). 159.59/70.62 thf(11212,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)],[924])). 159.59/70.62 thf(8061,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/sandbox/benchmark/theBenchmark.p',fact_3510_mod__mult__div__eq)). 159.59/70.62 thf(36027,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)],[8061])). 159.59/70.62 thf(7894,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4475_minf_I4_J)). 159.59/70.62 thf(35487,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7894])). 159.59/70.62 thf(6044,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (nat2 @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9470_even__nat__iff)). 159.59/70.62 thf(28583,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (nat2 @ A)) = (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6044])). 159.59/70.62 thf(7005,axiom,((! [A:real]: (((cosh_real @ A) = zero_zero_real) = ((power_power_real @ (exp_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus_uminus_real @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9362_cosh__zero__iff)). 159.59/70.62 thf(32372,plain,((! [A:real]: (((cosh_real @ A) = zero_zero_real) = ((power_power_real @ (exp_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus_uminus_real @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7005])). 159.59/70.62 thf(6425,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/sandbox/benchmark/theBenchmark.p',fact_4381_one__mod__2__pow__eq)). 159.59/70.62 thf(29949,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)],[6425])). 159.59/70.62 thf(6343,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F) @ A) = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) <= ((A = B) & (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_del__single__cont)). 159.59/70.62 thf(29618,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F) @ A) = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) | ~ ((A = B) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6343])). 159.59/70.62 thf(3469,axiom,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) => (ord_less_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3066_not__le__imp__less)). 159.59/70.62 thf(19396,plain,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) => (ord_less_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3469])). 159.59/70.62 thf(7391,axiom,((! [A:nat,B:real,C:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ B @ C)) => ((ord_less_real @ one_one_real @ B) => ((ord_less_real @ (log @ B @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6773_log__of__power__less)). 159.59/70.62 thf(33808,plain,((! [A:nat,B:real,C:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ B @ C)) => ((ord_less_real @ one_one_real @ B) => ((ord_less_real @ (log @ B @ (semiri5074537144036343181t_real @ A)) @ (semiri5074537144036343181t_real @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7391])). 159.59/70.62 thf(2069,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ (ln_ln_real @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5132_ln__bound)). 159.59/70.62 thf(14921,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)],[2069])). 159.59/70.62 thf(1644,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ (uminus_uminus_int @ one_one_int)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5970_bit_Oconj__one__right)). 159.59/70.62 thf(13583,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ (uminus_uminus_int @ one_one_int)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644])). 159.59/70.62 thf(2502,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/sandbox/benchmark/theBenchmark.p',fact_7042_suminf__mult2)). 159.59/70.62 thf(16307,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)],[2502])). 159.59/70.62 thf(632,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/sandbox/benchmark/theBenchmark.p',fact_5398_abs__divide)). 159.59/70.62 thf(10278,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)],[632])). 159.59/70.62 thf(1182,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/sandbox/benchmark/theBenchmark.p',fact_8147_Maclaurin__sin__expansion)). 159.59/70.62 thf(12037,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)],[1182])). 159.59/70.62 thf(3953,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = B) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1523_add__cancel__left__left)). 159.59/70.62 thf(20972,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = B) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3953])). 159.59/70.62 thf(7692,axiom,((! [A:nat]: ((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_nat @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_power2__eq__square)). 159.59/70.62 thf(34830,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)],[7692])). 159.59/70.62 thf(1536,axiom,((! [A:real,B:int]: ((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)))) => ((archim8280529875227126926d_real @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6147_round__unique_H)). 159.59/70.62 thf(13250,plain,((! [A:real,B:int]: ((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)))) => ((archim8280529875227126926d_real @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1536])). 159.59/70.62 thf(3145,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((C != A) <= (ord_less_real @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4473_minf_I4_J)). 159.59/70.62 thf(18372,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (C = A) | ~ (ord_less_real @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3145])). 159.59/70.62 thf(3000,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ bot_bot_set_nat) = (A = bot_bot_set_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2595_subset__empty)). 159.59/70.62 thf(17902,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)],[3000])). 159.59/70.62 thf(7437,axiom,((! [A:num,B:nat]: ((bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ B)) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6329_bit__numeral__Bit1__Suc__iff)). 159.59/70.62 thf(33940,plain,((! [A:num,B:nat]: ((bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ B)) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7437])). 159.59/70.62 thf(1189,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/sandbox/benchmark/theBenchmark.p',fact_6885_norm__mult__numeral2)). 159.59/70.62 thf(12058,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)],[1189])). 159.59/70.62 thf(3014,axiom,((! [A:real]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ zero_zero_int) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8186_floor__less__zero)). 159.59/70.62 thf(17945,plain,((! [A:real]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ zero_zero_int) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3014])). 159.59/70.62 thf(2863,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/sandbox/benchmark/theBenchmark.p',fact_7237_powr__less__cancel)). 159.59/70.62 thf(17467,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)],[2863])). 159.59/70.62 thf(4294,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/sandbox/benchmark/theBenchmark.p',fact_7010_sin__cos__squared__add)). 159.59/70.62 thf(22029,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)],[4294])). 159.59/70.62 thf(385,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B)) @ C) = (ord_less_real @ (uminus_uminus_real @ B) @ (real_V1485227260804924795R_real @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9281_pos__minus__divideR__less__eq)). 159.59/70.62 thf(9455,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B)) @ C) = (ord_less_real @ (uminus_uminus_real @ B) @ (real_V1485227260804924795R_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])). 159.59/70.62 thf(3265,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (comm_s7457072308508201937r_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8212_pochhammer__pos)). 159.59/70.62 thf(18764,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (comm_s7457072308508201937r_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3265])). 159.59/70.62 thf(8131,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/sandbox/benchmark/theBenchmark.p',fact_1749_div__mult__self1)). 159.59/70.62 thf(36247,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)],[8131])). 159.59/70.62 thf(7028,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/sandbox/benchmark/theBenchmark.p',fact_3872_even__mult__iff)). 159.59/70.62 thf(32441,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)],[7028])). 159.59/70.62 thf(142,axiom,((! [A:num]: ~ (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5142_not__zero__le__neg__numeral)). 159.59/70.62 thf(8683,plain,((! [A:num]: ~ (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 159.59/70.62 thf(4686,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/sandbox/benchmark/theBenchmark.p',fact_7924_sum__SucD)). 159.59/70.62 thf(23454,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)],[4686])). 159.59/70.62 thf(2237,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= ((A = B) & (ord_less_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1202_add__mono__thms__linordered__field_I2_J)). 159.59/70.62 thf(15471,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ ((A = B) & (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2237])). 159.59/70.62 thf(6717,axiom,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1937_lambda__zero)). 159.59/70.62 thf(31157,plain,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6717])). 159.59/70.62 thf(765,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/sandbox/benchmark/theBenchmark.p',fact_8000_power__diff__sumr2)). 159.59/70.62 thf(10721,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)],[765])). 159.59/70.62 thf(1633,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/sandbox/benchmark/theBenchmark.p',fact_7180_sin__plus__sin)). 159.59/70.62 thf(13551,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)],[1633])). 159.59/70.62 thf(7223,axiom,((bit_se7882103937844011126it_nat = (^ [A:nat,B:nat]: (bit_se1412395901928357646or_nat @ B @ (bit_se547839408752420682it_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9557_set__bit__nat__def)). 159.59/70.62 thf(33231,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)],[7223])). 159.59/70.62 thf(1710,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((C != A) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4471_minf_I3_J)). 159.59/70.62 thf(13778,plain,((! [A:int]: ? [B:int]: ! [C:int]: (~ (C = A) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710])). 159.59/70.62 thf(7550,axiom,((! [A:complex,B:num,C:complex]: (((divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = C) = ((((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) = zero_zero_complex) => (C = zero_zero_complex)) & ((A = (times_times_complex @ C @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)))) <= ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) != zero_zero_complex)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4831_divide__eq__eq__numeral1_I2_J)). 159.59/70.62 thf(34340,plain,((! [A:complex,B:num,C:complex]: (((divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = C) = ((((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) = zero_zero_complex) => (C = zero_zero_complex)) & ((A = (times_times_complex @ C @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)))) | ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B)) = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7550])). 159.59/70.62 thf(5849,axiom,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: (((B @ C) = one_one_nat) <= (member_nat @ C @ A))) => ((groups708209901874060359at_nat @ B @ A) = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8457_prod_Oneutral)). 159.59/70.62 thf(27869,plain,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: (((B @ C) = one_one_nat) | ~ (member_nat @ C @ A))) => ((groups708209901874060359at_nat @ (B) @ A) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5849])). 159.59/70.62 thf(3157,axiom,((! [A:real]: ((powr_real @ one_one_real @ A) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7210_powr__one__eq__one)). 159.59/70.62 thf(18415,plain,((! [A:real]: ((powr_real @ one_one_real @ A) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3157])). 159.59/70.62 thf(8041,axiom,(((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_Suc__1)). 159.59/70.62 thf(35956,plain,(((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8041])). 159.59/70.62 thf(4169,axiom,((! [A:int,B:nat,C:nat]: ((ord_less_int @ one_one_int @ A) => ((ord_less_nat @ B @ C) <= (ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_power__less__imp__less__exp)). 159.59/70.62 thf(21628,plain,((! [A:int,B:nat,C:nat]: ((ord_less_int @ one_one_int @ A) => ((ord_less_nat @ B @ C) | ~ (ord_less_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4169])). 159.59/70.62 thf(4379,axiom,((! [A:int,B:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ (uminus_uminus_int @ B)) = (ord_less_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4617_neg__less__iff__less)). 159.59/70.62 thf(22278,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)],[4379])). 159.59/70.62 thf(4296,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 @ A @ B) & (ord_less_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1205_add__mono__thms__linordered__field_I5_J)). 159.59/70.62 thf(22035,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 @ A @ B) & (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4296])). 159.59/70.62 thf(2145,axiom,((! [A:(nat > extended_enat),B:nat,C:nat]: ((! [D:nat]: (ord_le72135733267957522d_enat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_le72135733267957522d_enat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_lift__Suc__mono__less)). 159.59/70.62 thf(15174,plain,((! [A:(nat > extended_enat),B:nat,C:nat]: ((! [D:nat]: (ord_le72135733267957522d_enat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_le72135733267957522d_enat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2145])). 159.59/70.62 thf(2653,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_nat @ B @ (nat2 @ A)) = (ord_less_eq_int @ (semiri1314217659103216013at_int @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9446_le__nat__iff)). 159.59/70.62 thf(16801,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_nat @ B @ (nat2 @ A)) = (ord_less_eq_int @ (semiri1314217659103216013at_int @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2653])). 159.59/70.62 thf(6143,axiom,((! [A:(nat > $o),B:nat]: (finite_finite_nat @ (collect_nat @ (^ [C:nat]: ((A @ C) & (ord_less_nat @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3640_finite__M__bounded__by__nat)). 159.59/70.62 thf(28895,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)],[6143])). 159.59/70.62 thf(4033,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ (numera1916890842035813515d_enat @ (bit0 @ one))) = (plus_p3455044024723400733d_enat @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_mult__2__right)). 159.59/70.62 thf(21206,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ (numera1916890842035813515d_enat @ (bit0 @ one))) = (plus_p3455044024723400733d_enat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4033])). 159.59/70.62 thf(4279,axiom,((neg_nu8557863876264182079omplex = (^ [A:complex]: (plus_plus_complex @ (plus_plus_complex @ A @ A) @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5911_dbl__inc__def)). 159.59/70.62 thf(21979,plain,(((neg_nu8557863876264182079omplex) = (^ [A:complex]: (plus_plus_complex @ (plus_plus_complex @ A @ A) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4279])). 159.59/70.62 thf(1904,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/sandbox/benchmark/theBenchmark.p',fact_5813_of__int__0__le__iff)). 159.59/70.62 thf(14401,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)],[1904])). 159.59/70.62 thf(3467,axiom,((! [A:real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3375_double__eq__0__iff)). 159.59/70.62 thf(19390,plain,((! [A:real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3467])). 159.59/70.62 thf(2129,axiom,((! [A:real]: (((ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => (ord_less_eq_real @ (sin_real @ A) @ zero_zero_real)) <= (ord_less_eq_real @ pi @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6869_sin__le__zero)). 159.59/70.62 thf(15129,plain,((! [A:real]: (((ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => (ord_less_eq_real @ (sin_real @ A) @ zero_zero_real)) | ~ (ord_less_eq_real @ pi @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2129])). 159.59/70.62 thf(188,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/sandbox/benchmark/theBenchmark.p',fact_9583_or__int__def)). 159.59/70.62 thf(8832,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)],[188])). 159.59/70.62 thf(6272,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ A) => (ord_less_eq_nat @ (suc @ zero_zero_nat) @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2396_nat__one__le__power)). 159.59/70.62 thf(29385,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ A) => (ord_less_eq_nat @ (suc @ zero_zero_nat) @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6272])). 159.59/70.62 thf(2029,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((bit_se2925701944663578781it_nat @ B @ (nat2 @ A)) = (nat2 @ (bit_se2923211474154528505it_int @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9460_take__bit__nat__eq)). 159.59/70.62 thf(14804,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((bit_se2925701944663578781it_nat @ B @ (nat2 @ A)) = (nat2 @ (bit_se2923211474154528505it_int @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2029])). 159.59/70.62 thf(777,axiom,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((groups2073611262835488442omplex @ C @ (insert_nat @ B @ A)) = (plus_plus_complex @ (C @ B) @ (groups2073611262835488442omplex @ C @ A))) <= (~ (member_nat @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7342_sum_Oinsert)). 159.59/70.62 thf(10756,plain,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((groups2073611262835488442omplex @ (C) @ (insert_nat @ B @ A)) = (plus_plus_complex @ (C @ B) @ (groups2073611262835488442omplex @ (C) @ A))) | (member_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[777])). 159.59/70.62 thf(6500,axiom,((! [A:nat,B:real]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_real @ (root @ A @ B) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9523_odd__real__root__pow)). 159.59/70.62 thf(30246,plain,((! [A:nat,B:real]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_real @ (root @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6500])). 159.59/70.62 thf(7807,axiom,((! [A:nat]: ((plus_plus_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_add__2__eq__Suc_H)). 159.59/70.62 thf(35206,plain,((! [A:nat]: ((plus_plus_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7807])). 159.59/70.62 thf(5554,axiom,(((minus_minus_complex @ one_one_complex @ one_one_complex) = zero_zero_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1656_diff__numeral__special_I9_J)). 159.59/70.62 thf(26614,plain,(((minus_minus_complex @ one_one_complex @ one_one_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5554])). 159.59/70.62 thf(3672,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((ord_less_eq_real @ (groups6591440286371151544t_real @ B @ A) @ (groups6591440286371151544t_real @ C @ A)) <= (! [D:nat]: ((ord_less_eq_real @ (B @ D) @ (C @ D)) <= (member_nat @ D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7395_sum__mono)). 159.59/70.62 thf(20047,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((ord_less_eq_real @ (groups6591440286371151544t_real @ (B) @ A) @ (groups6591440286371151544t_real @ (C) @ A)) | ~ (! [D:nat]: ((ord_less_eq_real @ (B @ D) @ (C @ D)) | ~ (member_nat @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3672])). 159.59/70.62 thf(314,axiom,((! [A:real,B:real]: ((cosh_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ (times_times_real @ (cosh_real @ A) @ (cosh_real @ B)) @ (times_times_real @ (sinh_real @ A) @ (sinh_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9330_cosh__diff)). 159.59/70.62 thf(9217,plain,((! [A:real,B:real]: ((cosh_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ (times_times_real @ (cosh_real @ A) @ (cosh_real @ B)) @ (times_times_real @ (sinh_real @ A) @ (sinh_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 159.59/70.62 thf(5346,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/sandbox/benchmark/theBenchmark.p',fact_4364_in__set__replicate)). 159.59/70.62 thf(25838,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)],[5346])). 159.59/70.62 thf(5911,axiom,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1495_mult__zero__right)). 159.59/70.62 thf(28102,plain,((! [A:int]: ((times_times_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5911])). 159.59/70.62 thf(6178,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2935_order__less__imp__not__less)). 159.59/70.62 thf(29018,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6178])). 159.59/70.62 thf(4951,axiom,((! [A:complex,B:complex,C:complex]: (((A != zero_zero_complex) => ((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ B @ (times_times_complex @ C @ A)) @ A))) & (((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (uminus1482373934393186551omplex @ C)) <= (A = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5254_add__divide__eq__if__simps_I5_J)). 159.59/70.62 thf(24350,plain,((! [A:complex,B:complex,C:complex]: (((~ (A = zero_zero_complex)) => ((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (minus_minus_complex @ B @ (times_times_complex @ C @ A)) @ A))) & (((minus_minus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (uminus1482373934393186551omplex @ C)) | ~ (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4951])). 159.59/70.62 thf(1950,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/sandbox/benchmark/theBenchmark.p',fact_2438_divide__le__eq__1)). 159.59/70.62 thf(14541,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)],[1950])). 159.59/70.62 thf(3135,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ B @ C) => ((divide_divide_int @ C @ (divide_divide_int @ B @ A)) = (times_times_int @ (divide_divide_int @ C @ B) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4079_div__div__eq__right)). 159.59/70.62 thf(18340,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ B @ C) => ((divide_divide_int @ C @ (divide_divide_int @ B @ A)) = (times_times_int @ (divide_divide_int @ C @ B) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3135])). 159.59/70.62 thf(4804,axiom,((! [A:nat,B:(nat > real),C:nat,D:(nat > real),E:real]: (((! [F:nat]: (((D @ F) = zero_zero_real) <= (ord_less_nat @ C @ F))) => ((times_times_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (B @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ A)) @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (D @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ C))) = (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (groups6591440286371151544t_real @ (^ [G:nat]: (times_times_real @ (B @ G) @ (D @ (minus_minus_nat @ F @ G)))) @ (set_ord_atMost_nat @ F)) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ (plus_plus_nat @ A @ C))))) <= (! [F:nat]: (((B @ F) = zero_zero_real) <= (ord_less_nat @ A @ F)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8918_polynomial__product)). 159.59/70.62 thf(23841,plain,((! [A:nat,B:(nat > real),C:nat,D:(nat > real),E:real]: (((! [F:nat]: (((D @ F) = zero_zero_real) | ~ (ord_less_nat @ C @ F))) => ((times_times_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (B @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ A)) @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (D @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ C))) = (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (groups6591440286371151544t_real @ (^ [G:nat]: (times_times_real @ (B @ G) @ (D @ (minus_minus_nat @ F @ G)))) @ (set_ord_atMost_nat @ F)) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ (plus_plus_nat @ A @ C))))) | ~ (! [F:nat]: (((B @ F) = zero_zero_real) | ~ (ord_less_nat @ A @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4804])). 159.59/70.62 thf(1845,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/sandbox/benchmark/theBenchmark.p',fact_7876_sum_OlessThan__Suc)). 159.59/70.62 thf(14217,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)],[1845])). 159.59/70.62 thf(4659,axiom,((! [A:num]: ((minus_minus_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ one_one_real)) = (numeral_numeral_real @ (inc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5709_diff__numeral__special_I6_J)). 159.59/70.62 thf(23358,plain,((! [A:num]: ((minus_minus_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ one_one_real)) = (numeral_numeral_real @ (inc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4659])). 159.59/70.62 thf(2523,axiom,((! [A:num]: ((neg_numeral_dbl_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3860_dbl__simps_I5_J)). 159.59/70.62 thf(16371,plain,((! [A:num]: ((neg_numeral_dbl_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2523])). 159.59/70.62 thf(40,axiom,((! [A:complex]: ((sinh_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sinh_complex @ A)) @ (cosh_complex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9338_sinh__double)). 159.59/70.62 thf(8371,plain,((! [A:complex]: ((sinh_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (times_times_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ (sinh_complex @ A)) @ (cosh_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[40])). 159.59/70.62 thf(3197,axiom,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (semiri1314217659103216013at_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6666_of__nat__0__le__iff)). 159.59/70.62 thf(18535,plain,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (semiri1314217659103216013at_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3197])). 159.59/70.62 thf(8080,axiom,((! [A:num]: (one != (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_semiring__norm_I83_J)). 159.59/70.62 thf(36088,plain,((! [A:num]: ~ (one = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8080])). 159.59/70.62 thf(4782,axiom,(((semiri5074537144036343181t_real @ one_one_nat) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6551_of__nat__1)). 159.59/70.62 thf(23776,plain,(((semiri5074537144036343181t_real @ one_one_nat) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4782])). 159.59/70.62 thf(2910,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3147_dual__order_Ostrict__implies__order)). 159.59/70.62 thf(17623,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2910])). 159.59/70.62 thf(3387,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/sandbox/benchmark/theBenchmark.p',fact_6883_norm__divide__numeral)). 159.59/70.62 thf(19139,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)],[3387])). 159.59/70.62 thf(6212,axiom,((~ (! [A:nat]: ((some_nat @ A) != (vEBT_vebt_mint @ summary))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062summin_O_ASome_Asummin_A_061_Avebt__mint_Asummary_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 159.59/70.62 thf(29128,plain,((~ (! [A:nat]: ~ ((some_nat @ A) = (vEBT_vebt_mint @ summary))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6212])). 159.59/70.62 thf(6253,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/sandbox/benchmark/theBenchmark.p',fact_6568_of__nat__power__eq__of__nat__cancel__iff)). 159.59/70.62 thf(29261,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)],[6253])). 159.59/70.62 thf(2172,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/sandbox/benchmark/theBenchmark.p',fact_3523_cancel__div__mod__rules_I1_J)). 159.59/70.62 thf(15253,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)],[2172])). 159.59/70.62 thf(698,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/sandbox/benchmark/theBenchmark.p',fact_9514_sgn__real__def)). 159.59/70.62 thf(10490,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)],[698])). 159.59/70.62 thf(8246,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/sandbox/benchmark/theBenchmark.p',fact_1743_div__mult__self3)). 159.59/70.62 thf(36765,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)],[8246])). 159.59/70.62 thf(4877,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1899_old_Onat_Odistinct_I1_J)). 159.59/70.62 thf(24111,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4877])). 159.59/70.62 thf(6761,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (B = (ord_max_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_max_OorderE)). 159.59/70.62 thf(31314,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (B = (ord_max_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6761])). 159.59/70.62 thf(5480,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/sandbox/benchmark/theBenchmark.p',fact_2525_power__eq__if)). 159.59/70.62 thf(26378,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)],[5480])). 159.59/70.62 thf(4725,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ B) => (((divide_divide_nat @ B @ A) = C) = (B = (times_times_nat @ C @ A)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4139_dvd__div__eq__mult)). 159.59/70.62 thf(23577,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ B) => (((divide_divide_nat @ B @ A) = C) = (B = (times_times_nat @ C @ A)))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4725])). 159.59/70.62 thf(1265,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/sandbox/benchmark/theBenchmark.p',fact_3944_dvd__mult)). 159.59/70.62 thf(12340,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)],[1265])). 159.59/70.62 thf(7232,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6699_of__nat__dvd__iff)). 159.59/70.62 thf(33263,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)],[7232])). 159.59/70.62 thf(5462,axiom,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1081_mult_Oright__neutral)). 159.59/70.62 thf(26315,plain,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5462])). 159.59/70.62 thf(1855,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/sandbox/benchmark/theBenchmark.p',fact_6810_sin__2npi)). 159.59/70.62 thf(14248,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)],[1855])). 159.59/70.62 thf(2994,axiom,(((arcsin @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7378_arcsin__minus__1)). 159.59/70.62 thf(17887,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)],[2994])). 159.59/70.62 thf(3362,axiom,((! [A:real,B:complex,C:complex]: ((times_times_complex @ (real_V2046097035970521341omplex @ A @ B) @ C) = (real_V2046097035970521341omplex @ A @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9188_mult__scaleR__left)). 159.59/70.62 thf(19058,plain,((! [A:real,B:complex,C:complex]: ((times_times_complex @ (real_V2046097035970521341omplex @ A @ B) @ C) = (real_V2046097035970521341omplex @ A @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3362])). 159.59/70.62 thf(4158,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5237_pos__minus__divide__less__eq)). 159.59/70.62 thf(21591,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = (ord_less_real @ (uminus_uminus_real @ B) @ (times_times_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4158])). 159.59/70.62 thf(1244,axiom,((code_bit_cut_integer = (^ [A:code_integer]: (produc6677183202524767010eger_o @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9761_bit__cut__integer__def)). 159.59/70.62 thf(12279,plain,(((code_bit_cut_integer) = (^ [A:code_integer]: (produc6677183202524767010eger_o @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244])). 159.59/70.62 thf(7725,axiom,((sqrt = (root @ (numeral_numeral_nat @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9513_sqrt__def)). 159.59/70.62 thf(34959,plain,(((sqrt) = (root @ (numeral_numeral_nat @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7725])). 159.59/70.62 thf(2071,axiom,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => ((finite_finite_nat @ B) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3765_rev__finite__subset)). 159.59/70.62 thf(14926,plain,((! [A:set_nat,B:set_nat]: ((finite_finite_nat @ A) => ((finite_finite_nat @ B) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2071])). 159.59/70.62 thf(1892,axiom,((! [A:num,B:num,C:(num > extended_enat),D:extended_enat]: ((ord_less_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)) <= (ord_le2932123472753598470d_enat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3246_order__less__le__subst2)). 159.59/70.62 thf(14363,plain,((! [A:num,B:num,C:(num > extended_enat),D:extended_enat]: ((ord_less_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)) | ~ (ord_le2932123472753598470d_enat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1892])). 159.59/70.62 thf(7540,axiom,((one_one_complex != (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4974_one__neq__neg__one)). 159.59/70.62 thf(34308,plain,((~ (one_one_complex = (uminus1482373934393186551omplex @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7540])). 159.59/70.62 thf(4195,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (real_V7735802525324610683m_real @ A)) = (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6897_zero__less__norm__iff)). 159.59/70.62 thf(21700,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (real_V7735802525324610683m_real @ A)) = (~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4195])). 159.59/70.62 thf(4291,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le72135733267957522d_enat @ A @ C) <= (ord_le2932123472753598470d_enat @ B @ C)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3205_order__less__le__trans)). 159.59/70.62 thf(22015,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ C) | ~ (ord_le2932123472753598470d_enat @ B @ C) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4291])). 159.59/70.62 thf(226,axiom,((! [A:nat]: ((gbinomial_complex @ zero_zero_complex @ (suc @ A)) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8170_gbinomial__0_I2_J)). 159.59/70.62 thf(8942,plain,((! [A:nat]: ((gbinomial_complex @ zero_zero_complex @ (suc @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 159.59/70.62 thf(1719,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/sandbox/benchmark/theBenchmark.p',fact_7254_ln__powr)). 159.59/70.62 thf(13810,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)],[1719])). 159.59/70.62 thf(4381,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((B = (divide_divide_int @ C @ A)) = ((times_times_int @ B @ A) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4161_unit__eq__div2)). 159.59/70.62 thf(22284,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((B = (divide_divide_int @ C @ A)) = ((times_times_int @ B @ A) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4381])). 159.59/70.62 thf(1930,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3177_order__less__imp__le)). 159.59/70.62 thf(14477,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1930])). 159.59/70.62 thf(2990,axiom,((! [A:nat]: (((A != zero_zero_nat) => ((comm_s7457072308508201937r_real @ zero_zero_real @ A) = zero_zero_real)) & ((A = zero_zero_nat) => ((comm_s7457072308508201937r_real @ zero_zero_real @ A) = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8244_pochhammer__0__left)). 159.59/70.62 thf(17870,plain,((! [A:nat]: (((~ (A = zero_zero_nat)) => ((comm_s7457072308508201937r_real @ zero_zero_real @ A) = zero_zero_real)) & ((A = zero_zero_nat) => ((comm_s7457072308508201937r_real @ zero_zero_real @ A) = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2990])). 159.59/70.62 thf(2650,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/sandbox/benchmark/theBenchmark.p',fact_7902_sums__iff__shift)). 159.59/70.62 thf(16790,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)],[2650])). 159.59/70.62 thf(6764,axiom,((! [A:(nat > $o)]: ((~ (A @ zero_zero_nat)) => ((? [B:nat]: (~ (A @ B) & (A @ (suc @ B)))) <= (? [B:nat]: (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6135_exists__least__lemma)). 159.59/70.62 thf(31323,plain,((! [A:(nat > $o)]: ((~ (A @ zero_zero_nat)) => (? [B:nat]: (~ (A @ B) & (A @ (suc @ B))) | ~ (? [B:nat]: (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6764])). 159.59/70.62 thf(2210,axiom,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_ab__semigroup__add__class_Oadd__ac_I1_J)). 159.59/70.62 thf(15383,plain,((! [A:int,B:int,C:int]: ((plus_plus_int @ (plus_plus_int @ A @ B) @ C) = (plus_plus_int @ A @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2210])). 159.59/70.62 thf(5307,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_member @ (vEBT_Leaf @ A @ B) @ C) = (((C != zero_zero_nat) => ((C = one_one_nat) & ((C = one_one_nat) => (B)))) & ((A) <= (C = zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1808_vebt__member_Osimps_I1_J)). 159.59/70.62 thf(25649,plain,((! [A:$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)],[5307])). 159.59/70.62 thf(6347,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/sandbox/benchmark/theBenchmark.p',fact_5283_power2__eq__1__iff)). 159.59/70.62 thf(29633,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)],[6347])). 159.59/70.62 thf(1913,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/sandbox/benchmark/theBenchmark.p',fact_1577_zero__le__double__add__iff__zero__le__single__add)). 159.59/70.62 thf(14430,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)],[1913])). 159.59/70.62 thf(4439,axiom,((! [A:extended_enat,B:extended_enat]: (((times_7803423173614009249d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((A = zero_z5237406670263579293d_enat) | (B = zero_z5237406670263579293d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3322_imult__is__0)). 159.59/70.62 thf(22471,plain,((! [A:extended_enat,B:extended_enat]: (((times_7803423173614009249d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((A = zero_z5237406670263579293d_enat) | (B = zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4439])). 159.59/70.62 thf(2128,axiom,((! [A:(extended_enat > (extended_enat > $o)),B:set_nat,C:(nat > extended_enat),D:(nat > extended_enat)]: (((! [E:extended_enat,F:extended_enat,G:extended_enat,H:extended_enat]: (((A @ E @ G) & (A @ F @ H)) => (A @ (plus_p3455044024723400733d_enat @ E @ F) @ (plus_p3455044024723400733d_enat @ G @ H)))) => ((finite_finite_nat @ B) => ((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups7108830773950497114d_enat @ C @ B) @ (groups7108830773950497114d_enat @ D @ B))))) <= (A @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7483_sum_Orelated)). 159.59/70.62 thf(15103,plain,((! [A:(extended_enat > (extended_enat > $o)),B:set_nat,C:(nat > extended_enat),D:(nat > extended_enat)]: (((! [E:extended_enat,F:extended_enat,G:extended_enat,H:extended_enat]: (((A @ E @ G) & (A @ F @ H)) => (A @ (plus_p3455044024723400733d_enat @ E @ F) @ (plus_p3455044024723400733d_enat @ G @ H)))) => ((finite_finite_nat @ B) => ((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups7108830773950497114d_enat @ (C) @ B) @ (groups7108830773950497114d_enat @ (D) @ B))))) | ~ (A @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2128])). 159.59/70.62 thf(6064,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/sandbox/benchmark/theBenchmark.p',fact_1587_add__le__same__cancel2)). 159.59/70.62 thf(28643,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)],[6064])). 159.59/70.62 thf(4938,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ A @ C) @ D) = ((C != D) & (vEBT_V8194947554948674370ptions @ A @ D))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_dele__bmo__cont__corr)). 159.59/70.62 thf(24312,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((vEBT_V8194947554948674370ptions @ (vEBT_vebt_delete @ A @ C) @ D) = (~ (C = D) & (vEBT_V8194947554948674370ptions @ A @ D))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4938])). 159.59/70.62 thf(1401,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/sandbox/benchmark/theBenchmark.p',fact_8403_atMost__subset__iff)). 159.59/70.62 thf(12822,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)],[1401])). 159.59/70.62 thf(333,axiom,((! [A:complex]: ((plus_plus_complex @ A @ (cnj @ A)) = (real_V4546457046886955230omplex @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (re @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9701_complex__add__cnj)). 159.59/70.62 thf(9277,plain,((! [A:complex]: ((plus_plus_complex @ A @ (cnj @ A)) = (real_V4546457046886955230omplex @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (re @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 159.59/70.62 thf(2444,axiom,((! [A:num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2013_zero__less__numeral)). 159.59/70.62 thf(16123,plain,((! [A:num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2444])). 159.59/70.62 thf(663,axiom,((((=) @ list_nat) = (^ [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_list__eq__iff__nth__eq)). 159.59/70.62 thf(10369,plain,((((=) @ list_nat) = (^ [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[663])). 159.59/70.62 thf(5685,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/sandbox/benchmark/theBenchmark.p',fact_4759_left__minus__one__mult__self)). 159.59/70.62 thf(27082,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)],[5685])). 159.59/70.62 thf(2920,axiom,((plus_plus_real = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_add_Ocommute)). 159.59/70.62 thf(17659,plain,(((plus_plus_real) = (^ [A:real,B:real]: (plus_plus_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2920])). 159.59/70.62 thf(2840,axiom,((! [A:nat,B:real]: ((exp_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ B)) = (power_power_real @ (exp_real @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6733_exp__of__nat__mult)). 159.59/70.62 thf(17385,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)],[2840])). 159.59/70.62 thf(7956,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ (power_power_nat @ A @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_power__Suc2)). 159.59/70.62 thf(35685,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)],[7956])). 159.59/70.62 thf(2303,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((plus_p5714425477246183910nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B) @ (modulo364778990260209775nteger @ A @ B)) @ C) = (plus_p5714425477246183910nteger @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3521_cancel__div__mod__rules_I1_J)). 159.59/70.62 thf(15665,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((plus_p5714425477246183910nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B) @ (modulo364778990260209775nteger @ A @ B)) @ C) = (plus_p5714425477246183910nteger @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2303])). 159.59/70.62 thf(4164,axiom,((! [A:real,B:int]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ B) = (ord_less_eq_real @ A @ (minus_minus_real @ (ring_1_of_int_real @ B) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7143_ceiling__less__iff)). 159.59/70.62 thf(21611,plain,((! [A:real,B:int]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ B) = (ord_less_eq_real @ A @ (minus_minus_real @ (ring_1_of_int_real @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4164])). 159.59/70.62 thf(3721,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/sandbox/benchmark/theBenchmark.p',fact_6927_norm__triangle__ineq)). 159.59/70.62 thf(20220,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)],[3721])). 159.59/70.62 thf(587,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)) = (ord_less_real @ (real_V1485227260804924795R_real @ A @ B) @ C)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9258_pos__less__divideR__eq)). 159.59/70.62 thf(10116,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)) = (ord_less_real @ (real_V1485227260804924795R_real @ A @ B) @ C)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[587])). 159.59/70.62 thf(4918,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4067_unit__mult__left__cancel)). 159.59/70.62 thf(24253,plain,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4918])). 159.59/70.62 thf(1705,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6830_zdiv__int)). 159.59/70.62 thf(13763,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)],[1705])). 159.59/70.62 thf(8230,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2931_order__less__imp__not__eq2)). 159.59/70.62 thf(36565,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8230])). 159.59/70.62 thf(5206,axiom,((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5067_le__minus__one__simps_I2_J)). 159.59/70.62 thf(25293,plain,((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5206])). 159.59/70.62 thf(2547,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/sandbox/benchmark/theBenchmark.p',fact_1373_less__add__iff2)). 159.59/70.62 thf(16440,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)],[2547])). 159.59/70.62 thf(6305,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (power_power_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8154_fact__div__fact__le__pow)). 159.59/70.62 thf(29509,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (power_power_nat @ B @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6305])). 159.59/70.62 thf(6369,axiom,((divmod_nat = (^ [A:nat,B:nat]: (product_Pair_nat_nat @ (divide_divide_nat @ A @ B) @ (modulo_modulo_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5659_divmod__nat__def)). 159.59/70.62 thf(29701,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)],[6369])). 159.59/70.62 thf(5006,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3065_not__le__imp__less)). 159.59/70.62 thf(24576,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5006])). 159.59/70.62 thf(196,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((comm_s4660882817536571857er_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ B)) @ A) != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8289_pochhammer__of__nat__eq__0__lemma_H)). 159.59/70.62 thf(8852,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ ((comm_s4660882817536571857er_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ B)) @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[196])). 159.59/70.62 thf(5348,axiom,(((minus_minus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ one_one_complex)) = (numera6690914467698888265omplex @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4854_diff__numeral__special_I11_J)). 159.59/70.62 thf(25844,plain,(((minus_minus_complex @ one_one_complex @ (uminus1482373934393186551omplex @ one_one_complex)) = (numera6690914467698888265omplex @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5348])). 159.59/70.62 thf(936,axiom,((! [A:set_nat,B:(nat > real)]: (((A != bot_bot_set_nat) => ((! [C:nat]: ((ord_less_real @ one_one_real @ (B @ C)) <= (member_nat @ C @ A))) => (ord_less_real @ one_one_real @ (groups129246275422532515t_real @ B @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8650_less__1__prod)). 159.59/70.62 thf(11249,plain,((! [A:set_nat,B:(nat > real)]: (((~ (A = bot_bot_set_nat)) => ((! [C:nat]: ((ord_less_real @ one_one_real @ (B @ C)) | ~ (member_nat @ C @ A))) => (ord_less_real @ one_one_real @ (groups129246275422532515t_real @ (B) @ A)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[936])). 159.59/70.62 thf(7328,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/sandbox/benchmark/theBenchmark.p',fact_6618_of__nat__power__le__of__nat__cancel__iff)). 159.59/70.62 thf(33595,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)],[7328])). 159.59/70.62 thf(473,axiom,((! [A:real]: (ord_less_real @ (sinh_real @ A) @ (cosh_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9324_sinh__less__cosh__real)). 159.59/70.62 thf(9758,plain,((! [A:real]: (ord_less_real @ (sinh_real @ A) @ (cosh_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[473])). 159.59/70.62 thf(3488,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ B)) <= (ord_less_int @ zero_zero_int @ B)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2116_add__pos__pos)). 159.59/70.62 thf(19454,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_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)],[3488])). 159.59/70.62 thf(8167,axiom,((! [A:num]: ((ord_less_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (ord_less_num @ one @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_one__less__numeral__iff)). 159.59/70.62 thf(36370,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)],[8167])). 159.59/70.62 thf(6364,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((A = zero_zero_nat) | ? [C:nat]: ((A = (suc @ C)) & (ord_less_nat @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2191_less__Suc__eq__0__disj)). 159.59/70.62 thf(29686,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((A = zero_zero_nat) | ? [C:nat]: ((A = (suc @ C)) & (ord_less_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6364])). 159.59/70.62 thf(1990,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) & ! [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)) & ((sin_real @ B) = A) & (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/sandbox/benchmark/theBenchmark.p',fact_6873_sin__total)). 159.59/70.62 thf(14681,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) & ! [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)) & ((sin_real @ B) = A) & (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)],[1990])). 159.59/70.62 thf(4239,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((((divide6298287555418463151nteger @ B @ A) = C) = (B = (times_3573771949741848930nteger @ C @ A))) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4159_unit__eq__div1)). 159.59/70.62 thf(21855,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((((divide6298287555418463151nteger @ B @ A) = C) = (B = (times_3573771949741848930nteger @ C @ A))) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4239])). 159.59/70.62 thf(6720,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/sandbox/benchmark/theBenchmark.p',fact_7785_sum__gp__multiplied)). 159.59/70.62 thf(31164,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)],[6720])). 159.59/70.62 thf(2584,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ B) @ (uminus5710092332889474511et_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4930_compl__mono)). 159.59/70.62 thf(16556,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ B) @ (uminus5710092332889474511et_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2584])). 159.59/70.62 thf(5786,axiom,((! [A:nat]: ((modulo_modulo_nat @ (suc @ zero_zero_nat) @ A) = (zero_n2687167440665602831ol_nat @ (A != (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4352_Suc__0__mod__eq)). 159.59/70.62 thf(27489,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)],[5786])). 159.59/70.62 thf(8114,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_nat__neq__iff)). 159.59/70.62 thf(36188,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)],[8114])). 159.59/70.62 thf(780,axiom,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ B @ (modulo_modulo_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ 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 @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3578_divmod__digit__1_I1_J)). 159.59/70.62 thf(10765,plain,((! [A:int,B:int]: (((ord_less_int @ zero_zero_int @ B) => ((ord_less_eq_int @ B @ (modulo_modulo_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ 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 @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[780])). 159.59/70.62 thf(6296,axiom,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5171_neg__numeral__le__neg__one)). 159.59/70.62 thf(29480,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)],[6296])). 159.59/70.62 thf(1368,axiom,((! [A:nat,B:nat,C: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))) <= (C != one_one_complex)) & (((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))) <= (~ (ord_less_nat @ A @ B))) & ((ord_less_nat @ A @ B) => ((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7319_sum__gp)). 159.59/70.62 thf(12692,plain,((! [A:nat,B:nat,C: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))) | (C = one_one_complex)) & (((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))) | (ord_less_nat @ A @ B)) & ((ord_less_nat @ A @ B) => ((groups2073611262835488442omplex @ (power_power_complex @ C) @ (set_or1269000886237332187st_nat @ B @ A)) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368])). 159.59/70.62 thf(7626,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/sandbox/benchmark/theBenchmark.p',fact_9108_binomial__maximum_H)). 159.59/70.62 thf(34634,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)],[7626])). 159.59/70.62 thf(6391,axiom,((! [A:nat,B:nat]: (ord_less_nat @ (minus_minus_nat @ A @ B) @ (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_845_diff__less__Suc)). 159.59/70.62 thf(29806,plain,((! [A:nat,B:nat]: (ord_less_nat @ (minus_minus_nat @ A @ B) @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6391])). 159.59/70.62 thf(7372,axiom,(((ord_max_nat @ one_one_nat @ zero_zero_nat) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1711_max__0__1_I2_J)). 159.59/70.62 thf(33744,plain,(((ord_max_nat @ one_one_nat @ zero_zero_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7372])). 159.59/70.62 thf(4638,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/sandbox/benchmark/theBenchmark.p',fact_4922_le__minus__iff)). 159.59/70.62 thf(23282,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)],[4638])). 159.59/70.62 thf(1054,axiom,(((semiri8010041392384452111omplex @ one_one_nat) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6554_of__nat__1)). 159.59/70.62 thf(11629,plain,(((semiri8010041392384452111omplex @ one_one_nat) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054])). 159.59/70.62 thf(2566,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/sandbox/benchmark/theBenchmark.p',fact_2241_mult__strict__mono_H)). 159.59/70.62 thf(16497,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)],[2566])). 159.59/70.62 thf(3884,axiom,((! [A:real]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ zero_zero_int) = (ord_less_eq_real @ A @ (uminus_uminus_real @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6993_ceiling__less__zero)). 159.59/70.62 thf(20758,plain,((! [A:real]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ zero_zero_int) = (ord_less_eq_real @ A @ (uminus_uminus_real @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3884])). 159.59/70.62 thf(6110,axiom,((! [A:real]: ((sqrt @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6353_real__sqrt__abs)). 159.59/70.62 thf(28784,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)],[6110])). 159.59/70.62 thf(3622,axiom,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: ((if_Pro6206227464963214023at_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T)). 159.59/70.62 thf(19886,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)],[3622])). 159.59/70.62 thf(2713,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ (plus_plus_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ B))) @ (bit_ri631733984087533419it_int @ B @ A)) <= (ord_less_int @ A @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5343_signed__take__bit__int__greater__eq)). 159.59/70.62 thf(17005,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ (plus_plus_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ B))) @ (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)],[2713])). 159.59/70.62 thf(2943,axiom,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) != zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6674_of__nat__neq__0)). 159.59/70.62 thf(17726,plain,((! [A:nat]: ~ ((semiri1314217659103216013at_int @ (suc @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2943])). 159.59/70.62 thf(5972,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) => (ord_less_eq_real @ (abs_abs_real @ A) @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5532_abs__leI)). 159.59/70.62 thf(28350,plain,((! [A:real,B:real]: (((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) => (ord_less_eq_real @ (abs_abs_real @ A) @ B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5972])). 159.59/70.62 thf(5812,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = (! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ A)) & (B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_All__less__Suc)). 159.59/70.62 thf(27621,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = (! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ A)) & (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5812])). 159.59/70.62 thf(4722,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se727722235901077358nd_nat @ (bit_se727722235901077358nd_nat @ A @ B) @ C) = (bit_se727722235901077358nd_nat @ A @ (bit_se727722235901077358nd_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6050_and_Oassoc)). 159.59/70.62 thf(23568,plain,((! [A:nat,B:nat,C:nat]: ((bit_se727722235901077358nd_nat @ (bit_se727722235901077358nd_nat @ A @ B) @ C) = (bit_se727722235901077358nd_nat @ A @ (bit_se727722235901077358nd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4722])). 159.59/70.62 thf(1625,axiom,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (ord_le6747313008572928689nteger @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4618_neg__less__iff__less)). 159.59/70.62 thf(13530,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)],[1625])). 159.59/70.62 thf(1178,axiom,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ C @ B)) = (minus_minus_complex @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1088_add__diff__cancel__right)). 159.59/70.62 thf(12025,plain,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ C @ B)) = (minus_minus_complex @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178])). 159.59/70.62 thf(7806,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/sandbox/benchmark/theBenchmark.p',fact_242_power__add__numeral2)). 159.59/70.62 thf(35203,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)],[7806])). 159.59/70.62 thf(2847,axiom,((! [A:int,B:int]: ((ring_1_of_int_int @ (bit_se725231765392027082nd_int @ A @ B)) = (bit_se725231765392027082nd_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6033_of__int__and__eq)). 159.59/70.62 thf(17406,plain,((! [A:int,B:int]: ((ring_1_of_int_int @ (bit_se725231765392027082nd_int @ A @ B)) = (bit_se725231765392027082nd_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2847])). 159.59/70.62 thf(6853,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/sandbox/benchmark/theBenchmark.p',fact_4288_even__mod__4__div__2)). 159.59/70.62 thf(31713,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)],[6853])). 159.59/70.62 thf(7168,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/sandbox/benchmark/theBenchmark.p',fact_7170_cos__double__cos)). 159.59/70.62 thf(33018,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)],[7168])). 159.59/70.62 thf(7224,axiom,((zero_zero_int != one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1890_zero__neq__one)). 159.59/70.62 thf(33233,plain,((~ (zero_zero_int = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7224])). 159.59/70.62 thf(5638,axiom,((bit_se545348938243370406it_int = (^ [A:nat,B:int]: (times_times_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9566_push__bit__int__def)). 159.59/70.62 thf(26902,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)],[5638])). 159.59/70.62 thf(4349,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/sandbox/benchmark/theBenchmark.p',fact_6780_arctan__bounded)). 159.59/70.62 thf(22186,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)],[4349])). 159.59/70.62 thf(6700,axiom,((! [A:num,B:num]: ((ord_less_num @ (bit1 @ A) @ (bit1 @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5402_semiring__norm_I80_J)). 159.59/70.62 thf(31011,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)],[6700])). 159.59/70.62 thf(3113,axiom,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5170_neg__numeral__le__neg__one)). 159.59/70.62 thf(18268,plain,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3113])). 159.59/70.62 thf(6967,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/sandbox/benchmark/theBenchmark.p',fact_3454_mod__add__left__eq)). 159.59/70.62 thf(32119,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)],[6967])). 159.59/70.62 thf(3516,axiom,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1284_diff__diff__eq2)). 159.59/70.62 thf(19539,plain,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3516])). 159.59/70.62 thf(3002,axiom,((! [A:int,B:int,C:int]: ((((divide_divide_int @ B @ A) = (divide_divide_int @ C @ A)) = (B = C)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4097_unit__div__cancel)). 159.59/70.62 thf(17908,plain,((! [A:int,B:int,C:int]: ((((divide_divide_int @ B @ A) = (divide_divide_int @ C @ A)) = (B = C)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3002])). 159.59/70.62 thf(7014,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ zero_zero_nat @ (binomial @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9066_zero__less__binomial)). 159.59/70.62 thf(32399,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)],[7014])). 159.59/70.62 thf(7861,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2164_zero__less__power)). 159.59/70.62 thf(35375,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7861])). 159.59/70.62 thf(3088,axiom,((! [A:real]: ? [B:real]: ((ord_less_eq_real @ B @ pi) & ((sin_real @ B) = (sin_real @ A)) & ((cos_real @ B) = (cos_real @ A)) & (ord_less_real @ (uminus_uminus_real @ pi) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7150_sincos__principal__value)). 159.59/70.62 thf(18183,plain,((! [A:real]: ? [B:real]: ((ord_less_eq_real @ B @ pi) & ((sin_real @ B) = (sin_real @ A)) & ((cos_real @ B) = (cos_real @ A)) & (ord_less_real @ (uminus_uminus_real @ pi) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3088])). 159.59/70.62 thf(3204,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/sandbox/benchmark/theBenchmark.p',fact_5814_of__int__0__less__iff)). 159.59/70.62 thf(18557,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)],[3204])). 159.59/70.62 thf(6227,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:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ (suc @ D))))) => ((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))) => (((~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G)))) <= (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ zero_zero_nat) @ D @ E) @ F)))) <= (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ zero_zero_nat @ D @ E) @ F)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1943_vebt__delete_Ocases)). 159.59/70.62 thf(29173,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$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:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ 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:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ zero_zero_nat) @ D @ E) @ F))) | ~ (! [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)],[6227])). 159.59/70.62 thf(5822,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (plus_plus_nat @ A @ B) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2366_div__add__self1)). 159.59/70.62 thf(27704,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (plus_plus_nat @ A @ B) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5822])). 159.59/70.62 thf(4121,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/sandbox/benchmark/theBenchmark.p',fact_7231_powr__powr)). 159.59/70.62 thf(21470,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)],[4121])). 159.59/70.62 thf(788,axiom,((! [A:complex]: (((sin_complex @ A) = zero_zero_complex) <= ((cos_complex @ A) = one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7087_cos__one__sin__zero)). 159.59/70.62 thf(10794,plain,((! [A:complex]: (((sin_complex @ A) = zero_zero_complex) | ~ ((cos_complex @ A) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[788])). 159.59/70.62 thf(7702,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2836_dual__order_Ostrict__implies__not__eq)). 159.59/70.62 thf(34858,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7702])). 159.59/70.62 thf(4249,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/sandbox/benchmark/theBenchmark.p',fact_2074_mult__strict__left__mono)). 159.59/70.62 thf(21890,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)],[4249])). 159.59/70.62 thf(1885,axiom,((! [A:set_nat,B:(nat > real)]: ((((ln_ln_real @ (groups129246275422532515t_real @ B @ A)) = (groups6591440286371151544t_real @ (^ [C:nat]: (ln_ln_real @ (B @ C))) @ A)) <= (! [C:nat]: ((ord_less_real @ zero_zero_real @ (B @ C)) <= (member_nat @ C @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9126_ln__prod)). 159.59/70.62 thf(14338,plain,((! [A:set_nat,B:(nat > real)]: (((ln_ln_real @ (groups129246275422532515t_real @ (B) @ A)) = (groups6591440286371151544t_real @ (^ [C:nat]: (ln_ln_real @ (B @ C))) @ A)) | ~ (! [C:nat]: ((ord_less_real @ zero_zero_real @ (B @ C)) | ~ (member_nat @ C @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1885])). 159.59/70.62 thf(2750,axiom,((! [A:nat,B:nat,C:(nat > extended_enat),D:extended_enat]: ((ord_less_nat @ A @ B) => (((ord_le72135733267957522d_enat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F))))) <= (ord_le2932123472753598470d_enat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3248_order__less__le__subst2)). 159.59/70.62 thf(17114,plain,((! [A:nat,B:nat,C:(nat > extended_enat),D:extended_enat]: ((ord_less_nat @ A @ B) => ((ord_le72135733267957522d_enat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_nat @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)))) | ~ (ord_le2932123472753598470d_enat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2750])). 159.59/70.62 thf(6303,axiom,((! [A:real,B:real,C:real,D:real]: ((A != zero_zero_real) => ((B != 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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2443_frac__le__eq)). 159.59/70.62 thf(29502,plain,((! [A:real,B:real,C:real,D:real]: ((~ (A = zero_zero_real)) => ((~ (B = 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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6303])). 159.59/70.62 thf(7138,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/sandbox/benchmark/theBenchmark.p',fact_6354_bit__minus__numeral__int_I1_J)). 159.59/70.62 thf(32904,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)],[7138])). 159.59/70.62 thf(5438,axiom,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6006_and__numerals_I3_J)). 159.59/70.62 thf(26229,plain,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5438])). 159.59/70.62 thf(4505,axiom,((! [A:(nat > (nat > nat)),B:nat,C:nat,D:nat,E:nat]: ((((E = D) <= (ord_less_nat @ C @ B)) & ((~ (ord_less_nat @ C @ B)) => (E = (set_fo2584398358068434914at_nat @ A @ (plus_plus_nat @ B @ one_one_nat) @ C @ (A @ B @ D))))) <= ((set_fo2584398358068434914at_nat @ A @ B @ C @ D) = E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8810_fold__atLeastAtMost__nat_Oelims)). 159.59/70.62 thf(22741,plain,((! [A:(nat > (nat > nat)),B:nat,C:nat,D:nat,E:nat]: ((((E = D) | ~ (ord_less_nat @ C @ B)) & ((~ (ord_less_nat @ C @ B)) => (E = (set_fo2584398358068434914at_nat @ (A) @ (plus_plus_nat @ B @ one_one_nat) @ C @ (A @ B @ D))))) | ~ ((set_fo2584398358068434914at_nat @ (A) @ B @ C @ D) = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4505])). 159.59/70.62 thf(4205,axiom,((! [A:num]: ((neg_nu6075765906172075777c_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bitM @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5807_dbl__dec__simps_I5_J)). 159.59/70.62 thf(21732,plain,((! [A:num]: ((neg_nu6075765906172075777c_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4205])). 159.59/70.62 thf(7159,axiom,((! [A:int,B:int,C:(int > num),D:num]: ((((ord_less_eq_num @ (C @ A) @ D) <= (! [E:int,F:int]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_int @ E @ F)))) <= (ord_less_eq_num @ (C @ B) @ D)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2680_order__subst2)). 159.59/70.62 thf(32967,plain,((! [A:int,B:int,C:(int > num),D:num]: ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:int,F:int]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_int @ E @ F))) | ~ (ord_less_eq_num @ (C @ B) @ D) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7159])). 159.59/70.62 thf(7941,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ B @ C) @ (minus_minus_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_diff__le__diff__pow)). 159.59/70.62 thf(35639,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ B @ C) @ (minus_minus_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7941])). 159.59/70.62 thf(7906,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2804_dual__order_Oirrefl)). 159.59/70.62 thf(35528,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7906])). 159.59/70.62 thf(7607,axiom,((vEBT_VEBT_low = (^ [A:nat,B:nat]: (modulo_modulo_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3387_low__def)). 159.59/70.62 thf(34577,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)],[7607])). 159.59/70.62 thf(233,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/sandbox/benchmark/theBenchmark.p',fact_785_max_Obounded__iff)). 159.59/70.62 thf(8964,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)],[233])). 159.59/70.62 thf(6156,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/sandbox/benchmark/theBenchmark.p',fact_3581_verit__le__mono__div)). 159.59/70.62 thf(28935,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)],[6156])). 159.59/70.62 thf(3986,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ B @ A)))) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7243_powr__mono2_H)). 159.59/70.62 thf(21066,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ B @ A)))) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3986])). 159.59/70.62 thf(1410,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (abs_abs_real @ A)) = (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5410_zero__less__abs__iff)). 159.59/70.62 thf(12849,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)],[1410])). 159.59/70.62 thf(7854,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/sandbox/benchmark/theBenchmark.p',fact_2548_zero__le__even__power_H)). 159.59/70.62 thf(35354,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)],[7854])). 159.59/70.62 thf(2996,axiom,((! [A:real,B:int]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ B) = (ord_less_real @ A @ (plus_plus_real @ (ring_1_of_int_real @ B) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8302_floor__le__iff)). 159.59/70.62 thf(17891,plain,((! [A:real,B:int]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ B) = (ord_less_real @ A @ (plus_plus_real @ (ring_1_of_int_real @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2996])). 159.59/70.62 thf(5953,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/sandbox/benchmark/theBenchmark.p',fact_2412_mult__less__cancel__right1)). 159.59/70.62 thf(28291,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)],[5953])). 159.59/70.62 thf(2995,axiom,((bit_se8568078237143864401it_int = (^ [A:nat,B:int]: (divide_divide_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9738_drop__bit__int__def)). 159.59/70.62 thf(17889,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)],[2995])). 159.59/70.62 thf(5734,axiom,((! [A:num]: ((times_times_num @ one @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_semiring__norm_I12_J)). 159.59/70.62 thf(27241,plain,((! [A:num]: ((times_times_num @ one @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5734])). 159.59/70.62 thf(8155,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/sandbox/benchmark/theBenchmark.p',fact_9155_choose__square__sum)). 159.59/70.62 thf(36333,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)],[8155])). 159.59/70.62 thf(2651,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= ((ord_less_eq_real @ C @ D) & (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_add__mono__thms__linordered__semiring_I2_J)). 159.59/70.62 thf(16793,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ ((ord_less_eq_real @ C @ D) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2651])). 159.59/70.62 thf(6085,axiom,(((cos_real @ (numeral_numeral_real @ (bit0 @ one))) != zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7118_cos__two__neq__zero)). 159.59/70.62 thf(28704,plain,((~ ((cos_real @ (numeral_numeral_real @ (bit0 @ one))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6085])). 159.59/70.62 thf(2493,axiom,((! [A:real,B: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))) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7544_arccos__le__mono)). 159.59/70.62 thf(16274,plain,((! [A:real,B: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))) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2493])). 159.59/70.62 thf(194,axiom,((real_V1485227260804924795R_real = times_times_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9211_real__scaleR__def)). 159.59/70.62 thf(8847,plain,(((real_V1485227260804924795R_real) = (times_times_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[194])). 159.59/70.62 thf(4340,axiom,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5184_not__numeral__less__neg__one)). 159.59/70.62 thf(22159,plain,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4340])). 159.59/70.62 thf(7474,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/sandbox/benchmark/theBenchmark.p',fact_8322_gbinomial__negated__upper)). 159.59/70.62 thf(34076,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)],[7474])). 159.59/70.62 thf(1435,axiom,((! [A:extended_enat,B:(real > extended_enat),C:real,D:real]: ((((! [E:real,F:real]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) <= (ord_less_real @ C @ D)) <= (ord_le2932123472753598470d_enat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3214_order__le__less__subst1)). 159.59/70.62 thf(12930,plain,((! [A:extended_enat,B:(real > extended_enat),C:real,D:real]: (((! [E:real,F:real]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) | ~ (ord_less_real @ C @ D) | ~ (ord_le2932123472753598470d_enat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435])). 159.59/70.62 thf(5283,axiom,((! [A:real,B:real,C:nat]: (((times_times_real @ (power_power_real @ A @ C) @ B) = (times_times_real @ B @ (power_power_real @ A @ C))) <= ((times_times_real @ A @ B) = (times_times_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_power__commuting__commutes)). 159.59/70.62 thf(25562,plain,((! [A:real,B:real,C:nat]: (((times_times_real @ (power_power_real @ A @ C) @ B) = (times_times_real @ B @ (power_power_real @ A @ C))) | ~ ((times_times_real @ A @ B) = (times_times_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5283])). 159.59/70.62 thf(6843,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/sandbox/benchmark/theBenchmark.p',fact_4022_dvd__power__same)). 159.59/70.62 thf(31681,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)],[6843])). 159.59/70.62 thf(560,axiom,((~ (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5161_less__minus__one__simps_I3_J)). 159.59/70.62 thf(10035,plain,((~ (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[560])). 159.59/70.62 thf(4734,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_add__Suc)). 159.59/70.62 thf(23604,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)],[4734])). 159.59/70.62 thf(4611,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (A = (suc @ (minus_minus_nat @ A @ one_one_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2481_Suc__pred_H)). 159.59/70.62 thf(23190,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (A = (suc @ (minus_minus_nat @ A @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4611])). 159.59/70.62 thf(5744,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4181_dvd__imp__le)). 159.59/70.62 thf(27277,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5744])). 159.59/70.62 thf(5244,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ B @ zero_zero_real) & (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 @ (times_times_real @ A @ B) @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1977_split__mult__neg__le)). 159.59/70.62 thf(25416,plain,((! [A:real,B:real]: ((((ord_less_eq_real @ B @ zero_zero_real) & (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 @ (times_times_real @ A @ B) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5244])). 159.59/70.62 thf(2293,axiom,((! [A:real,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (gbinomial_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ C)) @ C)) @ (set_ord_atMost_nat @ B)) = (gbinomial_real @ (plus_plus_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8846_gbinomial__parallel__sum)). 159.59/70.62 thf(15638,plain,((! [A:real,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (gbinomial_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ C)) @ C)) @ (set_ord_atMost_nat @ B)) = (gbinomial_real @ (plus_plus_real @ (plus_plus_real @ A @ (semiri5074537144036343181t_real @ B)) @ one_one_real) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2293])). 159.59/70.62 thf(1532,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/sandbox/benchmark/theBenchmark.p',fact_3236_order__less__le__subst1)). 159.59/70.62 thf(13237,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)],[1532])). 159.59/70.62 thf(2705,axiom,((! [A:num,B:num]: ((ord_le72135733267957522d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (ord_less_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_enat__ord__number_I2_J)). 159.59/70.62 thf(16981,plain,((! [A:num,B:num]: ((ord_le72135733267957522d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (ord_less_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2705])). 159.59/70.62 thf(2261,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ C) => (ord_less_int @ A @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3087_order_Ostrict__trans1)). 159.59/70.62 thf(15546,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ B @ C) => (ord_less_int @ A @ C)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2261])). 159.59/70.62 thf(4806,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/sandbox/benchmark/theBenchmark.p',fact_7398_sum__product)). 159.59/70.62 thf(23854,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)],[4806])). 159.59/70.62 thf(4413,axiom,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1035_div__by__1)). 159.59/70.62 thf(22393,plain,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4413])). 159.59/70.62 thf(3880,axiom,((! [A:real,B:real,C: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))) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5277_neg__le__minus__divide__eq)). 159.59/70.62 thf(20745,plain,((! [A:real,B:real,C: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))) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3880])). 159.59/70.62 thf(947,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2770_order_Oasym)). 159.59/70.62 thf(11284,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[947])). 159.59/70.62 thf(2180,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ B @ C) => ((divide6298287555418463151nteger @ C @ (times_3573771949741848930nteger @ B @ A)) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ C @ B) @ A))) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4165_div__mult__unit2)). 159.59/70.62 thf(15279,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ B @ C) => ((divide6298287555418463151nteger @ C @ (times_3573771949741848930nteger @ B @ A)) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ C @ B) @ A))) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2180])). 159.59/70.62 thf(3180,axiom,((! [A:nat]: ((ord_le2932123472753598470d_enat @ (semiri4216267220026989637d_enat @ A) @ zero_z5237406670263579293d_enat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6576_of__nat__le__0__iff)). 159.59/70.62 thf(18481,plain,((! [A:nat]: ((ord_le2932123472753598470d_enat @ (semiri4216267220026989637d_enat @ A) @ zero_z5237406670263579293d_enat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3180])). 159.59/70.62 thf(3847,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (bit_se725231765392027082nd_int @ A @ C) @ B) <= (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6075_AND__upper1_H)). 159.59/70.62 thf(20637,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (bit_se725231765392027082nd_int @ A @ C) @ B) | ~ (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3847])). 159.59/70.62 thf(732,axiom,((! [A:complex,B:real,C:complex]: (((plus_plus_complex @ A @ (real_V2046097035970521341omplex @ B @ C)) = (plus_plus_complex @ C @ (real_V2046097035970521341omplex @ B @ A))) = ((C = A) | (B = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9194_scaleR__eq__iff)). 159.59/70.62 thf(10615,plain,((! [A:complex,B:real,C:complex]: (((plus_plus_complex @ A @ (real_V2046097035970521341omplex @ B @ C)) = (plus_plus_complex @ C @ (real_V2046097035970521341omplex @ B @ A))) = ((C = A) | (B = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[732])). 159.59/70.62 thf(2812,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/sandbox/benchmark/theBenchmark.p',fact_2080_mult__less__cancel__left__neg)). 159.59/70.62 thf(17296,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)],[2812])). 159.59/70.62 thf(823,axiom,((! [A:nat,B:nat]: ((divide6298287555418463151nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ ((ord_less_eq_nat @ B @ A) & ((power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) != zero_z3403309356797280102nteger))) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4524_exp__div__exp__eq)). 159.59/70.62 thf(10907,plain,((! [A:nat,B:nat]: ((divide6298287555418463151nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ ((ord_less_eq_nat @ B @ A) & ~ ((power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) = zero_z3403309356797280102nteger))) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[823])). 159.59/70.62 thf(6571,axiom,((! [A:nat,B:vEBT_VEBT,C:nat,D:vEBT_VEBT]: (((replicate_VEBT_VEBT @ A @ B) = (replicate_VEBT_VEBT @ C @ D)) = ((A = C) & ((A != zero_zero_nat) => (B = D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4332_replicate__eq__replicate)). 159.59/70.62 thf(30494,plain,((! [A:nat,B:vEBT_VEBT,C:nat,D:vEBT_VEBT]: (((replicate_VEBT_VEBT @ A @ B) = (replicate_VEBT_VEBT @ C @ D)) = ((A = C) & ((~ (A = zero_zero_nat)) => (B = D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6571])). 159.59/70.62 thf(1677,axiom,((! [A:real]: (ord_less_real @ zero_zero_real @ (cosh_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9333_cosh__real__pos)). 159.59/70.62 thf(13681,plain,((! [A:real]: (ord_less_real @ zero_zero_real @ (cosh_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677])). 159.59/70.62 thf(8001,axiom,((! [A:set_list_VEBT_VEBT]: ((? [B:nat]: ! [C:list_VEBT_VEBT]: ((ord_less_nat @ (size_s6755466524823107622T_VEBT @ C) @ B) <= (member2936631157270082147T_VEBT @ C @ A))) <= (finite3004134309566078307T_VEBT @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3741_finite__maxlen)). 159.59/70.62 thf(35820,plain,((! [A:set_list_VEBT_VEBT]: (? [B:nat]: ! [C:list_VEBT_VEBT]: ((ord_less_nat @ (size_s6755466524823107622T_VEBT @ C) @ B) | ~ (member2936631157270082147T_VEBT @ C @ A)) | ~ (finite3004134309566078307T_VEBT @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8001])). 159.59/70.62 thf(8212,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/sandbox/benchmark/theBenchmark.p',fact_455_power2__nat__le__imp__le)). 159.59/70.62 thf(36516,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)],[8212])). 159.59/70.62 thf(273,axiom,((! [A:num]: (zero_z3403309356797280102nteger != (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5035_zero__neq__neg__numeral)). 159.59/70.62 thf(9080,plain,((! [A:num]: ~ (zero_z3403309356797280102nteger = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[273])). 159.59/70.62 thf(7889,axiom,((! [A:nat]: ((suc @ (suc @ (suc @ A))) = (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5628_Suc3__eq__add__3)). 159.59/70.62 thf(35472,plain,((! [A:nat]: ((suc @ (suc @ (suc @ A))) = (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7889])). 159.59/70.62 thf(1589,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/sandbox/benchmark/theBenchmark.p',fact_1385_divide__divide__eq__left)). 159.59/70.62 thf(13411,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)],[1589])). 159.59/70.62 thf(4569,axiom,(((semiri1316708129612266289at_nat @ one_one_nat) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6553_of__nat__1)). 159.59/70.62 thf(23024,plain,(((semiri1316708129612266289at_nat @ one_one_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4569])). 159.59/70.62 thf(1621,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = A) = (B = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1521_add__cancel__left__right)). 159.59/70.62 thf(13515,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = A) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621])). 159.59/70.62 thf(1045,axiom,((! [A:code_integer,B:code_integer]: ((uminus1351360451143612070nteger @ (plus_p5714425477246183910nteger @ A @ B)) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4963_add_Oinverse__distrib__swap)). 159.59/70.62 thf(11602,plain,((! [A:code_integer,B:code_integer]: ((uminus1351360451143612070nteger @ (plus_p5714425477246183910nteger @ A @ B)) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045])). 159.59/70.62 thf(6248,axiom,((! [A:int,B:real]: (((ord_less_eq_real @ one_one_real @ B) | (A = zero_zero_int)) <= (ord_less_eq_real @ (abs_abs_real @ (ring_1_of_int_real @ A)) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5899_of__int__leD)). 159.59/70.62 thf(29237,plain,((! [A:int,B:real]: ((ord_less_eq_real @ one_one_real @ B) | (A = zero_zero_int) | ~ (ord_less_eq_real @ (abs_abs_real @ (ring_1_of_int_real @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6248])). 159.59/70.62 thf(6017,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/sandbox/benchmark/theBenchmark.p',fact_4801_semiring__norm_I172_J)). 159.59/70.62 thf(28493,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)],[6017])). 159.59/70.62 thf(4567,axiom,((((=) @ int) = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & (ord_less_eq_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2751_order__class_Oorder__eq__iff)). 159.59/70.62 thf(23018,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)],[4567])). 159.59/70.62 thf(7186,axiom,(((neg_nu6511756317524482435omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit1 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5673_dbl__dec__simps_I4_J)). 159.59/70.62 thf(33099,plain,(((neg_nu6511756317524482435omplex @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit1 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7186])). 159.59/70.62 thf(1811,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ C @ B) => (~ (ord_le72135733267957522d_enat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4482_minf_I7_J)). 159.59/70.62 thf(14100,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ C @ B) => (~ (ord_le72135733267957522d_enat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1811])). 159.59/70.62 thf(1308,axiom,((! [A:(nat > complex),B:nat,C:nat]: ((groups2073611262835488442omplex @ A @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups2073611262835488442omplex @ (^ [D:nat]: (plus_plus_complex @ (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/sandbox/benchmark/theBenchmark.p',fact_7787_sum_Oin__pairs)). 159.59/70.62 thf(12478,plain,((! [A:(nat > complex),B:nat,C:nat]: ((groups2073611262835488442omplex @ (A) @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups2073611262835488442omplex @ (^ [D:nat]: (plus_plus_complex @ (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)],[1308])). 159.59/70.62 thf(2722,axiom,((! [A:num]: ((invers8013647133539491842omplex @ (numera6690914467698888265omplex @ A)) = (divide1717551699836669952omplex @ one_one_complex @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9008_inverse__eq__divide__numeral)). 159.59/70.62 thf(17032,plain,((! [A:num]: ((invers8013647133539491842omplex @ (numera6690914467698888265omplex @ A)) = (divide1717551699836669952omplex @ one_one_complex @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2722])). 159.59/70.62 thf(886,axiom,((! [A:extended_enat]: ((comm_s3181272606743183617d_enat @ A @ zero_zero_nat) = one_on7984719198319812577d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8180_pochhammer__0)). 159.59/70.62 thf(11101,plain,((! [A:extended_enat]: ((comm_s3181272606743183617d_enat @ A @ zero_zero_nat) = one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[886])). 159.59/70.62 thf(2588,axiom,((! [A:real,B:real]: ((dvd_dvd_real @ A @ (plus_plus_real @ A @ B)) = (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3792_dvd__add__triv__left__iff)). 159.59/70.62 thf(16569,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)],[2588])). 159.59/70.62 thf(6815,axiom,((! [A:int]: (ord_less_eq_int @ A @ (abs_abs_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5481_abs__ge__self)). 159.59/70.62 thf(31493,plain,((! [A:int]: (ord_less_eq_int @ A @ (abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6815])). 159.59/70.62 thf(830,axiom,((! [A:(nat > complex),B:complex,C:set_nat,D:complex,E:(nat > complex)]: ((((D = (plus_plus_complex @ B @ (groups2073611262835488442omplex @ (^ [F:nat]: (minus_minus_complex @ (E @ F) @ (A @ F))) @ C))) => (sums_complex @ (^ [F:nat]: (if_complex @ (member_nat @ F @ C) @ (E @ F) @ (A @ F))) @ D)) <= (finite_finite_nat @ C)) <= (sums_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7951_sums__If__finite__set_H)). 159.59/70.62 thf(10926,plain,((! [A:(nat > complex),B:complex,C:set_nat,D:complex,E:(nat > complex)]: (((D = (plus_plus_complex @ B @ (groups2073611262835488442omplex @ (^ [F:nat]: (minus_minus_complex @ (E @ F) @ (A @ F))) @ C))) => (sums_complex @ (^ [F:nat]: (if_complex @ (member_nat @ F @ C) @ (E @ F) @ (A @ F))) @ D)) | ~ (finite_finite_nat @ C) | ~ (sums_complex @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[830])). 159.59/70.62 thf(3067,axiom,((! [A:int,B:int,C:(int > extended_enat),D:extended_enat]: ((((ord_le72135733267957522d_enat @ (C @ A) @ D) <= (! [E:int,F:int]: ((ord_less_int @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F))))) <= (ord_le2932123472753598470d_enat @ (C @ B) @ D)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3250_order__less__le__subst2)). 159.59/70.62 thf(18108,plain,((! [A:int,B:int,C:(int > extended_enat),D:extended_enat]: ((ord_le72135733267957522d_enat @ (C @ A) @ D) | ~ (! [E:int,F:int]: ((ord_less_int @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)))) | ~ (ord_le2932123472753598470d_enat @ (C @ B) @ D) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3067])). 159.59/70.62 thf(7570,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/sandbox/benchmark/theBenchmark.p',fact_2815_order_Ostrict__trans)). 159.59/70.62 thf(34461,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)],[7570])). 159.59/70.62 thf(5239,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((dvd_dvd_nat @ C @ D) => (dvd_dvd_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3967_mult__dvd__mono)). 159.59/70.62 thf(25402,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((dvd_dvd_nat @ C @ D) => (dvd_dvd_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5239])). 159.59/70.62 thf(2519,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/sandbox/benchmark/theBenchmark.p',fact_7175_sin__times__cos)). 159.59/70.62 thf(16360,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)],[2519])). 159.59/70.62 thf(3810,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1191_add__strict__right__mono)). 159.59/70.62 thf(20504,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3810])). 159.59/70.62 thf(3338,axiom,((! [A:(int > $o),B:$o]: ((A @ (zero_n2684676970156552555ol_int @ B)) = (((B) => (A @ one_one_int)) & ((~ (B)) => (A @ zero_zero_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4408_split__of__bool)). 159.59/70.62 thf(18989,plain,((! [A:(int > $o),B:$o]: ((A @ (zero_n2684676970156552555ol_int @ B)) = (((B) => (A @ one_one_int)) & ((~ (B)) => (A @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3338])). 159.59/70.62 thf(3916,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ C @ A)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1750_div__mult__self1)). 159.59/70.62 thf(20851,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ B @ (times_times_int @ C @ A)) @ A) = (plus_plus_int @ C @ (divide_divide_int @ B @ A))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3916])). 159.59/70.62 thf(2829,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/sandbox/benchmark/theBenchmark.p',fact_8001_power__diff__sumr2)). 159.59/70.62 thf(17346,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)],[2829])). 159.59/70.62 thf(5986,axiom,((! [A:nat]: ((bit_se2002935070580805687sk_nat @ (suc @ A)) = (bit_se1412395901928357646or_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2002935070580805687sk_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6094_mask__Suc__double)). 159.59/70.62 thf(28395,plain,((! [A:nat]: ((bit_se2002935070580805687sk_nat @ (suc @ A)) = (bit_se1412395901928357646or_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2002935070580805687sk_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5986])). 159.59/70.62 thf(5719,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 @ (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) != zero_zero_int) & (ord_less_eq_nat @ B @ A))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4523_exp__div__exp__eq)). 159.59/70.62 thf(27182,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 @ (~ ((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = zero_zero_int) & (ord_less_eq_nat @ B @ A))) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5719])). 159.59/70.62 thf(51,axiom,((! [A:real]: ((ord_less_real @ (sinh_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9308_sinh__real__neg__iff)). 159.59/70.62 thf(8403,plain,((! [A:real]: ((ord_less_real @ (sinh_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 159.59/70.62 thf(1543,axiom,((! [A:nat]: (((semiri8010041392384452111omplex @ A) = zero_zero_complex) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6511_of__nat__eq__0__iff)). 159.59/70.62 thf(13269,plain,((! [A:nat]: (((semiri8010041392384452111omplex @ A) = zero_zero_complex) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1543])). 159.59/70.62 thf(5828,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/sandbox/benchmark/theBenchmark.p',fact_852_le__diff__conv)). 159.59/70.62 thf(27722,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)],[5828])). 159.59/70.62 thf(2417,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: (((~ ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A))) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7372_sum__zero__power_H)). 159.59/70.62 thf(16019,plain,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: (((~ ((finite_finite_nat @ A) & (member_nat @ zero_zero_nat @ A))) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2417])). 159.59/70.62 thf(5892,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (sqrt @ A) @ (sqrt @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6368_real__sqrt__le__mono)). 159.59/70.62 thf(28024,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)],[5892])). 159.59/70.62 thf(5921,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ B @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4061_dvd__mult__unit__iff_H)). 159.59/70.62 thf(28134,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ B @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5921])). 159.59/70.62 thf(6345,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => ((? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))) <= (B = one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1470_deg__1__Leafy)). 159.59/70.62 thf(29626,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D)) | ~ (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6345])). 159.59/70.62 thf(5440,axiom,((! [A:num]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5700_add__neg__numeral__special_I5_J)). 159.59/70.62 thf(26234,plain,((! [A:num]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5440])). 159.59/70.62 thf(1902,axiom,((! [A:set_nat,B:nat]: ((ord_less_eq_set_nat @ A @ (uminus5710092332889474511et_nat @ (insert_nat @ B @ bot_bot_set_nat))) = (~ (member_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6173_subset__Compl__singleton)). 159.59/70.62 thf(14395,plain,((! [A:set_nat,B:nat]: ((ord_less_eq_set_nat @ A @ (uminus5710092332889474511et_nat @ (insert_nat @ B @ bot_bot_set_nat))) = (~ (member_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1902])). 159.59/70.62 thf(2955,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/sandbox/benchmark/theBenchmark.p',fact_1744_div__mult__self3)). 159.59/70.62 thf(17770,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)],[2955])). 159.59/70.62 thf(6467,axiom,((! [A:(nat > nat)]: ((summable_nat @ A) => (((ord_less_nat @ zero_zero_nat @ (suminf_nat @ A)) = (? [B:nat]: (ord_less_nat @ zero_zero_nat @ (A @ B)))) <= (! [B:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7082_suminf__pos__iff)). 159.59/70.62 thf(30131,plain,((! [A:(nat > nat)]: ((summable_nat @ (A)) => (((ord_less_nat @ zero_zero_nat @ (suminf_nat @ (A))) = (? [B:nat]: (ord_less_nat @ zero_zero_nat @ (A @ B)))) | ~ (! [B:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6467])). 159.59/70.62 thf(4163,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/sandbox/benchmark/theBenchmark.p',fact_7976_one__diff__power__eq)). 159.59/70.62 thf(21608,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)],[4163])). 159.59/70.62 thf(8145,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/sandbox/benchmark/theBenchmark.p',fact_3546_mod__mult2__eq)). 159.59/70.62 thf(36297,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)],[8145])). 159.59/70.62 thf(8013,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ C @ A @ D) @ B) = (nth_VEBT_VEBT @ C @ B)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_nth__list__update__neq)). 159.59/70.62 thf(35856,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ C @ A @ D) @ B) = (nth_VEBT_VEBT @ C @ B)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8013])). 159.59/70.62 thf(1823,axiom,((! [A:set_nat,B:set_nat,C:(set_nat > $o)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ A @ B) => (((C @ A) <= (! [D:nat,E:set_nat]: (((((C @ E) => (C @ (insert_nat @ D @ E))) <= (~ (member_nat @ D @ E))) <= (member_nat @ D @ B)) <= (finite_finite_nat @ E)))) <= (C @ bot_bot_set_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6251_finite__subset__induct)). 159.59/70.62 thf(14135,plain,((! [A:set_nat,B:set_nat,C:(set_nat > $o)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ A @ B) => ((C @ A) | ~ (! [D:nat,E:set_nat]: (((C @ E) => (C @ (insert_nat @ D @ E))) | (member_nat @ D @ E) | ~ (member_nat @ D @ B) | ~ (finite_finite_nat @ E))) | ~ (C @ bot_bot_set_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1823])). 159.59/70.62 thf(4254,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (comm_s4663373288045622133er_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8240_pochhammer__nonneg)). 159.59/70.62 thf(21905,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (comm_s4663373288045622133er_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4254])). 159.59/70.62 thf(3282,axiom,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1281_diff__add__eq)). 159.59/70.62 thf(18816,plain,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ (plus_plus_complex @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3282])). 159.59/70.62 thf(2134,axiom,((divide_divide_real = (^ [A:real,B:real]: (times_times_real @ (inverse_inverse_real @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9039_divide__inverse__commute)). 159.59/70.62 thf(15142,plain,(((divide_divide_real) = (^ [A:real,B:real]: (times_times_real @ (inverse_inverse_real @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2134])). 159.59/70.62 thf(5879,axiom,((! [A:$o,B:$o,C:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_Leaf @ A @ B) @ C))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1800_VEBT__internal_Omembermima_Osimps_I1_J)). 159.59/70.62 thf(27967,plain,((! [A:$o,B:$o,C:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_Leaf @ A @ B) @ C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5879])). 159.59/70.62 thf(2395,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/sandbox/benchmark/theBenchmark.p',fact_1134_add_Oassoc)). 159.59/70.62 thf(15947,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)],[2395])). 159.59/70.62 thf(278,axiom,((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ zero_z3403309356797280102nteger)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5158_less__minus__one__simps_I1_J)). 159.59/70.62 thf(9095,plain,((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ zero_z3403309356797280102nteger)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 159.59/70.62 thf(20,axiom,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((ord_less_eq_set_nat @ A @ B) => ((finite_finite_nat @ B) => ((groups2073611262835488442omplex @ C @ B) = (plus_plus_complex @ (groups2073611262835488442omplex @ C @ (minus_minus_set_nat @ B @ A)) @ (groups2073611262835488442omplex @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7638_sum_Osubset__diff)). 159.59/70.62 thf(8314,plain,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((ord_less_eq_set_nat @ A @ B) => ((finite_finite_nat @ B) => ((groups2073611262835488442omplex @ (C) @ B) = (plus_plus_complex @ (groups2073611262835488442omplex @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups2073611262835488442omplex @ (C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[20])). 159.59/70.62 thf(1158,axiom,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ one_one_Code_integer) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))) = (((power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) = zero_z3403309356797280102nteger) | (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4274_even__mask__div__iff)). 159.59/70.62 thf(11961,plain,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ one_one_Code_integer) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))) = (((power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) = zero_z3403309356797280102nteger) | (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158])). 159.59/70.62 thf(7886,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/sandbox/benchmark/theBenchmark.p',fact_5261_power2__eq__iff)). 159.59/70.62 thf(35458,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)],[7886])). 159.59/70.62 thf(6237,axiom,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => (((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F))))) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2675_order__subst2)). 159.59/70.62 thf(29205,plain,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6237])). 159.59/70.62 thf(4000,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/sandbox/benchmark/theBenchmark.p',fact_9452_nat__div__distrib_H)). 159.59/70.62 thf(21110,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)],[4000])). 159.59/70.62 thf(7527,axiom,((ord_max_nat = (^ [A:nat,B:nat]: (ord_max_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_878_max_Ocommute)). 159.59/70.62 thf(34272,plain,(((ord_max_nat) = (^ [A:nat,B:nat]: (ord_max_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7527])). 159.59/70.62 thf(2681,axiom,((! [A:(nat > complex)]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (suminf_complex @ A)) @ (suminf_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (A @ B))))) <= (summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7109_summable__norm)). 159.59/70.62 thf(16893,plain,((! [A:(nat > complex)]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (suminf_complex @ (A))) @ (suminf_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (A @ B))))) | ~ (summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2681])). 159.59/70.62 thf(3748,axiom,((! [A:int]: ~ (ord_less_int @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3671_verit__comp__simplify1_I1_J)). 159.59/70.62 thf(20309,plain,((! [A:int]: ~ (ord_less_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3748])). 159.59/70.62 thf(6342,axiom,((! [A:num,B:num]: ((bit_se1146084159140164899it_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_nat @ B)) = (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ (pred_numeral @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6344_bit__numeral__simps_I2_J)). 159.59/70.62 thf(29615,plain,((! [A:num,B:num]: ((bit_se1146084159140164899it_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_nat @ B)) = (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6342])). 159.59/70.62 thf(4135,axiom,((! [A:num,B:nat,C:nat]: ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ A) @ B) @ (semiri4939895301339042750nteger @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6637_numeral__power__le__of__nat__cancel__iff)). 159.59/70.62 thf(21511,plain,((! [A:num,B:nat,C:nat]: ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ A) @ B) @ (semiri4939895301339042750nteger @ C)) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4135])). 159.59/70.62 thf(7373,axiom,((suc = (^ [A:nat]: (plus_plus_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_Suc__eq__plus1)). 159.59/70.62 thf(33746,plain,(((suc) = (^ [A:nat]: (plus_plus_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7373])). 159.59/70.62 thf(591,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (ord_max_int @ B @ C)) = ((ord_less_eq_int @ A @ B) | (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_le__max__iff__disj)). 159.59/70.62 thf(10131,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ (ord_max_int @ B @ C)) = ((ord_less_eq_int @ A @ B) | (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[591])). 159.59/70.62 thf(6567,axiom,(((numeral_numeral_nat @ (bit1 @ one)) = (suc @ (suc @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5627_numeral__3__eq__3)). 159.59/70.62 thf(30483,plain,(((numeral_numeral_nat @ (bit1 @ one)) = (suc @ (suc @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6567])). 159.59/70.62 thf(3802,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/sandbox/benchmark/theBenchmark.p',fact_8359_pochhammer__times__pochhammer__half)). 159.59/70.62 thf(20481,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)],[3802])). 159.59/70.62 thf(763,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/sandbox/benchmark/theBenchmark.p',fact_3657_Euclidean__Division_Opos__mod__sign)). 159.59/70.62 thf(10716,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)],[763])). 159.59/70.62 thf(3674,axiom,((! [A:complex]: ((ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real) => (sums_complex @ (power_power_complex @ A) @ (divide1717551699836669952omplex @ one_one_complex @ (minus_minus_complex @ one_one_complex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8003_geometric__sums)). 159.59/70.62 thf(20052,plain,((! [A:complex]: ((ord_less_real @ (real_V1022390504157884413omplex @ A) @ one_one_real) => (sums_complex @ (power_power_complex @ A) @ (divide1717551699836669952omplex @ one_one_complex @ (minus_minus_complex @ one_one_complex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3674])). 159.59/70.62 thf(3734,axiom,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2954_set__eq__subset)). 159.59/70.62 thf(20264,plain,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3734])). 159.59/70.62 thf(4004,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 @ (plus_plus_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2114_add__pos__pos)). 159.59/70.62 thf(21123,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 @ (plus_plus_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4004])). 159.59/70.62 thf(3208,axiom,((! [A:nat]: (ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6754_of__nat__less__two__power)). 159.59/70.62 thf(18569,plain,((! [A:nat]: (ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3208])). 159.59/70.62 thf(2317,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ A @ C) => ((divide6298287555418463151nteger @ (minus_8373710615458151222nteger @ B @ C) @ A) = (minus_8373710615458151222nteger @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ C @ A)))) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3856_div__diff)). 159.59/70.62 thf(15702,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ A @ C) => ((divide6298287555418463151nteger @ (minus_8373710615458151222nteger @ B @ C) @ A) = (minus_8373710615458151222nteger @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ C @ A)))) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2317])). 159.59/70.62 thf(2387,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/sandbox/benchmark/theBenchmark.p',fact_1363_eq__add__iff2)). 159.59/70.62 thf(15915,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)],[2387])). 159.59/70.62 thf(5765,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/sandbox/benchmark/theBenchmark.p',fact_5218_power__minus)). 159.59/70.62 thf(27341,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)],[5765])). 159.59/70.62 thf(1381,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/sandbox/benchmark/theBenchmark.p',fact_1229_distrib__right)). 159.59/70.62 thf(12760,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)],[1381])). 159.59/70.62 thf(1288,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)))) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7818_arcsin__ubound)). 159.59/70.62 thf(12414,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)))) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288])). 159.59/70.62 thf(1604,axiom,((! [A:code_integer,B:code_integer]: ((uminus1351360451143612070nteger @ (plus_p5714425477246183910nteger @ A @ B)) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4638_minus__add__distrib)). 159.59/70.62 thf(13463,plain,((! [A:code_integer,B:code_integer]: ((uminus1351360451143612070nteger @ (plus_p5714425477246183910nteger @ A @ B)) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604])). 159.59/70.62 thf(92,axiom,((! [A:nat]: ((((comm_s4660882817536571857er_int @ zero_zero_int @ A) = one_one_int) <= (A = zero_zero_nat)) & ((A != zero_zero_nat) => ((comm_s4660882817536571857er_int @ zero_zero_int @ A) = zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8246_pochhammer__0__left)). 159.59/70.62 thf(8530,plain,((! [A:nat]: ((((comm_s4660882817536571857er_int @ zero_zero_int @ A) = one_one_int) | ~ (A = zero_zero_nat)) & ((~ (A = zero_zero_nat)) => ((comm_s4660882817536571857er_int @ zero_zero_int @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 159.59/70.62 thf(7827,axiom,((bit_se2002935070580805687sk_nat = (^ [A:nat]: (minus_minus_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6140_mask__eq__exp__minus__1)). 159.59/70.62 thf(35279,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)],[7827])). 159.59/70.62 thf(4629,axiom,((one_one_int != (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4973_one__neq__neg__one)). 159.59/70.62 thf(23254,plain,((~ (one_one_int = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4629])). 159.59/70.62 thf(6200,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ A) = (((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ B @ one_one_int)) & ((ord_less_eq_int @ one_one_int @ B) <= (ord_less_int @ A @ zero_zero_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2423_mult__le__cancel__left2)). 159.59/70.62 thf(29092,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (times_times_int @ A @ B) @ A) = (((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ B @ one_one_int)) & ((ord_less_eq_int @ one_one_int @ B) | ~ (ord_less_int @ A @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6200])). 159.59/70.62 thf(146,axiom,((! [A:real]: ((real_V1485227260804924795R_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9247_scaleR__2)). 159.59/70.62 thf(8694,plain,((! [A:real]: ((real_V1485227260804924795R_real @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 159.59/70.62 thf(1416,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/sandbox/benchmark/theBenchmark.p',fact_2331_neg__divide__less__eq)). 159.59/70.62 thf(12866,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)],[1416])). 159.59/70.62 thf(8140,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/sandbox/benchmark/theBenchmark.p',fact_888_power2__commute)). 159.59/70.62 thf(36284,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)],[8140])). 159.59/70.62 thf(398,axiom,((! [A:code_integer,B:code_integer]: ((if_Code_integer @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Code____Numeral__Ointeger_T)). 159.59/70.62 thf(9493,plain,((! [A:code_integer,B:code_integer]: ((if_Code_integer @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[398])). 159.59/70.62 thf(1415,axiom,((! [A:code_integer,B:nat,C:code_integer,D:nat]: ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ B) @ C) => ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ D) @ C) <= (ord_less_eq_nat @ D @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4113_power__le__dvd)). 159.59/70.62 thf(12863,plain,((! [A:code_integer,B:nat,C:code_integer,D:nat]: ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ B) @ C) => ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ D) @ C) | ~ (ord_less_eq_nat @ D @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415])). 159.59/70.62 thf(6137,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/sandbox/benchmark/theBenchmark.p',fact_243_power__add__numeral2)). 159.59/70.62 thf(28876,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)],[6137])). 159.59/70.62 thf(3592,axiom,((! [A:real,B:real,C:real,D:real]: (((A = B) & (C = D)) => ((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_add__mono__thms__linordered__semiring_I4_J)). 159.59/70.62 thf(19786,plain,((! [A:real,B:real,C:real,D:real]: (((A = B) & (C = D)) => ((plus_plus_real @ A @ C) = (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3592])). 159.59/70.62 thf(5595,axiom,((! [A:(nat > (nat > nat)),B:option_nat,C:option_nat,D:option_nat]: ((((D != none_nat) <= (B = none_nat)) => (((? [E:nat]: (B = (some_nat @ E))) => ((C = none_nat) => (D != none_nat))) => (~ (! [E:nat]: ((! [F:nat]: ((C = (some_nat @ F)) => (D != (some_nat @ (A @ E @ F))))) <= (B = (some_nat @ E))))))) <= ((vEBT_V4262088993061758097ft_nat @ A @ B @ C) = D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_VEBT__internal_Ooption__shift_Oelims)). 159.59/70.62 thf(26742,plain,((! [A:(nat > (nat > nat)),B:option_nat,C:option_nat,D:option_nat]: (((~ (D = none_nat) | ~ (B = none_nat)) => (((? [E:nat]: (B = (some_nat @ E))) => ((C = none_nat) => (~ (D = none_nat)))) => (~ (! [E:nat]: (! [F:nat]: ((C = (some_nat @ F)) => (~ (D = (some_nat @ (A @ E @ F))))) | ~ (B = (some_nat @ E))))))) | ~ ((vEBT_V4262088993061758097ft_nat @ (A) @ B @ C) = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5595])). 159.59/70.62 thf(8018,axiom,((! [A:nat,B:list_o,C:list_VEBT_VEBT]: (((nth_Pr6777367263587873994T_VEBT @ (product_o_VEBT_VEBT @ B @ C) @ A) = (produc2982872950893828659T_VEBT @ (nth_o @ 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_size_list_o @ B) @ (size_s6755466524823107622T_VEBT @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3593_product__nth)). 159.59/70.62 thf(35871,plain,((! [A:nat,B:list_o,C:list_VEBT_VEBT]: (((nth_Pr6777367263587873994T_VEBT @ (product_o_VEBT_VEBT @ B @ C) @ A) = (produc2982872950893828659T_VEBT @ (nth_o @ 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_size_list_o @ B) @ (size_s6755466524823107622T_VEBT @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8018])). 159.59/70.62 thf(2207,axiom,((! [A:extended_enat,B:(real > extended_enat),C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_le72135733267957522d_enat @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F))))) <= (ord_le72135733267957522d_enat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2889_order__less__subst1)). 159.59/70.62 thf(15373,plain,((! [A:extended_enat,B:(real > extended_enat),C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_le72135733267957522d_enat @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))))) | ~ (ord_le72135733267957522d_enat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2207])). 159.59/70.62 thf(65,axiom,(((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer) = zero_z3403309356797280102nteger)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4744_add__neg__numeral__special_I8_J)). 159.59/70.62 thf(8446,plain,(((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer) = zero_z3403309356797280102nteger)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 159.59/70.62 thf(1574,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/sandbox/benchmark/theBenchmark.p',fact_233_power__strict__increasing__iff)). 159.59/70.62 thf(13362,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)],[1574])). 159.59/70.62 thf(4424,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/sandbox/benchmark/theBenchmark.p',fact_4233_odd__iff__mod__2__eq__one)). 159.59/70.62 thf(22428,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)],[4424])). 159.59/70.62 thf(5625,axiom,(((modulo_modulo_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4858_minus__1__mod__2__eq)). 159.59/70.62 thf(26864,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)],[5625])). 159.59/70.62 thf(6101,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ A) => (B = A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2713_dual__order_Oantisym)). 159.59/70.62 thf(28752,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ A) => (B = A)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6101])). 159.59/70.62 thf(7058,axiom,((zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3323_zero__one__enat__neq_I1_J)). 159.59/70.62 thf(32555,plain,((~ (zero_z5237406670263579293d_enat = one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7058])). 159.59/70.62 thf(6949,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/sandbox/benchmark/theBenchmark.p',fact_1432_power__numeral__even)). 159.59/70.62 thf(32042,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)],[6949])). 159.59/70.62 thf(4613,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/sandbox/benchmark/theBenchmark.p',fact_6343_log__le__cancel__iff)). 159.59/70.62 thf(23195,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)],[4613])). 159.59/70.62 thf(8102,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/sandbox/benchmark/theBenchmark.p',fact_1203_add__mono__thms__linordered__field_I2_J)). 159.59/70.62 thf(36152,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)],[8102])). 159.59/70.62 thf(3919,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/sandbox/benchmark/theBenchmark.p',fact_6921_norm__power__ineq)). 159.59/70.62 thf(20861,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)],[3919])). 159.59/70.62 thf(2330,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A))) <= (dvd_dvd_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5122_dvd__neg__div)). 159.59/70.62 thf(15739,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A))) | ~ (dvd_dvd_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2330])). 159.59/70.62 thf(1378,axiom,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (minus_minus_complex @ (uminus1482373934393186551omplex @ A) @ B)) = (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6908_norm__uminus__minus)). 159.59/70.62 thf(12728,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)],[1378])). 159.59/70.62 thf(6373,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ A @ (power_power_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2466_self__le__power)). 159.59/70.62 thf(29711,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ A @ (power_power_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6373])). 159.59/70.62 thf(774,axiom,((! [A:real,B:real]: ((inverse_inverse_real @ (times_times_real @ A @ B)) = (times_times_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8978_inverse__mult__distrib)). 159.59/70.62 thf(10748,plain,((! [A:real,B:real]: ((inverse_inverse_real @ (times_times_real @ A @ B)) = (times_times_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[774])). 159.59/70.62 thf(7668,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: ((B = (plus_plus_nat @ A @ C)) => (C = zero_zero_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2112_canonically__ordered__monoid__add__class_OlessE)). 159.59/70.62 thf(34754,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: ((B = (plus_plus_nat @ A @ C)) => (C = zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7668])). 159.59/70.62 thf(96,axiom,(((cos_coeff @ zero_zero_nat) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8054_cos__coeff__0)). 159.59/70.62 thf(8545,plain,(((cos_coeff @ zero_zero_nat) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 159.59/70.62 thf(2815,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/sandbox/benchmark/theBenchmark.p',fact_1162_add__le__imp__le__left)). 159.59/70.62 thf(17306,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)],[2815])). 159.59/70.62 thf(5802,axiom,((! [A:nat]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4901_neg__one__odd__power)). 159.59/70.62 thf(27589,plain,((! [A:nat]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5802])). 159.59/70.62 thf(2557,axiom,((! [A:real,B:real]: ~ (ord_less_real @ (powr_real @ A @ B) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7232_powr__non__neg)). 159.59/70.62 thf(16472,plain,((! [A:real,B:real]: ~ (ord_less_real @ (powr_real @ A @ B) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2557])). 159.59/70.62 thf(5263,axiom,((! [A:num]: (ord_less_eq_num @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2603_dual__order_Orefl)). 159.59/70.62 thf(25480,plain,((! [A:num]: (ord_less_eq_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5263])). 159.59/70.62 thf(3554,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_real @ (sin_real @ A) @ (sin_real @ B)) = (ord_less_real @ A @ B)) <= (ord_less_eq_real @ B @ (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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6871_sin__mono__less__eq)). 159.59/70.62 thf(19652,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_real @ (sin_real @ A) @ (sin_real @ B)) = (ord_less_real @ A @ B)) | ~ (ord_less_eq_real @ B @ (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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3554])). 159.59/70.62 thf(8184,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (divide_divide_nat @ A @ C) @ B) <= (ord_less_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_less__mult__imp__div__less)). 159.59/70.62 thf(36421,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (divide_divide_nat @ A @ C) @ B) | ~ (ord_less_nat @ A @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8184])). 159.59/70.62 thf(1313,axiom,((! [A:complex,B:complex,C:complex]: ((A = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ C))) = (((C = zero_zero_complex) => (A = zero_zero_complex)) & (((times_times_complex @ A @ C) = (uminus1482373934393186551omplex @ B)) <= (C != zero_zero_complex)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5200_eq__minus__divide__eq)). 159.59/70.62 thf(12493,plain,((! [A:complex,B:complex,C:complex]: ((A = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ C))) = (((C = zero_zero_complex) => (A = zero_zero_complex)) & (((times_times_complex @ A @ C) = (uminus1482373934393186551omplex @ B)) | (C = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313])). 159.59/70.62 thf(1327,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/sandbox/benchmark/theBenchmark.p',fact_115_divide__le__eq__numeral1_I1_J)). 159.59/70.62 thf(12538,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)],[1327])). 159.59/70.62 thf(2769,axiom,((! [A:int,B:int]: (((ord_less_int @ B @ zero_zero_int) => (ord_less_int @ zero_zero_int @ (times_times_int @ A @ B))) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2106_mult__neg__neg)). 159.59/70.62 thf(17174,plain,((! [A:int,B:int]: (((ord_less_int @ B @ zero_zero_int) => (ord_less_int @ zero_zero_int @ (times_times_int @ A @ B))) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2769])). 159.59/70.62 thf(5684,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ B @ A)) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2855_order__less__asym_H)). 159.59/70.62 thf(27080,plain,((! [A:num,B:num]: (~ (ord_less_num @ B @ A) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5684])). 159.59/70.62 thf(2594,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((! [D:real]: ((ord_less_real @ A @ D) => ((ord_less_eq_real @ C @ D) <= (ord_less_real @ D @ B)))) => (ord_less_eq_real @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3102_dense__ge__bounded)). 159.59/70.62 thf(16588,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((! [D:real]: ((ord_less_real @ A @ D) => ((ord_less_eq_real @ C @ D) | ~ (ord_less_real @ D @ B)))) => (ord_less_eq_real @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2594])). 159.59/70.62 thf(5484,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/sandbox/benchmark/theBenchmark.p',fact_6639_numeral__power__le__of__nat__cancel__iff)). 159.59/70.62 thf(26389,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)],[5484])). 159.59/70.62 thf(1284,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/sandbox/benchmark/theBenchmark.p',fact_6299_of__int__round__gt)). 159.59/70.62 thf(12404,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)],[1284])). 159.59/70.62 thf(816,axiom,((! [A:complex,B:complex]: ((if_complex @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Complex__Ocomplex_T)). 159.59/70.62 thf(10887,plain,((! [A:complex,B:complex]: ((if_complex @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[816])). 159.59/70.62 thf(1569,axiom,((! [A:real,B:nat,C:real,D:nat]: ((dvd_dvd_real @ (power_power_real @ A @ B) @ C) => ((dvd_dvd_real @ (power_power_real @ A @ D) @ C) <= (ord_less_eq_nat @ D @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4115_power__le__dvd)). 159.59/70.62 thf(13347,plain,((! [A:real,B:nat,C:real,D:nat]: ((dvd_dvd_real @ (power_power_real @ A @ B) @ C) => ((dvd_dvd_real @ (power_power_real @ A @ D) @ C) | ~ (ord_less_eq_nat @ D @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569])). 159.59/70.62 thf(5876,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_812_Nat_Odiff__diff__right)). 159.59/70.62 thf(27958,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5876])). 159.59/70.62 thf(1392,axiom,((! [A:list_o,B:nat,C:$o]: (((list_update_o @ A @ B @ C) = A) <= (ord_less_eq_nat @ (size_size_list_o @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_list__update__beyond)). 159.59/70.62 thf(12792,plain,((! [A:list_o,B:nat,C:$o]: (((list_update_o @ A @ B @ C) = A) | ~ (ord_less_eq_nat @ (size_size_list_o @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392])). 159.59/70.62 thf(5272,axiom,((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5065_le__minus__one__simps_I2_J)). 159.59/70.62 thf(25512,plain,((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5272])). 159.59/70.62 thf(1527,axiom,((! [A:(nat > real),B:(nat > real)]: ((summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (A @ C)))) => (((times_times_real @ (suminf_real @ A) @ (suminf_real @ B)) = (suminf_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))) <= (summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (B @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8902_Cauchy__product)). 159.59/70.62 thf(13222,plain,((! [A:(nat > real),B:(nat > real)]: ((summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (A @ C)))) => (((times_times_real @ (suminf_real @ (A)) @ (suminf_real @ (B))) = (suminf_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))) | ~ (summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527])). 159.59/70.62 thf(4457,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3203_order__le__less__trans)). 159.59/70.62 thf(22528,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4457])). 159.59/70.62 thf(2789,axiom,((! [A:num]: ((semiri8010041392384452111omplex @ (numeral_numeral_nat @ A)) = (numera6690914467698888265omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6517_of__nat__numeral)). 159.59/70.62 thf(17232,plain,((! [A:num]: ((semiri8010041392384452111omplex @ (numeral_numeral_nat @ A)) = (numera6690914467698888265omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2789])). 159.59/70.62 thf(2285,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/sandbox/benchmark/theBenchmark.p',fact_6949_norm__triangle__ineq3)). 159.59/70.62 thf(15616,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)],[2285])). 159.59/70.62 thf(2804,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_int @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4451_pinf_I5_J)). 159.59/70.62 thf(17274,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)],[2804])). 159.59/70.62 thf(7837,axiom,((bit_se2925701944663578781it_nat = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (bit_se2925701944663578781it_nat @ (minus_minus_nat @ A @ one_one_nat) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4600_take__bit__rec)). 159.59/70.62 thf(35307,plain,(((bit_se2925701944663578781it_nat) = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (bit_se2925701944663578781it_nat @ (minus_minus_nat @ A @ one_one_nat) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7837])). 159.59/70.62 thf(7657,axiom,((nat_set_encode = (groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7733_set__encode__def)). 159.59/70.62 thf(34722,plain,(((nat_set_encode) = (groups3542108847815614940at_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7657])). 159.59/70.62 thf(2696,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2289_divide__nonneg__neg)). 159.59/70.62 thf(16949,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2696])). 159.59/70.62 thf(2158,axiom,((! [A:(nat > nat),B:(nat > nat)]: ((! [C:nat]: (ord_less_eq_nat @ (A @ C) @ (B @ C))) => (((summable_nat @ B) => (ord_less_eq_nat @ (suminf_nat @ A) @ (suminf_nat @ B))) <= (summable_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7034_suminf__le)). 159.59/70.62 thf(15211,plain,((! [A:(nat > nat),B:(nat > nat)]: ((! [C:nat]: (ord_less_eq_nat @ (A @ C) @ (B @ C))) => (((summable_nat @ (B)) => (ord_less_eq_nat @ (suminf_nat @ (A)) @ (suminf_nat @ (B)))) | ~ (summable_nat @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2158])). 159.59/70.62 thf(5436,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ A @ (set_ord_atMost_nat @ B)) = (plus_plus_nat @ (A @ zero_zero_nat) @ (groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8838_sum_OatMost__shift)). 159.59/70.62 thf(26222,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_ord_atMost_nat @ 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)],[5436])). 159.59/70.62 thf(2240,axiom,((ord_less_int = (^ [A:int]: (ord_less_eq_int @ (plus_plus_int @ A @ one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1451_discrete)). 159.59/70.62 thf(15481,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)],[2240])). 159.59/70.62 thf(2232,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (plus_plus_int @ A @ A)) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1593_zero__less__double__add__iff__zero__less__single__add)). 159.59/70.62 thf(15456,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)],[2232])). 159.59/70.62 thf(271,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/sandbox/benchmark/theBenchmark.p',fact_1301_max__add__distrib__right)). 159.59/70.62 thf(9073,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)],[271])). 159.59/70.62 thf(3632,axiom,((times_times_nat = (^ [A:nat,B:nat]: (nat2 @ (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9440_nat__times__as__int)). 159.59/70.62 thf(19918,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)],[3632])). 159.59/70.62 thf(3985,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/sandbox/benchmark/theBenchmark.p',fact_5927_floor__exists)). 159.59/70.62 thf(21063,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)],[3985])). 159.59/70.62 thf(3894,axiom,((! [A:nat,B:real]: ((((nat2 @ (archim6058952711729229775r_real @ B)) = A) <= (ord_less_real @ B @ (semiri5074537144036343181t_real @ (suc @ A)))) <= (ord_less_real @ (semiri5074537144036343181t_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9457_floor__eq3)). 159.59/70.62 thf(20787,plain,((! [A:nat,B:real]: (((nat2 @ (archim6058952711729229775r_real @ B)) = A) | ~ (ord_less_real @ B @ (semiri5074537144036343181t_real @ (suc @ A))) | ~ (ord_less_real @ (semiri5074537144036343181t_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3894])). 159.59/70.62 thf(357,axiom,((! [A:real,B:nat]: ((real_V1803761363581548252l_real @ (power_power_real @ A @ B)) = (power_power_real @ (real_V1803761363581548252l_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7333_of__real__power)). 159.59/70.62 thf(9355,plain,((! [A:real,B:nat]: ((real_V1803761363581548252l_real @ (power_power_real @ A @ B)) = (power_power_real @ (real_V1803761363581548252l_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])). 159.59/70.62 thf(5690,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/sandbox/benchmark/theBenchmark.p',fact_4232_odd__iff__mod__2__eq__one)). 159.59/70.62 thf(27095,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)],[5690])). 159.59/70.62 thf(4131,axiom,((! [A:(nat > real),B:real]: ((summable_real @ A) => (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7032_summable__mult2)). 159.59/70.62 thf(21498,plain,((! [A:(nat > real),B:real]: ((summable_real @ (A)) => (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4131])). 159.59/70.62 thf(2572,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/sandbox/benchmark/theBenchmark.p',fact_6789_of__nat__code__if)). 159.59/70.62 thf(16519,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)],[2572])). 159.59/70.62 thf(5547,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/sandbox/benchmark/theBenchmark.p',fact_5856_of__int__eq__neg__numeral__power__cancel__iff)). 159.59/70.62 thf(26595,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)],[5547])). 159.59/70.62 thf(5603,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) = (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3051_antisym__conv2)). 159.59/70.62 thf(26791,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)],[5603])). 159.59/70.62 thf(3813,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/sandbox/benchmark/theBenchmark.p',fact_5754_dbl__inc__simps_I1_J)). 159.59/70.62 thf(20513,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)],[3813])). 159.59/70.62 thf(4315,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_real @ zero_zero_real @ B)) | ((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2063_mult__less__cancel__right__disj)). 159.59/70.62 thf(22085,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_real @ zero_zero_real @ B)) | ((ord_less_real @ B @ zero_zero_real) & (ord_less_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4315])). 159.59/70.62 thf(7257,axiom,((! [A:(nat > nat),B:(nat > nat),C:nat,D:nat]: ((! [E:nat]: (ord_less_eq_nat @ (A @ E) @ (B @ E))) => (((ord_less_eq_nat @ C @ D) <= (sums_nat @ B @ D)) <= (sums_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7884_sums__le)). 159.59/70.62 thf(33342,plain,((! [A:(nat > nat),B:(nat > nat),C:nat,D:nat]: ((! [E:nat]: (ord_less_eq_nat @ (A @ E) @ (B @ E))) => ((ord_less_eq_nat @ C @ D) | ~ (sums_nat @ (B) @ D) | ~ (sums_nat @ (A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7257])). 159.59/70.62 thf(4393,axiom,((! [A:real]: ((gbinomial_real @ A @ zero_zero_nat) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8176_gbinomial__0_I1_J)). 159.59/70.62 thf(22322,plain,((! [A:real]: ((gbinomial_real @ A @ zero_zero_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4393])). 159.59/70.62 thf(8243,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/sandbox/benchmark/theBenchmark.p',fact_2096_mult__pos__neg)). 159.59/70.62 thf(36755,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)],[8243])). 159.59/70.62 thf(870,axiom,((! [A:int,B:int,C:int]: ((A = (minus_minus_int @ C @ B)) <= ((plus_plus_int @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1277_add__implies__diff)). 159.59/70.62 thf(11056,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)],[870])). 159.59/70.62 thf(3957,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) <= (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))))) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3243_order__less__le__subst2)). 159.59/70.62 thf(20985,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((ord_less_real @ (C @ A) @ D) | ~ (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))))) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3957])). 159.59/70.62 thf(2702,axiom,((! [A:nat,B:code_integer]: ((bit_se8260200283734997820nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se8260200283734997820nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3549_unset__bit__Suc)). 159.59/70.62 thf(16968,plain,((! [A:nat,B:code_integer]: ((bit_se8260200283734997820nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se8260200283734997820nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2702])). 159.59/70.62 thf(1278,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/sandbox/benchmark/theBenchmark.p',fact_8256_gbinomial__mult__1_H)). 159.59/70.62 thf(12382,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)],[1278])). 159.59/70.62 thf(3765,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => (! [D:complex,E:complex]: ((~ (dvd_dvd_complex @ A @ (plus_plus_complex @ D @ C))) = (~ (dvd_dvd_complex @ A @ (plus_plus_complex @ (minus_minus_complex @ D @ (times_times_complex @ E @ B)) @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4291_inf__period_I4_J)). 159.59/70.62 thf(20360,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => (! [D:complex,E:complex]: ((~ (dvd_dvd_complex @ A @ (plus_plus_complex @ D @ C))) = (~ (dvd_dvd_complex @ A @ (plus_plus_complex @ (minus_minus_complex @ D @ (times_times_complex @ E @ B)) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3765])). 159.59/70.62 thf(6796,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/sandbox/benchmark/theBenchmark.p',fact_5634_abs__square__eq__1)). 159.59/70.62 thf(31433,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)],[6796])). 159.59/70.62 thf(787,axiom,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ A) = B) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3839_dvd__div__mult__self)). 159.59/70.62 thf(10791,plain,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ A) = B) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[787])). 159.59/70.62 thf(2076,axiom,(((real_V7735802525324610683m_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6893_norm__one)). 159.59/70.62 thf(14941,plain,(((real_V7735802525324610683m_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2076])). 159.59/70.62 thf(7106,axiom,((! [A:int]: ((ord_less_eq_int @ A @ (uminus_uminus_int @ A)) = (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4670_less__eq__neg__nonpos)). 159.59/70.62 thf(32756,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)],[7106])). 159.59/70.62 thf(2282,axiom,((! [A:real,B:real]: ((((plus_plus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (times_times_real @ (times_times_real @ (plus_plus_real @ A @ B) @ (inverse_inverse_real @ A)) @ (inverse_inverse_real @ B))) <= (B != zero_zero_real)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9072_inverse__add)). 159.59/70.62 thf(15606,plain,((! [A:real,B:real]: (((plus_plus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (times_times_real @ (times_times_real @ (plus_plus_real @ A @ B) @ (inverse_inverse_real @ A)) @ (inverse_inverse_real @ B))) | (B = zero_zero_real) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2282])). 159.59/70.62 thf(6045,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/sandbox/benchmark/theBenchmark.p',fact_970_max_Ostrict__boundedE)). 159.59/70.62 thf(28586,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)],[6045])). 159.59/70.62 thf(6357,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/sandbox/benchmark/theBenchmark.p',fact_4246_even__flip__bit__iff)). 159.59/70.62 thf(29665,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)],[6357])). 159.59/70.62 thf(532,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/sandbox/benchmark/theBenchmark.p',fact_2592_Diff__eq__empty__iff)). 159.59/70.62 thf(9945,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)],[532])). 159.59/70.62 thf(4861,axiom,((! [A:nat]: (((semiri5074537144036343181t_real @ A) = zero_zero_real) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6508_of__nat__eq__0__iff)). 159.59/70.62 thf(24063,plain,((! [A:nat]: (((semiri5074537144036343181t_real @ A) = zero_zero_real) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4861])). 159.59/70.62 thf(323,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/sandbox/benchmark/theBenchmark.p',fact_9578_or__minus__minus__numerals)). 159.59/70.62 thf(9245,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)],[323])). 159.59/70.62 thf(3214,axiom,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real) = (((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ B @ zero_zero_real)) | ((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2101_mult__less__0__iff)). 159.59/70.62 thf(18586,plain,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real) = (((ord_less_real @ zero_zero_real @ A) & (ord_less_real @ 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)],[3214])). 159.59/70.62 thf(633,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) | (B = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1555_divide__eq__0__iff)). 159.59/70.62 thf(10281,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = zero_zero_real) = ((A = zero_zero_real) | (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[633])). 159.59/70.62 thf(29,axiom,((! [A:num,B:int]: ((bit_se6526347334894502574or_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = (bit_ri7919022796975470100ot_int @ (bit_se6526347334894502574or_int @ (neg_numeral_sub_int @ A @ one) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9768_xor__minus__numerals_I1_J)). 159.59/70.62 thf(8339,plain,((! [A:num,B:int]: ((bit_se6526347334894502574or_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ B) = (bit_ri7919022796975470100ot_int @ (bit_se6526347334894502574or_int @ (neg_numeral_sub_int @ A @ one) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 159.59/70.62 thf(884,axiom,((! [A:extended_enat]: ((~ (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A)) = (A = zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1476_not__gr__zero)). 159.59/70.62 thf(11096,plain,((! [A:extended_enat]: ((~ (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A)) = (A = zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[884])). 159.59/70.62 thf(513,axiom,((comm_s4660882817536571857er_int = (^ [A:int,B:nat]: (groups705719431365010083at_int @ (^ [C:nat]: (plus_plus_int @ A @ (semiri1314217659103216013at_int @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8895_pochhammer__prod__rev)). 159.59/70.62 thf(9889,plain,(((comm_s4660882817536571857er_int) = (^ [A:int,B:nat]: (groups705719431365010083at_int @ (^ [C:nat]: (plus_plus_int @ A @ (semiri1314217659103216013at_int @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[513])). 159.59/70.62 thf(7456,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B)) = (uminus1482373934393186551omplex @ (minus_minus_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4979_minus__diff__minus)). 159.59/70.62 thf(34008,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)],[7456])). 159.59/70.62 thf(5725,axiom,((! [A:nat,B:list_o,C:list_int]: ((ord_less_nat @ A @ (times_times_nat @ (size_size_list_o @ B) @ (size_size_list_int @ C))) => ((nth_Pr1649062631805364268_o_int @ (product_o_int @ B @ C) @ A) = (product_Pair_o_int @ (nth_o @ B @ (divide_divide_nat @ A @ (size_size_list_int @ C))) @ (nth_int @ C @ (modulo_modulo_nat @ A @ (size_size_list_int @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3596_product__nth)). 159.59/70.62 thf(27209,plain,((! [A:nat,B:list_o,C:list_int]: ((ord_less_nat @ A @ (times_times_nat @ (size_size_list_o @ B) @ (size_size_list_int @ C))) => ((nth_Pr1649062631805364268_o_int @ (product_o_int @ B @ C) @ A) = (product_Pair_o_int @ (nth_o @ B @ (divide_divide_nat @ A @ (size_size_list_int @ C))) @ (nth_int @ C @ (modulo_modulo_nat @ A @ (size_size_list_int @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5725])). 159.59/70.62 thf(4514,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ one_one_nat) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6013_or__numerals_I5_J)). 159.59/70.62 thf(22769,plain,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ one_one_nat) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4514])). 159.59/70.62 thf(478,axiom,((! [A:real,B:real]: ((times_times_complex @ (cis @ A) @ (cis @ B)) = (cis @ (plus_plus_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9379_cis__mult)). 159.59/70.62 thf(9773,plain,((! [A:real,B:real]: ((times_times_complex @ (cis @ A) @ (cis @ B)) = (cis @ (plus_plus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])). 159.59/70.62 thf(1330,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/sandbox/benchmark/theBenchmark.p',fact_819_add__diff__add)). 159.59/70.62 thf(12546,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)],[1330])). 159.59/70.62 thf(6665,axiom,((! [A:int,B:int]: ((A = B) => (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2673_order__eq__refl)). 159.59/70.62 thf(30832,plain,((! [A:int,B:int]: ((A = B) => (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6665])). 159.59/70.62 thf(3254,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/sandbox/benchmark/theBenchmark.p',fact_6943_norm__triangle__ineq2)). 159.59/70.62 thf(18718,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)],[3254])). 159.59/70.62 thf(2381,axiom,((! [A:real,B:real,C:real,D: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)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2373_diff__frac__eq)). 159.59/70.62 thf(15896,plain,((! [A:real,B:real,C:real,D: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) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2381])). 159.59/70.62 thf(5756,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ (power_power_int @ A @ B) @ zero_zero_int) = ((((A = zero_zero_int) & (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))) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4271_power__le__zero__eq)). 159.59/70.62 thf(27314,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ (power_power_int @ A @ B) @ zero_zero_int) = ((((A = zero_zero_int) & (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))) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5756])). 159.59/70.62 thf(5251,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/sandbox/benchmark/theBenchmark.p',fact_237_power__add__numeral)). 159.59/70.62 thf(25441,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)],[5251])). 159.59/70.62 thf(2458,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/sandbox/benchmark/theBenchmark.p',fact_7537_sum__power__add)). 159.59/70.62 thf(16163,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)],[2458])). 159.59/70.62 thf(2782,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ A) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4481_minf_I5_J)). 159.59/70.62 thf(17213,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ A) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2782])). 159.59/70.62 thf(3242,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/sandbox/benchmark/theBenchmark.p',fact_7985_suminf__split__initial__segment)). 159.59/70.62 thf(18677,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)],[3242])). 159.59/70.62 thf(6118,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/sandbox/benchmark/theBenchmark.p',fact_3356_Icc__eq__Icc)). 159.59/70.62 thf(28812,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)],[6118])). 159.59/70.62 thf(7033,axiom,((! [A:nat,B:nat]: (((semiri1316708129612266289at_nat @ A) = (semiri1316708129612266289at_nat @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6489_of__nat__eq__iff)). 159.59/70.62 thf(32455,plain,((! [A:nat,B:nat]: (((semiri1316708129612266289at_nat @ A) = (semiri1316708129612266289at_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7033])). 159.59/70.62 thf(2715,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/sandbox/benchmark/theBenchmark.p',fact_8204_floor__one__divide__eq__div__numeral)). 159.59/70.62 thf(17010,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)],[2715])). 159.59/70.62 thf(5841,axiom,((! [A:nat,B:vEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ (replicate_VEBT_VEBT @ A @ B)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4333_length__replicate)). 159.59/70.62 thf(27837,plain,((! [A:nat,B:vEBT_VEBT]: ((size_s6755466524823107622T_VEBT @ (replicate_VEBT_VEBT @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5841])). 159.59/70.62 thf(2849,axiom,((! [A:real]: ((ord_less_int @ zero_zero_int @ (archim6058952711729229775r_real @ A)) = (ord_less_eq_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8188_zero__less__floor)). 159.59/70.62 thf(17412,plain,((! [A:real]: ((ord_less_int @ zero_zero_int @ (archim6058952711729229775r_real @ A)) = (ord_less_eq_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2849])). 159.59/70.62 thf(5898,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/sandbox/benchmark/theBenchmark.p',fact_4866_Parity_Oring__1__class_Opower__minus__even)). 159.59/70.62 thf(28038,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)],[5898])). 159.59/70.62 thf(3704,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2797_dual__order_Oasym)). 159.59/70.62 thf(20148,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3704])). 159.59/70.62 thf(4578,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2925701944663578781it_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4876_even__take__bit__eq)). 159.59/70.62 thf(23049,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2925701944663578781it_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4578])). 159.59/70.62 thf(7967,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/sandbox/benchmark/theBenchmark.p',fact_454_power2__nat__le__eq__le)). 159.59/70.62 thf(35716,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)],[7967])). 159.59/70.62 thf(3773,axiom,((! [A:int]: ((~ (! [B:int]: (A != (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ one_one_int)))) <= (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4250_oddE)). 159.59/70.62 thf(20387,plain,((! [A:int]: (~ (! [B:int]: ~ (A = (plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ one_one_int))) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3773])). 159.59/70.62 thf(4185,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/sandbox/benchmark/theBenchmark.p',fact_4025_dvd__power__same)). 159.59/70.62 thf(21673,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)],[4185])). 159.59/70.62 thf(854,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le2932123472753598470d_enat @ B @ C) => (ord_le2932123472753598470d_enat @ B @ (plus_p3455044024723400733d_enat @ A @ C))) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2040_add__increasing)). 159.59/70.62 thf(11007,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le2932123472753598470d_enat @ B @ C) => (ord_le2932123472753598470d_enat @ B @ (plus_p3455044024723400733d_enat @ A @ C))) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[854])). 159.59/70.62 thf(8224,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/sandbox/benchmark/theBenchmark.p',fact_4893_power__minus1__even)). 159.59/70.62 thf(36548,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)],[8224])). 159.59/70.62 thf(7739,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_add__less__mono1)). 159.59/70.62 thf(35015,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7739])). 159.59/70.62 thf(7881,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/sandbox/benchmark/theBenchmark.p',fact_1069_add__less__cancel__right)). 159.59/70.62 thf(35443,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)],[7881])). 159.59/70.62 thf(719,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/sandbox/benchmark/theBenchmark.p',fact_2372_diff__divide__eq__iff)). 159.59/70.62 thf(10566,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)],[719])). 159.59/70.62 thf(8023,axiom,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: ((A @ B) & ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2807_exists__least__iff)). 159.59/70.62 thf(35888,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)],[8023])). 159.59/70.62 thf(5060,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/sandbox/benchmark/theBenchmark.p',fact_5642_cong__exp__iff__simps_I7_J)). 159.59/70.62 thf(24771,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)],[5060])). 159.59/70.62 thf(739,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5948_zero__and__eq)). 159.59/70.62 thf(10644,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[739])). 159.59/70.62 thf(61,axiom,((! [A:num]: ((ord_max_int @ one_one_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_max__0__1_I5_J)). 159.59/70.62 thf(8435,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)],[61])). 159.59/70.62 thf(1903,axiom,((! [A:complex,B:nat]: ((times_times_complex @ (power_power_complex @ A @ B) @ (invers8013647133539491842omplex @ A)) = (times_times_complex @ (invers8013647133539491842omplex @ A) @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9049_power__mult__inverse__distrib)). 159.59/70.62 thf(14398,plain,((! [A:complex,B:nat]: ((times_times_complex @ (power_power_complex @ A @ B) @ (invers8013647133539491842omplex @ A)) = (times_times_complex @ (invers8013647133539491842omplex @ A) @ (power_power_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1903])). 159.59/70.62 thf(3822,axiom,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_complex @ (C @ A) @ (groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7664_sum_OatLeast__Suc__atMost)). 159.59/70.62 thf(20538,plain,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (plus_plus_complex @ (C @ A) @ (groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3822])). 159.59/70.62 thf(3138,axiom,((numeral_numeral_nat = (^ [A:num]: (nat2 @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9427_nat__numeral__as__int)). 159.59/70.62 thf(18351,plain,(((numeral_numeral_nat) = (^ [A:num]: (nat2 @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3138])). 159.59/70.62 thf(7449,axiom,((! [A: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 @ A @ one_one_real)) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7318_cos__arcsin)). 159.59/70.62 thf(33989,plain,((! [A: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 @ A @ one_one_real) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7449])). 159.59/70.62 thf(6690,axiom,(((modulo_modulo_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4860_bits__minus__1__mod__2__eq)). 159.59/70.62 thf(30975,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)],[6690])). 159.59/70.62 thf(222,axiom,(((neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger) = (uminus1351360451143612070nteger @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5696_dbl__dec__simps_I2_J)). 159.59/70.62 thf(8931,plain,(((neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger) = (uminus1351360451143612070nteger @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[222])). 159.59/70.62 thf(4368,axiom,((! [A:(nat > complex),B:complex,C:nat]: ((sums_complex @ A @ B) => (sums_complex @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ C))) @ (minus_minus_complex @ B @ (groups2073611262835488442omplex @ A @ (set_ord_lessThan_nat @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7903_sums__split__initial__segment)). 159.59/70.62 thf(22241,plain,((! [A:(nat > complex),B:complex,C:nat]: ((sums_complex @ (A) @ B) => (sums_complex @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ C))) @ (minus_minus_complex @ B @ (groups2073611262835488442omplex @ (A) @ (set_ord_lessThan_nat @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4368])). 159.59/70.62 thf(7246,axiom,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ A @ A) = (times_3573771949741848930nteger @ B @ B)) = ((A = B) | (A = (uminus1351360451143612070nteger @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4959_square__eq__iff)). 159.59/70.62 thf(33310,plain,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ A @ A) = (times_3573771949741848930nteger @ B @ B)) = ((A = B) | (A = (uminus1351360451143612070nteger @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7246])). 159.59/70.62 thf(7114,axiom,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1690_less__Suc0)). 159.59/70.62 thf(32788,plain,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7114])). 159.59/70.62 thf(240,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se1080825931792720795nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) & (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6100_even__or__iff)). 159.59/70.62 thf(8984,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se1080825931792720795nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) & (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[240])). 159.59/70.62 thf(119,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/sandbox/benchmark/theBenchmark.p',fact_9675_Re__divide)). 159.59/70.62 thf(8619,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)],[119])). 159.59/70.62 thf(5981,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/sandbox/benchmark/theBenchmark.p',fact_9829_String_Ochar__of__ascii__of)). 159.59/70.62 thf(28382,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)],[5981])). 159.59/70.62 thf(7259,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/sandbox/benchmark/theBenchmark.p',fact_5869_neg__numeral__power__le__of__int__cancel__iff)). 159.59/70.62 thf(33348,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)],[7259])). 159.59/70.62 thf(6387,axiom,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1726_less__one)). 159.59/70.62 thf(29794,plain,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6387])). 159.59/70.62 thf(6736,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1264_right__diff__distrib)). 159.59/70.62 thf(31217,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6736])). 159.59/70.62 thf(3438,axiom,((! [A:nat]: ((bit_se1146084159140164899it_int @ one_one_int @ A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6385_bit__1__iff)). 159.59/70.62 thf(19302,plain,((! [A:nat]: ((bit_se1146084159140164899it_int @ one_one_int @ A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3438])). 159.59/70.62 thf(1937,axiom,((! [A:int,B:int,C:nat]: ((comm_s4660882817536571857er_int @ (plus_plus_int @ A @ B) @ C) = (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (times_times_int @ (semiri1314217659103216013at_int @ (binomial @ C @ D)) @ (comm_s4660882817536571857er_int @ A @ D)) @ (comm_s4660882817536571857er_int @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9151_pochhammer__binomial__sum)). 159.59/70.62 thf(14505,plain,((! [A:int,B:int,C:nat]: ((comm_s4660882817536571857er_int @ (plus_plus_int @ A @ B) @ C) = (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (times_times_int @ (semiri1314217659103216013at_int @ (binomial @ C @ D)) @ (comm_s4660882817536571857er_int @ A @ D)) @ (comm_s4660882817536571857er_int @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1937])). 159.59/70.62 thf(8253,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)) | ((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ A @ E) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4034_bezout__add__nat)). 159.59/70.62 thf(36787,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)) | ((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ A @ E) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8253])). 159.59/70.62 thf(6269,axiom,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8996_binomial__eq__0__iff)). 159.59/70.62 thf(29376,plain,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6269])). 159.59/70.62 thf(4392,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/sandbox/benchmark/theBenchmark.p',fact_7998_diff__power__eq__sum)). 159.59/70.62 thf(22319,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)],[4392])). 159.59/70.62 thf(3296,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/sandbox/benchmark/theBenchmark.p',fact_9548_push__bit__negative__int__iff)). 159.59/70.62 thf(18860,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)],[3296])). 159.59/70.62 thf(4057,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/sandbox/benchmark/theBenchmark.p',fact_5521_abs__triangle__ineq)). 159.59/70.62 thf(21275,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)],[4057])). 159.59/70.62 thf(5065,axiom,((! [A:num,B:num,C:num]: (((((((~ (ord_less_eq_num @ C @ A)) <= (ord_less_eq_num @ B @ C)) => (~ ((ord_less_eq_num @ C @ A) => (~ (ord_less_eq_num @ A @ B))))) <= ((ord_less_eq_num @ C @ B) => (~ (ord_less_eq_num @ B @ A)))) <= ((~ (ord_less_eq_num @ C @ B)) <= (ord_less_eq_num @ A @ C))) <= ((~ (ord_less_eq_num @ A @ C)) <= (ord_less_eq_num @ B @ A))) <= ((~ (ord_less_eq_num @ B @ C)) <= (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2752_le__cases3)). 159.59/70.62 thf(24786,plain,((! [A:num,B:num,C:num]: (((~ (ord_less_eq_num @ C @ A) | ~ (ord_less_eq_num @ B @ C)) => (~ ((ord_less_eq_num @ C @ A) => (~ (ord_less_eq_num @ A @ B))))) | ~ ((ord_less_eq_num @ C @ B) => (~ (ord_less_eq_num @ B @ A))) | ~ (~ (ord_less_eq_num @ C @ B) | ~ (ord_less_eq_num @ A @ C)) | ~ (~ (ord_less_eq_num @ A @ C) | ~ (ord_less_eq_num @ B @ A)) | ~ (~ (ord_less_eq_num @ B @ C) | ~ (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5065])). 159.59/70.62 thf(4705,axiom,((! [A:nat]: ((A != one_one_nat) => ((groups6591440286371151544t_real @ (^ [B:nat]: (times_times_real @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (semiri5074537144036343181t_real @ B)) @ (semiri5074537144036343181t_real @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9167_choose__alternating__linear__sum)). 159.59/70.62 thf(23518,plain,((! [A:nat]: ((~ (A = one_one_nat)) => ((groups6591440286371151544t_real @ (^ [B:nat]: (times_times_real @ (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (semiri5074537144036343181t_real @ B)) @ (semiri5074537144036343181t_real @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4705])). 159.59/70.62 thf(67,axiom,((! [A:(code_integer > $o),B:code_integer]: ((? [C:code_integer]: (A @ (times_3573771949741848930nteger @ B @ C))) = (? [C:code_integer]: ((dvd_dvd_Code_integer @ B @ (plus_p5714425477246183910nteger @ C @ zero_z3403309356797280102nteger)) & (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4298_unity__coeff__ex)). 159.59/70.62 thf(8451,plain,((! [A:(code_integer > $o),B:code_integer]: ((? [C:code_integer]: (A @ (times_3573771949741848930nteger @ B @ C))) = (? [C:code_integer]: ((dvd_dvd_Code_integer @ B @ (plus_p5714425477246183910nteger @ C @ zero_z3403309356797280102nteger)) & (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 159.59/70.62 thf(7502,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/sandbox/benchmark/theBenchmark.p',fact_4794_semiring__norm_I170_J)). 159.59/70.62 thf(34194,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)],[7502])). 159.59/70.62 thf(422,axiom,((! [A:real,B:real]: ((ord_less_real @ (tanh_real @ A) @ (tanh_real @ B)) = (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5400_tanh__real__less__iff)). 159.59/70.62 thf(9576,plain,((! [A:real,B:real]: ((ord_less_real @ (tanh_real @ A) @ (tanh_real @ B)) = (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])). 159.59/70.62 thf(8177,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/sandbox/benchmark/theBenchmark.p',fact_1193_add__strict__left__mono)). 159.59/70.62 thf(36402,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)],[8177])). 159.59/70.62 thf(3827,axiom,((! [A:nat,B:nat]: ((nat_prod_encode @ (nat_prod_decode_aux @ A @ B)) = (plus_plus_nat @ (nat_triangle @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10204_prod__encode__prod__decode__aux)). 159.59/70.62 thf(20553,plain,((! [A:nat,B:nat]: ((nat_prod_encode @ (nat_prod_decode_aux @ A @ B)) = (plus_plus_nat @ (nat_triangle @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3827])). 159.59/70.62 thf(3028,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((A != B) => (ord_less_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2792_linorder__cases)). 159.59/70.62 thf(17985,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((~ (A = B)) => (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3028])). 159.59/70.62 thf(8170,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) <= (ord_less_nat @ one_one_nat @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_power__strict__increasing)). 159.59/70.62 thf(36380,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) | ~ (ord_less_nat @ one_one_nat @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8170])). 159.59/70.62 thf(1887,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/sandbox/benchmark/theBenchmark.p',fact_7659_sum_OatLeast0__atMost__Suc)). 159.59/70.62 thf(14348,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)],[1887])). 159.59/70.62 thf(2451,axiom,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ C) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6934_norm__triangle__le__diff)). 159.59/70.62 thf(16144,plain,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B)) @ C) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2451])). 159.59/70.62 thf(4153,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/sandbox/benchmark/theBenchmark.p',fact_8230_gbinomial__pochhammer)). 159.59/70.62 thf(21577,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)],[4153])). 159.59/70.62 thf(7016,axiom,(((suc @ na) = m)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526__C8_C)). 159.59/70.62 thf(32404,plain,(((suc @ na) = m)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7016])). 159.59/70.62 thf(7828,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_times__div__less__eq__dividend)). 159.59/70.62 thf(35281,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)],[7828])). 159.59/70.62 thf(8059,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/sandbox/benchmark/theBenchmark.p',fact_3567_mult__exp__mod__exp__eq)). 159.59/70.62 thf(36020,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)],[8059])). 159.59/70.62 thf(5035,axiom,((! [A:int,B:(int > int),C:int,D:int]: (((ord_less_eq_int @ C @ D) => ((ord_less_eq_int @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))))) <= (ord_less_eq_int @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2692_order__subst1)). 159.59/70.62 thf(24670,plain,((! [A:int,B:(int > int),C:int,D:int]: (((ord_less_eq_int @ C @ D) => ((ord_less_eq_int @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))))) | ~ (ord_less_eq_int @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5035])). 159.59/70.62 thf(5514,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1965_mult__nonneg__nonpos2)). 159.59/70.62 thf(26499,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5514])). 159.59/70.62 thf(2046,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/sandbox/benchmark/theBenchmark.p',fact_5833_of__int__less__1__iff)). 159.59/70.62 thf(14855,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)],[2046])). 159.59/70.62 thf(4803,axiom,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: ((A != B) <= ((size_s6755466524823107622T_VEBT @ A) != (size_s6755466524823107622T_VEBT @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_size__neq__size__imp__neq)). 159.59/70.62 thf(23837,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)],[4803])). 159.59/70.62 thf(3286,axiom,((! [A:real,B:int]: ((((~ (ord_less_eq_int @ zero_zero_int @ B)) => ((powr_real @ A @ (ring_1_of_int_real @ B)) = (inverse_inverse_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/sandbox/benchmark/theBenchmark.p',fact_9471_powr__real__of__int)). 159.59/70.62 thf(18828,plain,((! [A:real,B:int]: ((((~ (ord_less_eq_int @ zero_zero_int @ B)) => ((powr_real @ A @ (ring_1_of_int_real @ B)) = (inverse_inverse_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)],[3286])). 159.59/70.62 thf(1898,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/sandbox/benchmark/theBenchmark.p',fact_8477_mod__prod__eq)). 159.59/70.62 thf(14381,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)],[1898])). 159.59/70.62 thf(896,axiom,((! [A:(nat > 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 @ D)) @ (A @ D))))) <= (summable_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7019_summable__comparison__test_H)). 159.59/70.62 thf(11128,plain,((! [A:(nat > 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 @ D)) @ (A @ D)))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[896])). 159.59/70.62 thf(4357,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ B @ C) => (ord_less_eq_set_nat @ A @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2956_subset__trans)). 159.59/70.62 thf(22209,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ B @ C) => (ord_less_eq_set_nat @ A @ C)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4357])). 159.59/70.62 thf(3521,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ (abs_abs_real @ B))) = ((B = zero_zero_real) | (ord_less_eq_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5433_zero__le__divide__abs__iff)). 159.59/70.62 thf(19556,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ (abs_abs_real @ B))) = ((B = zero_zero_real) | (ord_less_eq_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3521])). 159.59/70.62 thf(683,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/sandbox/benchmark/theBenchmark.p',fact_7165_cos__gt__zero)). 159.59/70.62 thf(10434,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)],[683])). 159.59/70.62 thf(4587,axiom,((! [A:real,B:real,C:nat]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) <= (ord_less_eq_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2151_power__mono)). 159.59/70.62 thf(23094,plain,((! [A:real,B:real,C:nat]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) | ~ (ord_less_eq_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4587])). 159.59/70.62 thf(5084,axiom,((! [A:num,B:num]: ((numera6690914467698888265omplex @ A) != (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4946_numeral__neq__neg__numeral)). 159.59/70.62 thf(24862,plain,((! [A:num,B:num]: ~ ((numera6690914467698888265omplex @ A) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5084])). 159.59/70.62 thf(5591,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) => (dvd_dvd_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3957_dvd__mult__left)). 159.59/70.62 thf(26732,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) => (dvd_dvd_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5591])). 159.59/70.62 thf(1120,axiom,((! [A:extended_enat,B:extended_enat]: ((power_8040749407984259932d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_p3455044024723400733d_enat @ (plus_p3455044024723400733d_enat @ (power_8040749407984259932d_enat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_8040749407984259932d_enat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_7803423173614009249d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_power2__sum)). 159.59/70.62 thf(11845,plain,((! [A:extended_enat,B:extended_enat]: ((power_8040749407984259932d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_p3455044024723400733d_enat @ (plus_p3455044024723400733d_enat @ (power_8040749407984259932d_enat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_8040749407984259932d_enat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_7803423173614009249d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120])). 159.59/70.62 thf(6123,axiom,((! [A:nat,B:nat]: ((size_size_list_nat @ (upt @ A @ B)) = (minus_minus_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10123_length__upt)). 159.59/70.62 thf(28827,plain,((! [A:nat,B:nat]: ((size_size_list_nat @ (upt @ A @ B)) = (minus_minus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6123])). 159.59/70.62 thf(1485,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 @ B @ one_one_real) => (ord_less_eq_real @ (powr_real @ B @ A) @ one_one_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7247_powr__le1)). 159.59/70.62 thf(13099,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 @ B @ one_one_real) => (ord_less_eq_real @ (powr_real @ B @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485])). 159.59/70.62 thf(2734,axiom,((dvd_dvd_real = (^ [A:real,B:real]: ? [C:real]: (B = (times_times_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3941_dvd__def)). 159.59/70.62 thf(17065,plain,(((dvd_dvd_real) = (^ [A:real,B:real]: ? [C:real]: (B = (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2734])). 159.59/70.62 thf(3832,axiom,((! [A:(real > (real > $o)),B:set_nat,C:(nat > real),D:(nat > real)]: ((A @ zero_zero_real @ zero_zero_real) => (((finite_finite_nat @ B) => ((A @ (groups6591440286371151544t_real @ C @ B) @ (groups6591440286371151544t_real @ D @ B)) <= (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))))) <= (! [E:real,F:real,G:real,H:real]: ((A @ (plus_plus_real @ E @ F) @ (plus_plus_real @ G @ H)) <= ((A @ E @ G) & (A @ F @ H)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7492_sum_Orelated)). 159.59/70.62 thf(20570,plain,((! [A:(real > (real > $o)),B:set_nat,C:(nat > real),D:(nat > real)]: ((A @ zero_zero_real @ zero_zero_real) => (((finite_finite_nat @ B) => ((A @ (groups6591440286371151544t_real @ (C) @ B) @ (groups6591440286371151544t_real @ (D) @ B)) | ~ (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))))) | ~ (! [E:real,F:real,G:real,H:real]: ((A @ (plus_plus_real @ E @ F) @ (plus_plus_real @ G @ H)) | ~ ((A @ E @ G) & (A @ F @ H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3832])). 159.59/70.62 thf(4214,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) <= (ord_less_eq_real @ C @ D)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_add__mono)). 159.59/70.62 thf(21771,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D)) | ~ (ord_less_eq_real @ C @ D) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4214])). 159.59/70.62 thf(4550,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/sandbox/benchmark/theBenchmark.p',fact_5445_semiring__norm_I16_J)). 159.59/70.62 thf(22969,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)],[4550])). 159.59/70.62 thf(4658,axiom,((! [A:nat]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (uminus_uminus_int @ one_one_int)) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ A)) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5224_take__bit__Suc__minus__1__eq)). 159.59/70.62 thf(23355,plain,((! [A:nat]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (uminus_uminus_int @ one_one_int)) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (suc @ A)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4658])). 159.59/70.62 thf(2092,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/sandbox/benchmark/theBenchmark.p',fact_4068_unit__mult__left__cancel)). 159.59/70.62 thf(14990,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)],[2092])). 159.59/70.62 thf(7018,axiom,((! [A:nat,B:nat]: (((ord_max_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1570_max__nat_Oeq__neutr__iff)). 159.59/70.62 thf(32409,plain,((! [A:nat,B:nat]: (((ord_max_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7018])). 159.59/70.62 thf(985,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/sandbox/benchmark/theBenchmark.p',fact_2279_field__le__epsilon)). 159.59/70.62 thf(11400,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)],[985])). 159.59/70.62 thf(4190,axiom,((! [A:int]: ((modulo_modulo_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3391_bits__mod__0)). 159.59/70.62 thf(21687,plain,((! [A:int]: ((modulo_modulo_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4190])). 159.59/70.62 thf(8138,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/sandbox/benchmark/theBenchmark.p',fact_3863_even__Suc__Suc__iff)). 159.59/70.62 thf(36279,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)],[8138])). 159.59/70.62 thf(1393,axiom,((! [A:set_nat,B:set_nat,C:nat,D:(nat > int)]: (((ord_less_eq_set_nat @ B @ A) => ((member_nat @ C @ (minus_minus_set_nat @ A @ B)) => (((! [E:nat]: ((member_nat @ E @ A) => (ord_less_eq_int @ zero_zero_int @ (D @ E)))) => (ord_less_int @ (groups3539618377306564664at_int @ D @ B) @ (groups3539618377306564664at_int @ D @ A))) <= (ord_less_int @ zero_zero_int @ (D @ C))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7742_sum__strict__mono2)). 159.59/70.62 thf(12796,plain,((! [A:set_nat,B:set_nat,C:nat,D:(nat > int)]: (((ord_less_eq_set_nat @ B @ A) => ((member_nat @ C @ (minus_minus_set_nat @ A @ B)) => (((! [E:nat]: ((member_nat @ E @ A) => (ord_less_eq_int @ zero_zero_int @ (D @ E)))) => (ord_less_int @ (groups3539618377306564664at_int @ (D) @ B) @ (groups3539618377306564664at_int @ (D) @ A))) | ~ (ord_less_int @ zero_zero_int @ (D @ C))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393])). 159.59/70.62 thf(4338,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4677_neg__0__less__iff__less)). 159.59/70.62 thf(22154,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)],[4338])). 159.59/70.62 thf(7213,axiom,((! [A:(nat > (nat > nat)),B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (groups3542108847815614940at_nat @ (A @ C) @ (set_ord_lessThan_nat @ C))) @ (set_ord_atMost_nat @ B)) = (groups3542108847815614940at_nat @ (^ [C:nat]: (groups3542108847815614940at_nat @ (^ [D:nat]: (A @ D @ C)) @ (set_or1269000886237332187st_nat @ (suc @ C) @ B))) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8767_sum_Onested__swap_H)). 159.59/70.62 thf(33200,plain,((! [A:(nat > (nat > nat)),B:nat]: ((groups3542108847815614940at_nat @ (^ [C:nat]: (groups3542108847815614940at_nat @ (A @ C) @ (set_ord_lessThan_nat @ C))) @ (set_ord_atMost_nat @ B)) = (groups3542108847815614940at_nat @ (^ [C:nat]: (groups3542108847815614940at_nat @ (^ [D:nat]: (A @ D @ C)) @ (set_or1269000886237332187st_nat @ (suc @ C) @ B))) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7213])). 159.59/70.62 thf(6173,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/sandbox/benchmark/theBenchmark.p',fact_6471_real__sqrt__sum__squares__mult__ge__zero)). 159.59/70.62 thf(29003,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)],[6173])). 159.59/70.62 thf(59,axiom,((exp_real = (^ [A:real]: (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9285_exp__def)). 159.59/70.62 thf(8429,plain,(((exp_real) = (^ [A:real]: (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 159.59/70.62 thf(2233,axiom,((! [A:int,B:int]: (((divide_divide_int @ B @ (uminus_uminus_int @ A)) = (uminus_uminus_int @ (divide_divide_int @ B @ A))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5117_dvd__div__neg)). 159.59/70.62 thf(15459,plain,((! [A:int,B:int]: (((divide_divide_int @ B @ (uminus_uminus_int @ A)) = (uminus_uminus_int @ (divide_divide_int @ B @ A))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2233])). 159.59/70.62 thf(2155,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => (((ord_less_real @ (arcsin @ A) @ (arcsin @ B)) = (ord_less_real @ A @ B)) <= (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7711_arcsin__less__mono)). 159.59/70.62 thf(15201,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => (((ord_less_real @ (arcsin @ A) @ (arcsin @ B)) = (ord_less_real @ A @ B)) | ~ (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2155])). 159.59/70.62 thf(361,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/sandbox/benchmark/theBenchmark.p',fact_9599_numeral__or__not__num__eq)). 159.59/70.62 thf(9376,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)],[361])). 159.59/70.62 thf(916,axiom,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1540_div__0)). 159.59/70.62 thf(11189,plain,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[916])). 159.59/70.62 thf(7311,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C))) = (! [C:nat]: ((B @ C) <= (member_nat @ C @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9580_all__nat__less__eq)). 159.59/70.62 thf(33544,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (B @ C))) = (! [C:nat]: ((B @ C) | ~ (member_nat @ C @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7311])). 159.59/70.62 thf(102,axiom,(((arg @ imaginary_unit) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9373_Arg__ii)). 159.59/70.62 thf(8567,plain,(((arg @ imaginary_unit) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[102])). 159.59/70.62 thf(6288,axiom,((! [A:nat]: ((A = zero_zero_nat) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1919_bot__nat__0_Oextremum__uniqueI)). 159.59/70.62 thf(29453,plain,((! [A:nat]: ((A = zero_zero_nat) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6288])). 159.59/70.62 thf(1568,axiom,((! [A:(nat > int),B:nat,C:int]: ? [D:(nat > int)]: ! [E:int]: ((groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (A @ F) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ B)) = (plus_plus_int @ (times_times_int @ (minus_minus_int @ E @ C) @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (D @ F) @ (power_power_int @ E @ F))) @ (set_ord_lessThan_nat @ B))) @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (A @ F) @ (power_power_int @ C @ F))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8886_polyfun__linear__factor)). 159.59/70.62 thf(13344,plain,((! [A:(nat > int),B:nat,C:int]: ? [D:(nat > int)]: ! [E:int]: ((groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (A @ F) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ B)) = (plus_plus_int @ (times_times_int @ (minus_minus_int @ E @ C) @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (D @ F) @ (power_power_int @ E @ F))) @ (set_ord_lessThan_nat @ B))) @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (A @ F) @ (power_power_int @ C @ F))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1568])). 159.59/70.62 thf(4538,axiom,((! [A:num]: ((ord_less_real @ one_one_real @ (numeral_numeral_real @ A)) = (ord_less_num @ one @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_one__less__numeral__iff)). 159.59/70.62 thf(22919,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)],[4538])). 159.59/70.62 thf(104,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/sandbox/benchmark/theBenchmark.p',fact_9679_Im__divide)). 159.59/70.62 thf(8572,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)],[104])). 159.59/70.62 thf(814,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => (ord_less_eq_real @ A @ (minus_minus_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1345_add__le__imp__le__diff)). 159.59/70.62 thf(10882,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ C) => (ord_less_eq_real @ A @ (minus_minus_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[814])). 159.59/70.62 thf(1602,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/sandbox/benchmark/theBenchmark.p',fact_2437_le__divide__eq__1)). 159.59/70.62 thf(13458,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)],[1602])). 159.59/70.62 thf(7787,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 = B) | ((ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) & ((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))))))) | (F = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1458_VEBT__internal_Omembermima_Osimps_I4_J)). 159.59/70.62 thf(35147,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 = B) | ((ord_less_nat @ (vEBT_VEBT_high @ F @ (divide_divide_nat @ (suc @ C) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ D)) & ((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))))))) | (F = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7787])). 159.59/70.62 thf(2191,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_eq_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2139_divide__nonpos__nonpos)). 159.59/70.62 thf(15313,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_eq_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2191])). 159.59/70.62 thf(7690,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (binomial @ B @ A) @ (binomial @ B @ (suc @ A))) <= (ord_less_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9129_binomial__less__binomial__Suc)). 159.59/70.62 thf(34826,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (binomial @ B @ A) @ (binomial @ B @ (suc @ A))) | ~ (ord_less_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7690])). 159.59/70.62 thf(1943,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/sandbox/benchmark/theBenchmark.p',fact_5098_group__cancel_Osub2)). 159.59/70.62 thf(14520,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)],[1943])). 159.59/70.62 thf(7177,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/sandbox/benchmark/theBenchmark.p',fact_1990_mult__left__mono)). 159.59/70.62 thf(33046,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)],[7177])). 159.59/70.62 thf(7890,axiom,((! [A:nat,B:num]: ((bit_se2925701944663578781it_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (bit_se2925701944663578781it_nat @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5264_take__bit__Suc__bit0)). 159.59/70.62 thf(35475,plain,((! [A:nat,B:num]: ((bit_se2925701944663578781it_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (bit_se2925701944663578781it_nat @ A @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7890])). 159.59/70.62 thf(2425,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: ((? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) <= (ord_less_int @ E @ F))) => ((? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F))))) <= (? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) <= (ord_less_int @ E @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4431_pinf_I1_J)). 159.59/70.62 thf(16055,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: ((? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) | ~ (ord_less_int @ E @ F))) => (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => (((A @ F) & (C @ F)) = ((D @ F) & (B @ F)))) | ~ (? [E:int]: ! [F:int]: (((C @ F) = (D @ F)) | ~ (ord_less_int @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2425])). 159.59/70.62 thf(2419,axiom,((! [A:set_nat,B:nat,C:(nat > real),D:(nat > real)]: (((((groups129246275422532515t_real @ (^ [E:nat]: (if_real @ (E = B) @ (C @ E) @ (D @ E))) @ A) = (groups129246275422532515t_real @ D @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)))) <= (~ (member_nat @ B @ A))) & (((groups129246275422532515t_real @ (^ [E:nat]: (if_real @ (E = B) @ (C @ E) @ (D @ E))) @ A) = (times_times_real @ (C @ B) @ (groups129246275422532515t_real @ D @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))) <= (member_nat @ B @ A))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8819_prod_Odelta__remove)). 159.59/70.62 thf(16031,plain,((! [A:set_nat,B:nat,C:(nat > real),D:(nat > real)]: (((((groups129246275422532515t_real @ (^ [E:nat]: (if_real @ (E = B) @ (C @ E) @ (D @ E))) @ A) = (groups129246275422532515t_real @ (D) @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)))) | (member_nat @ B @ A)) & (((groups129246275422532515t_real @ (^ [E:nat]: (if_real @ (E = B) @ (C @ E) @ (D @ E))) @ A) = (times_times_real @ (C @ B) @ (groups129246275422532515t_real @ (D) @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))) | ~ (member_nat @ B @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2419])). 159.59/70.62 thf(1818,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8990_inverse__positive__iff__positive)). 159.59/70.62 thf(14120,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1818])). 159.59/70.62 thf(2484,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ A @ B) => ((modulo_modulo_int @ A @ B) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3495_unique__euclidean__semiring__numeral__class_Omod__less)). 159.59/70.62 thf(16242,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_int @ A @ B) => ((modulo_modulo_int @ A @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2484])). 159.59/70.62 thf(1606,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/sandbox/benchmark/theBenchmark.p',fact_7178_cos__times__sin)). 159.59/70.62 thf(13468,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)],[1606])). 159.59/70.62 thf(3524,axiom,((! [A:real]: (((ord_less_real @ (sin_real @ A) @ zero_zero_real) <= (ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) <= (ord_less_real @ pi @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6861_sin__lt__zero)). 159.59/70.62 thf(19566,plain,((! [A:real]: ((ord_less_real @ (sin_real @ A) @ zero_zero_real) | ~ (ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) | ~ (ord_less_real @ pi @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3524])). 159.59/70.62 thf(6455,axiom,((semiri1316708129612266289at_nat = (^ [A:nat]: (semiri8422978514062236437ux_nat @ (^ [B:nat]: (plus_plus_nat @ B @ one_one_nat)) @ A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8164_of__nat__code)). 159.59/70.62 thf(30076,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)],[6455])). 159.59/70.62 thf(778,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/sandbox/benchmark/theBenchmark.p',fact_7408_sum__distrib__left)). 159.59/70.62 thf(10760,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)],[778])). 159.59/70.62 thf(1480,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ B @ C) => (ord_less_eq_set_nat @ A @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2723_order__trans)). 159.59/70.62 thf(13084,plain,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ B @ C) => (ord_less_eq_set_nat @ A @ C)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480])). 159.59/70.62 thf(1007,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ (ln_ln_real @ A)) = (ord_less_eq_real @ (exp_real @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6106_ln__ge__iff)). 159.59/70.62 thf(11467,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ (ln_ln_real @ A)) = (ord_less_eq_real @ (exp_real @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007])). 159.59/70.62 thf(4328,axiom,((! [A:num]: ~ (ord_le3102999989581377725nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5173_not__numeral__le__neg__one)). 159.59/70.62 thf(22124,plain,((! [A:num]: ~ (ord_le3102999989581377725nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4328])). 159.59/70.62 thf(6323,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5515_abs__ge__zero)). 159.59/70.62 thf(29563,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6323])). 159.59/70.62 thf(3971,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/sandbox/benchmark/theBenchmark.p',fact_2316_sum__squares__gt__zero__iff)). 159.59/70.62 thf(21026,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)],[3971])). 159.59/70.62 thf(2065,axiom,((! [A:num]: ((numeral_numeral_real @ (inc @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5727_numeral__inc)). 159.59/70.62 thf(14908,plain,((! [A:num]: ((numeral_numeral_real @ (inc @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2065])). 159.59/70.62 thf(1749,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/sandbox/benchmark/theBenchmark.p',fact_5001_concat__bit__eq__iff)). 159.59/70.62 thf(13899,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)],[1749])). 159.59/70.62 thf(2568,axiom,((! [A:(nat > int),B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_int @ (A @ B) @ (A @ C))) <= (! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_lift__Suc__mono__less)). 159.59/70.62 thf(16504,plain,((! [A:(nat > int),B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_int @ (A @ B) @ (A @ C))) | ~ (! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2568])). 159.59/70.62 thf(2612,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/sandbox/benchmark/theBenchmark.p',fact_5438_zdiv__numeral__Bit1)). 159.59/70.62 thf(16673,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)],[2612])). 159.59/70.62 thf(5017,axiom,((! [A:produc9072475918466114483BT_nat]: ((~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ C @ D @ E) @ F)))) <= (! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1823_VEBT__internal_Ovalid_H_Ocases)). 159.59/70.62 thf(24614,plain,((! [A:produc9072475918466114483BT_nat]: (~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ C @ D @ E) @ F))) | ~ (! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5017])). 159.59/70.62 thf(858,axiom,(((exp_complex @ zero_zero_complex) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5963_exp__zero)). 159.59/70.62 thf(11019,plain,(((exp_complex @ zero_zero_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[858])). 159.59/70.62 thf(4580,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2731_order_Otrans)). 159.59/70.62 thf(23055,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4580])). 159.59/70.62 thf(1226,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F)))))) <= (? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) <= (ord_less_int @ F @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4461_minf_I1_J)). 159.59/70.62 thf(12211,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F)))))) | ~ (? [E:int]: ! [F:int]: (((A @ F) = (B @ F)) | ~ (ord_less_int @ F @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226])). 159.59/70.62 thf(3433,axiom,((! [A:int]: ((ord_less_nat @ (suc @ zero_zero_nat) @ (nat2 @ A)) = (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9421_one__less__nat__eq)). 159.59/70.62 thf(19287,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)],[3433])). 159.59/70.62 thf(612,axiom,((comm_s2602460028002588243omplex = (^ [A:complex,B:nat]: (groups6464643781859351333omplex @ (^ [C:nat]: (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8892_pochhammer__prod__rev)). 159.59/70.62 thf(10203,plain,(((comm_s2602460028002588243omplex) = (^ [A:complex,B:nat]: (groups6464643781859351333omplex @ (^ [C:nat]: (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[612])). 159.59/70.62 thf(1146,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_eq_real @ zero_zero_real @ (cos_real @ A)) <= (ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7188_cos__ge__zero)). 159.59/70.62 thf(11923,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A) => ((ord_less_eq_real @ zero_zero_real @ (cos_real @ A)) | ~ (ord_less_eq_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146])). 159.59/70.62 thf(5394,axiom,((bit_se1148574629649215175it_nat = (^ [A:nat,B:nat]: (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) <= (B = zero_zero_nat)) & ((B != zero_zero_nat) => (bit_se1148574629649215175it_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6468_bit__rec)). 159.59/70.62 thf(26043,plain,(((bit_se1148574629649215175it_nat) = (^ [A:nat,B:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) | ~ (B = zero_zero_nat)) & ((~ (B = zero_zero_nat)) => (bit_se1148574629649215175it_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5394])). 159.59/70.62 thf(8173,axiom,(((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2460_zero__power2)). 159.59/70.62 thf(36389,plain,(((power_power_int @ zero_zero_int @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8173])). 159.59/70.62 thf(407,axiom,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((groups2073611262835488442omplex @ C @ (minus_minus_set_nat @ A @ B)) = (minus_minus_complex @ (groups2073611262835488442omplex @ C @ A) @ (groups2073611262835488442omplex @ C @ B))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7646_sum__diff)). 159.59/70.62 thf(9530,plain,((! [A:set_nat,B:set_nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((groups2073611262835488442omplex @ (C) @ (minus_minus_set_nat @ A @ B)) = (minus_minus_complex @ (groups2073611262835488442omplex @ (C) @ A) @ (groups2073611262835488442omplex @ (C) @ B))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])). 159.59/70.62 thf(6464,axiom,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ A @ ($true))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1804_VEBT__internal_OminNull_Osimps_I3_J)). 159.59/70.62 thf(30118,plain,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ A @ ($true))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6464])). 159.59/70.62 thf(7522,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_int @ A @ B)) <= (ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2539_power2__less__imp__less)). 159.59/70.62 thf(34258,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_int @ A @ B)) | ~ (ord_less_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)],[7522])). 159.59/70.62 thf(881,axiom,((! [A:nat,B:nat,C:list_nat,D:nat]: (((cons_nat @ A @ (cons_nat @ B @ C)) = (upt @ A @ D)) = ((cons_nat @ B @ C) = (upt @ (suc @ A) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10135_upt__conv__Cons__Cons)). 159.59/70.62 thf(11088,plain,((! [A:nat,B:nat,C:list_nat,D:nat]: (((cons_nat @ A @ (cons_nat @ B @ C)) = (upt @ A @ D)) = ((cons_nat @ B @ C) = (upt @ (suc @ A) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[881])). 159.59/70.62 thf(5175,axiom,((! [A:list_o,B:list_o]: (((size_size_list_o @ A) != (size_size_list_o @ B)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_neq__if__length__neq)). 159.59/70.62 thf(25165,plain,((! [A:list_o,B:list_o]: ((~ ((size_size_list_o @ A) = (size_size_list_o @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5175])). 159.59/70.62 thf(5314,axiom,(((neg_numeral_dbl_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3785_dbl__simps_I3_J)). 159.59/70.62 thf(25697,plain,(((neg_numeral_dbl_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5314])). 159.59/70.62 thf(418,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/sandbox/benchmark/theBenchmark.p',fact_9669_Im__power2)). 159.59/70.62 thf(9566,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)],[418])). 159.59/70.62 thf(6481,axiom,((! [A:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8353_floor__log2__div2)). 159.59/70.62 thf(30185,plain,((! [A:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6481])). 159.59/70.62 thf(6151,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/sandbox/benchmark/theBenchmark.p',fact_7946_powser__sums__zero)). 159.59/70.62 thf(28920,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)],[6151])). 159.59/70.62 thf(3917,axiom,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) != (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int)) => ((bit_se2923211474154528505it_int @ A @ (plus_plus_int @ B @ one_one_int)) = (plus_plus_int @ one_one_int @ (bit_se2923211474154528505it_int @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5327_take__bit__incr__eq)). 159.59/70.62 thf(20855,plain,((! [A:nat,B:int]: ((~ ((bit_se2923211474154528505it_int @ A @ B) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ one_one_int))) => ((bit_se2923211474154528505it_int @ A @ (plus_plus_int @ B @ one_one_int)) = (plus_plus_int @ one_one_int @ (bit_se2923211474154528505it_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3917])). 159.59/70.62 thf(4459,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/sandbox/benchmark/theBenchmark.p',fact_1969_mult__nonpos__nonneg)). 159.59/70.62 thf(22533,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)],[4459])). 159.59/70.62 thf(4703,axiom,((! [A:num]: ((plus_plus_int @ (numeral_numeral_int @ A) @ one_one_int) = (numeral_numeral_int @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_numeral__plus__one)). 159.59/70.62 thf(23511,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)],[4703])). 159.59/70.62 thf(2654,axiom,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) != (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6747_pi__half__neq__two)). 159.59/70.62 thf(16805,plain,((~ ((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) = (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2654])). 159.59/70.62 thf(3429,axiom,((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5081_less__minus__one__simps_I2_J)). 159.59/70.62 thf(19277,plain,((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3429])). 159.59/70.62 thf(1711,axiom,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6700_of__nat__dvd__iff)). 159.59/70.62 thf(13782,plain,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) = (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711])). 159.59/70.62 thf(5416,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2188_gr0__conv__Suc)). 159.59/70.62 thf(26139,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5416])). 159.59/70.62 thf(5168,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/sandbox/benchmark/theBenchmark.p',fact_6340_log__le__zero__cancel__iff)). 159.59/70.62 thf(25143,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)],[5168])). 159.59/70.62 thf(1758,axiom,((! [A:num]: ~ (ord_le6747313008572928689nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5183_not__one__less__neg__numeral)). 159.59/70.62 thf(13928,plain,((! [A:num]: ~ (ord_le6747313008572928689nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758])). 159.59/70.62 thf(1714,axiom,((! [A:list_int,B:nat,C:int]: ((ord_less_eq_nat @ (size_size_list_int @ A) @ B) => ((list_update_int @ A @ B @ C) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_list__update__beyond)). 159.59/70.62 thf(13790,plain,((! [A:list_int,B:nat,C:int]: ((ord_less_eq_nat @ (size_size_list_int @ A) @ B) => ((list_update_int @ A @ B @ C) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714])). 159.59/70.62 thf(4335,axiom,((~ (ord_less_int @ one_one_int @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5077_less__minus__one__simps_I4_J)). 159.59/70.62 thf(22145,plain,((~ (ord_less_int @ one_one_int @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4335])). 159.59/70.62 thf(286,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((arcosh_real @ (cosh_real @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9349_arcosh__cosh__real)). 159.59/70.62 thf(9117,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((arcosh_real @ (cosh_real @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 159.59/70.62 thf(2059,axiom,(((invers8013647133539491842omplex @ one_one_complex) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8981_inverse__1)). 159.59/70.62 thf(14893,plain,(((invers8013647133539491842omplex @ one_one_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2059])). 159.59/70.62 thf(4347,axiom,((! [A:nat,B:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6688_of__nat__less__imp__less)). 159.59/70.62 thf(22181,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)],[4347])). 159.59/70.62 thf(6435,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se2925701944663578781it_nat @ A @ (plus_plus_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ (bit_se2925701944663578781it_nat @ A @ C))) = (bit_se2925701944663578781it_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4914_take__bit__add)). 159.59/70.62 thf(29994,plain,((! [A:nat,B:nat,C:nat]: ((bit_se2925701944663578781it_nat @ A @ (plus_plus_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ (bit_se2925701944663578781it_nat @ A @ C))) = (bit_se2925701944663578781it_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6435])). 159.59/70.62 thf(6196,axiom,(((^ [A:complex]: (A)) = (times_times_complex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1413_lambda__one)). 159.59/70.62 thf(29081,plain,(((^ [A:complex]: (A)) = (times_times_complex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6196])). 159.59/70.62 thf(2067,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_int @ A @ B) => ((((((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_eq_int @ zero_zero_int @ E)) <= (ord_less_eq_int @ zero_zero_int @ D)) <= (ord_less_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2498_convex__bound__lt)). 159.59/70.62 thf(14914,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((ord_less_int @ A @ B) => ((((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_eq_int @ zero_zero_int @ E) | ~ (ord_less_eq_int @ zero_zero_int @ D) | ~ (ord_less_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2067])). 159.59/70.62 thf(3878,axiom,((! [A:nat]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ semiri4939895301339042750nteger @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ one_one_Code_integer))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7810_double__gauss__sum)). 159.59/70.62 thf(20739,plain,((! [A:nat]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ (semiri4939895301339042750nteger) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A))) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3878])). 159.59/70.62 thf(4350,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_succ @ A @ C) = (some_nat @ D)) = (vEBT_is_succ_in_set @ (vEBT_set_vebt @ A) @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_succ__correct)). 159.59/70.62 thf(22191,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_succ @ A @ C) = (some_nat @ D)) = (vEBT_is_succ_in_set @ (vEBT_set_vebt @ A) @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4350])). 159.59/70.62 thf(1916,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ (plus_plus_int @ B @ C)) = (dvd_dvd_int @ A @ C)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3993_dvd__add__right__iff)). 159.59/70.62 thf(14437,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ (plus_plus_int @ B @ C)) = (dvd_dvd_int @ A @ C)) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1916])). 159.59/70.62 thf(3012,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/sandbox/benchmark/theBenchmark.p',fact_5770_of__int__less__iff)). 159.59/70.62 thf(17939,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)],[3012])). 159.59/70.62 thf(7994,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/sandbox/benchmark/theBenchmark.p',fact_85_mult__numeral__left__semiring__numeral)). 159.59/70.62 thf(35798,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)],[7994])). 159.59/70.62 thf(2876,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/sandbox/benchmark/theBenchmark.p',fact_6834_sin__x__ge__neg__x)). 159.59/70.62 thf(17503,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)],[2876])). 159.59/70.62 thf(1207,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/sandbox/benchmark/theBenchmark.p',fact_2229_mult__right__le__imp__le)). 159.59/70.62 thf(12151,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)],[1207])). 159.59/70.62 thf(1662,axiom,((! [A:nat,B:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6520_of__nat__less__iff)). 159.59/70.62 thf(13635,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)],[1662])). 159.59/70.62 thf(2111,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/sandbox/benchmark/theBenchmark.p',fact_4533_pinf_I10_J)). 159.59/70.62 thf(15054,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2111])). 159.59/70.62 thf(2042,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ (times_times_complex @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1629_nonzero__mult__div__cancel__right)). 159.59/70.62 thf(14841,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)],[2042])). 159.59/70.62 thf(3729,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1232_distrib__left)). 159.59/70.62 thf(20248,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3729])). 159.59/70.62 thf(7231,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/sandbox/benchmark/theBenchmark.p',fact_4070_unit__mult__right__cancel)). 159.59/70.62 thf(33259,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)],[7231])). 159.59/70.62 thf(7768,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_851_add__diff__inverse__nat)). 159.59/70.62 thf(35097,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)],[7768])). 159.59/70.62 thf(3888,axiom,((! [A:real,B:real,C:(nat > complex),D:real]: ((((! [E:nat]: (ord_less_eq_real @ (times_times_real @ (real_V1022390504157884413omplex @ (C @ E)) @ (power_power_real @ B @ E)) @ D)) => (summable_real @ (^ [E:nat]: (times_times_real @ (real_V1022390504157884413omplex @ (C @ E)) @ (power_power_real @ A @ E))))) <= (ord_less_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7133_Abel__lemma)). 159.59/70.62 thf(20771,plain,((! [A:real,B:real,C:(nat > complex),D:real]: (((! [E:nat]: (ord_less_eq_real @ (times_times_real @ (real_V1022390504157884413omplex @ (C @ E)) @ (power_power_real @ B @ E)) @ D)) => (summable_real @ (^ [E:nat]: (times_times_real @ (real_V1022390504157884413omplex @ (C @ E)) @ (power_power_real @ A @ E))))) | ~ (ord_less_real @ A @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3888])). 159.59/70.62 thf(2666,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/sandbox/benchmark/theBenchmark.p',fact_8084_fact__fact__dvd__fact)). 159.59/70.62 thf(16847,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)],[2666])). 159.59/70.62 thf(760,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ (numera1916890842035813515d_enat @ one)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_mult__numeral__1__right)). 159.59/70.62 thf(10708,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ (numera1916890842035813515d_enat @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[760])). 159.59/70.62 thf(7599,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_less__irrefl__nat)). 159.59/70.62 thf(34557,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7599])). 159.59/70.62 thf(2217,axiom,((! [A:num]: ~ (ord_less_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5144_not__zero__less__neg__numeral)). 159.59/70.62 thf(15410,plain,((! [A:num]: ~ (ord_less_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2217])). 159.59/70.62 thf(7290,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (modulo_modulo_nat @ A @ B)) = (~ (dvd_dvd_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4184_mod__greater__zero__iff__not__dvd)). 159.59/70.62 thf(33448,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)],[7290])). 159.59/70.62 thf(1125,axiom,((! [A:num]: ((neg_numeral_dbl_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3861_dbl__simps_I5_J)). 159.59/70.62 thf(11860,plain,((! [A:num]: ((neg_numeral_dbl_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125])). 159.59/70.62 thf(2171,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => ((divide_divide_int @ (times_times_int @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1628_nonzero__mult__div__cancel__right)). 159.59/70.62 thf(15249,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => ((divide_divide_int @ (times_times_int @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2171])). 159.59/70.62 thf(4203,axiom,((! [A:code_integer,B:code_integer]: (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3959_dvd__triv__left)). 159.59/70.62 thf(21727,plain,((! [A:code_integer,B:code_integer]: (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4203])). 159.59/70.62 thf(6654,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat) <= (dvd_dvd_nat @ B @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3835_unit__prod)). 159.59/70.62 thf(30796,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat) | ~ (dvd_dvd_nat @ B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6654])). 159.59/70.62 thf(5243,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/sandbox/benchmark/theBenchmark.p',fact_4797_semiring__norm_I171_J)). 159.59/70.62 thf(25413,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)],[5243])). 159.59/70.62 thf(4397,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)) & (((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = C) <= (A = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2355_add__divide__eq__if__simps_I2_J)). 159.59/70.62 thf(22336,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)) & (((plus_plus_real @ (divide_divide_real @ B @ A) @ C) = C) | ~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4397])). 159.59/70.62 thf(6679,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/sandbox/benchmark/theBenchmark.p',fact_6346_bit__minus__numeral__Bit0__Suc__iff)). 159.59/70.62 thf(30888,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)],[6679])). 159.59/70.62 thf(5182,axiom,((! [A:nat]: (ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1316708129612266289at_nat @ (power_power_nat @ A @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8105_fact__le__power)). 159.59/70.62 thf(25192,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)],[5182])). 159.59/70.62 thf(6984,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/sandbox/benchmark/theBenchmark.p',fact_3440_mod__mult__right__eq)). 159.59/70.62 thf(32279,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)],[6984])). 159.59/70.62 thf(1214,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/sandbox/benchmark/theBenchmark.p',fact_370_power__divide)). 159.59/70.62 thf(12179,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)],[1214])). 159.59/70.62 thf(3234,axiom,((! [A:int]: ? [B:int]: (ord_less_int @ B @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2759_lt__ex)). 159.59/70.62 thf(18653,plain,((! [A:int]: ? [B:int]: (ord_less_int @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3234])). 159.59/70.62 thf(4950,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/sandbox/benchmark/theBenchmark.p',fact_2532_power__minus__mult)). 159.59/70.62 thf(24346,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)],[4950])). 159.59/70.62 thf(7443,axiom,((! [A:num,B:num,C:(num > num),D:num]: ((((C @ B) = D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))) => (ord_less_eq_num @ (C @ A) @ D))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2646_ord__le__eq__subst)). 159.59/70.62 thf(33961,plain,((! [A:num,B:num,C:(num > num),D:num]: ((((C @ B) = D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F)))) => (ord_less_eq_num @ (C @ A) @ D))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7443])). 159.59/70.62 thf(3846,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/sandbox/benchmark/theBenchmark.p',fact_2367_div__add__self1)). 159.59/70.62 thf(20633,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)],[3846])). 159.59/70.62 thf(5343,axiom,((! [A:nat]: (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6752_of__nat__less__two__power)). 159.59/70.62 thf(25829,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)],[5343])). 159.59/70.62 thf(7384,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/sandbox/benchmark/theBenchmark.p',fact_1790_power2__less__eq__zero__iff)). 159.59/70.62 thf(33782,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)],[7384])). 159.59/70.62 thf(3149,axiom,((! [A:real,B:real]: ((((ord_less_real @ (cos_real @ B) @ (cos_real @ A)) <= (ord_less_eq_real @ B @ pi)) <= (ord_less_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7121_cos__monotone__0__pi)). 159.59/70.62 thf(18386,plain,((! [A:real,B:real]: ((ord_less_real @ (cos_real @ B) @ (cos_real @ A)) | ~ (ord_less_eq_real @ B @ pi) | ~ (ord_less_real @ A @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3149])). 159.59/70.62 thf(7847,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/sandbox/benchmark/theBenchmark.p',fact_10079_mono__ge2__power__minus__self)). 159.59/70.62 thf(35334,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)],[7847])). 159.59/70.62 thf(8189,axiom,((bit_se2925701944663578781it_nat = (^ [A:nat,B:nat]: (modulo_modulo_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5266_take__bit__eq__mod)). 159.59/70.62 thf(36437,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)],[8189])). 159.59/70.62 thf(3368,axiom,((! [A:real,B:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) => ((ord_less_real @ B @ A) <= (ord_less_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9025_inverse__less__imp__less__neg)). 159.59/70.62 thf(19075,plain,((! [A:real,B:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) => ((ord_less_real @ B @ A) | ~ (ord_less_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3368])). 159.59/70.62 thf(4675,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/sandbox/benchmark/theBenchmark.p',fact_5632_abs__le__square__iff)). 159.59/70.62 thf(23418,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)],[4675])). 159.59/70.62 thf(3305,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ B)) = (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ C)) & ((ord_less_eq_real @ C @ A) <= (ord_less_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2290_divide__le__cancel)). 159.59/70.62 thf(18885,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ (divide_divide_real @ C @ B)) = (((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ C)) & ((ord_less_eq_real @ C @ A) | ~ (ord_less_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3305])). 159.59/70.62 thf(1447,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/sandbox/benchmark/theBenchmark.p',fact_8625_prod_Onat__diff__reindex)). 159.59/70.62 thf(12967,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)],[1447])). 159.59/70.62 thf(606,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/sandbox/benchmark/theBenchmark.p',fact_8449_prod_OatMost__Suc)). 159.59/70.62 thf(10185,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)],[606])). 159.59/70.62 thf(2993,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 @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) => ((((sin_real @ A) = (sin_real @ B)) => (A = B)) <= (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6863_sin__inj__pi)). 159.59/70.62 thf(17883,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 @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B) => ((((sin_real @ A) = (sin_real @ B)) => (A = B)) | ~ (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2993])). 159.59/70.62 thf(588,axiom,((zero_n356916108424825756nteger = (^ [A:$o]: (if_Code_integer @ A @ one_one_Code_integer @ zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4403_of__bool__def)). 159.59/70.62 thf(10120,plain,(((zero_n356916108424825756nteger) = (^ [A:$o]: (if_Code_integer @ A @ one_one_Code_integer @ zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[588])). 159.59/70.62 thf(4915,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2281_div__positive)). 159.59/70.62 thf(24241,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ B @ A)) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4915])). 159.59/70.62 thf(6459,axiom,(((neg_nu8804712462038260780nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4889_dbl__simps_I4_J)). 159.59/70.62 thf(30086,plain,(((neg_nu8804712462038260780nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6459])). 159.59/70.62 thf(4382,axiom,((! [A:real,B:real]: (((B != zero_zero_real) => ((minus_minus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (times_times_real @ (times_times_real @ (inverse_inverse_real @ A) @ (minus_minus_real @ B @ A)) @ (inverse_inverse_real @ B)))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9076_division__ring__inverse__diff)). 159.59/70.62 thf(22288,plain,((! [A:real,B:real]: (((~ (B = zero_zero_real)) => ((minus_minus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (times_times_real @ (times_times_real @ (inverse_inverse_real @ A) @ (minus_minus_real @ B @ A)) @ (inverse_inverse_real @ B)))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4382])). 159.59/70.62 thf(2546,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/sandbox/benchmark/theBenchmark.p',fact_4065_mult__unit__dvd__iff_H)). 159.59/70.62 thf(16436,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)],[2546])). 159.59/70.62 thf(4741,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1504_add__0)). 159.59/70.62 thf(23625,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4741])). 159.59/70.62 thf(973,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1131_add_Oleft__cancel)). 159.59/70.62 thf(11364,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)],[973])). 159.59/70.62 thf(450,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/sandbox/benchmark/theBenchmark.p',fact_9657_cmod__Im__le__iff)). 159.59/70.62 thf(9667,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)],[450])). 159.59/70.62 thf(1556,axiom,((! [A:int,B:int]: (((uminus_uminus_int @ A) = B) <= ((plus_plus_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5051_add_Oinverse__unique)). 159.59/70.62 thf(13308,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)],[1556])). 159.59/70.62 thf(4223,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/sandbox/benchmark/theBenchmark.p',fact_8287_pochhammer__eq__0__iff)). 159.59/70.62 thf(21813,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)],[4223])). 159.59/70.62 thf(4398,axiom,((! [A:real,B:real]: ((inverse_inverse_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8984_inverse__divide)). 159.59/70.62 thf(22343,plain,((! [A:real,B:real]: ((inverse_inverse_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4398])). 159.59/70.62 thf(7901,axiom,((! [A:num]: ((bit0 @ A) != one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_semiring__norm_I85_J)). 159.59/70.62 thf(35511,plain,((! [A:num]: ~ ((bit0 @ A) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7901])). 159.59/70.62 thf(2867,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/sandbox/benchmark/theBenchmark.p',fact_6302_log__base__10__eq1)). 159.59/70.62 thf(17478,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)],[2867])). 159.59/70.62 thf(6541,axiom,((! [A:num,B:nat,C:nat]: (((power_8256067586552552935nteger @ (numera6620942414471956472nteger @ A) @ B) = (semiri4939895301339042750nteger @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6597_numeral__power__eq__of__nat__cancel__iff)). 159.59/70.62 thf(30403,plain,((! [A:num,B:nat,C:nat]: (((power_8256067586552552935nteger @ (numera6620942414471956472nteger @ A) @ B) = (semiri4939895301339042750nteger @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6541])). 159.59/70.62 thf(1877,axiom,((inverse_inverse_real = (divide_divide_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9051_inverse__eq__divide)). 159.59/70.62 thf(14313,plain,(((inverse_inverse_real) = (divide_divide_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1877])). 159.59/70.62 thf(4452,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/sandbox/benchmark/theBenchmark.p',fact_7190_cos__double__sin)). 159.59/70.62 thf(22511,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)],[4452])). 159.59/70.62 thf(5366,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/sandbox/benchmark/theBenchmark.p',fact_4487_of__bool__odd__eq__mod__2)). 159.59/70.62 thf(25936,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)],[5366])). 159.59/70.62 thf(4548,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_less__Suc__eq__le)). 159.59/70.62 thf(22963,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)],[4548])). 159.59/70.62 thf(7111,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/sandbox/benchmark/theBenchmark.p',fact_4662_neg__0__le__iff__le)). 159.59/70.62 thf(32775,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)],[7111])). 159.59/70.62 thf(7678,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/sandbox/benchmark/theBenchmark.p',fact_3876_odd__add)). 159.59/70.62 thf(34789,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)],[7678])). 159.59/70.62 thf(4320,axiom,((! [A:nat,B:(nat > (nat > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:nat]: (B @ C @ D)))) = (? [C:list_nat]: (! [D:nat]: ((B @ D @ (nth_nat @ C @ D)) <= (ord_less_nat @ D @ A)) & ((size_size_list_nat @ C) = A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_Skolem__list__nth)). 159.59/70.62 thf(22100,plain,((! [A:nat,B:(nat > (nat > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:nat]: (B @ C @ D)))) = (? [C:list_nat]: (! [D:nat]: ((B @ D @ (nth_nat @ C @ D)) | ~ (ord_less_nat @ D @ A)) & ((size_size_list_nat @ C) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4320])). 159.59/70.62 thf(4207,axiom,((! [A:complex,B:num,C:complex]: (((divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B)) = C) = ((((numera6690914467698888265omplex @ B) = zero_zero_complex) => (C = zero_zero_complex)) & (((numera6690914467698888265omplex @ B) != zero_zero_complex) => (A = (times_times_complex @ C @ (numera6690914467698888265omplex @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1733_divide__eq__eq__numeral1_I1_J)). 159.59/70.62 thf(21739,plain,((! [A:complex,B:num,C:complex]: (((divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B)) = C) = ((((numera6690914467698888265omplex @ B) = zero_zero_complex) => (C = zero_zero_complex)) & ((~ ((numera6690914467698888265omplex @ B) = zero_zero_complex)) => (A = (times_times_complex @ C @ (numera6690914467698888265omplex @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4207])). 159.59/70.62 thf(2011,axiom,((! [A:real,B:num]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_real @ A @ (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8207_floor__le__neg__numeral)). 159.59/70.62 thf(14752,plain,((! [A:real,B:num]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_real @ A @ (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ B)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2011])). 159.59/70.62 thf(554,axiom,((! [A:code_integer,B:code_integer]: (((modulo364778990260209775nteger @ B @ A) = zero_z3403309356797280102nteger) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4178_unit__imp__mod__eq__0)). 159.59/70.62 thf(10015,plain,((! [A:code_integer,B:code_integer]: (((modulo364778990260209775nteger @ B @ A) = zero_z3403309356797280102nteger) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[554])). 159.59/70.62 thf(2394,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ one_on7984719198319812577d_enat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1074_mult__1)). 159.59/70.62 thf(15944,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ one_on7984719198319812577d_enat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2394])). 159.59/70.62 thf(2648,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/sandbox/benchmark/theBenchmark.p',fact_1233_distrib__left)). 159.59/70.62 thf(16786,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)],[2648])). 159.59/70.62 thf(3013,axiom,((! [A:real]: (((exp_real @ (ln_ln_real @ A)) = A) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6001_exp__ln__iff)). 159.59/70.62 thf(17942,plain,((! [A:real]: (((exp_real @ (ln_ln_real @ A)) = A) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3013])). 159.59/70.62 thf(7635,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/sandbox/benchmark/theBenchmark.p',fact_5611_power__numeral__odd)). 159.59/70.62 thf(34659,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)],[7635])). 159.59/70.62 thf(1614,axiom,((! [A:nat,B:nat,C:(nat > int),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7717_sum_Oub__add__nat)). 159.59/70.62 thf(13495,plain,((! [A:nat,B:nat,C:(nat > int),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614])). 159.59/70.62 thf(2348,axiom,((! [A:extended_enat,B:(nat > extended_enat),C:nat,D:nat]: ((ord_le2932123472753598470d_enat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3218_order__le__less__subst1)). 159.59/70.62 thf(15793,plain,((! [A:extended_enat,B:(nat > extended_enat),C:nat,D:nat]: ((ord_le2932123472753598470d_enat @ A @ (B @ C)) => ((ord_less_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2348])). 159.59/70.62 thf(1053,axiom,((! [A:set_nat,B:(nat > real)]: ((~ (finite_finite_nat @ A)) => ((groups129246275422532515t_real @ B @ A) = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8392_prod_Oinfinite)). 159.59/70.62 thf(11625,plain,((! [A:set_nat,B:(nat > real)]: ((~ (finite_finite_nat @ A)) => ((groups129246275422532515t_real @ (B) @ A) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053])). 159.59/70.62 thf(986,axiom,((! [A:real]: ? [B:nat]: (ord_less_real @ A @ (semiri5074537144036343181t_real @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6648_reals__Archimedean2)). 159.59/70.62 thf(11403,plain,((! [A:real]: ? [B:nat]: (ord_less_real @ A @ (semiri5074537144036343181t_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[986])). 159.59/70.62 thf(5796,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/sandbox/benchmark/theBenchmark.p',fact_9419_numeral__power__eq__nat__cancel__iff)). 159.59/70.62 thf(27518,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)],[5796])). 159.59/70.62 thf(1015,axiom,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ A @ (uminus1351360451143612070nteger @ B)) = (ord_le6747313008572928689nteger @ B @ (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4940_less__minus__iff)). 159.59/70.62 thf(11496,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)],[1015])). 159.59/70.62 thf(1128,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/sandbox/benchmark/theBenchmark.p',fact_8543_power__sum)). 159.59/70.62 thf(11869,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)],[1128])). 159.59/70.62 thf(4054,axiom,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1514_add__cancel__right__left)). 159.59/70.62 thf(21267,plain,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4054])). 159.59/70.62 thf(7431,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5396_abs__1)). 159.59/70.62 thf(33925,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7431])). 159.59/70.62 thf(1970,axiom,((! [A:int]: ((~ (((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) != one_one_int) <= (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))) <= ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) != zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4256_parity__cases)). 159.59/70.62 thf(14598,plain,((! [A:int]: (~ (~ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) | ~ ((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)],[1970])). 159.59/70.62 thf(7910,axiom,((! [A:list_VEBT_VEBT,B:nat]: ((list_u1324408373059187874T_VEBT @ A @ B @ (nth_VEBT_VEBT @ A @ B)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_list__update__id)). 159.59/70.62 thf(35539,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)],[7910])). 159.59/70.62 thf(7841,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/sandbox/benchmark/theBenchmark.p',fact_4042_concat__bit__assoc)). 159.59/70.62 thf(35317,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)],[7841])). 159.59/70.62 thf(666,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/sandbox/benchmark/theBenchmark.p',fact_9473_arctan__inverse)). 159.59/70.62 thf(10381,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)],[666])). 159.59/70.62 thf(7762,axiom,((inj_on_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/sandbox/benchmark/theBenchmark.p',fact_10113_inj__on__char__of__nat)). 159.59/70.62 thf(35079,plain,((inj_on_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)],[7762])). 159.59/70.62 thf(1094,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/sandbox/benchmark/theBenchmark.p',fact_5753_dbl__inc__simps_I1_J)). 159.59/70.62 thf(11757,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)],[1094])). 159.59/70.62 thf(158,axiom,((! [A:real]: (summable_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (real_V1485227260804924795R_real @ (cos_coeff @ B) @ (power_power_real @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9273_summable__norm__cos)). 159.59/70.62 thf(8743,plain,((! [A:real]: (summable_real @ (^ [B:nat]: (real_V7735802525324610683m_real @ (real_V1485227260804924795R_real @ (cos_coeff @ B) @ (power_power_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 159.59/70.62 thf(2756,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/sandbox/benchmark/theBenchmark.p',fact_8542_power__sum)). 159.59/70.62 thf(17133,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)],[2756])). 159.59/70.62 thf(654,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/sandbox/benchmark/theBenchmark.p',fact_7111_cos__diff)). 159.59/70.62 thf(10342,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)],[654])). 159.59/70.62 thf(2622,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/sandbox/benchmark/theBenchmark.p',fact_3811_dvd__mult__cancel__left)). 159.59/70.62 thf(16700,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)],[2622])). 159.59/70.62 thf(5106,axiom,((! [A:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4704_mult__minus1__right)). 159.59/70.62 thf(24931,plain,((! [A:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5106])). 159.59/70.62 thf(3583,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/sandbox/benchmark/theBenchmark.p',fact_1176_add__mono__thms__linordered__semiring_I1_J)). 159.59/70.62 thf(19758,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)],[3583])). 159.59/70.62 thf(7298,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1494_mult__zero__right)). 159.59/70.62 thf(33476,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7298])). 159.59/70.62 thf(1798,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/sandbox/benchmark/theBenchmark.p',fact_7179_sin__plus__sin)). 159.59/70.62 thf(14052,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)],[1798])). 159.59/70.62 thf(5656,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/sandbox/benchmark/theBenchmark.p',fact_3491_mod__geq)). 159.59/70.62 thf(26969,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)],[5656])). 159.59/70.62 thf(3003,axiom,((zero_n2684676970156552555ol_int = (^ [A:$o]: (if_int @ A @ one_one_int @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4402_of__bool__def)). 159.59/70.62 thf(17912,plain,(((zero_n2684676970156552555ol_int) = (^ [A:$o]: (if_int @ A @ one_one_int @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3003])). 159.59/70.62 thf(5115,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1524_add__cancel__left__left)). 159.59/70.62 thf(24957,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5115])). 159.59/70.62 thf(6149,axiom,((! [A:nat]: ((semiri2265585572941072030t_real @ (suc @ A)) = (times_times_real @ (semiri5074537144036343181t_real @ (suc @ A)) @ (semiri2265585572941072030t_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8063_fact__Suc)). 159.59/70.62 thf(28913,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)],[6149])). 159.59/70.62 thf(2699,axiom,((! [A:real,B:real,C:real,D:real]: (((C = D) & (ord_less_eq_real @ A @ B)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1180_add__mono__thms__linordered__semiring_I3_J)). 159.59/70.62 thf(16958,plain,((! [A:real,B:real,C:real,D:real]: (((C = D) & (ord_less_eq_real @ A @ B)) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2699])). 159.59/70.62 thf(5157,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/sandbox/benchmark/theBenchmark.p',fact_1891_VEBT__internal_Omembermima_Osimps_I2_J)). 159.59/70.62 thf(25101,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)],[5157])). 159.59/70.62 thf(8068,axiom,((! [A:nat,B:nat]: ((bit_se2925701944663578781it_nat @ (suc @ A) @ B) = (plus_plus_nat @ (times_times_nat @ (bit_se2925701944663578781it_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5334_take__bit__Suc)). 159.59/70.62 thf(36052,plain,((! [A:nat,B:nat]: ((bit_se2925701944663578781it_nat @ (suc @ A) @ B) = (plus_plus_nat @ (times_times_nat @ (bit_se2925701944663578781it_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8068])). 159.59/70.62 thf(3,axiom,((! [A:real]: (sums_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (cos_coeff @ B) @ (power_power_real @ A @ B))) @ (cos_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9267_cos__converges)). 159.59/70.62 thf(8258,plain,((! [A:real]: (sums_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (cos_coeff @ B) @ (power_power_real @ A @ B))) @ (cos_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 159.59/70.62 thf(4769,axiom,((! [A:nat]: (ord_less_eq_nat @ (suc @ zero_zero_nat) @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8151_fact__ge__Suc__0__nat)). 159.59/70.62 thf(23740,plain,((! [A:nat]: (ord_less_eq_nat @ (suc @ zero_zero_nat) @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4769])). 159.59/70.62 thf(4136,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le72135733267957522d_enat @ A @ C) <= (ord_le72135733267957522d_enat @ B @ C)) <= (ord_le2932123472753598470d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3198_order__le__less__trans)). 159.59/70.62 thf(21514,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ C) | ~ (ord_le72135733267957522d_enat @ B @ C) | ~ (ord_le2932123472753598470d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4136])). 159.59/70.62 thf(5769,axiom,((! [A:real,B:real]: ((times_times_real @ (uminus_uminus_real @ A) @ B) = (uminus_uminus_real @ (times_times_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4631_mult__minus__left)). 159.59/70.62 thf(27356,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)],[5769])). 159.59/70.62 thf(4417,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/sandbox/benchmark/theBenchmark.p',fact_1436_times__divide__times__eq)). 159.59/70.62 thf(22409,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)],[4417])). 159.59/70.62 thf(5356,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ A) => ((! [C:$o,D:$o]: (((~ (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ (vEBT_Leaf @ C @ D))) <= (((((C) => (B = (some_nat @ zero_zero_nat))) & ((~ (C)) => (B = none_nat))) <= (~ (D))) & ((B = (some_nat @ one_one_nat)) <= (D)))) <= (A = (vEBT_Leaf @ C @ D)))) => ((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((B = none_nat) => (~ (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((~ (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))) <= (B = (some_nat @ D))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))))))) <= ((vEBT_vebt_maxt @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9747_vebt__maxt_Opelims)). 159.59/70.62 thf(25876,plain,((! [A:vEBT_VEBT,B:option_nat]: (((accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ A) => ((! [C:$o,D:$o]: (~ (accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ (vEBT_Leaf @ C @ D)) | ~ (((((C) => (B = (some_nat @ zero_zero_nat))) & ((~ (C)) => (B = none_nat))) | (D)) & ((B = (some_nat @ one_one_nat)) | ~ (D))) | ~ (A = (vEBT_Leaf @ C @ D)))) => ((! [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]: (~ (accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)) | ~ (B = (some_nat @ D)) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))))))) | ~ ((vEBT_vebt_maxt @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5356])). 159.59/70.62 thf(6049,axiom,((! [A:num,B:nat]: ((ord_less_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (ord_less_nat @ (pred_numeral @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5684_less__numeral__Suc)). 159.59/70.62 thf(28596,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)],[6049])). 159.59/70.62 thf(8120,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/sandbox/benchmark/theBenchmark.p',fact_382_power__add)). 159.59/70.62 thf(36205,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)],[8120])). 159.59/70.62 thf(1422,axiom,((ord_less_real = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3112_dual__order_Ostrict__iff__order)). 159.59/70.62 thf(12885,plain,(((ord_less_real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422])). 159.59/70.62 thf(6957,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4928_le__imp__neg__le)). 159.59/70.62 thf(32064,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6957])). 159.59/70.62 thf(7354,axiom,((! [A:nat,B:num,C:nat]: (((semiri4939895301339042750nteger @ A) = (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6603_real__of__nat__eq__numeral__power__cancel__iff)). 159.59/70.62 thf(33686,plain,((! [A:nat,B:num,C:nat]: (((semiri4939895301339042750nteger @ A) = (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7354])). 159.59/70.62 thf(7561,axiom,((ord_less_eq_real @ one_one_real @ one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_le__numeral__extra_I4_J)). 159.59/70.62 thf(34374,plain,((ord_less_eq_real @ one_one_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7561])). 159.59/70.62 thf(6947,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/sandbox/benchmark/theBenchmark.p',fact_6428_real__le__rsqrt)). 159.59/70.62 thf(32037,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)],[6947])). 159.59/70.62 thf(4544,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/sandbox/benchmark/theBenchmark.p',fact_4564_signed__take__bit__Suc__bit0)). 159.59/70.62 thf(22952,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)],[4544])). 159.59/70.62 thf(7568,axiom,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2716_dual__order_Oeq__iff)). 159.59/70.62 thf(34457,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)],[7568])). 159.59/70.62 thf(4745,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ A @ C) <= (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2726_order__trans)). 159.59/70.62 thf(23635,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ A @ C) | ~ (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4745])). 159.59/70.62 thf(734,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/sandbox/benchmark/theBenchmark.p',fact_8143_Maclaurin__exp__lt)). 159.59/70.62 thf(10620,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)],[734])). 159.59/70.62 thf(6697,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/sandbox/benchmark/theBenchmark.p',fact_7670_sum_OSuc__reindex__ivl)). 159.59/70.62 thf(31000,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)],[6697])). 159.59/70.62 thf(748,axiom,((! [A:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) = (A != zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2622_i0__less)). 159.59/70.62 thf(10671,plain,((! [A:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) = (~ (A = zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[748])). 159.59/70.62 thf(2245,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/sandbox/benchmark/theBenchmark.p',fact_3844_div__add)). 159.59/70.62 thf(15495,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)],[2245])). 159.59/70.62 thf(434,axiom,(((tan_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7277_tan__45)). 159.59/70.62 thf(9609,plain,(((tan_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[434])). 159.59/70.62 thf(3879,axiom,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_add_Oleft__cancel)). 159.59/70.62 thf(20742,plain,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3879])). 159.59/70.62 thf(929,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/sandbox/benchmark/theBenchmark.p',fact_93_add__numeral__left)). 159.59/70.62 thf(11229,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)],[929])). 159.59/70.62 thf(8240,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1817_zero__power)). 159.59/70.62 thf(36746,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)],[8240])). 159.59/70.62 thf(934,axiom,((! [A:num,B:real]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8206_neg__numeral__less__floor)). 159.59/70.62 thf(11243,plain,((! [A:num,B:real]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[934])). 159.59/70.62 thf(7184,axiom,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1248_mult_Ocomm__neutral)). 159.59/70.62 thf(33094,plain,((! [A:real]: ((times_times_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7184])). 159.59/70.62 thf(5007,axiom,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1568_diff__self__eq__0)). 159.59/70.62 thf(24578,plain,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5007])). 159.59/70.62 thf(5670,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/sandbox/benchmark/theBenchmark.p',fact_6640_of__nat__le__numeral__power__cancel__iff)). 159.59/70.62 thf(27016,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)],[5670])). 159.59/70.62 thf(7946,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 @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_mono__nat__linear__lb)). 159.59/70.62 thf(35655,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 @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7946])). 159.59/70.62 thf(2593,axiom,((! [A:(nat > real),B:real,C:set_nat,D:real,E:(nat > real)]: ((((sums_real @ (^ [F:nat]: (if_real @ (member_nat @ F @ C) @ (E @ F) @ (A @ F))) @ D) <= (D = (plus_plus_real @ B @ (groups6591440286371151544t_real @ (^ [F:nat]: (minus_minus_real @ (E @ F) @ (A @ F))) @ C)))) <= (finite_finite_nat @ C)) <= (sums_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7952_sums__If__finite__set_H)). 159.59/70.62 thf(16583,plain,((! [A:(nat > real),B:real,C:set_nat,D:real,E:(nat > real)]: ((sums_real @ (^ [F:nat]: (if_real @ (member_nat @ F @ C) @ (E @ F) @ (A @ F))) @ D) | ~ (D = (plus_plus_real @ B @ (groups6591440286371151544t_real @ (^ [F:nat]: (minus_minus_real @ (E @ F) @ (A @ F))) @ C))) | ~ (finite_finite_nat @ C) | ~ (sums_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2593])). 159.59/70.62 thf(6396,axiom,((! [A:(nat > extended_enat),B:nat]: (((A @ zero_zero_nat) = zero_z5237406670263579293d_enat) => ((groups7108830773950497114d_enat @ A @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups7108830773950497114d_enat @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7651_sum__shift__lb__Suc0__0)). 159.59/70.62 thf(29838,plain,((! [A:(nat > extended_enat),B:nat]: (((A @ zero_zero_nat) = zero_z5237406670263579293d_enat) => ((groups7108830773950497114d_enat @ (A) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups7108830773950497114d_enat @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6396])). 159.59/70.62 thf(3199,axiom,((! [A:set_nat,B:set_nat,C:(nat > extended_enat),D:(nat > nat),E:(nat > extended_enat)]: (((((! [F:nat]: ((member_nat @ F @ A) => (? [G:nat]: ((member_nat @ G @ B) & (ord_le2932123472753598470d_enat @ (E @ F) @ (C @ G)) & ((D @ G) = F))))) => (ord_le2932123472753598470d_enat @ (groups7108830773950497114d_enat @ E @ A) @ (groups7108830773950497114d_enat @ C @ B))) <= (! [F:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (C @ F)) <= (member_nat @ F @ B)))) <= (finite_finite_nat @ B)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7456_sum__le__included)). 159.59/70.62 thf(18540,plain,((! [A:set_nat,B:set_nat,C:(nat > extended_enat),D:(nat > nat),E:(nat > extended_enat)]: (((! [F:nat]: ((member_nat @ F @ A) => (? [G:nat]: ((member_nat @ G @ B) & (ord_le2932123472753598470d_enat @ (E @ F) @ (C @ G)) & ((D @ G) = F))))) => (ord_le2932123472753598470d_enat @ (groups7108830773950497114d_enat @ (E) @ A) @ (groups7108830773950497114d_enat @ (C) @ B))) | ~ (! [F:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (C @ F)) | ~ (member_nat @ F @ B))) | ~ (finite_finite_nat @ B) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3199])). 159.59/70.62 thf(2627,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/sandbox/benchmark/theBenchmark.p',fact_2354_add__divide__eq__if__simps_I1_J)). 159.59/70.62 thf(16715,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)],[2627])). 159.59/70.62 thf(2352,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/sandbox/benchmark/theBenchmark.p',fact_1435_times__divide__times__eq)). 159.59/70.62 thf(15803,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)],[2352])). 159.59/70.62 thf(4310,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ B @ A) <= (~ (ord_less_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3031_leI)). 159.59/70.62 thf(22072,plain,((! [A:int,B:int]: ((ord_less_eq_int @ B @ A) | (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4310])). 159.59/70.62 thf(5452,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1477_not__gr__zero)). 159.59/70.62 thf(26274,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5452])). 159.59/70.62 thf(6182,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (ord_max_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_max_Ostrict__coboundedI1)). 159.59/70.62 thf(29028,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (ord_max_nat @ B @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6182])). 159.59/70.62 thf(7651,axiom,((vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_xnin)). 159.59/70.62 thf(34708,plain,((vEBT_V8194947554948674370ptions @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7651])). 159.59/70.62 thf(3679,axiom,((! [A:num,B:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5030_neg__numeral__le__numeral)). 159.59/70.62 thf(20069,plain,((! [A:num,B:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3679])). 159.59/70.62 thf(5850,axiom,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ ($true) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1805_VEBT__internal_OminNull_Osimps_I2_J)). 159.59/70.62 thf(27874,plain,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ ($true) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5850])). 159.59/70.62 thf(5160,axiom,((! [A:nat]: (((suc @ (minus_minus_nat @ A @ one_one_nat)) = A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1780_Suc__diff__1)). 159.59/70.62 thf(25120,plain,((! [A:nat]: (((suc @ (minus_minus_nat @ A @ one_one_nat)) = A) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5160])). 159.59/70.62 thf(1395,axiom,((! [A:nat,B:nat]: ((image_nat_nat @ suc @ (set_or1269000886237332187st_nat @ A @ B)) = (set_or1269000886237332187st_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9804_image__Suc__atLeastAtMost)). 159.59/70.62 thf(12803,plain,((! [A:nat,B:nat]: ((image_nat_nat @ (suc) @ (set_or1269000886237332187st_nat @ A @ B)) = (set_or1269000886237332187st_nat @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395])). 159.59/70.62 thf(8,axiom,((! [A:real,B:complex]: ((im @ (real_V2046097035970521341omplex @ A @ B)) = (times_times_real @ A @ (im @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9654_scaleR__complex_Osimps_I2_J)). 159.59/70.62 thf(8275,plain,((! [A:real,B:complex]: ((im @ (real_V2046097035970521341omplex @ A @ B)) = (times_times_real @ A @ (im @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 159.59/70.62 thf(1620,axiom,((! [A:nat]: ((finite_card_nat @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))) = (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9709_card__Collect__le__nat)). 159.59/70.62 thf(13512,plain,((! [A:nat]: ((finite_card_nat @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))) = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1620])). 159.59/70.62 thf(4094,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/sandbox/benchmark/theBenchmark.p',fact_5778_of__int__mult)). 159.59/70.62 thf(21389,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)],[4094])). 159.59/70.62 thf(7482,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/sandbox/benchmark/theBenchmark.p',fact_9148_binomial__ring)). 159.59/70.62 thf(34135,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)],[7482])). 159.59/70.62 thf(5883,axiom,((! [A:num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_one__le__numeral)). 159.59/70.62 thf(27999,plain,((! [A:num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5883])). 159.59/70.62 thf(7554,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/sandbox/benchmark/theBenchmark.p',fact_2305_mult__le__one)). 159.59/70.62 thf(34354,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)],[7554])). 159.59/70.62 thf(5782,axiom,((! [A:vEBT_VEBT,B:nat,C:option_nat]: (((vEBT_vebt_pred @ A @ B) = C) => (((! [D:$o,E:$o]: (((B = zero_zero_nat) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ zero_zero_nat))) <= (C = none_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) @ (suc @ zero_zero_nat) @ E @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ 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))) <= (((C = (some_nat @ E)) <= (ord_less_nat @ E @ B)) & ((~ (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_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_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_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]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F) @ B))) <= (C = none_nat)) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F))))) <= (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B))) <= (C = none_nat))))) <= (! [D:$o,E:$o]: ((! [F:nat]: ((B = (suc @ (suc @ F))) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ (suc @ F))))) <= (((E) => (C = (some_nat @ one_one_nat))) & ((((C = none_nat) <= (~ (D))) & ((C = (some_nat @ zero_zero_nat)) <= (D))) <= (~ (E))))))) <= (A = (vEBT_Leaf @ D @ E))))) <= (! [D:$o,E:$o]: (((B = (suc @ zero_zero_nat)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ zero_zero_nat)))) <= (((C = none_nat) <= (~ (D))) & ((D) => (C = (some_nat @ zero_zero_nat)))))) <= (A = (vEBT_Leaf @ D @ E)))))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ (produc738532404422230701BT_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3310_vebt__pred_Opelims)). 159.59/70.62 thf(27396,plain,((! [A:vEBT_VEBT,B:nat,C:option_nat]: (((vEBT_vebt_pred @ A @ B) = C) => (((! [D:$o,E:$o]: (((B = zero_zero_nat) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ zero_zero_nat)) | ~ (C = none_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) @ (suc @ zero_zero_nat) @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ 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)) | ~ (((C = (some_nat @ E)) | ~ (ord_less_nat @ E @ B)) & ((~ (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_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_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_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]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F) @ B)) | ~ (C = none_nat) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F)))) | ~ (! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B)) | ~ (C = none_nat)))) | ~ (! [D:$o,E:$o]: (! [F:nat]: ((B = (suc @ (suc @ F))) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ (suc @ F)))) | ~ (((E) => (C = (some_nat @ one_one_nat))) & ((((C = none_nat) | (D)) & ((C = (some_nat @ zero_zero_nat)) | ~ (D))) | (E))))) | ~ (A = (vEBT_Leaf @ D @ E)))) | ~ (! [D:$o,E:$o]: (((B = (suc @ zero_zero_nat)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ zero_zero_nat))) | ~ (((C = none_nat) | (D)) & ((D) => (C = (some_nat @ zero_zero_nat)))))) | ~ (A = (vEBT_Leaf @ D @ E)))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_pred_rel) @ (produc738532404422230701BT_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5782])). 159.59/70.62 thf(2056,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ (times_times_int @ C @ A)) = (dvd_dvd_int @ B @ C)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4056_dvd__mult__unit__iff)). 159.59/70.62 thf(14882,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ (times_times_int @ C @ A)) = (dvd_dvd_int @ B @ C)) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2056])). 159.59/70.62 thf(280,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/sandbox/benchmark/theBenchmark.p',fact_9682_inverse__complex_Ocode)). 159.59/70.62 thf(9100,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)],[280])). 159.59/70.62 thf(1195,axiom,((! [A:nat,B:nat]: ((bit_se2923211474154528505it_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (times_times_int @ (zero_n2684676970156552555ol_int @ (ord_less_nat @ B @ A)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4907_take__bit__of__exp)). 159.59/70.62 thf(12091,plain,((! [A:nat,B:nat]: ((bit_se2923211474154528505it_int @ A @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) = (times_times_int @ (zero_n2684676970156552555ol_int @ (ord_less_nat @ B @ A)) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195])). 159.59/70.62 thf(6362,axiom,((! [A:(product_prod_nat_nat > nat)]: ((size_o8335143837870341156at_nat @ A @ none_P5556105721700978146at_nat) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4587_option_Osize__gen_I1_J)). 159.59/70.62 thf(29679,plain,((! [A:(product_prod_nat_nat > nat)]: ((size_o8335143837870341156at_nat @ (A) @ none_P5556105721700978146at_nat) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6362])). 159.59/70.62 thf(4718,axiom,((! [A:nat]: ((bit_se1412395901928357646or_nat @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5944_or_Oidem)). 159.59/70.62 thf(23556,plain,((! [A:nat]: ((bit_se1412395901928357646or_nat @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4718])). 159.59/70.62 thf(5126,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/sandbox/benchmark/theBenchmark.p',fact_5251_minus__divide__diff__eq__iff)). 159.59/70.62 thf(24989,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)],[5126])). 159.59/70.62 thf(4931,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_max_nat @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3294_max__absorb2)). 159.59/70.62 thf(24293,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)],[4931])). 159.59/70.62 thf(4576,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/sandbox/benchmark/theBenchmark.p',fact_2559_odd__power__less__zero)). 159.59/70.62 thf(23043,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)],[4576])). 159.59/70.62 thf(6374,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/sandbox/benchmark/theBenchmark.p',fact_4895_neg__one__even__power)). 159.59/70.62 thf(29714,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)],[6374])). 159.59/70.62 thf(2665,axiom,((! [A:nat,B:num,C:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6641_of__nat__le__numeral__power__cancel__iff)). 159.59/70.62 thf(16844,plain,((! [A:nat,B:num,C:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2665])). 159.59/70.62 thf(6749,axiom,((! [A:produc6271795597528267376eger_o]: ~ (! [B:code_integer,C:$o]: (A != (produc6677183202524767010eger_o @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3687_old_Oprod_Oexhaust)). 159.59/70.62 thf(31275,plain,((! [A:produc6271795597528267376eger_o]: ~ (! [B:code_integer,C:$o]: ~ (A = (produc6677183202524767010eger_o @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6749])). 159.59/70.62 thf(2767,axiom,((! [A:set_nat,B:(nat > int)]: ((finite_finite_nat @ A) => (((! [C:nat]: ((member_nat @ C @ A) => (ord_less_int @ one_one_int @ (B @ C)))) => (ord_less_int @ one_one_int @ (groups705719431365010083at_int @ B @ A))) <= (A != bot_bot_set_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8656_less__1__prod)). 159.59/70.62 thf(17165,plain,((! [A:set_nat,B:(nat > int)]: ((finite_finite_nat @ A) => (((! [C:nat]: ((member_nat @ C @ A) => (ord_less_int @ one_one_int @ (B @ C)))) => (ord_less_int @ one_one_int @ (groups705719431365010083at_int @ (B) @ A))) | (A = bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2767])). 159.59/70.62 thf(2751,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ B) @ C) => (dvd_dvd_complex @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3970_dvd__mult__right)). 159.59/70.62 thf(17118,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ B) @ C) => (dvd_dvd_complex @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2751])). 159.59/70.62 thf(7364,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/sandbox/benchmark/theBenchmark.p',fact_1304_max__add__distrib__left)). 159.59/70.62 thf(33712,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)],[7364])). 159.59/70.62 thf(2177,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/sandbox/benchmark/theBenchmark.p',fact_4573_signed__take__bit__int__less__self__iff)). 159.59/70.62 thf(15270,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)],[2177])). 159.59/70.62 thf(3531,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6682_less__imp__of__nat__less)). 159.59/70.62 thf(19588,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)],[3531])). 159.59/70.62 thf(3120,axiom,((! [A:set_nat]: ~ (member_nat @ zero_zero_nat @ (image_nat_nat @ suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9806_zero__notin__Suc__image)). 159.59/70.62 thf(18289,plain,((! [A:set_nat]: ~ (member_nat @ zero_zero_nat @ (image_nat_nat @ (suc) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3120])). 159.59/70.62 thf(1300,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/sandbox/benchmark/theBenchmark.p',fact_1316_add__mono__thms__linordered__field_I3_J)). 159.59/70.62 thf(12454,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)],[1300])). 159.59/70.62 thf(7382,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/sandbox/benchmark/theBenchmark.p',fact_805_left__diff__distrib__numeral)). 159.59/70.62 thf(33777,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)],[7382])). 159.59/70.62 thf(3733,axiom,((! [A:complex]: (((times_times_complex @ (invers8013647133539491842omplex @ A) @ A) = one_one_complex) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9006_left__inverse)). 159.59/70.62 thf(20261,plain,((! [A:complex]: (((times_times_complex @ (invers8013647133539491842omplex @ A) @ A) = one_one_complex) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3733])). 159.59/70.62 thf(4151,axiom,((sin_complex = (^ [A:complex]: (cos_complex @ (minus_minus_complex @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one))) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7796_sin__cos__eq)). 159.59/70.62 thf(21572,plain,(((sin_complex) = (^ [A:complex]: (cos_complex @ (minus_minus_complex @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4151])). 159.59/70.62 thf(6968,axiom,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: ((A != B) <= ((size_s6755466524823107622T_VEBT @ A) != (size_s6755466524823107622T_VEBT @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_neq__if__length__neq)). 159.59/70.62 thf(32122,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)],[6968])). 159.59/70.62 thf(2326,axiom,((! [A:nat,B:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6525_of__nat__le__iff)). 159.59/70.62 thf(15728,plain,((! [A:nat,B:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) = (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2326])). 159.59/70.62 thf(1104,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/sandbox/benchmark/theBenchmark.p',fact_3094_order_Ostrict__trans2)). 159.59/70.62 thf(11797,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)],[1104])). 159.59/70.62 thf(1514,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/sandbox/benchmark/theBenchmark.p',fact_7176_sin__times__cos)). 159.59/70.62 thf(13184,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)],[1514])). 159.59/70.62 thf(6103,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((A = (suc @ B)) | (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_le__Suc__eq)). 159.59/70.62 thf(28757,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)],[6103])). 159.59/70.62 thf(4435,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_eq_int @ C @ A) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4507_minf_I6_J)). 159.59/70.62 thf(22460,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)],[4435])). 159.59/70.62 thf(4068,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) = ((A = B) | (ord_le72135733267957522d_enat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2818_not__less__iff__gr__or__eq)). 159.59/70.62 thf(21306,plain,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) = ((A = B) | (ord_le72135733267957522d_enat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4068])). 159.59/70.62 thf(2002,axiom,((! [A:real,B:real,C:nat]: ((A != zero_zero_real) => ((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))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7845_lemma__termdiff2)). 159.59/70.62 thf(14719,plain,((! [A:real,B:real,C:nat]: ((~ (A = zero_zero_real)) => ((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))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2002])). 159.59/70.62 thf(861,axiom,((! [A:nat,B:list_nat]: ((member_nat @ (nth_nat @ B @ A) @ (set_nat2 @ B)) <= (ord_less_nat @ A @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_nth__mem)). 159.59/70.62 thf(11026,plain,((! [A:nat,B:list_nat]: ((member_nat @ (nth_nat @ B @ A) @ (set_nat2 @ B)) | ~ (ord_less_nat @ A @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[861])). 159.59/70.62 thf(7010,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/sandbox/benchmark/theBenchmark.p',fact_4785_diff__numeral__simps_I2_J)). 159.59/70.62 thf(32387,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)],[7010])). 159.59/70.62 thf(2551,axiom,((! [A:int,B:nat]: ((ord_less_int @ one_one_int @ A) => (ord_less_int @ one_one_int @ (power_power_int @ A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_power__gt1)). 159.59/70.62 thf(16451,plain,((! [A:int,B:nat]: ((ord_less_int @ one_one_int @ A) => (ord_less_int @ one_one_int @ (power_power_int @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2551])). 159.59/70.62 thf(3335,axiom,((! [A:real,B:real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (uminus_uminus_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4983_minus__divide__left)). 159.59/70.62 thf(18978,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)],[3335])). 159.59/70.62 thf(6489,axiom,(((uminus_uminus_real @ (numeral_numeral_real @ one)) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5211_uminus__numeral__One)). 159.59/70.62 thf(30210,plain,(((uminus_uminus_real @ (numeral_numeral_real @ one)) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6489])). 159.59/70.62 thf(8107,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ C @ D) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4087_div__mult__div__if__dvd)). 159.59/70.62 thf(36169,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ C @ D) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8107])). 159.59/70.62 thf(622,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/sandbox/benchmark/theBenchmark.p',fact_2075_mult__strict__left__mono__neg)). 159.59/70.62 thf(10239,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)],[622])). 159.59/70.62 thf(6346,axiom,((! [A:real]: ((archim7802044766580827645g_real @ (minus_minus_real @ A @ one_one_real)) = (minus_minus_int @ (archim7802044766580827645g_real @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6989_ceiling__diff__one)). 159.59/70.62 thf(29630,plain,((! [A:real]: ((archim7802044766580827645g_real @ (minus_minus_real @ A @ one_one_real)) = (minus_minus_int @ (archim7802044766580827645g_real @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6346])). 159.59/70.62 thf(8159,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit0 @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1427_numeral__code_I2_J)). 159.59/70.62 thf(36348,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)],[8159])). 159.59/70.62 thf(6624,axiom,((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5150_le__minus__one__simps_I1_J)). 159.59/70.62 thf(30688,plain,((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6624])). 159.59/70.62 thf(5284,axiom,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4368_triangle__Suc)). 159.59/70.62 thf(25566,plain,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5284])). 159.59/70.62 thf(5605,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_nat_Oinject)). 159.59/70.62 thf(26796,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5605])). 159.59/70.62 thf(3233,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/sandbox/benchmark/theBenchmark.p',fact_9735_max__Suc2)). 159.59/70.62 thf(18650,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)],[3233])). 159.59/70.62 thf(5912,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/sandbox/benchmark/theBenchmark.p',fact_359_power__commutes)). 159.59/70.62 thf(28105,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)],[5912])). 159.59/70.62 thf(5797,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_nat)) => (dvd_dvd_nat @ B @ (power_power_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4216_dvd__power)). 159.59/70.62 thf(27521,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_nat)) => (dvd_dvd_nat @ B @ (power_power_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5797])). 159.59/70.62 thf(3737,axiom,((! [A:nat,B:nat,C:(nat > real),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7719_sum_Oub__add__nat)). 159.59/70.62 thf(20271,plain,((! [A:nat,B:nat,C:(nat > real),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3737])). 159.59/70.62 thf(4208,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ A)) = (divide1717551699836669952omplex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1650_nonzero__mult__divide__mult__cancel__left2)). 159.59/70.62 thf(21742,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ A)) = (divide1717551699836669952omplex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4208])). 159.59/70.62 thf(7942,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/sandbox/benchmark/theBenchmark.p',fact_3827_dvd__add__times__triv__left__iff)). 159.59/70.62 thf(35642,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)],[7942])). 159.59/70.62 thf(3404,axiom,((! [A:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6891_norm__le__zero__iff)). 159.59/70.62 thf(19195,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)],[3404])). 159.59/70.62 thf(6928,axiom,((! [A:num,B:(nat > num),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [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)))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2659_ord__eq__le__subst)). 159.59/70.62 thf(31950,plain,((! [A:num,B:(nat > num),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [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)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6928])). 159.59/70.62 thf(379,axiom,((! [A:num,B:num]: (((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 @ 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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_max__number__of_I1_J)). 159.59/70.62 thf(9429,plain,((! [A:num,B:num]: (((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 @ 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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[379])). 159.59/70.62 thf(2221,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ C) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ C) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3845_div__add)). 159.59/70.62 thf(15421,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ C) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ C) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2221])). 159.59/70.62 thf(2360,axiom,((! [A:(nat > real),B:real]: (((summable_real @ A) <= (! [C:nat]: (ord_less_eq_real @ (groups6591440286371151544t_real @ A @ (set_ord_atMost_nat @ C)) @ B))) <= (! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8761_bounded__imp__summable)). 159.59/70.62 thf(15830,plain,((! [A:(nat > real),B:real]: ((summable_real @ (A)) | ~ (! [C:nat]: (ord_less_eq_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_atMost_nat @ C)) @ B)) | ~ (! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2360])). 159.59/70.62 thf(229,axiom,((! [A:complex]: (((ord_less_eq_real @ zero_zero_real @ (im @ (csqrt @ A))) & ((re @ (csqrt @ A)) = zero_zero_real)) | (ord_less_real @ zero_zero_real @ (re @ (csqrt @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9662_csqrt__principal)). 159.59/70.62 thf(8952,plain,((! [A:complex]: (((ord_less_eq_real @ zero_zero_real @ (im @ (csqrt @ A))) & ((re @ (csqrt @ A)) = zero_zero_real)) | (ord_less_real @ zero_zero_real @ (re @ (csqrt @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 159.59/70.62 thf(7112,axiom,((! [A:nat]: ((ord_max_nat @ A @ bot_bot_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2587_max__bot2)). 159.59/70.62 thf(32778,plain,((! [A:nat]: ((ord_max_nat @ A @ bot_bot_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7112])). 159.59/70.62 thf(7066,axiom,((! [A:option4927543243414619207at_nat,B:product_prod_nat_nat]: ((A != none_P5556105721700978146at_nat) <= (A = (some_P7363390416028606310at_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_option_OdiscI)). 159.59/70.62 thf(32597,plain,((! [A:option4927543243414619207at_nat,B:product_prod_nat_nat]: (~ (A = none_P5556105721700978146at_nat) | ~ (A = (some_P7363390416028606310at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7066])). 159.59/70.62 thf(1354,axiom,((! [A:real,B:real,C:real,D:real]: (((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)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5550_sin__bound__lemma)). 159.59/70.62 thf(12622,plain,((! [A:real,B:real,C:real,D:real]: ((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) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354])). 159.59/70.62 thf(7052,axiom,((! [A:complex,B:complex]: (((A = zero_zero_complex) | (B = zero_zero_complex)) <= ((times_times_complex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1864_divisors__zero)). 159.59/70.62 thf(32527,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)],[7052])). 159.59/70.62 thf(697,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ B @ one_one_real) => (ord_less_real @ (arccos @ B) @ (arccos @ A))) <= (ord_less_real @ A @ B)) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7686_arccos__less__arccos)). 159.59/70.62 thf(10487,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ one_one_real) => (ord_less_real @ (arccos @ B) @ (arccos @ A))) | ~ (ord_less_real @ A @ B) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[697])). 159.59/70.62 thf(2644,axiom,((! [A:product_prod_nat_nat,B:(nat > (nat > $o))]: ((! [C:nat,D:nat]: ((A = (product_Pair_nat_nat @ C @ D)) => (B @ C @ D))) => (produc6081775807080527818_nat_o @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5363_case__prodI2)). 159.59/70.62 thf(16773,plain,((! [A:product_prod_nat_nat,B:(nat > (nat > $o))]: ((! [C:nat,D:nat]: ((A = (product_Pair_nat_nat @ C @ D)) => (B @ C @ D))) => (produc6081775807080527818_nat_o @ (B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2644])). 159.59/70.62 thf(4897,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/sandbox/benchmark/theBenchmark.p',fact_8961_fact__code)). 159.59/70.62 thf(24176,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)],[4897])). 159.59/70.62 thf(4468,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/sandbox/benchmark/theBenchmark.p',fact_375_power__mult)). 159.59/70.62 thf(22618,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)],[4468])). 159.59/70.62 thf(891,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/sandbox/benchmark/theBenchmark.p',fact_1220_diff__eq__diff__less)). 159.59/70.62 thf(11116,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)],[891])). 159.59/70.62 thf(5526,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/sandbox/benchmark/theBenchmark.p',fact_9422_nat__numeral__diff__1)). 159.59/70.62 thf(26535,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)],[5526])). 159.59/70.62 thf(4118,axiom,(((arccos @ one_one_real) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7337_arccos__1)). 159.59/70.62 thf(21463,plain,(((arccos @ one_one_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4118])). 159.59/70.62 thf(1582,axiom,((ord_less_int = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3166_order__less__le)). 159.59/70.62 thf(13387,plain,(((ord_less_int) = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582])). 159.59/70.62 thf(3077,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((finite_finite_nat @ A) <= (finite_finite_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3759_finite__subset)). 159.59/70.62 thf(18137,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((finite_finite_nat @ A) | ~ (finite_finite_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3077])). 159.59/70.62 thf(7970,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2119_add__neg__neg)). 159.59/70.62 thf(35724,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7970])). 159.59/70.62 thf(1256,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (ord_less_int @ B @ C)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3580_mult__less__iff1)). 159.59/70.62 thf(12314,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (ord_less_int @ B @ C)) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256])). 159.59/70.62 thf(7288,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real),D:real,E:real]: ((! [F:nat]: ((ord_less_eq_real @ zero_zero_real @ (B @ F)) <= (member_nat @ F @ A))) => (((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (C @ F) @ (B @ F))) @ A) @ D)) @ E) <= (! [F:nat]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (C @ F) @ D)) @ E) <= (member_nat @ F @ A)))) <= ((groups6591440286371151544t_real @ B @ A) = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7762_convex__sum__bound__le)). 159.59/70.63 thf(33435,plain,((! [A:set_nat,B:(nat > real),C:(nat > real),D:real,E:real]: ((! [F:nat]: ((ord_less_eq_real @ zero_zero_real @ (B @ F)) | ~ (member_nat @ F @ A))) => ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (C @ F) @ (B @ F))) @ A) @ D)) @ E) | ~ (! [F:nat]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (C @ F) @ D)) @ E) | ~ (member_nat @ F @ A))) | ~ ((groups6591440286371151544t_real @ (B) @ A) = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7288])). 159.59/70.63 thf(3962,axiom,((! [A:int,B:int]: (((~ (ord_less_int @ A @ B)) = (A = B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3052_antisym__conv2)). 159.59/70.63 thf(21001,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)],[3962])). 159.59/70.63 thf(1185,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/sandbox/benchmark/theBenchmark.p',fact_7005_cos__npi2)). 159.59/70.63 thf(12045,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)],[1185])). 159.59/70.63 thf(3698,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4674_neg__less__0__iff__less)). 159.59/70.63 thf(20129,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)],[3698])). 159.59/70.63 thf(2095,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = B) = (A = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1525_add__cancel__left__left)). 159.59/70.63 thf(15001,plain,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = B) = (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2095])). 159.59/70.63 thf(3657,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((ord_less_eq_real @ (arcsin @ A) @ pi) & ((sin_real @ (arcsin @ A)) = A) & (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7836_arcsin__pi)). 159.59/70.63 thf(19997,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((ord_less_eq_real @ (arcsin @ A) @ pi) & ((sin_real @ (arcsin @ A)) = A) & (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arcsin @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3657])). 159.59/70.63 thf(4866,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/sandbox/benchmark/theBenchmark.p',fact_5670_signed__take__bit__numeral__minus__bit1)). 159.59/70.63 thf(24079,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)],[4866])). 159.59/70.63 thf(5908,axiom,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5166_neg__one__le__numeral)). 159.59/70.63 thf(28095,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)],[5908])). 159.59/70.63 thf(2250,axiom,((ord_less_real = (^ [A:real,B:real]: (ord_less_real @ (minus_minus_real @ A @ B) @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2146_less__iff__diff__less__0)). 159.59/70.63 thf(15510,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)],[2250])). 159.59/70.63 thf(7677,axiom,((! [A:nat]: (((divide_divide_nat @ (plus_plus_nat @ A @ one_one_nat) @ (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/sandbox/benchmark/theBenchmark.p',fact_3907_even__succ__div__two)). 159.59/70.63 thf(34786,plain,((! [A:nat]: (((divide_divide_nat @ (plus_plus_nat @ A @ one_one_nat) @ (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)],[7677])). 159.59/70.63 thf(5870,axiom,((! [A:int,B:(num > int),C:num,D:num]: ((A = (B @ C)) => ((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))) => (ord_less_eq_int @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2658_ord__eq__le__subst)). 159.59/70.63 thf(27937,plain,((! [A:int,B:(num > int),C:num,D:num]: ((A = (B @ C)) => ((ord_less_eq_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))) => (ord_less_eq_int @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5870])). 159.59/70.63 thf(2170,axiom,((! [A:real]: (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arctan @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6781_arctan__lbound)). 159.59/70.63 thf(15247,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)],[2170])). 159.59/70.63 thf(4517,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_complex @ zero_zero_complex @ A) = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1820_zero__power)). 159.59/70.63 thf(22778,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_complex @ zero_zero_complex @ A) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4517])). 159.59/70.63 thf(5434,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)) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2647_ord__le__eq__subst)). 159.59/70.63 thf(26210,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)) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5434])). 159.59/70.63 thf(6628,axiom,((semiri1406184849735516958ct_int = (^ [A:nat]: (semiri1314217659103216013at_int @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8762_fact__prod)). 159.59/70.63 thf(30698,plain,(((semiri1406184849735516958ct_int) = (^ [A:nat]: (semiri1314217659103216013at_int @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6628])). 159.59/70.63 thf(307,axiom,((filterlim_real_real @ (^ [A:real]: (divide_divide_real @ (ln_ln_real @ A) @ A)) @ (topolo2815343760600316023s_real @ zero_zero_real) @ at_top_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9958_ln__x__over__x__tendsto__0)). 159.59/70.63 thf(9200,plain,((filterlim_real_real @ (^ [A:real]: (divide_divide_real @ (ln_ln_real @ A) @ A)) @ (topolo2815343760600316023s_real @ zero_zero_real) @ at_top_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 159.59/70.63 thf(5259,axiom,(((numera1916890842035813515d_enat @ one) = one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_numeral__One)). 159.59/70.63 thf(25470,plain,(((numera1916890842035813515d_enat @ one) = one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5259])). 159.59/70.63 thf(5337,axiom,((! [A:num,B:num]: ((bit_se1146084159140164899it_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_nat @ B)) = (bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ (pred_numeral @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6347_bit__numeral__simps_I3_J)). 159.59/70.63 thf(25794,plain,((! [A:num,B:num]: ((bit_se1146084159140164899it_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)],[5337])). 159.59/70.63 thf(6569,axiom,((! [A:int,B:(nat > int),C:nat,D:nat]: ((((! [E:nat,F:nat]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_int @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_int @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2691_order__subst1)). 159.59/70.63 thf(30487,plain,((! [A:int,B:(nat > int),C:nat,D:nat]: (((! [E:nat,F:nat]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_int @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_int @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6569])). 159.59/70.63 thf(4483,axiom,((! [A:nat,B:nat]: ((member_nat @ A @ (set_ord_atMost_nat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8374_atMost__iff)). 159.59/70.63 thf(22673,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)],[4483])). 159.59/70.63 thf(1479,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ A @ C) <= (ord_le2932123472753598470d_enat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3088_order_Ostrict__trans2)). 159.59/70.63 thf(13081,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ A @ C) | ~ (ord_le2932123472753598470d_enat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479])). 159.59/70.63 thf(4955,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/sandbox/benchmark/theBenchmark.p',fact_428_set__update__memI)). 159.59/70.63 thf(24366,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)],[4955])). 159.59/70.63 thf(2264,axiom,((! [A:code_integer,B:code_integer]: (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3974_dvd__triv__right)). 159.59/70.63 thf(15555,plain,((! [A:code_integer,B:code_integer]: (dvd_dvd_Code_integer @ A @ (times_3573771949741848930nteger @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2264])). 159.59/70.63 thf(6821,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1077_mult__1)). 159.59/70.63 thf(31509,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6821])). 159.59/70.63 thf(7526,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/sandbox/benchmark/theBenchmark.p',fact_251_power__increasing__iff)). 159.59/70.63 thf(34268,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)],[7526])). 159.59/70.63 thf(4751,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2650_ord__le__eq__subst)). 159.59/70.63 thf(23657,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((C @ B) = D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4751])). 159.59/70.63 thf(114,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 @ A) & (ord_less_eq_real @ zero_zero_real @ B))) => (ord_less_eq_real @ zero_zero_real @ (real_V1485227260804924795R_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9241_split__scaleR__pos__le)). 159.59/70.63 thf(8599,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 @ A) & (ord_less_eq_real @ zero_zero_real @ B))) => (ord_less_eq_real @ zero_zero_real @ (real_V1485227260804924795R_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 159.59/70.63 thf(7101,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1107_ab__semigroup__mult__class_Omult__ac_I1_J)). 159.59/70.63 thf(32736,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7101])). 159.59/70.63 thf(1290,axiom,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: (((minus_8373710615458151222nteger @ D @ A) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ B) @ (minus_8373710615458151222nteger @ D @ C))) <= (A = (plus_p5714425477246183910nteger @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5101_group__cancel_Osub2)). 159.59/70.63 thf(12418,plain,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: (((minus_8373710615458151222nteger @ D @ A) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ B) @ (minus_8373710615458151222nteger @ D @ C))) | ~ (A = (plus_p5714425477246183910nteger @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290])). 159.59/70.63 thf(2820,axiom,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_complex @ (C @ (suc @ B)) @ (groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7660_sum_Onat__ivl__Suc_H)). 159.59/70.63 thf(17318,plain,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (plus_plus_complex @ (C @ (suc @ B)) @ (groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2820])). 159.59/70.63 thf(3593,axiom,((! [A:num]: ((semiri4216267220026989637d_enat @ (numeral_numeral_nat @ A)) = (numera1916890842035813515d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6513_of__nat__numeral)). 159.59/70.63 thf(19790,plain,((! [A:num]: ((semiri4216267220026989637d_enat @ (numeral_numeral_nat @ A)) = (numera1916890842035813515d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3593])). 159.59/70.63 thf(4723,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/sandbox/benchmark/theBenchmark.p',fact_7831_double__gauss__sum__from__Suc__0)). 159.59/70.63 thf(23571,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)],[4723])). 159.59/70.63 thf(5627,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/sandbox/benchmark/theBenchmark.p',fact_156_left__add__twice)). 159.59/70.63 thf(26870,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)],[5627])). 159.59/70.63 thf(2858,axiom,((! [A:real,B:real,C:(nat > real)]: ((ord_less_real @ (real_V7735802525324610683m_real @ A) @ B) => ((summable_real @ (^ [D:nat]: (times_times_real @ (diffs_real @ C @ D) @ (power_power_real @ A @ D)))) <= (! [D:real]: ((summable_real @ (^ [E:nat]: (times_times_real @ (C @ E) @ (power_power_real @ D @ E)))) <= (ord_less_real @ (real_V7735802525324610683m_real @ D) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8136_termdiff__converges)). 159.59/70.63 thf(17450,plain,((! [A:real,B:real,C:(nat > real)]: ((ord_less_real @ (real_V7735802525324610683m_real @ A) @ B) => ((summable_real @ (^ [D:nat]: (times_times_real @ (diffs_real @ C @ D) @ (power_power_real @ A @ D)))) | ~ (! [D:real]: ((summable_real @ (^ [E:nat]: (times_times_real @ (C @ E) @ (power_power_real @ D @ E)))) | ~ (ord_less_real @ (real_V7735802525324610683m_real @ D) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2858])). 159.59/70.63 thf(3964,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/sandbox/benchmark/theBenchmark.p',fact_1371_ordered__ring__class_Ole__add__iff1)). 159.59/70.63 thf(21006,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)],[3964])). 159.59/70.63 thf(6783,axiom,((! [A:real,B:real,C:num]: ((A = (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ C)))) = ((((uminus_uminus_real @ (numeral_numeral_real @ C)) != zero_zero_real) => ((times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ C))) = B)) & ((A = zero_zero_real) <= ((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4828_eq__divide__eq__numeral1_I2_J)). 159.59/70.63 thf(31397,plain,((! [A:real,B:real,C:num]: ((A = (divide_divide_real @ B @ (uminus_uminus_real @ (numeral_numeral_real @ C)))) = (((~ ((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real)) => ((times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ C))) = B)) & ((A = zero_zero_real) | ~ ((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6783])). 159.59/70.63 thf(6415,axiom,((! [A:nat]: (ord_less_eq_nat @ bot_bot_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3278_bot_Oextremum)). 159.59/70.63 thf(29917,plain,((! [A:nat]: (ord_less_eq_nat @ bot_bot_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6415])). 159.59/70.63 thf(1286,axiom,((! [A:int,B:int,C:int]: ((bit_se1409905431419307370or_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = (bit_se1409905431419307370or_int @ A @ (bit_se1409905431419307370or_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6051_or_Oassoc)). 159.59/70.63 thf(12408,plain,((! [A:int,B:int,C:int]: ((bit_se1409905431419307370or_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = (bit_se1409905431419307370or_int @ A @ (bit_se1409905431419307370or_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286])). 159.59/70.63 thf(2138,axiom,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6527_of__nat__le__iff)). 159.59/70.63 thf(15151,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)],[2138])). 159.59/70.63 thf(7074,axiom,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9022_binomial__eq__0)). 159.59/70.63 thf(32628,plain,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7074])). 159.59/70.63 thf(6809,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/sandbox/benchmark/theBenchmark.p',fact_8610_prod_Oin__pairs__0)). 159.59/70.63 thf(31474,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)],[6809])). 159.59/70.63 thf(4147,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/sandbox/benchmark/theBenchmark.p',fact_5843_of__int__le__of__int__power__cancel__iff)). 159.59/70.63 thf(21559,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)],[4147])). 159.59/70.63 thf(4234,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => ((ord_less_eq_int @ A @ B) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3045_antisym__conv1)). 159.59/70.63 thf(21841,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)],[4234])). 159.59/70.63 thf(2834,axiom,((! [A:nat,B:nat,C:int]: ((ord_less_nat @ A @ B) => ((ord_less_int @ one_one_int @ C) => (ord_less_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_power__strict__increasing)). 159.59/70.63 thf(17360,plain,((! [A:nat,B:nat,C:int]: ((ord_less_nat @ A @ B) => ((ord_less_int @ one_one_int @ C) => (ord_less_int @ (power_power_int @ C @ A) @ (power_power_int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2834])). 159.59/70.63 thf(7789,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/sandbox/benchmark/theBenchmark.p',fact_4865_Power_Oring__1__class_Opower__minus__even)). 159.59/70.63 thf(35153,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)],[7789])). 159.59/70.63 thf(4590,axiom,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_complex @ (A @ zero_zero_nat) @ (groups6464643781859351333omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8479_prod_OatMost__Suc__shift)). 159.59/70.63 thf(23103,plain,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_complex @ (A @ zero_zero_nat) @ (groups6464643781859351333omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4590])). 159.59/70.63 thf(3945,axiom,((ord_less_int = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3117_dual__order_Ostrict__iff__order)). 159.59/70.63 thf(20940,plain,(((ord_less_int) = (^ [A:int,B:int]: ((ord_less_eq_int @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3945])). 159.59/70.63 thf(2788,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/sandbox/benchmark/theBenchmark.p',fact_6073_AND__upper1)). 159.59/70.63 thf(17229,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)],[2788])). 159.59/70.63 thf(4060,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/sandbox/benchmark/theBenchmark.p',fact_6737_real__of__nat__div)). 159.59/70.63 thf(21284,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)],[4060])). 159.59/70.63 thf(3057,axiom,((! [A:(nat > real),B:real]: (((sums_real @ A @ B) <= (sums_real @ (^ [C:nat]: (A @ (suc @ C))) @ B)) <= ((A @ zero_zero_nat) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7930_sums__Suc__imp)). 159.59/70.63 thf(18076,plain,((! [A:(nat > real),B:real]: ((sums_real @ (A) @ B) | ~ (sums_real @ (^ [C:nat]: (A @ (suc @ C))) @ B) | ~ ((A @ zero_zero_nat) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3057])). 159.59/70.63 thf(210,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/sandbox/benchmark/theBenchmark.p',fact_9613_atLeast1__lessThan__eq__remove0)). 159.59/70.63 thf(8891,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)],[210])). 159.59/70.63 thf(4577,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) <= (dvd_dvd_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4033_dvd__pos__nat)). 159.59/70.63 thf(23046,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) | ~ (dvd_dvd_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4577])). 159.59/70.63 thf(6242,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/sandbox/benchmark/theBenchmark.p',fact_4302_unity__coeff__ex)). 159.59/70.63 thf(29220,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)],[6242])). 159.59/70.63 thf(2941,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ one_one_complex) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1036_div__by__1)). 159.59/70.63 thf(17720,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ one_one_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2941])). 159.59/70.63 thf(1309,axiom,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ A) @ (collect_nat @ B)) <= (! [C:nat]: ((A @ C) => (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2961_Collect__mono)). 159.59/70.63 thf(12481,plain,((! [A:(nat > $o),B:(nat > $o)]: ((ord_less_eq_set_nat @ (collect_nat @ (A)) @ (collect_nat @ (B))) | ~ (! [C:nat]: ((A @ C) => (B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309])). 159.59/70.63 thf(6129,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 @ zero_zero_int @ (times_times_int @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1976_mult__nonneg__nonneg)). 159.59/70.63 thf(28848,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 @ zero_zero_int @ (times_times_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6129])). 159.59/70.63 thf(2206,axiom,((! [A:real,B:nat]: ? [C:real]: (((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_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8139_Maclaurin__cos__expansion)). 159.59/70.63 thf(15369,plain,((! [A:real,B:nat]: ? [C:real]: (((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_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2206])). 159.59/70.63 thf(3159,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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2242_mult__right__less__imp__less)). 159.59/70.63 thf(18421,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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3159])). 159.59/70.63 thf(1575,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/sandbox/benchmark/theBenchmark.p',fact_1739_divide__less__0__1__iff)). 159.59/70.63 thf(13366,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)],[1575])). 159.59/70.63 thf(6952,axiom,((! [A:$o]: ((A = ($false)) | (A = ($true))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T)). 159.59/70.63 thf(32051,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6952])). 159.59/70.63 thf(6597,axiom,((ord_less_eq_nat @ one_one_nat @ na)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193__C11_C)). 159.59/70.63 thf(30595,plain,((ord_less_eq_nat @ one_one_nat @ na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6597])). 159.59/70.63 thf(717,axiom,((! [A:real,B:real,C:complex]: ((real_V2046097035970521341omplex @ (plus_plus_real @ A @ B) @ C) = (plus_plus_complex @ (real_V2046097035970521341omplex @ A @ C) @ (real_V2046097035970521341omplex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9217_scaleR__left__distrib)). 159.59/70.63 thf(10560,plain,((! [A:real,B:real,C:complex]: ((real_V2046097035970521341omplex @ (plus_plus_real @ A @ B) @ C) = (plus_plus_complex @ (real_V2046097035970521341omplex @ A @ C) @ (real_V2046097035970521341omplex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[717])). 159.59/70.63 thf(4807,axiom,((! [A:real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1498_mult__zero__left)). 159.59/70.63 thf(23857,plain,((! [A:real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4807])). 159.59/70.63 thf(5894,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ one_one_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6004_and__numerals_I5_J)). 159.59/70.63 thf(28027,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit0 @ A)) @ one_one_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5894])). 159.59/70.63 thf(3152,axiom,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) = (((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ zero_zero_int @ B)) | ((ord_less_int @ zero_zero_int @ A) & (ord_less_int @ B @ zero_zero_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2102_mult__less__0__iff)). 159.59/70.63 thf(18396,plain,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) = (((ord_less_int @ A @ zero_zero_int) & (ord_less_int @ zero_zero_int @ B)) | ((ord_less_int @ zero_zero_int @ A) & (ord_less_int @ B @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3152])). 159.59/70.63 thf(6578,axiom,((! [A:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ A @ A) = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1659_div__self)). 159.59/70.63 thf(30519,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => ((divide_divide_nat @ A @ A) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6578])). 159.59/70.63 thf(1718,axiom,((! [A:int,B:int,C:int]: ((A = B) => ((ord_less_int @ A @ C) <= (ord_less_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2778_ord__eq__less__trans)). 159.59/70.63 thf(13805,plain,((! [A:int,B:int,C:int]: ((A = B) => ((ord_less_int @ A @ C) | ~ (ord_less_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718])). 159.59/70.63 thf(2403,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/sandbox/benchmark/theBenchmark.p',fact_4155_unit__div__eq__0__iff)). 159.59/70.63 thf(15972,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)],[2403])). 159.59/70.63 thf(3468,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/sandbox/benchmark/theBenchmark.p',fact_7293_complex__norm)). 159.59/70.63 thf(19393,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)],[3468])). 159.59/70.63 thf(4266,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/sandbox/benchmark/theBenchmark.p',fact_3579_mult__less__iff1)). 159.59/70.63 thf(21944,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)],[4266])). 159.59/70.63 thf(8060,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/sandbox/benchmark/theBenchmark.p',fact_6739_mod__mult2__eq_H)). 159.59/70.63 thf(36024,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)],[8060])). 159.59/70.63 thf(7032,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/sandbox/benchmark/theBenchmark.p',fact_1856_mult__left__cancel)). 159.59/70.63 thf(32451,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)],[7032])). 159.59/70.63 thf(1981,axiom,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5147_neg__numeral__less__zero)). 159.59/70.63 thf(14655,plain,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1981])). 159.59/70.63 thf(4797,axiom,((! [A:num]: ((one_one_real = (numeral_numeral_real @ A)) = (one = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_one__eq__numeral__iff)). 159.59/70.63 thf(23818,plain,((! [A:num]: ((one_one_real = (numeral_numeral_real @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4797])). 159.59/70.63 thf(7981,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/sandbox/benchmark/theBenchmark.p',fact_95_add__numeral__left)). 159.59/70.63 thf(35756,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)],[7981])). 159.59/70.63 thf(2618,axiom,(((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ one_one_complex) = zero_zero_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4743_add__neg__numeral__special_I8_J)). 159.59/70.63 thf(16690,plain,(((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ one_one_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2618])). 159.59/70.63 thf(5948,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2399_div__greater__zero__iff)). 159.59/70.63 thf(28275,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5948])). 159.59/70.63 thf(3630,axiom,((! [A:nat,B:set_nat,C:nat]: (((insert_nat @ A @ B) = (insert_nat @ C @ bot_bot_set_nat)) = ((A = C) & (ord_less_eq_set_nat @ B @ (insert_nat @ C @ bot_bot_set_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6159_singleton__insert__inj__eq_H)). 159.59/70.63 thf(19911,plain,((! [A:nat,B:set_nat,C:nat]: (((insert_nat @ A @ B) = (insert_nat @ C @ bot_bot_set_nat)) = ((A = C) & (ord_less_eq_set_nat @ B @ (insert_nat @ C @ bot_bot_set_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3630])). 159.59/70.63 thf(3757,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/sandbox/benchmark/theBenchmark.p',fact_1241_ring__class_Oring__distribs_I1_J)). 159.59/70.63 thf(20335,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)],[3757])). 159.59/70.63 thf(4474,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4257_zero__le__power__eq)). 159.59/70.63 thf(22641,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ 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)],[4474])). 159.59/70.63 thf(2898,axiom,((! [A:real,B:real,C: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))) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5276_neg__minus__divide__le__eq)). 159.59/70.63 thf(17582,plain,((! [A:real,B:real,C: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))) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2898])). 159.59/70.63 thf(4143,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ B) = (minus_minus_complex @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4712_uminus__add__conv__diff)). 159.59/70.63 thf(21543,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ B) = (minus_minus_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4143])). 159.59/70.63 thf(8098,axiom,((! [A:nat]: (ord_less_nat @ (bit_se2002935070580805687sk_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6117_mask__nat__less__exp)). 159.59/70.63 thf(36140,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)],[8098])). 159.59/70.63 thf(2280,axiom,((! [A:code_integer,B:code_integer]: ? [C:code_integer]: ! [D:code_integer]: ((ord_le6747313008572928689nteger @ C @ D) => ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ B)) = (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4526_pinf_I9_J)). 159.59/70.63 thf(15602,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2280])). 159.59/70.63 thf(2008,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/sandbox/benchmark/theBenchmark.p',fact_6657_of__nat__less__of__int__iff)). 159.59/70.63 thf(14740,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)],[2008])). 159.59/70.63 thf(4614,axiom,((! [A:nat]: ((bit_se8570568707652914677it_nat @ A @ (suc @ zero_zero_nat)) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9739_drop__bit__of__Suc__0)). 159.59/70.63 thf(23199,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)],[4614])). 159.59/70.63 thf(2194,axiom,((! [A:(real > (real > $o)),B:real,C:real]: (((! [D:real]: (A @ D @ D)) => ((! [D:real,E:real]: ((A @ D @ E) <= (A @ E @ D))) => (A @ B @ C))) <= (! [D:real,E:real]: ((ord_less_real @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2809_linorder__less__wlog)). 159.59/70.63 thf(15322,plain,((! [A:(real > (real > $o)),B:real,C:real]: (((! [D:real]: (A @ D @ D)) => ((! [D:real,E:real]: ((A @ D @ E) | ~ (A @ E @ D))) => (A @ B @ C))) | ~ (! [D:real,E:real]: ((ord_less_real @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2194])). 159.59/70.63 thf(5874,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8149_fact__ge__self)). 159.59/70.63 thf(27954,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5874])). 159.59/70.63 thf(2663,axiom,((! [A:real,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => ((comm_s7457072308508201937r_real @ A @ C) != zero_zero_real)) <= ((comm_s7457072308508201937r_real @ A @ B) != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8218_pochhammer__neq__0__mono)). 159.59/70.63 thf(16837,plain,((! [A:real,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) => (~ ((comm_s7457072308508201937r_real @ A @ C) = zero_zero_real))) | ((comm_s7457072308508201937r_real @ A @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2663])). 159.59/70.63 thf(1325,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/sandbox/benchmark/theBenchmark.p',fact_7994_lemma__termdiff1)). 159.59/70.63 thf(12532,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)],[1325])). 159.59/70.63 thf(6740,axiom,((! [A:nat]: ((semiri5074537144036343181t_real @ (suc @ A)) != zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6673_of__nat__neq__0)). 159.59/70.63 thf(31229,plain,((! [A:nat]: ~ ((semiri5074537144036343181t_real @ (suc @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6740])). 159.59/70.63 thf(4489,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/sandbox/benchmark/theBenchmark.p',fact_4611_neg__le__iff__le)). 159.59/70.63 thf(22690,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)],[4489])). 159.59/70.63 thf(7139,axiom,(((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera6690914467698888265omplex @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_one__add__one)). 159.59/70.63 thf(32907,plain,(((plus_plus_complex @ one_one_complex @ one_one_complex) = (numera6690914467698888265omplex @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7139])). 159.59/70.63 thf(4353,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/sandbox/benchmark/theBenchmark.p',fact_8120_fact__num__eq__if)). 159.59/70.63 thf(22201,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)],[4353])). 159.59/70.63 thf(5761,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/sandbox/benchmark/theBenchmark.p',fact_8482_prod_OatMost__Suc__shift)). 159.59/70.63 thf(27329,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)],[5761])). 159.59/70.63 thf(7420,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/sandbox/benchmark/theBenchmark.p',fact_8334_pochhammer__same)). 159.59/70.63 thf(33888,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)],[7420])). 159.59/70.63 thf(5753,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ (suc @ B)) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3488_mod__Suc__le__divisor)). 159.59/70.63 thf(27305,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ (suc @ B)) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5753])). 159.59/70.63 thf(53,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/sandbox/benchmark/theBenchmark.p',fact_8306_Suc__times__gbinomial)). 159.59/70.63 thf(8410,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)],[53])). 159.59/70.63 thf(515,axiom,((! [A:real,B:real,C:nat]: ((power_power_real @ (real_V1485227260804924795R_real @ A @ B) @ C) = (real_V1485227260804924795R_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9195_scaleR__power)). 159.59/70.63 thf(9893,plain,((! [A:real,B:real,C:nat]: ((power_power_real @ (real_V1485227260804924795R_real @ A @ B) @ C) = (real_V1485227260804924795R_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])). 159.59/70.63 thf(5141,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((A @ zero_zero_nat) <= (! [C:nat]: ((A @ C) <= (A @ (suc @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1905_zero__induct)). 159.59/70.63 thf(25038,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((A @ zero_zero_nat) | ~ (! [C:nat]: ((A @ C) | ~ (A @ (suc @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5141])). 159.59/70.63 thf(4018,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((((arcsin @ A) = (arcsin @ B)) = (A = B)) <= (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7567_arcsin__eq__iff)). 159.59/70.63 thf(21162,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((((arcsin @ A) = (arcsin @ B)) = (A = B)) | ~ (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4018])). 159.59/70.63 thf(6580,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/sandbox/benchmark/theBenchmark.p',fact_184_sum__squares__bound)). 159.59/70.63 thf(30525,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)],[6580])). 159.59/70.63 thf(5880,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_max_nat @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_max_Oabsorb__iff1)). 159.59/70.63 thf(27980,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_max_nat @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5880])). 159.59/70.63 thf(7588,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/sandbox/benchmark/theBenchmark.p',fact_4892_power__minus1__even)). 159.59/70.63 thf(34525,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)],[7588])). 159.59/70.63 thf(728,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1218_diff__strict__left__mono)). 159.59/70.63 thf(10603,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (minus_minus_real @ C @ B) @ (minus_minus_real @ C @ A)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[728])). 159.59/70.63 thf(2433,axiom,(((invers8013647133539491842omplex @ (numera6690914467698888265omplex @ one)) = (numera6690914467698888265omplex @ one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9036_inverse__numeral__1)). 159.59/70.63 thf(16083,plain,(((invers8013647133539491842omplex @ (numera6690914467698888265omplex @ one)) = (numera6690914467698888265omplex @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2433])). 159.59/70.63 thf(2443,axiom,((! [A:(real > $o),B:real]: ((((ord_less_real @ zero_zero_real @ B) => (A @ B)) <= (! [C:nat]: ((A @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ C))) <= (C != zero_zero_nat)))) <= (! [C:real,D:real]: ((ord_less_real @ C @ D) => ((A @ C) => (A @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9097_forall__pos__mono)). 159.59/70.63 thf(16112,plain,((! [A:(real > $o),B:real]: (((ord_less_real @ zero_zero_real @ B) => (A @ B)) | ~ (! [C:nat]: ((A @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ C))) | (C = zero_zero_nat))) | ~ (! [C:real,D:real]: ((ord_less_real @ C @ D) => ((A @ C) => (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2443])). 159.59/70.63 thf(1417,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/sandbox/benchmark/theBenchmark.p',fact_1366_eq__add__iff1)). 159.59/70.63 thf(12870,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)],[1417])). 159.59/70.63 thf(7175,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/sandbox/benchmark/theBenchmark.p',fact_5826_of__int__1__le__iff)). 159.59/70.63 thf(33039,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)],[7175])). 159.59/70.63 thf(6207,axiom,((! [A:num]: ((ring_18347121197199848620nteger @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5908_of__int__neg__numeral)). 159.59/70.63 thf(29114,plain,((! [A:num]: ((ring_18347121197199848620nteger @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6207])). 159.59/70.63 thf(3789,axiom,((! [A:(nat > real),B:nat,C:nat]: ((summable_real @ A) => ((! [D:nat]: ((ord_less_eq_real @ zero_zero_real @ (A @ D)) <= (ord_less_eq_nat @ B @ 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/sandbox/benchmark/theBenchmark.p',fact_8011_sum__less__suminf2)). 159.59/70.63 thf(20434,plain,((! [A:(nat > real),B:nat,C:nat]: ((summable_real @ (A)) => ((! [D:nat]: ((ord_less_eq_real @ zero_zero_real @ (A @ D)) | ~ (ord_less_eq_nat @ B @ 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)],[3789])). 159.59/70.63 thf(4656,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/sandbox/benchmark/theBenchmark.p',fact_6744_nat__less__real__le)). 159.59/70.63 thf(23352,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)],[4656])). 159.59/70.63 thf(4660,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_VEBT_valid @ A @ B) = C) => ((~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ D @ E @ F @ G)) => (C = (~ ((E = B) & ! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ F)) => (vEBT_VEBT_valid @ H @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))))) & (vEBT_VEBT_valid @ G @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))))) & ((size_s6755466524823107622T_VEBT @ F) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))))) & (case_o184042715313410164at_nat @ (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H)) & ! [H:vEBT_VEBT]: ((~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ F)))) @ (produc6081775807080527818_nat_o @ (^ [H:nat,I:nat]: ((ord_less_eq_nat @ H @ I) & (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)) & ! [J:nat]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [K:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ F @ J) @ K)) = (vEBT_V8194947554948674370ptions @ G @ J))) & (((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))) @ F @ I) & ! [J:nat]: (((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))) @ F @ J) => ((ord_less_eq_nat @ J @ I) & (ord_less_nat @ H @ J))) <= (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)))) <= (H != I)) & ((H = I) => (! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ F)) => (~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K))))))))) @ D))))))) <= ((C = (B != one_one_nat)) <= (? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10067_VEBT__internal_Ovalid_H_Oelims_I1_J)). 159.59/70.63 thf(23361,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_VEBT_valid @ A @ B) = C) => (~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: ((A = (vEBT_Node @ D @ E @ F @ G)) => (C = (~ ((E = B) & ! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ F)) => (vEBT_VEBT_valid @ H @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))))) & (vEBT_VEBT_valid @ G @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))))) & ((size_s6755466524823107622T_VEBT @ F) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))))) & (case_o184042715313410164at_nat @ (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H)) & ! [H:vEBT_VEBT]: (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ F)))) @ (produc6081775807080527818_nat_o @ (^ [H:nat,I:nat]: ((ord_less_eq_nat @ H @ I) & (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)) & ! [J:nat]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ E @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [K:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ F @ J) @ K)) = (vEBT_V8194947554948674370ptions @ G @ J))) & (((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))) @ F @ I) & ! [J:nat]: (((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ E @ (numeral_numeral_nat @ (bit0 @ one))) @ F @ J) => ((ord_less_eq_nat @ J @ I) & (ord_less_nat @ H @ J))) | ~ (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)))) | (H = I)) & ((H = I) => (! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ F)) => (~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K))))))))) @ D)))))) | ~ ((C = (~ (B = one_one_nat))) | ~ (? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4660])). 159.59/70.63 thf(7198,axiom,((! [A:num]: ((bit_or_not_num_neg @ (bit1 @ A) @ one) = one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6218_or__not__num__neg_Osimps_I7_J)). 159.59/70.63 thf(33137,plain,((! [A:num]: ((bit_or_not_num_neg @ (bit1 @ A) @ one) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7198])). 159.59/70.63 thf(6791,axiom,((! [A:(nat > (nat > nat)),B:(product_prod_nat_nat > nat)]: (((produc6842872674320459806at_nat @ A) = B) <= (! [C:nat,D:nat]: ((A @ C @ D) = (B @ (product_Pair_nat_nat @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5003_cond__case__prod__eta)). 159.59/70.63 thf(31418,plain,((! [A:(nat > (nat > nat)),B:(product_prod_nat_nat > nat)]: (((produc6842872674320459806at_nat @ A) = (B)) | ~ (! [C:nat,D:nat]: ((A @ C @ D) = (B @ (product_Pair_nat_nat @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6791])). 159.59/70.63 thf(4047,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/sandbox/benchmark/theBenchmark.p',fact_7997_diff__power__eq__sum)). 159.59/70.63 thf(21246,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)],[4047])). 159.59/70.63 thf(5064,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ zero_zero_nat @ C) => ((ord_less_nat @ zero_zero_nat @ B) => (A = C))) <= (ord_less_eq_nat @ zero_zero_nat @ A)) <= ((power_power_nat @ A @ B) = (power_power_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1929_power__eq__imp__eq__base)). 159.59/70.63 thf(24783,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => ((ord_less_nat @ zero_zero_nat @ B) => (A = C))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A) | ~ ((power_power_nat @ A @ B) = (power_power_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5064])). 159.59/70.63 thf(308,axiom,((! [A:code_integer,B:code_integer]: (((uminus1351360451143612070nteger @ A) = B) = ((plus_p5714425477246183910nteger @ A @ B) = zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5045_neg__eq__iff__add__eq__0)). 159.59/70.63 thf(9201,plain,((! [A:code_integer,B:code_integer]: (((uminus1351360451143612070nteger @ A) = B) = ((plus_p5714425477246183910nteger @ A @ B) = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 159.59/70.63 thf(6940,axiom,((times_times_complex = (^ [A:complex,B:complex]: (times_times_complex @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_mult_Ocommute)). 159.59/70.63 thf(32002,plain,(((times_times_complex) = (^ [A:complex,B:complex]: (times_times_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6940])). 159.59/70.63 thf(3568,axiom,((! [A:int,B:nat]: (((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = A) => ((((bit_se2923211474154528505it_int @ B @ A) = zero_zero_int) <= (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) & ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((bit_se2923211474154528505it_int @ B @ A) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ one_one_int))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5339_stable__imp__take__bit__eq)). 159.59/70.63 thf(19711,plain,((! [A:int,B:nat]: (((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = A) => ((((bit_se2923211474154528505it_int @ B @ A) = zero_zero_int) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) & ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((bit_se2923211474154528505it_int @ B @ A) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ one_one_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3568])). 159.59/70.63 thf(5338,axiom,((! [A:nat]: ((bit_se2925701944663578781it_nat @ (suc @ A) @ one_one_nat) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4727_take__bit__Suc__1)). 159.59/70.63 thf(25797,plain,((! [A:nat]: ((bit_se2925701944663578781it_nat @ (suc @ A) @ one_one_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5338])). 159.59/70.63 thf(599,axiom,((! [A:(nat > real),B:(nat > real)]: ((((plus_plus_real @ (suminf_real @ A) @ (suminf_real @ B)) = (suminf_real @ (^ [C:nat]: (plus_plus_real @ (A @ C) @ (B @ C))))) <= (summable_real @ B)) <= (summable_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7046_suminf__add)). 159.59/70.63 thf(10158,plain,((! [A:(nat > real),B:(nat > real)]: (((plus_plus_real @ (suminf_real @ (A)) @ (suminf_real @ (B))) = (suminf_real @ (^ [C:nat]: (plus_plus_real @ (A @ C) @ (B @ C))))) | ~ (summable_real @ (B)) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[599])). 159.59/70.63 thf(5492,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2030_add__nonneg__nonneg)). 159.59/70.63 thf(26419,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5492])). 159.59/70.63 thf(2072,axiom,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ (insert_nat @ C @ B)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6192_subset__insertI2)). 159.59/70.63 thf(14929,plain,((! [A:set_nat,B:set_nat,C:nat]: ((ord_less_eq_set_nat @ A @ (insert_nat @ C @ B)) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2072])). 159.59/70.63 thf(4518,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/sandbox/benchmark/theBenchmark.p',fact_2541_sum__power2__le__zero__iff)). 159.59/70.63 thf(22781,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)],[4518])). 159.59/70.63 thf(3178,axiom,((! [A:real]: ((((cos_real @ (arcsin @ A)) != zero_zero_real) <= (ord_less_real @ A @ one_one_real)) <= (ord_less_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7773_cos__arcsin__nonzero)). 159.59/70.63 thf(18476,plain,((! [A:real]: (~ ((cos_real @ (arcsin @ A)) = zero_zero_real) | ~ (ord_less_real @ A @ one_one_real) | ~ (ord_less_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3178])). 159.59/70.63 thf(5029,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/sandbox/benchmark/theBenchmark.p',fact_4760_left__minus__one__mult__self)). 159.59/70.63 thf(24651,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)],[5029])). 159.59/70.63 thf(6002,axiom,((! [A:nat]: (ord_less_eq_real @ (semiri2265585572941072030t_real @ A) @ (semiri5074537144036343181t_real @ (power_power_nat @ A @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8104_fact__le__power)). 159.59/70.63 thf(28450,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)],[6002])). 159.59/70.63 thf(3523,axiom,((! [A:set_nat,B:nat,C:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (groups7108830773950497114d_enat @ C @ A)) <= (! [D:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (C @ D)) <= (member_nat @ D @ A)))) <= (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (C @ B))) <= (member_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7547_sum__pos2)). 159.59/70.63 thf(19562,plain,((! [A:set_nat,B:nat,C:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (groups7108830773950497114d_enat @ (C) @ A)) | ~ (! [D:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (C @ D)) | ~ (member_nat @ D @ A))) | ~ (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (C @ B)) | ~ (member_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3523])). 159.59/70.63 thf(7754,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/sandbox/benchmark/theBenchmark.p',fact_3504_cong__exp__iff__simps_I8_J)). 159.59/70.63 thf(35055,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)],[7754])). 159.59/70.63 thf(7824,axiom,((! [A:nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_mult__2__right)). 159.59/70.63 thf(35270,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)],[7824])). 159.59/70.63 thf(528,axiom,((! [A:int,B:int,C:int]: ((ord_max_int @ A @ (ord_max_int @ B @ C)) = (ord_max_int @ B @ (ord_max_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_max_Oleft__commute)). 159.59/70.63 thf(9932,plain,((! [A:int,B:int,C:int]: ((ord_max_int @ A @ (ord_max_int @ B @ C)) = (ord_max_int @ B @ (ord_max_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[528])). 159.59/70.63 thf(8199,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/sandbox/benchmark/theBenchmark.p',fact_3439_mod2__gr__0)). 159.59/70.63 thf(36469,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)],[8199])). 159.59/70.63 thf(3137,axiom,((! [A:int,B:nat]: ((((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))) <= (ord_less_nat @ zero_zero_nat @ B)) <= (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3923_even__succ__div__exp)). 159.59/70.63 thf(18347,plain,((! [A:int,B:nat]: (((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))) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3137])). 159.59/70.63 thf(2628,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/sandbox/benchmark/theBenchmark.p',fact_7135_sin__double)). 159.59/70.63 thf(16722,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)],[2628])). 159.59/70.63 thf(6335,axiom,((! [A:num]: ((inc @ (bitM @ A)) = (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5890_inc__BitM__eq)). 159.59/70.63 thf(29594,plain,((! [A:num]: ((inc @ (bitM @ A)) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6335])). 159.59/70.63 thf(1738,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/sandbox/benchmark/theBenchmark.p',fact_5306_take__bit__int__greater__eq__self__iff)). 159.59/70.63 thf(13868,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)],[1738])). 159.59/70.63 thf(4046,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/sandbox/benchmark/theBenchmark.p',fact_6644_even__of__nat)). 159.59/70.63 thf(21243,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)],[4046])). 159.59/70.63 thf(7649,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_not__add__less1)). 159.59/70.63 thf(34702,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7649])). 159.59/70.63 thf(3359,axiom,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1511_add__cancel__right__right)). 159.59/70.63 thf(19049,plain,((! [A:real,B:real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3359])). 159.59/70.63 thf(4087,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > int),D:int]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_less_int @ (C @ B) @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_int @ (C @ E) @ (C @ F)))) => (ord_less_int @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2902_order__less__subst2)). 159.59/70.63 thf(21368,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > int),D:int]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_less_int @ (C @ B) @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_int @ (C @ E) @ (C @ F)))) => (ord_less_int @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4087])). 159.59/70.63 thf(690,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/sandbox/benchmark/theBenchmark.p',fact_9445_nat__le__eq__zle)). 159.59/70.63 thf(10455,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)],[690])). 159.59/70.63 thf(3856,axiom,((! [A:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4728_take__bit__numeral__1)). 159.59/70.63 thf(20666,plain,((! [A:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3856])). 159.59/70.63 thf(4868,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/sandbox/benchmark/theBenchmark.p',fact_9729_drop__bit__numeral__minus__bit0)). 159.59/70.63 thf(24084,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)],[4868])). 159.59/70.63 thf(4925,axiom,((! [A:nat,B:complex,C:complex]: ((ord_less_eq_nat @ one_one_nat @ A) => (((power_power_complex @ B @ A) = C) = ((groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (if_complex @ (D = zero_zero_nat) @ (uminus1482373934393186551omplex @ C) @ (if_complex @ (D = A) @ one_one_complex @ zero_zero_complex)) @ (power_power_complex @ B @ D))) @ (set_ord_atMost_nat @ A)) = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8944_root__polyfun)). 159.59/70.63 thf(24273,plain,((! [A:nat,B:complex,C:complex]: ((ord_less_eq_nat @ one_one_nat @ A) => (((power_power_complex @ B @ A) = C) = ((groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (if_complex @ (D = zero_zero_nat) @ (uminus1482373934393186551omplex @ C) @ (if_complex @ (D = A) @ one_one_complex @ zero_zero_complex)) @ (power_power_complex @ B @ D))) @ (set_ord_atMost_nat @ A)) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4925])). 159.59/70.63 thf(4343,axiom,((! [A:extended_enat,B:extended_enat]: ((plus_p3455044024723400733d_enat @ A @ (plus_p3455044024723400733d_enat @ A @ B)) = (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_left__add__twice)). 159.59/70.63 thf(22168,plain,((! [A:extended_enat,B:extended_enat]: ((plus_p3455044024723400733d_enat @ A @ (plus_p3455044024723400733d_enat @ A @ B)) = (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4343])). 159.59/70.63 thf(597,axiom,((! [A:real]: ((cos_real @ (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ A)) = (cos_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7003_cos__2pi__minus)). 159.59/70.63 thf(10148,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)],[597])). 159.59/70.63 thf(3623,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((~ (ord_less_real @ B @ A)) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2787_antisym__conv3)). 159.59/70.63 thf(19889,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => ((~ (ord_less_real @ B @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3623])). 159.59/70.63 thf(7411,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:nat,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => (((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ E)) @ A @ D @ F) @ C) = none_nat) <= (ord_less_eq_nat @ (size_s6755466524823107622T_VEBT @ D) @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_succ__list__to__short)). 159.59/70.63 thf(33861,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:nat,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => (((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ E)) @ A @ D @ F) @ C) = none_nat) | ~ (ord_less_eq_nat @ (size_s6755466524823107622T_VEBT @ D) @ (vEBT_VEBT_high @ C @ (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)],[7411])). 159.59/70.63 thf(1689,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/sandbox/benchmark/theBenchmark.p',fact_8292_pochhammer__product_H)). 159.59/70.63 thf(13718,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)],[1689])). 159.59/70.63 thf(284,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/sandbox/benchmark/theBenchmark.p',fact_9672_norm__complex__def)). 159.59/70.63 thf(9112,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)],[284])). 159.59/70.63 thf(264,axiom,((! [A:real]: ((ord_less_eq_real @ (sinh_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9310_sinh__real__nonpos__iff)). 159.59/70.63 thf(9053,plain,((! [A:real]: ((ord_less_eq_real @ (sinh_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[264])). 159.59/70.63 thf(7961,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 @ (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))))) => (vEBT_V8194947554948674370ptions @ (vEBT_Node @ A @ B @ C @ D) @ F)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_both__member__options__ding)). 159.59/70.63 thf(35698,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 @ (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))))) => (vEBT_V8194947554948674370ptions @ (vEBT_Node @ A @ B @ C @ D) @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7961])). 159.59/70.63 thf(3042,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/sandbox/benchmark/theBenchmark.p',fact_7260_complex__mult)). 159.59/70.63 thf(18027,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)],[3042])). 159.59/70.63 thf(6985,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/sandbox/benchmark/theBenchmark.p',fact_5486_abs__mult)). 159.59/70.63 thf(32282,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)],[6985])). 159.59/70.63 thf(1863,axiom,((! [A:code_integer,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ one_one_Code_integer @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))) <= (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3924_even__succ__div__exp)). 159.59/70.63 thf(14271,plain,((! [A:code_integer,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ one_one_Code_integer @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))) | ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1863])). 159.59/70.63 thf(642,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/sandbox/benchmark/theBenchmark.p',fact_6091_AND__upper2_H_H)). 159.59/70.63 thf(10306,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)],[642])). 159.59/70.63 thf(7008,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/sandbox/benchmark/theBenchmark.p',fact_6728_of__nat__diff)). 159.59/70.63 thf(32381,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)],[7008])). 159.59/70.63 thf(589,axiom,((! [A:nat,B:nat,C:int]: ((((bit_se2923211474154528505it_int @ A @ (bit_se7879613467334960850it_int @ B @ C)) = (bit_se2923211474154528505it_int @ A @ C)) <= (ord_less_eq_nat @ A @ B)) & ((~ (ord_less_eq_nat @ A @ B)) => ((bit_se2923211474154528505it_int @ A @ (bit_se7879613467334960850it_int @ B @ C)) = (bit_se7879613467334960850it_int @ B @ (bit_se2923211474154528505it_int @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5112_take__bit__set__bit__eq)). 159.59/70.63 thf(10122,plain,((! [A:nat,B:nat,C:int]: ((((bit_se2923211474154528505it_int @ A @ (bit_se7879613467334960850it_int @ B @ C)) = (bit_se2923211474154528505it_int @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)) & ((~ (ord_less_eq_nat @ A @ B)) => ((bit_se2923211474154528505it_int @ A @ (bit_se7879613467334960850it_int @ B @ C)) = (bit_se7879613467334960850it_int @ B @ (bit_se2923211474154528505it_int @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[589])). 159.59/70.63 thf(6322,axiom,(((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1782_bits__1__div__2)). 159.59/70.63 thf(29561,plain,(((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6322])). 159.59/70.63 thf(251,axiom,((! [A:(code_integer > $o),B:$o]: ((A @ (zero_n356916108424825756nteger @ B)) = (((A @ one_one_Code_integer) <= (B)) & ((~ (B)) => (A @ zero_z3403309356797280102nteger)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4409_split__of__bool)). 159.59/70.63 thf(9017,plain,((! [A:(code_integer > $o),B:$o]: ((A @ (zero_n356916108424825756nteger @ B)) = (((A @ one_one_Code_integer) | ~ (B)) & ((~ (B)) => (A @ zero_z3403309356797280102nteger)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[251])). 159.59/70.63 thf(5485,axiom,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2058_zero__less__one__class_Ozero__le__one)). 159.59/70.63 thf(26392,plain,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5485])). 159.59/70.63 thf(7830,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (modulo_modulo_nat @ B @ A)) | ((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (plus_plus_nat @ (modulo_modulo_nat @ B @ A) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3569_mod__double__modulus)). 159.59/70.63 thf(35285,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (modulo_modulo_nat @ B @ A)) | ((modulo_modulo_nat @ B @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (plus_plus_nat @ (modulo_modulo_nat @ B @ A) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7830])). 159.59/70.63 thf(5631,axiom,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5140_neg__numeral__le__zero)). 159.59/70.63 thf(26883,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)],[5631])). 159.59/70.63 thf(2182,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/sandbox/benchmark/theBenchmark.p',fact_6742_field__char__0__class_Oof__nat__div)). 159.59/70.63 thf(15285,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)],[2182])). 159.59/70.63 thf(3861,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/sandbox/benchmark/theBenchmark.p',fact_3826_dvd__add__times__triv__left__iff)). 159.59/70.63 thf(20681,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)],[3861])). 159.59/70.63 thf(4698,axiom,((! [A:nat,B:nat,C:(nat > complex),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (times_times_complex @ (groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8806_prod_Oub__add__nat)). 159.59/70.63 thf(23496,plain,((! [A:nat,B:nat,C:(nat > complex),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (times_times_complex @ (groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4698])). 159.59/70.63 thf(565,axiom,((! [A:code_integer,B:code_integer]: ((((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ B @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))) = (divide6298287555418463151nteger @ B @ A)) <= (ord_le6747313008572928689nteger @ (modulo364778990260209775nteger @ B @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) @ A)) <= (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3564_divmod__digit__0_I1_J)). 159.59/70.63 thf(10047,plain,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ B @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))) = (divide6298287555418463151nteger @ B @ A)) | ~ (ord_le6747313008572928689nteger @ (modulo364778990260209775nteger @ B @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) @ A) | ~ (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[565])). 159.59/70.63 thf(813,axiom,((! [A:real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1526_double__zero__sym)). 159.59/70.63 thf(10879,plain,((! [A:real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[813])). 159.59/70.63 thf(968,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => ((((divide1717551699836669952omplex @ B @ A) = (divide1717551699836669952omplex @ C @ A)) = (B = C)) <= (dvd_dvd_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4011_dvd__div__eq__iff)). 159.59/70.63 thf(11347,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => ((((divide1717551699836669952omplex @ B @ A) = (divide1717551699836669952omplex @ C @ A)) = (B = C)) | ~ (dvd_dvd_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[968])). 159.59/70.63 thf(7949,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/sandbox/benchmark/theBenchmark.p',fact_5348_divmod__algorithm__code_I5_J)). 159.59/70.63 thf(35666,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)],[7949])). 159.59/70.63 thf(2690,axiom,((! [A:real,B:real]: (((ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real) <= (ord_less_real @ B @ zero_zero_real)) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2268_add__nonpos__neg)). 159.59/70.63 thf(16932,plain,((! [A:real,B:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real) | ~ (ord_less_real @ B @ zero_zero_real) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2690])). 159.59/70.63 thf(7992,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/sandbox/benchmark/theBenchmark.p',fact_392_list__eq__iff__nth__eq)). 159.59/70.63 thf(35793,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)],[7992])). 159.59/70.63 thf(2424,axiom,((! [A:real,B:real,C:nat]: (((real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ C)) @ (power_power_real @ (plus_plus_real @ A @ B) @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D)) @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (minus_minus_nat @ C @ D))) @ (power_power_real @ B @ (minus_minus_nat @ C @ D))))) @ (set_ord_atMost_nat @ C))) <= ((times_times_real @ A @ B) = (times_times_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9294_exp__series__add__commuting)). 159.59/70.63 thf(16051,plain,((! [A:real,B:real,C:nat]: (((real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ C)) @ (power_power_real @ (plus_plus_real @ A @ B) @ C)) = (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ D)) @ (power_power_real @ A @ D)) @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (minus_minus_nat @ C @ D))) @ (power_power_real @ B @ (minus_minus_nat @ C @ D))))) @ (set_ord_atMost_nat @ C))) | ~ ((times_times_real @ A @ B) = (times_times_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2424])). 159.59/70.63 thf(4724,axiom,((! [A:num]: (((uminus1351360451143612070nteger @ one_one_Code_integer) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4756_neg__one__eq__numeral__iff)). 159.59/70.63 thf(23574,plain,((! [A:num]: (((uminus1351360451143612070nteger @ one_one_Code_integer) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4724])). 159.59/70.63 thf(4253,axiom,((! [A:nat,B:code_integer]: ((bit_se2793503036327961859nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se2793503036327961859nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3573_set__bit__Suc)). 159.59/70.63 thf(21902,plain,((! [A:nat,B:code_integer]: ((bit_se2793503036327961859nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se2793503036327961859nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4253])). 159.59/70.63 thf(2887,axiom,(((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4742_add__neg__numeral__special_I8_J)). 159.59/70.63 thf(17546,plain,(((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ one_one_int) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2887])). 159.59/70.63 thf(2165,axiom,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ one_one_Code_integer @ A)) = (divide6298287555418463151nteger @ B @ A)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3866_unit__mult__div__div)). 159.59/70.63 thf(15232,plain,((! [A:code_integer,B:code_integer]: (((times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ one_one_Code_integer @ A)) = (divide6298287555418463151nteger @ B @ A)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2165])). 159.59/70.63 thf(8112,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/sandbox/benchmark/theBenchmark.p',fact_2073_mult__strict__left__mono)). 159.59/70.63 thf(36183,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)],[8112])). 159.59/70.63 thf(6657,axiom,((! [A:nat,B:nat,C:(nat > complex)]: (((groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (times_times_complex @ (C @ (suc @ B)) @ (groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8736_prod_Onat__ivl__Suc_H)). 159.59/70.63 thf(30805,plain,((! [A:nat,B:nat,C:(nat > complex)]: (((groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (times_times_complex @ (C @ (suc @ B)) @ (groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ B)))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6657])). 159.59/70.63 thf(1440,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/sandbox/benchmark/theBenchmark.p',fact_5787_of__int__eq__of__int__power__cancel__iff)). 159.59/70.63 thf(12946,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)],[1440])). 159.59/70.63 thf(5417,axiom,((! [A:nat,B:(nat > complex),C:complex,D:complex]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_complex @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (B @ E) @ (power_power_complex @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (B @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_complex @ (minus_minus_complex @ C @ D) @ (groups2073611262835488442omplex @ (^ [E:nat]: (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (times_times_complex @ (B @ (plus_plus_nat @ (plus_plus_nat @ E @ F) @ one_one_nat)) @ (power_power_complex @ D @ F)) @ (power_power_complex @ C @ E))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ E)))) @ (set_ord_lessThan_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8953_polyfun__diff__alt)). 159.59/70.63 thf(26142,plain,((! [A:nat,B:(nat > complex),C:complex,D:complex]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_complex @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (B @ E) @ (power_power_complex @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (B @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_complex @ (minus_minus_complex @ C @ D) @ (groups2073611262835488442omplex @ (^ [E:nat]: (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (times_times_complex @ (B @ (plus_plus_nat @ (plus_plus_nat @ E @ F) @ one_one_nat)) @ (power_power_complex @ D @ F)) @ (power_power_complex @ C @ E))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ E)))) @ (set_ord_lessThan_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5417])). 159.59/70.63 thf(3823,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ B @ (times_times_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ (divide_divide_real @ B @ A))) @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7151_ceiling__divide__upper)). 159.59/70.63 thf(20542,plain,((! [A:real,B:real]: ((ord_less_eq_real @ B @ (times_times_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ (divide_divide_real @ B @ A))) @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3823])). 159.59/70.63 thf(2927,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ D @ A) = (plus_plus_real @ B @ (plus_plus_real @ D @ C))) <= (A = (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1138_group__cancel_Oadd2)). 159.59/70.63 thf(17678,plain,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ D @ A) = (plus_plus_real @ B @ (plus_plus_real @ D @ C))) | ~ (A = (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2927])). 159.59/70.63 thf(6878,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/sandbox/benchmark/theBenchmark.p',fact_8547_prod_Oshift__bounds__cl__nat__ivl)). 159.59/70.63 thf(31788,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)],[6878])). 159.59/70.63 thf(5835,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/sandbox/benchmark/theBenchmark.p',fact_4261_zero__le__even__power)). 159.59/70.63 thf(27786,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)],[5835])). 159.59/70.63 thf(4539,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => ((ord_less_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_nat @ B @ C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_848_less__diff__iff)). 159.59/70.63 thf(22922,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => ((ord_less_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_nat @ B @ C))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4539])). 159.59/70.63 thf(5860,axiom,((! [A:num,B:num]: ((power_power_real @ (numeral_numeral_real @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_real @ (pow @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4604_power__numeral)). 159.59/70.63 thf(27905,plain,((! [A:num,B:num]: ((power_power_real @ (numeral_numeral_real @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_real @ (pow @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5860])). 159.59/70.63 thf(4431,axiom,((! [A:code_integer,B:code_integer,C:nat]: ((power_8256067586552552935nteger @ (plus_p5714425477246183910nteger @ A @ B) @ C) = (groups7501900531339628137nteger @ (^ [D:nat]: (times_3573771949741848930nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ (binomial @ C @ D)) @ (power_8256067586552552935nteger @ A @ D)) @ (power_8256067586552552935nteger @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9147_binomial__ring)). 159.59/70.63 thf(22450,plain,((! [A:code_integer,B:code_integer,C:nat]: ((power_8256067586552552935nteger @ (plus_p5714425477246183910nteger @ A @ B) @ C) = (groups7501900531339628137nteger @ (^ [D:nat]: (times_3573771949741848930nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ (binomial @ C @ D)) @ (power_8256067586552552935nteger @ A @ D)) @ (power_8256067586552552935nteger @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4431])). 159.59/70.63 thf(2482,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/sandbox/benchmark/theBenchmark.p',fact_8364_pochhammer__code)). 159.59/70.63 thf(16237,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)],[2482])). 159.59/70.63 thf(2025,axiom,((ord_less_real = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3075_order_Ostrict__iff__order)). 159.59/70.63 thf(14794,plain,(((ord_less_real) = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2025])). 159.59/70.63 thf(170,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ zero_zero_real) = (((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_real @ zero_zero_real @ A)) | (A = zero_zero_real) | ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9237_scaleR__le__0__iff)). 159.59/70.63 thf(8775,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ zero_zero_real) = (((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_real @ zero_zero_real @ A)) | (A = zero_zero_real) | ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 159.59/70.63 thf(3774,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/sandbox/benchmark/theBenchmark.p',fact_1216_diff__strict__right__mono)). 159.59/70.63 thf(20391,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)],[3774])). 159.59/70.63 thf(5371,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/sandbox/benchmark/theBenchmark.p',fact_84_mult__numeral__left__semiring__numeral)). 159.59/70.63 thf(25951,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)],[5371])). 159.59/70.63 thf(244,axiom,((! [A:nat,B:complex]: ((ord_less_nat @ zero_zero_nat @ A) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8338_gbinomial__reduce__nat)). 159.59/70.63 thf(8995,plain,((! [A:nat,B:complex]: ((ord_less_nat @ zero_zero_nat @ A) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 159.59/70.63 thf(6327,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/sandbox/benchmark/theBenchmark.p',fact_5675_take__bit__Suc__minus__bit1)). 159.59/70.63 thf(29573,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)],[6327])). 159.59/70.63 thf(58,axiom,((! [A:code_integer,B:code_integer]: ((A != zero_z3403309356797280102nteger) => ((dvd_dvd_Code_integer @ B @ one_one_Code_integer) => ((divide6298287555418463151nteger @ A @ (times_3573771949741848930nteger @ A @ B)) = (divide6298287555418463151nteger @ one_one_Code_integer @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4198_is__unit__div__mult__cancel__left)). 159.59/70.63 thf(8425,plain,((! [A:code_integer,B:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((dvd_dvd_Code_integer @ B @ one_one_Code_integer) => ((divide6298287555418463151nteger @ A @ (times_3573771949741848930nteger @ A @ B)) = (divide6298287555418463151nteger @ one_one_Code_integer @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[58])). 159.59/70.63 thf(1255,axiom,((! [A:int,B:nat]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((bit_se1146084159140164899it_int @ A @ B) = ((B = zero_zero_nat) | (bit_se1146084159140164899it_int @ (minus_minus_int @ A @ one_one_int) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6453_odd__bit__iff__bit__pred)). 159.59/70.63 thf(12310,plain,((! [A:int,B:nat]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((bit_se1146084159140164899it_int @ A @ B) = ((B = zero_zero_nat) | (bit_se1146084159140164899it_int @ (minus_minus_int @ A @ one_one_int) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255])). 159.59/70.63 thf(2239,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/sandbox/benchmark/theBenchmark.p',fact_1372_less__add__iff2)). 159.59/70.63 thf(15478,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)],[2239])). 159.59/70.63 thf(3470,axiom,((semiri5044797733671781792omplex = (comm_s2602460028002588243omplex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8220_pochhammer__fact)). 159.59/70.63 thf(19398,plain,(((semiri5044797733671781792omplex) = (comm_s2602460028002588243omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3470])). 159.59/70.63 thf(6996,axiom,((! [A:real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ one)) @ A) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5201_mult__1s__ring__1_I1_J)). 159.59/70.63 thf(32344,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)],[6996])). 159.59/70.63 thf(2084,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ B @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2847_order__less__asym)). 159.59/70.63 thf(14965,plain,((! [A:int,B:int]: (~ (ord_less_int @ B @ A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2084])). 159.59/70.63 thf(6191,axiom,((! [A:num]: (one_one_int != (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5091_one__neq__neg__numeral)). 159.59/70.63 thf(29064,plain,((! [A:num]: ~ (one_one_int = (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6191])). 159.59/70.63 thf(953,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/sandbox/benchmark/theBenchmark.p',fact_8471_prod_Odistrib)). 159.59/70.63 thf(11300,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)],[953])). 159.59/70.63 thf(7716,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_add__right__cancel)). 159.59/70.63 thf(34923,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)],[7716])). 159.59/70.63 thf(4144,axiom,((! [A:list_int,B:nat,C:int]: ((size_size_list_int @ (list_update_int @ A @ B @ C)) = (size_size_list_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_length__list__update)). 159.59/70.63 thf(21546,plain,((! [A:list_int,B:nat,C:int]: ((size_size_list_int @ (list_update_int @ A @ B @ C)) = (size_size_list_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4144])). 159.59/70.63 thf(724,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (B @ D)) @ one_one_real))) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (groups6464643781859351333omplex @ B @ A) @ (groups6464643781859351333omplex @ C @ A))) @ (groups6591440286371151544t_real @ (^ [D:nat]: (real_V1022390504157884413omplex @ (minus_minus_complex @ (B @ D) @ (C @ D)))) @ A)) <= (! [D:nat]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (C @ D)) @ one_one_real) <= (member_nat @ D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8831_norm__prod__diff)). 159.59/70.63 thf(10588,plain,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (B @ D)) @ one_one_real))) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (groups6464643781859351333omplex @ (B) @ A) @ (groups6464643781859351333omplex @ (C) @ A))) @ (groups6591440286371151544t_real @ (^ [D:nat]: (real_V1022390504157884413omplex @ (minus_minus_complex @ (B @ D) @ (C @ D)))) @ A)) | ~ (! [D:nat]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (C @ D)) @ one_one_real) | ~ (member_nat @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[724])). 159.59/70.63 thf(7885,axiom,((! [A:num,B:num]: ((power_power_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (pow @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4605_power__numeral)). 159.59/70.63 thf(35455,plain,((! [A:num,B:num]: ((power_power_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_nat @ (pow @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7885])). 159.59/70.63 thf(5063,axiom,((! [A:complex]: ((times_times_complex @ A @ (numera6690914467698888265omplex @ (bit0 @ one))) = (plus_plus_complex @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_mult__2__right)). 159.59/70.63 thf(24780,plain,((! [A:complex]: ((times_times_complex @ A @ (numera6690914467698888265omplex @ (bit0 @ one))) = (plus_plus_complex @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5063])). 159.59/70.63 thf(433,axiom,((! [A:real]: (ord_less_eq_real @ (sinh_real @ A) @ (cosh_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9323_sinh__le__cosh__real)). 159.59/70.63 thf(9607,plain,((! [A:real]: (ord_less_eq_real @ (sinh_real @ A) @ (cosh_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[433])). 159.59/70.63 thf(6141,axiom,((! [A:nat,B:nat,C:(nat > int)]: (((groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (times_times_int @ (C @ (suc @ B)) @ (groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8739_prod_Onat__ivl__Suc_H)). 159.59/70.63 thf(28888,plain,((! [A:nat,B:nat,C:(nat > int)]: (((groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (times_times_int @ (C @ (suc @ B)) @ (groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ B)))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6141])). 159.59/70.63 thf(5311,axiom,((! [A:num,B:num]: ((times_times_num @ (bit1 @ A) @ (bit0 @ B)) = (bit0 @ (times_times_num @ (bit1 @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5424_semiring__norm_I15_J)). 159.59/70.63 thf(25688,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)],[5311])). 159.59/70.63 thf(7836,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/sandbox/benchmark/theBenchmark.p',fact_1139_group__cancel_Oadd2)). 159.59/70.63 thf(35302,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)],[7836])). 159.59/70.63 thf(2802,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ B) = (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4924_minus__le__iff)). 159.59/70.63 thf(17267,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)],[2802])). 159.59/70.63 thf(5096,axiom,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2509_zero__le__power2)). 159.59/70.63 thf(24899,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)],[5096])). 159.59/70.63 thf(18,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_790_max_Oabsorb2)). 159.59/70.63 thf(8307,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)],[18])). 159.59/70.63 thf(6256,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: ((((! [D:$o,E:$o]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B))) <= (C = (((B = zero_zero_nat) => (D)) & ((((B = one_one_nat) => (E)) & (B = one_one_nat)) <= (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)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ 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)) => ((~ (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]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F) @ B))) <= (~ (C))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ 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 = ((B != D) => ((B != E) => (((~ (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)))) <= (~ (ord_less_nat @ B @ D))) & ~ (ord_less_nat @ B @ D))))) => (~ (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))))))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ A @ B))) <= ((vEBT_vebt_member @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3313_vebt__member_Opelims_I1_J)). 159.59/70.63 thf(29270,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((! [D:$o,E:$o]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ B)) | ~ (C = (((B = zero_zero_nat) => (D)) & ((((B = one_one_nat) => (E)) & (B = one_one_nat)) | (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)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ 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)) => (~ (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]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F) @ B)) | (C) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ 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 = ((~ (B = D)) => ((~ (B = E)) => (((~ (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))) | (ord_less_nat @ B @ D)) & ~ (ord_less_nat @ B @ D))))) => (~ (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))))))))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ A @ B)) | ~ ((vEBT_vebt_member @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6256])). 159.59/70.63 thf(3689,axiom,((! [A:set_nat,B:nat,C:(nat > complex),D:(nat > complex)]: ((finite_finite_nat @ A) => (((~ (member_nat @ B @ A)) => ((groups6464643781859351333omplex @ (^ [E:nat]: (if_complex @ (E = B) @ (C @ E) @ (D @ E))) @ A) = (groups6464643781859351333omplex @ D @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))) & ((member_nat @ B @ A) => ((groups6464643781859351333omplex @ (^ [E:nat]: (if_complex @ (E = B) @ (C @ E) @ (D @ E))) @ A) = (times_times_complex @ (C @ B) @ (groups6464643781859351333omplex @ D @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8815_prod_Odelta__remove)). 159.59/70.63 thf(20097,plain,((! [A:set_nat,B:nat,C:(nat > complex),D:(nat > complex)]: ((finite_finite_nat @ A) => (((~ (member_nat @ B @ A)) => ((groups6464643781859351333omplex @ (^ [E:nat]: (if_complex @ (E = B) @ (C @ E) @ (D @ E))) @ A) = (groups6464643781859351333omplex @ (D) @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))) & ((member_nat @ B @ A) => ((groups6464643781859351333omplex @ (^ [E:nat]: (if_complex @ (E = B) @ (C @ E) @ (D @ E))) @ A) = (times_times_complex @ (C @ B) @ (groups6464643781859351333omplex @ (D) @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3689])). 159.59/70.63 thf(430,axiom,((! [A:(nat > complex),B:nat,C:nat]: ((groups6464643781859351333omplex @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo1517530859248394432omplex @ (^ [D:nat]: (times_times_complex @ (A @ D))) @ B @ C @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8518_prod__atLeastAtMost__code)). 159.59/70.63 thf(9598,plain,((! [A:(nat > complex),B:nat,C:nat]: ((groups6464643781859351333omplex @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo1517530859248394432omplex @ (^ [D:nat]: (times_times_complex @ (A @ D))) @ B @ C @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])). 159.59/70.63 thf(939,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/sandbox/benchmark/theBenchmark.p',fact_8019_sum__pos__lt__pair)). 159.59/70.63 thf(11261,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)],[939])). 159.59/70.63 thf(713,axiom,((filterlim_real_real @ arctan @ (topolo2815343760600316023s_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) @ at_bot_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9945_tendsto__arctan__at__bot)). 159.59/70.63 thf(10550,plain,((filterlim_real_real @ (arctan) @ (topolo2815343760600316023s_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) @ at_bot_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[713])). 159.59/70.63 thf(1048,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/sandbox/benchmark/theBenchmark.p',fact_1279_diff__add__eq__diff__diff__swap)). 159.59/70.63 thf(11610,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)],[1048])). 159.59/70.63 thf(6208,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/sandbox/benchmark/theBenchmark.p',fact_5649_abs__square__le__1)). 159.59/70.63 thf(29117,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)],[6208])). 159.59/70.63 thf(3334,axiom,((! [A:nat,B:nat]: ((bit_se1146084159140164899it_int @ (semiri1314217659103216013at_int @ A) @ B) = (bit_se1148574629649215175it_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6655_bit__of__nat__iff__bit)). 159.59/70.63 thf(18975,plain,((! [A:nat,B:nat]: ((bit_se1146084159140164899it_int @ (semiri1314217659103216013at_int @ A) @ B) = (bit_se1148574629649215175it_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3334])). 159.59/70.63 thf(1394,axiom,((! [A:complex]: (((invers8013647133539491842omplex @ A) = one_one_complex) = (A = one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8983_inverse__eq__1__iff)). 159.59/70.63 thf(12800,plain,((! [A:complex]: (((invers8013647133539491842omplex @ A) = one_one_complex) = (A = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394])). 159.59/70.63 thf(4228,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/sandbox/benchmark/theBenchmark.p',fact_7008_sin__cos__squared__add2)). 159.59/70.63 thf(21826,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)],[4228])). 159.59/70.63 thf(2926,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/sandbox/benchmark/theBenchmark.p',fact_111_distrib__left__numeral)). 159.59/70.63 thf(17675,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)],[2926])). 159.59/70.63 thf(5306,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/sandbox/benchmark/theBenchmark.p',fact_1261_left__diff__distrib_H)). 159.59/70.63 thf(25646,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)],[5306])). 159.59/70.63 thf(3171,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1592_zero__less__double__add__iff__zero__less__single__add)). 159.59/70.63 thf(18452,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)],[3171])). 159.59/70.63 thf(3212,axiom,((zero_zero_int = (abs_Integ @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9774_zero__int__def)). 159.59/70.63 thf(18581,plain,((zero_zero_int = (abs_Integ @ (product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3212])). 159.59/70.63 thf(7176,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => ((B != zero_zero_complex) => ((times_times_complex @ A @ B) != zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1859_no__zero__divisors)). 159.59/70.63 thf(33042,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)],[7176])). 159.59/70.63 thf(5213,axiom,((! [A:int]: (((ord_less_eq_int @ A @ one_one_int) => (ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_int)) <= (ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5311_square__le__1)). 159.59/70.63 thf(25313,plain,((! [A:int]: (((ord_less_eq_int @ A @ one_one_int) => (ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_int)) | ~ (ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5213])). 159.59/70.63 thf(573,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/sandbox/benchmark/theBenchmark.p',fact_9556_XOR__lower)). 159.59/70.63 thf(10075,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)],[573])). 159.59/70.63 thf(1681,axiom,((! [A:complex,B:complex,C:complex,D:complex]: (((minus_minus_complex @ A @ D) = (plus_plus_complex @ B @ (minus_minus_complex @ C @ D))) <= (A = (plus_plus_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1296_group__cancel_Osub1)). 159.59/70.63 thf(13693,plain,((! [A:complex,B:complex,C:complex,D:complex]: (((minus_minus_complex @ A @ D) = (plus_plus_complex @ B @ (minus_minus_complex @ C @ D))) | ~ (A = (plus_plus_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681])). 159.59/70.63 thf(3424,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ (divide6298287555418463151nteger @ B @ A) @ C) = (dvd_dvd_Code_integer @ B @ C)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4101_div__unit__dvd__iff)). 159.59/70.63 thf(19262,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ (divide6298287555418463151nteger @ 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)],[3424])). 159.59/70.63 thf(2537,axiom,(((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) != zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6759_pi__half__neq__zero)). 159.59/70.63 thf(16410,plain,((~ ((divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2537])). 159.59/70.63 thf(5094,axiom,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ (minus_minus_nat @ B @ A)) = (minus_minus_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6726_of__nat__diff)). 159.59/70.63 thf(24893,plain,((! [A:nat,B:nat]: (((semiri5074537144036343181t_real @ (minus_minus_nat @ B @ A)) = (minus_minus_real @ (semiri5074537144036343181t_real @ B) @ (semiri5074537144036343181t_real @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5094])). 159.59/70.63 thf(1612,axiom,((! [A:real,B:int]: ((plus_plus_int @ (archim6058952711729229775r_real @ A) @ B) = (archim6058952711729229775r_real @ (plus_plus_real @ A @ (ring_1_of_int_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8227_floor__add__int)). 159.59/70.63 thf(13490,plain,((! [A:real,B:int]: ((plus_plus_int @ (archim6058952711729229775r_real @ A) @ B) = (archim6058952711729229775r_real @ (plus_plus_real @ A @ (ring_1_of_int_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1612])). 159.59/70.63 thf(1359,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ A @ C) <= (B = C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2780_ord__less__eq__trans)). 159.59/70.63 thf(12641,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ C) | ~ (B = C) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359])). 159.59/70.63 thf(6745,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/sandbox/benchmark/theBenchmark.p',fact_5595_power__minus__Bit1)). 159.59/70.63 thf(31246,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)],[6745])). 159.59/70.63 thf(883,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) = ((A = B) | ~ (ord_le2932123472753598470d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3032_nless__le)). 159.59/70.63 thf(11093,plain,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) = ((A = B) | ~ (ord_le2932123472753598470d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[883])). 159.59/70.63 thf(6486,axiom,(((sqrt @ one_one_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6313_real__sqrt__one)). 159.59/70.63 thf(30202,plain,(((sqrt @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6486])). 159.59/70.63 thf(6943,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3697_verit__comp__simplify1_I3_J)). 159.59/70.63 thf(32019,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6943])). 159.59/70.63 thf(3116,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6685_less__imp__of__nat__less)). 159.59/70.63 thf(18276,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3116])). 159.59/70.63 thf(7405,axiom,(((vEBT_vebt_buildup @ zero_zero_nat) = (vEBT_Leaf @ ($false) @ ($false)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2637_vebt__buildup_Osimps_I1_J)). 159.59/70.63 thf(33846,plain,(((vEBT_vebt_buildup @ zero_zero_nat) = (vEBT_Leaf @ ($false) @ ($false)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7405])). 159.59/70.63 thf(6607,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_VEBT_valid @ (vEBT_Node @ A @ B @ C @ D) @ E) = ((case_o184042715313410164at_nat @ (! [F:vEBT_VEBT]: ((~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) <= (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ D @ F))) @ (produc6081775807080527818_nat_o @ (^ [F:nat,G:nat]: ((ord_less_eq_nat @ F @ G) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & ! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ I)) = (vEBT_V8194947554948674370ptions @ D @ H))) & (((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ C @ G) & ! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ C @ H) => ((ord_less_eq_nat @ H @ G) & (ord_less_nat @ F @ H))))) <= (F != G)) & ((F = G) => (! [H:vEBT_VEBT]: ((~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))))))) @ A) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) & (vEBT_VEBT_valid @ D @ (minus_minus_nat @ B @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) & ! [F:vEBT_VEBT]: ((vEBT_VEBT_valid @ F @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) <= (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & (B = E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10069_VEBT__internal_Ovalid_H_Osimps_I2_J)). 159.59/70.63 thf(30627,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_VEBT_valid @ (vEBT_Node @ A @ B @ C @ D) @ E) = ((case_o184042715313410164at_nat @ (! [F:vEBT_VEBT]: (~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G)) | ~ (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & ~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ D @ F))) @ (produc6081775807080527818_nat_o @ (^ [F:nat,G:nat]: ((ord_less_eq_nat @ F @ G) & (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & ! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [I:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ H) @ I)) = (vEBT_V8194947554948674370ptions @ D @ H))) & (((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ C @ G) & ! [H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ C @ H) => ((ord_less_eq_nat @ H @ G) & (ord_less_nat @ F @ H))))) | (F = G)) & ((F = G) => (! [H:vEBT_VEBT]: (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))))))) @ A) & ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))) & (vEBT_VEBT_valid @ D @ (minus_minus_nat @ B @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) & ! [F:vEBT_VEBT]: ((vEBT_VEBT_valid @ F @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ C))) & (B = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6607])). 159.59/70.63 thf(943,axiom,((vEBT_VEBT_mul = (vEBT_V4262088993061758097ft_nat @ times_times_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1029_mul__def)). 159.59/70.63 thf(11274,plain,(((vEBT_VEBT_mul) = (vEBT_V4262088993061758097ft_nat @ times_times_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[943])). 159.59/70.63 thf(5176,axiom,((! [A:int,B:int,C:(int > int),D:int]: ((((! [E:int,F:int]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_int @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2654_ord__le__eq__subst)). 159.59/70.63 thf(25169,plain,((! [A:int,B:int,C:(int > int),D:int]: (((! [E:int,F:int]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_int @ E @ F))) => (ord_less_eq_int @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5176])). 159.59/70.63 thf(3342,axiom,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ A)) = (dvd_dvd_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3796_dvd__add__triv__right__iff)). 159.59/70.63 thf(18998,plain,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ A)) = (dvd_dvd_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3342])). 159.59/70.63 thf(6487,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/sandbox/benchmark/theBenchmark.p',fact_3444_mult__mod__right)). 159.59/70.63 thf(30204,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)],[6487])). 159.59/70.63 thf(4055,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ C) <= (dvd_dvd_complex @ (times_times_complex @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3955_dvd__mult__left)). 159.59/70.63 thf(21270,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ C) | ~ (dvd_dvd_complex @ (times_times_complex @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4055])). 159.59/70.63 thf(5758,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ one_one_real @ (root @ A @ B)) = (ord_less_eq_real @ one_one_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9492_real__root__ge__1__iff)). 159.59/70.63 thf(27319,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ one_one_real @ (root @ A @ B)) = (ord_less_eq_real @ one_one_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5758])). 159.59/70.63 thf(6527,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_diff__Suc__Suc)). 159.59/70.63 thf(30347,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)],[6527])). 159.59/70.63 thf(1404,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/sandbox/benchmark/theBenchmark.p',fact_235_power__strict__increasing__iff)). 159.59/70.63 thf(12831,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)],[1404])). 159.59/70.63 thf(531,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ A @ (ord_max_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_899_max_OcoboundedI2)). 159.59/70.63 thf(9942,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ A @ (ord_max_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[531])). 159.59/70.63 thf(852,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/sandbox/benchmark/theBenchmark.p',fact_8013_one__diff__power__eq_H)). 159.59/70.63 thf(11000,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)],[852])). 159.59/70.63 thf(3857,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/sandbox/benchmark/theBenchmark.p',fact_1453_less__half__sum)). 159.59/70.63 thf(20669,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)],[3857])). 159.59/70.63 thf(3812,axiom,((! [A:nat]: ~ (ord_le72135733267957522d_enat @ (semiri4216267220026989637d_enat @ A) @ zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6667_of__nat__less__0__iff)). 159.59/70.63 thf(20510,plain,((! [A:nat]: ~ (ord_le72135733267957522d_enat @ (semiri4216267220026989637d_enat @ A) @ zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3812])). 159.59/70.63 thf(819,axiom,((! [A:(nat > int),B:nat,C:nat]: ((! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_int @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_lift__Suc__mono__less__iff)). 159.59/70.63 thf(10894,plain,((! [A:(nat > int),B:nat,C:nat]: ((! [D:nat]: (ord_less_int @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_int @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[819])). 159.59/70.63 thf(5012,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6177_and__nat__numerals_I4_J)). 159.59/70.63 thf(24593,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)],[5012])). 159.59/70.63 thf(6039,axiom,((! [A:num]: (zero_zero_complex != (numera6690914467698888265omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1846_zero__neq__numeral)). 159.59/70.63 thf(28564,plain,((! [A:num]: ~ (zero_zero_complex = (numera6690914467698888265omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6039])). 159.59/70.63 thf(4278,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (minus_minus_int @ C @ B) @ (minus_minus_int @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1219_diff__strict__left__mono)). 159.59/70.63 thf(21976,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (minus_minus_int @ C @ B) @ (minus_minus_int @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4278])). 159.59/70.63 thf(269,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/sandbox/benchmark/theBenchmark.p',fact_9668_cmod__power2)). 159.59/70.63 thf(9068,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)],[269])). 159.59/70.63 thf(6769,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/sandbox/benchmark/theBenchmark.p',fact_5294_neg__one__power__add__eq__neg__one__power__diff)). 159.59/70.63 thf(31350,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)],[6769])). 159.59/70.63 thf(1171,axiom,((! [A:nat]: (ord_less_int @ zero_zero_int @ (semiri1406184849735516958ct_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8076_fact__gt__zero)). 159.59/70.63 thf(12005,plain,((! [A:nat]: (ord_less_int @ zero_zero_int @ (semiri1406184849735516958ct_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171])). 159.59/70.63 thf(6848,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/sandbox/benchmark/theBenchmark.p',fact_2206_diff__less)). 159.59/70.63 thf(31695,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)],[6848])). 159.59/70.63 thf(2509,axiom,((! [A:num]: ((numera1916890842035813515d_enat @ (bit0 @ A)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1424_numeral__code_I2_J)). 159.59/70.63 thf(16328,plain,((! [A:num]: ((numera1916890842035813515d_enat @ (bit0 @ A)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2509])). 159.59/70.63 thf(3502,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((C != A) <= (ord_le72135733267957522d_enat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4442_pinf_I4_J)). 159.59/70.63 thf(19498,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: (~ (C = A) | ~ (ord_le72135733267957522d_enat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3502])). 159.59/70.63 thf(5322,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/sandbox/benchmark/theBenchmark.p',fact_699_add__le__mono1)). 159.59/70.63 thf(25720,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)],[5322])). 159.59/70.63 thf(4993,axiom,((numeral_numeral_nat = (^ [A:num]: (suc @ (pred_numeral @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5717_numeral__eq__Suc)). 159.59/70.63 thf(24525,plain,(((numeral_numeral_nat) = (^ [A:num]: (suc @ (pred_numeral @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4993])). 159.59/70.63 thf(6856,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ C) <= (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3972_dvd__mult__right)). 159.59/70.63 thf(31724,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)],[6856])). 159.59/70.63 thf(2549,axiom,((! [A:real,B:real]: ((ord_less_real @ (exp_real @ A) @ (exp_real @ B)) = (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5957_exp__less__cancel__iff)). 159.59/70.63 thf(16445,plain,((! [A:real,B:real]: ((ord_less_real @ (exp_real @ A) @ (exp_real @ B)) = (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2549])). 159.59/70.63 thf(1911,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ C @ D)) = (plus_plus_complex @ (minus_minus_complex @ A @ C) @ (minus_minus_complex @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_add__diff__add)). 159.59/70.63 thf(14424,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ (plus_plus_complex @ C @ D)) = (plus_plus_complex @ (minus_minus_complex @ A @ C) @ (minus_minus_complex @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1911])). 159.59/70.63 thf(1704,axiom,((! [A:$o]: ((ord_less_int @ zero_zero_int @ (zero_n2684676970156552555ol_int @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4342_zero__less__of__bool__iff)). 159.59/70.63 thf(13758,plain,((! [A:$o]: ((ord_less_int @ zero_zero_int @ (zero_n2684676970156552555ol_int @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704])). 159.59/70.63 thf(614,axiom,((! [A:real,B:real,C:real]: ((((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)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2434_divide__left__mono)). 159.59/70.63 thf(10212,plain,((! [A:real,B:real,C:real]: ((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) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[614])). 159.59/70.63 thf(2710,axiom,((! [A:complex,B:complex]: (((times_times_complex @ (invers8013647133539491842omplex @ A) @ B) = (times_times_complex @ B @ (invers8013647133539491842omplex @ A))) <= ((times_times_complex @ A @ B) = (times_times_complex @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9018_mult__commute__imp__mult__inverse__commute)). 159.59/70.63 thf(16996,plain,((! [A:complex,B:complex]: (((times_times_complex @ (invers8013647133539491842omplex @ A) @ B) = (times_times_complex @ B @ (invers8013647133539491842omplex @ A))) | ~ ((times_times_complex @ A @ B) = (times_times_complex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2710])). 159.59/70.63 thf(4669,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: (((! [D:nat]: (((ord_less_nat @ (B @ D) @ (C @ D)) & (ord_less_eq_nat @ zero_zero_nat @ (B @ D))) <= (member_nat @ D @ A))) => ((A != bot_bot_set_nat) => (ord_less_nat @ (groups708209901874060359at_nat @ B @ A) @ (groups708209901874060359at_nat @ C @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8778_prod__mono__strict)). 159.59/70.63 thf(23397,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: (((! [D:nat]: (((ord_less_nat @ (B @ D) @ (C @ D)) & (ord_less_eq_nat @ zero_zero_nat @ (B @ D))) | ~ (member_nat @ D @ A))) => ((~ (A = bot_bot_set_nat)) => (ord_less_nat @ (groups708209901874060359at_nat @ (B) @ A) @ (groups708209901874060359at_nat @ (C) @ A)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4669])). 159.59/70.63 thf(4719,axiom,((! [A:complex]: (((times_times_complex @ A @ A) = one_one_complex) = ((A = (uminus1482373934393186551omplex @ one_one_complex)) | (A = one_one_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5096_square__eq__1__iff)). 159.59/70.63 thf(23559,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)],[4719])). 159.59/70.63 thf(1623,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => ((A != B) => (ord_less_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2795_linorder__cases)). 159.59/70.63 thf(13522,plain,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) => ((~ (A = B)) => (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623])). 159.59/70.63 thf(4972,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/sandbox/benchmark/theBenchmark.p',fact_8128_fact__reduce)). 159.59/70.63 thf(24466,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)],[4972])). 159.59/70.63 thf(6105,axiom,((! [A:$o,B:$o]: ~ (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1467_Leaf__0__not)). 159.59/70.63 thf(28763,plain,((! [A:$o,B:$o]: ~ (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6105])). 159.59/70.63 thf(863,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ A) <= (A = (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3936_dvdI)). 159.59/70.63 thf(11031,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)],[863])). 159.59/70.63 thf(2068,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le2932123472753598470d_enat @ C @ A) => (ord_le72135733267957522d_enat @ C @ B)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3125_dual__order_Ostrict__trans2)). 159.59/70.63 thf(14918,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le2932123472753598470d_enat @ C @ A) => (ord_le72135733267957522d_enat @ C @ B)) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2068])). 159.59/70.63 thf(5831,axiom,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (times_times_complex @ (groups6464643781859351333omplex @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8728_prod_OatLeast0__atMost__Suc)). 159.59/70.63 thf(27730,plain,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (times_times_complex @ (groups6464643781859351333omplex @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5831])). 159.59/70.63 thf(7351,axiom,((zero_zero_real != one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1888_zero__neq__one)). 159.59/70.63 thf(33671,plain,((~ (zero_zero_real = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7351])). 159.59/70.63 thf(1586,axiom,((! [A:nat]: ~ (ord_less_int @ (bit_se2000444600071755411sk_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6084_not__mask__negative__int)). 159.59/70.63 thf(13398,plain,((! [A:nat]: ~ (ord_less_int @ (bit_se2000444600071755411sk_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586])). 159.59/70.63 thf(235,axiom,((! [A:real]: (filterlim_real_real @ (^ [B:real]: (powr_real @ (plus_plus_real @ one_one_real @ (divide_divide_real @ A @ B)) @ B)) @ (topolo2815343760600316023s_real @ (exp_real @ A)) @ at_top_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9960_tendsto__exp__limit__at__top)). 159.59/70.63 thf(8971,plain,((! [A:real]: (filterlim_real_real @ (^ [B:real]: (powr_real @ (plus_plus_real @ one_one_real @ (divide_divide_real @ A @ B)) @ B)) @ (topolo2815343760600316023s_real @ (exp_real @ A)) @ at_top_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[235])). 159.59/70.63 thf(4282,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/sandbox/benchmark/theBenchmark.p',fact_5816_of__int__less__0__iff)). 159.59/70.63 thf(21986,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)],[4282])). 159.59/70.63 thf(3455,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/sandbox/benchmark/theBenchmark.p',fact_6750_real__of__nat__div__aux)). 159.59/70.63 thf(19354,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)],[3455])). 159.59/70.63 thf(408,axiom,((! [A:real]: ((real_V7735802525324610683m_real @ (plus_plus_real @ (real_V1803761363581548252l_real @ A) @ one_one_real)) = (abs_abs_real @ (plus_plus_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7366_norm__of__real__add1)). 159.59/70.63 thf(9534,plain,((! [A:real]: ((real_V7735802525324610683m_real @ (plus_plus_real @ (real_V1803761363581548252l_real @ A) @ one_one_real)) = (abs_abs_real @ (plus_plus_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])). 159.59/70.63 thf(177,axiom,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ (plus_plus_int @ (minus_minus_int @ A @ (semiri1314217659103216013at_int @ B)) @ one_one_int) @ B) = (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (comm_s4660882817536571857er_int @ (uminus_uminus_int @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8341_pochhammer__minus_H)). 159.59/70.63 thf(8796,plain,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ (plus_plus_int @ (minus_minus_int @ A @ (semiri1314217659103216013at_int @ B)) @ one_one_int) @ B) = (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (comm_s4660882817536571857er_int @ (uminus_uminus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[177])). 159.59/70.63 thf(3230,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ one_one_int) = (numeral_numeral_int @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5990_or__numerals_I8_J)). 159.59/70.63 thf(18640,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ one_one_int) = (numeral_numeral_int @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3230])). 159.59/70.63 thf(5400,axiom,((! [A:nat]: ((binomial @ (suc @ A) @ A) = (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8986_binomial__Suc__n)). 159.59/70.63 thf(26064,plain,((! [A:nat]: ((binomial @ (suc @ A) @ A) = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5400])). 159.59/70.63 thf(6879,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/sandbox/benchmark/theBenchmark.p',fact_289_one__le__power)). 159.59/70.63 thf(31791,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)],[6879])). 159.59/70.63 thf(1982,axiom,((! [A:complex]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ zero_zero_real) = (A = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6892_norm__le__zero__iff)). 159.59/70.63 thf(14657,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)],[1982])). 159.59/70.63 thf(5405,axiom,((! [A:real]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ zero_zero_int) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6977_ceiling__le__zero)). 159.59/70.63 thf(26079,plain,((! [A:real]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ zero_zero_int) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5405])). 159.59/70.63 thf(4706,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/sandbox/benchmark/theBenchmark.p',fact_515_nat__add__left__cancel__le)). 159.59/70.63 thf(23521,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)],[4706])). 159.59/70.63 thf(791,axiom,((! [A:int,B:num]: (((ring_17405671764205052669omplex @ A) = (numera6690914467698888265omplex @ B)) = (A = (numeral_numeral_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5764_of__int__eq__numeral__iff)). 159.59/70.63 thf(10802,plain,((! [A:int,B:num]: (((ring_17405671764205052669omplex @ A) = (numera6690914467698888265omplex @ B)) = (A = (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[791])). 159.59/70.63 thf(925,axiom,((! [A:complex,B:complex,C:complex]: (((B = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ C @ A))) = ((times_times_complex @ B @ A) = (uminus1482373934393186551omplex @ C))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5194_nonzero__neg__divide__eq__eq2)). 159.59/70.63 thf(11216,plain,((! [A:complex,B:complex,C:complex]: (((B = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ C @ A))) = ((times_times_complex @ B @ A) = (uminus1482373934393186551omplex @ C))) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[925])). 159.59/70.63 thf(2184,axiom,((! [A:complex,B:complex,C:complex]: (((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ C)) = (dvd_dvd_complex @ A @ C)) <= (dvd_dvd_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3990_dvd__add__right__iff)). 159.59/70.63 thf(15290,plain,((! [A:complex,B:complex,C:complex]: (((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ C)) = (dvd_dvd_complex @ A @ C)) | ~ (dvd_dvd_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2184])). 159.59/70.63 thf(2107,axiom,(((cosh_complex @ zero_zero_complex) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9312_cosh__0)). 159.59/70.63 thf(15039,plain,(((cosh_complex @ zero_zero_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2107])). 159.59/70.63 thf(6250,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ B)) = (times_times_real @ (power_power_real @ A @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_power__Suc2)). 159.59/70.63 thf(29253,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)],[6250])). 159.59/70.63 thf(6146,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/sandbox/benchmark/theBenchmark.p',fact_1581_le__add__same__cancel2)). 159.59/70.63 thf(28903,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)],[6146])). 159.59/70.63 thf(4608,axiom,((! [A:num]: ((semiri5044797733671781792omplex @ (numeral_numeral_nat @ A)) = (times_times_complex @ (numera6690914467698888265omplex @ A) @ (semiri5044797733671781792omplex @ (pred_numeral @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8111_fact__numeral)). 159.59/70.63 thf(23182,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)],[4608])). 159.59/70.63 thf(5984,axiom,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (times_times_nat @ A @ B)) = (times_times_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6533_of__nat__mult)). 159.59/70.63 thf(28390,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)],[5984])). 159.59/70.63 thf(5320,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/sandbox/benchmark/theBenchmark.p',fact_860_vebt__maxt_Osimps_I2_J)). 159.59/70.63 thf(25714,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)],[5320])). 159.59/70.63 thf(7279,axiom,(((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_one__add__one)). 159.59/70.63 thf(33407,plain,(((plus_plus_real @ one_one_real @ one_one_real) = (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7279])). 159.59/70.63 thf(2258,axiom,(((semiri4216267220026989637d_enat @ zero_zero_nat) = zero_z5237406670263579293d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6495_of__nat__0)). 159.59/70.63 thf(15538,plain,(((semiri4216267220026989637d_enat @ zero_zero_nat) = zero_z5237406670263579293d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2258])). 159.59/70.63 thf(3912,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((produc6081775807080527818_nat_o @ A @ (product_Pair_nat_nat @ B @ C)) = (A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4657_case__prod__conv)). 159.59/70.63 thf(20840,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((produc6081775807080527818_nat_o @ (A) @ (product_Pair_nat_nat @ B @ C)) = (A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3912])). 159.59/70.63 thf(662,axiom,((! [A:num]: ((nat2 @ (numeral_numeral_int @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9413_nat__numeral)). 159.59/70.63 thf(10366,plain,((! [A:num]: ((nat2 @ (numeral_numeral_int @ A)) = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[662])). 159.59/70.63 thf(6705,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2046_add__decreasing)). 159.59/70.63 thf(31025,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6705])). 159.59/70.63 thf(726,axiom,(((real_V4546457046886955230omplex @ one_one_real) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7324_of__real__1)). 159.59/70.63 thf(10597,plain,(((real_V4546457046886955230omplex @ one_one_real) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[726])). 159.59/70.63 thf(6674,axiom,((! [A:nat,B:list_nat]: ((member_nat @ A @ (set_nat2 @ B)) => (ord_less_nat @ zero_zero_nat @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2394_length__pos__if__in__set)). 159.59/70.63 thf(30869,plain,((! [A:nat,B:list_nat]: ((member_nat @ A @ (set_nat2 @ B)) => (ord_less_nat @ zero_zero_nat @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6674])). 159.59/70.63 thf(8256,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 @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4539_minf_I9_J)). 159.59/70.63 thf(36806,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8256])). 159.59/70.63 thf(3845,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_real @ one_one_real @ (log @ A @ B)) = (ord_less_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6333_one__less__log__cancel__iff)). 159.59/70.63 thf(20629,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_real @ one_one_real @ (log @ A @ B)) = (ord_less_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3845])). 159.59/70.63 thf(795,axiom,((! [A:real]: ((ord_less_real @ (sqrt @ A) @ one_one_real) = (ord_less_real @ A @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6319_real__sqrt__lt__1__iff)). 159.59/70.63 thf(10815,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)],[795])). 159.59/70.63 thf(6618,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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4871_power__minus__odd)). 159.59/70.63 thf(30663,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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6618])). 159.59/70.63 thf(3982,axiom,((! [A:(nat > nat),B:nat]: (((! [C:nat]: (ord_less_eq_nat @ (groups3542108847815614940at_nat @ A @ (set_ord_lessThan_nat @ C)) @ B)) => (ord_less_eq_nat @ (suminf_nat @ A) @ B)) <= (summable_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7954_suminf__le__const)). 159.59/70.63 thf(21055,plain,((! [A:(nat > nat),B:nat]: (((! [C:nat]: (ord_less_eq_nat @ (groups3542108847815614940at_nat @ (A) @ (set_ord_lessThan_nat @ C)) @ B)) => (ord_less_eq_nat @ (suminf_nat @ (A)) @ B)) | ~ (summable_nat @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3982])). 159.59/70.63 thf(2432,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/sandbox/benchmark/theBenchmark.p',fact_4579_crossproduct__eq)). 159.59/70.63 thf(16080,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)],[2432])). 159.59/70.63 thf(5846,axiom,((! [A:num,B:num]: ((bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ B)) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ (pred_numeral @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6348_bit__numeral__simps_I3_J)). 159.59/70.63 thf(27859,plain,((! [A:num,B:num]: ((bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ B)) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5846])). 159.59/70.63 thf(4180,axiom,((! [A:nat,B:nat]: ((ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6521_of__nat__less__iff)). 159.59/70.63 thf(21659,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)],[4180])). 159.59/70.63 thf(7019,axiom,(((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4848_diff__numeral__special_I10_J)). 159.59/70.63 thf(32412,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)],[7019])). 159.59/70.63 thf(5676,axiom,((! [A:num,B:num]: ((power_8040749407984259932d_enat @ (numera1916890842035813515d_enat @ A) @ (numeral_numeral_nat @ B)) = (numera1916890842035813515d_enat @ (pow @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4602_power__numeral)). 159.59/70.63 thf(27057,plain,((! [A:num,B:num]: ((power_8040749407984259932d_enat @ (numera1916890842035813515d_enat @ A) @ (numeral_numeral_nat @ B)) = (numera1916890842035813515d_enat @ (pow @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5676])). 159.59/70.63 thf(6510,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/sandbox/benchmark/theBenchmark.p',fact_1792_zero__less__power2)). 159.59/70.63 thf(30275,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)],[6510])). 159.59/70.63 thf(2811,axiom,((! [A:nat]: ((semiri1406184849735516958ct_int @ (suc @ A)) = (times_times_int @ (semiri1314217659103216013at_int @ (suc @ A)) @ (semiri1406184849735516958ct_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8060_fact__Suc)). 159.59/70.63 thf(17293,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)],[2811])). 159.59/70.63 thf(919,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/sandbox/benchmark/theBenchmark.p',fact_3905_odd__succ__div__two)). 159.59/70.63 thf(11197,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)],[919])). 159.59/70.63 thf(5181,axiom,((! [A:(real > $o),B:real,C:(real > $o)]: (((! [D:real,E:real]: (((C @ D) & (A @ D)) = ((A @ (minus_minus_real @ D @ (times_times_real @ E @ B))) & (C @ (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/sandbox/benchmark/theBenchmark.p',fact_4517_inf__period_I1_J)). 159.59/70.63 thf(25188,plain,((! [A:(real > $o),B:real,C:(real > $o)]: (! [D:real,E:real]: (((C @ D) & (A @ D)) = ((A @ (minus_minus_real @ D @ (times_times_real @ E @ B))) & (C @ (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)],[5181])). 159.59/70.63 thf(6747,axiom,((! [A:set_nat,B:(set_nat > $o),C:(nat > int)]: (((B @ bot_bot_set_nat) => ((! [D:nat,E:set_nat]: ((finite_finite_nat @ E) => ((! [F:nat]: ((member_nat @ F @ E) => (ord_less_eq_int @ (C @ F) @ (C @ D)))) => ((B @ (insert_nat @ D @ E)) <= (B @ E))))) => (B @ A))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6231_finite__ranking__induct)). 159.59/70.63 thf(31253,plain,((! [A:set_nat,B:(set_nat > $o),C:(nat > int)]: (((B @ bot_bot_set_nat) => ((! [D:nat,E:set_nat]: ((finite_finite_nat @ E) => ((! [F:nat]: ((member_nat @ F @ E) => (ord_less_eq_int @ (C @ F) @ (C @ D)))) => ((B @ (insert_nat @ D @ E)) | ~ (B @ E))))) => (B @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6747])). 159.59/70.63 thf(2034,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/sandbox/benchmark/theBenchmark.p',fact_7159_sin__squared__eq)). 159.59/70.63 thf(14821,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)],[2034])). 159.59/70.63 thf(5050,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (B = (ord_max_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_max_Oorder__iff)). 159.59/70.63 thf(24743,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: (B = (ord_max_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5050])). 159.59/70.63 thf(1124,axiom,((! [A:int]: ((! [B:nat]: (A != (semiri1314217659103216013at_int @ B))) => (~ (! [B:nat]: (A != (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ B))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6819_int__cases)). 159.59/70.63 thf(11856,plain,((! [A:int]: ((! [B:nat]: ~ (A = (semiri1314217659103216013at_int @ B))) => (~ (! [B:nat]: ~ (A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124])). 159.59/70.63 thf(3189,axiom,((! [A:num]: ((neg_nu7009210354673126013omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3859_dbl__simps_I5_J)). 159.59/70.63 thf(18508,plain,((! [A:num]: ((neg_nu7009210354673126013omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3189])). 159.59/70.63 thf(1634,axiom,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5187_neg__one__less__numeral)). 159.59/70.63 thf(13554,plain,((! [A:num]: (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634])). 159.59/70.63 thf(4983,axiom,((! [A:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => (ord_less_nat @ A @ (bit_se2002935070580805687sk_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6096_less__mask)). 159.59/70.63 thf(24498,plain,((! [A:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => (ord_less_nat @ A @ (bit_se2002935070580805687sk_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4983])). 159.59/70.63 thf(3037,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (divide6298287555418463151nteger @ C @ B)) <= (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4086_dvd__mult__imp__div)). 159.59/70.63 thf(18012,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (divide6298287555418463151nteger @ C @ B)) | ~ (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3037])). 159.59/70.63 thf(5290,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ (log @ A @ B) @ one_one_real) = (ord_less_eq_real @ B @ A)) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6342_log__le__one__cancel__iff)). 159.59/70.63 thf(25583,plain,((! [A:real,B:real]: (((ord_less_eq_real @ (log @ A @ B) @ one_one_real) = (ord_less_eq_real @ B @ A)) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5290])). 159.59/70.63 thf(4072,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => ((~ (ord_le72135733267957522d_enat @ A @ B)) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3046_antisym__conv2)). 159.59/70.63 thf(21317,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => ((~ (ord_le72135733267957522d_enat @ A @ B)) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4072])). 159.59/70.63 thf(3048,axiom,((bit_se725231765392027082nd_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_se725231765392027082nd_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6133_and__int__rec)). 159.59/70.63 thf(18049,plain,(((bit_se725231765392027082nd_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_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)],[3048])). 159.59/70.63 thf(653,axiom,((! [A:complex,B:complex,C:complex,D:complex]: (((B != zero_zero_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)))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2374_diff__frac__eq)). 159.59/70.63 thf(10338,plain,((! [A:complex,B:complex,C:complex,D:complex]: (((~ (B = zero_zero_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)))) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[653])). 159.59/70.63 thf(1530,axiom,((! [A:int,B:int,C:int]: (((minus_minus_int @ A @ B) = C) = (A = (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1295_diff__eq__eq)). 159.59/70.63 thf(13232,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)],[1530])). 159.59/70.63 thf(3447,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/sandbox/benchmark/theBenchmark.p',fact_1070_add__less__cancel__right)). 159.59/70.63 thf(19332,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)],[3447])). 159.59/70.63 thf(1388,axiom,((! [A:nat]: ~ (ord_less_real @ (semiri2265585572941072030t_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8074_fact__not__neg)). 159.59/70.63 thf(12783,plain,((! [A:nat]: ~ (ord_less_real @ (semiri2265585572941072030t_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388])). 159.59/70.63 thf(5236,axiom,((! [A:nat,B:nat,C:(nat > real),D:(nat > real)]: (((ord_less_eq_nat @ B @ A) => ((groups6591440286371151544t_real @ (^ [E:nat]: (if_real @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_real @ (E = B) @ zero_zero_real @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups6591440286371151544t_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 @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8940_sum_Ozero__middle)). 159.59/70.63 thf(25393,plain,((! [A:nat,B:nat,C:(nat > real),D:(nat > real)]: (((ord_less_eq_nat @ B @ A) => ((groups6591440286371151544t_real @ (^ [E:nat]: (if_real @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_real @ (E = B) @ zero_zero_real @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups6591440286371151544t_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 @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5236])). 159.59/70.63 thf(4247,axiom,((! [A:int,B:int,C:nat]: ((power_power_int @ (plus_plus_int @ A @ B) @ C) = (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (times_times_int @ (semiri1314217659103216013at_int @ (binomial @ C @ D)) @ (power_power_int @ A @ D)) @ (power_power_int @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9145_binomial__ring)). 159.59/70.63 thf(21883,plain,((! [A:int,B:int,C:nat]: ((power_power_int @ (plus_plus_int @ A @ B) @ C) = (groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (times_times_int @ (semiri1314217659103216013at_int @ (binomial @ C @ D)) @ (power_power_int @ A @ D)) @ (power_power_int @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4247])). 159.59/70.63 thf(7110,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/sandbox/benchmark/theBenchmark.p',fact_8456_prod_Ocl__ivl__Suc)). 159.59/70.63 thf(32768,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)],[7110])). 159.59/70.63 thf(6708,axiom,(((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4846_add__neg__numeral__special_I9_J)). 159.59/70.63 thf(31112,plain,(((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6708])). 159.59/70.63 thf(5124,axiom,((! [A:set_nat,B:nat]: (((finite_finite_nat @ A) => (~ (? [C:nat]: ((ord_less_nat @ B @ C) & (member_nat @ C @ A))))) <= (~ (? [C:nat]: (vEBT_is_succ_in_set @ A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3601_succ__none__empty)). 159.59/70.63 thf(24985,plain,((! [A:set_nat,B:nat]: (((finite_finite_nat @ A) => (~ (? [C:nat]: ((ord_less_nat @ B @ C) & (member_nat @ C @ A))))) | ? [C:nat]: (vEBT_is_succ_in_set @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5124])). 159.59/70.63 thf(1168,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/sandbox/benchmark/theBenchmark.p',fact_1443_diff__divide__distrib)). 159.59/70.63 thf(11997,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)],[1168])). 159.59/70.63 thf(3226,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2067_mult__strict__right__mono)). 159.59/70.63 thf(18626,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3226])). 159.59/70.63 thf(2127,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/sandbox/benchmark/theBenchmark.p',fact_5273_take__bit__int__less__exp)). 159.59/70.63 thf(15101,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)],[2127])). 159.59/70.63 thf(5737,axiom,((! [A:nat,B:(nat > complex),C:nat,D:(nat > complex),E:complex]: ((((times_times_complex @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (B @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ A)) @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (D @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ C))) = (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (groups2073611262835488442omplex @ (^ [G:nat]: (times_times_complex @ (B @ G) @ (D @ (minus_minus_nat @ F @ G)))) @ (set_ord_atMost_nat @ F)) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ (plus_plus_nat @ A @ C)))) <= (! [F:nat]: ((ord_less_nat @ C @ F) => ((D @ F) = zero_zero_complex)))) <= (! [F:nat]: ((ord_less_nat @ A @ F) => ((B @ F) = zero_zero_complex)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8916_polynomial__product)). 159.59/70.63 thf(27249,plain,((! [A:nat,B:(nat > complex),C:nat,D:(nat > complex),E:complex]: (((times_times_complex @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (B @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ A)) @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (D @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ C))) = (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (groups2073611262835488442omplex @ (^ [G:nat]: (times_times_complex @ (B @ G) @ (D @ (minus_minus_nat @ F @ G)))) @ (set_ord_atMost_nat @ F)) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ (plus_plus_nat @ A @ C)))) | ~ (! [F:nat]: ((ord_less_nat @ C @ F) => ((D @ F) = zero_zero_complex))) | ~ (! [F:nat]: ((ord_less_nat @ A @ F) => ((B @ F) = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5737])). 159.59/70.63 thf(85,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (real_V1803761363581548252l_real @ A) @ (real_V1803761363581548252l_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7713_norm__of__real__diff)). 159.59/70.63 thf(8512,plain,((! [A:real,B:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (real_V1803761363581548252l_real @ A) @ (real_V1803761363581548252l_real @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 159.59/70.63 thf(242,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (sinh_real @ A) @ (sinh_real @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9307_sinh__real__le__iff)). 159.59/70.63 thf(8989,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (sinh_real @ A) @ (sinh_real @ B)) = (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[242])). 159.59/70.63 thf(6300,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/sandbox/benchmark/theBenchmark.p',fact_3426_Suc__mod__mult__self1)). 159.59/70.63 thf(29493,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)],[6300])). 159.59/70.63 thf(5578,axiom,((one_one_Code_integer != (uminus1351360451143612070nteger @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4975_one__neq__neg__one)). 159.59/70.63 thf(26691,plain,((~ (one_one_Code_integer = (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5578])). 159.59/70.63 thf(5197,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat]: ((! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ F @ B))) => (((((E = (plus_plus_nat @ B @ D)) => (((! [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))))) <= (D = (suc @ B))) <= ((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) <= (vEBT_invar_vebt @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_invar__vebt_Ointros_I3_J)). 159.59/70.63 thf(25239,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat]: ((! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ F @ B))) => (((E = (plus_plus_nat @ B @ D)) => (((! [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))) | ~ (D = (suc @ 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)],[5197])). 159.59/70.63 thf(4763,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/sandbox/benchmark/theBenchmark.p',fact_2212_vebt__member_Osimps_I3_J)). 159.59/70.63 thf(23716,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)],[4763])). 159.59/70.63 thf(6033,axiom,((! [A:nat,B:num]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (bit_se2923211474154528505it_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5263_take__bit__Suc__bit0)). 159.59/70.63 thf(28544,plain,((! [A:nat,B:num]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (bit_se2923211474154528505it_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6033])). 159.59/70.63 thf(2246,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/sandbox/benchmark/theBenchmark.p',fact_6944_norm__triangle__ineq2)). 159.59/70.63 thf(15499,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)],[2246])). 159.59/70.63 thf(7737,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ D @ E) <= (A @ E @ D)))) <= (! [D:nat]: (A @ D @ D))) <= (! [D:nat,E:nat]: ((A @ D @ E) <= (ord_less_nat @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2811_linorder__less__wlog)). 159.59/70.63 thf(34994,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ D @ E) | ~ (A @ E @ D))) | ~ (! [D:nat]: (A @ D @ D)) | ~ (! [D:nat,E:nat]: ((A @ D @ E) | ~ (ord_less_nat @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7737])). 159.59/70.63 thf(6439,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)))) & ((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/sandbox/benchmark/theBenchmark.p',fact_5287_uminus__power__if)). 159.59/70.63 thf(30006,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)))) & ((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)],[6439])). 159.59/70.63 thf(7559,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/sandbox/benchmark/theBenchmark.p',fact_7805_double__arith__series)). 159.59/70.63 thf(34369,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)],[7559])). 159.59/70.63 thf(8217,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/sandbox/benchmark/theBenchmark.p',fact_6296_or__nat__unfold)). 159.59/70.63 thf(36529,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)],[8217])). 159.59/70.63 thf(1967,axiom,(((^ [A:extended_enat]: (zero_z5237406670263579293d_enat)) = (times_7803423173614009249d_enat @ zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1934_lambda__zero)). 159.59/70.63 thf(14590,plain,(((^ [A:extended_enat]: (zero_z5237406670263579293d_enat)) = (times_7803423173614009249d_enat @ zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1967])). 159.59/70.63 thf(457,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (((divide6298287555418463151nteger @ B @ A) = zero_z3403309356797280102nteger) = (B = zero_z3403309356797280102nteger))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4050_dvd__div__eq__0__iff)). 159.59/70.63 thf(9689,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (((divide6298287555418463151nteger @ B @ A) = zero_z3403309356797280102nteger) = (B = zero_z3403309356797280102nteger))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])). 159.59/70.63 thf(7852,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/sandbox/benchmark/theBenchmark.p',fact_1072_add__less__cancel__left)). 159.59/70.63 thf(35348,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)],[7852])). 159.59/70.63 thf(1782,axiom,((arcsin = (^ [A:real]: (the_real @ (^ [B:real]: ((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((sin_real @ B) = A) & (ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9406_arcsin__def)). 159.59/70.63 thf(14008,plain,(((arcsin) = (^ [A:real]: (the_real @ (^ [B:real]: ((ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((sin_real @ B) = A) & (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)],[1782])). 159.59/70.63 thf(380,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (archim2898591450579166408c_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9059_frac__ge__0)). 159.59/70.63 thf(9436,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (archim2898591450579166408c_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])). 159.59/70.63 thf(2582,axiom,((! [A:nat,B:nat,C:int]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((bit_se2923211474154528505it_int @ A @ (bit_ri631733984087533419it_int @ B @ C)) = (bit_se2923211474154528505it_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5137_take__bit__signed__take__bit)). 159.59/70.63 thf(16548,plain,((! [A:nat,B:nat,C:int]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((bit_se2923211474154528505it_int @ A @ (bit_ri631733984087533419it_int @ B @ C)) = (bit_se2923211474154528505it_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2582])). 159.59/70.63 thf(6693,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/sandbox/benchmark/theBenchmark.p',fact_3889_power__less__zero__eq)). 159.59/70.63 thf(30988,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)],[6693])). 159.59/70.63 thf(3800,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/sandbox/benchmark/theBenchmark.p',fact_7790_sum_Oin__pairs)). 159.59/70.63 thf(20476,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)],[3800])). 159.59/70.63 thf(7866,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ one_one_nat) @ (plus_plus_nat @ B @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1327_add__mono1)). 159.59/70.63 thf(35390,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ one_one_nat) @ (plus_plus_nat @ B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7866])). 159.59/70.63 thf(1824,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ B @ (plus_plus_int @ C @ A))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2035_add__increasing2)). 159.59/70.63 thf(14157,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ B @ (plus_plus_int @ C @ A))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1824])). 159.59/70.63 thf(299,axiom,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se8260200283734997820nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4238_even__unset__bit__iff)). 159.59/70.63 thf(9176,plain,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se8260200283734997820nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 159.59/70.63 thf(7902,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/sandbox/benchmark/theBenchmark.p',fact_3_pow__sum)). 159.59/70.63 thf(35515,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)],[7902])). 159.59/70.63 thf(4126,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1532_add_Oright__neutral)). 159.59/70.63 thf(21485,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4126])). 159.59/70.63 thf(8254,axiom,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = (uminus_uminus_real @ B)) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5259_power2__eq__iff)). 159.59/70.63 thf(36793,plain,((! [A:real,B:real]: (((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = (uminus_uminus_real @ B)) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8254])). 159.59/70.63 thf(705,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/sandbox/benchmark/theBenchmark.p',fact_7391_sum__mono)). 159.59/70.63 thf(10524,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)],[705])). 159.59/70.63 thf(4283,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/sandbox/benchmark/theBenchmark.p',fact_2871_ord__eq__less__subst)). 159.59/70.63 thf(21989,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)],[4283])). 159.59/70.63 thf(754,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/sandbox/benchmark/theBenchmark.p',fact_6915_norm__mult__ineq)). 159.59/70.63 thf(10689,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)],[754])). 159.59/70.63 thf(2476,axiom,((! [A:real]: ((archim7802044766580827645g_real @ (plus_plus_real @ A @ one_one_real)) = (plus_plus_int @ (archim7802044766580827645g_real @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6987_ceiling__add__one)). 159.59/70.63 thf(16220,plain,((! [A:real]: ((archim7802044766580827645g_real @ (plus_plus_real @ A @ one_one_real)) = (plus_plus_int @ (archim7802044766580827645g_real @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2476])). 159.59/70.63 thf(3405,axiom,((sin_real = (^ [A:real]: (cos_real @ (minus_minus_real @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7795_sin__cos__eq)). 159.59/70.63 thf(19198,plain,(((sin_real) = (^ [A:real]: (cos_real @ (minus_minus_real @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3405])). 159.59/70.63 thf(5741,axiom,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_bits__div__by__1)). 159.59/70.63 thf(27268,plain,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5741])). 159.59/70.63 thf(7407,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/sandbox/benchmark/theBenchmark.p',fact_6778_log__of__power__le)). 159.59/70.63 thf(33851,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)],[7407])). 159.59/70.63 thf(4730,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1655_diff__add__zero)). 159.59/70.63 thf(23591,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)],[4730])). 159.59/70.63 thf(4096,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/sandbox/benchmark/theBenchmark.p',fact_8340_pochhammer__minus_H)). 159.59/70.63 thf(21395,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)],[4096])). 159.59/70.63 thf(7262,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/sandbox/benchmark/theBenchmark.p',fact_4548_option_Osize__gen_I2_J)). 159.59/70.63 thf(33356,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)],[7262])). 159.59/70.63 thf(4941,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/sandbox/benchmark/theBenchmark.p',fact_857_diff__Suc__eq__diff__pred)). 159.59/70.63 thf(24320,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)],[4941])). 159.59/70.63 thf(4908,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_max_nat @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_794_max_Oabsorb1)). 159.59/70.63 thf(24217,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)],[4908])). 159.59/70.63 thf(466,axiom,(((tan_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit1 @ one)))) = (sqrt @ (numeral_numeral_real @ (bit1 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7281_tan__60)). 159.59/70.63 thf(9716,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)],[466])). 159.59/70.63 thf(7301,axiom,((! [A:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ one) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_mult__numeral__1)). 159.59/70.63 thf(33488,plain,((! [A:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7301])). 159.59/70.63 thf(5390,axiom,((sqr = (^ [A:num]: (times_times_num @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9798_sqr__conv__mult)). 159.59/70.63 thf(26022,plain,(((sqr) = (^ [A:num]: (times_times_num @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5390])). 159.59/70.63 thf(2535,axiom,((! [A:real,B:real]: (sums_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (if_real @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (times_times_real @ (real_V1485227260804924795R_real @ (uminus_uminus_real @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C))) @ (power_power_real @ A @ D)) @ (power_power_real @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_real)) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ (sin_real @ A) @ (sin_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9176_sin__x__sin__y)). 159.59/70.63 thf(16405,plain,((! [A:real,B:real]: (sums_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (if_real @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (times_times_real @ (real_V1485227260804924795R_real @ (uminus_uminus_real @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C))) @ (power_power_real @ A @ D)) @ (power_power_real @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_real)) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ (sin_real @ A) @ (sin_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2535])). 159.59/70.63 thf(57,axiom,((! [A:nat,B:nat]: (((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ (semiri4939895301339042750nteger @ A)) @ B) = zero_z3403309356797280102nteger) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8285_pochhammer__of__nat__eq__0__iff)). 159.59/70.63 thf(8422,plain,((! [A:nat,B:nat]: (((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ (semiri4939895301339042750nteger @ A)) @ B) = zero_z3403309356797280102nteger) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 159.59/70.63 thf(7835,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3670_verit__comp__simplify1_I1_J)). 159.59/70.63 thf(35299,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7835])). 159.59/70.63 thf(5201,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2678_order__subst2)). 159.59/70.63 thf(25276,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_nat @ (C @ A) @ D)) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5201])). 159.59/70.63 thf(248,axiom,((! [A:real]: ((ord_less_real @ (tanh_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5430_tanh__real__neg__iff)). 159.59/70.63 thf(9008,plain,((! [A:real]: ((ord_less_real @ (tanh_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 159.59/70.63 thf(7563,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ A @ (times_times_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3947_dvd__mult)). 159.59/70.63 thf(34378,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ A @ (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7563])). 159.59/70.63 thf(2288,axiom,((! [A:real]: (ord_less_real @ A @ (plus_plus_real @ A @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1329_less__add__one)). 159.59/70.63 thf(15624,plain,((! [A:real]: (ord_less_real @ A @ (plus_plus_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2288])). 159.59/70.63 thf(7499,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)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2150_zero__le__power)). 159.59/70.63 thf(34185,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)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7499])). 159.59/70.63 thf(203,axiom,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ (uminus_uminus_int @ A) @ B) = (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (comm_s4660882817536571857er_int @ (plus_plus_int @ (minus_minus_int @ A @ (semiri1314217659103216013at_int @ B)) @ one_one_int) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8345_pochhammer__minus)). 159.59/70.63 thf(8871,plain,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ (uminus_uminus_int @ A) @ B) = (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ B) @ (comm_s4660882817536571857er_int @ (plus_plus_int @ (minus_minus_int @ A @ (semiri1314217659103216013at_int @ B)) @ one_one_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[203])). 159.59/70.63 thf(7241,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/sandbox/benchmark/theBenchmark.p',fact_4126_nat__dvd__not__less)). 159.59/70.63 thf(33291,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)],[7241])). 159.59/70.63 thf(4574,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (modulo_modulo_nat @ B @ A) @ A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3487_mod__less__divisor)). 159.59/70.63 thf(23037,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)],[4574])). 159.59/70.63 thf(571,axiom,((! [A:num]: ((re @ (numera6690914467698888265omplex @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9627_complex__Re__numeral)). 159.59/70.63 thf(10069,plain,((! [A:num]: ((re @ (numera6690914467698888265omplex @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[571])). 159.59/70.63 thf(4461,axiom,((! [A:$o,B:$o,C:$o,D:$o]: (((vEBT_Leaf @ A @ B) = (vEBT_Leaf @ C @ D)) = ((A = C) & (B = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1473_VEBT_Oinject_I2_J)). 159.59/70.63 thf(22540,plain,((! [A:$o,B:$o,C:$o,D:$o]: (((vEBT_Leaf @ A @ B) = (vEBT_Leaf @ C @ D)) = ((A = C) & (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4461])). 159.59/70.63 thf(7029,axiom,((! [A:nat,B:int]: (ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (bit_ri631733984087533419it_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5298_signed__take__bit__int__greater__eq__minus__exp)). 159.59/70.63 thf(32444,plain,((! [A:nat,B:int]: (ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ (bit_ri631733984087533419it_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7029])). 159.59/70.63 thf(6902,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (times_times_int @ B @ A)) = (((ord_less_int @ B @ one_one_int) <= (ord_less_eq_int @ A @ zero_zero_int)) & ((ord_less_int @ one_one_int @ B) <= (ord_less_eq_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2413_mult__less__cancel__right1)). 159.59/70.63 thf(31863,plain,((! [A:int,B:int]: ((ord_less_int @ A @ (times_times_int @ B @ A)) = (((ord_less_int @ B @ one_one_int) | ~ (ord_less_eq_int @ A @ zero_zero_int)) & ((ord_less_int @ one_one_int @ B) | ~ (ord_less_eq_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6902])). 159.59/70.63 thf(4212,axiom,((! [A:$o,B:$o]: ((ord_le6747313008572928689nteger @ (zero_n356916108424825756nteger @ A) @ (zero_n356916108424825756nteger @ B)) = ((B) & ~ (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4319_of__bool__less__iff)). 159.59/70.63 thf(21759,plain,((! [A:$o,B:$o]: ((ord_le6747313008572928689nteger @ (zero_n356916108424825756nteger @ A) @ (zero_n356916108424825756nteger @ B)) = ((B) & ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4212])). 159.59/70.63 thf(2954,axiom,((! [A:nat,B:nat]: ((map_nat_nat @ suc @ (upt @ A @ B)) = (upt @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10138_map__Suc__upt)). 159.59/70.63 thf(17767,plain,((! [A:nat,B:nat]: ((map_nat_nat @ (suc) @ (upt @ A @ B)) = (upt @ (suc @ A) @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2954])). 159.59/70.63 thf(2189,axiom,((! [A:real,B:real]: ((real_V4546457046886955230omplex @ (times_times_real @ A @ B)) = (times_times_complex @ (real_V4546457046886955230omplex @ A) @ (real_V4546457046886955230omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7328_of__real__mult)). 159.59/70.63 thf(15307,plain,((! [A:real,B:real]: ((real_V4546457046886955230omplex @ (times_times_real @ A @ B)) = (times_times_complex @ (real_V4546457046886955230omplex @ A) @ (real_V4546457046886955230omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2189])). 159.59/70.63 thf(2423,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ C) <= (ord_less_real @ B @ (times_times_real @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2327_mult__imp__div__pos__less)). 159.59/70.63 thf(16048,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ C) | ~ (ord_less_real @ B @ (times_times_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2423])). 159.59/70.63 thf(2132,axiom,((! [A:nat,B:nat]: (((set_or1269000886237332187st_nat @ A @ B) = bot_bot_set_nat) = (~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3344_atLeastatMost__empty__iff)). 159.59/70.63 thf(15136,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)],[2132])). 159.59/70.63 thf(5778,axiom,((! [A:complex,B:nat]: ((times_times_complex @ (minus_minus_complex @ one_one_complex @ A) @ (groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_atMost_nat @ B))) = (minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8870_sum__gp__basic)). 159.59/70.63 thf(27383,plain,((! [A:complex,B:nat]: ((times_times_complex @ (minus_minus_complex @ one_one_complex @ A) @ (groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_atMost_nat @ B))) = (minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5778])). 159.59/70.63 thf(4581,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/sandbox/benchmark/theBenchmark.p',fact_3209_order__less__le__trans)). 159.59/70.63 thf(23058,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)],[4581])). 159.59/70.63 thf(7816,axiom,((! [A:code_integer,B:code_integer]: (((power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_8256067586552552935nteger @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = B) | (A = (uminus1351360451143612070nteger @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5262_power2__eq__iff)). 159.59/70.63 thf(35230,plain,((! [A:code_integer,B:code_integer]: (((power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_8256067586552552935nteger @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = ((A = B) | (A = (uminus1351360451143612070nteger @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7816])). 159.59/70.63 thf(7402,axiom,((! [A:int,B:nat,C:nat]: (((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)))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2475_power__diff)). 159.59/70.63 thf(33836,plain,((! [A:int,B:nat,C:nat]: (((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)))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7402])). 159.59/70.63 thf(3064,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/sandbox/benchmark/theBenchmark.p',fact_3834_unit__prod)). 159.59/70.63 thf(18100,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)],[3064])). 159.59/70.63 thf(8176,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:nat]: (((A = B) & (ord_less_nat @ A @ C)) => ((B != C) => ((((vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F) => ((E = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ G)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ H @ (the_nat @ (vEBT_vebt_mint @ G))))))) => (((vEBT_VEBT_low @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = I) => ((ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)) = none_nat) @ E @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ H @ F @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ H @ F @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ (vEBT_vebt_delete @ G @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (plus_plus_nat @ (times_times_nat @ F @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ H @ F @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ F)))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ H @ F @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ G))))))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1401_del__x__mi)). 159.59/70.63 thf(36397,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:nat]: (((A = B) & (ord_less_nat @ A @ C)) => ((~ (B = C)) => ((((vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F) => ((E = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ G)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ H @ (the_nat @ (vEBT_vebt_mint @ G))))))) => (((vEBT_VEBT_low @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = I) => ((ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)) = none_nat) @ E @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ H @ F @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ G @ F)))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ H @ F @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ (vEBT_vebt_delete @ G @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (plus_plus_nat @ (times_times_nat @ F @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ H @ F @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ F)))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ H @ F @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) @ G))))))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8176])). 159.59/70.63 thf(4743,axiom,((ord_less_eq_int @ zero_zero_int @ zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1831_le__numeral__extra_I3_J)). 159.59/70.63 thf(23631,plain,((ord_less_eq_int @ zero_zero_int @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4743])). 159.59/70.63 thf(6378,axiom,((! [A:nat,B:vEBT_VEBT]: (((vEBT_vebt_buildup @ A) = B) => ((((A = (suc @ zero_zero_nat)) => (B != (vEBT_Leaf @ ($false) @ ($false)))) => (~ (! [C:nat]: ((~ (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C))) => (B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C))))))) <= (A = (suc @ (suc @ C))))))) <= ((A = zero_zero_nat) => (B != (vEBT_Leaf @ ($false) @ ($false)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4305_vebt__buildup_Oelims)). 159.59/70.63 thf(29726,plain,((! [A:nat,B:vEBT_VEBT]: (((vEBT_vebt_buildup @ A) = B) => ((((A = (suc @ zero_zero_nat)) => (~ (B = (vEBT_Leaf @ ($false) @ ($false))))) => (~ (! [C:nat]: (~ (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C))) => (B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C))))) | ~ (A = (suc @ (suc @ C))))))) | ~ ((A = zero_zero_nat) => (~ (B = (vEBT_Leaf @ ($false) @ ($false))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6378])). 159.59/70.63 thf(3741,axiom,((~ (ord_le3102999989581377725nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5063_le__minus__one__simps_I4_J)). 159.59/70.63 thf(20290,plain,((~ (ord_le3102999989581377725nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3741])). 159.59/70.63 thf(1708,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/sandbox/benchmark/theBenchmark.p',fact_1239_comm__semiring__class_Odistrib)). 159.59/70.63 thf(13772,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)],[1708])). 159.59/70.63 thf(7695,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/sandbox/benchmark/theBenchmark.p',fact_9545_xor__nat__rec)). 159.59/70.63 thf(34840,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)],[7695])). 159.59/70.63 thf(1260,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/sandbox/benchmark/theBenchmark.p',fact_5522_abs__triangle__ineq)). 159.59/70.63 thf(12329,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)],[1260])). 159.59/70.63 thf(5907,axiom,((! [A:nat]: ((power_power_real @ one_one_real @ A) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_power__one)). 159.59/70.63 thf(28092,plain,((! [A:nat]: ((power_power_real @ one_one_real @ A) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5907])). 159.59/70.63 thf(5378,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1914_not__gr0)). 159.59/70.63 thf(25983,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5378])). 159.59/70.63 thf(5562,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/sandbox/benchmark/theBenchmark.p',fact_4586_signed__take__bit__int__less__eq)). 159.59/70.63 thf(26640,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)],[5562])). 159.59/70.63 thf(6897,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ one_one_nat) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5987_and__numerals_I8_J)). 159.59/70.63 thf(31846,plain,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ one_one_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6897])). 159.59/70.63 thf(4664,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_le__SucI)). 159.59/70.63 thf(23384,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)],[4664])). 159.59/70.63 thf(5661,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = A) = ((A = zero_zero_int) | (B = one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1622_mult__cancel__left2)). 159.59/70.63 thf(26986,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)],[5661])). 159.59/70.63 thf(2959,axiom,(((cis @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) = (uminus1482373934393186551omplex @ imaginary_unit))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9374_cis__minus__pi__half)). 159.59/70.63 thf(17784,plain,(((cis @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) = (uminus1482373934393186551omplex @ imaginary_unit))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2959])). 159.59/70.63 thf(3669,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ C @ B) @ A) = (plus_plus_int @ (divide_divide_int @ C @ A) @ (divide_divide_int @ B @ A))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4094_div__plus__div__distrib__dvd__right)). 159.59/70.63 thf(20037,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ (plus_plus_int @ C @ B) @ A) = (plus_plus_int @ (divide_divide_int @ C @ A) @ (divide_divide_int @ B @ A))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3669])). 159.59/70.63 thf(6145,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ (modulo_modulo_nat @ A @ B) @ B) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3412_mod__div__trivial)). 159.59/70.63 thf(28900,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)],[6145])). 159.59/70.63 thf(1437,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ C @ D) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2226_mult__le__less__imp__less)). 159.59/70.63 thf(12938,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ C @ D) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1437])). 159.59/70.63 thf(1809,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/sandbox/benchmark/theBenchmark.p',fact_1298_group__cancel_Osub1)). 159.59/70.63 thf(14092,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)],[1809])). 159.59/70.63 thf(6488,axiom,((! [A:complex]: ((power_power_complex @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_power__one__right)). 159.59/70.63 thf(30207,plain,((! [A:complex]: ((power_power_complex @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6488])). 159.59/70.63 thf(3264,axiom,((! [A:extended_enat,B:extended_enat]: (((B != zero_z5237406670263579293d_enat) & (A != zero_z5237406670263579293d_enat)) <= ((times_7803423173614009249d_enat @ A @ B) != zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1868_mult__not__zero)). 159.59/70.63 thf(18757,plain,((! [A:extended_enat,B:extended_enat]: ((~ (B = zero_z5237406670263579293d_enat) & ~ (A = zero_z5237406670263579293d_enat)) | ((times_7803423173614009249d_enat @ A @ B) = zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3264])). 159.59/70.63 thf(297,axiom,((tan_real = (^ [A:real]: (divide_divide_real @ (sin_real @ A) @ (cos_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7261_tan__def)). 159.59/70.63 thf(9171,plain,(((tan_real) = (^ [A:real]: (divide_divide_real @ (sin_real @ A) @ (cos_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 159.59/70.63 thf(7548,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => (((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D)) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C))) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1342_add__le__add__imp__diff__le)). 159.59/70.63 thf(34332,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => (((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D)) | ~ (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)],[7548])). 159.59/70.63 thf(5546,axiom,((! [A:option_nat]: ((! [B:nat]: (A != (some_nat @ B))) = (A = none_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_not__Some__eq)). 159.59/70.63 thf(26592,plain,((! [A:option_nat]: ((! [B:nat]: ~ (A = (some_nat @ B))) = (A = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5546])). 159.59/70.63 thf(2263,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/sandbox/benchmark/theBenchmark.p',fact_6377_bit__and__int__iff)). 159.59/70.63 thf(15552,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)],[2263])). 159.59/70.63 thf(6891,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ B @ A) <= (A = (times_times_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3937_dvdI)). 159.59/70.63 thf(31827,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)],[6891])). 159.59/70.63 thf(4404,axiom,((! [A:real,B:real,C:real]: (((log @ B @ (powr_real @ A @ C)) = (times_times_real @ C @ (log @ B @ A))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7255_log__powr)). 159.59/70.63 thf(22358,plain,((! [A:real,B:real,C:real]: (((log @ B @ (powr_real @ A @ C)) = (times_times_real @ C @ (log @ B @ A))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4404])). 159.59/70.63 thf(4464,axiom,((! [A:(num > (num > $o)),B:num,C:num]: (((! [D:num]: (A @ D @ D)) => ((A @ B @ C) <= (! [D:num,E:num]: ((A @ E @ D) => (A @ D @ E))))) <= (! [D:num,E:num]: ((ord_less_num @ D @ E) => (A @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2810_linorder__less__wlog)). 159.59/70.63 thf(22590,plain,((! [A:(num > (num > $o)),B:num,C:num]: (((! [D:num]: (A @ D @ D)) => ((A @ B @ C) | ~ (! [D:num,E:num]: ((A @ E @ D) => (A @ D @ E))))) | ~ (! [D:num,E:num]: ((ord_less_num @ D @ E) => (A @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4464])). 159.59/70.63 thf(4453,axiom,((! [A:nat,B:nat,C:nat]: ((A = (minus_minus_nat @ C @ B)) <= ((plus_plus_nat @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1276_add__implies__diff)). 159.59/70.63 thf(22514,plain,((! [A:nat,B:nat,C:nat]: ((A = (minus_minus_nat @ C @ B)) | ~ ((plus_plus_nat @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4453])). 159.59/70.63 thf(1098,axiom,((divide_divide_nat = (^ [A:nat,B:nat]: (nat2 @ (divide_divide_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9443_nat__div__as__int)). 159.59/70.63 thf(11777,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)],[1098])). 159.59/70.63 thf(837,axiom,((! [A:nat,B:nat]: ((bit_se1745604003318907178nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ (ord_less_nat @ B @ A)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4906_take__bit__of__exp)). 159.59/70.63 thf(10951,plain,((! [A:nat,B:nat]: ((bit_se1745604003318907178nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ (ord_less_nat @ B @ A)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[837])). 159.59/70.63 thf(5411,axiom,((! [A:num]: ((numera6620942414471956472nteger @ A) != (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5089_numeral__neq__neg__one)). 159.59/70.63 thf(26096,plain,((! [A:num]: ~ ((numera6620942414471956472nteger @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5411])). 159.59/70.63 thf(1498,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5937_and_Oidem)). 159.59/70.63 thf(13137,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1498])). 159.59/70.63 thf(1033,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((~ (ord_le2932123472753598470d_enat @ C @ A)) <= (ord_le72135733267957522d_enat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4493_pinf_I6_J)). 159.59/70.63 thf(11559,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: (~ (ord_le2932123472753598470d_enat @ C @ A) | ~ (ord_le72135733267957522d_enat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033])). 159.59/70.63 thf(227,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ C) = (ord_less_eq_real @ B @ (real_V1485227260804924795R_real @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9256_pos__divideR__le__eq)). 159.59/70.63 thf(8945,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ C) = (ord_less_eq_real @ B @ (real_V1485227260804924795R_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[227])). 159.59/70.63 thf(873,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/sandbox/benchmark/theBenchmark.p',fact_3554_unique__euclidean__semiring__numeral__class_Omod__mult2__eq)). 159.59/70.63 thf(11065,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)],[873])). 159.59/70.63 thf(2825,axiom,((! [A:set_nat]: ((finite_finite_nat @ A) => (? [B:list_nat]: ((set_nat2 @ B) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3638_finite__list)). 159.59/70.63 thf(17335,plain,((! [A:set_nat]: ((finite_finite_nat @ A) => (? [B:list_nat]: ((set_nat2 @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2825])). 159.59/70.63 thf(2160,axiom,((! [A:nat,B:nat,C:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6617_of__nat__power__le__of__nat__cancel__iff)). 159.59/70.63 thf(15215,plain,((! [A:nat,B:nat,C:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2160])). 159.59/70.63 thf(117,axiom,((! [A:real,B:real]: (((ord_less_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real) => ((archim2898591450579166408c_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)))) & (((archim2898591450579166408c_real @ (plus_plus_real @ A @ B)) = (minus_minus_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real)) <= (~ (ord_less_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9121_frac__add)). 159.59/70.63 thf(8609,plain,((! [A:real,B:real]: (((ord_less_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real) => ((archim2898591450579166408c_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)))) & (((archim2898591450579166408c_real @ (plus_plus_real @ A @ B)) = (minus_minus_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real)) | (ord_less_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 159.59/70.63 thf(7481,axiom,((! [A:nat,B:list_o,C:$o]: ((((list_update_o @ B @ A @ C) = B) = ((nth_o @ B @ A) = C)) <= (ord_less_nat @ A @ (size_size_list_o @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_list__update__same__conv)). 159.59/70.63 thf(34131,plain,((! [A:nat,B:list_o,C:$o]: ((((list_update_o @ B @ A @ C) = B) = ((nth_o @ B @ A) = C)) | ~ (ord_less_nat @ A @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7481])). 159.59/70.63 thf(5216,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (power_power_real @ A @ (suc @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2448_power__Suc__le__self)). 159.59/70.63 thf(25320,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (power_power_real @ A @ (suc @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5216])). 159.59/70.63 thf(962,axiom,(((inverse_inverse_real @ (numeral_numeral_real @ one)) = (numeral_numeral_real @ one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9035_inverse__numeral__1)). 159.59/70.63 thf(11328,plain,(((inverse_inverse_real @ (numeral_numeral_real @ one)) = (numeral_numeral_real @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[962])). 159.59/70.63 thf(2057,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/sandbox/benchmark/theBenchmark.p',fact_5196_nonzero__neg__divide__eq__eq)). 159.59/70.63 thf(14886,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)],[2057])). 159.59/70.63 thf(4825,axiom,((! [A:real]: ((sqrt @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (sqrt @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6372_real__sqrt__minus)). 159.59/70.63 thf(23948,plain,((! [A:real]: ((sqrt @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4825])). 159.59/70.63 thf(1742,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ C @ B)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3948_dvd__mult)). 159.59/70.63 thf(13879,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)],[1742])). 159.59/70.63 thf(2498,axiom,((ord_less_int @ (uminus_uminus_int @ one_one_int) @ one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5080_less__minus__one__simps_I2_J)). 159.59/70.63 thf(16296,plain,((ord_less_int @ (uminus_uminus_int @ one_one_int) @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2498])). 159.59/70.63 thf(7190,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (case_nat_o @ ($false) @ (ord_less_eq_nat @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9734_less__eq__nat_Osimps_I2_J)). 159.59/70.63 thf(33109,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (case_nat_o @ ($false) @ (ord_less_eq_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7190])). 159.59/70.63 thf(6025,axiom,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = ((A = zero_zero_int) | (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1485_mult__cancel__left)). 159.59/70.63 thf(28521,plain,((! [A:int,B:int,C:int]: (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = ((A = zero_zero_int) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6025])). 159.59/70.63 thf(7043,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (suc @ (numeral_numeral_nat @ (bit0 @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5592_eval__nat__numeral_I3_J)). 159.59/70.63 thf(32495,plain,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (suc @ (numeral_numeral_nat @ (bit0 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7043])). 159.59/70.63 thf(2708,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ C) = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ A @ (divide6298287555418463151nteger @ B @ C)) @ (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ (modulo364778990260209775nteger @ B @ C)) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3527_div__mult1__eq)). 159.59/70.63 thf(16990,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ C) = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ A @ (divide6298287555418463151nteger @ B @ C)) @ (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ (modulo364778990260209775nteger @ B @ C)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2708])). 159.59/70.63 thf(5271,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4671_neg__less__eq__nonneg)). 159.59/70.63 thf(25509,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)],[5271])). 159.59/70.63 thf(526,axiom,((! [A:real,B:real]: ((real_V1803761363581548252l_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V1803761363581548252l_real @ A) @ (real_V1803761363581548252l_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7331_of__real__divide)). 159.59/70.63 thf(9925,plain,((! [A:real,B:real]: ((real_V1803761363581548252l_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (real_V1803761363581548252l_real @ A) @ (real_V1803761363581548252l_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[526])). 159.59/70.63 thf(1271,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/sandbox/benchmark/theBenchmark.p',fact_2246_mult__less__cancel__left)). 159.59/70.63 thf(12361,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)],[1271])). 159.59/70.63 thf(578,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ A @ B) => ((((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ D))) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9238_scaleR__mono)). 159.59/70.63 thf(10090,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ A @ B) => (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ D))) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[578])). 159.59/70.63 thf(1430,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1610_diff__gt__0__iff__gt)). 159.59/70.63 thf(12913,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)],[1430])). 159.59/70.63 thf(3696,axiom,((! [A:int,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => (((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)))) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3788_even__succ__mod__exp)). 159.59/70.63 thf(20120,plain,((! [A:int,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => (((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)))) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3696])). 159.59/70.63 thf(8161,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/sandbox/benchmark/theBenchmark.p',fact_1788_power2__eq__iff__nonneg)). 159.59/70.63 thf(36353,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)],[8161])). 159.59/70.63 thf(2836,axiom,((! [A:(nat > real),B:real,C:nat]: ((~ (! [D:(nat > real)]: ~ (! [E:real]: ((groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (A @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ C)) = (times_times_real @ (minus_minus_real @ E @ B) @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (D @ F) @ (power_power_real @ E @ F))) @ (set_ord_lessThan_nat @ C))))))) <= ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D))) @ (set_ord_atMost_nat @ C)) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8884_polyfun__linear__factor__root)). 159.59/70.63 thf(17367,plain,((! [A:(nat > real),B:real,C:nat]: (~ (! [D:(nat > real)]: ~ (! [E:real]: ((groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (A @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ C)) = (times_times_real @ (minus_minus_real @ E @ B) @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (D @ F) @ (power_power_real @ E @ F))) @ (set_ord_lessThan_nat @ C)))))) | ~ ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D))) @ (set_ord_atMost_nat @ C)) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2836])). 159.59/70.63 thf(3896,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/sandbox/benchmark/theBenchmark.p',fact_9641_csqrt_Ocode)). 159.59/70.63 thf(20793,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)],[3896])). 159.59/70.63 thf(3150,axiom,((! [A:int,B:int]: ((A != B) = ((ord_less_int @ A @ B) | (ord_less_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2852_linorder__neq__iff)). 159.59/70.63 thf(18389,plain,((! [A:int,B:int]: ((~ (A = B)) = ((ord_less_int @ A @ B) | (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3150])). 159.59/70.63 thf(4396,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((times_times_int @ (divide_divide_int @ B @ A) @ C) = (divide_divide_int @ (times_times_int @ B @ C) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4073_dvd__div__mult)). 159.59/70.63 thf(22332,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ B) => ((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)],[4396])). 159.59/70.63 thf(6589,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (~ ((A != zero_zero_nat) => (! [C:nat]: (((dvd_dvd_nat @ C @ one_one_nat) => (((((divide_divide_nat @ B @ A) != (times_times_nat @ B @ C)) <= ((times_times_nat @ A @ C) = one_one_nat)) <= ((divide_divide_nat @ one_one_nat @ C) = A)) <= ((divide_divide_nat @ one_one_nat @ A) = C))) <= (C != zero_zero_nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4193_is__unitE)). 159.59/70.63 thf(30557,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (~ ((~ (A = zero_zero_nat)) => (! [C:nat]: (((dvd_dvd_nat @ C @ one_one_nat) => (~ ((divide_divide_nat @ B @ A) = (times_times_nat @ B @ C)) | ~ ((times_times_nat @ A @ C) = one_one_nat) | ~ ((divide_divide_nat @ one_one_nat @ C) = A) | ~ ((divide_divide_nat @ one_one_nat @ A) = C))) | (C = zero_zero_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6589])). 159.59/70.63 thf(3616,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((ord_less_eq_int @ A @ B) & (ord_less_int @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1321_add__mono__thms__linordered__field_I4_J)). 159.59/70.63 thf(19871,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ ((ord_less_eq_int @ A @ B) & (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3616])). 159.59/70.63 thf(5768,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))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = one_one_Code_integer))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5319_minus__one__power__iff)). 159.59/70.63 thf(27349,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))) & ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5768])). 159.59/70.63 thf(5245,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/sandbox/benchmark/theBenchmark.p',fact_840_diff__mult__distrib)). 159.59/70.63 thf(25419,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)],[5245])). 159.59/70.63 thf(185,axiom,((! [A:real,B:real]: (((((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 @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ 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/sandbox/benchmark/theBenchmark.p',fact_7288_tan__mono__lt__eq)). 159.59/70.63 thf(8824,plain,((! [A:real,B:real]: (((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 @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ 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)],[185])). 159.59/70.63 thf(8108,axiom,((vEBT_vebt_member @ summary @ (vEBT_VEBT_high @ ma @ na))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461__092_060open_062vebt__member_Asummary_A_Ihigh_Ama_An_J_092_060close_062)). 159.59/70.63 thf(36173,plain,((vEBT_vebt_member @ summary @ (vEBT_VEBT_high @ ma @ na))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8108])). 159.59/70.63 thf(4812,axiom,((! [A:nat]: ((image_nat_nat @ suc @ (set_ord_atMost_nat @ A)) = (set_or1269000886237332187st_nat @ one_one_nat @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9808_image__Suc__atMost)). 159.59/70.63 thf(23878,plain,((! [A:nat]: ((image_nat_nat @ (suc) @ (set_ord_atMost_nat @ A)) = (set_or1269000886237332187st_nat @ one_one_nat @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4812])). 159.59/70.63 thf(4502,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/sandbox/benchmark/theBenchmark.p',fact_5868_neg__numeral__power__le__of__int__cancel__iff)). 159.59/70.63 thf(22731,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)],[4502])). 159.59/70.63 thf(5983,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/sandbox/benchmark/theBenchmark.p',fact_6186_or__minus__numerals_I4_J)). 159.59/70.63 thf(28387,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)],[5983])). 159.59/70.63 thf(6616,axiom,((! [A:nat,B:real]: (((root @ A @ (times_times_real @ (sgn_sgn_real @ B) @ (power_power_real @ (abs_abs_real @ B) @ A))) = B) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9504_root__sgn__power)). 159.59/70.63 thf(30656,plain,((! [A:nat,B:real]: (((root @ A @ (times_times_real @ (sgn_sgn_real @ B) @ (power_power_real @ (abs_abs_real @ B) @ A))) = B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6616])). 159.59/70.63 thf(2839,axiom,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2923211474154528505it_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4875_even__take__bit__eq)). 159.59/70.63 thf(17382,plain,((! [A:nat,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2923211474154528505it_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2839])). 159.59/70.63 thf(293,axiom,((! [A:code_integer,B:code_integer,C:nat]: ((comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ A @ B) @ C) = (groups7501900531339628137nteger @ (^ [D:nat]: (times_3573771949741848930nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ (binomial @ C @ D)) @ (comm_s8582702949713902594nteger @ A @ D)) @ (comm_s8582702949713902594nteger @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9153_pochhammer__binomial__sum)). 159.59/70.63 thf(9137,plain,((! [A:code_integer,B:code_integer,C:nat]: ((comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ A @ B) @ C) = (groups7501900531339628137nteger @ (^ [D:nat]: (times_3573771949741848930nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ (binomial @ C @ D)) @ (comm_s8582702949713902594nteger @ A @ D)) @ (comm_s8582702949713902594nteger @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[293])). 159.59/70.63 thf(6742,axiom,((! [A:num]: ((semiri1408675320244567234ct_nat @ (numeral_numeral_nat @ A)) = (times_times_nat @ (numeral_numeral_nat @ A) @ (semiri1408675320244567234ct_nat @ (pred_numeral @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8114_fact__numeral)). 159.59/70.63 thf(31236,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)],[6742])). 159.59/70.63 thf(5569,axiom,(((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4851_diff__numeral__special_I10_J)). 159.59/70.63 thf(26662,plain,(((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5569])). 159.59/70.63 thf(7846,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/sandbox/benchmark/theBenchmark.p',fact_4863_Power_Oring__1__class_Opower__minus__even)). 159.59/70.63 thf(35331,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)],[7846])). 159.59/70.63 thf(6842,axiom,((! [A:vEBT_VEBT,B:nat]: (((((! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ G @ C @ E)) => ((((vEBT_invar_vebt @ E @ F) => (((((~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ E @ H))) => (~ (! [H:vEBT_VEBT]: ((~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))))) <= (G = (plus_plus_nat @ D @ F))) <= (F = (suc @ D))) <= ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ 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:nat,I:nat]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ H @ I)) @ G @ C @ E)) => ((((vEBT_invar_vebt @ E @ F) => (((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => ((((((ord_less_eq_nat @ H @ I) => ((~ ((! [J:nat]: ((! [K:nat]: (((ord_less_eq_nat @ K @ I) & (ord_less_nat @ H @ K)) <= ((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)))) <= (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)))) <= (H != I))) <= (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ G)))) <= ((! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K))))) <= (H = I))) <= (! [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))))) <= (G = (plus_plus_nat @ D @ F))) <= (F = (suc @ D))))) <= (! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ J @ D)))) <= (B = G))))) <= (! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat,H:nat,I:nat]: ((((((((G = (plus_plus_nat @ D @ F)) => ((! [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)))) => (((! [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]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ I @ D)) <= ((vEBT_VEBT_high @ I @ D) = J)) & ! [K:nat]: ((((vEBT_VEBT_high @ K @ D) = J) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ K @ D))) => ((ord_less_eq_nat @ K @ I) & (ord_less_nat @ H @ K)))))))) <= (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ G))))))) <= (F = D)) <= ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F))) <= (vEBT_invar_vebt @ E @ F)) <= (! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ J @ D)))) <= (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]: (((B = G) => (((((F = D) => (((~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ E @ H))) => (~ (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))))))) <= (G = (plus_plus_nat @ D @ F)))) <= ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F))) <= (vEBT_invar_vebt @ E @ F)) <= (! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ D) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ G @ C @ E))))) <= ((B != (suc @ zero_zero_nat)) <= (? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2565_invar__vebt_Ocases)). 159.59/70.63 thf(31583,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ G @ C @ E)) => (((vEBT_invar_vebt @ E @ F) => (((~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ E @ H))) => (~ (! [H:vEBT_VEBT]: (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))))) | ~ (G = (plus_plus_nat @ D @ F)) | ~ (F = (suc @ D)) | ~ ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ 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:nat,I:nat]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ H @ I)) @ G @ C @ E)) => (((vEBT_invar_vebt @ E @ F) => (((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (((ord_less_eq_nat @ H @ I) => (~ (! [J:nat]: ((! [K:nat]: (((ord_less_eq_nat @ K @ I) & (ord_less_nat @ H @ K)) | ~ ((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)))) | ~ (ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F))) | (H = I)) | ~ (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ G)))) | ~ (! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (~ (? [K:nat]: (vEBT_V8194947554948674370ptions @ J @ K)))) | ~ (H = I)) | ~ (! [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)))) | ~ (G = (plus_plus_nat @ D @ F)) | ~ (F = (suc @ D))))) | ~ (! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ J @ D))) | ~ (B = G)))) | ~ (! [C:list_VEBT_VEBT,D:nat,E:vEBT_VEBT,F:nat,G:nat,H:nat,I:nat]: (((G = (plus_plus_nat @ D @ F)) => ((! [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)))) => ((! [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]: ((ord_less_nat @ J @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) => (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ I @ D)) | ~ ((vEBT_VEBT_high @ I @ D) = J)) & ! [K:nat]: ((((vEBT_VEBT_high @ K @ D) = J) & (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ C @ J) @ (vEBT_VEBT_low @ K @ D))) => ((ord_less_eq_nat @ K @ I) & (ord_less_nat @ H @ K))))))) | ~ (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ G))))))) | ~ (F = D) | ~ ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) | ~ (vEBT_invar_vebt @ E @ F) | ~ (! [J:vEBT_VEBT]: ((member_VEBT_VEBT @ J @ (set_VEBT_VEBT2 @ C)) => (vEBT_invar_vebt @ J @ D))) | ~ (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]: (((B = G) => (((F = D) => (((~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ E @ H))) => (~ (! [H:vEBT_VEBT]: ((member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)) => (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))))))) | ~ (G = (plus_plus_nat @ D @ F)))) | ~ ((size_s6755466524823107622T_VEBT @ C) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ F)) | ~ (vEBT_invar_vebt @ E @ F) | ~ (! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ D) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ C)))))) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ G @ C @ E)))) | ~ (~ (B = (suc @ zero_zero_nat)) | ~ (? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D)))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6842])). 159.59/70.63 thf(3785,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (((plus_plus_int @ A @ B) = zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int)))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2023_add__nonneg__eq__0__iff)). 159.59/70.63 thf(20422,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (((plus_plus_int @ A @ B) = zero_zero_int) = ((A = zero_zero_int) & (B = zero_zero_int)))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3785])). 159.59/70.63 thf(4030,axiom,((! [A:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5055_ab__group__add__class_Oab__left__minus)). 159.59/70.63 thf(21197,plain,((! [A:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4030])). 159.59/70.63 thf(1914,axiom,((vEBT_VEBT_add = (vEBT_V4262088993061758097ft_nat @ plus_plus_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1030_add__def)). 159.59/70.63 thf(14433,plain,(((vEBT_VEBT_add) = (vEBT_V4262088993061758097ft_nat @ plus_plus_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1914])). 159.59/70.63 thf(3589,axiom,((! [A:real,B:nat]: ? [C:real]: (((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_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8138_Maclaurin__exp__le)). 159.59/70.63 thf(19775,plain,((! [A:real,B:nat]: ? [C:real]: (((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_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3589])). 159.59/70.63 thf(5250,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/sandbox/benchmark/theBenchmark.p',fact_5828_of__int__le__1__iff)). 159.59/70.63 thf(25438,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)],[5250])). 159.59/70.63 thf(6963,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ (times_times_int @ B @ A) @ B)) <= (ord_less_eq_int @ A @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2309_mult__left__le)). 159.59/70.63 thf(32094,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ (times_times_int @ B @ A) @ B)) | ~ (ord_less_eq_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6963])). 159.59/70.63 thf(6333,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3030_leI)). 159.59/70.63 thf(29590,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6333])). 159.59/70.63 thf(5847,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/sandbox/benchmark/theBenchmark.p',fact_8354_fact__double)). 159.59/70.63 thf(27862,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)],[5847])). 159.59/70.63 thf(6516,axiom,((! [A:real]: ((((sqrt @ A) = zero_zero_real) => (A = zero_zero_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6389_real__sqrt__eq__zero__cancel)). 159.59/70.63 thf(30296,plain,((! [A:real]: ((((sqrt @ A) = zero_zero_real) => (A = zero_zero_real)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6516])). 159.59/70.63 thf(6969,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/sandbox/benchmark/theBenchmark.p',fact_5286_power2__eq__1__iff)). 159.59/70.63 thf(32126,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)],[6969])). 159.59/70.63 thf(6034,axiom,(((bitM @ one) = one)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5886_semiring__norm_I26_J)). 159.59/70.63 thf(28547,plain,(((bitM @ one) = one)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6034])). 159.59/70.63 thf(3419,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ B @ A) <= (~ (ord_le2932123472753598470d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3062_not__le__imp__less)). 159.59/70.63 thf(19245,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ B @ A) | (ord_le2932123472753598470d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3419])). 159.59/70.63 thf(6818,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ B @ A) <= (~ (ord_less_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3029_leI)). 159.59/70.63 thf(31501,plain,((! [A:num,B:num]: ((ord_less_eq_num @ B @ A) | (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6818])). 159.59/70.63 thf(1562,axiom,((! [A:int,B:int,C:nat]: (((bit_se1146084159140164899it_int @ (plus_plus_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ C) = (((C != zero_zero_nat) => (bit_se1146084159140164899it_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ C)) & ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) <= (C = zero_zero_nat)))) <= (! [D:nat]: ~ (bit_se1146084159140164899it_int @ A @ (suc @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6464_bit__sum__mult__2__cases)). 159.59/70.63 thf(13326,plain,((! [A:int,B:int,C:nat]: (((bit_se1146084159140164899it_int @ (plus_plus_int @ A @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) @ C) = (((~ (C = zero_zero_nat)) => (bit_se1146084159140164899it_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) @ C)) & (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) | ~ (C = zero_zero_nat)))) | ~ (! [D:nat]: ~ (bit_se1146084159140164899it_int @ A @ (suc @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562])). 159.59/70.63 thf(6356,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/sandbox/benchmark/theBenchmark.p',fact_3085_order_Ostrict__trans1)). 159.59/70.63 thf(29662,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)],[6356])). 159.59/70.63 thf(3507,axiom,((! [A:extended_enat,B:extended_enat]: (((times_7803423173614009249d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((B = zero_z5237406670263579293d_enat) | (A = zero_z5237406670263579293d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1486_mult__eq__0__iff)). 159.59/70.63 thf(19511,plain,((! [A:extended_enat,B:extended_enat]: (((times_7803423173614009249d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((B = zero_z5237406670263579293d_enat) | (A = zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3507])). 159.59/70.63 thf(2880,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ (uminus_uminus_real @ B)) = zero_zero_real) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4655_real__add__minus__iff)). 159.59/70.63 thf(17514,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)],[2880])). 159.59/70.63 thf(417,axiom,((! [A:nat,B:nat,C:int]: (((comm_s4660882817536571857er_int @ C @ B) = (times_times_int @ (comm_s4660882817536571857er_int @ C @ A) @ (comm_s4660882817536571857er_int @ (plus_plus_int @ C @ (semiri1314217659103216013at_int @ A)) @ (minus_minus_nat @ B @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8313_pochhammer__product)). 159.59/70.63 thf(9562,plain,((! [A:nat,B:nat,C:int]: (((comm_s4660882817536571857er_int @ C @ B) = (times_times_int @ (comm_s4660882817536571857er_int @ C @ A) @ (comm_s4660882817536571857er_int @ (plus_plus_int @ C @ (semiri1314217659103216013at_int @ A)) @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[417])). 159.59/70.63 thf(6766,axiom,((! [A:set_nat,B:set_nat,C:(nat > int),D:(nat > nat),E:(nat > int)]: ((finite_finite_nat @ A) => ((finite_finite_nat @ B) => (((! [F:nat]: ((member_nat @ F @ A) => (? [G:nat]: ((member_nat @ G @ B) & (ord_less_eq_int @ (E @ F) @ (C @ G)) & ((D @ G) = F))))) => (ord_less_eq_int @ (groups3539618377306564664at_int @ E @ A) @ (groups3539618377306564664at_int @ C @ B))) <= (! [F:nat]: ((ord_less_eq_int @ zero_zero_int @ (C @ F)) <= (member_nat @ F @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7462_sum__le__included)). 159.59/70.63 thf(31333,plain,((! [A:set_nat,B:set_nat,C:(nat > int),D:(nat > nat),E:(nat > int)]: ((finite_finite_nat @ A) => ((finite_finite_nat @ B) => (((! [F:nat]: ((member_nat @ F @ A) => (? [G:nat]: ((member_nat @ G @ B) & (ord_less_eq_int @ (E @ F) @ (C @ G)) & ((D @ G) = F))))) => (ord_less_eq_int @ (groups3539618377306564664at_int @ (E) @ A) @ (groups3539618377306564664at_int @ (C) @ B))) | ~ (! [F:nat]: ((ord_less_eq_int @ zero_zero_int @ (C @ F)) | ~ (member_nat @ F @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6766])). 159.59/70.63 thf(8027,axiom,((! [A:num]: ((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1682_power__zero__numeral)). 159.59/70.63 thf(35898,plain,((! [A:num]: ((power_power_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8027])). 159.59/70.63 thf(5608,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (times_times_nat @ (groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8808_prod_Oub__add__nat)). 159.59/70.63 thf(26806,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (times_times_nat @ (groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups708209901874060359at_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)],[5608])). 159.59/70.63 thf(544,axiom,((! [A:complex]: ((re @ (exp_complex @ A)) = (times_times_real @ (exp_real @ (re @ A)) @ (cos_real @ (im @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9665_Re__exp)). 159.59/70.63 thf(9985,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)],[544])). 159.59/70.63 thf(5520,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/sandbox/benchmark/theBenchmark.p',fact_695_add__leD1)). 159.59/70.63 thf(26518,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)],[5520])). 159.59/70.63 thf(2044,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((times_3573771949741848930nteger @ C @ (divide6298287555418463151nteger @ B @ A)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ C @ B) @ A)) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4077_div__mult__swap)). 159.59/70.63 thf(14848,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((times_3573771949741848930nteger @ C @ (divide6298287555418463151nteger @ B @ A)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ C @ B) @ A)) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2044])). 159.59/70.63 thf(1257,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ C) => ((dvd_dvd_Code_integer @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ C @ A)) = (dvd_dvd_Code_integer @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3804_div__dvd__div)). 159.59/70.63 thf(12318,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ C) => ((dvd_dvd_Code_integer @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ C @ A)) = (dvd_dvd_Code_integer @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257])). 159.59/70.63 thf(4323,axiom,((! [A:nat]: ((set_ord_lessThan_nat @ (suc @ A)) = (insert_nat @ A @ (set_ord_lessThan_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7916_lessThan__Suc)). 159.59/70.63 thf(22109,plain,((! [A:nat]: ((set_ord_lessThan_nat @ (suc @ A)) = (insert_nat @ A @ (set_ord_lessThan_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4323])). 159.59/70.63 thf(4678,axiom,((! [A:num]: ~ (ord_less_num @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2803_dual__order_Oirrefl)). 159.59/70.63 thf(23425,plain,((! [A:num]: ~ (ord_less_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4678])). 159.59/70.63 thf(1807,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/sandbox/benchmark/theBenchmark.p',fact_3421_mod__mult__self1)). 159.59/70.63 thf(14085,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)],[1807])). 159.59/70.63 thf(847,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ (divide_divide_int @ B @ A) @ C) = (dvd_dvd_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4100_div__unit__dvd__iff)). 159.59/70.63 thf(10983,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ (divide_divide_int @ B @ A) @ C) = (dvd_dvd_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[847])). 159.59/70.63 thf(4412,axiom,((! [A:nat]: ((ord_less_int @ zero_zero_int @ (semiri1314217659103216013at_int @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6589_of__nat__0__less__iff)). 159.59/70.63 thf(22390,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)],[4412])). 159.59/70.63 thf(4356,axiom,((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2056_zero__less__one__class_Ozero__le__one)). 159.59/70.63 thf(22208,plain,((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4356])). 159.59/70.63 thf(4689,axiom,((! [A:vEBT_VEBT]: ((~ (vEBT_VEBT_minNull @ A)) => (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_not__min__Null__member)). 159.59/70.63 thf(23467,plain,((! [A:vEBT_VEBT]: ((~ (vEBT_VEBT_minNull @ A)) => (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4689])). 159.59/70.63 thf(5780,axiom,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6020_and__numerals_I6_J)). 159.59/70.63 thf(27388,plain,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5780])). 159.59/70.63 thf(6337,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/sandbox/benchmark/theBenchmark.p',fact_6805_powser__zero)). 159.59/70.63 thf(29601,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)],[6337])). 159.59/70.63 thf(2790,axiom,((! [A:real]: (ord_less_eq_real @ (sin_real @ A) @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6815_sin__le__one)). 159.59/70.63 thf(17235,plain,((! [A:real]: (ord_less_eq_real @ (sin_real @ A) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2790])). 159.59/70.63 thf(5173,axiom,((! [A:nat]: (((numeral_numeral_nat @ (num_of_nat @ A)) = A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9787_numeral__num__of__nat)). 159.59/70.63 thf(25160,plain,((! [A:nat]: (((numeral_numeral_nat @ (num_of_nat @ A)) = A) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5173])). 159.59/70.63 thf(1346,axiom,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((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)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7207_cos__tan)). 159.59/70.63 thf(12596,plain,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((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)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346])). 159.59/70.63 thf(7888,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:list_VEBT_VEBT,J:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) & (ord_less_nat @ A @ B)) => (((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((((vEBT_VEBT_low @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F) => ((((((vEBT_VEBT_minNull @ G) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ H @ J) @ B) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ J @ E)) = none_nat) @ A @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ J @ E)))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ I @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ J @ E)))))))) @ C))) @ D @ I @ (vEBT_vebt_delete @ J @ E)))) & ((~ (vEBT_VEBT_minNull @ G)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ H @ J) @ B) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (plus_plus_nat @ (times_times_nat @ E @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ I @ E)))) @ C))) @ D @ I @ J)))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H))) <= (I = (list_u1324408373059187874T_VEBT @ H @ E @ G))) <= (G = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ E) @ F)))) <= ((vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = E))) <= (A != C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1397_del__x__not__mi)). 159.59/70.63 thf(35464,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:list_VEBT_VEBT,J:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) & (ord_less_nat @ A @ B)) => (((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((((vEBT_VEBT_low @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F) => ((((vEBT_VEBT_minNull @ G) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ H @ J) @ B) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ J @ E)) = none_nat) @ A @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ J @ E)))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ I @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ J @ E)))))))) @ C))) @ D @ I @ (vEBT_vebt_delete @ J @ E)))) & ((~ (vEBT_VEBT_minNull @ G)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ H @ J) @ B) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (plus_plus_nat @ (times_times_nat @ E @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ I @ E)))) @ C))) @ D @ I @ J)))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)) | ~ (I = (list_u1324408373059187874T_VEBT @ H @ E @ G)) | ~ (G = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ E) @ F)))) | ~ ((vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = E))) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7888])). 159.59/70.63 thf(3970,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/sandbox/benchmark/theBenchmark.p',fact_1396_zdiv__numeral__Bit0)). 159.59/70.63 thf(21023,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)],[3970])). 159.59/70.63 thf(5673,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_maxt @ A) = B) => ((! [C:$o,D:$o]: ((~ (((D) => (B = (some_nat @ one_one_nat))) & ((~ (D)) => (((C) => (B = (some_nat @ zero_zero_nat))) & ((~ (C)) => (B = none_nat)))))) <= (A = (vEBT_Leaf @ C @ D)))) => ((~ (! [C:nat,D:nat]: ((? [E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))) => (B != (some_nat @ D))))) <= ((? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) => (B != none_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2409_vebt__maxt_Oelims)). 159.59/70.63 thf(27025,plain,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_maxt @ A) = B) => ((! [C:$o,D:$o]: (~ (((D) => (B = (some_nat @ one_one_nat))) & ((~ (D)) => (((C) => (B = (some_nat @ zero_zero_nat))) & ((~ (C)) => (B = none_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)) @ E @ F @ G))) => (~ (B = (some_nat @ D))))) | ~ ((? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) => (~ (B = none_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5673])). 159.59/70.63 thf(5924,axiom,((bit_se2925701944663578781it_nat = (^ [A:nat,B:nat]: (bit_se727722235901077358nd_nat @ B @ (bit_se2002935070580805687sk_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6036_take__bit__eq__mask)). 159.59/70.63 thf(28144,plain,(((bit_se2925701944663578781it_nat) = (^ [A:nat,B:nat]: (bit_se727722235901077358nd_nat @ B @ (bit_se2002935070580805687sk_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5924])). 159.59/70.63 thf(4477,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 @ zero_zero_int @ A) | (ord_less_eq_int @ A @ zero_zero_int)) & ((ord_less_eq_int @ zero_zero_int @ B) | (ord_less_eq_int @ B @ zero_zero_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5555_abs__eq__mult)). 159.59/70.63 thf(22650,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 @ zero_zero_int @ A) | (ord_less_eq_int @ A @ zero_zero_int)) & ((ord_less_eq_int @ zero_zero_int @ B) | (ord_less_eq_int @ B @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4477])). 159.59/70.63 thf(4187,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/sandbox/benchmark/theBenchmark.p',fact_4488_of__bool__odd__eq__mod__2)). 159.59/70.63 thf(21678,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)],[4187])). 159.59/70.63 thf(6734,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_le__antisym)). 159.59/70.63 thf(31211,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (A = B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6734])). 159.59/70.63 thf(6782,axiom,((! [A:nat,B:nat,C:(nat > real)]: ((ord_less_eq_nat @ A @ B) => ((times_times_real @ (groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (times_times_real @ (C @ A) @ (groups129246275422532515t_real @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8745_prod_OSuc__reindex__ivl)). 159.59/70.63 thf(31393,plain,((! [A:nat,B:nat,C:(nat > real)]: ((ord_less_eq_nat @ A @ B) => ((times_times_real @ (groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (times_times_real @ (C @ A) @ (groups129246275422532515t_real @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6782])). 159.59/70.63 thf(3177,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => ((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2350_add__frac__num)). 159.59/70.63 thf(18472,plain,((! [A:complex,B:complex,C:complex]: ((~ (A = zero_zero_complex)) => ((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = (divide1717551699836669952omplex @ (plus_plus_complex @ B @ (times_times_complex @ C @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3177])). 159.59/70.63 thf(7204,axiom,((! [A:int]: ((times_times_int @ (uminus_uminus_int @ (numeral_numeral_int @ one)) @ A) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5202_mult__1s__ring__1_I1_J)). 159.59/70.63 thf(33154,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)],[7204])). 159.59/70.63 thf(4786,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/sandbox/benchmark/theBenchmark.p',fact_5714_signed__take__bit__numeral__minus__bit0)). 159.59/70.63 thf(23785,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)],[4786])). 159.59/70.63 thf(909,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1880_add_Ocomm__neutral)). 159.59/70.63 thf(11165,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[909])). 159.59/70.63 thf(7302,axiom,((! [A:num]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (uminus_uminus_real @ one_one_real)) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4749_numeral__eq__neg__one__iff)). 159.59/70.63 thf(33491,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)],[7302])). 159.59/70.63 thf(5857,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ (modulo_modulo_nat @ B @ C)) <= (dvd_dvd_nat @ A @ C)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4027_dvd__mod)). 159.59/70.63 thf(27896,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (modulo_modulo_nat @ B @ C)) | ~ (dvd_dvd_nat @ A @ C) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5857])). 159.59/70.63 thf(2772,axiom,((! [A:(nat > real),B:real,C:real]: (((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)))))) <= (summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7051_powser__insidea)). 159.59/70.63 thf(17182,plain,((! [A:(nat > real),B:real,C:real]: (((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)))))) | ~ (summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2772])). 159.59/70.63 thf(3464,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (! [C:extended_enat]: ((C = zero_z5237406670263579293d_enat) <= (B = (plus_p3455044024723400733d_enat @ A @ C))))) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2111_canonically__ordered__monoid__add__class_OlessE)). 159.59/70.63 thf(19380,plain,((! [A:extended_enat,B:extended_enat]: (~ (! [C:extended_enat]: ((C = zero_z5237406670263579293d_enat) | ~ (B = (plus_p3455044024723400733d_enat @ A @ C)))) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3464])). 159.59/70.63 thf(4122,axiom,((topolo6980174941875973593q_real = (^ [A:(nat > real)]: (! [B:nat]: (ord_less_eq_real @ (A @ (suc @ B)) @ (A @ B)) | ! [B:nat]: (ord_less_eq_real @ (A @ B) @ (A @ (suc @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8032_monoseq__Suc)). 159.59/70.63 thf(21473,plain,(((topolo6980174941875973593q_real) = (^ [A:(nat > real)]: (! [B:nat]: (ord_less_eq_real @ (A @ (suc @ B)) @ (A @ B)) | ! [B:nat]: (ord_less_eq_real @ (A @ B) @ (A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4122])). 159.59/70.63 thf(6921,axiom,((modulo_modulo_nat = (^ [A:nat,B:nat]: (minus_minus_nat @ A @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3547_modulo__nat__def)). 159.59/70.63 thf(31931,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)],[6921])). 159.59/70.63 thf(1350,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/sandbox/benchmark/theBenchmark.p',fact_7338_sum__abs)). 159.59/70.63 thf(12609,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)],[1350])). 159.59/70.63 thf(4017,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/sandbox/benchmark/theBenchmark.p',fact_9616_or__not__numerals_I9_J)). 159.59/70.63 thf(21159,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)],[4017])). 159.59/70.63 thf(1598,axiom,((! [A:complex,B:complex,C:complex]: ((A != zero_zero_complex) => (((divide1717551699836669952omplex @ B @ A) = C) = (B = (times_times_complex @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2169_nonzero__divide__eq__eq)). 159.59/70.63 thf(13444,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)],[1598])). 159.59/70.63 thf(2859,axiom,((! [A:real,B:real,C:real,D: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)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2447_frac__less__eq)). 159.59/70.63 thf(17454,plain,((! [A:real,B:real,C:real,D: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) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2859])). 159.59/70.63 thf(2490,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/sandbox/benchmark/theBenchmark.p',fact_9455_div__abs__eq__div__nat)). 159.59/70.63 thf(16265,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)],[2490])). 159.59/70.63 thf(2554,axiom,((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6771_pi__half__ge__zero)). 159.59/70.63 thf(16464,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)],[2554])). 159.59/70.63 thf(395,axiom,((! [A:code_integer]: ((bit_se1080825931792720795nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5971_bit_Odisj__one__left)). 159.59/70.63 thf(9484,plain,((! [A:code_integer]: ((bit_se1080825931792720795nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])). 159.59/70.63 thf(2826,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (vEBT_VEBT_valid @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9622_valid__eq1)). 159.59/70.63 thf(17338,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (vEBT_VEBT_valid @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2826])). 159.59/70.63 thf(4295,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/sandbox/benchmark/theBenchmark.p',fact_7538_Complex__add__complex__of__real)). 159.59/70.63 thf(22032,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)],[4295])). 159.59/70.63 thf(6022,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (ord_max_nat @ A @ B) @ C) => (~ ((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_943_max_OboundedE)). 159.59/70.63 thf(28508,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (ord_max_nat @ A @ B) @ C) => (~ (~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6022])). 159.59/70.63 thf(320,axiom,((! [A:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ zero_z3403309356797280102nteger) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6578_of__nat__le__0__iff)). 159.59/70.63 thf(9237,plain,((! [A:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ zero_z3403309356797280102nteger) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 159.59/70.63 thf(5232,axiom,((! [A:real]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ one_one_int) = (ord_less_eq_real @ A @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6983_ceiling__le__one)). 159.59/70.63 thf(25383,plain,((! [A:real]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ one_one_int) = (ord_less_eq_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5232])). 159.59/70.63 thf(752,axiom,((! [A:nat]: ((bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ one_one_int)) = (bit_se2000444600071755411sk_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5999_take__bit__minus__one__eq__mask)). 159.59/70.63 thf(10683,plain,((! [A:nat]: ((bit_se2923211474154528505it_int @ A @ (uminus_uminus_int @ one_one_int)) = (bit_se2000444600071755411sk_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[752])). 159.59/70.63 thf(3091,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1737_divide__less__eq__1__pos)). 159.59/70.63 thf(18196,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3091])). 159.59/70.63 thf(7045,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))) & ((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/sandbox/benchmark/theBenchmark.p',fact_5316_minus__one__power__iff)). 159.59/70.63 thf(32500,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))) & ((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)],[7045])). 159.59/70.63 thf(4757,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ (log @ A @ B)) = (ord_less_eq_real @ one_one_real @ B))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6339_zero__le__log__cancel__iff)). 159.59/70.63 thf(23693,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ (log @ A @ B)) = (ord_less_eq_real @ one_one_real @ B))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4757])). 159.59/70.63 thf(1250,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3497_unique__euclidean__semiring__numeral__class_Opos__mod__sign)). 159.59/70.63 thf(12295,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (modulo_modulo_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250])). 159.59/70.63 thf(259,axiom,((! [A:nat]: ((cos_coeff @ (suc @ A)) = (divide_divide_real @ (uminus_uminus_real @ (sin_coeff @ A)) @ (semiri5074537144036343181t_real @ (suc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8156_cos__coeff__Suc)). 159.59/70.63 thf(9040,plain,((! [A:nat]: ((cos_coeff @ (suc @ A)) = (divide_divide_real @ (uminus_uminus_real @ (sin_coeff @ A)) @ (semiri5074537144036343181t_real @ (suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[259])). 159.59/70.63 thf(470,axiom,((! [A:$o]: ((divide6298287555418463151nteger @ (zero_n356916108424825756nteger @ A) @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4374_of__bool__half__eq__0)). 159.59/70.63 thf(9726,plain,((! [A:$o]: ((divide6298287555418463151nteger @ (zero_n356916108424825756nteger @ A) @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[470])). 159.59/70.63 thf(6975,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4119_le__imp__power__dvd)). 159.59/70.63 thf(32233,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6975])). 159.59/70.63 thf(3058,axiom,((! [A:nat,B:complex,C:complex,D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (times_times_complex @ (gbinomial_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ B) @ E) @ (power_power_complex @ C @ E)) @ (power_power_complex @ D @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A)) = (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (times_times_complex @ (gbinomial_complex @ (uminus1482373934393186551omplex @ B) @ E) @ (power_power_complex @ (uminus1482373934393186551omplex @ C) @ E)) @ (power_power_complex @ (plus_plus_complex @ C @ D) @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8941_gbinomial__partial__sum__poly)). 159.59/70.63 thf(18080,plain,((! [A:nat,B:complex,C:complex,D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (times_times_complex @ (gbinomial_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ B) @ E) @ (power_power_complex @ C @ E)) @ (power_power_complex @ D @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A)) = (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (times_times_complex @ (gbinomial_complex @ (uminus1482373934393186551omplex @ B) @ E) @ (power_power_complex @ (uminus1482373934393186551omplex @ C) @ E)) @ (power_power_complex @ (plus_plus_complex @ C @ D) @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3058])). 159.59/70.63 thf(4442,axiom,((! [A:int,B:int,C:int]: (((uminus_uminus_int @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ C))) <= (A = (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4965_group__cancel_Oneg1)). 159.59/70.63 thf(22479,plain,((! [A:int,B:int,C:int]: (((uminus_uminus_int @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ C))) | ~ (A = (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4442])). 159.59/70.63 thf(5274,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/sandbox/benchmark/theBenchmark.p',fact_1063_add__le__cancel__right)). 159.59/70.63 thf(25515,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)],[5274])). 159.59/70.63 thf(4286,axiom,((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2128_zero__less__one)). 159.59/70.63 thf(22001,plain,((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4286])). 159.59/70.63 thf(3902,axiom,((! [A:real]: ((ord_less_real @ A @ zero_zero_real) => ((abs_abs_real @ A) = (uminus_uminus_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5573_abs__of__neg)). 159.59/70.63 thf(20812,plain,((! [A:real]: ((ord_less_real @ A @ zero_zero_real) => ((abs_abs_real @ A) = (uminus_uminus_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3902])). 159.59/70.63 thf(6729,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/sandbox/benchmark/theBenchmark.p',fact_903_max_OcoboundedI1)). 159.59/70.63 thf(31196,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)],[6729])). 159.59/70.63 thf(1018,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/sandbox/benchmark/theBenchmark.p',fact_3954_dvd__mult__left)). 159.59/70.63 thf(11506,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)],[1018])). 159.59/70.63 thf(2982,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/sandbox/benchmark/theBenchmark.p',fact_5832_of__int__less__1__iff)). 159.59/70.63 thf(17848,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)],[2982])). 159.59/70.63 thf(2033,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6879_sin__zero__lemma)). 159.59/70.63 thf(14816,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2033])). 159.59/70.63 thf(5864,axiom,((! [A:num]: ((one_one_complex = (numera6690914467698888265omplex @ A)) = (one = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_one__eq__numeral__iff)). 159.59/70.63 thf(27917,plain,((! [A:num]: ((one_one_complex = (numera6690914467698888265omplex @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5864])). 159.59/70.63 thf(2561,axiom,((! [A:complex,B:complex]: (((B != zero_zero_complex) => ((minus_minus_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B)) = (times_times_complex @ (times_times_complex @ (invers8013647133539491842omplex @ A) @ (minus_minus_complex @ B @ A)) @ (invers8013647133539491842omplex @ B)))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9077_division__ring__inverse__diff)). 159.59/70.63 thf(16483,plain,((! [A:complex,B:complex]: (((~ (B = zero_zero_complex)) => ((minus_minus_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B)) = (times_times_complex @ (times_times_complex @ (invers8013647133539491842omplex @ A) @ (minus_minus_complex @ B @ A)) @ (invers8013647133539491842omplex @ B)))) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2561])). 159.59/70.63 thf(1074,axiom,((! [A:extended_enat]: (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2633_i0__lb)). 159.59/70.63 thf(11692,plain,((! [A:extended_enat]: (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074])). 159.59/70.63 thf(3154,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/sandbox/benchmark/theBenchmark.p',fact_7808_double__gauss__sum)). 159.59/70.63 thf(18403,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)],[3154])). 159.59/70.63 thf(1541,axiom,(((sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6807_sin__two__pi)). 159.59/70.63 thf(13264,plain,(((sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1541])). 159.59/70.63 thf(2967,axiom,((sinh_complex = (^ [A:complex]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (numeral_numeral_real @ (bit0 @ one))) @ (minus_minus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9369_sinh__def)). 159.59/70.63 thf(17806,plain,(((sinh_complex) = (^ [A:complex]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (numeral_numeral_real @ (bit0 @ one))) @ (minus_minus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2967])). 159.59/70.63 thf(5773,axiom,((! [A:num]: ((semiri1406184849735516958ct_int @ (numeral_numeral_nat @ A)) = (times_times_int @ (numeral_numeral_int @ A) @ (semiri1406184849735516958ct_int @ (pred_numeral @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8112_fact__numeral)). 159.59/70.63 thf(27368,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)],[5773])). 159.59/70.63 thf(6384,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3025_leD)). 159.59/70.63 thf(29766,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6384])). 159.59/70.63 thf(4305,axiom,((! [A:num]: ((real_V1022390504157884413omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6890_norm__neg__numeral)). 159.59/70.63 thf(22059,plain,((! [A:num]: ((real_V1022390504157884413omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4305])). 159.59/70.63 thf(2531,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/sandbox/benchmark/theBenchmark.p',fact_30_less__divide__eq__numeral1_I1_J)). 159.59/70.63 thf(16395,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)],[2531])). 159.59/70.63 thf(3676,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (minus_minus_int @ A @ B) @ B) = (modulo_modulo_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3396_minus__mod__self2)). 159.59/70.63 thf(20060,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)],[3676])). 159.59/70.63 thf(6289,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 @ C) => (A = C)) <= (ord_less_eq_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2359_power__inject__base)). 159.59/70.63 thf(29456,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 @ C) => (A = C)) | ~ (ord_less_eq_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6289])). 159.59/70.63 thf(8010,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/sandbox/benchmark/theBenchmark.p',fact_3431_mod2__Suc__Suc)). 159.59/70.63 thf(35847,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)],[8010])). 159.59/70.63 thf(3109,axiom,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ D @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (minus_minus_int @ D @ C))) <= (A = (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5099_group__cancel_Osub2)). 159.59/70.63 thf(18255,plain,((! [A:int,B:int,C:int,D:int]: (((minus_minus_int @ D @ A) = (plus_plus_int @ (uminus_uminus_int @ B) @ (minus_minus_int @ D @ C))) | ~ (A = (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3109])). 159.59/70.63 thf(1090,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/sandbox/benchmark/theBenchmark.p',fact_8004_power__half__series)). 159.59/70.63 thf(11747,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)],[1090])). 159.59/70.63 thf(6605,axiom,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1250_mult_Ocomm__neutral)). 159.59/70.63 thf(30621,plain,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6605])). 159.59/70.63 thf(356,axiom,((! [A:(nat > real),B:nat,C:nat]: ((groups129246275422532515t_real @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo3111899725591712190t_real @ (^ [D:nat]: (times_times_real @ (A @ D))) @ B @ C @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8519_prod__atLeastAtMost__code)). 159.59/70.63 thf(9352,plain,((! [A:(nat > real),B:nat,C:nat]: ((groups129246275422532515t_real @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo3111899725591712190t_real @ (^ [D:nat]: (times_times_real @ (A @ D))) @ B @ C @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])). 159.59/70.63 thf(5567,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/sandbox/benchmark/theBenchmark.p',fact_8481_prod_OatMost__Suc__shift)). 159.59/70.63 thf(26655,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)],[5567])). 159.59/70.63 thf(214,axiom,((! [A:real]: ((real_V1485227260804924795R_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9189_scaleR__one)). 159.59/70.63 thf(8903,plain,((! [A:real]: ((real_V1485227260804924795R_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 159.59/70.63 thf(1651,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (abs_abs_real @ A) @ B) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5523_abs__mult__less)). 159.59/70.63 thf(13603,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_real @ (abs_abs_real @ A) @ B) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651])). 159.59/70.63 thf(2807,axiom,((! [A:extended_enat,B:extended_enat]: (((ord_le72135733267957522d_enat @ A @ B) <= (A != B)) <= (ord_le2932123472753598470d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3184_order__le__neq__trans)). 159.59/70.63 thf(17282,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) | (A = B) | ~ (ord_le2932123472753598470d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2807])). 159.59/70.63 thf(4946,axiom,((ord_less_num = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & ~ (ord_less_eq_num @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3059_less__le__not__le)). 159.59/70.63 thf(24336,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)],[4946])). 159.59/70.63 thf(1077,axiom,((! [A:real,B:nat]: ((A = (ring_1_of_int_real @ (archim6058952711729229775r_real @ A))) => ((archim6058952711729229775r_real @ (power_power_real @ A @ B)) = (power_power_int @ (archim6058952711729229775r_real @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8234_floor__power)). 159.59/70.63 thf(11710,plain,((! [A:real,B:nat]: ((A = (ring_1_of_int_real @ (archim6058952711729229775r_real @ A))) => ((archim6058952711729229775r_real @ (power_power_real @ A @ B)) = (power_power_int @ (archim6058952711729229775r_real @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077])). 159.59/70.63 thf(1467,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ A @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups3539618377306564664at_int @ (^ [C:nat]: (plus_plus_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/sandbox/benchmark/theBenchmark.p',fact_8913_sum_Oin__pairs__0)). 159.59/70.63 thf(13041,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (A) @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups3539618377306564664at_int @ (^ [C:nat]: (plus_plus_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)],[1467])). 159.59/70.63 thf(2439,axiom,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ A @ B) @ (times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ A @ B))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3509_mod__mult__div__eq)). 159.59/70.63 thf(16100,plain,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ A @ B) @ (times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ A @ B))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2439])). 159.59/70.63 thf(2014,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/sandbox/benchmark/theBenchmark.p',fact_7894_sums__divide)). 159.59/70.63 thf(14762,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)],[2014])). 159.59/70.63 thf(1901,axiom,((! [A:set_nat,B:nat,C:(nat > extended_enat)]: ((((member_nat @ B @ A) => ((groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (B = D) @ (C @ D) @ one_on7984719198319812577d_enat)) @ A) = (C @ B))) & (((groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (B = D) @ (C @ D) @ one_on7984719198319812577d_enat)) @ A) = one_on7984719198319812577d_enat) <= (~ (member_nat @ B @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8406_prod_Odelta_H)). 159.59/70.63 thf(14388,plain,((! [A:set_nat,B:nat,C:(nat > extended_enat)]: ((((member_nat @ B @ A) => ((groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (B = D) @ (C @ D) @ one_on7984719198319812577d_enat)) @ A) = (C @ B))) & (((groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (B = D) @ (C @ D) @ one_on7984719198319812577d_enat)) @ A) = one_on7984719198319812577d_enat) | (member_nat @ B @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1901])). 159.59/70.63 thf(4835,axiom,((! [A:num]: (((numeral_numeral_real @ A) = one_one_real) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_numeral__eq__one__iff)). 159.59/70.63 thf(23985,plain,((! [A:num]: (((numeral_numeral_real @ A) = one_one_real) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4835])). 159.59/70.63 thf(3599,axiom,((! [A:extended_enat,B:(num > extended_enat),C:num,D:num]: ((((! [E:num,F:num]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) <= (ord_less_num @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) <= (ord_less_num @ C @ D)) <= (ord_le72135733267957522d_enat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2890_order__less__subst1)). 159.59/70.63 thf(19809,plain,((! [A:extended_enat,B:(num > extended_enat),C:num,D:num]: (((! [E:num,F:num]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) | ~ (ord_less_num @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) | ~ (ord_less_num @ C @ D) | ~ (ord_le72135733267957522d_enat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3599])). 159.59/70.63 thf(7988,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/sandbox/benchmark/theBenchmark.p',fact_5461_div__Suc__eq__div__add3)). 159.59/70.63 thf(35775,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)],[7988])). 159.59/70.63 thf(4414,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/sandbox/benchmark/theBenchmark.p',fact_6916_norm__mult__ineq)). 159.59/70.63 thf(22396,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)],[4414])). 159.59/70.63 thf(2136,axiom,((! [A:nat]: ((groups7501900531339628137nteger @ semiri4939895301339042750nteger @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ one_one_Code_integer)) @ (numera6620942414471956472nteger @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7825_gauss__sum)). 159.59/70.63 thf(15147,plain,((! [A:nat]: ((groups7501900531339628137nteger @ (semiri4939895301339042750nteger) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ A)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ one_one_Code_integer)) @ (numera6620942414471956472nteger @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2136])). 159.59/70.63 thf(2595,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/sandbox/benchmark/theBenchmark.p',fact_3991_dvd__add__right__iff)). 159.59/70.63 thf(16593,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)],[2595])). 159.59/70.63 thf(6847,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/sandbox/benchmark/theBenchmark.p',fact_4894_neg__one__even__power)). 159.59/70.63 thf(31692,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)],[6847])). 159.59/70.63 thf(5752,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ B @ (divide_divide_nat @ C @ A)) = (divide_divide_nat @ (times_times_nat @ B @ C) @ A)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4169_unit__div__mult__swap)). 159.59/70.63 thf(27301,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ B @ (divide_divide_nat @ C @ A)) = (divide_divide_nat @ (times_times_nat @ B @ C) @ A)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5752])). 159.59/70.63 thf(2078,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_is_succ_in_set @ (vEBT_VEBT_set_vebt @ A) @ B @ C) = ((ord_less_nat @ B @ C) & ! [D:nat]: ((ord_less_eq_nat @ C @ D) <= ((ord_less_nat @ B @ D) & (vEBT_vebt_member @ A @ D))) & (vEBT_vebt_member @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_succ__member)). 159.59/70.63 thf(14946,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_is_succ_in_set @ (vEBT_VEBT_set_vebt @ A) @ B @ C) = ((ord_less_nat @ B @ C) & ! [D:nat]: ((ord_less_eq_nat @ C @ D) | ~ ((ord_less_nat @ B @ D) & (vEBT_vebt_member @ A @ D))) & (vEBT_vebt_member @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2078])). 159.59/70.63 thf(6249,axiom,((! [A:$o,B:$o]: (((((B) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ one_one_nat))) & ((~ (B)) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = none_nat))) <= (~ (A))) & ((A) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1946_vebt__mint_Osimps_I1_J)). 159.59/70.63 thf(29240,plain,((! [A:$o,B:$o]: (((((B) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ one_one_nat))) & ((~ (B)) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = none_nat))) | (A)) & ((A) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6249])). 159.59/70.63 thf(6257,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/sandbox/benchmark/theBenchmark.p',fact_7256_Complex__eq__neg__1)). 159.59/70.63 thf(29316,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)],[6257])). 159.59/70.63 thf(5665,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ B @ A) => (A = B)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4384_dvd__antisym)). 159.59/70.63 thf(27001,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)],[5665])). 159.59/70.63 thf(7093,axiom,(((semiri2265585572941072030t_real @ (suc @ zero_zero_nat)) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8058_fact__Suc__0)). 159.59/70.63 thf(32714,plain,(((semiri2265585572941072030t_real @ (suc @ zero_zero_nat)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7093])). 159.59/70.63 thf(5966,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/sandbox/benchmark/theBenchmark.p',fact_5688_le__numeral__Suc)). 159.59/70.63 thf(28331,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)],[5966])). 159.59/70.63 thf(1630,axiom,((! [A:(nat > complex),B:nat,C:complex]: ((sums_complex @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ B))) @ C) = (sums_complex @ A @ (plus_plus_complex @ C @ (groups2073611262835488442omplex @ A @ (set_ord_lessThan_nat @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7901_sums__iff__shift)). 159.59/70.63 thf(13544,plain,((! [A:(nat > complex),B:nat,C:complex]: ((sums_complex @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ B))) @ C) = (sums_complex @ (A) @ (plus_plus_complex @ C @ (groups2073611262835488442omplex @ (A) @ (set_ord_lessThan_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630])). 159.59/70.63 thf(3717,axiom,((! [A:real]: (((inverse_inverse_real @ A) = one_one_real) = (A = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8982_inverse__eq__1__iff)). 159.59/70.63 thf(20207,plain,((! [A:real]: (((inverse_inverse_real @ A) = one_one_real) = (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3717])). 159.59/70.63 thf(1519,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/sandbox/benchmark/theBenchmark.p',fact_7154_cos__times__cos)). 159.59/70.63 thf(13201,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)],[1519])). 159.59/70.63 thf(4432,axiom,((! [A:real,B:real]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ (archim7802044766580827645g_real @ B)) => (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7064_ceiling__less__cancel)). 159.59/70.63 thf(22453,plain,((! [A:real,B:real]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ (archim7802044766580827645g_real @ B)) => (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4432])). 159.59/70.63 thf(5863,axiom,((! [A:(nat > (nat > nat)),B:option_nat]: ((vEBT_V4262088993061758097ft_nat @ A @ none_nat @ B) = none_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_835_VEBT__internal_Ooption__shift_Osimps_I1_J)). 159.59/70.63 thf(27914,plain,((! [A:(nat > (nat > nat)),B:option_nat]: ((vEBT_V4262088993061758097ft_nat @ (A) @ none_nat @ B) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5863])). 159.59/70.63 thf(2404,axiom,((! [A:real,B:real]: ((((powr_real @ A @ B) = one_one_real) = (B = zero_zero_real)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7216_powr__eq__one__iff)). 159.59/70.63 thf(15976,plain,((! [A:real,B:real]: ((((powr_real @ A @ B) = one_one_real) = (B = zero_zero_real)) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2404])). 159.59/70.63 thf(899,axiom,((! [A:int]: (((ring_17405671764205052669omplex @ A) = one_one_complex) = (A = one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5774_of__int__eq__1__iff)). 159.59/70.63 thf(11138,plain,((! [A:int]: (((ring_17405671764205052669omplex @ A) = one_one_complex) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[899])). 159.59/70.63 thf(6793,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/sandbox/benchmark/theBenchmark.p',fact_8038_sum__bounds__lt__plus1)). 159.59/70.63 thf(31424,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)],[6793])). 159.59/70.63 thf(2465,axiom,((! [A:real]: (ord_less_eq_real @ (real_V7735802525324610683m_real @ (exp_real @ A)) @ (exp_real @ (real_V7735802525324610683m_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6842_norm__exp)). 159.59/70.63 thf(16188,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)],[2465])). 159.59/70.63 thf(2307,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/sandbox/benchmark/theBenchmark.p',fact_5855_of__int__less__numeral__power__cancel__iff)). 159.59/70.63 thf(15675,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)],[2307])). 159.59/70.63 thf(4547,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9540_xor__nat__numerals_I4_J)). 159.59/70.63 thf(22960,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)],[4547])). 159.59/70.63 thf(401,axiom,((! [A:real,B:real]: ((((archim6058952711729229775r_real @ (plus_plus_real @ A @ B)) = (plus_plus_int @ (plus_plus_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) @ one_one_int)) <= (~ (ord_less_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real))) & ((ord_less_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real) => ((archim6058952711729229775r_real @ (plus_plus_real @ A @ B)) = (plus_plus_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9159_floor__add)). 159.59/70.63 thf(9502,plain,((! [A:real,B:real]: ((((archim6058952711729229775r_real @ (plus_plus_real @ A @ B)) = (plus_plus_int @ (plus_plus_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) @ one_one_int)) | (ord_less_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real)) & ((ord_less_real @ (plus_plus_real @ (archim2898591450579166408c_real @ A) @ (archim2898591450579166408c_real @ B)) @ one_one_real) => ((archim6058952711729229775r_real @ (plus_plus_real @ A @ B)) = (plus_plus_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])). 159.59/70.63 thf(6094,axiom,((! [A:nat,B:set_nat]: ((vimage_nat_nat @ suc @ (insert_nat @ (suc @ A) @ B)) = (insert_nat @ A @ (vimage_nat_nat @ suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10190_vimage__Suc__insert__Suc)). 159.59/70.63 thf(28731,plain,((! [A:nat,B:set_nat]: ((vimage_nat_nat @ (suc) @ (insert_nat @ (suc @ A) @ B)) = (insert_nat @ A @ (vimage_nat_nat @ (suc) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6094])). 159.59/70.63 thf(1231,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (exp_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (divide_divide_real @ (ln_ln_real @ B) @ B) @ (divide_divide_real @ (ln_ln_real @ A) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6107_ln__x__over__x__mono)). 159.59/70.63 thf(12233,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (exp_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (divide_divide_real @ (ln_ln_real @ B) @ B) @ (divide_divide_real @ (ln_ln_real @ A) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231])). 159.59/70.63 thf(3272,axiom,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1877_add_Ocomm__neutral)). 159.59/70.63 thf(18787,plain,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3272])). 159.59/70.63 thf(7785,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/sandbox/benchmark/theBenchmark.p',fact_9824_UNIV__char__of__nat)). 159.59/70.63 thf(35142,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)],[7785])). 159.59/70.63 thf(5152,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_Nat_Oadd__diff__assoc)). 159.59/70.63 thf(25085,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ B) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5152])). 159.59/70.63 thf(5504,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_nat @ (A @ C) @ (A @ B)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_lift__Suc__antimono__le)). 159.59/70.63 thf(26471,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D))) => ((ord_less_eq_nat @ (A @ C) @ (A @ B)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5504])). 159.59/70.63 thf(3647,axiom,((! [A:set_nat,B:(nat > int)]: ((~ (finite_finite_nat @ A)) => ((groups705719431365010083at_int @ B @ A) = one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8397_prod_Oinfinite)). 159.59/70.63 thf(19963,plain,((! [A:set_nat,B:(nat > int)]: ((~ (finite_finite_nat @ A)) => ((groups705719431365010083at_int @ (B) @ A) = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3647])). 159.59/70.63 thf(3577,axiom,((! [A:real,B:real,C:real]: ((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2343_divide__add__eq__iff)). 159.59/70.63 thf(19740,plain,((! [A:real,B:real,C:real]: ((~ (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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3577])). 159.59/70.63 thf(1398,axiom,((! [A:complex,B:complex]: ((((cos_complex @ B) != zero_zero_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 @ A) != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7309_tan__add)). 159.59/70.63 thf(12813,plain,((! [A:complex,B:complex]: (((~ ((cos_complex @ B) = zero_zero_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 @ A) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398])). 159.59/70.63 thf(1857,axiom,((! [A:code_integer,B:code_integer]: (A = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B) @ (modulo364778990260209775nteger @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3518_mod__div__decomp)). 159.59/70.63 thf(14254,plain,((! [A:code_integer,B:code_integer]: (A = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B) @ (modulo364778990260209775nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1857])). 159.59/70.63 thf(5234,axiom,(((semiri5044797733671781792omplex @ (suc @ zero_zero_nat)) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8056_fact__Suc__0)). 159.59/70.63 thf(25388,plain,(((semiri5044797733671781792omplex @ (suc @ zero_zero_nat)) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5234])). 159.59/70.63 thf(3172,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/sandbox/benchmark/theBenchmark.p',fact_2351_add__frac__eq)). 159.59/70.63 thf(18455,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)],[3172])). 159.59/70.63 thf(3784,axiom,((! [A:nat]: ~ (ord_less_int @ (semiri1406184849735516958ct_int @ A) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8073_fact__not__neg)). 159.59/70.63 thf(20419,plain,((! [A:nat]: ~ (ord_less_int @ (semiri1406184849735516958ct_int @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3784])). 159.59/70.63 thf(6627,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A))) @ one_one_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6022_and__minus__numerals_I5_J)). 159.59/70.63 thf(30695,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)],[6627])). 159.59/70.63 thf(464,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ (semiri4939895301339042750nteger @ B)) @ A) != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8291_pochhammer__of__nat__eq__0__lemma_H)). 159.59/70.63 thf(9709,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ ((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ (semiri4939895301339042750nteger @ B)) @ A) = zero_z3403309356797280102nteger))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[464])). 159.59/70.63 thf(7269,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/sandbox/benchmark/theBenchmark.p',fact_369_power__commuting__commutes)). 159.59/70.63 thf(33375,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)],[7269])). 159.59/70.63 thf(7171,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2604_dual__order_Orefl)). 159.59/70.63 thf(33027,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7171])). 159.59/70.63 thf(5309,axiom,((! [A:(nat > $o),B:nat]: (((! [C:nat]: (((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C)))) <= (ord_less_nat @ zero_zero_nat @ C))) => (A @ B)) <= (A @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1910_infinite__descent0)). 159.59/70.63 thf(25669,plain,((! [A:(nat > $o),B:nat]: (((! [C:nat]: (((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C)))) | ~ (ord_less_nat @ zero_zero_nat @ C))) => (A @ B)) | ~ (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5309])). 159.59/70.63 thf(4559,axiom,((! [A:nat]: ((semiri1408675320244567234ct_nat @ (suc @ A)) = (times_times_nat @ (semiri1316708129612266289at_nat @ (suc @ A)) @ (semiri1408675320244567234ct_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8064_fact__Suc)). 159.59/70.63 thf(22995,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)],[4559])). 159.59/70.63 thf(7535,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/sandbox/benchmark/theBenchmark.p',fact_3433_not__mod__2__eq__1__eq__0)). 159.59/70.63 thf(34295,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)],[7535])). 159.59/70.63 thf(1497,axiom,(((semiri4939895301339042750nteger @ one_one_nat) = one_one_Code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6555_of__nat__1)). 159.59/70.63 thf(13135,plain,(((semiri4939895301339042750nteger @ one_one_nat) = one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497])). 159.59/70.63 thf(6329,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8278_pochhammer__of__nat__eq__0__lemma)). 159.59/70.63 thf(29579,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((comm_s7457072308508201937r_real @ (uminus_uminus_real @ (semiri5074537144036343181t_real @ A)) @ B) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6329])). 159.59/70.63 thf(6422,axiom,((! [A:num]: (ord_less_num @ one @ (bit1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5428_semiring__norm_I77_J)). 159.59/70.63 thf(29939,plain,((! [A:num]: (ord_less_num @ one @ (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6422])). 159.59/70.63 thf(3641,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ one_one_real @ (powr_real @ A @ B))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7246_gr__one__powr)). 159.59/70.63 thf(19941,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ one_one_real @ (powr_real @ A @ B))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3641])). 159.59/70.63 thf(5188,axiom,((! [A:num,B:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (bit_se2923211474154528505it_int @ (pred_numeral @ A) @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5737_take__bit__numeral__bit0)). 159.59/70.63 thf(25207,plain,((! [A:num,B:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (bit_se2923211474154528505it_int @ (pred_numeral @ A) @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5188])). 159.59/70.63 thf(7699,axiom,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: (((size_s6755466524823107622T_VEBT @ A) = (size_s6755466524823107622T_VEBT @ B)) => ((A = B) <= (! [C:nat]: ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)) => ((nth_VEBT_VEBT @ A @ C) = (nth_VEBT_VEBT @ B @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_nth__equalityI)). 159.59/70.63 thf(34850,plain,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: (((size_s6755466524823107622T_VEBT @ A) = (size_s6755466524823107622T_VEBT @ B)) => ((A = B) | ~ (! [C:nat]: ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)) => ((nth_VEBT_VEBT @ A @ C) = (nth_VEBT_VEBT @ B @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7699])). 159.59/70.63 thf(6225,axiom,((! [A:nat,B:nat,C:nat]: (((take_nat @ B @ (upt @ A @ C)) = (upt @ A @ (plus_plus_nat @ A @ B))) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10181_take__upt)). 159.59/70.63 thf(29166,plain,((! [A:nat,B:nat,C:nat]: (((take_nat @ B @ (upt @ A @ C)) = (upt @ A @ (plus_plus_nat @ A @ B))) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6225])). 159.59/70.63 thf(7810,axiom,((! [A:set_list_int]: ((finite3922522038869484883st_int @ A) => (? [B:nat]: ! [C:list_int]: ((ord_less_nat @ (size_size_list_int @ C) @ B) <= (member_list_int @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3744_finite__maxlen)). 159.59/70.63 thf(35215,plain,((! [A:set_list_int]: ((finite3922522038869484883st_int @ A) => (? [B:nat]: ! [C:list_int]: ((ord_less_nat @ (size_size_list_int @ C) @ B) | ~ (member_list_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7810])). 159.59/70.63 thf(4954,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/sandbox/benchmark/theBenchmark.p',fact_5610_power__numeral__odd)). 159.59/70.63 thf(24363,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)],[4954])). 159.59/70.63 thf(7412,axiom,((! [A:num]: (ord_less_eq_int @ one_one_int @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_one__le__numeral)). 159.59/70.63 thf(33865,plain,((! [A:num]: (ord_less_eq_int @ one_one_int @ (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7412])). 159.59/70.63 thf(8133,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((((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 @ B) & (dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) & (((times_times_nat @ (plus_plus_nat @ B @ C) @ F) = (plus_plus_nat @ (times_times_nat @ B @ G) @ A)) | ((times_times_nat @ B @ F) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ B @ C) @ G) @ A)))))) <= (dvd_dvd_nat @ A @ C)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4035_bezout__lemma__nat)). 159.59/70.63 thf(36256,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((((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 @ B) & (dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) & (((times_times_nat @ (plus_plus_nat @ B @ C) @ F) = (plus_plus_nat @ (times_times_nat @ B @ G) @ A)) | ((times_times_nat @ B @ F) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ B @ C) @ G) @ A)))))) | ~ (dvd_dvd_nat @ A @ C) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8133])). 159.59/70.63 thf(1605,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/sandbox/benchmark/theBenchmark.p',fact_6925_norm__triangle__le)). 159.59/70.63 thf(13466,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)],[1605])). 159.59/70.63 thf(288,axiom,((! [A:complex]: ((gbinomial_complex @ A @ zero_zero_nat) = one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8175_gbinomial__0_I1_J)). 159.59/70.63 thf(9122,plain,((! [A:complex]: ((gbinomial_complex @ A @ zero_zero_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 159.59/70.63 thf(4011,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/sandbox/benchmark/theBenchmark.p',fact_3517_div__mult__mod__eq)). 159.59/70.63 thf(21142,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)],[4011])). 159.59/70.63 thf(7419,axiom,((! [A:nat,B:nat,C:(nat > int),D:int]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_int @ (C @ B) @ D) => ((ord_less_eq_int @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2679_order__subst2)). 159.59/70.63 thf(33884,plain,((! [A:nat,B:nat,C:(nat > int),D:int]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_int @ (C @ B) @ D) => ((ord_less_eq_int @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7419])). 159.59/70.63 thf(6441,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_membermima @ A @ B) => ((! [C:nat,D:nat]: ((~ ((B = D) | (B = C))) <= (? [E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F))))) => ((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: ((~ ((B = C) | (B = D) | (((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))))) <= (? [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]: ((~ (((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)))) <= (? [E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2562_VEBT__internal_Omembermima_Oelims_I2_J)). 159.59/70.63 thf(30016,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_membermima @ A @ B) => ((! [C:nat,D:nat]: (~ ((B = D) | (B = C)) | ~ (? [E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ zero_zero_nat @ E @ F))))) => ((! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT]: (~ ((B = C) | (B = D) | (((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)))) | ~ (? [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]: (~ (((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))) | ~ (? [E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ C) @ D @ E))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6441])). 159.59/70.63 thf(3796,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3997_unit__imp__dvd)). 159.59/70.63 thf(20466,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3796])). 159.59/70.63 thf(215,axiom,((! [A:complex,B:nat]: ((im @ (divide1717551699836669952omplex @ A @ (semiri8010041392384452111omplex @ B))) = (divide_divide_real @ (im @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9648_Im__divide__of__nat)). 159.59/70.63 thf(8906,plain,((! [A:complex,B:nat]: ((im @ (divide1717551699836669952omplex @ A @ (semiri8010041392384452111omplex @ B))) = (divide_divide_real @ (im @ A) @ (semiri5074537144036343181t_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 159.59/70.63 thf(5262,axiom,((! [A:num]: ((bit_se1745604003318907178nteger @ (numeral_numeral_nat @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5225_take__bit__numeral__minus__1__eq)). 159.59/70.63 thf(25477,plain,((! [A:num]: ((bit_se1745604003318907178nteger @ (numeral_numeral_nat @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5262])). 159.59/70.63 thf(7823,axiom,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ na) <= (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_allvalidinlist)). 159.59/70.63 thf(35268,plain,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ na) | ~ (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7823])). 159.59/70.63 thf(2633,axiom,((! [A:real]: ((comm_s7457072308508201937r_real @ A @ zero_zero_nat) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8182_pochhammer__0)). 159.59/70.63 thf(16737,plain,((! [A:real]: ((comm_s7457072308508201937r_real @ A @ zero_zero_nat) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2633])). 159.59/70.63 thf(3251,axiom,((! [A:num,B:num]: ((plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ B)) = (numera6690914467698888265omplex @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_numeral__plus__numeral)). 159.59/70.63 thf(18709,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)],[3251])). 159.59/70.63 thf(1866,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/sandbox/benchmark/theBenchmark.p',fact_3514_mod__div__mult__eq)). 159.59/70.63 thf(14281,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)],[1866])). 159.59/70.63 thf(2983,axiom,((! [A:code_integer,B:code_integer,C:nat]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ (^ [D:nat]: (plus_p5714425477246183910nteger @ A @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_3573771949741848930nteger @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ C) @ one_one_Code_integer) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7804_double__arith__series)). 159.59/70.63 thf(17851,plain,((! [A:code_integer,B:code_integer,C:nat]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ (^ [D:nat]: (plus_p5714425477246183910nteger @ A @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_3573771949741848930nteger @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ C) @ one_one_Code_integer) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2983])). 159.59/70.63 thf(3720,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/sandbox/benchmark/theBenchmark.p',fact_1225_combine__common__factor)). 159.59/70.63 thf(20217,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)],[3720])). 159.59/70.63 thf(5186,axiom,((! [A:int]: ((times_times_int @ (abs_abs_int @ A) @ (abs_abs_int @ A)) = (times_times_int @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5392_abs__mult__self__eq)). 159.59/70.63 thf(25201,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)],[5186])). 159.59/70.63 thf(563,axiom,((arsinh_real = (^ [A:real]: (ln_ln_real @ (plus_plus_real @ A @ (powr_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) @ (real_V1803761363581548252l_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7843_arsinh__def)). 159.59/70.63 thf(10043,plain,(((arsinh_real) = (^ [A:real]: (ln_ln_real @ (plus_plus_real @ A @ (powr_real @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real) @ (real_V1803761363581548252l_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[563])). 159.59/70.63 thf(3162,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/sandbox/benchmark/theBenchmark.p',fact_5980_and__nonnegative__int__iff)). 159.59/70.63 thf(18428,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)],[3162])). 159.59/70.63 thf(4665,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) <= (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_le__neq__implies__less)). 159.59/70.63 thf(23386,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)],[4665])). 159.59/70.63 thf(1895,axiom,((! [A:int]: (ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ (abs_abs_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5614_abs__add__one__gt__zero)). 159.59/70.63 thf(14373,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)],[1895])). 159.59/70.63 thf(1764,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/sandbox/benchmark/theBenchmark.p',fact_4912_signed__take__bit__minus)). 159.59/70.63 thf(13947,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)],[1764])). 159.59/70.63 thf(1365,axiom,((! [A:complex]: (dvd_dvd_complex @ one_one_complex @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4002_one__dvd)). 159.59/70.63 thf(12683,plain,((! [A:complex]: (dvd_dvd_complex @ one_one_complex @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365])). 159.59/70.63 thf(2163,axiom,((! [A:nat,B:int]: ((bit_concat_bit @ A @ (bit_se2923211474154528505it_int @ A @ B)) = (bit_concat_bit @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5000_concat__bit__take__bit__eq)). 159.59/70.63 thf(15226,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)],[2163])). 159.59/70.63 thf(2503,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ C @ B)) = (dvd_dvd_Code_integer @ A @ C)) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3984_dvd__add__left__iff)). 159.59/70.63 thf(16311,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ C @ B)) = (dvd_dvd_Code_integer @ A @ C)) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2503])). 159.59/70.63 thf(5193,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => (((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ B)) <= (dvd_dvd_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4128_dvd__diffD)). 159.59/70.63 thf(25229,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => (((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ B)) | ~ (dvd_dvd_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5193])). 159.59/70.63 thf(1248,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/sandbox/benchmark/theBenchmark.p',fact_6142_exp__bound)). 159.59/70.63 thf(12290,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)],[1248])). 159.59/70.63 thf(850,axiom,((! [A:nat,B:real]: (((power_power_real @ (exp_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A))) @ A) = (exp_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6756_exp__divide__power__eq)). 159.59/70.63 thf(10993,plain,((! [A:nat,B:real]: (((power_power_real @ (exp_real @ (divide_divide_real @ B @ (semiri5074537144036343181t_real @ A))) @ A) = (exp_real @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[850])). 159.59/70.63 thf(8233,axiom,((! [A:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ ma @ na)) <= ((vEBT_VEBT_high @ ma @ na) = A)) & ! [B:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ B @ na)) & ((vEBT_VEBT_high @ B @ na) = A)) => ((ord_less_eq_nat @ B @ ma) & (ord_less_nat @ mi @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117__C7b_C)). 159.59/70.63 thf(36636,plain,((! [A:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ ma @ na)) | ~ ((vEBT_VEBT_high @ ma @ na) = A)) & ! [B:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ B @ na)) & ((vEBT_VEBT_high @ B @ na) = A)) => ((ord_less_eq_nat @ B @ ma) & (ord_less_nat @ mi @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8233])). 159.59/70.63 thf(7429,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/sandbox/benchmark/theBenchmark.p',fact_4844_add__neg__numeral__special_I9_J)). 159.59/70.63 thf(33920,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)],[7429])). 159.59/70.63 thf(4634,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ B @ A) | (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2666_linorder__linear)). 159.59/70.63 thf(23271,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)],[4634])). 159.59/70.63 thf(1363,axiom,((! [A:(int > (int > $o)),B:set_nat,C:(nat > int),D:(nat > int)]: ((A @ zero_zero_int @ zero_zero_int) => ((! [E:int,F:int,G:int,H:int]: (((A @ E @ G) & (A @ F @ H)) => (A @ (plus_plus_int @ E @ F) @ (plus_plus_int @ G @ H)))) => ((finite_finite_nat @ B) => ((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups3539618377306564664at_int @ C @ B) @ (groups3539618377306564664at_int @ D @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7488_sum_Orelated)). 159.59/70.63 thf(12654,plain,((! [A:(int > (int > $o)),B:set_nat,C:(nat > int),D:(nat > int)]: ((A @ zero_zero_int @ zero_zero_int) => ((! [E:int,F:int,G:int,H:int]: (((A @ E @ G) & (A @ F @ H)) => (A @ (plus_plus_int @ E @ F) @ (plus_plus_int @ G @ H)))) => ((finite_finite_nat @ B) => ((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups3539618377306564664at_int @ (C) @ B) @ (groups3539618377306564664at_int @ (D) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363])). 159.59/70.63 thf(169,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat)]: ((finite_finite_nat @ A) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7950_sum__diff__nat)). 159.59/70.63 thf(8771,plain,((! [A:set_nat,B:set_nat,C:(nat > nat)]: ((finite_finite_nat @ A) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 159.59/70.63 thf(503,axiom,((! [A:real,B:real,C:real,D:real]: ((A != zero_zero_real) => ((B = (plus_plus_real @ (real_V1485227260804924795R_real @ A @ C) @ D)) = ((minus_minus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ D)) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9251_real__vector__eq__affinity)). 159.59/70.63 thf(9853,plain,((! [A:real,B:real,C:real,D:real]: ((~ (A = zero_zero_real)) => ((B = (plus_plus_real @ (real_V1485227260804924795R_real @ A @ C) @ D)) = ((minus_minus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ D)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[503])). 159.59/70.63 thf(4361,axiom,((! [A:list_o,B:list_int]: ((size_s2953683556165314199_o_int @ (product_o_int @ A @ B)) = (times_times_nat @ (size_size_list_o @ A) @ (size_size_list_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3629_length__product)). 159.59/70.63 thf(22220,plain,((! [A:list_o,B:list_int]: ((size_s2953683556165314199_o_int @ (product_o_int @ A @ B)) = (times_times_nat @ (size_size_list_o @ A) @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4361])). 159.59/70.63 thf(441,axiom,((! [A:real,B: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))))) <= ((cos_real @ A) != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7294_add__tan__eq)). 159.59/70.63 thf(9635,plain,((! [A:real,B: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))))) | ((cos_real @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])). 159.59/70.63 thf(647,axiom,((! [A:int,B:int]: ((~ (! [C:int]: (B != (times_times_int @ A @ C)))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3933_dvdE)). 159.59/70.63 thf(10321,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)],[647])). 159.59/70.63 thf(4150,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => ((ord_less_eq_real @ (cosh_real @ A) @ (cosh_real @ B)) = (ord_less_eq_real @ B @ A))) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9336_cosh__real__nonpos__le__iff)). 159.59/70.63 thf(21568,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => ((ord_less_eq_real @ (cosh_real @ A) @ (cosh_real @ B)) = (ord_less_eq_real @ B @ A))) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4150])). 159.59/70.63 thf(7722,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ C) @ A) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_nth__list__update__eq)). 159.59/70.63 thf(34942,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ C) @ A) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7722])). 159.59/70.63 thf(6646,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/sandbox/benchmark/theBenchmark.p',fact_7673_sum__Suc__diff)). 159.59/70.63 thf(30772,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)],[6646])). 159.59/70.63 thf(6684,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (((ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) & (ord_less_eq_nat @ A @ B)) <= (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_mi__ma__2__deg)). 159.59/70.63 thf(30916,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (((ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) & (ord_less_eq_nat @ A @ B)) | ~ (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)],[6684])). 159.59/70.63 thf(7537,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/sandbox/benchmark/theBenchmark.p',fact_5095_square__eq__1__iff)). 159.59/70.63 thf(34300,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)],[7537])). 159.59/70.63 thf(1565,axiom,((! [A:real]: (((times_times_real @ A @ (inverse_inverse_real @ A)) = one_one_real) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9003_right__inverse)). 159.59/70.63 thf(13336,plain,((! [A:real]: (((times_times_real @ A @ (inverse_inverse_real @ A)) = one_one_real) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565])). 159.59/70.63 thf(3283,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ A)) = (ord_less_eq_real @ one_one_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4779_ln__ge__zero__iff)). 159.59/70.63 thf(18819,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ A)) = (ord_less_eq_real @ one_one_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3283])). 159.59/70.63 thf(2301,axiom,((! [A:(nat > set_nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_set_nat @ (A @ B) @ (A @ C))) <= (! [D:nat]: (ord_less_eq_set_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_lift__Suc__mono__le)). 159.59/70.63 thf(15660,plain,((! [A:(nat > set_nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_set_nat @ (A @ B) @ (A @ C))) | ~ (! [D:nat]: (ord_less_eq_set_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2301])). 159.59/70.63 thf(6063,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/sandbox/benchmark/theBenchmark.p',fact_9135_fact__binomial)). 159.59/70.63 thf(28640,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)],[6063])). 159.59/70.63 thf(5868,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ D)) @ A @ E @ F) @ C) = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_option_nat @ ((vEBT_VEBT_less @ (some_nat @ (vEBT_VEBT_low @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ C @ (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 @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_succ @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1407_succ__greatereq__min)). 159.59/70.63 thf(27929,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ D)) @ A @ E @ F) @ C) = (if_option_nat @ (ord_less_nat @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_option_nat @ ((vEBT_VEBT_less @ (some_nat @ (vEBT_VEBT_low @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))) & ~ ((vEBT_vebt_maxt @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ C @ (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 @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_succ @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (if_option_nat @ ((vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_succ @ F @ (vEBT_VEBT_high @ C @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5868])). 159.59/70.63 thf(2963,axiom,((! [A:(nat > real)]: ((! [B:nat]: (ord_less_eq_real @ (A @ B) @ (A @ (suc @ B)))) => (topolo6980174941875973593q_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8020_mono__SucI1)). 159.59/70.63 thf(17795,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)],[2963])). 159.59/70.63 thf(6658,axiom,((! [A:nat,B:real]: (((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_real)) => (dvd_dvd_real @ B @ (power_power_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4217_dvd__power)). 159.59/70.63 thf(30809,plain,((! [A:nat,B:real]: (((ord_less_nat @ zero_zero_nat @ A) | (B = one_one_real)) => (dvd_dvd_real @ B @ (power_power_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6658])). 159.59/70.63 thf(5406,axiom,((! [A: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))))))) <= (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6882_arctan__series)). 159.59/70.63 thf(26082,plain,((! [A: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))))))) | ~ (ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5406])). 159.59/70.63 thf(3615,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/sandbox/benchmark/theBenchmark.p',fact_7200_sincos__total__pi__half)). 159.59/70.63 thf(19861,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)],[3615])). 159.59/70.63 thf(1187,axiom,((! [A:list_int,B:nat]: ((list_update_int @ A @ B @ (nth_int @ A @ B)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_list__update__id)). 159.59/70.63 thf(12052,plain,((! [A:list_int,B:nat]: ((list_update_int @ A @ B @ (nth_int @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187])). 159.59/70.63 thf(154,axiom,((! [A:real,B:real,C:real]: ((real_V1485227260804924795R_real @ A @ (real_V1485227260804924795R_real @ B @ C)) = (real_V1485227260804924795R_real @ (times_times_real @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9191_scaleR__scaleR)). 159.59/70.63 thf(8718,plain,((! [A:real,B:real,C:real]: ((real_V1485227260804924795R_real @ A @ (real_V1485227260804924795R_real @ B @ C)) = (real_V1485227260804924795R_real @ (times_times_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 159.59/70.63 thf(3030,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/sandbox/benchmark/theBenchmark.p',fact_8237_gbinomial__of__nat__symmetric)). 159.59/70.63 thf(17991,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)],[3030])). 159.59/70.63 thf(6060,axiom,((semiri5044797733671781792omplex = (^ [A:nat]: (semiri8010041392384452111omplex @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8962_fact__code)). 159.59/70.63 thf(28633,plain,(((semiri5044797733671781792omplex) = (^ [A:nat]: (semiri8010041392384452111omplex @ (set_fo2584398358068434914at_nat @ times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6060])). 159.59/70.63 thf(2992,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/sandbox/benchmark/theBenchmark.p',fact_9136_binomial__fact)). 159.59/70.63 thf(17880,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)],[2992])). 159.59/70.63 thf(7239,axiom,((semiri1316708129612266289at_nat = (^ [A:nat]: (A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9184_of__nat__id)). 159.59/70.63 thf(33286,plain,(((semiri1316708129612266289at_nat) = (^ [A:nat]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7239])). 159.59/70.63 thf(3211,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/sandbox/benchmark/theBenchmark.p',fact_2328_pos__less__divide__eq)). 159.59/70.63 thf(18577,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)],[3211])). 159.59/70.63 thf(7714,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)) = ((ord_less_nat @ A @ B) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3898_even__diff__nat)). 159.59/70.63 thf(34919,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)) = ((ord_less_nat @ A @ B) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7714])). 159.59/70.63 thf(5720,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))) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_power_complex @ (uminus1482373934393186551omplex @ B) @ A) = (uminus1482373934393186551omplex @ (power_power_complex @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5289_uminus__power__if)). 159.59/70.63 thf(27185,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))) & ((~ (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)],[5720])). 159.59/70.63 thf(7616,axiom,((! [A:nat,B:nat]: (((bit_se727722235901077358nd_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = zero_zero_nat) = (~ (bit_se1148574629649215175it_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6437_and__exp__eq__0__iff__not__bit)). 159.59/70.63 thf(34601,plain,((! [A:nat,B:nat]: (((bit_se727722235901077358nd_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = zero_zero_nat) = (~ (bit_se1148574629649215175it_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7616])). 159.59/70.63 thf(4202,axiom,((! [A:nat]: ((set_ord_lessThan_nat @ (suc @ A)) = (insert_nat @ zero_zero_nat @ (image_nat_nat @ suc @ (set_ord_lessThan_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9811_lessThan__Suc__eq__insert__0)). 159.59/70.63 thf(21724,plain,((! [A:nat]: ((set_ord_lessThan_nat @ (suc @ A)) = (insert_nat @ zero_zero_nat @ (image_nat_nat @ (suc) @ (set_ord_lessThan_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4202])). 159.59/70.63 thf(5104,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/sandbox/benchmark/theBenchmark.p',fact_4594_divmod__step__def)). 159.59/70.63 thf(24925,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)],[5104])). 159.59/70.63 thf(6471,axiom,((! [A:num,B:num,C:num]: ((A = B) => ((ord_less_num @ B @ C) => (ord_less_num @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2776_ord__eq__less__trans)). 159.59/70.63 thf(30143,plain,((! [A:num,B:num,C:num]: ((A = B) => ((ord_less_num @ B @ C) => (ord_less_num @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6471])). 159.59/70.63 thf(3772,axiom,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1529_add_Oright__neutral)). 159.59/70.63 thf(20384,plain,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3772])). 159.59/70.63 thf(446,axiom,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((groups6464643781859351333omplex @ C @ A) = (times_times_complex @ (C @ B) @ (groups6464643781859351333omplex @ C @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))) <= (member_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8789_prod_Oremove)). 159.59/70.63 thf(9650,plain,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((groups6464643781859351333omplex @ (C) @ A) = (times_times_complex @ (C @ B) @ (groups6464643781859351333omplex @ (C) @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))) | ~ (member_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[446])). 159.59/70.63 thf(3105,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/sandbox/benchmark/theBenchmark.p',fact_1387_times__divide__eq__left)). 159.59/70.63 thf(18242,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)],[3105])). 159.59/70.63 thf(8003,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/sandbox/benchmark/theBenchmark.p',fact_1431_power__numeral__even)). 159.59/70.63 thf(35825,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)],[8003])). 159.59/70.63 thf(204,axiom,((real_V1803761363581548252l_real = (^ [A:real]: (real_V1485227260804924795R_real @ A @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9220_of__real__def)). 159.59/70.63 thf(8874,plain,(((real_V1803761363581548252l_real) = (^ [A:real]: (real_V1485227260804924795R_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 159.59/70.63 thf(5470,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => ((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_mint @ (nth_VEBT_VEBT @ E @ (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 @ E @ (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 @ 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 @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1406_pred__lesseq__max)). 159.59/70.63 thf(26339,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => ((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_mint @ (nth_VEBT_VEBT @ E @ (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 @ E @ (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 @ 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 @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5470])). 159.59/70.63 thf(2019,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/sandbox/benchmark/theBenchmark.p',fact_7906_sums__iff__shift_H)). 159.59/70.63 thf(14776,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)],[2019])). 159.59/70.63 thf(2676,axiom,((! [A:nat,B:nat,C:(nat > extended_enat)]: ((((groups7108830773950497114d_enat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_z5237406670263579293d_enat) <= (ord_less_nat @ (suc @ A) @ B)) & (((groups7108830773950497114d_enat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_p3455044024723400733d_enat @ (groups7108830773950497114d_enat @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) <= (~ (ord_less_nat @ (suc @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7359_sum_Ocl__ivl__Suc)). 159.59/70.63 thf(16876,plain,((! [A:nat,B:nat,C:(nat > extended_enat)]: ((((groups7108830773950497114d_enat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_z5237406670263579293d_enat) | ~ (ord_less_nat @ (suc @ A) @ B)) & (((groups7108830773950497114d_enat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (plus_p3455044024723400733d_enat @ (groups7108830773950497114d_enat @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) | (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2676])). 159.59/70.63 thf(541,axiom,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: (((B != zero_z3403309356797280102nteger) => ((dvd_dvd_Code_integer @ A @ C) => ((dvd_dvd_Code_integer @ B @ D) => (((divide6298287555418463151nteger @ C @ A) = (divide6298287555418463151nteger @ D @ B)) = ((times_3573771949741848930nteger @ C @ B) = (times_3573771949741848930nteger @ A @ D)))))) <= (A != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4150_dvd__div__div__eq__mult)). 159.59/70.63 thf(9974,plain,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: (((~ (B = zero_z3403309356797280102nteger)) => ((dvd_dvd_Code_integer @ A @ C) => ((dvd_dvd_Code_integer @ B @ D) => (((divide6298287555418463151nteger @ C @ A) = (divide6298287555418463151nteger @ D @ B)) = ((times_3573771949741848930nteger @ C @ B) = (times_3573771949741848930nteger @ A @ D)))))) | (A = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[541])). 159.59/70.63 thf(6219,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) => ((ord_less_eq_real @ zero_zero_real @ C) => (A = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2357_power__inject__base)). 159.59/70.63 thf(29149,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) => ((ord_less_eq_real @ zero_zero_real @ C) => (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6219])). 159.59/70.63 thf(1319,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2760_gt__ex)). 159.59/70.63 thf(12513,plain,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319])). 159.59/70.63 thf(5360,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/sandbox/benchmark/theBenchmark.p',fact_7947_powser__sums__zero)). 159.59/70.63 thf(25919,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)],[5360])). 159.59/70.63 thf(1034,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_eq_real @ B @ C) <= (ord_less_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2255_mult__le__cancel__left)). 159.59/70.63 thf(11561,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_eq_real @ B @ C) | ~ (ord_less_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034])). 159.59/70.63 thf(2514,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3277_bot_Oextremum)). 159.59/70.63 thf(16343,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2514])). 159.59/70.63 thf(7315,axiom,((! [A:nat,B:list_o,C:$o]: (((nth_o @ (list_update_o @ B @ A @ C) @ A) = C) <= (ord_less_nat @ A @ (size_size_list_o @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_nth__list__update__eq)). 159.59/70.63 thf(33552,plain,((! [A:nat,B:list_o,C:$o]: (((nth_o @ (list_update_o @ B @ A @ C) @ A) = C) | ~ (ord_less_nat @ A @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7315])). 159.59/70.63 thf(4636,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2672_order__eq__refl)). 159.59/70.63 thf(23276,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4636])). 159.59/70.63 thf(1464,axiom,((! [A:real,B:real]: ((dvd_dvd_real @ A @ B) => (~ (! [C:real]: (B != (times_times_real @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3931_dvdE)). 159.59/70.63 thf(13031,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)],[1464])). 159.59/70.63 thf(4384,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (((times_3573771949741848930nteger @ B @ A) = (times_3573771949741848930nteger @ C @ A)) = (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4069_unit__mult__right__cancel)). 159.59/70.63 thf(22296,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (((times_3573771949741848930nteger @ B @ A) = (times_3573771949741848930nteger @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4384])). 159.59/70.63 thf(3710,axiom,((! [A:nat]: ((gbinomial_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8172_gbinomial__0_I2_J)). 159.59/70.63 thf(20185,plain,((! [A:nat]: ((gbinomial_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3710])). 159.59/70.63 thf(5806,axiom,((! [A:int,B:nat]: (ord_less_eq_int @ zero_zero_int @ (power_power_int @ (abs_abs_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5568_zero__le__power__abs)). 159.59/70.63 thf(27599,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)],[5806])). 159.59/70.63 thf(5353,axiom,((! [A:real,B:nat]: ((ord_less_real @ (power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ zero_zero_real) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2558_odd__power__less__zero)). 159.59/70.63 thf(25864,plain,((! [A:real,B:nat]: ((ord_less_real @ (power_power_real @ A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ zero_zero_real) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5353])). 159.59/70.63 thf(817,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2607_order__refl)). 159.59/70.63 thf(10890,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[817])). 159.59/70.63 thf(3933,axiom,((! [A:real,B:nat]: ((((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)) = (semiri5074537144036343181t_real @ B)) <= (A = one_one_real)) & ((A != one_one_real) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7992_sum__gp__strict)). 159.59/70.63 thf(20899,plain,((! [A:real,B:nat]: ((((groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_lessThan_nat @ B)) = (semiri5074537144036343181t_real @ B)) | ~ (A = one_one_real)) & ((~ (A = one_one_real)) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3933])). 159.59/70.63 thf(6820,axiom,((! [A:num]: ((archim7802044766580827645g_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6986_ceiling__neg__numeral)). 159.59/70.63 thf(31506,plain,((! [A:num]: ((archim7802044766580827645g_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6820])). 159.59/70.63 thf(3146,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/sandbox/benchmark/theBenchmark.p',fact_3693_zmod__zmult2__eq)). 159.59/70.63 thf(18376,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)],[3146])). 159.59/70.63 thf(6259,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/sandbox/benchmark/theBenchmark.p',fact_9142_binomial)). 159.59/70.63 thf(29321,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)],[6259])). 159.59/70.63 thf(2600,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((finite_finite_nat @ A) => (((ord_less_real @ (groups129246275422532515t_real @ B @ A) @ (groups129246275422532515t_real @ C @ A)) <= (A != bot_bot_set_nat)) <= (! [D:nat]: ((member_nat @ D @ A) => ((ord_less_real @ (B @ D) @ (C @ D)) & (ord_less_eq_real @ zero_zero_real @ (B @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8770_prod__mono__strict)). 159.59/70.63 thf(16612,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((finite_finite_nat @ A) => ((ord_less_real @ (groups129246275422532515t_real @ (B) @ A) @ (groups129246275422532515t_real @ (C) @ A)) | (A = bot_bot_set_nat) | ~ (! [D:nat]: ((member_nat @ D @ A) => ((ord_less_real @ (B @ D) @ (C @ D)) & (ord_less_eq_real @ zero_zero_real @ (B @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2600])). 159.59/70.63 thf(7648,axiom,((! [A:nat,B:nat]: ((A = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((semiri5074537144036343181t_real @ B) = (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6769_log2__of__power__eq)). 159.59/70.63 thf(34698,plain,((! [A:nat,B:nat]: ((A = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((semiri5074537144036343181t_real @ B) = (log @ (numeral_numeral_real @ (bit0 @ one)) @ (semiri5074537144036343181t_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7648])). 159.59/70.63 thf(4520,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se2925701944663578781it_nat @ A @ (bit_se727722235901077358nd_nat @ B @ C)) = (bit_se727722235901077358nd_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ (bit_se2925701944663578781it_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5959_take__bit__and)). 159.59/70.63 thf(22787,plain,((! [A:nat,B:nat,C:nat]: ((bit_se2925701944663578781it_nat @ A @ (bit_se727722235901077358nd_nat @ B @ C)) = (bit_se727722235901077358nd_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ (bit_se2925701944663578781it_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4520])). 159.59/70.63 thf(4270,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3145_order_Ostrict__implies__order)). 159.59/70.63 thf(21954,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4270])). 159.59/70.63 thf(1552,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/sandbox/benchmark/theBenchmark.p',fact_6633_of__nat__less__numeral__power__cancel__iff)). 159.59/70.63 thf(13296,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)],[1552])). 159.59/70.63 thf(4245,axiom,((! [A:num]: ~ (ord_le2932123472753598470d_enat @ (numera1916890842035813515d_enat @ A) @ zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1951_not__numeral__le__zero)). 159.59/70.63 thf(21877,plain,((! [A:num]: ~ (ord_le2932123472753598470d_enat @ (numera1916890842035813515d_enat @ A) @ zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4245])). 159.59/70.63 thf(1804,axiom,((bit_se727722235901077358nd_nat = (^ [A:nat,B:nat]: (nat2 @ (bit_se725231765392027082nd_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9438_and__nat__def)). 159.59/70.63 thf(14072,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)],[1804])). 159.59/70.63 thf(3853,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ B @ (plus_plus_int @ A @ C)) <= (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2262_add__strict__increasing)). 159.59/70.63 thf(20657,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ B @ (plus_plus_int @ A @ C)) | ~ (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3853])). 159.59/70.63 thf(6072,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_less__SucI)). 159.59/70.63 thf(28665,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6072])). 159.59/70.63 thf(6365,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/sandbox/benchmark/theBenchmark.p',fact_6785_Bernoulli__inequality__even)). 159.59/70.63 thf(29689,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)],[6365])). 159.59/70.63 thf(80,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (real_V1485227260804924795R_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_real @ zero_zero_real @ A)) | (A = zero_zero_real) | ((ord_less_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9236_zero__le__scaleR__iff)). 159.59/70.63 thf(8495,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (real_V1485227260804924795R_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_real @ zero_zero_real @ A)) | (A = zero_zero_real) | ((ord_less_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[80])). 159.59/70.63 thf(6752,axiom,((! [A:nat,B:nat]: (((A = zero_zero_nat) | (B = one_one_nat)) <= (A = (times_times_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2211_mult__eq__self__implies__10)). 159.59/70.63 thf(31285,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)],[6752])). 159.59/70.63 thf(7706,axiom,((! [A:num]: (ord_less_num @ one @ (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_semiring__norm_I76_J)). 159.59/70.63 thf(34872,plain,((! [A:num]: (ord_less_num @ one @ (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7706])). 159.59/70.63 thf(3775,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ (times_times_real @ B @ A)) = (divide_divide_real @ one_one_real @ B)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1752_nonzero__divide__mult__cancel__right)). 159.59/70.63 thf(20394,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ (times_times_real @ B @ A)) = (divide_divide_real @ one_one_real @ B)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3775])). 159.59/70.63 thf(4037,axiom,((! [A:nat,B:nat]: (((semiri4939895301339042750nteger @ (minus_minus_nat @ B @ A)) = (minus_8373710615458151222nteger @ (semiri4939895301339042750nteger @ B) @ (semiri4939895301339042750nteger @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6730_of__nat__diff)). 159.59/70.63 thf(21218,plain,((! [A:nat,B:nat]: (((semiri4939895301339042750nteger @ (minus_minus_nat @ B @ A)) = (minus_8373710615458151222nteger @ (semiri4939895301339042750nteger @ B) @ (semiri4939895301339042750nteger @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4037])). 159.59/70.63 thf(2309,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/sandbox/benchmark/theBenchmark.p',fact_6746_nat__le__real__less)). 159.59/70.63 thf(15681,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)],[2309])). 159.59/70.63 thf(4119,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4577_add__0__iff)). 159.59/70.63 thf(21465,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ A @ B)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4119])). 159.59/70.63 thf(2637,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1434_linordered__field__no__ub)). 159.59/70.63 thf(16750,plain,((! [A:real]: ? [B:real]: (ord_less_real @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2637])). 159.59/70.63 thf(8076,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/sandbox/benchmark/theBenchmark.p',fact_1190_add__strict__right__mono)). 159.59/70.63 thf(36076,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)],[8076])). 159.59/70.63 thf(5530,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4501_pinf_I8_J)). 159.59/70.63 thf(26545,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5530])). 159.59/70.63 thf(6639,axiom,((! [A:num]: (one_one_complex != (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5092_one__neq__neg__numeral)). 159.59/70.63 thf(30741,plain,((! [A:num]: ~ (one_one_complex = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6639])). 159.59/70.63 thf(3660,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2844_order__less__asym)). 159.59/70.63 thf(20009,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3660])). 159.59/70.63 thf(7903,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4440_pinf_I3_J)). 159.59/70.63 thf(35518,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7903])). 159.59/70.63 thf(1179,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ one_one_int) = (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6110_and__one__eq)). 159.59/70.63 thf(12028,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ A @ one_one_int) = (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179])). 159.59/70.63 thf(1686,axiom,((! [A:nat,B:nat]: (ord_less_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ A))) @ (semiri1314217659103216013at_int @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6799_negative__zless)). 159.59/70.63 thf(13710,plain,((! [A:nat,B:nat]: (ord_less_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ A))) @ (semiri1314217659103216013at_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686])). 159.59/70.63 thf(2147,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (ord_less_eq_real @ C @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4504_minf_I6_J)). 159.59/70.63 thf(15180,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ B) => (ord_less_eq_real @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2147])). 159.59/70.63 thf(4526,axiom,((! [A:num,B:num]: ((((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit1 @ B)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ A)))) <= (ord_less_eq_num @ A @ B)) & (((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit1 @ B)) = (unique5026877609467782581ep_nat @ (bit1 @ B) @ (unique5055182867167087721od_nat @ (bit0 @ A) @ (bit0 @ (bit1 @ B))))) <= (~ (ord_less_eq_num @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5473_divmod__algorithm__code_I7_J)). 159.59/70.63 thf(22831,plain,((! [A:num,B:num]: ((((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit1 @ B)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ A)))) | ~ (ord_less_eq_num @ A @ B)) & (((unique5055182867167087721od_nat @ (bit0 @ A) @ (bit1 @ B)) = (unique5026877609467782581ep_nat @ (bit1 @ B) @ (unique5055182867167087721od_nat @ (bit0 @ A) @ (bit0 @ (bit1 @ B))))) | (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4526])). 159.59/70.63 thf(6160,axiom,((! [A:nat]: ((ord_min_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10167_min__0L)). 159.59/70.63 thf(28947,plain,((! [A:nat]: ((ord_min_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6160])). 159.59/70.63 thf(2117,axiom,((! [A:complex,B:complex,C:complex]: (((minus_minus_complex @ A @ B) = C) = (A = (plus_plus_complex @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1293_diff__eq__eq)). 159.59/70.63 thf(15070,plain,((! [A:complex,B:complex,C:complex]: (((minus_minus_complex @ A @ B) = C) = (A = (plus_plus_complex @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2117])). 159.59/70.63 thf(6929,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/sandbox/benchmark/theBenchmark.p',fact_9316_i__even__power)). 159.59/70.63 thf(31958,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)],[6929])). 159.59/70.63 thf(5257,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((modulo_modulo_nat @ A @ B) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3399_mod__less)). 159.59/70.63 thf(25464,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((modulo_modulo_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5257])). 159.59/70.63 thf(2087,axiom,((! [A:complex,B:nat,C:nat]: ((times_times_complex @ (power_power_complex @ A @ B) @ (power_power_complex @ (invers8013647133539491842omplex @ A) @ C)) = (times_times_complex @ (power_power_complex @ (invers8013647133539491842omplex @ A) @ C) @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9047_power__mult__power__inverse__commute)). 159.59/70.63 thf(14974,plain,((! [A:complex,B:nat,C:nat]: ((times_times_complex @ (power_power_complex @ A @ B) @ (power_power_complex @ (invers8013647133539491842omplex @ A) @ C)) = (times_times_complex @ (power_power_complex @ (invers8013647133539491842omplex @ A) @ C) @ (power_power_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2087])). 159.59/70.63 thf(5701,axiom,((! [A:real,B:real]: (((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)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5647_power2__le__iff__abs__le)). 159.59/70.63 thf(27128,plain,((! [A:real,B:real]: (((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)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5701])). 159.59/70.63 thf(679,axiom,((! [A:nat]: ((finite_card_nat @ (set_ord_atMost_nat @ A)) = (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9708_card__atMost)). 159.59/70.63 thf(10425,plain,((! [A:nat]: ((finite_card_nat @ (set_ord_atMost_nat @ A)) = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[679])). 159.59/70.63 thf(1296,axiom,((! [A:real,B:(extended_enat > real),C:extended_enat,D:extended_enat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_le72135733267957522d_enat @ C @ D) => ((ord_less_real @ A @ (B @ D)) <= (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3213_order__le__less__subst1)). 159.59/70.63 thf(12441,plain,((! [A:real,B:(extended_enat > real),C:extended_enat,D:extended_enat]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_le72135733267957522d_enat @ C @ D) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296])). 159.59/70.63 thf(7137,axiom,((! [A:nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ A) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1719_power__Suc__0)). 159.59/70.63 thf(32901,plain,((! [A:nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ A) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7137])). 159.59/70.63 thf(5509,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/sandbox/benchmark/theBenchmark.p',fact_5897_of__int__nonneg)). 159.59/70.63 thf(26486,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)],[5509])). 159.59/70.63 thf(2691,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ A @ C) => (dvd_dvd_real @ A @ (plus_plus_real @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3981_dvd__add)). 159.59/70.63 thf(16935,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ A @ C) => (dvd_dvd_real @ A @ (plus_plus_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2691])). 159.59/70.63 thf(4508,axiom,((! [A:complex]: (((cosh_complex @ A) = zero_zero_complex) = ((power_power_complex @ (exp_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1482373934393186551omplex @ one_one_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9363_cosh__zero__iff)). 159.59/70.63 thf(22753,plain,((! [A:complex]: (((cosh_complex @ A) = zero_zero_complex) = ((power_power_complex @ (exp_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (uminus1482373934393186551omplex @ one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4508])). 159.59/70.63 thf(1607,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/sandbox/benchmark/theBenchmark.p',fact_6567_of__nat__power__eq__of__nat__cancel__iff)). 159.59/70.63 thf(13471,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)],[1607])). 159.59/70.63 thf(4176,axiom,((! [A:num]: ((ring_17405671764205052669omplex @ (numeral_numeral_int @ A)) = (numera6690914467698888265omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5761_of__int__numeral)). 159.59/70.63 thf(21647,plain,((! [A:num]: ((ring_17405671764205052669omplex @ (numeral_numeral_int @ A)) = (numera6690914467698888265omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4176])). 159.59/70.63 thf(4785,axiom,((! [A:num]: (ord_less_eq_num @ one @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_semiring__norm_I68_J)). 159.59/70.63 thf(23783,plain,((! [A:num]: (ord_less_eq_num @ one @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4785])). 159.59/70.63 thf(609,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/sandbox/benchmark/theBenchmark.p',fact_3853_unit__div__1__div__1)). 159.59/70.63 thf(10194,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)],[609])). 159.59/70.63 thf(216,axiom,(((im @ imaginary_unit) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9652_imaginary__unit_Osimps_I2_J)). 159.59/70.63 thf(8909,plain,(((im @ imaginary_unit) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 159.59/70.63 thf(5949,axiom,((! [A:real,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_real @ A @ (power_power_real @ A @ B))) <= (ord_less_eq_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2465_self__le__power)). 159.59/70.63 thf(28278,plain,((! [A:real,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_real @ A @ (power_power_real @ A @ B))) | ~ (ord_less_eq_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5949])). 159.59/70.63 thf(3195,axiom,((! [A:real]: ((ord_less_eq_int @ zero_zero_int @ (archim7802044766580827645g_real @ A)) = (ord_less_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6994_zero__le__ceiling)). 159.59/70.63 thf(18529,plain,((! [A:real]: ((ord_less_eq_int @ zero_zero_int @ (archim7802044766580827645g_real @ A)) = (ord_less_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3195])). 159.59/70.63 thf(3750,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/sandbox/benchmark/theBenchmark.p',fact_4592_signed__take__bit__rec)). 159.59/70.63 thf(20315,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)],[3750])). 159.59/70.63 thf(996,axiom,((! [A:complex]: ((((divide1717551699836669952omplex @ A @ A) = one_one_complex) <= (A != zero_zero_complex)) & ((A = zero_zero_complex) => ((divide1717551699836669952omplex @ A @ A) = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1669_divide__self__if)). 159.59/70.63 thf(11434,plain,((! [A:complex]: ((((divide1717551699836669952omplex @ A @ A) = one_one_complex) | (A = zero_zero_complex)) & ((A = zero_zero_complex) => ((divide1717551699836669952omplex @ A @ A) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[996])). 159.59/70.63 thf(7148,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/sandbox/benchmark/theBenchmark.p',fact_9488_real__root__ge__0__iff)). 159.59/70.63 thf(32933,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)],[7148])). 159.59/70.63 thf(4870,axiom,((one_one_real != (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4972_one__neq__neg__one)). 159.59/70.63 thf(24089,plain,((~ (one_one_real = (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4870])). 159.59/70.63 thf(1442,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 @ A @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ 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 @ zero_zero_real @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5281_divide__less__eq__numeral_I2_J)). 159.59/70.63 thf(12951,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 @ A @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ 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 @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442])). 159.59/70.63 thf(7444,axiom,((! [A:num]: ((numeral_numeral_nat @ (inc @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5728_numeral__inc)). 159.59/70.63 thf(33969,plain,((! [A:num]: ((numeral_numeral_nat @ (inc @ A)) = (plus_plus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7444])). 159.59/70.63 thf(1367,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/sandbox/benchmark/theBenchmark.p',fact_4103_dvd__div__unit__iff)). 159.59/70.63 thf(12688,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)],[1367])). 159.59/70.63 thf(267,axiom,((! [A:code_integer,B:code_integer]: (((plus_p5714425477246183910nteger @ A @ B) = zero_z3403309356797280102nteger) = (B = (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5061_add__eq__0__iff)). 159.59/70.63 thf(9062,plain,((! [A:code_integer,B:code_integer]: (((plus_p5714425477246183910nteger @ A @ B) = zero_z3403309356797280102nteger) = (B = (uminus1351360451143612070nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 159.59/70.63 thf(5009,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (ord_max_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_928_max_Ocobounded1)). 159.59/70.63 thf(24583,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (ord_max_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5009])). 159.59/70.63 thf(1926,axiom,((neg_nu3811975205180677377ec_int = (^ [A:int]: (minus_minus_int @ (plus_plus_int @ A @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5736_dbl__dec__def)). 159.59/70.63 thf(14466,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)],[1926])). 159.59/70.63 thf(3739,axiom,((! [A:set_nat,B:(nat > extended_enat)]: (((groups7961826882256487087d_enat @ B @ A) = one_on7984719198319812577d_enat) <= (~ (finite_finite_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8388_prod_Oinfinite)). 159.59/70.63 thf(20278,plain,((! [A:set_nat,B:(nat > extended_enat)]: (((groups7961826882256487087d_enat @ (B) @ A) = one_on7984719198319812577d_enat) | (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3739])). 159.59/70.63 thf(7689,axiom,((! [A:num,B:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6019_and__numerals_I4_J)). 159.59/70.63 thf(34823,plain,((! [A:num,B:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit1 @ B))) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7689])). 159.59/70.63 thf(7133,axiom,((! [A:int,B:int]: (((times_times_int @ A @ B) = B) = ((B = zero_zero_int) | (A = one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1616_mult__cancel__right2)). 159.59/70.63 thf(32888,plain,((! [A:int,B:int]: (((times_times_int @ A @ B) = B) = ((B = zero_zero_int) | (A = one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7133])). 159.59/70.63 thf(5747,axiom,((! [A:num]: (zero_zero_nat != (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1848_zero__neq__numeral)). 159.59/70.63 thf(27286,plain,((! [A:num]: ~ (zero_zero_nat = (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5747])). 159.59/70.63 thf(1810,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/sandbox/benchmark/theBenchmark.p',fact_6912_power__eq__imp__eq__norm)). 159.59/70.63 thf(14097,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)],[1810])). 159.59/70.63 thf(8051,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/sandbox/benchmark/theBenchmark.p',fact_886_power2__commute)). 159.59/70.63 thf(35994,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)],[8051])). 159.59/70.63 thf(7922,axiom,((! [A:real]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (times_times_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_power2__eq__square)). 159.59/70.63 thf(35576,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)],[7922])). 159.59/70.63 thf(4107,axiom,((cosh_real = (^ [A:real]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (numeral_numeral_real @ (bit0 @ one))) @ (plus_plus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9365_cosh__def)). 159.59/70.63 thf(21428,plain,(((cosh_real) = (^ [A:real]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (numeral_numeral_real @ (bit0 @ one))) @ (plus_plus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4107])). 159.59/70.63 thf(964,axiom,((! [A:set_nat,B:(nat > extended_enat),C:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((A != bot_bot_set_nat) => ((ord_le72135733267957522d_enat @ (groups7108830773950497114d_enat @ B @ A) @ (groups7108830773950497114d_enat @ C @ A)) <= (! [D:nat]: ((ord_le72135733267957522d_enat @ (B @ D) @ (C @ D)) <= (member_nat @ D @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7494_sum__strict__mono)). 159.59/70.63 thf(11333,plain,((! [A:set_nat,B:(nat > extended_enat),C:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((~ (A = bot_bot_set_nat)) => ((ord_le72135733267957522d_enat @ (groups7108830773950497114d_enat @ (B) @ A) @ (groups7108830773950497114d_enat @ (C) @ A)) | ~ (! [D:nat]: ((ord_le72135733267957522d_enat @ (B @ D) @ (C @ D)) | ~ (member_nat @ D @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[964])). 159.59/70.63 thf(5590,axiom,((! [A:num,B:nat,C:nat]: (((power_8040749407984259932d_enat @ (numera1916890842035813515d_enat @ A) @ B) = (semiri4216267220026989637d_enat @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6592_numeral__power__eq__of__nat__cancel__iff)). 159.59/70.63 thf(26729,plain,((! [A:num,B:nat,C:nat]: (((power_8040749407984259932d_enat @ (numera1916890842035813515d_enat @ A) @ B) = (semiri4216267220026989637d_enat @ C)) = ((power_power_nat @ (numeral_numeral_nat @ A) @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5590])). 159.59/70.63 thf(4014,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/sandbox/benchmark/theBenchmark.p',fact_1734_zero__less__divide__1__iff)). 159.59/70.63 thf(21151,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)],[4014])). 159.59/70.63 thf(2013,axiom,((! [A:num]: (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4153_even__numeral)). 159.59/70.63 thf(14760,plain,((! [A:num]: (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2013])). 159.59/70.63 thf(8110,axiom,((! [A:nat]: ((ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = ((A = (suc @ zero_zero_nat)) | (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2521_less__2__cases__iff)). 159.59/70.63 thf(36177,plain,((! [A:nat]: ((ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = ((A = (suc @ zero_zero_nat)) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8110])). 159.59/70.63 thf(2385,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/sandbox/benchmark/theBenchmark.p',fact_9463_modulo__int__def)). 159.59/70.63 thf(15909,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)],[2385])). 159.59/70.63 thf(6126,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((((vEBT_vebt_mint @ A) = (some_nat @ C)) => ((vEBT_vebt_member @ A @ D) => (ord_less_eq_nat @ C @ D))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_mint__corr__help)). 159.59/70.63 thf(28838,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((((vEBT_vebt_mint @ A) = (some_nat @ C)) => ((vEBT_vebt_member @ A @ D) => (ord_less_eq_nat @ C @ D))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6126])). 159.59/70.63 thf(7517,axiom,(((plus_plus_nat @ one_one_nat) = suc)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_plus__1__eq__Suc)). 159.59/70.63 thf(34243,plain,(((plus_plus_nat @ one_one_nat) = (suc))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7517])). 159.59/70.63 thf(6276,axiom,((! [A:nat]: ((semiri1316708129612266289at_nat @ (bit_se2002935070580805687sk_nat @ A)) = (bit_se2002935070580805687sk_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6722_of__nat__mask__eq)). 159.59/70.63 thf(29396,plain,((! [A:nat]: ((semiri1316708129612266289at_nat @ (bit_se2002935070580805687sk_nat @ A)) = (bit_se2002935070580805687sk_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6276])). 159.59/70.63 thf(3825,axiom,((ord_less_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2131_zero__less__one)). 159.59/70.63 thf(20549,plain,((ord_less_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3825])). 159.59/70.63 thf(4657,axiom,((ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6745_pi__ge__two)). 159.59/70.63 thf(23354,plain,((ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4657])). 159.59/70.63 thf(5630,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/sandbox/benchmark/theBenchmark.p',fact_5215_power__minus)). 159.59/70.63 thf(26880,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)],[5630])). 159.59/70.63 thf(7063,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/sandbox/benchmark/theBenchmark.p',fact_2417_mult__less__cancel__left1)). 159.59/70.63 thf(32589,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)],[7063])). 159.59/70.63 thf(3275,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1228_distrib__right)). 159.59/70.63 thf(18795,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3275])). 159.59/70.63 thf(3063,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/sandbox/benchmark/theBenchmark.p',fact_2233_mult__le__cancel__left__pos)). 159.59/70.63 thf(18096,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)],[3063])). 159.59/70.63 thf(5859,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/sandbox/benchmark/theBenchmark.p',fact_5328_power__minus1__odd)). 159.59/70.63 thf(27902,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)],[5859])). 159.59/70.63 thf(7794,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/sandbox/benchmark/theBenchmark.p',fact_516_nat__add__left__cancel__less)). 159.59/70.63 thf(35168,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)],[7794])). 159.59/70.63 thf(7639,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((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 @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2560_VEBT__internal_Oexp__split__high__low_I1_J)). 159.59/70.63 thf(34672,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => ((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 @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7639])). 159.59/70.63 thf(6823,axiom,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2054_linordered__nonzero__semiring__class_Ozero__le__one)). 159.59/70.63 thf(31515,plain,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6823])). 159.59/70.63 thf(1117,axiom,((! [A:num,B:num,C:extended_enat]: ((plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ B) @ C)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ (plus_plus_num @ A @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__numeral__left)). 159.59/70.63 thf(11836,plain,((! [A:num,B:num,C:extended_enat]: ((plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ B) @ C)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ (plus_plus_num @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117])). 159.59/70.63 thf(7729,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2090_mult__pos__neg2)). 159.59/70.63 thf(34973,plain,((! [A:nat,B:nat]: (((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7729])). 159.59/70.63 thf(3106,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/sandbox/benchmark/theBenchmark.p',fact_3620_mod__pos__pos__trivial)). 159.59/70.63 thf(18245,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)],[3106])). 159.59/70.63 thf(7081,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/sandbox/benchmark/theBenchmark.p',fact_5842_of__int__le__of__int__power__cancel__iff)). 159.59/70.63 thf(32648,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)],[7081])). 159.59/70.63 thf(1453,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/sandbox/benchmark/theBenchmark.p',fact_1204_add__mono__thms__linordered__field_I2_J)). 159.59/70.63 thf(12986,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)],[1453])). 159.59/70.63 thf(8196,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/sandbox/benchmark/theBenchmark.p',fact_1146_add__mono__thms__linordered__semiring_I4_J)). 159.59/70.63 thf(36456,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)],[8196])). 159.59/70.63 thf(712,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/sandbox/benchmark/theBenchmark.p',fact_1120_add_Oleft__commute)). 159.59/70.63 thf(10547,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)],[712])). 159.59/70.63 thf(7380,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/sandbox/benchmark/theBenchmark.p',fact_9521_odd__real__root__power__cancel)). 159.59/70.63 thf(33769,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)],[7380])). 159.59/70.63 thf(5800,axiom,((! [A:set_nat,B:nat]: (((member_nat @ B @ A) => (? [C:nat]: ((member_nat @ C @ A) & ! [D:nat]: (((ord_less_eq_nat @ C @ D) => (C = D)) <= (member_nat @ D @ A)) & (ord_less_eq_nat @ B @ C)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3749_finite__has__maximal2)). 159.59/70.63 thf(27531,plain,((! [A:set_nat,B:nat]: (((member_nat @ B @ A) => (? [C:nat]: ((member_nat @ C @ A) & ! [D:nat]: (((ord_less_eq_nat @ C @ D) => (C = D)) | ~ (member_nat @ D @ A)) & (ord_less_eq_nat @ B @ C)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5800])). 159.59/70.63 thf(3614,axiom,((! [A:(nat > real),B:real,C:real]: ((summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D)))) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7119_powser__inside)). 159.59/70.63 thf(19858,plain,((! [A:(nat > real),B:real,C:real]: ((summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ B @ D)))) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3614])). 159.59/70.63 thf(1477,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/sandbox/benchmark/theBenchmark.p',fact_1585_le__add__same__cancel1)). 159.59/70.63 thf(13075,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)],[1477])). 159.59/70.63 thf(1405,axiom,(((nat2 @ one_one_int) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9414_nat__1)). 159.59/70.63 thf(12835,plain,(((nat2 @ one_one_int) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405])). 159.59/70.63 thf(2093,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (! [D:code_integer,E:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ C)) = (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ (minus_8373710615458151222nteger @ D @ (times_3573771949741848930nteger @ E @ B)) @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4294_inf__period_I3_J)). 159.59/70.63 thf(14994,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (! [D:code_integer,E:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ C)) = (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ (minus_8373710615458151222nteger @ D @ (times_3573771949741848930nteger @ E @ B)) @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2093])). 159.59/70.63 thf(213,axiom,((! [A:real,B:real]: ((cosh_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (cosh_real @ A) @ (cosh_real @ B)) @ (times_times_real @ (sinh_real @ A) @ (sinh_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9326_cosh__add)). 159.59/70.63 thf(8900,plain,((! [A:real,B:real]: ((cosh_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (cosh_real @ A) @ (cosh_real @ B)) @ (times_times_real @ (sinh_real @ A) @ (sinh_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 159.59/70.63 thf(2965,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/sandbox/benchmark/theBenchmark.p',fact_6901_norm__mult)). 159.59/70.63 thf(17800,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)],[2965])). 159.59/70.63 thf(3601,axiom,((! [A:int,B:int]: (((dvd_dvd_int @ (divide_divide_int @ A @ B) @ one_one_int) <= (dvd_dvd_int @ B @ one_one_int)) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3847_unit__div)). 159.59/70.63 thf(19817,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (divide_divide_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)],[3601])). 159.59/70.63 thf(611,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/sandbox/benchmark/theBenchmark.p',fact_6658_of__nat__less__of__int__iff)). 159.59/70.63 thf(10200,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)],[611])). 159.59/70.63 thf(2104,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((cos_real @ (arccos @ A)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7712_cos__arccos__abs)). 159.59/70.63 thf(15030,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((cos_real @ (arccos @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2104])). 159.59/70.63 thf(1211,axiom,((! [A:extended_enat,B:extended_enat]: (((B != zero_z5237406670263579293d_enat) => ((times_7803423173614009249d_enat @ A @ B) != zero_z5237406670263579293d_enat)) <= (A != zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1858_no__zero__divisors)). 159.59/70.63 thf(12170,plain,((! [A:extended_enat,B:extended_enat]: (((~ (B = zero_z5237406670263579293d_enat)) => (~ ((times_7803423173614009249d_enat @ A @ B) = zero_z5237406670263579293d_enat))) | (A = zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211])). 159.59/70.63 thf(651,axiom,((! [A:real]: (ord_less_real @ (arctan @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6776_arctan__ubound)). 159.59/70.63 thf(10334,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)],[651])). 159.59/70.63 thf(1140,axiom,((! [A:int,B:int,C:int]: ((A = (minus_minus_int @ B @ C)) = ((plus_plus_int @ A @ C) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1292_eq__diff__eq)). 159.59/70.63 thf(11905,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)],[1140])). 159.59/70.63 thf(2934,axiom,((! [A:nat]: (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6753_of__nat__less__two__power)). 159.59/70.63 thf(17700,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)],[2934])). 159.59/70.63 thf(73,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ C) = (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ B)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9254_neg__divideR__le__eq)). 159.59/70.63 thf(8470,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B) @ C) = (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ C) @ B)) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 159.59/70.63 thf(841,axiom,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (groups6464643781859351333omplex @ (^ [C:nat]: (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8920_pochhammer__Suc__prod__rev)). 159.59/70.63 thf(10963,plain,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (groups6464643781859351333omplex @ (^ [C:nat]: (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[841])). 159.59/70.63 thf(1152,axiom,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ (plus_p5714425477246183910nteger @ A @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4642_minus__add__cancel)). 159.59/70.63 thf(11941,plain,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ (plus_p5714425477246183910nteger @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152])). 159.59/70.63 thf(6663,axiom,((! [A:real,B:real]: ((A = (times_times_real @ B @ A)) = ((A = zero_zero_real) | (B = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1618_mult__cancel__right1)). 159.59/70.63 thf(30826,plain,((! [A:real,B:real]: ((A = (times_times_real @ B @ A)) = ((A = zero_zero_real) | (B = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6663])). 159.59/70.63 thf(6925,axiom,((! [A:nat,B:nat,C:nat]: ((~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C)))) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_add__leE)). 159.59/70.63 thf(31941,plain,((! [A:nat,B:nat,C:nat]: (~ ((ord_less_eq_nat @ A @ C) => (~ (ord_less_eq_nat @ B @ C))) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6925])). 159.59/70.63 thf(1252,axiom,((minus_8373710615458151222nteger = (^ [A:code_integer,B:code_integer]: (plus_p5714425477246183910nteger @ A @ (uminus1351360451143612070nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5109_ab__group__add__class_Oab__diff__conv__add__uminus)). 159.59/70.63 thf(12301,plain,(((minus_8373710615458151222nteger) = (^ [A:code_integer,B:code_integer]: (plus_p5714425477246183910nteger @ A @ (uminus1351360451143612070nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252])). 159.59/70.63 thf(5694,axiom,((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ mi @ ma)) @ deg @ treeList @ summary) @ deg)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494__C10_C)). 159.59/70.63 thf(27109,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)],[5694])). 159.59/70.63 thf(4521,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_V5719532721284313246member @ A @ B) = C) => ((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) & ((B = one_one_nat) => (E))) <= (B != zero_zero_nat)) & ((D) <= (B = zero_zero_nat))))))) => ((! [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)))) => (~ (! [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))))))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3317_VEBT__internal_Onaive__member_Opelims_I1_J)). 159.59/70.63 thf(22790,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((vEBT_V5719532721284313246member @ A @ B) = C) => ((accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ A @ B)) => ((! [D:$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) & ((B = one_one_nat) => (E))) | (B = zero_zero_nat)) & ((D) | ~ (B = zero_zero_nat))))))) => ((! [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)))) => (~ (! [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))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4521])). 159.59/70.63 thf(411,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/sandbox/benchmark/theBenchmark.p',fact_7649_sum__diff)). 159.59/70.63 thf(9543,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)],[411])). 159.59/70.63 thf(7979,axiom,((! [A:num]: ((sqr @ (bit0 @ A)) = (bit0 @ (bit0 @ (sqr @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9796_sqr_Osimps_I2_J)). 159.59/70.63 thf(35750,plain,((! [A:num]: ((sqr @ (bit0 @ A)) = (bit0 @ (bit0 @ (sqr @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7979])). 159.59/70.63 thf(2984,axiom,((! [A:set_nat,B:nat]: ((ord_less_eq_set_nat @ A @ (set_or4665077453230672383an_nat @ B @ (plus_plus_nat @ B @ (finite_card_nat @ A)))) => (A = (set_or4665077453230672383an_nat @ B @ (plus_plus_nat @ B @ (finite_card_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9716_subset__card__intvl__is__intvl)). 159.59/70.63 thf(17854,plain,((! [A:set_nat,B:nat]: ((ord_less_eq_set_nat @ A @ (set_or4665077453230672383an_nat @ B @ (plus_plus_nat @ B @ (finite_card_nat @ A)))) => (A = (set_or4665077453230672383an_nat @ B @ (plus_plus_nat @ B @ (finite_card_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2984])). 159.59/70.63 thf(7084,axiom,((! [A:num,B:num]: ((ord_less_num @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5446_semiring__norm_I79_J)). 159.59/70.63 thf(32680,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)],[7084])). 159.59/70.63 thf(6317,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1333_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse)). 159.59/70.63 thf(29547,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)],[6317])). 159.59/70.63 thf(7286,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/sandbox/benchmark/theBenchmark.p',fact_1269_left__diff__distrib)). 159.59/70.63 thf(33428,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)],[7286])). 159.59/70.63 thf(928,axiom,((! [A:extended_enat,B:extended_enat]: (((ord_le72135733267957522d_enat @ B @ zero_z5237406670263579293d_enat) => (ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ zero_z5237406670263579293d_enat)) <= (ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2117_add__neg__neg)). 159.59/70.63 thf(11226,plain,((! [A:extended_enat,B:extended_enat]: (((ord_le72135733267957522d_enat @ B @ zero_z5237406670263579293d_enat) => (ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ zero_z5237406670263579293d_enat)) | ~ (ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[928])). 159.59/70.63 thf(7943,axiom,((! [A:num]: (one != (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3703_verit__eq__simplify_I10_J)). 159.59/70.63 thf(35645,plain,((! [A:num]: ~ (one = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7943])). 159.59/70.63 thf(5534,axiom,((! [A:num,B:complex,C:complex]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (divide1717551699836669952omplex @ B @ C)) = (((C != zero_zero_complex) => ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ C) = B)) & ((C = zero_zero_complex) => ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = zero_zero_complex)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5244_eq__divide__eq__numeral_I2_J)). 159.59/70.63 thf(26555,plain,((! [A:num,B:complex,C:complex]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (divide1717551699836669952omplex @ B @ C)) = (((~ (C = zero_zero_complex)) => ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ C) = B)) & ((C = zero_zero_complex) => ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5534])). 159.59/70.63 thf(7051,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/sandbox/benchmark/theBenchmark.p',fact_1481_mult__cancel__right)). 159.59/70.63 thf(32524,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)],[7051])). 159.59/70.63 thf(2669,axiom,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ A @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1386_divide__divide__eq__left)). 159.59/70.63 thf(16855,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)],[2669])). 159.59/70.63 thf(254,axiom,(((bit_se1409905431419307370or_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ one_one_int)) = (bit_ri7919022796975470100ot_int @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9586_or__not__numerals_I1_J)). 159.59/70.63 thf(9025,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)],[254])). 159.59/70.63 thf(6199,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/sandbox/benchmark/theBenchmark.p',fact_2152_power__mono)). 159.59/70.63 thf(29089,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)],[6199])). 159.59/70.63 thf(6239,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ A) <= (ord_less_num @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4479_minf_I5_J)). 159.59/70.63 thf(29212,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)],[6239])). 159.59/70.63 thf(463,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/sandbox/benchmark/theBenchmark.p',fact_9681_complex__unit__circle)). 159.59/70.63 thf(9706,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)],[463])). 159.59/70.63 thf(285,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/sandbox/benchmark/theBenchmark.p',fact_9670_Re__power2)). 159.59/70.63 thf(9114,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)],[285])). 159.59/70.63 thf(1961,axiom,((neg_nu8295874005876285629c_real = (^ [A:real]: (plus_plus_real @ (plus_plus_real @ A @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5912_dbl__inc__def)). 159.59/70.63 thf(14572,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)],[1961])). 159.59/70.63 thf(5589,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/sandbox/benchmark/theBenchmark.p',fact_4547_option_Osize__gen_I2_J)). 159.59/70.63 thf(26726,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)],[5589])). 159.59/70.63 thf(4800,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]: ((((B @ D) = zero_zero_nat) <= (C != D)) <= (member_nat @ D @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7926_sum__eq__1__iff)). 159.59/70.63 thf(23827,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]: (((B @ D) = zero_zero_nat) | (C = D) | ~ (member_nat @ D @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4800])). 159.59/70.63 thf(7371,axiom,((! [A:nat,B:nat,C:(nat > complex)]: ((((groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_complex @ (groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) <= (~ (ord_less_nat @ (suc @ A) @ B))) & ((ord_less_nat @ (suc @ A) @ B) => ((groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8453_prod_Ocl__ivl__Suc)). 159.59/70.63 thf(33737,plain,((! [A:nat,B:nat,C:(nat > complex)]: ((((groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_times_complex @ (groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) | (ord_less_nat @ (suc @ A) @ B)) & ((ord_less_nat @ (suc @ A) @ B) => ((groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7371])). 159.59/70.63 thf(7892,axiom,((! [A:num]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5619_odd__numeral)). 159.59/70.63 thf(35481,plain,((! [A:num]: ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7892])). 159.59/70.63 thf(6546,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/sandbox/benchmark/theBenchmark.p',fact_1158_add__le__imp__le__right)). 159.59/70.63 thf(30416,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)],[6546])). 159.59/70.63 thf(6136,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1915_gr0I)). 159.59/70.63 thf(28873,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6136])). 159.59/70.63 thf(8095,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_nat @ zero_zero_nat @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2061_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)). 159.59/70.63 thf(36132,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8095])). 159.59/70.63 thf(5398,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => (((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ C)) <= (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4129_dvd__diffD1)). 159.59/70.63 thf(26059,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) => (((ord_less_eq_nat @ C @ B) => (dvd_dvd_nat @ A @ C)) | ~ (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5398])). 159.59/70.63 thf(2895,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > real),D:real]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_less_real @ (C @ B) @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_less_real @ (C @ E) @ (C @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_real @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2899_order__less__subst2)). 159.59/70.63 thf(17573,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > real),D:real]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_less_real @ (C @ B) @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_less_real @ (C @ E) @ (C @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_real @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2895])). 159.59/70.63 thf(6069,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/sandbox/benchmark/theBenchmark.p',fact_2392_length__pos__if__in__set)). 159.59/70.63 thf(28657,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)],[6069])). 159.59/70.63 thf(5070,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/sandbox/benchmark/theBenchmark.p',fact_3432_Suc__times__numeral__mod__eq)). 159.59/70.63 thf(24813,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)],[5070])). 159.59/70.63 thf(6927,axiom,((! [A:(nat > nat),B:nat]: (((summable_nat @ A) <= (! [C:nat]: (ord_less_eq_nat @ (groups3542108847815614940at_nat @ A @ (set_ord_atMost_nat @ C)) @ B))) <= (! [C:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8760_bounded__imp__summable)). 159.59/70.63 thf(31947,plain,((! [A:(nat > nat),B:nat]: ((summable_nat @ (A)) | ~ (! [C:nat]: (ord_less_eq_nat @ (groups3542108847815614940at_nat @ (A) @ (set_ord_atMost_nat @ C)) @ B)) | ~ (! [C:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6927])). 159.59/70.63 thf(6233,axiom,((! [A:int,B:int]: ((times_times_int @ A @ (uminus_uminus_int @ B)) = (uminus_uminus_int @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4624_mult__minus__right)). 159.59/70.63 thf(29193,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)],[6233])). 159.59/70.63 thf(3158,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/sandbox/benchmark/theBenchmark.p',fact_5779_of__int__mult)). 159.59/70.63 thf(18418,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)],[3158])). 159.59/70.63 thf(1328,axiom,((! [A:complex,B:complex]: ((if_complex @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Complex__Ocomplex_T)). 159.59/70.63 thf(12541,plain,((! [A:complex,B:complex]: ((if_complex @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328])). 159.59/70.63 thf(3643,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/sandbox/benchmark/theBenchmark.p',fact_4379_one__div__2__pow__eq)). 159.59/70.63 thf(19949,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)],[3643])). 159.59/70.63 thf(211,axiom,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ (bit_ri7919022796975470100ot_int @ A) @ B) = (~ (bit_se1146084159140164899it_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9579_bit__not__int__iff)). 159.59/70.63 thf(8894,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)],[211])). 159.59/70.63 thf(1639,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2041_add__increasing)). 159.59/70.63 thf(13569,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639])). 159.59/70.63 thf(2455,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B))) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2062_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)). 159.59/70.63 thf(16154,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ zero_zero_int @ C) => (ord_less_int @ (times_times_int @ C @ A) @ (times_times_int @ C @ B))) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2455])). 159.59/70.63 thf(3185,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/sandbox/benchmark/theBenchmark.p',fact_8336_gbinomial__minus)). 159.59/70.63 thf(18494,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)],[3185])). 159.59/70.63 thf(5935,axiom,((! [A:nat,B:nat,C:nat]: ((((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 @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9082_choose__mult)). 159.59/70.63 thf(28190,plain,((! [A:nat,B:nat,C:nat]: (((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 @ B @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5935])). 159.59/70.63 thf(3781,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => (dvd_dvd_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3951_dvd__mult2)). 159.59/70.63 thf(20411,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ B) => (dvd_dvd_real @ A @ (times_times_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3781])). 159.59/70.63 thf(8136,axiom,(((numeral_numeral_nat @ one) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_numerals_I1_J)). 159.59/70.63 thf(36273,plain,(((numeral_numeral_nat @ one) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8136])). 159.59/70.63 thf(2904,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/sandbox/benchmark/theBenchmark.p',fact_6053_plus__and__or)). 159.59/70.63 thf(17605,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)],[2904])). 159.59/70.63 thf(894,axiom,((! [A:num]: (ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ (numera1916890842035813515d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_one__le__numeral)). 159.59/70.63 thf(11124,plain,((! [A:num]: (ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ (numera1916890842035813515d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[894])). 159.59/70.63 thf(7964,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_add__less__imp__less__left)). 159.59/70.63 thf(35708,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ C) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7964])). 159.59/70.63 thf(2469,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => ((ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_eq_real @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9002_inverse__le__iff__le__neg)). 159.59/70.63 thf(16199,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => ((ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_eq_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2469])). 159.59/70.63 thf(1216,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ (sin_real @ A) @ (sin_real @ B)) <= (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (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/sandbox/benchmark/theBenchmark.p',fact_6865_sin__monotone__2pi__le)). 159.59/70.63 thf(12184,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (sin_real @ A) @ (sin_real @ B)) | ~ (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (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)],[1216])). 159.59/70.63 thf(6735,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ (sqrt @ A) @ B) <= (ord_less_eq_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6439_real__le__lsqrt)). 159.59/70.63 thf(31214,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (sqrt @ A) @ B) | ~ (ord_less_eq_real @ A @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6735])). 159.59/70.63 thf(1698,axiom,((! [A:extended_enat]: (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1826_zero__le)). 159.59/70.63 thf(13745,plain,((! [A:extended_enat]: (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698])). 159.59/70.63 thf(2533,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/sandbox/benchmark/theBenchmark.p',fact_8525_prod_OatMost__shift)). 159.59/70.63 thf(16400,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)],[2533])). 159.59/70.63 thf(2576,axiom,((! [A:int,B:nat]: ((ord_less_eq_nat @ (nat2 @ A) @ B) = (ord_less_eq_int @ A @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9434_nat__le__iff)). 159.59/70.63 thf(16532,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)],[2576])). 159.59/70.63 thf(6538,axiom,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1715_div__by__Suc__0)). 159.59/70.63 thf(30390,plain,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6538])). 159.59/70.63 thf(8008,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ A @ (divide_divide_nat @ B @ A)) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3840_dvd__mult__div__cancel)). 159.59/70.63 thf(35840,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((times_times_nat @ A @ (divide_divide_nat @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8008])). 159.59/70.63 thf(1407,axiom,((! [A:real]: ((times_times_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6092_exp__minus__inverse)). 159.59/70.63 thf(12840,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)],[1407])). 159.59/70.63 thf(6983,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (modulo_modulo_nat @ A @ B) @ B) = (modulo_modulo_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3388_mod__mod__trivial)). 159.59/70.63 thf(32276,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)],[6983])). 159.59/70.63 thf(1951,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6831_nat__less__as__int)). 159.59/70.63 thf(14544,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)],[1951])). 159.59/70.63 thf(3409,axiom,((! [A:num]: ((numera1916890842035813515d_enat @ (inc @ A)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5725_numeral__inc)). 159.59/70.63 thf(19215,plain,((! [A:num]: ((numera1916890842035813515d_enat @ (inc @ A)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3409])). 159.59/70.63 thf(6354,axiom,((! [A:nat]: ((binomial @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8995_binomial__1)). 159.59/70.63 thf(29655,plain,((! [A:nat]: ((binomial @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6354])). 159.59/70.63 thf(1637,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/sandbox/benchmark/theBenchmark.p',fact_3053_dense__ge)). 159.59/70.63 thf(13563,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)],[1637])). 159.59/70.63 thf(147,axiom,((! [A:complex]: (summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (real_V2046097035970521341omplex @ (cos_coeff @ B) @ (power_power_complex @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9274_summable__norm__cos)). 159.59/70.63 thf(8697,plain,((! [A:complex]: (summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (real_V2046097035970521341omplex @ (cos_coeff @ B) @ (power_power_complex @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 159.59/70.63 thf(2946,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/sandbox/benchmark/theBenchmark.p',fact_1286_diff__diff__eq2)). 159.59/70.63 thf(17737,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)],[2946])). 159.59/70.63 thf(1122,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/sandbox/benchmark/theBenchmark.p',fact_1367_eq__add__iff1)). 159.59/70.63 thf(11851,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)],[1122])). 159.59/70.63 thf(623,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ C) => ((nth_nat @ (upt @ A @ C) @ B) = (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10127_nth__upt)). 159.59/70.63 thf(10242,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ C) => ((nth_nat @ (upt @ A @ C) @ B) = (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[623])). 159.59/70.63 thf(6266,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/sandbox/benchmark/theBenchmark.p',fact_3891_power__less__zero__eq__numeral)). 159.59/70.63 thf(29368,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)],[6266])). 159.59/70.63 thf(6741,axiom,((! [A:nat]: ((bit_se1412395901928357646or_nat @ one_one_nat @ A) = (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6129_one__or__eq)). 159.59/70.63 thf(31233,plain,((! [A:nat]: ((bit_se1412395901928357646or_nat @ one_one_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)],[6741])). 159.59/70.63 thf(1547,axiom,((! [A:real,B:real]: ((ord_less_real @ B @ A) | (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3253_linorder__le__less__linear)). 159.59/70.63 thf(13281,plain,((! [A:real,B:real]: ((ord_less_real @ B @ A) | (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547])). 159.59/70.63 thf(6810,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/sandbox/benchmark/theBenchmark.p',fact_6643_of__nat__le__numeral__power__cancel__iff)). 159.59/70.63 thf(31477,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)],[6810])). 159.59/70.63 thf(8093,axiom,((! [A:nat]: ((bit_se547839408752420682it_nat @ A @ (suc @ zero_zero_nat)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9552_push__bit__of__Suc__0)). 159.59/70.63 thf(36126,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)],[8093])). 159.59/70.63 thf(5138,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/sandbox/benchmark/theBenchmark.p',fact_1703_mult__eq__1__iff)). 159.59/70.63 thf(25029,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)],[5138])). 159.59/70.63 thf(2494,axiom,((! [A:$o,B:nat]: ((bit_se1146084159140164899it_int @ (zero_n2684676970156552555ol_int @ A) @ B) = ((B = zero_zero_nat) & (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6396_bit__of__bool__iff)). 159.59/70.63 thf(16278,plain,((! [A:$o,B:nat]: ((bit_se1146084159140164899it_int @ (zero_n2684676970156552555ol_int @ A) @ B) = ((B = zero_zero_nat) & (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2494])). 159.59/70.63 thf(2086,axiom,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ A @ (times_times_complex @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1440_divide__divide__eq__left_H)). 159.59/70.63 thf(14971,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)],[2086])). 159.59/70.63 thf(4536,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (bitM @ A)) = (minus_minus_complex @ (numera6690914467698888265omplex @ (bit0 @ A)) @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5915_numeral__BitM)). 159.59/70.63 thf(22912,plain,((! [A:num]: ((numera6690914467698888265omplex @ (bitM @ A)) = (minus_minus_complex @ (numera6690914467698888265omplex @ (bit0 @ A)) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4536])). 159.59/70.63 thf(3556,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: (((ord_less_eq_set_nat @ B @ A) => (((ord_less_eq_int @ (groups705719431365010083at_int @ C @ B) @ (groups705719431365010083at_int @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ B) => (ord_less_eq_int @ zero_zero_int @ (C @ D))))) <= (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => (ord_less_eq_int @ one_one_int @ (C @ D)))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8858_prod__mono2)). 159.59/70.63 thf(19659,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: (((ord_less_eq_set_nat @ B @ A) => ((ord_less_eq_int @ (groups705719431365010083at_int @ (C) @ B) @ (groups705719431365010083at_int @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ B) => (ord_less_eq_int @ zero_zero_int @ (C @ D)))) | ~ (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => (ord_less_eq_int @ one_one_int @ (C @ D)))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3556])). 159.59/70.63 thf(6473,axiom,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = ((B != A) & (ord_less_eq_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2757_nle__le)). 159.59/70.63 thf(30151,plain,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = (~ (B = A) & (ord_less_eq_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6473])). 159.59/70.63 thf(6100,axiom,((! [A:(nat > nat)]: (((! [B:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ B))) => (((suminf_nat @ A) = zero_zero_nat) = (! [B:nat]: ((A @ B) = zero_zero_nat)))) <= (summable_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7057_suminf__eq__zero__iff)). 159.59/70.63 thf(28749,plain,((! [A:(nat > nat)]: (((! [B:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ B))) => (((suminf_nat @ (A)) = zero_zero_nat) = (! [B:nat]: ((A @ B) = zero_zero_nat)))) | ~ (summable_nat @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6100])). 159.59/70.63 thf(4589,axiom,((! [A:nat]: ((power_power_int @ one_one_int @ A) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_power__one)). 159.59/70.63 thf(23100,plain,((! [A:nat]: ((power_power_int @ one_one_int @ A) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4589])). 159.59/70.63 thf(6326,axiom,((! [A:nat]: ((bit_se1412395901928357646or_nat @ A @ one_one_nat) = (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6126_or__one__eq)). 159.59/70.63 thf(29570,plain,((! [A:nat]: ((bit_se1412395901928357646or_nat @ A @ one_one_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)],[6326])). 159.59/70.63 thf(6466,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/sandbox/benchmark/theBenchmark.p',fact_7786_sum__gp__multiplied)). 159.59/70.63 thf(30127,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)],[6466])). 159.59/70.63 thf(6556,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3143_order_Ostrict__implies__order)). 159.59/70.63 thf(30448,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6556])). 159.59/70.63 thf(6000,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)) & (((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/sandbox/benchmark/theBenchmark.p',fact_5317_minus__one__power__iff)). 159.59/70.63 thf(28440,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)) & (((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)],[6000])). 159.59/70.63 thf(26,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ (real_V1485227260804924795R_real @ A @ B)) <= (ord_less_eq_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9245_scaleR__nonpos__nonpos)). 159.59/70.63 thf(8332,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ (real_V1485227260804924795R_real @ A @ B)) | ~ (ord_less_eq_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 159.59/70.63 thf(8017,axiom,((! [A:num]: ((one_one_nat = (numeral_numeral_nat @ A)) = (one = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_one__eq__numeral__iff)). 159.59/70.63 thf(35868,plain,((! [A:num]: ((one_one_nat = (numeral_numeral_nat @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8017])). 159.59/70.63 thf(716,axiom,((! [A:real,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (gbinomial_real @ A @ C) @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ C))) @ (set_ord_atMost_nat @ B)) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (gbinomial_real @ (minus_minus_real @ A @ one_one_real) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8927_gbinomial__sum__lower__neg)). 159.59/70.63 thf(10557,plain,((! [A:real,B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (gbinomial_real @ A @ C) @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ C))) @ (set_ord_atMost_nat @ B)) = (times_times_real @ (power_power_real @ (uminus_uminus_real @ one_one_real) @ B) @ (gbinomial_real @ (minus_minus_real @ A @ one_one_real) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[716])). 159.59/70.63 thf(1787,axiom,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1518_add__cancel__left__right)). 159.59/70.63 thf(14021,plain,((! [A:complex,B:complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1787])). 159.59/70.63 thf(3436,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (arctan @ A) @ (arctan @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5882_arctan__monotone)). 159.59/70.63 thf(19296,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (arctan @ A) @ (arctan @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3436])). 159.59/70.63 thf(5420,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/sandbox/benchmark/theBenchmark.p',fact_4795_semiring__norm_I170_J)). 159.59/70.63 thf(26163,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)],[5420])). 159.59/70.63 thf(7336,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/sandbox/benchmark/theBenchmark.p',fact_4102_dvd__div__unit__iff)). 159.59/70.63 thf(33621,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)],[7336])). 159.59/70.63 thf(5971,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/sandbox/benchmark/theBenchmark.p',fact_190_power2__sum)). 159.59/70.63 thf(28347,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)],[5971])). 159.59/70.63 thf(7025,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/sandbox/benchmark/theBenchmark.p',fact_5609_power__numeral__odd)). 159.59/70.63 thf(32432,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)],[7025])). 159.59/70.63 thf(2120,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/sandbox/benchmark/theBenchmark.p',fact_8360_pochhammer__times__pochhammer__half)). 159.59/70.63 thf(15079,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)],[2120])). 159.59/70.63 thf(7935,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/sandbox/benchmark/theBenchmark.p',fact_7814_Sum__Icc__nat)). 159.59/70.63 thf(35613,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)],[7935])). 159.59/70.63 thf(157,axiom,((! [A:complex,B:complex]: ((cosh_complex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (cosh_complex @ A) @ (cosh_complex @ B)) @ (times_times_complex @ (sinh_complex @ A) @ (sinh_complex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9325_cosh__add)). 159.59/70.63 thf(8740,plain,((! [A:complex,B:complex]: ((cosh_complex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (cosh_complex @ A) @ (cosh_complex @ B)) @ (times_times_complex @ (sinh_complex @ A) @ (sinh_complex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[157])). 159.59/70.63 thf(5550,axiom,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3962_dvd__triv__left)). 159.59/70.63 thf(26604,plain,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5550])). 159.59/70.63 thf(6177,axiom,((! [A:(nat > $o),B:(nat > (nat > nat)),C:product_prod_nat_nat]: ((A @ (produc6842872674320459806at_nat @ B @ C)) => (~ (! [D:nat,E:nat]: ((~ (A @ (B @ D @ E))) <= (C = (product_Pair_nat_nat @ D @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5013_case__prodE2)). 159.59/70.63 thf(29014,plain,((! [A:(nat > $o),B:(nat > (nat > nat)),C:product_prod_nat_nat]: ((A @ (produc6842872674320459806at_nat @ (B) @ C)) => (~ (! [D:nat,E:nat]: (~ (A @ (B @ D @ E)) | ~ (C = (product_Pair_nat_nat @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6177])). 159.59/70.63 thf(1881,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/sandbox/benchmark/theBenchmark.p',fact_7802_double__arith__series)). 159.59/70.63 thf(14326,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)],[1881])). 159.59/70.63 thf(7409,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/sandbox/benchmark/theBenchmark.p',fact_5526_abs__triangle__ineq2__sym)). 159.59/70.63 thf(33856,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)],[7409])). 159.59/70.63 thf(6602,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: (((! [D:nat]: (C @ D @ (suc @ D))) => ((C @ A @ B) <= (! [D:nat,E:nat,F:nat]: (((ord_less_nat @ E @ F) => ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) <= (ord_less_nat @ D @ E))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_less__Suc__induct)). 159.59/70.63 thf(30608,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: (((! [D:nat]: (C @ D @ (suc @ D))) => ((C @ A @ B) | ~ (! [D:nat,E:nat,F:nat]: (((ord_less_nat @ E @ F) => ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) | ~ (ord_less_nat @ D @ E))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6602])). 159.59/70.63 thf(4529,axiom,((! [A:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ A) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5407_abs__le__self__iff)). 159.59/70.63 thf(22890,plain,((! [A:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ A) = (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4529])). 159.59/70.63 thf(7457,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_less__imp__diff__less)). 159.59/70.63 thf(34011,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7457])). 159.59/70.63 thf(6972,axiom,((! [A:vEBT_VEBT,B:nat,C:option_nat]: ((((? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E))) => ((B = zero_zero_nat) => (C != none_nat))) => (((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((? [F:nat]: (B = (suc @ (suc @ F)))) => (~ (((~ (E)) => (((C = (some_nat @ zero_zero_nat)) <= (D)) & ((~ (D)) => (C = none_nat)))) & ((C = (some_nat @ one_one_nat)) <= (E))))))) => (((? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))) => (C != none_nat)) => ((((? [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]: ((~ (((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_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_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_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)) <= (~ (ord_less_nat @ E @ B))))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))))) <= ((C != none_nat) <= (? [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:$o]: ((? [E:$o]: (A = (vEBT_Leaf @ D @ E))) => ((B = (suc @ zero_zero_nat)) => (~ (((D) => (C = (some_nat @ zero_zero_nat))) & ((~ (D)) => (C = none_nat))))))))) <= ((vEBT_vebt_pred @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1463_vebt__pred_Oelims)). 159.59/70.63 thf(32135,plain,((! [A:vEBT_VEBT,B:nat,C:option_nat]: ((((? [D:$o,E:$o]: (A = (vEBT_Leaf @ D @ E))) => ((B = zero_zero_nat) => (~ (C = none_nat)))) => (((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((? [F:nat]: (B = (suc @ (suc @ F)))) => (~ (((~ (E)) => (((C = (some_nat @ zero_zero_nat)) | ~ (D)) & ((~ (D)) => (C = none_nat)))) & ((C = (some_nat @ one_one_nat)) | ~ (E))))))) => (((? [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))) => (~ (C = none_nat))) => ((((? [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]: (~ (((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_mint @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_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_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)) | (ord_less_nat @ E @ B))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)))))) | ~ (~ (C = none_nat) | ~ (? [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:$o]: ((? [E:$o]: (A = (vEBT_Leaf @ D @ E))) => ((B = (suc @ zero_zero_nat)) => (~ (((D) => (C = (some_nat @ zero_zero_nat))) & ((~ (D)) => (C = none_nat))))))))) | ~ ((vEBT_vebt_pred @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6972])). 159.59/70.63 thf(6834,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/sandbox/benchmark/theBenchmark.p',fact_1759_power__eq__0__iff)). 159.59/70.63 thf(31558,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)],[6834])). 159.59/70.63 thf(2936,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/sandbox/benchmark/theBenchmark.p',fact_5854_of__int__less__numeral__power__cancel__iff)). 159.59/70.63 thf(17705,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)],[2936])). 159.59/70.63 thf(5214,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/sandbox/benchmark/theBenchmark.p',fact_6806_powser__zero)). 159.59/70.63 thf(25315,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)],[5214])). 159.59/70.63 thf(5177,axiom,((! [A:(nat > int),B:nat]: (((A @ zero_zero_nat) = zero_zero_int) => ((groups3539618377306564664at_int @ A @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups3539618377306564664at_int @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7653_sum__shift__lb__Suc0__0)). 159.59/70.63 thf(25177,plain,((! [A:(nat > int),B:nat]: (((A @ zero_zero_nat) = zero_zero_int) => ((groups3539618377306564664at_int @ (A) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups3539618377306564664at_int @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5177])). 159.59/70.63 thf(5355,axiom,((! [A:(nat > nat),B:set_nat,C:(nat > nat),D:nat]: (((groups3542108847815614940at_nat @ A @ B) = (groups3542108847815614940at_nat @ C @ B)) => ((! [E:nat]: ((member_nat @ E @ B) => (ord_less_eq_nat @ (A @ E) @ (C @ E)))) => ((((A @ D) = (C @ D)) <= (finite_finite_nat @ B)) <= (member_nat @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7444_sum__mono__inv)). 159.59/70.63 thf(25870,plain,((! [A:(nat > nat),B:set_nat,C:(nat > nat),D:nat]: (((groups3542108847815614940at_nat @ (A) @ B) = (groups3542108847815614940at_nat @ (C) @ B)) => ((! [E:nat]: ((member_nat @ E @ B) => (ord_less_eq_nat @ (A @ E) @ (C @ E)))) => (((A @ D) = (C @ D)) | ~ (finite_finite_nat @ B) | ~ (member_nat @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5355])). 159.59/70.63 thf(4196,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/sandbox/benchmark/theBenchmark.p',fact_4303_unity__coeff__ex)). 159.59/70.63 thf(21703,plain,((! [A:(int > $o),B:int]: ((? [C:int]: (A @ (times_times_int @ B @ C))) = (? [C:int]: ((A @ C) & (dvd_dvd_int @ B @ (plus_plus_int @ C @ zero_zero_int))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4196])). 159.59/70.63 thf(425,axiom,((tan_complex = (^ [A:complex]: (divide1717551699836669952omplex @ (sin_complex @ A) @ (cos_complex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7262_tan__def)). 159.59/70.63 thf(9585,plain,(((tan_complex) = (^ [A:complex]: (divide1717551699836669952omplex @ (sin_complex @ A) @ (cos_complex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])). 159.59/70.63 thf(5003,axiom,((! [A:int]: ((times_times_int @ (numeral_numeral_int @ one) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_mult__numeral__1)). 159.59/70.63 thf(24567,plain,((! [A:int]: ((times_times_int @ (numeral_numeral_int @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5003])). 159.59/70.63 thf(3347,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) <= (ord_less_real @ B @ zero_zero_real)) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2162_divide__neg__neg)). 159.59/70.63 thf(19015,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) | ~ (ord_less_real @ B @ zero_zero_real) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3347])). 159.59/70.63 thf(1731,axiom,((! [A:int,B:int]: ((if_int @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Int__Oint_T)). 159.59/70.63 thf(13847,plain,((! [A:int,B:int]: ((if_int @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731])). 159.59/70.63 thf(5281,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/sandbox/benchmark/theBenchmark.p',fact_4665_neg__le__0__iff__le)). 159.59/70.63 thf(25557,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)],[5281])). 159.59/70.63 thf(7326,axiom,((! [A:num,B:num]: ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) != (numera6690914467698888265omplex @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4950_neg__numeral__neq__numeral)). 159.59/70.63 thf(33588,plain,((! [A:num,B:num]: ~ ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7326])). 159.59/70.63 thf(1390,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (arctan @ A) @ (arctan @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5884_arctan__monotone_H)). 159.59/70.63 thf(12787,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)],[1390])). 159.59/70.63 thf(1258,axiom,((! [A:(nat > complex),B:complex]: (((sums_complex @ (^ [C:nat]: (A @ (suc @ C))) @ B) => (sums_complex @ A @ B)) <= ((A @ zero_zero_nat) = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7929_sums__Suc__imp)). 159.59/70.63 thf(12322,plain,((! [A:(nat > complex),B:complex]: (((sums_complex @ (^ [C:nat]: (A @ (suc @ C))) @ B) => (sums_complex @ (A) @ B)) | ~ ((A @ zero_zero_nat) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258])). 159.59/70.63 thf(3591,axiom,((! [A:set_nat,B:(nat > int),C:(nat > int)]: ((finite_finite_nat @ A) => (((? [D:nat]: ((member_nat @ D @ A) & (ord_less_int @ (B @ D) @ (C @ D)))) => (ord_less_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/sandbox/benchmark/theBenchmark.p',fact_7478_sum__strict__mono__ex1)). 159.59/70.63 thf(19782,plain,((! [A:set_nat,B:(nat > int),C:(nat > int)]: ((finite_finite_nat @ A) => (((? [D:nat]: ((member_nat @ D @ A) & (ord_less_int @ (B @ D) @ (C @ D)))) => (ord_less_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)],[3591])). 159.59/70.63 thf(3975,axiom,((! [A:real,B:real]: (((real_V4546457046886955230omplex @ (divide_divide_real @ B @ A)) = (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ B) @ (real_V4546457046886955230omplex @ A))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7514_nonzero__of__real__divide)). 159.59/70.63 thf(21035,plain,((! [A:real,B:real]: (((real_V4546457046886955230omplex @ (divide_divide_real @ B @ A)) = (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ B) @ (real_V4546457046886955230omplex @ A))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3975])). 159.59/70.63 thf(5389,axiom,((! [A:product_prod_nat_nat]: ((size_s170228958280169651at_nat @ (some_P7363390416028606310at_nat @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2194_option_Osize_I4_J)). 159.59/70.63 thf(26019,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)],[5389])). 159.59/70.63 thf(6635,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => (((divide_divide_nat @ A @ (times_times_nat @ B @ A)) = (divide_divide_nat @ one_one_nat @ B)) <= (dvd_dvd_nat @ B @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4199_is__unit__div__mult__cancel__right)). 159.59/70.63 thf(30728,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => (((divide_divide_nat @ A @ (times_times_nat @ B @ A)) = (divide_divide_nat @ one_one_nat @ B)) | ~ (dvd_dvd_nat @ B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6635])). 159.59/70.63 thf(3324,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (divide1717551699836669952omplex @ A @ B) @ C) = (divide1717551699836669952omplex @ (times_times_complex @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1388_times__divide__eq__left)). 159.59/70.63 thf(18944,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)],[3324])). 159.59/70.63 thf(4889,axiom,((! [A:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((abs_abs_int @ A) = (uminus_uminus_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5437_abs__of__nonpos)). 159.59/70.63 thf(24151,plain,((! [A:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((abs_abs_int @ A) = (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4889])). 159.59/70.63 thf(2755,axiom,((! [A:code_integer,B:num,C:num]: ((divide6298287555418463151nteger @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ B)) @ (numera6620942414471956472nteger @ C)) = (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (times_times_num @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_div__mult2__numeral__eq)). 159.59/70.63 thf(17130,plain,((! [A:code_integer,B:num,C:num]: ((divide6298287555418463151nteger @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ B)) @ (numera6620942414471956472nteger @ C)) = (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (times_times_num @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2755])). 159.59/70.63 thf(3396,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/sandbox/benchmark/theBenchmark.p',fact_1231_distrib__right)). 159.59/70.63 thf(19170,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)],[3396])). 159.59/70.63 thf(8180,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/sandbox/benchmark/theBenchmark.p',fact_3420_mod__mult__self1)). 159.59/70.63 thf(36409,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)],[8180])). 159.59/70.63 thf(8048,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/sandbox/benchmark/theBenchmark.p',fact_5260_power2__eq__iff)). 159.59/70.63 thf(35984,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)],[8048])). 159.59/70.63 thf(1078,axiom,((! [A:real,B:real]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (real_V4546457046886955230omplex @ A) @ (real_V4546457046886955230omplex @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7714_norm__of__real__diff)). 159.59/70.63 thf(11714,plain,((! [A:real,B:real]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ (real_V4546457046886955230omplex @ A) @ (real_V4546457046886955230omplex @ B))) @ (abs_abs_real @ (minus_minus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078])). 159.59/70.63 thf(6371,axiom,((diffs_real = (^ [A:(nat > real),B:nat]: (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8106_diffs__def)). 159.59/70.63 thf(29706,plain,(((diffs_real) = (^ [A:(nat > real),B:nat]: (times_times_real @ (semiri5074537144036343181t_real @ (suc @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6371])). 159.59/70.63 thf(4042,axiom,((! [A:real,B:real]: ((A != B) = ((ord_less_real @ B @ A) | (ord_less_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2849_linorder__neq__iff)). 159.59/70.63 thf(21233,plain,((! [A:real,B:real]: ((~ (A = B)) = ((ord_less_real @ B @ A) | (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4042])). 159.59/70.63 thf(7833,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/sandbox/benchmark/theBenchmark.p',fact_449_power__even__eq)). 159.59/70.63 thf(35295,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)],[7833])). 159.59/70.63 thf(8168,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/sandbox/benchmark/theBenchmark.p',fact_450_power__even__eq)). 159.59/70.63 thf(36373,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)],[8168])). 159.59/70.63 thf(1795,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ (times_times_int @ A @ B) @ one_one_int) <= (dvd_dvd_int @ B @ one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3836_unit__prod)). 159.59/70.63 thf(14044,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ (times_times_int @ A @ B) @ one_one_int) | ~ (dvd_dvd_int @ B @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1795])). 159.59/70.63 thf(1446,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/sandbox/benchmark/theBenchmark.p',fact_7192_cos__arctan)). 159.59/70.63 thf(12964,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)],[1446])). 159.59/70.63 thf(4277,axiom,((semiri4216267220026989637d_enat = (^ [A:nat]: (if_Extended_enat @ (A = zero_zero_nat) @ zero_z5237406670263579293d_enat @ (produc2676513652042109336d_enat @ (^ [B:nat,C:nat]: (if_Extended_enat @ (C = zero_zero_nat) @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (semiri4216267220026989637d_enat @ B)) @ (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (semiri4216267220026989637d_enat @ B)) @ one_on7984719198319812577d_enat))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6787_of__nat__code__if)). 159.59/70.63 thf(21974,plain,(((semiri4216267220026989637d_enat) = (^ [A:nat]: (if_Extended_enat @ (A = zero_zero_nat) @ zero_z5237406670263579293d_enat @ (produc2676513652042109336d_enat @ (^ [B:nat,C:nat]: (if_Extended_enat @ (C = zero_zero_nat) @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (semiri4216267220026989637d_enat @ B)) @ (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (semiri4216267220026989637d_enat @ B)) @ one_on7984719198319812577d_enat))) @ (divmod_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4277])). 159.59/70.63 thf(1496,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ C @ B)) => (((A = C) <= (dvd_dvd_complex @ B @ C)) <= (dvd_dvd_complex @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4016_dvd__div__eq__cancel)). 159.59/70.63 thf(13132,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ C @ B)) => ((A = C) | ~ (dvd_dvd_complex @ B @ C) | ~ (dvd_dvd_complex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496])). 159.59/70.63 thf(6089,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ (times_times_nat @ B @ A)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2383_n__less__m__mult__n)). 159.59/70.63 thf(28716,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ (times_times_nat @ B @ A)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6089])). 159.59/70.63 thf(7564,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (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 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6457_sqrt__sum__squares__le__sum)). 159.59/70.63 thf(34381,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (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 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7564])). 159.59/70.63 thf(7480,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/sandbox/benchmark/theBenchmark.p',fact_4018_div__div__div__same)). 159.59/70.63 thf(34127,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)],[7480])). 159.59/70.63 thf(7493,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/sandbox/benchmark/theBenchmark.p',fact_5840_of__int__power__le__of__int__cancel__iff)). 159.59/70.63 thf(34166,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)],[7493])). 159.59/70.63 thf(7907,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4455_pinf_I7_J)). 159.59/70.63 thf(35531,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)],[7907])). 159.59/70.63 thf(4515,axiom,((! [A:nat,B:real,C:nat]: (((semiri5074537144036343181t_real @ A) = (power_power_real @ B @ C)) => (((semiri5074537144036343181t_real @ C) = (log @ B @ (semiri5074537144036343181t_real @ A))) <= (ord_less_real @ one_one_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6748_log__of__power__eq)). 159.59/70.63 thf(22772,plain,((! [A:nat,B:real,C:nat]: (((semiri5074537144036343181t_real @ A) = (power_power_real @ B @ C)) => (((semiri5074537144036343181t_real @ C) = (log @ B @ (semiri5074537144036343181t_real @ A))) | ~ (ord_less_real @ one_one_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4515])). 159.59/70.63 thf(1011,axiom,((! [A:real,B:real,C:nat]: ((dvd_dvd_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4023_dvd__power__same)). 159.59/70.63 thf(11483,plain,((! [A:real,B:real,C:nat]: ((dvd_dvd_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011])). 159.59/70.63 thf(3280,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/sandbox/benchmark/theBenchmark.p',fact_468_field__less__half__sum)). 159.59/70.63 thf(18812,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)],[3280])). 159.59/70.63 thf(3297,axiom,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (? [C:nat]: (ord_less_real @ B @ (power_power_real @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_real__arch__pow)). 159.59/70.63 thf(18863,plain,((! [A:real,B:real]: ((ord_less_real @ one_one_real @ A) => (? [C:nat]: (ord_less_real @ B @ (power_power_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3297])). 159.59/70.63 thf(2924,axiom,((! [A:(product_prod_nat_nat > $o)]: ((produc6081775807080527818_nat_o @ (^ [B:nat,C:nat]: (A @ (product_Pair_nat_nat @ B @ C)))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5007_case__prod__eta)). 159.59/70.63 thf(17669,plain,((! [A:(product_prod_nat_nat > $o)]: ((produc6081775807080527818_nat_o @ (^ [B:nat,C:nat]: (A @ (product_Pair_nat_nat @ B @ C)))) = (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2924])). 159.59/70.63 thf(634,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/sandbox/benchmark/theBenchmark.p',fact_371_power__divide)). 159.59/70.63 thf(10284,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)],[634])). 159.59/70.63 thf(4721,axiom,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (times_times_int @ (groups705719431365010083at_int @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8731_prod_OatLeast0__atMost__Suc)). 159.59/70.63 thf(23565,plain,((! [A:(nat > int),B:nat]: ((groups705719431365010083at_int @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (times_times_int @ (groups705719431365010083at_int @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4721])). 159.59/70.63 thf(6280,axiom,((! [A:set_nat,B:nat]: ((member_nat @ zero_zero_nat @ A) => ((finite_card_nat @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ (suc @ B)) & (member_nat @ C @ A))))) != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9715_card__less)). 159.59/70.63 thf(29428,plain,((! [A:set_nat,B:nat]: ((member_nat @ zero_zero_nat @ A) => (~ ((finite_card_nat @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ (suc @ B)) & (member_nat @ C @ A))))) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6280])). 159.59/70.63 thf(3186,axiom,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F))) => (ord_less_real @ A @ (B @ D))) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3219_order__le__less__subst1)). 159.59/70.63 thf(18497,plain,((! [A:real,B:(nat > real),C:nat,D:nat]: ((ord_less_eq_real @ A @ (B @ C)) => (((! [E:nat,F:nat]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))) => (ord_less_real @ A @ (B @ D))) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3186])). 159.59/70.63 thf(5277,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/sandbox/benchmark/theBenchmark.p',fact_5329_power__minus1__odd)). 159.59/70.63 thf(25525,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)],[5277])). 159.59/70.63 thf(3868,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]: ((((A = (cos_real @ C)) => (B != (sin_real @ C))) <= (ord_less_real @ C @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) <= (ord_less_eq_real @ zero_zero_real @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6960_sincos__total__2pi)). 159.59/70.63 thf(20705,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]: (((A = (cos_real @ C)) => (~ (B = (sin_real @ C)))) | ~ (ord_less_real @ C @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) | ~ (ord_less_eq_real @ zero_zero_real @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3868])). 159.59/70.63 thf(6518,axiom,((! [A:(nat > nat),B:nat]: ((finite_finite_nat @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ (A @ C) @ B)))) <= (! [C:nat]: (ord_less_eq_nat @ C @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3641_finite__less__ub)). 159.59/70.63 thf(30303,plain,((! [A:(nat > nat),B:nat]: ((finite_finite_nat @ (collect_nat @ (^ [C:nat]: (ord_less_eq_nat @ (A @ C) @ B)))) | ~ (! [C:nat]: (ord_less_eq_nat @ C @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6518])). 159.59/70.63 thf(4206,axiom,((! [A:int,B:int]: ((B != A) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2837_dual__order_Ostrict__implies__not__eq)). 159.59/70.63 thf(21735,plain,((! [A:int,B:int]: (~ (B = A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4206])). 159.59/70.63 thf(1518,axiom,((! [A:real,B:real]: ((((ord_less_real @ zero_zero_real @ (log @ A @ B)) = (ord_less_real @ one_one_real @ B)) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6331_zero__less__log__cancel__iff)). 159.59/70.63 thf(13197,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ (log @ A @ B)) = (ord_less_real @ one_one_real @ B)) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518])). 159.59/70.63 thf(1572,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((~ (ord_less_real @ A @ C)) <= (ord_less_real @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4483_minf_I7_J)). 159.59/70.63 thf(13358,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (ord_less_real @ A @ C) | ~ (ord_less_real @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572])). 159.59/70.63 thf(1234,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/sandbox/benchmark/theBenchmark.p',fact_1729_zero__le__divide__1__iff)). 159.59/70.63 thf(12242,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)],[1234])). 159.59/70.63 thf(21,axiom,((! [A:code_integer,B:code_integer]: (((ord_le3102999989581377725nteger @ A @ B) => (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (divide6298287555418463151nteger @ B @ A))) <= (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2280_div__positive)). 159.59/70.63 thf(8318,plain,((! [A:code_integer,B:code_integer]: (((ord_le3102999989581377725nteger @ A @ B) => (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (divide6298287555418463151nteger @ B @ A))) | ~ (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 159.59/70.63 thf(1974,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/sandbox/benchmark/theBenchmark.p',fact_7939_lessThan__nat__numeral)). 159.59/70.63 thf(14619,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)],[1974])). 159.59/70.63 thf(1752,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2923_order__less__imp__not__eq)). 159.59/70.63 thf(13908,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752])). 159.59/70.63 thf(4446,axiom,((! [A:real]: ((ord_less_real @ one_one_real @ (exp_real @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6087_exp__gt__one)). 159.59/70.63 thf(22491,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)],[4446])). 159.59/70.63 thf(1938,axiom,((! [A:complex]: (((divide1717551699836669952omplex @ A @ A) = one_one_complex) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1671_divide__self)). 159.59/70.63 thf(14508,plain,((! [A:complex]: (((divide1717551699836669952omplex @ A @ A) = one_one_complex) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1938])). 159.59/70.63 thf(4702,axiom,((bit_se2161824704523386999it_nat = (^ [A:nat,B:nat]: (bit_se6528837805403552850or_nat @ B @ (bit_se547839408752420682it_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9558_flip__bit__nat__def)). 159.59/70.63 thf(23509,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)],[4702])). 159.59/70.63 thf(6661,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/sandbox/benchmark/theBenchmark.p',fact_5594_power__minus__Bit1)). 159.59/70.63 thf(30819,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)],[6661])). 159.59/70.63 thf(3398,axiom,((! [A:extended_enat,B:extended_enat]: (((plus_p3455044024723400733d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((A = zero_z5237406670263579293d_enat) & (B = zero_z5237406670263579293d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1508_add__eq__0__iff__both__eq__0)). 159.59/70.63 thf(19176,plain,((! [A:extended_enat,B:extended_enat]: (((plus_p3455044024723400733d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((A = zero_z5237406670263579293d_enat) & (B = zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3398])). 159.59/70.63 thf(4948,axiom,((! [A:num]: ((bit_or_not_num_neg @ one @ (bit0 @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6264_or__not__num__neg_Osimps_I2_J)). 159.59/70.63 thf(24340,plain,((! [A:num]: ((bit_or_not_num_neg @ one @ (bit0 @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4948])). 159.59/70.63 thf(2294,axiom,((! [A:real,B:real]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8209_floor__mono)). 159.59/70.63 thf(15641,plain,((! [A:real,B:real]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2294])). 159.59/70.63 thf(3001,axiom,((! [A:real,B:num,C:real]: (((divide_divide_real @ A @ (numeral_numeral_real @ B)) = C) = ((((numeral_numeral_real @ B) = zero_zero_real) => (C = zero_zero_real)) & (((numeral_numeral_real @ B) != zero_zero_real) => (A = (times_times_real @ C @ (numeral_numeral_real @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1732_divide__eq__eq__numeral1_I1_J)). 159.59/70.63 thf(17905,plain,((! [A:real,B:num,C:real]: (((divide_divide_real @ A @ (numeral_numeral_real @ B)) = C) = ((((numeral_numeral_real @ B) = zero_zero_real) => (C = zero_zero_real)) & ((~ ((numeral_numeral_real @ B) = zero_zero_real)) => (A = (times_times_real @ C @ (numeral_numeral_real @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3001])). 159.59/70.63 thf(2009,axiom,((! [A:$o]: ((divide_divide_int @ (zero_n2684676970156552555ol_int @ A) @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4373_of__bool__half__eq__0)). 159.59/70.64 thf(14743,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)],[2009])). 159.59/70.64 thf(6765,axiom,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_le__numeral__extra_I4_J)). 159.59/70.64 thf(31332,plain,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6765])). 159.59/70.64 thf(2971,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/sandbox/benchmark/theBenchmark.p',fact_5922_real__of__int__div3)). 159.59/70.64 thf(17818,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)],[2971])). 159.59/70.64 thf(5203,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/sandbox/benchmark/theBenchmark.p',fact_9481_real__root__eq__0__iff)). 159.59/70.64 thf(25283,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)],[5203])). 159.59/70.64 thf(1471,axiom,((! [A:real,B:(nat > real),C:real]: ((sums_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ C) => ((A != zero_zero_real) => (sums_real @ B @ (divide_divide_real @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7927_sums__mult__D)). 159.59/70.64 thf(13054,plain,((! [A:real,B:(nat > real),C:real]: ((sums_real @ (^ [D:nat]: (times_times_real @ A @ (B @ D))) @ C) => ((~ (A = zero_zero_real)) => (sums_real @ (B) @ (divide_divide_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471])). 159.59/70.64 thf(7864,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_nat @ A @ C) & (A = B)) => ((B != C) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F) @ A) = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1404_del__x__mia)). 159.59/70.64 thf(35383,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((ord_less_nat @ A @ C) & (A = B)) => ((~ (B = C)) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F) @ A) = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ F @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) = C) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ F)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ E @ (the_nat @ (vEBT_vebt_mint @ F)))))) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7864])). 159.59/70.64 thf(529,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/sandbox/benchmark/theBenchmark.p',fact_4245_even__flip__bit__iff)). 159.59/70.64 thf(9935,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)],[529])). 159.59/70.64 thf(5518,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6665_of__nat__0__le__iff)). 159.59/70.64 thf(26512,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5518])). 159.59/70.64 thf(7225,axiom,((! [A:(nat > complex),B:nat,C:nat]: ((groups6464643781859351333omplex @ A @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups6464643781859351333omplex @ (^ [D:nat]: (times_times_complex @ (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/sandbox/benchmark/theBenchmark.p',fact_8903_prod_Oin__pairs)). 159.59/70.64 thf(33236,plain,((! [A:(nat > complex),B:nat,C:nat]: ((groups6464643781859351333omplex @ (A) @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups6464643781859351333omplex @ (^ [D:nat]: (times_times_complex @ (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)],[7225])). 159.59/70.64 thf(2929,axiom,((! [A:complex,B:complex,C:complex,D:complex,E:complex]: (((plus_plus_complex @ (times_times_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ D @ B) @ E)) = (C = (plus_plus_complex @ (times_times_complex @ (minus_minus_complex @ D @ A) @ B) @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1362_eq__add__iff2)). 159.59/70.64 thf(17686,plain,((! [A:complex,B:complex,C:complex,D:complex,E:complex]: (((plus_plus_complex @ (times_times_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ D @ B) @ E)) = (C = (plus_plus_complex @ (times_times_complex @ (minus_minus_complex @ D @ A) @ B) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2929])). 159.59/70.64 thf(1066,axiom,((! [A:code_integer,B:nat,C:nat]: ((modulo364778990260209775nteger @ A @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ B) @ (semiri4939895301339042750nteger @ C))) = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ B) @ (modulo364778990260209775nteger @ (divide6298287555418463151nteger @ A @ (semiri4939895301339042750nteger @ B)) @ (semiri4939895301339042750nteger @ C))) @ (modulo364778990260209775nteger @ A @ (semiri4939895301339042750nteger @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6740_mod__mult2__eq_H)). 159.59/70.64 thf(11671,plain,((! [A:code_integer,B:nat,C:nat]: ((modulo364778990260209775nteger @ A @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ B) @ (semiri4939895301339042750nteger @ C))) = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ B) @ (modulo364778990260209775nteger @ (divide6298287555418463151nteger @ A @ (semiri4939895301339042750nteger @ B)) @ (semiri4939895301339042750nteger @ C))) @ (modulo364778990260209775nteger @ A @ (semiri4939895301339042750nteger @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066])). 159.59/70.64 thf(5936,axiom,((! [A:vEBT_VEBT]: (((accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ A) => ((! [B:$o]: ((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ ($true) @ B))) <= (A = (vEBT_Leaf @ ($true) @ B)))) => ((~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E))))) <= (! [B:$o]: ((A = (vEBT_Leaf @ B @ ($true))) => (~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ B @ ($true))))))))) <= (~ (vEBT_VEBT_minNull @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9757_VEBT__internal_OminNull_Opelims_I3_J)). 159.59/70.64 thf(28194,plain,((! [A:vEBT_VEBT]: (((accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ A) => ((! [B:$o]: (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Leaf @ ($true) @ B)) | ~ (A = (vEBT_Leaf @ ($true) @ B)))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E)) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E)))) | ~ (! [B:$o]: ((A = (vEBT_Leaf @ B @ ($true))) => (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Leaf @ B @ ($true))))))))) | (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5936])). 159.59/70.64 thf(1859,axiom,((! [A:int,B:int]: ((ring_17405671764205052669omplex @ (times_times_int @ A @ B)) = (times_times_complex @ (ring_17405671764205052669omplex @ A) @ (ring_17405671764205052669omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5777_of__int__mult)). 159.59/70.64 thf(14258,plain,((! [A:int,B:int]: ((ring_17405671764205052669omplex @ (times_times_int @ A @ B)) = (times_times_complex @ (ring_17405671764205052669omplex @ A) @ (ring_17405671764205052669omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1859])). 159.59/70.64 thf(5051,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1913_not__less0)). 159.59/70.64 thf(24745,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5051])). 159.59/70.64 thf(4932,axiom,((! [A:nat,B:nat]: ((gbinomial_nat @ A @ (suc @ B)) = (divide_divide_nat @ (groups708209901874060359at_nat @ (^ [C:nat]: (minus_minus_nat @ A @ (semiri1316708129612266289at_nat @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (semiri1408675320244567234ct_nat @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8934_gbinomial__Suc)). 159.59/70.64 thf(24296,plain,((! [A:nat,B:nat]: ((gbinomial_nat @ A @ (suc @ B)) = (divide_divide_nat @ (groups708209901874060359at_nat @ (^ [C:nat]: (minus_minus_nat @ A @ (semiri1316708129612266289at_nat @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (semiri1408675320244567234ct_nat @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4932])). 159.59/70.64 thf(2725,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ (uminus5710092332889474511et_nat @ A)) <= (ord_less_eq_set_nat @ A @ (uminus5710092332889474511et_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4932_compl__le__swap1)). 159.59/70.64 thf(17041,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ (uminus5710092332889474511et_nat @ A)) | ~ (ord_less_eq_set_nat @ A @ (uminus5710092332889474511et_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2725])). 159.59/70.64 thf(5413,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4474_minf_I4_J)). 159.59/70.64 thf(26102,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5413])). 159.59/70.64 thf(3426,axiom,(((semiri4216267220026989637d_enat @ one_one_nat) = one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6550_of__nat__1)). 159.59/70.64 thf(19269,plain,(((semiri4216267220026989637d_enat @ one_one_nat) = one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3426])). 159.59/70.64 thf(1560,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/sandbox/benchmark/theBenchmark.p',fact_9444_nat__less__eq__zless)). 159.59/70.64 thf(13319,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)],[1560])). 159.59/70.64 thf(6285,axiom,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2674_order__subst2)). 159.59/70.64 thf(29443,plain,((! [A:num,B:num,C:(num > num),D:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6285])). 159.59/70.64 thf(7178,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/sandbox/benchmark/theBenchmark.p',fact_5691_max__Suc__numeral)). 159.59/70.64 thf(33049,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)],[7178])). 159.59/70.64 thf(3357,axiom,((! [A:complex,B:complex]: (((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ B @ A)) = (divide_divide_real @ (real_V1022390504157884413omplex @ B) @ (real_V1022390504157884413omplex @ A))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6910_nonzero__norm__divide)). 159.59/70.64 thf(19042,plain,((! [A:complex,B:complex]: (((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ B @ A)) = (divide_divide_real @ (real_V1022390504157884413omplex @ B) @ (real_V1022390504157884413omplex @ A))) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3357])). 159.59/70.64 thf(6185,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 @ A) => ((A = B) <= (ord_less_eq_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2505_power2__eq__imp__eq)). 159.59/70.64 thf(29046,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 @ A) => ((A = B) | ~ (ord_less_eq_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6185])). 159.59/70.64 thf(6566,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/sandbox/benchmark/theBenchmark.p',fact_5072_numeral__times__minus__swap)). 159.59/70.64 thf(30480,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)],[6566])). 159.59/70.64 thf(6841,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/sandbox/benchmark/theBenchmark.p',fact_4793_semiring__norm_I170_J)). 159.59/70.64 thf(31580,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)],[6841])). 159.59/70.64 thf(3809,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/sandbox/benchmark/theBenchmark.p',fact_1379_real__average__minus__first)). 159.59/70.64 thf(20501,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)],[3809])). 159.59/70.64 thf(1899,axiom,((minus_minus_real = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5106_ab__group__add__class_Oab__diff__conv__add__uminus)). 159.59/70.64 thf(14384,plain,(((minus_minus_real) = (^ [A:real,B:real]: (plus_plus_real @ A @ (uminus_uminus_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1899])). 159.59/70.64 thf(2988,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/sandbox/benchmark/theBenchmark.p',fact_8017_sum__split__even__odd)). 159.59/70.64 thf(17865,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)],[2988])). 159.59/70.64 thf(6336,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/sandbox/benchmark/theBenchmark.p',fact_831_le__diff__iff)). 159.59/70.64 thf(29597,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)],[6336])). 159.59/70.64 thf(426,axiom,((! [A:complex]: ((times_times_complex @ A @ (cnj @ A)) = (real_V4546457046886955230omplex @ (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/sandbox/benchmark/theBenchmark.p',fact_9688_complex__mult__cnj)). 159.59/70.64 thf(9587,plain,((! [A:complex]: ((times_times_complex @ A @ (cnj @ A)) = (real_V4546457046886955230omplex @ (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)],[426])). 159.59/70.64 thf(7950,axiom,((! [A:nat]: ((A != bot_bot_nat) = (ord_less_nat @ bot_bot_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3288_bot_Onot__eq__extremum)). 159.59/70.64 thf(35669,plain,((! [A:nat]: ((~ (A = bot_bot_nat)) = (ord_less_nat @ bot_bot_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7950])). 159.59/70.64 thf(1805,axiom,((! [A:num,B:(extended_enat > num),C:extended_enat,D:extended_enat]: ((A = (B @ C)) => ((ord_le72135733267957522d_enat @ C @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_less_num @ (B @ E) @ (B @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_num @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2865_ord__eq__less__subst)). 159.59/70.64 thf(14074,plain,((! [A:num,B:(extended_enat > num),C:extended_enat,D:extended_enat]: ((A = (B @ C)) => ((ord_le72135733267957522d_enat @ C @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_less_num @ (B @ E) @ (B @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_num @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1805])). 159.59/70.64 thf(1766,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/sandbox/benchmark/theBenchmark.p',fact_7809_double__gauss__sum)). 159.59/70.64 thf(13953,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)],[1766])). 159.59/70.64 thf(2949,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ B @ C) => (ord_less_int @ B @ (plus_plus_int @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2110_pos__add__strict)). 159.59/70.64 thf(17744,plain,((! [A:int,B:int,C:int]: ((ord_less_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)],[2949])). 159.59/70.64 thf(6218,axiom,((order_mono_nat_nat @ suc)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10075_mono__Suc)). 159.59/70.64 thf(29148,plain,((order_mono_nat_nat @ (suc))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6218])). 159.59/70.64 thf(4168,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => ((? [C:real]: ((ord_less_real @ zero_zero_real @ C) & ((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 @ C @ A))) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8140_Maclaurin__cos__expansion2)). 159.59/70.64 thf(21622,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [C:real]: ((ord_less_real @ zero_zero_real @ C) & ((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 @ C @ A)) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4168])). 159.59/70.64 thf(289,axiom,((! [A:complex,B:complex]: ((ord_less_eq_real @ (re @ (divide1717551699836669952omplex @ A @ B)) @ zero_zero_real) = (ord_less_eq_real @ (re @ (times_times_complex @ A @ (cnj @ B))) @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9693_Re__complex__div__le__0)). 159.59/70.64 thf(9125,plain,((! [A:complex,B:complex]: ((ord_less_eq_real @ (re @ (divide1717551699836669952omplex @ A @ B)) @ zero_zero_real) = (ord_less_eq_real @ (re @ (times_times_complex @ A @ (cnj @ B))) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 159.59/70.64 thf(2338,axiom,((! [A:nat]: (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (semiri4216267220026989637d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6662_of__nat__0__le__iff)). 159.59/70.64 thf(15765,plain,((! [A:nat]: (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (semiri4216267220026989637d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2338])). 159.59/70.64 thf(8154,axiom,((! [A:num]: ((divide_divide_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_numeral__Bit0__div__2)). 159.59/70.64 thf(36330,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)],[8154])). 159.59/70.64 thf(7720,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/sandbox/benchmark/theBenchmark.p',fact_2115_add__pos__pos)). 159.59/70.64 thf(34936,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)],[7720])). 159.59/70.64 thf(1525,axiom,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (sin_real @ A)) @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6837_abs__sin__le__one)). 159.59/70.64 thf(13217,plain,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (sin_real @ A)) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525])). 159.59/70.64 thf(7848,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/sandbox/benchmark/theBenchmark.p',fact_2549_zero__le__even__power_H)). 159.59/70.64 thf(35336,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)],[7848])). 159.59/70.64 thf(7553,axiom,((! [A:list_nat,B:list_nat]: ((A != B) <= ((size_size_list_nat @ A) != (size_size_list_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_size__neq__size__imp__neq)). 159.59/70.64 thf(34350,plain,((! [A:list_nat,B:list_nat]: (~ (A = B) | ((size_size_list_nat @ A) = (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7553])). 159.59/70.64 thf(6307,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ B)) <= (ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2537_power2__less__imp__less)). 159.59/70.64 thf(29515,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ B)) | ~ (ord_less_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)],[6307])). 159.59/70.64 thf(4676,axiom,((! [A:nat]: ((root @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9475_real__root__zero)). 159.59/70.64 thf(23421,plain,((! [A:nat]: ((root @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4676])). 159.59/70.64 thf(4879,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_Suc__le__mono)). 159.59/70.64 thf(24119,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)],[4879])). 159.59/70.64 thf(5332,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => (((modulo_modulo_nat @ (times_times_nat @ A @ D) @ B) = (modulo_modulo_nat @ (times_times_nat @ C @ E) @ B)) <= ((modulo_modulo_nat @ D @ B) = (modulo_modulo_nat @ E @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3448_mod__mult__cong)). 159.59/70.64 thf(25754,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => (((modulo_modulo_nat @ (times_times_nat @ A @ D) @ B) = (modulo_modulo_nat @ (times_times_nat @ C @ E) @ B)) | ~ ((modulo_modulo_nat @ D @ B) = (modulo_modulo_nat @ E @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5332])). 159.59/70.64 thf(5598,axiom,((! [A:(nat > int),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_int @ (A @ C) @ (A @ B))) <= (! [D:nat]: (ord_less_eq_int @ (A @ (suc @ D)) @ (A @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_lift__Suc__antimono__le)). 159.59/70.64 thf(26772,plain,((! [A:(nat > int),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_int @ (A @ C) @ (A @ B))) | ~ (! [D:nat]: (ord_less_eq_int @ (A @ (suc @ D)) @ (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5598])). 159.59/70.64 thf(5183,axiom,((suc = (plus_plus_nat @ one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_Suc__eq__plus1__left)). 159.59/70.64 thf(25194,plain,(((suc) = (plus_plus_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5183])). 159.59/70.64 thf(1693,axiom,((! [A:real]: ((divide_divide_real @ A @ (numeral_numeral_real @ one)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_divide__numeral__1)). 159.59/70.64 thf(13730,plain,((! [A:real]: ((divide_divide_real @ A @ (numeral_numeral_real @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1693])). 159.59/70.64 thf(6394,axiom,(((semiri4449623510593786356d_enat @ one_one_nat) = one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8049_fact__1)). 159.59/70.64 thf(29822,plain,(((semiri4449623510593786356d_enat @ one_one_nat) = one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6394])). 159.59/70.64 thf(4069,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ one_one_Code_integer @ A) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3903_even__succ__div__2)). 159.59/70.64 thf(21309,plain,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ one_one_Code_integer @ A) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4069])). 159.59/70.64 thf(5242,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/sandbox/benchmark/theBenchmark.p',fact_2377_vebt__member_Osimps_I4_J)). 159.59/70.64 thf(25410,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)],[5242])). 159.59/70.64 thf(3659,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/sandbox/benchmark/theBenchmark.p',fact_3481_mod__eqE)). 159.59/70.64 thf(20005,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)],[3659])). 159.59/70.64 thf(836,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ B)) @ A) != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8290_pochhammer__of__nat__eq__0__lemma_H)). 159.59/70.64 thf(10948,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ ((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ B)) @ A) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[836])). 159.59/70.64 thf(2766,axiom,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_is__num__normalize_I1_J)). 159.59/70.64 thf(17162,plain,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2766])). 159.59/70.64 thf(5199,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((((! [D:nat]: (((ord_less_nat @ D @ B) => ((C @ (suc @ D)) <= (C @ D))) <= (ord_less_eq_nat @ A @ D))) => (C @ B)) <= (C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_dec__induct)). 159.59/70.64 thf(25255,plain,((! [A:nat,B:nat,C:(nat > $o)]: (((! [D:nat]: (((ord_less_nat @ D @ B) => ((C @ (suc @ D)) | ~ (C @ D))) | ~ (ord_less_eq_nat @ A @ D))) => (C @ B)) | ~ (C @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5199])). 159.59/70.64 thf(4551,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/sandbox/benchmark/theBenchmark.p',fact_566_nat__add__max__right)). 159.59/70.64 thf(22972,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)],[4551])). 159.59/70.64 thf(3181,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/sandbox/benchmark/theBenchmark.p',fact_7400_sum__product)). 159.59/70.64 thf(18484,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)],[3181])). 159.59/70.64 thf(871,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3183_order__less__imp__le)). 159.59/70.64 thf(11060,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[871])). 159.59/70.64 thf(1783,axiom,(((size_size_num @ one) = zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1896_num_Osize_I4_J)). 159.59/70.64 thf(14010,plain,(((size_size_num @ one) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1783])). 159.59/70.64 thf(5655,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/sandbox/benchmark/theBenchmark.p',fact_2526_power__eq__if)). 159.59/70.64 thf(26967,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)],[5655])). 159.59/70.64 thf(4026,axiom,((! [A:code_integer]: ((bit_se1080825931792720795nteger @ one_one_Code_integer @ A) = (plus_p5714425477246183910nteger @ A @ (zero_n356916108424825756nteger @ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6127_one__or__eq)). 159.59/70.64 thf(21186,plain,((! [A:code_integer]: ((bit_se1080825931792720795nteger @ one_one_Code_integer @ A) = (plus_p5714425477246183910nteger @ A @ (zero_n356916108424825756nteger @ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4026])). 159.59/70.64 thf(3978,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/sandbox/benchmark/theBenchmark.p',fact_6918_norm__triangle__lt)). 159.59/70.64 thf(21045,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)],[3978])). 159.59/70.64 thf(2646,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/sandbox/benchmark/theBenchmark.p',fact_8168_gchoose__row__sum__weighted)). 159.59/70.64 thf(16779,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)],[2646])). 159.59/70.64 thf(5453,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/sandbox/benchmark/theBenchmark.p',fact_8355_fact__double)). 159.59/70.64 thf(26277,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)],[5453])). 159.59/70.64 thf(1336,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_succ @ A @ C) = (some_nat @ D)) = (vEBT_is_succ_in_set @ (vEBT_VEBT_set_vebt @ A) @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_succ__corr)). 159.59/70.64 thf(12566,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_succ @ A @ C) = (some_nat @ D)) = (vEBT_is_succ_in_set @ (vEBT_VEBT_set_vebt @ A) @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336])). 159.59/70.64 thf(1616,axiom,((! [A:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4691_ab__left__minus)). 159.59/70.64 thf(13503,plain,((! [A:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616])). 159.59/70.64 thf(3451,axiom,((! [A:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ one))) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_numeral__Bit0__div__2)). 159.59/70.64 thf(19345,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)],[3451])). 159.59/70.64 thf(4284,axiom,(((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4741_add__neg__numeral__special_I8_J)). 159.59/70.64 thf(21997,plain,(((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ one_one_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4284])). 159.59/70.64 thf(3098,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (numeral_numeral_int @ (bit1 @ A))) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5984_and__numerals_I2_J)). 159.59/70.64 thf(18218,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (numeral_numeral_int @ (bit1 @ A))) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3098])). 159.59/70.64 thf(5832,axiom,((! [A:vEBT_VEBT,B:$o]: (((vEBT_VEBT_minNull @ A) = B) => (((((B) => (~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ ($false) @ ($false))))) <= (A = (vEBT_Leaf @ ($false) @ ($false)))) => ((! [C:$o]: (((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ ($true) @ C))) <= (~ (B))) <= (A = (vEBT_Leaf @ ($true) @ C)))) => ((! [C:$o]: ((A = (vEBT_Leaf @ C @ ($true))) => ((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ C @ ($true)))) <= (~ (B))))) => ((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => ((B) => (~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))) => (~ (! [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ (B)) => (~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F)))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F))))))))) <= (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9756_VEBT__internal_OminNull_Opelims_I1_J)). 159.59/70.64 thf(27733,plain,((! [A:vEBT_VEBT,B:$o]: (((vEBT_VEBT_minNull @ A) = B) => (((((B) => (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Leaf @ ($false) @ ($false))))) | ~ (A = (vEBT_Leaf @ ($false) @ ($false)))) => ((! [C:$o]: (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Leaf @ ($true) @ C)) | (B) | ~ (A = (vEBT_Leaf @ ($true) @ C)))) => ((! [C:$o]: ((A = (vEBT_Leaf @ C @ ($true))) => (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Leaf @ C @ ($true))) | (B)))) => ((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => ((B) => (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))) => (~ (! [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ (B)) => (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F)))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F))))))))) | ~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5832])). 159.59/70.64 thf(6115,axiom,((! [A:real,B:nat,C:nat]: ((A != zero_zero_real) => (((power_power_real @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_real @ (power_power_real @ A @ C) @ (power_power_real @ A @ B))) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2474_power__diff)). 159.59/70.64 thf(28800,plain,((! [A:real,B:nat,C:nat]: ((~ (A = zero_zero_real)) => (((power_power_real @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_real @ (power_power_real @ A @ C) @ (power_power_real @ A @ B))) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6115])). 159.59/70.64 thf(3415,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6832_nat__leq__as__int)). 159.59/70.64 thf(19234,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)],[3415])). 159.59/70.64 thf(1942,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/sandbox/benchmark/theBenchmark.p',fact_7969_sumr__diff__mult__const2)). 159.59/70.64 thf(14517,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)],[1942])). 159.59/70.64 thf(5525,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/sandbox/benchmark/theBenchmark.p',fact_2404_div__less__dividend)). 159.59/70.64 thf(26532,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)],[5525])). 159.59/70.64 thf(5045,axiom,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (semiri1406184849735516958ct_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8070_fact__ge__zero)). 159.59/70.64 thf(24700,plain,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (semiri1406184849735516958ct_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5045])). 159.59/70.64 thf(1483,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (((ln_ln_real @ A) = (minus_minus_real @ A @ one_one_real)) => (A = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5234_ln__eq__minus__one)). 159.59/70.64 thf(13093,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (((ln_ln_real @ A) = (minus_minus_real @ A @ one_one_real)) => (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1483])). 159.59/70.64 thf(7127,axiom,((! [A:real,B:real,C:real]: (((A != zero_zero_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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5253_add__divide__eq__if__simps_I5_J)). 159.59/70.64 thf(32856,plain,((! [A:real,B:real,C:real]: (((~ (A = zero_zero_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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7127])). 159.59/70.64 thf(7065,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D)) <= ((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1214_diff__eq__diff__less__eq)). 159.59/70.64 thf(32594,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D)) | ~ ((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7065])). 159.59/70.64 thf(6812,axiom,((! [A:nat,B:nat,C:(nat > nat)]: (((groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (times_times_nat @ (C @ (suc @ B)) @ (groups708209901874060359at_nat @ C @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8738_prod_Onat__ivl__Suc_H)). 159.59/70.64 thf(31483,plain,((! [A:nat,B:nat,C:(nat > nat)]: (((groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (times_times_nat @ (C @ (suc @ B)) @ (groups708209901874060359at_nat @ (C) @ (set_or1269000886237332187st_nat @ A @ B)))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6812])). 159.59/70.64 thf(1864,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/sandbox/benchmark/theBenchmark.p',fact_8967_gbinomial__r__part__sum)). 159.59/70.64 thf(14275,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)],[1864])). 159.59/70.64 thf(3496,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/sandbox/benchmark/theBenchmark.p',fact_5393_abs__add__abs)). 159.59/70.64 thf(19479,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)],[3496])). 159.59/70.64 thf(1017,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4446_pinf_I4_J)). 159.59/70.64 thf(11502,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017])). 159.59/70.64 thf(2961,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/sandbox/benchmark/theBenchmark.p',fact_4694_add__neg__numeral__simps_I3_J)). 159.59/70.64 thf(17789,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)],[2961])). 159.59/70.64 thf(6480,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((B = (ord_max_nat @ B @ A)) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_max_Ostrict__order__iff)). 159.59/70.64 thf(30183,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((B = (ord_max_nat @ B @ A)) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6480])). 159.59/70.64 thf(1579,axiom,(((ring_1_of_int_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5772_of__int__1)). 159.59/70.64 thf(13380,plain,(((ring_1_of_int_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579])). 159.59/70.64 thf(2860,axiom,((! [A:complex]: ((cosh_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (plus_plus_complex @ (power_power_complex @ (cosh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (sinh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9352_cosh__double)). 159.59/70.64 thf(17458,plain,((! [A:complex]: ((cosh_complex @ (times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)) = (plus_plus_complex @ (power_power_complex @ (cosh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_complex @ (sinh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2860])). 159.59/70.64 thf(7783,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/sandbox/benchmark/theBenchmark.p',fact_9143_choose__two)). 159.59/70.64 thf(35136,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)],[7783])). 159.59/70.64 thf(656,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ zero_zero_real @ (comm_s7457072308508201937r_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8239_pochhammer__nonneg)). 159.59/70.64 thf(10348,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ zero_zero_real @ (comm_s7457072308508201937r_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[656])). 159.59/70.64 thf(5580,axiom,((! [A:set_nat,B:nat]: ((~ (member_nat @ zero_zero_nat @ A)) => ((finite_card_nat @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ B) & (member_nat @ (suc @ C) @ A))))) = (finite_card_nat @ (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ (suc @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9713_card__less__Suc2)). 159.59/70.64 thf(26697,plain,((! [A:set_nat,B:nat]: ((~ (member_nat @ zero_zero_nat @ A)) => ((finite_card_nat @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ B) & (member_nat @ (suc @ C) @ A))))) = (finite_card_nat @ (collect_nat @ (^ [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ (suc @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5580])). 159.59/70.64 thf(3664,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/sandbox/benchmark/theBenchmark.p',fact_6858_sin__pi__divide__n__ge__0)). 159.59/70.64 thf(20019,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)],[3664])). 159.59/70.64 thf(6666,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) => (ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_diff__less__mono2)). 159.59/70.64 thf(30836,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) => (ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6666])). 159.59/70.64 thf(121,axiom,((filterlim_real_real @ sqrt @ at_top_real @ at_top_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9953_sqrt__at__top)). 159.59/70.64 thf(8624,plain,((filterlim_real_real @ (sqrt) @ at_top_real @ at_top_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 159.59/70.64 thf(566,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)))) & ((tan_real @ B) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7289_lemma__tan__total1)). 159.59/70.64 thf(10051,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)))) & ((tan_real @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[566])). 159.59/70.64 thf(1063,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/sandbox/benchmark/theBenchmark.p',fact_6976_sin__cos__squared__add3)). 159.59/70.64 thf(11662,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)],[1063])). 159.59/70.64 thf(992,axiom,((! [A:real,B:nat,C:nat]: ((times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ (inverse_inverse_real @ A) @ C)) = (times_times_real @ (power_power_real @ (inverse_inverse_real @ A) @ C) @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9046_power__mult__power__inverse__commute)). 159.59/70.64 thf(11423,plain,((! [A:real,B:nat,C:nat]: ((times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ (inverse_inverse_real @ A) @ C)) = (times_times_real @ (power_power_real @ (inverse_inverse_real @ A) @ C) @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[992])). 159.59/70.64 thf(3463,axiom,((! [A:int,B:int,C:int]: (((bit_se725231765392027082nd_int @ A @ B) = zero_zero_int) => ((((B = C) <= ((bit_se1409905431419307370or_int @ A @ C) = (uminus_uminus_int @ one_one_int))) <= ((bit_se725231765392027082nd_int @ A @ C) = zero_zero_int)) <= ((bit_se1409905431419307370or_int @ A @ B) = (uminus_uminus_int @ one_one_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6061_bit_Ocomplement__unique)). 159.59/70.64 thf(19376,plain,((! [A:int,B:int,C:int]: (((bit_se725231765392027082nd_int @ A @ B) = zero_zero_int) => ((B = C) | ~ ((bit_se1409905431419307370or_int @ A @ C) = (uminus_uminus_int @ one_one_int)) | ~ ((bit_se725231765392027082nd_int @ A @ C) = zero_zero_int) | ~ ((bit_se1409905431419307370or_int @ A @ B) = (uminus_uminus_int @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3463])). 159.59/70.64 thf(5350,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/sandbox/benchmark/theBenchmark.p',fact_6441_real__sqrt__sum__squares__eq__cancel2)). 159.59/70.64 thf(25854,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)],[5350])). 159.59/70.64 thf(4117,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/sandbox/benchmark/theBenchmark.p',fact_4514_exp__mod__exp)). 159.59/70.64 thf(21460,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)],[4117])). 159.59/70.64 thf(7142,axiom,((! [A:nat]: ((A = zero_zero_nat) = (case_nat_o @ ($true) @ (^ [B:nat]: (($false))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9731_nat_Odisc__eq__case_I1_J)). 159.59/70.64 thf(32915,plain,((! [A:nat]: ((A = zero_zero_nat) = (case_nat_o @ ($true) @ (^ [B:nat]: (($false))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7142])). 159.59/70.64 thf(7859,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((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/sandbox/benchmark/theBenchmark.p',fact_4090_div__plus__div__distrib__dvd__left)). 159.59/70.64 thf(35368,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((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)],[7859])). 159.59/70.64 thf(1299,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3881_even__mod__2__iff)). 159.59/70.64 thf(12451,plain,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299])). 159.59/70.64 thf(79,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ (numeral_numeral_int @ (bit0 @ A)))) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9593_and__not__numerals_I2_J)). 159.59/70.64 thf(8492,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)],[79])). 159.59/70.64 thf(7628,axiom,(((power_power_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_one__power2)). 159.59/70.64 thf(34640,plain,(((power_power_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7628])). 159.59/70.64 thf(975,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1505_add__0)). 159.59/70.64 thf(11370,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[975])). 159.59/70.64 thf(4020,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/sandbox/benchmark/theBenchmark.p',fact_7157_cos__plus__cos)). 159.59/70.64 thf(21169,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)],[4020])). 159.59/70.64 thf(5146,axiom,((! [A:set_Pr1261947904930325089at_nat,B:(product_prod_nat_nat > int),C:(product_prod_nat_nat > int),D:int,E:int]: ((((! [F:product_prod_nat_nat]: ((member8440522571783428010at_nat @ F @ A) => (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (C @ F) @ D)) @ E))) => (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (groups975429370522433651at_int @ (^ [F:product_prod_nat_nat]: (times_times_int @ (C @ F) @ (B @ F))) @ A) @ D)) @ E)) <= ((groups975429370522433651at_int @ B @ A) = one_one_int)) <= (! [F:product_prod_nat_nat]: ((ord_less_eq_int @ zero_zero_int @ (B @ F)) <= (member8440522571783428010at_nat @ F @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7761_convex__sum__bound__le)). 159.59/70.64 thf(25061,plain,((! [A:set_Pr1261947904930325089at_nat,B:(product_prod_nat_nat > int),C:(product_prod_nat_nat > int),D:int,E:int]: (((! [F:product_prod_nat_nat]: ((member8440522571783428010at_nat @ F @ A) => (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (C @ F) @ D)) @ E))) => (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (groups975429370522433651at_int @ (^ [F:product_prod_nat_nat]: (times_times_int @ (C @ F) @ (B @ F))) @ A) @ D)) @ E)) | ~ ((groups975429370522433651at_int @ (B) @ A) = one_one_int) | ~ (! [F:product_prod_nat_nat]: ((ord_less_eq_int @ zero_zero_int @ (B @ F)) | ~ (member8440522571783428010at_nat @ F @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5146])). 159.59/70.64 thf(159,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/sandbox/benchmark/theBenchmark.p',fact_8323_gbinomial__negated__upper)). 159.59/70.64 thf(8745,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)],[159])). 159.59/70.64 thf(3284,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)))) & (ord_less_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8146_Maclaurin__sin__expansion2)). 159.59/70.64 thf(18822,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)))) & (ord_less_eq_real @ (abs_abs_real @ C) @ (abs_abs_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3284])). 159.59/70.64 thf(16,axiom,((! [A:real]: ((real_V1022390504157884413omplex @ (cis @ A)) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9375_norm__cis)). 159.59/70.64 thf(8300,plain,((! [A:real]: ((real_V1022390504157884413omplex @ (cis @ A)) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 159.59/70.64 thf(6491,axiom,((! [A:num]: (((uminus_uminus_real @ one_one_real) = (uminus_uminus_real @ (numeral_numeral_real @ A))) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4753_neg__one__eq__numeral__iff)). 159.59/70.64 thf(30215,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)],[6491])). 159.59/70.64 thf(3960,axiom,((! [A:set_nat,B:nat]: (((A = bot_bot_set_nat) | (A = (insert_nat @ B @ bot_bot_set_nat))) <= (ord_less_eq_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6210_subset__singletonD)). 159.59/70.64 thf(20995,plain,((! [A:set_nat,B:nat]: ((A = bot_bot_set_nat) | (A = (insert_nat @ B @ bot_bot_set_nat)) | ~ (ord_less_eq_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3960])). 159.59/70.64 thf(615,axiom,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_complex @ (groups6464643781859351333omplex @ A @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8444_prod_OlessThan__Suc)). 159.59/70.64 thf(10215,plain,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_complex @ (groups6464643781859351333omplex @ (A) @ (set_ord_lessThan_nat @ B)) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[615])). 159.59/70.64 thf(4240,axiom,((! [A:real]: ((summable_real @ (power_power_real @ A)) <= (ord_less_real @ (real_V7735802525324610683m_real @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7095_complete__algebra__summable__geometric)). 159.59/70.64 thf(21859,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)],[4240])). 159.59/70.64 thf(3060,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/sandbox/benchmark/theBenchmark.p',fact_8216_pochhammer__eq__0__mono)). 159.59/70.64 thf(18086,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)],[3060])). 159.59/70.64 thf(479,axiom,((! [A:code_integer,B:code_integer]: ((A != zero_z3403309356797280102nteger) => ((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1630_nonzero__mult__div__cancel__right)). 159.59/70.64 thf(9776,plain,((! [A:code_integer,B:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])). 159.59/70.64 thf(3224,axiom,((! [A:nat]: (((A != zero_zero_nat) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = zero_zero_nat)) & (((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = one_one_nat) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8245_pochhammer__0__left)). 159.59/70.64 thf(18616,plain,((! [A:nat]: (((~ (A = zero_zero_nat)) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = zero_zero_nat)) & (((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = one_one_nat) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3224])). 159.59/70.64 thf(1069,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/sandbox/benchmark/theBenchmark.p',fact_5022_take__bit__int__less__eq__self__iff)). 159.59/70.64 thf(11678,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)],[1069])). 159.59/70.64 thf(2426,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ B @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2937_order__less__imp__not__less)). 159.59/70.64 thf(16065,plain,((! [A:int,B:int]: (~ (ord_less_int @ B @ A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2426])). 159.59/70.64 thf(5218,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_add__le__imp__le__left)). 159.59/70.64 thf(25326,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5218])). 159.59/70.64 thf(2912,axiom,((! [A:extended_enat,B:(extended_enat > extended_enat),C:extended_enat,D:extended_enat]: (((ord_le72135733267957522d_enat @ C @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)))) => (ord_le72135733267957522d_enat @ A @ (B @ D)))) <= (ord_le2932123472753598470d_enat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3212_order__le__less__subst1)). 159.59/70.64 thf(17628,plain,((! [A:extended_enat,B:(extended_enat > extended_enat),C:extended_enat,D:extended_enat]: (((ord_le72135733267957522d_enat @ C @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)))) => (ord_le72135733267957522d_enat @ A @ (B @ D)))) | ~ (ord_le2932123472753598470d_enat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2912])). 159.59/70.64 thf(3492,axiom,((! [A:real,B:real]: ((exp_real @ (minus_minus_real @ A @ B)) = (divide_divide_real @ (exp_real @ A) @ (exp_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6081_exp__diff)). 159.59/70.64 thf(19466,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)],[3492])). 159.59/70.64 thf(3650,axiom,((sin_complex = (^ [A:complex]: (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (sin_coeff @ B) @ (power_power_complex @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9266_sin__def)). 159.59/70.64 thf(19973,plain,(((sin_complex) = (^ [A:complex]: (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (sin_coeff @ B) @ (power_power_complex @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3650])). 159.59/70.64 thf(2278,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > extended_enat),D:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le2932123472753598470d_enat @ (C @ B) @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3242_order__less__le__subst2)). 159.59/70.64 thf(15594,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > extended_enat),D:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le2932123472753598470d_enat @ (C @ B) @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2278])). 159.59/70.64 thf(7022,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/sandbox/benchmark/theBenchmark.p',fact_6849_int__cases3)). 159.59/70.64 thf(32418,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)],[7022])). 159.59/70.64 thf(4847,axiom,((! [A:(list_o > $o),B:list_o]: ((A @ B) <= (! [C:list_o]: ((! [D:list_o]: ((A @ D) <= (ord_less_nat @ (size_size_list_o @ D) @ (size_size_list_o @ C)))) => (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_length__induct)). 159.59/70.64 thf(24022,plain,((! [A:(list_o > $o),B:list_o]: ((A @ B) | ~ (! [C:list_o]: ((! [D:list_o]: ((A @ D) | ~ (ord_less_nat @ (size_size_list_o @ D) @ (size_size_list_o @ C)))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4847])). 159.59/70.64 thf(1291,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/sandbox/benchmark/theBenchmark.p',fact_2620_div__pos__pos__trivial)). 159.59/70.64 thf(12423,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)],[1291])). 159.59/70.64 thf(2392,axiom,((! [A:real]: ((! [B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) <= (ord_less_real @ zero_zero_real @ B))) => (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5553_dense__eq0__I)). 159.59/70.64 thf(15936,plain,((! [A:real]: ((! [B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) | ~ (ord_less_real @ zero_zero_real @ B))) => (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2392])). 159.59/70.64 thf(31,axiom,((! [A:nat]: ((ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (semiri4939895301339042750nteger @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6591_of__nat__0__less__iff)). 159.59/70.64 thf(8344,plain,((! [A:nat]: ((ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (semiri4939895301339042750nteger @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 159.59/70.64 thf(5230,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_le__imp__less__Suc)). 159.59/70.64 thf(25378,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)],[5230])). 159.59/70.64 thf(5962,axiom,((! [A:real,B:nat]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ (abs_abs_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5567_zero__le__power__abs)). 159.59/70.64 thf(28319,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)],[5962])). 159.59/70.64 thf(7122,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ A) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2363_div__add__self2)). 159.59/70.64 thf(32837,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ (plus_plus_nat @ B @ A) @ A) = (plus_plus_nat @ (divide_divide_nat @ B @ A) @ one_one_nat)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7122])). 159.59/70.64 thf(4764,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((A @ (suc @ C)) <= (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1903_nat__induct)). 159.59/70.64 thf(23719,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ (suc @ C)) | ~ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4764])). 159.59/70.64 thf(3005,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/sandbox/benchmark/theBenchmark.p',fact_2076_mult__strict__left__mono__neg)). 159.59/70.64 thf(17918,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)],[3005])). 159.59/70.64 thf(399,axiom,((! [A:int,B:int]: ((ord_max_int @ (ord_max_int @ A @ B) @ B) = (ord_max_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_max_Oright__idem)). 159.59/70.64 thf(9496,plain,((! [A:int,B:int]: ((ord_max_int @ (ord_max_int @ A @ B) @ B) = (ord_max_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])). 159.59/70.64 thf(1806,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/sandbox/benchmark/theBenchmark.p',fact_8966_gbinomial__r__part__sum)). 159.59/70.64 thf(14082,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)],[1806])). 159.59/70.64 thf(5623,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/sandbox/benchmark/theBenchmark.p',fact_2517_exp__not__zero__imp__exp__diff__not__zero)). 159.59/70.64 thf(26857,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)],[5623])). 159.59/70.64 thf(4213,axiom,((! [A:num,B:num]: ((plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (numera1916890842035813515d_enat @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_numeral__plus__numeral)). 159.59/70.64 thf(21768,plain,((! [A:num,B:num]: ((plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (numera1916890842035813515d_enat @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4213])). 159.59/70.64 thf(5074,axiom,((! [A:num]: ((minus_minus_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ one_one_complex)) = (numera6690914467698888265omplex @ (inc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5711_diff__numeral__special_I6_J)). 159.59/70.64 thf(24833,plain,((! [A:num]: ((minus_minus_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ one_one_complex)) = (numera6690914467698888265omplex @ (inc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5074])). 159.59/70.64 thf(1924,axiom,(((ln_ln_real @ one_one_real) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4730_ln__one)). 159.59/70.64 thf(14461,plain,(((ln_ln_real @ one_one_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1924])). 159.59/70.64 thf(6186,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1985_mult__right__mono)). 159.59/70.64 thf(29049,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ (times_times_int @ A @ C) @ (times_times_int @ B @ C)) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6186])). 159.59/70.64 thf(4015,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/sandbox/benchmark/theBenchmark.p',fact_6145_exp__lower__Taylor__quadratic)). 159.59/70.64 thf(21154,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)],[4015])). 159.59/70.64 thf(1966,axiom,((! [A:nat]: (((bit_se2923211474154528505it_int @ A @ one_one_int) = zero_zero_int) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4776_take__bit__of__1__eq__0__iff)). 159.59/70.64 thf(14587,plain,((! [A:nat]: (((bit_se2923211474154528505it_int @ A @ one_one_int) = zero_zero_int) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1966])). 159.59/70.64 thf(5552,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/sandbox/benchmark/theBenchmark.p',fact_236_power__add__numeral)). 159.59/70.64 thf(26609,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)],[5552])). 159.59/70.64 thf(7203,axiom,(((numeral_numeral_real @ one) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_numeral__One)). 159.59/70.64 thf(33152,plain,(((numeral_numeral_real @ one) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7203])). 159.59/70.64 thf(3954,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/sandbox/benchmark/theBenchmark.p',fact_2313_not__sum__squares__lt__zero)). 159.59/70.64 thf(20975,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)],[3954])). 159.59/70.64 thf(4248,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/sandbox/benchmark/theBenchmark.p',fact_3251_order__less__le__subst2)). 159.59/70.64 thf(21886,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)],[4248])). 159.59/70.64 thf(7510,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/sandbox/benchmark/theBenchmark.p',fact_399_nth__mem)). 159.59/70.64 thf(34218,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)],[7510])). 159.59/70.64 thf(2169,axiom,((! [A:(nat > (nat > real)),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (A @ C) @ (set_ord_lessThan_nat @ C))) @ (set_ord_atMost_nat @ B)) = (groups6591440286371151544t_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (A @ D @ C)) @ (set_or1269000886237332187st_nat @ (suc @ C) @ B))) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8768_sum_Onested__swap_H)). 159.59/70.64 thf(15244,plain,((! [A:(nat > (nat > real)),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (A @ C) @ (set_ord_lessThan_nat @ C))) @ (set_ord_atMost_nat @ B)) = (groups6591440286371151544t_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (A @ D @ C)) @ (set_or1269000886237332187st_nat @ (suc @ C) @ B))) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2169])). 159.59/70.64 thf(5331,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)) & (((ord_less_eq_real @ A @ zero_zero_real) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))) | ((A = zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3917_power__le__zero__eq__numeral)). 159.59/70.64 thf(25751,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)) & (((ord_less_eq_real @ A @ zero_zero_real) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))) | ((A = zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5331])). 159.59/70.64 thf(5683,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/sandbox/benchmark/theBenchmark.p',fact_5850_of__int__le__numeral__power__cancel__iff)). 159.59/70.64 thf(27077,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)],[5683])). 159.59/70.64 thf(3923,axiom,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2009_not__numeral__less__zero)). 159.59/70.64 thf(20872,plain,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3923])). 159.59/70.64 thf(1663,axiom,((! [A:complex,B:complex]: ((sin_complex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (sin_complex @ A) @ (cos_complex @ B)) @ (times_times_complex @ (cos_complex @ A) @ (sin_complex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7089_sin__add)). 159.59/70.64 thf(13638,plain,((! [A:complex,B:complex]: ((sin_complex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (sin_complex @ A) @ (cos_complex @ B)) @ (times_times_complex @ (cos_complex @ A) @ (sin_complex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663])). 159.59/70.64 thf(2106,axiom,((! [A:nat]: ((bit_ri631733984087533419it_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4732_signed__take__bit__of__minus__1)). 159.59/70.64 thf(15036,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)],[2106])). 159.59/70.64 thf(3034,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/sandbox/benchmark/theBenchmark.p',fact_1358_diff__less__eq)). 159.59/70.64 thf(18003,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)],[3034])). 159.59/70.64 thf(7525,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (times_times_int @ B @ A)) = (((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ B @ one_one_int)) & ((ord_less_eq_int @ one_one_int @ B) <= (ord_less_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2421_mult__le__cancel__right1)). 159.59/70.64 thf(34265,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ (times_times_int @ B @ A)) = (((ord_less_int @ A @ zero_zero_int) => (ord_less_eq_int @ B @ one_one_int)) & ((ord_less_eq_int @ one_one_int @ B) | ~ (ord_less_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7525])). 159.59/70.64 thf(6864,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/sandbox/benchmark/theBenchmark.p',fact_83_mult__numeral__left__semiring__numeral)). 159.59/70.64 thf(31746,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)],[6864])). 159.59/70.64 thf(3967,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/sandbox/benchmark/theBenchmark.p',fact_4175_is__unit__power__iff)). 159.59/70.64 thf(21014,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)],[3967])). 159.59/70.64 thf(7600,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = one_one_nat) <= ((times_times_nat @ A @ B) = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_left__right__inverse__power)). 159.59/70.64 thf(34560,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = one_one_nat) | ~ ((times_times_nat @ A @ B) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7600])). 159.59/70.64 thf(337,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/sandbox/benchmark/theBenchmark.p',fact_4769_max__number__of_I4_J)). 159.59/70.64 thf(9290,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)],[337])). 159.59/70.64 thf(1953,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ B) @ B) = (modulo_modulo_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3393_mod__add__self2)). 159.59/70.64 thf(14549,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)],[1953])). 159.59/70.64 thf(7363,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3137_dual__order_Ostrict__iff__not)). 159.59/70.64 thf(33710,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)],[7363])). 159.59/70.64 thf(6931,axiom,((! [A:num,B:num]: ((modulo_modulo_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) != zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5621_cong__exp__iff__simps_I3_J)). 159.59/70.64 thf(31964,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)],[6931])). 159.59/70.64 thf(6036,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/sandbox/benchmark/theBenchmark.p',fact_6341_one__le__log__cancel__iff)). 159.59/70.64 thf(28553,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)],[6036])). 159.59/70.64 thf(5465,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/sandbox/benchmark/theBenchmark.p',fact_2449_power__Suc__le__self)). 159.59/70.64 thf(26324,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)],[5465])). 159.59/70.64 thf(7681,axiom,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: ((size_s7466405169056248089T_VEBT @ (produc4743750530478302277T_VEBT @ A @ B)) = (times_times_nat @ (size_s6755466524823107622T_VEBT @ A) @ (size_s6755466524823107622T_VEBT @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3622_length__product)). 159.59/70.64 thf(34799,plain,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBT]: ((size_s7466405169056248089T_VEBT @ (produc4743750530478302277T_VEBT @ A @ B)) = (times_times_nat @ (size_s6755466524823107622T_VEBT @ A) @ (size_s6755466524823107622T_VEBT @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7681])). 159.59/70.64 thf(1875,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4645_add__minus__cancel)). 159.59/70.64 thf(14307,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1875])). 159.59/70.64 thf(4781,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6522_of__nat__less__iff)). 159.59/70.64 thf(23773,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)],[4781])). 159.59/70.64 thf(6961,axiom,((! [A:num]: (((numeral_numeral_int @ A) = one_one_int) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_numeral__eq__one__iff)). 159.59/70.64 thf(32088,plain,((! [A:num]: (((numeral_numeral_int @ A) = one_one_int) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6961])). 159.59/70.64 thf(3786,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/sandbox/benchmark/theBenchmark.p',fact_8012_one__diff__power__eq_H)). 159.59/70.64 thf(20426,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)],[3786])). 159.59/70.64 thf(2328,axiom,((! [A:int,B:int,C:int,D:int]: (((A != B) & (C != D)) = ((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/sandbox/benchmark/theBenchmark.p',fact_4585_crossproduct__noteq)). 159.59/70.64 thf(15733,plain,((! [A:int,B:int,C:int,D:int]: ((~ (A = B) & ~ (C = D)) = (~ ((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)],[2328])). 159.59/70.64 thf(4789,axiom,((! [A:nat,B:nat,C:(nat > int)]: (((groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_int @ (C @ A) @ (groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8735_prod_OatLeast__Suc__atMost)). 159.59/70.64 thf(23794,plain,((! [A:nat,B:nat,C:(nat > int)]: (((groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_int @ (C @ A) @ (groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4789])). 159.59/70.64 thf(1402,axiom,((! [A:nat,B:nat,C:nat]: (((semiri8010041392384452111omplex @ A) = (power_power_complex @ (semiri8010041392384452111omplex @ B) @ C)) = (A = (power_power_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6569_of__nat__power__eq__of__nat__cancel__iff)). 159.59/70.64 thf(12825,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)],[1402])). 159.59/70.64 thf(2647,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((uminus1351360451143612070nteger @ A) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ C))) <= (A = (plus_p5714425477246183910nteger @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4967_group__cancel_Oneg1)). 159.59/70.64 thf(16782,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((uminus1351360451143612070nteger @ A) = (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ C))) | ~ (A = (plus_p5714425477246183910nteger @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2647])). 159.59/70.64 thf(1210,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/sandbox/benchmark/theBenchmark.p',fact_105_distrib__right__numeral)). 159.59/70.64 thf(12167,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)],[1210])). 159.59/70.64 thf(4051,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/sandbox/benchmark/theBenchmark.p',fact_4007_dvd__diff__commute)). 159.59/70.64 thf(21257,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)],[4051])). 159.59/70.64 thf(7088,axiom,((! [A:num,B:num]: ((power_power_complex @ (numera6690914467698888265omplex @ A) @ (numeral_numeral_nat @ B)) = (numera6690914467698888265omplex @ (pow @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4603_power__numeral)). 159.59/70.64 thf(32698,plain,((! [A:num,B:num]: ((power_power_complex @ (numera6690914467698888265omplex @ A) @ (numeral_numeral_nat @ B)) = (numera6690914467698888265omplex @ (pow @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7088])). 159.59/70.64 thf(2485,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) | (ord_le72135733267957522d_enat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3252_linorder__le__less__linear)). 159.59/70.64 thf(16246,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) | (ord_le72135733267957522d_enat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2485])). 159.59/70.64 thf(1891,axiom,((! [A:nat]: ((sin_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6803_sin__npi)). 159.59/70.64 thf(14360,plain,((! [A:nat]: ((sin_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ pi)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1891])). 159.59/70.64 thf(6973,axiom,((! [A:nat,B:nat,C:int,D:int,E:int]: ((bit_concat_bit @ A @ (bit_concat_bit @ B @ C @ D) @ E) = (bit_concat_bit @ (ord_min_nat @ A @ B) @ C @ (bit_concat_bit @ (minus_minus_nat @ A @ B) @ D @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10174_concat__bit__assoc__sym)). 159.59/70.64 thf(32199,plain,((! [A:nat,B:nat,C:int,D:int,E:int]: ((bit_concat_bit @ A @ (bit_concat_bit @ B @ C @ D) @ E) = (bit_concat_bit @ (ord_min_nat @ A @ B) @ C @ (bit_concat_bit @ (minus_minus_nat @ A @ B) @ D @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6973])). 159.59/70.64 thf(1050,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ (divide_divide_real @ A @ (sqrt @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6440_lemma__real__divide__sqrt__less)). 159.59/70.64 thf(11618,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ (divide_divide_real @ A @ (sqrt @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050])). 159.59/70.64 thf(3076,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/sandbox/benchmark/theBenchmark.p',fact_5902_of__int__pos)). 159.59/70.64 thf(18135,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)],[3076])). 159.59/70.64 thf(5838,axiom,((! [A:vEBT_VEBT,B:nat]: ((~ (vEBT_vebt_member @ A @ B)) => ((((((~ (! [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 @ 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)))) <= (B != D)))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G))))) <= (! [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)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ (suc @ zero_zero_nat) @ D @ E) @ B)))))) <= (! [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:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E) @ B))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))))) <= (! [C:$o,D:$o]: (((((B = zero_zero_nat) => (C)) & ((((B = one_one_nat) => (D)) & (B = one_one_nat)) <= (B != zero_zero_nat))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B))) <= (A = (vEBT_Leaf @ C @ D))))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3314_vebt__member_Opelims_I3_J)). 159.59/70.64 thf(27794,plain,((! [A:vEBT_VEBT,B:nat]: ((~ (vEBT_vebt_member @ A @ B)) => (~ (! [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 @ 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)))) | (B = D)))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G)))) | ~ (! [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)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ (suc @ zero_zero_nat) @ D @ E) @ B))))) | ~ (! [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:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E) @ B)) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) | ~ (! [C:$o,D:$o]: ((((B = zero_zero_nat) => (C)) & ((((B = one_one_nat) => (D)) & (B = one_one_nat)) | (B = zero_zero_nat))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) | ~ (A = (vEBT_Leaf @ C @ D)))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5838])). 159.59/70.64 thf(1138,axiom,((! [A:real]: (((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((arctan @ (tan_real @ A)) = A)) <= (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7306_arctan__tan)). 159.59/70.64 thf(11900,plain,((! [A:real]: (((ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) => ((arctan @ (tan_real @ A)) = 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)],[1138])). 159.59/70.64 thf(6537,axiom,(((ord_less_eq_nat @ mi @ xa) & (ord_less_eq_nat @ xa @ ma))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_inrg)). 159.59/70.64 thf(30387,plain,(((ord_less_eq_nat @ mi @ xa) & (ord_less_eq_nat @ xa @ ma))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6537])). 159.59/70.64 thf(5688,axiom,((! [A:(nat > nat)]: ((summable_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (suminf_nat @ A)) <= (! [B:nat]: (ord_less_nat @ zero_zero_nat @ (A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7060_suminf__pos)). 159.59/70.64 thf(27090,plain,((! [A:(nat > nat)]: ((summable_nat @ (A)) => ((ord_less_nat @ zero_zero_nat @ (suminf_nat @ (A))) | ~ (! [B:nat]: (ord_less_nat @ zero_zero_nat @ (A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5688])). 159.59/70.64 thf(2779,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ one_one_real) => ((ord_less_eq_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ B) => (((ord_less_eq_real @ B @ (arcsin @ A)) = (ord_less_eq_real @ (sin_real @ B) @ A)) <= (ord_less_eq_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7838_le__arcsin__iff)). 159.59/70.64 thf(17204,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ one_one_real) => ((ord_less_eq_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ B) => (((ord_less_eq_real @ B @ (arcsin @ A)) = (ord_less_eq_real @ (sin_real @ B) @ A)) | ~ (ord_less_eq_real @ B @ (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)],[2779])). 159.59/70.64 thf(5079,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/sandbox/benchmark/theBenchmark.p',fact_361_power__commutes)). 159.59/70.64 thf(24848,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)],[5079])). 159.59/70.64 thf(8204,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((power_power_nat @ (divide_divide_nat @ B @ A) @ C) = (divide_divide_nat @ (power_power_nat @ B @ C) @ (power_power_nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4105_div__power)). 159.59/70.64 thf(36492,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((power_power_nat @ (divide_divide_nat @ B @ A) @ C) = (divide_divide_nat @ (power_power_nat @ B @ C) @ (power_power_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8204])). 159.59/70.64 thf(7620,axiom,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((C) <= (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2916_order__less__imp__triv)). 159.59/70.64 thf(34614,plain,((! [A:nat,B:nat,C:$o]: ((ord_less_nat @ A @ B) => ((C) | ~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7620])). 159.59/70.64 thf(3670,axiom,((! [A:complex]: ((real_V4546457046886955230omplex @ (power_power_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = (times_times_complex @ A @ (cnj @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9700_complex__norm__square)). 159.59/70.64 thf(20041,plain,((! [A:complex]: ((real_V4546457046886955230omplex @ (power_power_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = (times_times_complex @ A @ (cnj @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3670])). 159.59/70.64 thf(2461,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/sandbox/benchmark/theBenchmark.p',fact_5923_even__of__int__iff)). 159.59/70.64 thf(16174,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)],[2461])). 159.59/70.64 thf(3454,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/sandbox/benchmark/theBenchmark.p',fact_2121_add__less__zeroD)). 159.59/70.64 thf(19352,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)],[3454])). 159.59/70.64 thf(2960,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]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (B @ D)) @ (C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7387_sum__norm__le)). 159.59/70.64 thf(17786,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]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (B @ D)) @ (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2960])). 159.59/70.64 thf(2809,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/sandbox/benchmark/theBenchmark.p',fact_7129_powser__split__head_I2_J)). 159.59/70.64 thf(17287,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)],[2809])). 159.59/70.64 thf(6530,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 @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2006_mult__mono)). 159.59/70.64 thf(30358,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 @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6530])). 159.59/70.64 thf(2040,axiom,((! [A:nat]: ((bit_se2923211474154528505it_int @ (suc @ A) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4726_take__bit__Suc__1)). 159.59/70.64 thf(14835,plain,((! [A:nat]: ((bit_se2923211474154528505it_int @ (suc @ A) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2040])). 159.59/70.64 thf(7542,axiom,((! [A:real]: ((ord_less_eq_real @ (sqrt @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6318_real__sqrt__le__0__iff)). 159.59/70.64 thf(34314,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)],[7542])). 159.59/70.64 thf(660,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/sandbox/benchmark/theBenchmark.p',fact_1065_add__le__cancel__left)). 159.59/70.64 thf(10361,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)],[660])). 159.59/70.64 thf(1789,axiom,((! [A:nat]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ semiri4939895301339042750nteger @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ one_one_Code_integer))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7830_double__gauss__sum__from__Suc__0)). 159.59/70.64 thf(14027,plain,((! [A:nat]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ (semiri4939895301339042750nteger) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ A))) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ A) @ one_one_Code_integer))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1789])). 159.59/70.64 thf(3153,axiom,((! [A:complex,B:complex]: ((A != zero_zero_complex) => (((divide1717551699836669952omplex @ B @ A) = one_one_complex) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2181_right__inverse__eq)). 159.59/70.64 thf(18399,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)],[3153])). 159.59/70.64 thf(1451,axiom,((! [A:(nat > nat),B:nat]: ((summable_nat @ A) => ((ord_less_nat @ (groups3542108847815614940at_nat @ A @ (set_ord_lessThan_nat @ B)) @ (suminf_nat @ A)) <= (! [C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ zero_zero_nat @ (A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7989_sum__less__suminf)). 159.59/70.64 thf(12979,plain,((! [A:(nat > nat),B:nat]: ((summable_nat @ (A)) => ((ord_less_nat @ (groups3542108847815614940at_nat @ (A) @ (set_ord_lessThan_nat @ B)) @ (suminf_nat @ (A))) | ~ (! [C:nat]: ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ zero_zero_nat @ (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451])). 159.59/70.64 thf(1652,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (~ (! [B:nat]: ~ (ord_less_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (suc @ B))) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6751_nat__approx__posE)). 159.59/70.64 thf(13606,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (~ (! [B:nat]: ~ (ord_less_real @ (divide_divide_real @ one_one_real @ (semiri5074537144036343181t_real @ (suc @ B))) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652])). 159.59/70.64 thf(676,axiom,((! [A:nat,B:nat]: ((nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))) = (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9435_nat__int__add)). 159.59/70.64 thf(10416,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)],[676])). 159.59/70.64 thf(7234,axiom,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1843_less__numeral__extra_I3_J)). 159.59/70.64 thf(33268,plain,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7234])). 159.59/70.64 thf(7623,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/sandbox/benchmark/theBenchmark.p',fact_3862_even__Suc)). 159.59/70.64 thf(34625,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)],[7623])). 159.59/70.64 thf(4061,axiom,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ B) => (((divide1717551699836669952omplex @ B @ A) = zero_zero_complex) = (B = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4049_dvd__div__eq__0__iff)). 159.59/70.64 thf(21287,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)],[4061])). 159.59/70.64 thf(4091,axiom,((! [A:extended_enat]: (dvd_dv3785147216227455552d_enat @ one_on7984719198319812577d_enat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4001_one__dvd)). 159.59/70.64 thf(21381,plain,((! [A:extended_enat]: (dvd_dv3785147216227455552d_enat @ one_on7984719198319812577d_enat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4091])). 159.59/70.64 thf(6709,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/sandbox/benchmark/theBenchmark.p',fact_5612_power__numeral__odd)). 159.59/70.64 thf(31114,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)],[6709])). 159.59/70.64 thf(603,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/sandbox/benchmark/theBenchmark.p',fact_4820_neg__numeral__less__iff)). 159.59/70.64 thf(10176,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)],[603])). 159.59/70.64 thf(276,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (ord_max_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_max_Ocobounded2)). 159.59/70.64 thf(9089,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (ord_max_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 159.59/70.64 thf(5976,axiom,((! [A:nat]: ((power_8040749407984259932d_enat @ one_on7984719198319812577d_enat @ A) = one_on7984719198319812577d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_power__one)). 159.59/70.64 thf(28368,plain,((! [A:nat]: ((power_8040749407984259932d_enat @ one_on7984719198319812577d_enat @ A) = one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5976])). 159.59/70.64 thf(327,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/sandbox/benchmark/theBenchmark.p',fact_1309_max__diff__distrib__left)). 159.59/70.64 thf(9258,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)],[327])). 159.59/70.64 thf(341,axiom,((! [A:code_integer]: ((bit_se9216721137139052372nteger @ A @ zero_zero_nat) = (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6350_bit__0)). 159.59/70.64 thf(9307,plain,((! [A:code_integer]: ((bit_se9216721137139052372nteger @ A @ zero_zero_nat) = (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 159.59/70.64 thf(7583,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/sandbox/benchmark/theBenchmark.p',fact_4802_semiring__norm_I172_J)). 159.59/70.64 thf(34503,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)],[7583])). 159.59/70.64 thf(7984,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/sandbox/benchmark/theBenchmark.p',fact_777_power__minus__is__div)). 159.59/70.64 thf(35764,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)],[7984])). 159.59/70.64 thf(2319,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((~ (ord_less_eq_int @ A @ C)) <= (ord_less_int @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4512_minf_I8_J)). 159.59/70.64 thf(15708,plain,((! [A:int]: ? [B:int]: ! [C:int]: (~ (ord_less_eq_int @ A @ C) | ~ (ord_less_int @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2319])). 159.59/70.64 thf(3163,axiom,((! [A:complex,B:nat]: ((real_V1022390504157884413omplex @ (power_power_complex @ A @ B)) = (power_power_real @ (real_V1022390504157884413omplex @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6906_norm__power)). 159.59/70.64 thf(18431,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)],[3163])). 159.59/70.64 thf(3637,axiom,((! [A:num]: (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (numera1916890842035813515d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1955_zero__le__numeral)). 159.59/70.64 thf(19930,plain,((! [A:num]: (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (numera1916890842035813515d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3637])). 159.59/70.64 thf(7187,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/sandbox/benchmark/theBenchmark.p',fact_3611_prod_Oinject)). 159.59/70.64 thf(33101,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)],[7187])). 159.59/70.64 thf(6262,axiom,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ one_one_nat) => (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1469_deg__1__Leaf)). 159.59/70.64 thf(29336,plain,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ one_one_nat) => (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6262])). 159.59/70.64 thf(2156,axiom,((bit_se2923211474154528505it_int = (^ [A:nat,B:int]: (modulo_modulo_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5265_take__bit__eq__mod)). 159.59/70.64 thf(15205,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)],[2156])). 159.59/70.64 thf(5777,axiom,((! [A:num,B:num,C:num]: (((ord_less_num @ C @ B) <= (ord_less_eq_num @ C @ A)) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3129_dual__order_Ostrict__trans2)). 159.59/70.64 thf(27380,plain,((! [A:num,B:num,C:num]: ((ord_less_num @ C @ B) | ~ (ord_less_eq_num @ C @ A) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5777])). 159.59/70.64 thf(4774,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1971_mult__nonneg__nonpos)). 159.59/70.64 thf(23751,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4774])). 159.59/70.64 thf(3182,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((! [D:nat]: (((ord_less_eq_real @ zero_zero_real @ (B @ D)) & (ord_less_eq_real @ (B @ D) @ (C @ D))) <= (member_nat @ D @ A))) => (ord_less_eq_real @ (groups129246275422532515t_real @ B @ A) @ (groups129246275422532515t_real @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8494_prod__mono)). 159.59/70.64 thf(18487,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((! [D:nat]: (((ord_less_eq_real @ zero_zero_real @ (B @ D)) & (ord_less_eq_real @ (B @ D) @ (C @ 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)],[3182])). 159.59/70.64 thf(8187,axiom,((! [A:(nat > nat),B:(nat > nat)]: (((summable_nat @ B) => (summable_nat @ (^ [C:nat]: (plus_plus_nat @ (A @ C) @ (B @ C))))) <= (summable_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7023_summable__add)). 159.59/70.64 thf(36429,plain,((! [A:(nat > nat),B:(nat > nat)]: (((summable_nat @ (B)) => (summable_nat @ (^ [C:nat]: (plus_plus_nat @ (A @ C) @ (B @ C))))) | ~ (summable_nat @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8187])). 159.59/70.64 thf(5031,axiom,((! [A:product_prod_nat_nat]: ? [B:nat,C:nat]: (A = (product_Pair_nat_nat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3685_surj__pair)). 159.59/70.64 thf(24656,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)],[5031])). 159.59/70.64 thf(4146,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((A = (B @ C)) => (((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) <= (ord_less_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2869_ord__eq__less__subst)). 159.59/70.64 thf(21551,plain,((! [A:real,B:(real > real),C:real,D:real]: ((A = (B @ C)) => (((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D))) | ~ (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4146])). 159.59/70.64 thf(5207,axiom,((! [A:nat,B:list_VEBT_VEBT,C:(vEBT_VEBT > $o)]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((C @ (nth_VEBT_VEBT @ B @ A)) <= (! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ B)) => (C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_list__ball__nth)). 159.59/70.64 thf(25294,plain,((! [A:nat,B:list_VEBT_VEBT,C:(vEBT_VEBT > $o)]: ((ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B)) => ((C @ (nth_VEBT_VEBT @ B @ A)) | ~ (! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ B)) => (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5207])). 159.59/70.64 thf(324,axiom,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ A @ (uminus1351360451143612070nteger @ A)) = (ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4685_less__neg__neg)). 159.59/70.64 thf(9248,plain,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ A @ (uminus1351360451143612070nteger @ A)) = (ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 159.59/70.64 thf(2393,axiom,((! [A:extended_enat,B:extended_enat]: ((if_Extended_enat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Extended____Nat__Oenat_T)). 159.59/70.64 thf(15941,plain,((! [A:extended_enat,B:extended_enat]: ((if_Extended_enat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2393])). 159.59/70.64 thf(2567,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 @ C @ (times_times_real @ B @ A)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2347_add__num__frac)). 159.59/70.64 thf(16500,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 @ C @ (times_times_real @ B @ A)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2567])). 159.59/70.64 thf(567,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (tanh_real @ A) @ (tanh_real @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5401_tanh__real__le__iff)). 159.59/70.64 thf(10056,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)],[567])). 159.59/70.64 thf(7672,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6099_even__and__iff)). 159.59/70.64 thf(34767,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_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)],[7672])). 159.59/70.64 thf(7818,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/sandbox/benchmark/theBenchmark.p',fact_6606_of__nat__less__of__nat__power__cancel__iff)). 159.59/70.64 thf(35237,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)],[7818])). 159.59/70.64 thf(451,axiom,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1537_div__by__0)). 159.59/70.64 thf(9670,plain,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[451])). 159.59/70.64 thf(5287,axiom,((! [A:real,B:nat,C:nat]: (((ord_less_real @ A @ one_one_real) => ((ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_nat @ C @ B))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1770_power__strict__decreasing__iff)). 159.59/70.64 thf(25574,plain,((! [A:real,B:nat,C:nat]: (((ord_less_real @ A @ one_one_real) => ((ord_less_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_nat @ C @ B))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5287])). 159.59/70.64 thf(1936,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((A != B) => (ord_less_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3185_order__le__neq__trans)). 159.59/70.64 thf(14502,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)],[1936])). 159.59/70.64 thf(5576,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((finite_finite_nat @ A) => ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D)))) => ((? [D:nat]: ((member_nat @ D @ A) & (ord_less_nat @ (B @ D) @ (C @ D)))) => (ord_less_nat @ (groups3542108847815614940at_nat @ B @ A) @ (groups3542108847815614940at_nat @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7480_sum__strict__mono__ex1)). 159.59/70.64 thf(26684,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((finite_finite_nat @ A) => ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D)))) => ((? [D:nat]: ((member_nat @ D @ A) & (ord_less_nat @ (B @ D) @ (C @ D)))) => (ord_less_nat @ (groups3542108847815614940at_nat @ (B) @ A) @ (groups3542108847815614940at_nat @ (C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5576])). 159.59/70.64 thf(4321,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))))) = ((B != zero_zero_real) | (A != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2544_sum__power2__gt__zero__iff)). 159.59/70.64 thf(22103,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))))) = (~ (B = zero_zero_real) | ~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4321])). 159.59/70.64 thf(497,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/sandbox/benchmark/theBenchmark.p',fact_9589_xor__int__def)). 159.59/70.64 thf(9835,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)],[497])). 159.59/70.64 thf(3702,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/sandbox/benchmark/theBenchmark.p',fact_5193_nonzero__neg__divide__eq__eq2)). 159.59/70.64 thf(20141,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)],[3702])). 159.59/70.64 thf(366,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/sandbox/benchmark/theBenchmark.p',fact_9603_and__not__numerals_I5_J)). 159.59/70.64 thf(9390,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)],[366])). 159.59/70.64 thf(3127,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (((ord_less_real @ (times_times_real @ A @ C) @ B) <= (ord_less_real @ zero_zero_real @ C)) & ((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_real @ A @ zero_zero_real) <= (~ (ord_less_real @ C @ zero_zero_real))) & ((ord_less_real @ B @ (times_times_real @ A @ C)) <= (ord_less_real @ C @ zero_zero_real)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2332_less__divide__eq)). 159.59/70.64 thf(18309,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (divide_divide_real @ B @ C)) = (((ord_less_real @ (times_times_real @ A @ C) @ B) | ~ (ord_less_real @ zero_zero_real @ C)) & ((~ (ord_less_real @ zero_zero_real @ C)) => (((ord_less_real @ A @ zero_zero_real) | (ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ B @ (times_times_real @ A @ C)) | ~ (ord_less_real @ C @ zero_zero_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3127])). 159.59/70.64 thf(5071,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/sandbox/benchmark/theBenchmark.p',fact_6187_or__minus__numerals_I7_J)). 159.59/70.64 thf(24817,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)],[5071])). 159.59/70.64 thf(6542,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/sandbox/benchmark/theBenchmark.p',fact_8524_prod_OatMost__shift)). 159.59/70.64 thf(30406,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)],[6542])). 159.59/70.64 thf(2986,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (cosh_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9334_cosh__real__nonneg)). 159.59/70.64 thf(17860,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (cosh_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2986])). 159.59/70.64 thf(3247,axiom,((! [A:nat,B:nat]: ((archim6058952711729229775r_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))) = (semiri1314217659103216013at_int @ (divide_divide_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8248_floor__divide__of__nat__eq)). 159.59/70.64 thf(18695,plain,((! [A:nat,B:nat]: ((archim6058952711729229775r_real @ (divide_divide_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))) = (semiri1314217659103216013at_int @ (divide_divide_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3247])). 159.59/70.64 thf(6871,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2248_mult__strict__mono)). 159.59/70.64 thf(31767,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6871])). 159.59/70.64 thf(4369,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ A) => (((ord_less_real @ zero_zero_real @ (suminf_real @ A)) <= (ord_less_real @ zero_zero_real @ (A @ B))) <= (! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7084_suminf__pos2)). 159.59/70.64 thf(22244,plain,((! [A:(nat > real),B:nat]: ((summable_real @ (A)) => ((ord_less_real @ zero_zero_real @ (suminf_real @ (A))) | ~ (ord_less_real @ zero_zero_real @ (A @ B)) | ~ (! [C:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4369])). 159.59/70.64 thf(7488,axiom,((vEBT_VEBT_minNull @ (vEBT_Leaf @ ($false) @ ($false)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1806_VEBT__internal_OminNull_Osimps_I1_J)). 159.59/70.64 thf(34154,plain,((vEBT_VEBT_minNull @ (vEBT_Leaf @ ($false) @ ($false)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7488])). 159.59/70.64 thf(1591,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/sandbox/benchmark/theBenchmark.p',fact_3529_div__mult1__eq)). 159.59/70.64 thf(13417,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)],[1591])). 159.59/70.64 thf(8207,axiom,((! [A:nat,B:list_VEBT_VEBT,C:list_int]: (((nth_Pr6837108013167703752BT_int @ (produc7292646706713671643BT_int @ B @ C) @ A) = (produc736041933913180425BT_int @ (nth_VEBT_VEBT @ B @ (divide_divide_nat @ A @ (size_size_list_int @ C))) @ (nth_int @ C @ (modulo_modulo_nat @ A @ (size_size_list_int @ C))))) <= (ord_less_nat @ A @ (times_times_nat @ (size_s6755466524823107622T_VEBT @ B) @ (size_size_list_int @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3592_product__nth)). 159.59/70.64 thf(36502,plain,((! [A:nat,B:list_VEBT_VEBT,C:list_int]: (((nth_Pr6837108013167703752BT_int @ (produc7292646706713671643BT_int @ B @ C) @ A) = (produc736041933913180425BT_int @ (nth_VEBT_VEBT @ B @ (divide_divide_nat @ A @ (size_size_list_int @ C))) @ (nth_int @ C @ (modulo_modulo_nat @ A @ (size_size_list_int @ C))))) | ~ (ord_less_nat @ A @ (times_times_nat @ (size_s6755466524823107622T_VEBT @ B) @ (size_size_list_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8207])). 159.59/70.64 thf(6732,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/sandbox/benchmark/theBenchmark.p',fact_6292_Suc__0__or__eq)). 159.59/70.64 thf(31205,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)],[6732])). 159.59/70.64 thf(7470,axiom,((! [A:(nat > num),B:nat,C:nat]: ((! [D:nat]: (ord_less_num @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_num @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_lift__Suc__mono__less__iff)). 159.59/70.64 thf(34060,plain,((! [A:(nat > num),B:nat,C:nat]: ((! [D:nat]: (ord_less_num @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_num @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7470])). 159.59/70.64 thf(4498,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3262_order__le__imp__less__or__eq)). 159.59/70.64 thf(22719,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)],[4498])). 159.59/70.64 thf(2846,axiom,((! [A:complex,B:complex,C:complex]: ((A = (times_times_complex @ B @ C)) => (dvd_dvd_complex @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3935_dvdI)). 159.59/70.64 thf(17401,plain,((! [A:complex,B:complex,C:complex]: ((A = (times_times_complex @ B @ C)) => (dvd_dvd_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2846])). 159.59/70.64 thf(1778,axiom,((! [A:nat]: ((bit_se2000444600071755411sk_int @ (suc @ A)) = (bit_se1409905431419307370or_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2000444600071755411sk_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6095_mask__Suc__double)). 159.59/70.64 thf(13995,plain,((! [A:nat]: ((bit_se2000444600071755411sk_int @ (suc @ A)) = (bit_se1409905431419307370or_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2000444600071755411sk_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778])). 159.59/70.64 thf(2824,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/sandbox/benchmark/theBenchmark.p',fact_2141_divide__nonneg__nonpos)). 159.59/70.64 thf(17332,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)],[2824])). 159.59/70.64 thf(5980,axiom,((! [A:nat,B:nat]: ((tl_nat @ (upt @ A @ B)) = (upt @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10155_tl__upt)). 159.59/70.64 thf(28379,plain,((! [A:nat,B:nat]: ((tl_nat @ (upt @ A @ B)) = (upt @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5980])). 159.59/70.64 thf(1297,axiom,((! [A:set_nat]: ((groups705719431365010083at_int @ (^ [B:nat]: (one_one_int)) @ A) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8376_prod_Oneutral__const)). 159.59/70.64 thf(12445,plain,((! [A:set_nat]: ((groups705719431365010083at_int @ (^ [B:nat]: (one_one_int)) @ A) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297])). 159.59/70.64 thf(3565,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > int),D:int]: ((ord_le72135733267957522d_enat @ A @ B) => (((C @ B) = D) => ((! [E:extended_enat,F:extended_enat]: ((ord_less_int @ (C @ E) @ (C @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_int @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2877_ord__less__eq__subst)). 159.59/70.64 thf(19698,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > int),D:int]: ((ord_le72135733267957522d_enat @ A @ B) => (((C @ B) = D) => ((! [E:extended_enat,F:extended_enat]: ((ord_less_int @ (C @ E) @ (C @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_int @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3565])). 159.59/70.64 thf(4647,axiom,((! [A:num]: ((times_times_num @ A @ one) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_semiring__norm_I11_J)). 159.59/70.64 thf(23314,plain,((! [A:num]: ((times_times_num @ A @ one) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4647])). 159.59/70.64 thf(3382,axiom,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5188_neg__one__less__numeral)). 159.59/70.64 thf(19121,plain,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3382])). 159.59/70.64 thf(322,axiom,(((arcosh_real @ one_one_real) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3779_arcosh__1)). 159.59/70.64 thf(9243,plain,(((arcosh_real @ one_one_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 159.59/70.64 thf(1001,axiom,((! [A:num]: ~ (bit_se1146084159140164899it_int @ one_one_int @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6383_bit__numeral__simps_I1_J)). 159.59/70.64 thf(11451,plain,((! [A:num]: ~ (bit_se1146084159140164899it_int @ one_one_int @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001])). 159.59/70.64 thf(4822,axiom,(((ord_max_nat @ zero_zero_nat @ one_one_nat) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1706_max__0__1_I1_J)). 159.59/70.64 thf(23939,plain,(((ord_max_nat @ zero_zero_nat @ one_one_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4822])). 159.59/70.64 thf(7743,axiom,(((inc @ one) = (bit0 @ one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5718_inc_Osimps_I1_J)). 159.59/70.64 thf(35027,plain,(((inc @ one) = (bit0 @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7743])). 159.59/70.64 thf(2579,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => (~ (ord_le72135733267957522d_enat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3020_leD)). 159.59/70.64 thf(16542,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => (~ (ord_le72135733267957522d_enat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2579])). 159.59/70.64 thf(1869,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/sandbox/benchmark/theBenchmark.p',fact_6874_sin__pi__divide__n__gt__0)). 159.59/70.64 thf(14290,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)],[1869])). 159.59/70.64 thf(8128,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/sandbox/benchmark/theBenchmark.p',fact_4075_div__mult__swap)). 159.59/70.64 thf(36238,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)],[8128])). 159.59/70.64 thf(7757,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/sandbox/benchmark/theBenchmark.p',fact_3474_cong__exp__iff__simps_I9_J)). 159.59/70.64 thf(35065,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)],[7757])). 159.59/70.64 thf(3724,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = zero_zero_real) = (B = (uminus_uminus_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5058_add__eq__0__iff)). 159.59/70.64 thf(20228,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)],[3724])). 159.59/70.64 thf(7622,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:list_VEBT_VEBT,J:vEBT_VEBT]: (((A != C) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((((G = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ E) @ F)) => ((~ (vEBT_VEBT_minNull @ G)) => ((((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ H @ J) @ B) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (plus_plus_nat @ (times_times_nat @ E @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ I @ E)))) @ C))) @ D @ I @ J)) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H))) <= (I = (list_u1324408373059187874T_VEBT @ H @ E @ G))))) <= ((vEBT_VEBT_low @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F)) <= ((vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = E)))) <= ((ord_less_nat @ A @ B) & (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_del__x__not__mi__newnode__not__nil)). 159.59/70.64 thf(34620,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:list_VEBT_VEBT,J:vEBT_VEBT]: (((~ (A = C)) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => (((G = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ E) @ F)) => ((~ (vEBT_VEBT_minNull @ G)) => (((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ H @ J) @ B) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (plus_plus_nat @ (times_times_nat @ E @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ I @ E)))) @ C))) @ D @ I @ J)) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)) | ~ (I = (list_u1324408373059187874T_VEBT @ H @ E @ G))))) | ~ ((vEBT_VEBT_low @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F) | ~ ((vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = E)))) | ~ ((ord_less_nat @ A @ B) & (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7622])). 159.59/70.64 thf(353,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/sandbox/benchmark/theBenchmark.p',fact_9660_plus__complex_Ocode)). 159.59/70.64 thf(9344,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)],[353])). 159.59/70.64 thf(1192,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/sandbox/benchmark/theBenchmark.p',fact_1045_add__diff__cancel__left)). 159.59/70.64 thf(12082,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)],[1192])). 159.59/70.64 thf(8067,axiom,((! [A:num]: ~ (ord_less_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2010_not__numeral__less__zero)). 159.59/70.64 thf(36049,plain,((! [A:num]: ~ (ord_less_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8067])). 159.59/70.64 thf(2256,axiom,((! [A:complex,B:complex]: ((invers8013647133539491842omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8979_inverse__mult__distrib)). 159.59/70.64 thf(15530,plain,((! [A:complex,B:complex]: ((invers8013647133539491842omplex @ (times_times_complex @ A @ B)) = (times_times_complex @ (invers8013647133539491842omplex @ A) @ (invers8013647133539491842omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2256])). 159.59/70.64 thf(8178,axiom,((vEBT_V8194947554948674370ptions @ summary @ (vEBT_VEBT_high @ ma @ na))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73__092_060open_062both__member__options_Asummary_A_Ihigh_Ama_An_J_092_060close_062)). 159.59/70.64 thf(36405,plain,((vEBT_V8194947554948674370ptions @ summary @ (vEBT_VEBT_high @ ma @ na))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8178])). 159.59/70.64 thf(2411,axiom,((exp_complex = (^ [A:complex]: (plus_plus_complex @ (plus_plus_complex @ one_one_complex @ A) @ (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (plus_plus_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_complex @ A @ (plus_plus_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9183_exp__first__two__terms)). 159.59/70.64 thf(16000,plain,(((exp_complex) = (^ [A:complex]: (plus_plus_complex @ (plus_plus_complex @ one_one_complex @ A) @ (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (plus_plus_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_complex @ A @ (plus_plus_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2411])). 159.59/70.64 thf(1396,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A) => (((ord_le3102999989581377725nteger @ B @ (modulo364778990260209775nteger @ A @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))) => ((plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))) @ one_one_Code_integer) = (divide6298287555418463151nteger @ A @ B))) <= (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3576_divmod__digit__1_I1_J)). 159.59/70.64 thf(12806,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A) => (((ord_le3102999989581377725nteger @ B @ (modulo364778990260209775nteger @ A @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))) => ((plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))) @ one_one_Code_integer) = (divide6298287555418463151nteger @ A @ B))) | ~ (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396])). 159.59/70.64 thf(6202,axiom,((! [A:nat,B:nat]: (((~ (! [C:nat]: ((ord_less_nat @ A @ C) => (B != (suc @ C))))) <= (B != (suc @ A))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_Nat_OlessE)). 159.59/70.64 thf(29098,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (~ (B = (suc @ C))))) | (B = (suc @ A)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6202])). 159.59/70.64 thf(5706,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/sandbox/benchmark/theBenchmark.p',fact_5860_neg__numeral__power__eq__of__int__cancel__iff)). 159.59/70.64 thf(27144,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)],[5706])). 159.59/70.64 thf(6086,axiom,((! [A:num]: ((~ (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)))) = (A != one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4824_not__neg__one__le__neg__numeral__iff)). 159.59/70.64 thf(28707,plain,((! [A:num]: ((~ (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)))) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6086])). 159.59/70.64 thf(7252,axiom,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6510_of__nat__eq__0__iff)). 159.59/70.64 thf(33328,plain,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7252])). 159.59/70.64 thf(1653,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/sandbox/benchmark/theBenchmark.p',fact_5326_signed__take__bit__eq__take__bit__shift)). 159.59/70.64 thf(13609,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)],[1653])). 159.59/70.64 thf(378,axiom,((! [A:complex,B:complex]: ((((csqrt @ B) = A) <= ((ord_less_real @ zero_zero_real @ (re @ A)) | ((ord_less_eq_real @ zero_zero_real @ (im @ A)) & ((re @ A) = zero_zero_real)))) <= ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9677_csqrt__unique)). 159.59/70.64 thf(9422,plain,((! [A:complex,B:complex]: (((csqrt @ B) = A) | ~ ((ord_less_real @ zero_zero_real @ (re @ A)) | ((ord_less_eq_real @ zero_zero_real @ (im @ A)) & ((re @ A) = zero_zero_real))) | ~ ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])). 159.59/70.64 thf(2435,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/sandbox/benchmark/theBenchmark.p',fact_8273_pochhammer__rec_H)). 159.59/70.64 thf(16088,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)],[2435])). 159.59/70.64 thf(2632,axiom,((ord_less_real = (^ [A:real,B:real]: (~ (ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3133_dual__order_Ostrict__iff__not)). 159.59/70.64 thf(16735,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)],[2632])). 159.59/70.64 thf(4920,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3144_order_Ostrict__implies__order)). 159.59/70.64 thf(24260,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4920])). 159.59/70.64 thf(7307,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/sandbox/benchmark/theBenchmark.p',fact_4223_power__dvd__imp__le)). 159.59/70.64 thf(33509,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)],[7307])). 159.59/70.64 thf(4140,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]: ((ord_less_real @ E @ F) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F))))) <= (? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) <= (ord_less_real @ E @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4428_pinf_I1_J)). 159.59/70.64 thf(21527,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]: ((ord_less_real @ E @ F) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F)))) | ~ (? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) | ~ (ord_less_real @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4140])). 159.59/70.64 thf(7494,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (times_times_real @ A @ B)) = (((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ one_one_real @ B)) & ((ord_less_eq_real @ B @ one_one_real) <= (ord_less_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2424_mult__le__cancel__left1)). 159.59/70.64 thf(34169,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ (times_times_real @ A @ B)) = (((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ one_one_real @ B)) & ((ord_less_eq_real @ B @ one_one_real) | ~ (ord_less_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7494])). 159.59/70.64 thf(6609,axiom,((! [A:num,B:num]: (((ord_less_eq_num @ B @ A) = (B = A)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2640_order__antisym__conv)). 159.59/70.64 thf(30633,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)],[6609])). 159.59/70.64 thf(2205,axiom,((divide1717551699836669952omplex = (^ [A:complex,B:complex]: (times_times_complex @ A @ (invers8013647133539491842omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9044_field__class_Ofield__divide__inverse)). 159.59/70.64 thf(15367,plain,(((divide1717551699836669952omplex) = (^ [A:complex,B:complex]: (times_times_complex @ A @ (invers8013647133539491842omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2205])). 159.59/70.64 thf(7653,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/sandbox/benchmark/theBenchmark.p',fact_448_power__even__eq)). 159.59/70.64 thf(34711,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)],[7653])). 159.59/70.64 thf(6313,axiom,((! [A:real,B:real]: ((times_times_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (times_times_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4627_minus__mult__minus)). 159.59/70.64 thf(29530,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)],[6313])). 159.59/70.64 thf(2677,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/sandbox/benchmark/theBenchmark.p',fact_6298_of__int__round__ge)). 159.59/70.64 thf(16883,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)],[2677])). 159.59/70.64 thf(2244,axiom,((! [A:int,B: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/sandbox/benchmark/theBenchmark.p',fact_1613_sum__squares__eq__zero__iff)). 159.59/70.64 thf(15492,plain,((! [A:int,B: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)],[2244])). 159.59/70.64 thf(4129,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/sandbox/benchmark/theBenchmark.p',fact_2105_mult__neg__neg)). 159.59/70.64 thf(21493,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)],[4129])). 159.59/70.64 thf(598,axiom,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((member_nat @ B @ A) => ((groups2073611262835488442omplex @ C @ (insert_nat @ B @ A)) = (groups2073611262835488442omplex @ C @ A))) & (((groups2073611262835488442omplex @ C @ (insert_nat @ B @ A)) = (plus_plus_complex @ (C @ B) @ (groups2073611262835488442omplex @ C @ A))) <= (~ (member_nat @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7505_sum_Oinsert__if)). 159.59/70.64 thf(10151,plain,((! [A:set_nat,B:nat,C:(nat > complex)]: ((finite_finite_nat @ A) => (((member_nat @ B @ A) => ((groups2073611262835488442omplex @ (C) @ (insert_nat @ B @ A)) = (groups2073611262835488442omplex @ (C) @ A))) & (((groups2073611262835488442omplex @ (C) @ (insert_nat @ B @ A)) = (plus_plus_complex @ (C @ B) @ (groups2073611262835488442omplex @ (C) @ A))) | (member_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[598])). 159.59/70.64 thf(1739,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2159_divide__pos__pos)). 159.59/70.64 thf(13871,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739])). 159.59/70.64 thf(7342,axiom,((! [A:num,B:num]: ((numeral_numeral_real @ A) != (uminus_uminus_real @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4944_numeral__neq__neg__numeral)). 159.59/70.64 thf(33641,plain,((! [A:num,B:num]: ~ ((numeral_numeral_real @ A) = (uminus_uminus_real @ (numeral_numeral_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7342])). 159.59/70.64 thf(2316,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/sandbox/benchmark/theBenchmark.p',fact_8121_fact__num__eq__if)). 159.59/70.64 thf(15700,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)],[2316])). 159.59/70.64 thf(2216,axiom,((! [A:int,B:int,C:int]: (((((divide_divide_int @ B @ A) = (divide_divide_int @ C @ A)) = (B = C)) <= (dvd_dvd_int @ A @ C)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4010_dvd__div__eq__iff)). 159.59/70.64 thf(15406,plain,((! [A:int,B:int,C:int]: ((((divide_divide_int @ B @ A) = (divide_divide_int @ C @ A)) = (B = C)) | ~ (dvd_dvd_int @ A @ C) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2216])). 159.59/70.64 thf(3605,axiom,((! [A:(nat > (nat > $o)),B:product_prod_nat_nat]: ((~ (! [C:nat,D:nat]: ((B = (product_Pair_nat_nat @ C @ D)) => (~ (A @ C @ D))))) <= (produc6081775807080527818_nat_o @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5512_case__prodE)). 159.59/70.64 thf(19829,plain,((! [A:(nat > (nat > $o)),B:product_prod_nat_nat]: (~ (! [C:nat,D:nat]: ((B = (product_Pair_nat_nat @ C @ D)) => (~ (A @ C @ D)))) | ~ (produc6081775807080527818_nat_o @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3605])). 159.59/70.64 thf(6759,axiom,((! [A:nat]: (none_nat != (some_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_option_Odistinct_I1_J)). 159.59/70.64 thf(31307,plain,((! [A:nat]: ~ (none_nat = (some_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6759])). 159.59/70.64 thf(7327,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/sandbox/benchmark/theBenchmark.p',fact_8491_prod__nonneg)). 159.59/70.64 thf(33592,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)],[7327])). 159.59/70.64 thf(5642,axiom,((! [A:set_nat,B:nat]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ B @ C))) => (inj_on_nat_nat @ (^ [C:nat]: (minus_minus_nat @ C @ B)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10112_inj__on__diff__nat)). 159.59/70.64 thf(26911,plain,((! [A:set_nat,B:nat]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_less_eq_nat @ B @ C))) => (inj_on_nat_nat @ (^ [C:nat]: (minus_minus_nat @ C @ B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5642])). 159.59/70.64 thf(6727,axiom,((! [A:(nat > $o),B:$o]: ((A @ (zero_n2687167440665602831ol_nat @ B)) = (~ (((B) & ~ (A @ one_one_nat)) | (~ (A @ zero_zero_nat) & ~ (B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4413_split__of__bool__asm)). 159.59/70.64 thf(31190,plain,((! [A:(nat > $o),B:$o]: ((A @ (zero_n2687167440665602831ol_nat @ B)) = (~ (((B) & ~ (A @ one_one_nat)) | (~ (A @ zero_zero_nat) & ~ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6727])). 159.59/70.64 thf(646,axiom,((! [A:(nat > complex),B:complex,C:nat]: ((~ (! [D:(nat > complex)]: ~ (! [E:complex]: ((groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (A @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ C)) = (times_times_complex @ (minus_minus_complex @ E @ B) @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (D @ F) @ (power_power_complex @ E @ F))) @ (set_ord_lessThan_nat @ C))))))) <= ((groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ (power_power_complex @ B @ D))) @ (set_ord_atMost_nat @ C)) = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8882_polyfun__linear__factor__root)). 159.59/70.64 thf(10317,plain,((! [A:(nat > complex),B:complex,C:nat]: (~ (! [D:(nat > complex)]: ~ (! [E:complex]: ((groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (A @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ C)) = (times_times_complex @ (minus_minus_complex @ E @ B) @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (D @ F) @ (power_power_complex @ E @ F))) @ (set_ord_lessThan_nat @ C)))))) | ~ ((groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ (power_power_complex @ B @ D))) @ (set_ord_atMost_nat @ C)) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[646])). 159.59/70.64 thf(681,axiom,(((semiri1314217659103216013at_int @ one_one_nat) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6829_int__ops_I2_J)). 159.59/70.64 thf(10429,plain,(((semiri1314217659103216013at_int @ one_one_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[681])). 159.59/70.64 thf(3292,axiom,((! [A:num]: ((inverse_inverse_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (divide_divide_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9012_inverse__eq__divide__neg__numeral)). 159.59/70.64 thf(18849,plain,((! [A:num]: ((inverse_inverse_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (divide_divide_real @ one_one_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3292])). 159.59/70.64 thf(8125,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) = (((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))) & (ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ (suc @ B) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1459_VEBT__internal_Onaive__member_Osimps_I3_J)). 159.59/70.64 thf(36228,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) = (((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))) & (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)],[8125])). 159.59/70.64 thf(3735,axiom,((! [A:(nat > real),B:real,C:nat]: ((sums_real @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ C))) @ (minus_minus_real @ B @ (groups6591440286371151544t_real @ A @ (set_ord_lessThan_nat @ C)))) <= (sums_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7904_sums__split__initial__segment)). 159.59/70.64 thf(20266,plain,((! [A:(nat > real),B:real,C:nat]: ((sums_real @ (^ [D:nat]: (A @ (plus_plus_nat @ D @ C))) @ (minus_minus_real @ B @ (groups6591440286371151544t_real @ (A) @ (set_ord_lessThan_nat @ C)))) | ~ (sums_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3735])). 159.59/70.64 thf(824,axiom,((neg_nu7009210354673126013omplex = (^ [A:complex]: (plus_plus_complex @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4131_dbl__def)). 159.59/70.64 thf(10910,plain,(((neg_nu7009210354673126013omplex) = (^ [A:complex]: (plus_plus_complex @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[824])). 159.59/70.64 thf(4534,axiom,((! [A:num]: (one_one_real != (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5090_one__neq__neg__numeral)). 159.59/70.64 thf(22905,plain,((! [A:num]: ~ (one_one_real = (uminus_uminus_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4534])). 159.59/70.64 thf(8135,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1314_add__le__less__mono)). 159.59/70.64 thf(36270,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_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)],[8135])). 159.59/70.64 thf(4810,axiom,((! [A:nat,B:(nat > int),C:int]: ((! [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))) => (((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/sandbox/benchmark/theBenchmark.p',fact_5739_nat__ivt__aux)). 159.59/70.64 thf(23867,plain,((! [A:nat,B:(nat > int),C:int]: ((! [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))) => (((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)],[4810])). 159.59/70.64 thf(355,axiom,((! [A:real,B:real,C:real]: ((real_V1485227260804924795R_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9214_scaleR__left_Oadd)). 159.59/70.64 thf(9349,plain,((! [A:real,B:real,C:real]: ((real_V1485227260804924795R_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[355])). 159.59/70.64 thf(6833,axiom,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ A) = (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ B @ one_one_real)) & ((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_real @ one_one_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2414_mult__less__cancel__left2)). 159.59/70.64 thf(31555,plain,((! [A:real,B:real]: ((ord_less_real @ (times_times_real @ A @ B) @ A) = (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ B @ one_one_real)) & ((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_real @ one_one_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6833])). 159.59/70.64 thf(7940,axiom,((! [A:option_nat,B:option_nat]: (((A = none_nat) = (B = none_nat)) => ((A = B) <= ((A != none_nat) => ((B != none_nat) => ((the_nat @ A) = (the_nat @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_option_Oexpand)). 159.59/70.64 thf(35630,plain,((! [A:option_nat,B:option_nat]: (((A = none_nat) = (B = none_nat)) => ((A = B) | ~ ((~ (A = none_nat)) => ((~ (B = none_nat)) => ((the_nat @ A) = (the_nat @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7940])). 159.59/70.64 thf(1362,axiom,((! [A:real,B:real,C:real,D:real]: ((((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 @ B @ A)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2293_frac__le)). 159.59/70.64 thf(12651,plain,((! [A:real,B:real,C:real,D:real]: (((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 @ B @ A) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362])). 159.59/70.64 thf(1454,axiom,((! [A:real]: (((ord_less_eq_real @ A @ pi) => ((arccos @ (cos_real @ A)) = A)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7709_arccos__cos)). 159.59/70.64 thf(12990,plain,((! [A:real]: (((ord_less_eq_real @ A @ pi) => ((arccos @ (cos_real @ A)) = A)) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1454])). 159.59/70.64 thf(8053,axiom,((! [A:code_integer]: ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (power_8256067586552552935nteger @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4840_power2__minus)). 159.59/70.64 thf(35999,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)],[8053])). 159.59/70.64 thf(6807,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/sandbox/benchmark/theBenchmark.p',fact_9494_real__root__pow__pos2)). 159.59/70.64 thf(31466,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)],[6807])). 159.59/70.64 thf(7532,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/sandbox/benchmark/theBenchmark.p',fact_6888_norm__mult__numeral1)). 159.59/70.64 thf(34286,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)],[7532])). 159.59/70.64 thf(2054,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/sandbox/benchmark/theBenchmark.p',fact_6434_bit__iff__odd)). 159.59/70.64 thf(14878,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)],[2054])). 159.59/70.64 thf(7161,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (modulo_modulo_nat @ B @ A) @ A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3472_unique__euclidean__semiring__numeral__class_Opos__mod__bound)). 159.59/70.64 thf(32974,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)],[7161])). 159.59/70.64 thf(5516,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 @ D @ B)) @ A @ E @ F) @ C) = (some_nat @ B)) <= (ord_less_nat @ B @ C)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_720_pred__max)). 159.59/70.64 thf(26505,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 @ D @ B)) @ A @ E @ F) @ C) = (some_nat @ B)) | ~ (ord_less_nat @ B @ C) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5516])). 159.59/70.64 thf(2552,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/sandbox/benchmark/theBenchmark.p',fact_1728_divide__le__0__1__iff)). 159.59/70.64 thf(16454,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)],[2552])). 159.59/70.64 thf(153,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (ord_max_int @ B @ C)) = ((ord_less_int @ A @ B) | (ord_less_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_965_less__max__iff__disj)). 159.59/70.64 thf(8715,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (ord_max_int @ B @ C)) = ((ord_less_int @ A @ B) | (ord_less_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 159.59/70.64 thf(1019,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/sandbox/benchmark/theBenchmark.p',fact_8208_floor__minus__one__divide__eq__div__numeral)). 159.59/70.64 thf(11508,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)],[1019])). 159.59/70.64 thf(5102,axiom,((! [A:nat]: ((ord_max_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1573_max__nat_Oright__neutral)). 159.59/70.64 thf(24919,plain,((! [A:nat]: ((ord_max_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5102])). 159.59/70.64 thf(7926,axiom,((bit_se1412395901928357646or_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_se1412395901928357646or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6294_or__nat__rec)). 159.59/70.64 thf(35587,plain,(((bit_se1412395901928357646or_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_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)],[7926])). 159.59/70.64 thf(3889,axiom,((! [A:int,B:int]: ? [C:int]: ! [D:int]: ((ord_less_int @ C @ D) => ((~ (dvd_dvd_int @ A @ (plus_plus_int @ D @ B))) = (~ (dvd_dvd_int @ A @ (plus_plus_int @ D @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4535_pinf_I10_J)). 159.59/70.64 thf(20774,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3889])). 159.59/70.64 thf(7271,axiom,((! [A:nat]: ? [B:list_o]: ((size_size_list_o @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_Ex__list__of__length)). 159.59/70.64 thf(33382,plain,((! [A:nat]: ? [B:list_o]: ((size_size_list_o @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7271])). 159.59/70.64 thf(7237,axiom,((! [A:num,B:num]: ((uminus_uminus_int @ (numeral_numeral_int @ A)) != (numeral_numeral_int @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4949_neg__numeral__neq__numeral)). 159.59/70.64 thf(33279,plain,((! [A:num,B:num]: ~ ((uminus_uminus_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7237])). 159.59/70.64 thf(4978,axiom,((! [A:num,B:num]: ((numeral_numeral_int @ A) != (uminus_uminus_int @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4945_numeral__neq__neg__numeral)). 159.59/70.64 thf(24484,plain,((! [A:num,B:num]: ~ ((numeral_numeral_int @ A) = (uminus_uminus_int @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4978])). 159.59/70.64 thf(1149,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/sandbox/benchmark/theBenchmark.p',fact_113_distrib__left__numeral)). 159.59/70.64 thf(11932,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)],[1149])). 159.59/70.64 thf(5804,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/sandbox/benchmark/theBenchmark.p',fact_8964_fact__code)). 159.59/70.64 thf(27594,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)],[5804])). 159.59/70.64 thf(5275,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/sandbox/benchmark/theBenchmark.p',fact_3435_not__mod__2__eq__0__eq__1)). 159.59/70.64 thf(25518,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)],[5275])). 159.59/70.64 thf(178,axiom,((! [A:num,B:num,C:num,D:real]: ((real_V1485227260804924795R_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) @ (times_times_real @ (numeral_numeral_real @ C) @ D)) = (real_V1485227260804924795R_real @ (divide_divide_real @ (times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ C)) @ (numeral_numeral_real @ B)) @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9207_fraction__scaleR__times)). 159.59/70.64 thf(8799,plain,((! [A:num,B:num,C:num,D:real]: ((real_V1485227260804924795R_real @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) @ (times_times_real @ (numeral_numeral_real @ C) @ D)) = (real_V1485227260804924795R_real @ (divide_divide_real @ (times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ C)) @ (numeral_numeral_real @ B)) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[178])). 159.59/70.64 thf(8007,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/sandbox/benchmark/theBenchmark.p',fact_1740_div__mult__self4)). 159.59/70.64 thf(35836,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)],[8007])). 159.59/70.64 thf(4268,axiom,((! [A:complex]: ~ (ord_less_real @ (real_V1022390504157884413omplex @ A) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6899_norm__not__less__zero)). 159.59/70.64 thf(21950,plain,((! [A:complex]: ~ (ord_less_real @ (real_V1022390504157884413omplex @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4268])). 159.59/70.64 thf(8249,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/sandbox/benchmark/theBenchmark.p',fact_1097_mult_Oleft__commute)). 159.59/70.64 thf(36776,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)],[8249])). 159.59/70.64 thf(570,axiom,((! [A:complex,B:complex]: ((sinh_complex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (sinh_complex @ A) @ (cosh_complex @ B)) @ (times_times_complex @ (cosh_complex @ A) @ (sinh_complex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9327_sinh__add)). 159.59/70.64 thf(10066,plain,((! [A:complex,B:complex]: ((sinh_complex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (sinh_complex @ A) @ (cosh_complex @ B)) @ (times_times_complex @ (cosh_complex @ A) @ (sinh_complex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[570])). 159.59/70.64 thf(2368,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_eq_real @ (arccos @ B) @ (arccos @ A)) <= (ord_less_eq_real @ B @ one_one_real)) <= (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7542_arccos__le__arccos)). 159.59/70.64 thf(15853,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ (arccos @ B) @ (arccos @ A)) | ~ (ord_less_eq_real @ B @ one_one_real) | ~ (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2368])). 159.59/70.64 thf(2192,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/sandbox/benchmark/theBenchmark.p',fact_3415_mod__mult__self4)). 159.59/70.64 thf(15316,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)],[2192])). 159.59/70.64 thf(3065,axiom,((! [A:nat,B:complex,C:complex,D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (times_times_complex @ (gbinomial_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ B) @ E) @ (power_power_complex @ C @ E)) @ (power_power_complex @ D @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A)) = (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (times_times_complex @ (gbinomial_complex @ (minus_minus_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ E) @ B) @ one_one_complex) @ E) @ (power_power_complex @ C @ E)) @ (power_power_complex @ (plus_plus_complex @ C @ D) @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8951_gbinomial__partial__sum__poly__xpos)). 159.59/70.64 thf(18103,plain,((! [A:nat,B:complex,C:complex,D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (times_times_complex @ (gbinomial_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ B) @ E) @ (power_power_complex @ C @ E)) @ (power_power_complex @ D @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A)) = (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (times_times_complex @ (gbinomial_complex @ (minus_minus_complex @ (plus_plus_complex @ (semiri8010041392384452111omplex @ E) @ B) @ one_one_complex) @ E) @ (power_power_complex @ C @ E)) @ (power_power_complex @ (plus_plus_complex @ C @ D) @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3065])). 159.59/70.64 thf(2249,axiom,((! [A:nat]: ((one_one_Code_integer = (semiri4939895301339042750nteger @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6549_of__nat__1__eq__iff)). 159.59/70.64 thf(15507,plain,((! [A:nat]: ((one_one_Code_integer = (semiri4939895301339042750nteger @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2249])). 159.59/70.64 thf(4967,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((root @ A @ (abs_abs_real @ B)) = (abs_abs_real @ (root @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9510_real__root__abs)). 159.59/70.64 thf(24452,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((root @ A @ (abs_abs_real @ B)) = (abs_abs_real @ (root @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4967])). 159.59/70.64 thf(7452,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((B = A) <= (ord_less_nat @ A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_less__antisym)). 159.59/70.64 thf(33996,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)],[7452])). 159.59/70.64 thf(3202,axiom,((! [A:real]: ((cos_real @ (plus_plus_real @ pi @ A)) = (uminus_uminus_real @ (cos_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6974_cos__periodic__pi2)). 159.59/70.64 thf(18551,plain,((! [A:real]: ((cos_real @ (plus_plus_real @ pi @ A)) = (uminus_uminus_real @ (cos_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3202])). 159.59/70.64 thf(6298,axiom,((! [A:num]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5701_add__neg__numeral__special_I6_J)). 159.59/70.64 thf(29486,plain,((! [A:num]: ((plus_plus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6298])). 159.59/70.64 thf(5456,axiom,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: ((ord_less_nat @ zero_zero_nat @ (B @ C)) <= (member_nat @ C @ A))) => (ord_less_nat @ zero_zero_nat @ (groups708209901874060359at_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8504_prod__pos)). 159.59/70.64 thf(26292,plain,((! [A:set_nat,B:(nat > nat)]: ((! [C:nat]: ((ord_less_nat @ zero_zero_nat @ (B @ C)) | ~ (member_nat @ C @ A))) => (ord_less_nat @ zero_zero_nat @ (groups708209901874060359at_nat @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5456])). 159.59/70.64 thf(4854,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_le__iff__add)). 159.59/70.64 thf(24043,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)],[4854])). 159.59/70.64 thf(3023,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (bit_se725231765392027082nd_int @ B @ A) @ A) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6074_AND__upper2)). 159.59/70.64 thf(17971,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (bit_se725231765392027082nd_int @ B @ A) @ A) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3023])). 159.59/70.64 thf(5054,axiom,((~ (ord_less_nat @ one_one_nat @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2126_not__one__less__zero)). 159.59/70.64 thf(24753,plain,((~ (ord_less_nat @ one_one_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5054])). 159.59/70.64 thf(1474,axiom,((! [A:real,B:real]: (((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)))) @ 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 @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7301_tan__mono__le__eq)). 159.59/70.64 thf(13064,plain,((! [A:real,B:real]: (((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)))) @ 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 @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474])). 159.59/70.64 thf(750,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/sandbox/benchmark/theBenchmark.p',fact_126_is__num__normalize_I1_J)). 159.59/70.64 thf(10677,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)],[750])). 159.59/70.64 thf(7312,axiom,(((divide_divide_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4856_minus__1__div__2__eq)). 159.59/70.64 thf(33547,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)],[7312])). 159.59/70.64 thf(5135,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_int @ A @ B) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2504_power2__le__imp__le)). 159.59/70.64 thf(25020,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => ((ord_less_eq_int @ A @ B) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5135])). 159.59/70.64 thf(6713,axiom,((! [A:vEBT_VEBT,B:nat]: (((! [C:$o,D:$o]: ((((B = zero_zero_nat) => (C)) & ((B != zero_zero_nat) => (((B = one_one_nat) => (D)) & (B = one_one_nat)))) <= (A = (vEBT_Leaf @ C @ D)))) => ((! [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ C @ zero_zero_nat @ D @ E))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT]: ((? [F:vEBT_VEBT]: (A = (vEBT_Node @ C @ (suc @ D) @ E @ F))) => (((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)))))))) <= (~ (vEBT_V5719532721284313246member @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2489_VEBT__internal_Onaive__member_Oelims_I3_J)). 159.59/70.64 thf(31126,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:$o,D:$o]: ((((B = zero_zero_nat) => (C)) & ((~ (B = zero_zero_nat)) => (((B = one_one_nat) => (D)) & (B = one_one_nat)))) | ~ (A = (vEBT_Leaf @ C @ D)))) => ((! [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (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))) => (((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)))))))) | (vEBT_V5719532721284313246member @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6713])). 159.59/70.64 thf(1181,axiom,((! [A:real,B:real]: ((divide_divide_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (divide_divide_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4985_minus__divide__divide)). 159.59/70.64 thf(12034,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)],[1181])). 159.59/70.64 thf(1353,axiom,((! [A:int,B:int,C:int]: ((bit_se1409905431419307370or_int @ A @ (bit_se1409905431419307370or_int @ B @ C)) = (bit_se1409905431419307370or_int @ B @ (bit_se1409905431419307370or_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6043_or_Oleft__commute)). 159.59/70.64 thf(12619,plain,((! [A:int,B:int,C:int]: ((bit_se1409905431419307370or_int @ A @ (bit_se1409905431419307370or_int @ B @ C)) = (bit_se1409905431419307370or_int @ B @ (bit_se1409905431419307370or_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353])). 159.59/70.64 thf(4793,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/sandbox/benchmark/theBenchmark.p',fact_1110_ab__semigroup__mult__class_Omult__ac_I1_J)). 159.59/70.64 thf(23805,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)],[4793])). 159.59/70.64 thf(1131,axiom,((divide_divide_real = (^ [A:real,B:real]: (times_times_real @ A @ (inverse_inverse_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9058_divide__real__def)). 159.59/70.64 thf(11878,plain,(((divide_divide_real) = (^ [A:real,B:real]: (times_times_real @ A @ (inverse_inverse_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131])). 159.59/70.64 thf(3899,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7279_add__log__eq__powr)). 159.59/70.64 thf(20801,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => (((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3899])). 159.59/70.64 thf(3776,axiom,((! [A:set_nat,B:(nat > extended_enat)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ C)))) => (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (groups7108830773950497114d_enat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7418_sum__nonneg)). 159.59/70.64 thf(20398,plain,((! [A:set_nat,B:(nat > extended_enat)]: ((! [C:nat]: ((member_nat @ C @ A) => (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ C)))) => (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (groups7108830773950497114d_enat @ (B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3776])). 159.59/70.64 thf(4542,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_V5719532721284313246member @ (vEBT_Leaf @ A @ B) @ C) = (((A) <= (C = zero_zero_nat)) & ((C != zero_zero_nat) => (((B) <= (C = one_one_nat)) & (C = one_one_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1799_VEBT__internal_Onaive__member_Osimps_I1_J)). 159.59/70.64 thf(22932,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_V5719532721284313246member @ (vEBT_Leaf @ A @ B) @ C) = (((A) | ~ (C = zero_zero_nat)) & ((~ (C = zero_zero_nat)) => (((B) | ~ (C = one_one_nat)) & (C = one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4542])). 159.59/70.64 thf(4351,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ one_on7984719198319812577d_enat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1079_mult_Oright__neutral)). 159.59/70.64 thf(22195,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ one_on7984719198319812577d_enat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4351])). 159.59/70.64 thf(346,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/sandbox/benchmark/theBenchmark.p',fact_9570_xor__int__unfold)). 159.59/70.64 thf(9322,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)],[346])). 159.59/70.64 thf(5301,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ C @ B)) <= (ord_less_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1771_power__strict__decreasing__iff)). 159.59/70.64 thf(25618,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ C @ B)) | ~ (ord_less_nat @ A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5301])). 159.59/70.64 thf(202,axiom,((! [A:complex,B:complex]: ((ord_less_eq_real @ zero_zero_real @ (im @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_eq_real @ zero_zero_real @ (im @ (times_times_complex @ A @ (cnj @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9696_Im__complex__div__ge__0)). 159.59/70.64 thf(8868,plain,((! [A:complex,B:complex]: ((ord_less_eq_real @ zero_zero_real @ (im @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_eq_real @ zero_zero_real @ (im @ (times_times_complex @ A @ (cnj @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[202])). 159.59/70.64 thf(3909,axiom,((! [A:(nat > real)]: (((! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B))) => (ord_less_eq_real @ zero_zero_real @ (suminf_real @ A))) <= (summable_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7053_suminf__nonneg)). 159.59/70.64 thf(20833,plain,((! [A:(nat > real)]: (((! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B))) => (ord_less_eq_real @ zero_zero_real @ (suminf_real @ (A)))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3909])). 159.59/70.64 thf(4616,axiom,((! [A:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ one_one_int)) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5226_take__bit__numeral__minus__1__eq)). 159.59/70.64 thf(23206,plain,((! [A:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (uminus_uminus_int @ one_one_int)) = (minus_minus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_nat @ A)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4616])). 159.59/70.64 thf(2631,axiom,((! [A:real]: ((ord_less_int @ one_one_int @ (archim7802044766580827645g_real @ A)) = (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6984_one__less__ceiling)). 159.59/70.64 thf(16732,plain,((! [A:real]: ((ord_less_int @ one_one_int @ (archim7802044766580827645g_real @ A)) = (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2631])). 159.59/70.64 thf(2023,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/sandbox/benchmark/theBenchmark.p',fact_1612_sum__squares__eq__zero__iff)). 159.59/70.64 thf(14788,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)],[2023])). 159.59/70.64 thf(820,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ A @ B) & (ord_less_eq_int @ C @ D)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1318_add__mono__thms__linordered__field_I3_J)). 159.59/70.64 thf(10898,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ A @ B) & (ord_less_eq_int @ C @ D)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[820])). 159.59/70.64 thf(1537,axiom,((! [A:int,B:int]: ((ring_1_of_int_int @ (bit_se1409905431419307370or_int @ A @ B)) = (bit_se1409905431419307370or_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6032_of__int__or__eq)). 159.59/70.64 thf(13253,plain,((! [A:int,B:int]: ((ring_1_of_int_int @ (bit_se1409905431419307370or_int @ A @ B)) = (bit_se1409905431419307370or_int @ (ring_1_of_int_int @ A) @ (ring_1_of_int_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537])). 159.59/70.64 thf(5474,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ one_one_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6005_and__numerals_I5_J)). 159.59/70.64 thf(26352,plain,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ one_one_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5474])). 159.59/70.64 thf(5538,axiom,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1078_mult__1)). 159.59/70.64 thf(26568,plain,((! [A:int]: ((times_times_int @ one_one_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5538])). 159.59/70.64 thf(2406,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/sandbox/benchmark/theBenchmark.p',fact_1361_square__diff__square__factored)). 159.59/70.64 thf(15983,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)],[2406])). 159.59/70.64 thf(8209,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/sandbox/benchmark/theBenchmark.p',fact_107_distrib__right__numeral)). 159.59/70.64 thf(36507,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)],[8209])). 159.59/70.64 thf(5999,axiom,(((some_nat @ summin) = (vEBT_vebt_mint @ summary))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500__092_060open_062Some_Asummin_A_061_Avebt__mint_Asummary_092_060close_062)). 159.59/70.64 thf(28438,plain,(((some_nat @ summin) = (vEBT_vebt_mint @ summary))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5999])). 159.59/70.64 thf(1086,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/sandbox/benchmark/theBenchmark.p',fact_3508_mult__div__mod__eq)). 159.59/70.64 thf(11735,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)],[1086])). 159.59/70.64 thf(4801,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2190_gr0__implies__Suc)). 159.59/70.64 thf(23831,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4801])). 159.59/70.64 thf(6544,axiom,((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5152_le__minus__one__simps_I1_J)). 159.59/70.64 thf(30412,plain,((ord_less_eq_int @ (uminus_uminus_int @ one_one_int) @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6544])). 159.59/70.64 thf(2771,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (arctan @ A) @ (arctan @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5885_arctan__le__iff)). 159.59/70.64 thf(17179,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)],[2771])). 159.59/70.64 thf(5113,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/sandbox/benchmark/theBenchmark.p',fact_7806_double__arith__series)). 159.59/70.64 thf(24951,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)],[5113])). 159.59/70.64 thf(2851,axiom,((! [A:num]: ~ (ord_less_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5178_not__neg__one__less__neg__numeral)). 159.59/70.64 thf(17418,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)],[2851])). 159.59/70.64 thf(6397,axiom,((! [A:nat]: (ord_less_eq_real @ one_one_real @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_two__realpow__ge__one)). 159.59/70.64 thf(29842,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)],[6397])). 159.59/70.64 thf(3331,axiom,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ A) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_add__diff__cancel__left_H)). 159.59/70.64 thf(18966,plain,((! [A:int,B:int]: ((minus_minus_int @ (plus_plus_int @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3331])). 159.59/70.64 thf(3510,axiom,((! [A:real]: ((sin_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (sin_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6809_sin__periodic)). 159.59/70.64 thf(19520,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)],[3510])). 159.59/70.64 thf(7771,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/sandbox/benchmark/theBenchmark.p',fact_9544_xor__nat__unfold)). 159.59/70.64 thf(35106,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)],[7771])). 159.59/70.64 thf(2692,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2857_order__less__asym_H)). 159.59/70.64 thf(16938,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2692])). 159.59/70.64 thf(7244,axiom,((! [A:num,B:num]: ((minus_minus_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (numera6690914467698888265omplex @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4786_diff__numeral__simps_I2_J)). 159.59/70.64 thf(33300,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)],[7244])). 159.59/70.64 thf(5142,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/sandbox/benchmark/theBenchmark.p',fact_5222_power__minus__Bit0)). 159.59/70.64 thf(25048,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)],[5142])). 159.59/70.64 thf(302,axiom,((! [A:complex,B:num]: ((im @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B))) = (divide_divide_real @ (im @ A) @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9647_Im__divide__numeral)). 159.59/70.64 thf(9185,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)],[302])). 159.59/70.64 thf(1114,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/sandbox/benchmark/theBenchmark.p',fact_6824_complex__mod__triangle__ineq2)). 159.59/70.64 thf(11829,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)],[1114])). 159.59/70.64 thf(5854,axiom,((! [A:num]: ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5620_odd__numeral)). 159.59/70.64 thf(27887,plain,((! [A:num]: ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5854])). 159.59/70.64 thf(1715,axiom,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ B) => (summable_real @ (^ [C:nat]: (plus_plus_real @ (A @ C) @ (B @ C))))) <= (summable_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7022_summable__add)). 159.59/70.64 thf(13794,plain,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ (B)) => (summable_real @ (^ [C:nat]: (plus_plus_real @ (A @ C) @ (B @ C))))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715])). 159.59/70.64 thf(6617,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((modulo_modulo_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ A)) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8101_fact__mod)). 159.59/70.64 thf(30660,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((modulo_modulo_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ A)) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6617])). 159.59/70.64 thf(3465,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (ln_ln_real @ A)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5135_ln__gt__zero)). 159.59/70.64 thf(19385,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)],[3465])). 159.59/70.64 thf(5775,axiom,((! [A:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4705_mult__minus1__right)). 159.59/70.64 thf(27374,plain,((! [A:code_integer]: ((times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5775])). 159.59/70.64 thf(7660,axiom,((! [A:num]: (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4152_even__numeral)). 159.59/70.64 thf(34731,plain,((! [A:num]: (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7660])). 159.59/70.64 thf(6023,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/sandbox/benchmark/theBenchmark.p',fact_6016_or__minus__numerals_I2_J)). 159.59/70.64 thf(28511,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)],[6023])). 159.59/70.64 thf(8040,axiom,((! [A:num]: ~ (ord_less_nat @ (numeral_numeral_nat @ A) @ one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_not__numeral__less__one)). 159.59/70.64 thf(35953,plain,((! [A:num]: ~ (ord_less_nat @ (numeral_numeral_nat @ A) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8040])). 159.59/70.64 thf(1215,axiom,(((cos_complex @ (real_V4546457046886955230omplex @ pi)) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7356_cos__of__real__pi)). 159.59/70.64 thf(12182,plain,(((cos_complex @ (real_V4546457046886955230omplex @ pi)) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215])). 159.59/70.64 thf(6321,axiom,((pred_numeral = (^ [A:num]: (minus_minus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5724_pred__numeral__def)). 159.59/70.64 thf(29559,plain,(((pred_numeral) = (^ [A:num]: (minus_minus_nat @ (numeral_numeral_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6321])). 159.59/70.64 thf(7611,axiom,((! [A:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => ((? [B:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ A) @ B)) = (vEBT_V8194947554948674370ptions @ summary @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119__C111_C)). 159.59/70.64 thf(34588,plain,((! [A:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => ((? [B:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ A) @ B)) = (vEBT_V8194947554948674370ptions @ summary @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7611])). 159.59/70.64 thf(561,axiom,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: (((ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ D) @ (minus_minus_set_nat @ B @ C)) <= (ord_less_eq_set_nat @ C @ D)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2999_Diff__mono)). 159.59/70.64 thf(10037,plain,((! [A:set_nat,B:set_nat,C:set_nat,D:set_nat]: ((ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ D) @ (minus_minus_set_nat @ B @ C)) | ~ (ord_less_eq_set_nat @ C @ D) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[561])). 159.59/70.64 thf(5208,axiom,((! [A:num]: ((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5708_diff__numeral__special_I5_J)). 159.59/70.64 thf(25298,plain,((! [A:num]: ((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5208])). 159.59/70.64 thf(5066,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: (((vEBT_V8194947554948674370ptions @ A @ C) = (vEBT_vebt_member @ A @ C)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_both__member__options__equiv__member)). 159.59/70.64 thf(24800,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: (((vEBT_V8194947554948674370ptions @ A @ C) = (vEBT_vebt_member @ A @ C)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5066])). 159.59/70.64 thf(4882,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/sandbox/benchmark/theBenchmark.p',fact_5419_abs__power__minus)). 159.59/70.64 thf(24129,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)],[4882])). 159.59/70.64 thf(4479,axiom,((! [A:real]: ~ (ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2510_power2__less__0)). 159.59/70.64 thf(22661,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)],[4479])). 159.59/70.64 thf(7615,axiom,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_one__add__one)). 159.59/70.64 thf(34599,plain,(((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7615])). 159.59/70.64 thf(7686,axiom,(((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_hprolist)). 159.59/70.64 thf(34814,plain,(((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7686])). 159.59/70.64 thf(5166,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/sandbox/benchmark/theBenchmark.p',fact_6476_cos__x__y__le__one)). 159.59/70.64 thf(25138,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)],[5166])). 159.59/70.64 thf(941,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/sandbox/benchmark/theBenchmark.p',fact_5305_take__bit__int__less__self__iff)). 159.59/70.64 thf(11268,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)],[941])). 159.59/70.64 thf(4653,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/sandbox/benchmark/theBenchmark.p',fact_9114_times__binomial__minus1__eq)). 159.59/70.64 thf(23335,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)],[4653])). 159.59/70.64 thf(4183,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/sandbox/benchmark/theBenchmark.p',fact_1324_less__1__mult)). 159.59/70.64 thf(21667,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)],[4183])). 159.59/70.64 thf(5450,axiom,((! [A:num,B:num]: ((A != B) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2830_order_Ostrict__implies__not__eq)). 159.59/70.64 thf(26267,plain,((! [A:num,B:num]: (~ (A = B) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5450])). 159.59/70.64 thf(6142,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/sandbox/benchmark/theBenchmark.p',fact_9418_nat__eq__numeral__power__cancel__iff)). 159.59/70.64 thf(28892,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)],[6142])). 159.59/70.64 thf(1928,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/sandbox/benchmark/theBenchmark.p',fact_6887_norm__mult__numeral1)). 159.59/70.64 thf(14471,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)],[1928])). 159.59/70.64 thf(2980,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/sandbox/benchmark/theBenchmark.p',fact_5811_of__int__le__0__iff)). 159.59/70.64 thf(17841,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)],[2980])). 159.59/70.64 thf(5498,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (~ (ord_less_eq_nat @ B @ C))) => (((((~ ((~ (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ C @ A))) <= ((~ (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C))) <= ((~ (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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2753_le__cases3)). 159.59/70.64 thf(26436,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ B) => (~ (ord_less_eq_nat @ B @ C))) => (~ (~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ A)) | ~ (~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ C)) | ~ (~ (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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5498])). 159.59/70.64 thf(420,axiom,((! [A:real]: ((tan_real @ (plus_plus_real @ A @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))) = (tan_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7229_tan__periodic)). 159.59/70.64 thf(9570,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)],[420])). 159.59/70.64 thf(6598,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((upt @ A @ (plus_plus_nat @ B @ C)) = (append_nat @ (upt @ A @ B) @ (upt @ B @ (plus_plus_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10142_upt__add__eq__append)). 159.59/70.64 thf(30596,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((upt @ A @ (plus_plus_nat @ B @ C)) = (append_nat @ (upt @ A @ B) @ (upt @ B @ (plus_plus_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6598])). 159.59/70.64 thf(1031,axiom,((! [A:int]: (ord_less_int @ A @ (plus_plus_int @ A @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1331_less__add__one)). 159.59/70.64 thf(11554,plain,((! [A:int]: (ord_less_int @ A @ (plus_plus_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031])). 159.59/70.64 thf(8126,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/sandbox/benchmark/theBenchmark.p',fact_3901_even__succ__div__2)). 159.59/70.64 thf(36231,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)],[8126])). 159.59/70.64 thf(8079,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/sandbox/benchmark/theBenchmark.p',fact_7813_arith__series__nat)). 159.59/70.64 thf(36085,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)],[8079])). 159.59/70.64 thf(1700,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (nat_prod_encode @ (product_Pair_nat_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10205_le__prod__encode__2)). 159.59/70.64 thf(13749,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (nat_prod_encode @ (product_Pair_nat_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700])). 159.59/70.64 thf(7381,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => (((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3456_mod__add__cong)). 159.59/70.64 thf(33773,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => (((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7381])). 159.59/70.64 thf(1264,axiom,((! [A:num]: ~ (ord_le3102999989581377725nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5176_not__one__le__neg__numeral)). 159.59/70.64 thf(12337,plain,((! [A:num]: ~ (ord_le3102999989581377725nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264])). 159.59/70.64 thf(2597,axiom,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1127_add_Oright__cancel)). 159.59/70.64 thf(16600,plain,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ C @ B)) = (A = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2597])). 159.59/70.64 thf(6148,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/sandbox/benchmark/theBenchmark.p',fact_7228_powr__numeral)). 159.59/70.64 thf(28909,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)],[6148])). 159.59/70.64 thf(469,axiom,((! [A:nat,B:nat]: (((comm_s4660882817536571857er_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ B) = zero_zero_int) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8283_pochhammer__of__nat__eq__0__iff)). 159.59/70.64 thf(9723,plain,((! [A:nat,B:nat]: (((comm_s4660882817536571857er_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ B) = zero_zero_int) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])). 159.59/70.64 thf(6258,axiom,((! [A:int]: (ord_less_eq_int @ (uminus_uminus_int @ A) @ (abs_abs_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5543_abs__ge__minus__self)). 159.59/70.64 thf(29319,plain,((! [A:int]: (ord_less_eq_int @ (uminus_uminus_int @ A) @ (abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6258])). 159.59/70.64 thf(3716,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/sandbox/benchmark/theBenchmark.p',fact_5815_of__int__0__less__iff)). 159.59/70.64 thf(20204,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)],[3716])). 159.59/70.64 thf(6477,axiom,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_lessI)). 159.59/70.64 thf(30164,plain,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6477])). 159.59/70.64 thf(1879,axiom,((! [A:extended_enat,B:extended_enat]: ? [C:extended_enat]: ! [D:extended_enat]: ((ord_le72135733267957522d_enat @ D @ C) => ((~ (dvd_dv3785147216227455552d_enat @ A @ (plus_p3455044024723400733d_enat @ D @ B))) = (~ (dvd_dv3785147216227455552d_enat @ A @ (plus_p3455044024723400733d_enat @ D @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4542_minf_I10_J)). 159.59/70.64 thf(14322,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1879])). 159.59/70.64 thf(4401,axiom,((! [A:extended_enat,B:extended_enat]: (((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ A @ B)) <= (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B)) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2271_add__nonneg__pos)). 159.59/70.64 thf(22350,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ A @ B)) | ~ (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4401])). 159.59/70.64 thf(296,axiom,((! [A:(set_nat > $o),B:set_nat]: ((((~ (finite_finite_nat @ B)) => (A @ B)) => ((! [C:set_nat]: ((finite_finite_nat @ C) => ((C != bot_bot_set_nat) => ((ord_less_eq_set_nat @ C @ B) => ((! [D:nat]: ((member_nat @ D @ C) => (A @ (minus_minus_set_nat @ C @ (insert_nat @ D @ bot_bot_set_nat))))) => (A @ C)))))) => (A @ B))) <= (A @ bot_bot_set_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6270_remove__induct)). 159.59/70.64 thf(9146,plain,((! [A:(set_nat > $o),B:set_nat]: ((((~ (finite_finite_nat @ B)) => (A @ B)) => ((! [C:set_nat]: ((finite_finite_nat @ C) => ((~ (C = bot_bot_set_nat)) => ((ord_less_eq_set_nat @ C @ B) => ((! [D:nat]: ((member_nat @ D @ C) => (A @ (minus_minus_set_nat @ C @ (insert_nat @ D @ bot_bot_set_nat))))) => (A @ C)))))) => (A @ B))) | ~ (A @ bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 159.59/70.64 thf(2861,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/sandbox/benchmark/theBenchmark.p',fact_1285_diff__diff__eq2)). 159.59/70.64 thf(17461,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)],[2861])). 159.59/70.64 thf(555,axiom,((! [A:complex,B:num]: ((re @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B))) = (divide_divide_real @ (re @ A) @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9631_Re__divide__numeral)). 159.59/70.64 thf(10019,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)],[555])). 159.59/70.64 thf(4194,axiom,((summable_real @ (power_power_real @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7038_summable__zero__power)). 159.59/70.64 thf(21699,plain,((summable_real @ (power_power_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4194])). 159.59/70.64 thf(2343,axiom,((abs_abs_real = (^ [A:real]: (if_real @ (ord_less_real @ A @ zero_zero_real) @ (uminus_uminus_real @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5570_abs__if__raw)). 159.59/70.64 thf(15778,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)],[2343])). 159.59/70.64 thf(4174,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => (((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) <= (ord_less_eq_real @ zero_zero_real @ C)) <= (ord_less_real @ zero_zero_real @ B))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2247_mult__strict__mono)). 159.59/70.64 thf(21642,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) | ~ (ord_less_eq_real @ zero_zero_real @ C) | ~ (ord_less_real @ zero_zero_real @ B))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4174])). 159.59/70.64 thf(638,axiom,((! [A:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ one_one_real) = ((ord_less_eq_real @ A @ zero_zero_real) | (ord_less_real @ one_one_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9089_inverse__less__1__iff)). 159.59/70.64 thf(10296,plain,((! [A:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ one_one_real) = ((ord_less_eq_real @ A @ zero_zero_real) | (ord_less_real @ one_one_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[638])). 159.59/70.64 thf(6301,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/sandbox/benchmark/theBenchmark.p',fact_2708_dual__order_Otrans)). 159.59/70.64 thf(29496,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)],[6301])). 159.59/70.64 thf(6330,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1879_add_Ocomm__neutral)). 159.59/70.64 thf(29582,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6330])). 159.59/70.64 thf(6312,axiom,((! [A:produc6271795597528267376eger_o]: ? [B:code_integer,C:$o]: (A = (produc6677183202524767010eger_o @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3682_surj__pair)). 159.59/70.64 thf(29527,plain,((! [A:produc6271795597528267376eger_o]: ? [B:code_integer,C:$o]: (A = (produc6677183202524767010eger_o @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6312])). 159.59/70.64 thf(7707,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2483_dividend__less__times__div)). 159.59/70.64 thf(34874,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7707])). 159.59/70.64 thf(2672,axiom,((! [A:real]: ((real_V1022390504157884413omplex @ (complex2 @ (cos_real @ A) @ (sin_real @ A))) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7227_norm__cos__sin)). 159.59/70.64 thf(16864,plain,((! [A:real]: ((real_V1022390504157884413omplex @ (complex2 @ (cos_real @ A) @ (sin_real @ A))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2672])). 159.59/70.64 thf(5636,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/sandbox/benchmark/theBenchmark.p',fact_1213_diff__right__mono)). 159.59/70.64 thf(26896,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)],[5636])). 159.59/70.64 thf(5164,axiom,((! [A:num]: ~ (bit_se1148574629649215175it_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6384_bit__numeral__simps_I1_J)). 159.59/70.64 thf(25132,plain,((! [A:num]: ~ (bit_se1148574629649215175it_nat @ one_one_nat @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5164])). 159.59/70.64 thf(7632,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/sandbox/benchmark/theBenchmark.p',fact_9571_Sum__Ico__nat)). 159.59/70.64 thf(34650,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)],[7632])). 159.59/70.64 thf(8219,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)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2401_nat__mult__div__cancel1)). 159.59/70.64 thf(36534,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)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8219])). 159.59/70.64 thf(4727,axiom,((! [A:set_nat]: ((finite_finite_nat @ (vimage_nat_nat @ suc @ A)) = (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10192_finite__vimage__Suc__iff)). 159.59/70.64 thf(23584,plain,((! [A:set_nat]: ((finite_finite_nat @ (vimage_nat_nat @ (suc) @ A)) = (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4727])). 159.59/70.64 thf(6353,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((ord_less_eq_nat @ B @ C) => ((power_power_nat @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2473_power__diff)). 159.59/70.64 thf(29651,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((ord_less_eq_nat @ B @ C) => ((power_power_nat @ A @ (minus_minus_nat @ C @ B)) = (divide_divide_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6353])). 159.59/70.64 thf(7026,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se1412395901928357646or_nat @ (bit_se1412395901928357646or_nat @ A @ B) @ C) = (bit_se1412395901928357646or_nat @ A @ (bit_se1412395901928357646or_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6052_or_Oassoc)). 159.59/70.64 thf(32435,plain,((! [A:nat,B:nat,C:nat]: ((bit_se1412395901928357646or_nat @ (bit_se1412395901928357646or_nat @ A @ B) @ C) = (bit_se1412395901928357646or_nat @ A @ (bit_se1412395901928357646or_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7026])). 159.59/70.64 thf(1522,axiom,((abs_abs_real = (^ [A:real]: (if_real @ (ord_less_real @ A @ zero_zero_real) @ (uminus_uminus_real @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5547_abs__real__def)). 159.59/70.64 thf(13210,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)],[1522])). 159.59/70.64 thf(483,axiom,((! [A:int]: ((ord_less_int @ (bit_ri7919022796975470100ot_int @ A) @ zero_zero_int) = (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9575_not__negative__int__iff)). 159.59/70.64 thf(9789,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)],[483])). 159.59/70.64 thf(2231,axiom,((! [A:real,B:real,C:real]: ((real_V2046097035970521341omplex @ A @ (complex2 @ B @ C)) = (complex2 @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9222_complex__scaleR)). 159.59/70.64 thf(15453,plain,((! [A:real,B:real,C:real]: ((real_V2046097035970521341omplex @ A @ (complex2 @ B @ C)) = (complex2 @ (times_times_real @ A @ B) @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2231])). 159.59/70.64 thf(1425,axiom,((! [A:num,B:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5040_neg__numeral__less__numeral)). 159.59/70.64 thf(12894,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)],[1425])). 159.59/70.64 thf(6445,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/sandbox/benchmark/theBenchmark.p',fact_4823_not__neg__one__le__neg__numeral__iff)). 159.59/70.64 thf(30040,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)],[6445])). 159.59/70.64 thf(7574,axiom,((! [A:product_prod_nat_nat]: ~ (! [B:nat,C:nat]: (A != (product_Pair_nat_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4186_prod__decode__aux_Ocases)). 159.59/70.64 thf(34472,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)],[7574])). 159.59/70.64 thf(5418,axiom,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((C @ D) => (C @ (suc @ D))))) => (C @ B))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_nat__induct__at__least)). 159.59/70.64 thf(26146,plain,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => ((! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((C @ D) => (C @ (suc @ D))))) => (C @ B))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5418])). 159.59/70.64 thf(2480,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/sandbox/benchmark/theBenchmark.p',fact_1437_divide__divide__times__eq)). 159.59/70.64 thf(16231,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)],[2480])). 159.59/70.64 thf(3708,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ (times_times_complex @ C @ A))) = (dvd_dvd_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3830_dvd__add__times__triv__right__iff)). 159.59/70.64 thf(20179,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ (times_times_complex @ C @ A))) = (dvd_dvd_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3708])). 159.59/70.64 thf(7422,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/sandbox/benchmark/theBenchmark.p',fact_1210_diff__left__mono)). 159.59/70.64 thf(33895,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)],[7422])). 159.59/70.64 thf(2321,axiom,((! [A:real]: ((ord_less_eq_int @ one_one_int @ (archim7802044766580827645g_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6982_one__le__ceiling)). 159.59/70.64 thf(15713,plain,((! [A:real]: ((ord_less_eq_int @ one_one_int @ (archim7802044766580827645g_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2321])). 159.59/70.64 thf(4222,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/sandbox/benchmark/theBenchmark.p',fact_9480_zero__le__sgn__iff)). 159.59/70.64 thf(21810,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)],[4222])). 159.59/70.64 thf(4316,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/sandbox/benchmark/theBenchmark.p',fact_6875_sin__arctan)). 159.59/70.64 thf(22088,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)],[4316])). 159.59/70.64 thf(6626,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/sandbox/benchmark/theBenchmark.p',fact_154_left__add__twice)). 159.59/70.64 thf(30692,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)],[6626])). 159.59/70.64 thf(5402,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_int @ zero_zero_int @ A) = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1819_zero__power)). 159.59/70.64 thf(26070,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_int @ zero_zero_int @ A) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5402])). 159.59/70.64 thf(5347,axiom,((! [A:nat]: ((A != zero_zero_nat) = (case_nat_o @ ($false) @ (^ [B:nat]: (($true))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9732_nat_Odisc__eq__case_I2_J)). 159.59/70.64 thf(25841,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (case_nat_o @ ($false) @ (^ [B:nat]: (($true))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5347])). 159.59/70.64 thf(5817,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) <= (ord_less_nat @ B @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2269_add__nonpos__neg)). 159.59/70.64 thf(27690,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_nat @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5817])). 159.59/70.64 thf(4428,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/sandbox/benchmark/theBenchmark.p',fact_844_mult__diff__mult)). 159.59/70.64 thf(22439,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)],[4428])). 159.59/70.64 thf(7875,axiom,(((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2461_zero__power2)). 159.59/70.64 thf(35427,plain,(((power_power_complex @ zero_zero_complex @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7875])). 159.59/70.64 thf(2299,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1599_less__add__same__cancel1)). 159.59/70.64 thf(15654,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)],[2299])). 159.59/70.64 thf(3082,axiom,((! [A:set_nat]: (((A != bot_bot_set_nat) => (? [B:nat]: ((member_nat @ B @ A) & ! [C:nat]: (((B = C) <= (ord_less_eq_nat @ C @ B)) <= (member_nat @ C @ A))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3776_finite__has__minimal)). 159.59/70.64 thf(18150,plain,((! [A:set_nat]: (((~ (A = bot_bot_set_nat)) => (? [B:nat]: ((member_nat @ B @ A) & ! [C:nat]: ((B = C) | ~ (ord_less_eq_nat @ C @ B) | ~ (member_nat @ C @ A))))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3082])). 159.59/70.64 thf(7953,axiom,((! [A:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (plus_plus_nat @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_mult__2)). 159.59/70.64 thf(35676,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)],[7953])). 159.59/70.64 thf(397,axiom,((bit_se6528837805403552850or_nat = (^ [A:nat,B:nat]: (nat2 @ (bit_se6526347334894502574or_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9560_xor__nat__def)). 159.59/70.64 thf(9491,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)],[397])). 159.59/70.64 thf(2462,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/sandbox/benchmark/theBenchmark.p',fact_1645_nonzero__mult__divide__mult__cancel__right2)). 159.59/70.64 thf(16177,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)],[2462])). 159.59/70.64 thf(1387,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (exp_real @ A) @ (exp_real @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5960_exp__le__cancel__iff)). 159.59/70.64 thf(12780,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)],[1387])). 159.59/70.64 thf(1955,axiom,((! [A:int,B:int]: (((plus_plus_int @ (minus_minus_int @ B @ A) @ A) = B) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1028_le__add__diff__inverse2)). 159.59/70.64 thf(14555,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)],[1955])). 159.59/70.64 thf(6636,axiom,((! [A:nat]: (((suc @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))) = A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1760_Suc__pred)). 159.59/70.64 thf(30732,plain,((! [A:nat]: (((suc @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))) = A) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6636])). 159.59/70.64 thf(1964,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/sandbox/benchmark/theBenchmark.p',fact_6931_norm__diff__triangle__less)). 159.59/70.64 thf(14581,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)],[1964])). 159.59/70.64 thf(1163,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2287_divide__nonpos__neg)). 159.59/70.64 thf(11979,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_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)],[1163])). 159.59/70.64 thf(4209,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 @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2043_add__increasing)). 159.59/70.64 thf(21746,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 @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4209])). 159.59/70.64 thf(4142,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/sandbox/benchmark/theBenchmark.p',fact_8446_prod_OlessThan__Suc)). 159.59/70.64 thf(21540,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)],[4142])). 159.59/70.64 thf(2049,axiom,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ (suc @ B) @ (suc @ C))) = (groups6591440286371151544t_real @ (^ [D:nat]: (A @ (suc @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7453_sum_Oshift__bounds__cl__Suc__ivl)). 159.59/70.64 thf(14865,plain,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ (suc @ B) @ (suc @ C))) = (groups6591440286371151544t_real @ (^ [D:nat]: (A @ (suc @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2049])). 159.59/70.64 thf(955,axiom,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ C @ (times_times_complex @ B @ A)) @ A)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2348_add__num__frac)). 159.59/70.64 thf(11306,plain,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ C @ (times_times_complex @ B @ A)) @ A)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[955])). 159.59/70.64 thf(5503,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/sandbox/benchmark/theBenchmark.p',fact_374_power__mult)). 159.59/70.64 thf(26468,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)],[5503])). 159.59/70.64 thf(4936,axiom,((! [A:(nat > (nat > nat)),B:nat]: ((vEBT_V4262088993061758097ft_nat @ A @ (some_nat @ B) @ none_nat) = none_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_VEBT__internal_Ooption__shift_Osimps_I2_J)). 159.59/70.64 thf(24307,plain,((! [A:(nat > (nat > nat)),B:nat]: ((vEBT_V4262088993061758097ft_nat @ (A) @ (some_nat @ B) @ none_nat) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4936])). 159.59/70.64 thf(1460,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4637_minus__add__distrib)). 159.59/70.64 thf(13018,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)],[1460])). 159.59/70.64 thf(4377,axiom,((! [A:set_nat,B:set_nat]: (((A = B) <= (ord_less_eq_set_nat @ B @ A)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2700_antisym)). 159.59/70.64 thf(22273,plain,((! [A:set_nat,B:set_nat]: ((A = B) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4377])). 159.59/70.64 thf(2272,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/sandbox/benchmark/theBenchmark.p',fact_1168_add__left__mono)). 159.59/70.64 thf(15577,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)],[2272])). 159.59/70.64 thf(5127,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => (? [B:real]: ((ord_less_eq_real @ B @ (minus_minus_real @ A @ one_one_real)) & ((exp_real @ B) = A) & (ord_less_eq_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6105_lemma__exp__total)). 159.59/70.64 thf(24993,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => (? [B:real]: ((ord_less_eq_real @ B @ (minus_minus_real @ A @ one_one_real)) & ((exp_real @ B) = A) & (ord_less_eq_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5127])). 159.59/70.64 thf(7144,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/sandbox/benchmark/theBenchmark.p',fact_9502_real__root__pos__pos__le)). 159.59/70.64 thf(32920,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)],[7144])). 159.59/70.64 thf(7873,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: (((divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) = C) => (A @ C))) => ((! [C:nat,D:$o]: ((A @ C) => ((A @ (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ D) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) <= ((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 @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4490_bits__induct)). 159.59/70.64 thf(35412,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: (((divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) = C) => (A @ C))) => ((! [C:nat,D:$o]: ((A @ C) => ((A @ (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ D) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) | ~ ((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 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7873])). 159.59/70.64 thf(4575,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/sandbox/benchmark/theBenchmark.p',fact_894_power2__diff)). 159.59/70.64 thf(23040,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)],[4575])). 159.59/70.64 thf(1520,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/sandbox/benchmark/theBenchmark.p',fact_9293_complex__inverse)). 159.59/70.64 thf(13204,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)],[1520])). 159.59/70.64 thf(7267,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_add__diff__cancel__left_H)). 159.59/70.64 thf(33370,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7267])). 159.59/70.64 thf(1421,axiom,((! [A:nat]: ((image_nat_nat @ suc @ (set_ord_lessThan_nat @ A)) = (set_or1269000886237332187st_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9807_image__Suc__lessThan)). 159.59/70.64 thf(12882,plain,((! [A:nat]: ((image_nat_nat @ (suc) @ (set_ord_lessThan_nat @ A)) = (set_or1269000886237332187st_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421])). 159.59/70.64 thf(2354,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ A @ (set_ord_atMost_nat @ B)) = (plus_plus_real @ (A @ zero_zero_nat) @ (groups6591440286371151544t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8839_sum_OatMost__shift)). 159.59/70.64 thf(15810,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (A) @ (set_ord_atMost_nat @ 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)],[2354])). 159.59/70.64 thf(3448,axiom,((! [A:nat,B:nat,C:real]: (((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)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8312_pochhammer__product)). 159.59/70.64 thf(19335,plain,((! [A:nat,B:nat,C:real]: (((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)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3448])). 159.59/70.64 thf(5702,axiom,((! [A:nat,B:nat]: (((A = B) <= ((minus_minus_nat @ B @ A) = zero_zero_nat)) <= ((minus_minus_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1925_diffs0__imp__equal)). 159.59/70.64 thf(27132,plain,((! [A:nat,B:nat]: ((A = B) | ~ ((minus_minus_nat @ B @ A) = zero_zero_nat) | ~ ((minus_minus_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5702])). 159.59/70.64 thf(7778,axiom,(((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1784_one__div__two__eq__zero)). 159.59/70.64 thf(35123,plain,(((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7778])). 159.59/70.64 thf(3801,axiom,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (cos_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7106_cos__ge__minus__one)). 159.59/70.64 thf(20479,plain,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ (cos_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3801])). 159.59/70.64 thf(7799,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1764_div__mult__self1__is__m)). 159.59/70.64 thf(35180,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7799])). 159.59/70.64 thf(2526,axiom,((! [A:int,B:real]: ((times_times_real @ (inverse_inverse_real @ (ring_1_of_int_real @ A)) @ B) = (times_times_real @ B @ (inverse_inverse_real @ (ring_1_of_int_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9056_mult__inverse__of__int__commute)). 159.59/70.64 thf(16381,plain,((! [A:int,B:real]: ((times_times_real @ (inverse_inverse_real @ (ring_1_of_int_real @ A)) @ B) = (times_times_real @ B @ (inverse_inverse_real @ (ring_1_of_int_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2526])). 159.59/70.64 thf(5092,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/sandbox/benchmark/theBenchmark.p',fact_7811_double__gauss__sum)). 159.59/70.64 thf(24887,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)],[5092])). 159.59/70.64 thf(6332,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/sandbox/benchmark/theBenchmark.p',fact_8324_gbinomial__index__swap)). 159.59/70.64 thf(29587,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)],[6332])). 159.59/70.64 thf(3924,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/sandbox/benchmark/theBenchmark.p',fact_9424_numeral__power__less__nat__cancel__iff)). 159.59/70.64 thf(20875,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)],[3924])). 159.59/70.64 thf(6268,axiom,((! [A:real,B:real]: (((ord_less_eq_int @ (times_times_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) @ (archim6058952711729229775r_real @ (times_times_real @ A @ B))) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8300_le__mult__floor)). 159.59/70.64 thf(29373,plain,((! [A:real,B:real]: ((ord_less_eq_int @ (times_times_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) @ (archim6058952711729229775r_real @ (times_times_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)],[6268])). 159.59/70.64 thf(6986,axiom,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ (suc @ A)) & (B @ C))) = ((B @ zero_zero_nat) | ? [C:nat]: ((B @ (suc @ C)) & (ord_less_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2187_Ex__less__Suc2)). 159.59/70.64 thf(32285,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ (suc @ A)) & (B @ C))) = ((B @ zero_zero_nat) | ? [C:nat]: ((B @ (suc @ C)) & (ord_less_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6986])). 159.59/70.64 thf(4666,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1512_add__cancel__right__right)). 159.59/70.64 thf(23389,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4666])). 159.59/70.64 thf(631,axiom,((! [A:$o,B:$o]: ((zero_n356916108424825756nteger @ ((B) & (A))) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ A) @ (zero_n356916108424825756nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4389_of__bool__conj)). 159.59/70.64 thf(10265,plain,((! [A:$o,B:$o]: ((zero_n356916108424825756nteger @ ((B) & (A))) = (times_3573771949741848930nteger @ (zero_n356916108424825756nteger @ A) @ (zero_n356916108424825756nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[631])). 159.59/70.64 thf(7455,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3174_linorder__not__less)). 159.59/70.64 thf(34005,plain,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7455])). 159.59/70.64 thf(7733,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/sandbox/benchmark/theBenchmark.p',fact_195_list__update__overwrite)). 159.59/70.64 thf(34985,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)],[7733])). 159.59/70.64 thf(3511,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/sandbox/benchmark/theBenchmark.p',fact_2118_add__neg__neg)). 159.59/70.64 thf(19523,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)],[3511])). 159.59/70.64 thf(7860,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 @ (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) != zero_zero_nat) & (ord_less_eq_nat @ B @ A))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4522_exp__div__exp__eq)). 159.59/70.64 thf(35372,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 @ (~ ((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = zero_zero_nat) & (ord_less_eq_nat @ B @ A))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7860])). 159.59/70.64 thf(2489,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/sandbox/benchmark/theBenchmark.p',fact_1326_add__mono1)). 159.59/70.64 thf(16263,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)],[2489])). 159.59/70.64 thf(8158,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((((vEBT_V8194947554948674370ptions @ (vEBT_vebt_insert @ A @ D) @ C) <= (vEBT_V8194947554948674370ptions @ A @ C)) <= (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/sandbox/benchmark/theBenchmark.p',fact_169_valid__insert__both__member__options__pres)). 159.59/70.64 thf(36345,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_V8194947554948674370ptions @ (vEBT_vebt_insert @ A @ D) @ C) | ~ (vEBT_V8194947554948674370ptions @ A @ C) | ~ (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)],[8158])). 159.59/70.64 thf(6519,axiom,((! [A:nat]: (((semiri5074537144036343181t_real @ A) = one_one_real) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6539_of__nat__eq__1__iff)). 159.59/70.64 thf(30306,plain,((! [A:nat]: (((semiri5074537144036343181t_real @ A) = one_one_real) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6519])). 159.59/70.64 thf(7856,axiom,(((sqr @ one) = one)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9797_sqr_Osimps_I1_J)). 159.59/70.64 thf(35359,plain,(((sqr @ one) = one)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7856])). 159.59/70.64 thf(5445,axiom,((! [A:int,B:nat,C:int]: (((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ A @ C)) <= (ord_less_eq_int @ (power_power_int @ A @ (suc @ B)) @ (power_power_int @ C @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2362_power__le__imp__le__base)). 159.59/70.64 thf(26252,plain,((! [A:int,B:nat,C:int]: (((ord_less_eq_int @ zero_zero_int @ C) => (ord_less_eq_int @ A @ C)) | ~ (ord_less_eq_int @ (power_power_int @ A @ (suc @ B)) @ (power_power_int @ C @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5445])). 159.59/70.64 thf(1236,axiom,((! [A:(nat > int),B:set_nat,C:(nat > int),D:nat]: (((! [E:nat]: ((ord_less_eq_int @ (A @ E) @ (C @ E)) <= (member_nat @ E @ B))) => ((member_nat @ D @ B) => ((finite_finite_nat @ B) => ((A @ D) = (C @ D))))) <= ((groups3539618377306564664at_int @ A @ B) = (groups3539618377306564664at_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7442_sum__mono__inv)). 159.59/70.64 thf(12248,plain,((! [A:(nat > int),B:set_nat,C:(nat > int),D:nat]: (((! [E:nat]: ((ord_less_eq_int @ (A @ E) @ (C @ E)) | ~ (member_nat @ E @ B))) => ((member_nat @ D @ B) => ((finite_finite_nat @ B) => ((A @ D) = (C @ D))))) | ~ ((groups3539618377306564664at_int @ (A) @ B) = (groups3539618377306564664at_int @ (C) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236])). 159.59/70.64 thf(7165,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat]: (A @ D @ zero_zero_nat)) => ((A @ B @ C) <= (! [D:nat,E:nat]: ((ord_less_nat @ zero_zero_nat @ E) => ((A @ D @ E) <= (A @ E @ (modulo_modulo_nat @ D @ E))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3781_gcd__nat__induct)). 159.59/70.64 thf(33006,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat]: (A @ D @ zero_zero_nat)) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((ord_less_nat @ zero_zero_nat @ E) => ((A @ D @ E) | ~ (A @ E @ (modulo_modulo_nat @ D @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7165])). 159.59/70.64 thf(7432,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/sandbox/benchmark/theBenchmark.p',fact_187_power2__sum)). 159.59/70.64 thf(33927,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)],[7432])). 159.59/70.64 thf(310,axiom,((! [A:real,B:real,C:real]: ((real_V1485227260804924795R_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (real_V1485227260804924795R_real @ A @ B) @ (real_V1485227260804924795R_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9212_scaleR__right__distrib)). 159.59/70.64 thf(9206,plain,((! [A:real,B:real,C:real]: ((real_V1485227260804924795R_real @ A @ (plus_plus_real @ B @ C)) = (plus_plus_real @ (real_V1485227260804924795R_real @ A @ B) @ (real_V1485227260804924795R_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 159.59/70.64 thf(3273,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/sandbox/benchmark/theBenchmark.p',fact_3447_mod__mult__mult2)). 159.59/70.64 thf(18790,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)],[3273])). 159.59/70.64 thf(8119,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/sandbox/benchmark/theBenchmark.p',fact_229_power__mult__numeral)). 159.59/70.64 thf(36202,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)],[8119])). 159.59/70.64 thf(2915,axiom,((! [A:real,B:real,C:real]: ((A = C) <= ((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_add__right__imp__eq)). 159.59/70.64 thf(17637,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)],[2915])). 159.59/70.64 thf(3626,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (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) @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6028_or__numerals_I6_J)). 159.59/70.64 thf(19898,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit1 @ A)) @ (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) @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3626])). 159.59/70.64 thf(6286,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/sandbox/benchmark/theBenchmark.p',fact_7798_gauss__sum__nat)). 159.59/70.64 thf(29447,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)],[6286])). 159.59/70.64 thf(4650,axiom,((! [A:nat,B:nat,C:nat]: (((B = (divide_divide_nat @ C @ A)) = ((times_times_nat @ B @ A) = C)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4160_unit__eq__div2)). 159.59/70.64 thf(23324,plain,((! [A:nat,B:nat,C:nat]: (((B = (divide_divide_nat @ C @ A)) = ((times_times_nat @ B @ A) = C)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4650])). 159.59/70.64 thf(7152,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (minus_minus_real @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_atMost_nat @ B)) = (minus_minus_real @ (A @ zero_zero_nat) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8754_sum__telescope)). 159.59/70.64 thf(32947,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (^ [C:nat]: (minus_minus_real @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_atMost_nat @ B)) = (minus_minus_real @ (A @ zero_zero_nat) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7152])). 159.59/70.64 thf(504,axiom,((! [A:nat]: ((zero_z3403309356797280102nteger = (semiri4939895301339042750nteger @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6506_of__nat__0__eq__iff)). 159.59/70.64 thf(9857,plain,((! [A:nat]: ((zero_z3403309356797280102nteger = (semiri4939895301339042750nteger @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[504])). 159.59/70.64 thf(2706,axiom,((! [A:extended_enat,B:extended_enat]: (((ord_le72135733267957522d_enat @ A @ B) | (A = B)) <= (ord_le2932123472753598470d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3257_order__le__imp__less__or__eq)). 159.59/70.64 thf(16984,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) | (A = B) | ~ (ord_le2932123472753598470d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2706])). 159.59/70.64 thf(4299,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ A @ B)) @ C) = (((ord_less_eq_real @ (uminus_uminus_real @ A) @ (times_times_real @ C @ B)) <= (ord_less_real @ zero_zero_real @ B)) & ((~ (ord_less_real @ zero_zero_real @ 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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5278_minus__divide__le__eq)). 159.59/70.64 thf(22041,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (uminus_uminus_real @ (divide_divide_real @ A @ B)) @ C) = (((ord_less_eq_real @ (uminus_uminus_real @ A) @ (times_times_real @ C @ B)) | ~ (ord_less_real @ zero_zero_real @ B)) & ((~ (ord_less_real @ zero_zero_real @ 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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4299])). 159.59/70.64 thf(7552,axiom,((! [A:int,B:nat]: ((A != zero_zero_int) => ((power_power_int @ A @ B) != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1894_power__not__zero)). 159.59/70.64 thf(34346,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)],[7552])). 159.59/70.64 thf(1923,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/sandbox/benchmark/theBenchmark.p',fact_7840_gauss__sum__from__Suc__0)). 159.59/70.64 thf(14458,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)],[1923])). 159.59/70.64 thf(7996,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/sandbox/benchmark/theBenchmark.p',fact_6435_bit__iff__odd)). 159.59/70.64 thf(35804,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)],[7996])). 159.59/70.64 thf(6454,axiom,((! [A:set_nat,B:nat,C:(nat > complex)]: (((~ (member_nat @ B @ A)) => ((groups6464643781859351333omplex @ C @ (insert_nat @ B @ A)) = (times_times_complex @ (C @ B) @ (groups6464643781859351333omplex @ C @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8426_prod_Oinsert)). 159.59/70.64 thf(30072,plain,((! [A:set_nat,B:nat,C:(nat > complex)]: (((~ (member_nat @ B @ A)) => ((groups6464643781859351333omplex @ (C) @ (insert_nat @ B @ A)) = (times_times_complex @ (C @ B) @ (groups6464643781859351333omplex @ (C) @ A)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6454])). 159.59/70.64 thf(2235,axiom,((! [A:int,B:int,C:nat]: ((ord_less_int @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_int @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ A) @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6850_zmult__zless__mono2__lemma)). 159.59/70.64 thf(15465,plain,((! [A:int,B:int,C:nat]: ((ord_less_int @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_int @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ A) @ (times_times_int @ (semiri1314217659103216013at_int @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2235])). 159.59/70.64 thf(2375,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/sandbox/benchmark/theBenchmark.p',fact_3465_power__mod)). 159.59/70.64 thf(15880,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)],[2375])). 159.59/70.64 thf(3693,axiom,((! [A:complex,B:(nat > complex),C:complex]: (((A != zero_zero_complex) => (sums_complex @ B @ (divide1717551699836669952omplex @ C @ A))) <= (sums_complex @ (^ [D:nat]: (times_times_complex @ A @ (B @ D))) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7928_sums__mult__D)). 159.59/70.64 thf(20112,plain,((! [A:complex,B:(nat > complex),C:complex]: (((~ (A = zero_zero_complex)) => (sums_complex @ (B) @ (divide1717551699836669952omplex @ C @ A))) | ~ (sums_complex @ (^ [D:nat]: (times_times_complex @ A @ (B @ D))) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3693])). 159.59/70.64 thf(1615,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ C) => ((dvd_dvd_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A)) = (dvd_dvd_int @ B @ C))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3803_div__dvd__div)). 159.59/70.64 thf(13499,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ A @ C) => ((dvd_dvd_int @ (divide_divide_int @ B @ A) @ (divide_divide_int @ C @ A)) = (dvd_dvd_int @ B @ C))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1615])). 159.59/70.64 thf(3477,axiom,(((semiri1314217659103216013at_int @ one_one_nat) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6552_of__nat__1)). 159.59/70.64 thf(19421,plain,(((semiri1314217659103216013at_int @ one_one_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3477])). 159.59/70.64 thf(839,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ A @ (times_times_real @ C @ B)) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3946_dvd__mult)). 159.59/70.64 thf(10957,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)],[839])). 159.59/70.64 thf(1154,axiom,((! [A:set_nat,B:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((A != bot_bot_set_nat) => ((! [C:nat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (B @ C)) <= (member_nat @ C @ A))) => (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (groups7108830773950497114d_enat @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7558_sum__pos)). 159.59/70.64 thf(11947,plain,((! [A:set_nat,B:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((~ (A = bot_bot_set_nat)) => ((! [C:nat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (B @ C)) | ~ (member_nat @ C @ A))) => (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (groups7108830773950497114d_enat @ (B) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154])). 159.59/70.64 thf(4985,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/sandbox/benchmark/theBenchmark.p',fact_363_power__mult__distrib)). 159.59/70.64 thf(24503,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)],[4985])). 159.59/70.64 thf(3458,axiom,((~ (ord_less_real @ one_one_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_less__numeral__extra_I4_J)). 159.59/70.64 thf(19362,plain,((~ (ord_less_real @ one_one_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3458])). 159.59/70.64 thf(5960,axiom,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = ((ord_less_eq_num @ B @ A) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2755_nle__le)). 159.59/70.64 thf(28312,plain,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) = ((ord_less_eq_num @ B @ A) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5960])). 159.59/70.64 thf(2289,axiom,((! [A:real,B:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ (plus_plus_real @ A @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4639_minus__add__cancel)). 159.59/70.64 thf(15626,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)],[2289])). 159.59/70.64 thf(2577,axiom,((! [A:complex,B:complex,C:complex]: (((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = C) = ((((uminus1482373934393186551omplex @ A) = (times_times_complex @ C @ B)) <= (B != zero_zero_complex)) & ((C = zero_zero_complex) <= (B = zero_zero_complex)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5198_minus__divide__eq__eq)). 159.59/70.64 thf(16535,plain,((! [A:complex,B:complex,C:complex]: (((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = C) = ((((uminus1482373934393186551omplex @ 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)],[2577])). 159.59/70.64 thf(3035,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/sandbox/benchmark/theBenchmark.p',fact_5870_neg__numeral__power__less__of__int__cancel__iff)). 159.59/70.64 thf(18006,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)],[3035])). 159.59/70.64 thf(4232,axiom,((pi = (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (the_real @ (^ [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) & ((cos_real @ A) = zero_zero_real) & (ord_less_eq_real @ A @ (numeral_numeral_real @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9403_pi__def)). 159.59/70.64 thf(21837,plain,((pi = (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (the_real @ (^ [A:real]: ((ord_less_eq_real @ zero_zero_real @ 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)],[4232])). 159.59/70.64 thf(671,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2743_ord__eq__le__trans)). 159.59/70.64 thf(10397,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[671])). 159.59/70.64 thf(2416,axiom,((! [A:real,B:real]: ((A != zero_zero_real) => ((divide_divide_real @ (times_times_real @ A @ B) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1632_nonzero__mult__div__cancel__left)). 159.59/70.64 thf(16015,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real)) => ((divide_divide_real @ (times_times_real @ A @ B) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2416])). 159.59/70.64 thf(2212,axiom,((! [A:nat,B:nat,C:(nat > extended_enat)]: ((((groups7961826882256487087d_enat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_7803423173614009249d_enat @ (groups7961826882256487087d_enat @ C @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) <= (~ (ord_less_nat @ (suc @ A) @ B))) & (((groups7961826882256487087d_enat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_on7984719198319812577d_enat) <= (ord_less_nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8452_prod_Ocl__ivl__Suc)). 159.59/70.64 thf(15389,plain,((! [A:nat,B:nat,C:(nat > extended_enat)]: ((((groups7961826882256487087d_enat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = (times_7803423173614009249d_enat @ (groups7961826882256487087d_enat @ (C) @ (set_or1269000886237332187st_nat @ B @ A)) @ (C @ (suc @ A)))) | (ord_less_nat @ (suc @ A) @ B)) & (((groups7961826882256487087d_enat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_on7984719198319812577d_enat) | ~ (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2212])). 159.59/70.64 thf(2226,axiom,((! [A:real,B:(nat > real)]: ((ord_less_real @ zero_zero_real @ A) => ((? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_real @ (real_V7735802525324610683m_real @ (suminf_real @ (^ [E:nat]: (B @ (plus_plus_nat @ E @ D))))) @ A))) <= (summable_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7130_suminf__exist__split)). 159.59/70.64 thf(15438,plain,((! [A:real,B:(nat > real)]: ((ord_less_real @ zero_zero_real @ A) => (? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_real @ (real_V7735802525324610683m_real @ (suminf_real @ (^ [E:nat]: (B @ (plus_plus_nat @ E @ D))))) @ A)) | ~ (summable_real @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2226])). 159.59/70.64 thf(4322,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/sandbox/benchmark/theBenchmark.p',fact_5767_of__int__le__iff)). 159.59/70.64 thf(22106,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)],[4322])). 159.59/70.64 thf(4430,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((modulo364778990260209775nteger @ (modulo364778990260209775nteger @ C @ B) @ A) = (modulo364778990260209775nteger @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4029_mod__mod__cancel)). 159.59/70.64 thf(22446,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((modulo364778990260209775nteger @ (modulo364778990260209775nteger @ C @ B) @ A) = (modulo364778990260209775nteger @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4430])). 159.59/70.64 thf(7740,axiom,((! [A:nat,B:nat]: (((A != B) => (ord_less_nat @ B @ A)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2794_linorder__cases)). 159.59/70.64 thf(35018,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)],[7740])). 159.59/70.64 thf(4358,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((B = A) | (ord_less_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3105_dual__order_Oorder__iff__strict)). 159.59/70.64 thf(22212,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((B = A) | (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4358])). 159.59/70.64 thf(5248,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_trans__le__add2)). 159.59/70.64 thf(25432,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5248])). 159.59/70.64 thf(4740,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (bit_se2002935070580805687sk_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6062_less__eq__mask)). 159.59/70.64 thf(23623,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (bit_se2002935070580805687sk_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4740])). 159.59/70.64 thf(6450,axiom,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (? [C:real]: (((power_power_real @ C @ A) = B) & ! [D:real]: ((D = C) <= (((power_power_real @ D @ A) = B) & (ord_less_real @ zero_zero_real @ D))) & (ord_less_real @ zero_zero_real @ C)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3005_realpow__pos__nth__unique)). 159.59/70.64 thf(30055,plain,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (? [C:real]: (((power_power_real @ C @ A) = B) & ! [D:real]: ((D = C) | ~ (((power_power_real @ D @ A) = B) & (ord_less_real @ zero_zero_real @ D))) & (ord_less_real @ zero_zero_real @ C)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6450])). 159.59/70.64 thf(2174,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/sandbox/benchmark/theBenchmark.p',fact_3877_odd__add)). 159.59/70.64 thf(15259,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)],[2174])). 159.59/70.64 thf(7512,axiom,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3977_dvd__triv__right)). 159.59/70.64 thf(34223,plain,((! [A:nat,B:nat]: (dvd_dvd_nat @ A @ (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7512])). 159.59/70.64 thf(7042,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ one_one_nat @ A) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6109_one__and__eq)). 159.59/70.64 thf(32492,plain,((! [A:nat]: ((bit_se727722235901077358nd_nat @ one_one_nat @ A) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7042])). 159.59/70.64 thf(6382,axiom,((! [A:num,B:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (numeral_numeral_int @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5031_neg__numeral__le__numeral)). 159.59/70.64 thf(29761,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)],[6382])). 159.59/70.64 thf(3992,axiom,((ord_less_real @ (uminus_uminus_real @ one_one_real) @ one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5079_less__minus__one__simps_I2_J)). 159.59/70.64 thf(21084,plain,((ord_less_real @ (uminus_uminus_real @ one_one_real) @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3992])). 159.59/70.64 thf(1647,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/sandbox/benchmark/theBenchmark.p',fact_7977_one__diff__power__eq)). 159.59/70.64 thf(13592,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)],[1647])). 159.59/70.64 thf(5024,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/sandbox/benchmark/theBenchmark.p',fact_1995_mult__left__mono__neg)). 159.59/70.64 thf(24639,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)],[5024])). 159.59/70.64 thf(7387,axiom,(((modulo_modulo_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3428_bits__one__mod__two__eq__one)). 159.59/70.64 thf(33792,plain,(((modulo_modulo_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7387])). 159.59/70.64 thf(3743,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ B @ (divide6298287555418463151nteger @ C @ A)) = (dvd_dvd_Code_integer @ B @ C)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4104_dvd__div__unit__iff)). 159.59/70.64 thf(20295,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ B @ (divide6298287555418463151nteger @ 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)],[3743])). 159.59/70.64 thf(604,axiom,((! [A:real,B:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) => (ord_less_real @ A @ B)) & ((ord_less_real @ B @ A) <= (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9086_inverse__less__iff)). 159.59/70.64 thf(10179,plain,((! [A:real,B:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) => (ord_less_real @ A @ B)) & ((ord_less_real @ B @ A) | ~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[604])). 159.59/70.64 thf(1372,axiom,((ord_less_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6760_pi__half__less__two)). 159.59/70.64 thf(12712,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)],[1372])). 159.59/70.64 thf(1734,axiom,(((ring_1_of_int_real @ one_one_int) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5773_of__int__1)). 159.59/70.64 thf(13857,plain,(((ring_1_of_int_real @ one_one_int) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734])). 159.59/70.64 thf(7755,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_mult_Ocommute)). 159.59/70.64 thf(35059,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7755])). 159.59/70.64 thf(1561,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/sandbox/benchmark/theBenchmark.p',fact_8344_pochhammer__minus)). 159.59/70.64 thf(13323,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)],[1561])). 159.59/70.64 thf(6154,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((((bit_se2925701944663578781it_nat @ D @ B) = (bit_se2925701944663578781it_nat @ D @ C)) <= (ord_less_eq_nat @ D @ A)) <= ((bit_se2925701944663578781it_nat @ A @ B) = (bit_se2925701944663578781it_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4916_take__bit__tightened)). 159.59/70.64 thf(28928,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((bit_se2925701944663578781it_nat @ D @ B) = (bit_se2925701944663578781it_nat @ D @ C)) | ~ (ord_less_eq_nat @ D @ A) | ~ ((bit_se2925701944663578781it_nat @ A @ B) = (bit_se2925701944663578781it_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6154])). 159.59/70.64 thf(3768,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/sandbox/benchmark/theBenchmark.p',fact_7944_powser__sums__if)). 159.59/70.64 thf(20371,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)],[3768])). 159.59/70.64 thf(5482,axiom,((! [A:nat,B:nat,C:nat]: (((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))) <= (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8356_floor__log__nat__eq__if)). 159.59/70.64 thf(26383,plain,((! [A:nat,B:nat,C:nat]: (((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))) | ~ (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5482])). 159.59/70.64 thf(4670,axiom,((! [A:num]: ((plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat) = (numera1916890842035813515d_enat @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_numeral__plus__one)). 159.59/70.64 thf(23403,plain,((! [A:num]: ((plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat) = (numera1916890842035813515d_enat @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4670])). 159.59/70.64 thf(3427,axiom,((! [A:complex,B:complex]: ((one_one_complex = (divide1717551699836669952omplex @ A @ B)) = ((B != zero_zero_complex) & (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1673_one__eq__divide__iff)). 159.59/70.64 thf(19271,plain,((! [A:complex,B:complex]: ((one_one_complex = (divide1717551699836669952omplex @ A @ B)) = (~ (B = zero_zero_complex) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3427])). 159.59/70.64 thf(2260,axiom,((! [A:nat]: ((groups6591440286371151544t_real @ (^ [B:nat]: (divide_divide_real @ (gbinomial_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ A @ B)) @ B) @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ B))) @ (set_ord_atMost_nat @ A)) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8950_gbinomial__sum__nat__pow2)). 159.59/70.64 thf(15543,plain,((! [A:nat]: ((groups6591440286371151544t_real @ (^ [B:nat]: (divide_divide_real @ (gbinomial_real @ (semiri5074537144036343181t_real @ (plus_plus_nat @ A @ B)) @ B) @ (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ B))) @ (set_ord_atMost_nat @ A)) = (power_power_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2260])). 159.59/70.64 thf(133,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/sandbox/benchmark/theBenchmark.p',fact_9588_unset__bit__int__def)). 159.59/70.64 thf(8661,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)],[133])). 159.59/70.64 thf(991,axiom,((! [A:real,B:real,C:(real > num),D:num]: ((ord_less_real @ A @ B) => ((ord_less_num @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))) => (ord_less_num @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2905_order__less__subst2)). 159.59/70.64 thf(11419,plain,((! [A:real,B:real,C:(real > num),D:num]: ((ord_less_real @ A @ B) => ((ord_less_num @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))) => (ord_less_num @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[991])). 159.59/70.64 thf(1136,axiom,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_real @ A @ (B @ C)) => (((ord_less_real @ A @ (B @ D)) <= (! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F)))) <= (ord_less_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2894_order__less__subst1)). 159.59/70.64 thf(11893,plain,((! [A:real,B:(real > real),C:real,D:real]: ((ord_less_real @ A @ (B @ C)) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:real,F:real]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))) | ~ (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136])). 159.59/70.64 thf(1774,axiom,((! [A:$o]: ((zero_n356916108424825756nteger @ (~ (A))) = (minus_8373710615458151222nteger @ one_one_Code_integer @ (zero_n356916108424825756nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4351_of__bool__not__iff)). 159.59/70.64 thf(13980,plain,((! [A:$o]: ((zero_n356916108424825756nteger @ (~ (A))) = (minus_8373710615458151222nteger @ one_one_Code_integer @ (zero_n356916108424825756nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774])). 159.59/70.64 thf(495,axiom,((! [A:nat]: ((semiri3624122377584611663nteger @ (suc @ A)) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ (suc @ A)) @ (semiri3624122377584611663nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8062_fact__Suc)). 159.59/70.64 thf(9830,plain,((! [A:nat]: ((semiri3624122377584611663nteger @ (suc @ A)) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ (suc @ A)) @ (semiri3624122377584611663nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[495])). 159.59/70.64 thf(922,axiom,((! [A:nat,B:int,C:int]: (((dvd_dvd_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) = (dvd_dvd_int @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3871_pow__divides__pow__iff)). 159.59/70.64 thf(11205,plain,((! [A:nat,B:int,C:int]: (((dvd_dvd_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)) = (dvd_dvd_int @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[922])). 159.59/70.64 thf(443,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/sandbox/benchmark/theBenchmark.p',fact_9667_times__complex_Ocode)). 159.59/70.64 thf(9642,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)],[443])). 159.59/70.64 thf(87,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/sandbox/benchmark/theBenchmark.p',fact_9683_Complex__divide)). 159.59/70.64 thf(8517,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)],[87])). 159.59/70.64 thf(735,axiom,((! [A:int,B:int]: ((divide_divide_int @ (modulo_modulo_int @ A @ B) @ B) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3413_mod__div__trivial)). 159.59/70.64 thf(10628,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)],[735])). 159.59/70.64 thf(7113,axiom,((! [A:nat,B:nat,C:nat]: ((((bit_se2925701944663578781it_nat @ A @ (bit_se4205575877204974255it_nat @ B @ C)) = (bit_se4205575877204974255it_nat @ B @ (bit_se2925701944663578781it_nat @ A @ C))) <= (~ (ord_less_eq_nat @ A @ B))) & ((ord_less_eq_nat @ A @ B) => ((bit_se2925701944663578781it_nat @ A @ (bit_se4205575877204974255it_nat @ B @ C)) = (bit_se2925701944663578781it_nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5111_take__bit__unset__bit__eq)). 159.59/70.64 thf(32781,plain,((! [A:nat,B:nat,C:nat]: ((((bit_se2925701944663578781it_nat @ A @ (bit_se4205575877204974255it_nat @ B @ C)) = (bit_se4205575877204974255it_nat @ B @ (bit_se2925701944663578781it_nat @ A @ C))) | (ord_less_eq_nat @ A @ B)) & ((ord_less_eq_nat @ A @ B) => ((bit_se2925701944663578781it_nat @ A @ (bit_se4205575877204974255it_nat @ B @ C)) = (bit_se2925701944663578781it_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7113])). 159.59/70.64 thf(550,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ (times_times_complex @ A @ (cnj @ B)) @ (times_times_complex @ (cnj @ A) @ B)) = (real_V4546457046886955230omplex @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (re @ (times_times_complex @ A @ (cnj @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9704_cnj__add__mult__eq__Re)). 159.59/70.64 thf(10005,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ (times_times_complex @ A @ (cnj @ B)) @ (times_times_complex @ (cnj @ A) @ B)) = (real_V4546457046886955230omplex @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (re @ (times_times_complex @ A @ (cnj @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[550])). 159.59/70.64 thf(6751,axiom,((! [A:nat]: ((one_one_nat = (semiri1316708129612266289at_nat @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6547_of__nat__1__eq__iff)). 159.59/70.64 thf(31282,plain,((! [A:nat]: ((one_one_nat = (semiri1316708129612266289at_nat @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6751])). 159.59/70.64 thf(6960,axiom,((! [A:$o,B:$o,C:nat]: ((((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ one_one_nat)) <= (A)) & ((~ (A)) => (((~ (B)) => ((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = none_nat)) & (((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ zero_zero_nat)) <= (B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2218_vebt__pred_Osimps_I3_J)). 159.59/70.64 thf(32071,plain,((! [A:$o,B:$o,C:nat]: ((((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ one_one_nat)) | ~ (A)) & ((~ (A)) => (((~ (B)) => ((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = none_nat)) & (((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ zero_zero_nat)) | ~ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6960])). 159.59/70.64 thf(7843,axiom,(((semiri1406184849735516958ct_int @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_int @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8067_fact__2)). 159.59/70.64 thf(35323,plain,(((semiri1406184849735516958ct_int @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_int @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7843])). 159.59/70.64 thf(6687,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat,F:nat,G:nat]: (((((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((D = (suc @ B)) => (((((F = G) => (! [H:vEBT_VEBT]: ((~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I))) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A))))) => ((((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ E @ A @ C) @ E) <= ((! [H:nat]: ((! [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))) & ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ G @ B)) <= ((vEBT_VEBT_high @ G @ B) = H))) <= (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)))) <= (F != G))) <= (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E))) <= (ord_less_eq_nat @ F @ G))) <= (! [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))))) <= (E = (plus_plus_nat @ B @ D))))) <= (vEBT_invar_vebt @ C @ D)) <= (! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ B) <= (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_714_invar__vebt_Ointros_I5_J)). 159.59/70.64 thf(30925,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat,F:nat,G:nat]: ((((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((D = (suc @ B)) => ((((F = G) => (! [H:vEBT_VEBT]: (~ (? [I:nat]: (vEBT_V8194947554948674370ptions @ H @ I)) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A))))) => ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ F @ G)) @ E @ A @ C) @ E) | ~ (! [H:nat]: ((! [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))) & ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ A @ H) @ (vEBT_VEBT_low @ G @ B)) | ~ ((vEBT_VEBT_high @ G @ B) = H))) | ~ (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) | (F = G)) | ~ (ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)) | ~ (ord_less_eq_nat @ F @ G))) | ~ (! [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)))) | ~ (E = (plus_plus_nat @ B @ D))))) | ~ (vEBT_invar_vebt @ C @ D) | ~ (! [H:vEBT_VEBT]: ((vEBT_invar_vebt @ H @ B) | ~ (member_VEBT_VEBT @ H @ (set_VEBT_VEBT2 @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6687])). 159.59/70.64 thf(6595,axiom,((! [A:int,B:int,C:nat]: ((((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = (ord_less_eq_int @ A @ B))) <= (ord_less_eq_int @ zero_zero_int @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1779_power__mono__iff)). 159.59/70.64 thf(30588,plain,((! [A:int,B:int,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) = (ord_less_eq_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)],[6595])). 159.59/70.64 thf(7334,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A)) <= (ord_less_eq_nat @ C @ one_one_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2463_power__decreasing)). 159.59/70.64 thf(33614,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A)) | ~ (ord_less_eq_nat @ C @ one_one_nat) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7334])). 159.59/70.64 thf(3816,axiom,((divide_divide_real = (^ [A:real,B:real]: (times_times_real @ A @ (inverse_inverse_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9043_field__class_Ofield__divide__inverse)). 159.59/70.64 thf(20522,plain,(((divide_divide_real) = (^ [A:real,B:real]: (times_times_real @ A @ (inverse_inverse_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3816])). 159.59/70.64 thf(3364,axiom,((! [A:extended_enat]: ((plus_p3455044024723400733d_enat @ A @ zero_z5237406670263579293d_enat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1528_add_Oright__neutral)). 159.59/70.64 thf(19064,plain,((! [A:extended_enat]: ((plus_p3455044024723400733d_enat @ A @ zero_z5237406670263579293d_enat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3364])). 159.59/70.64 thf(5674,axiom,((! [A:real,B:nat,C:nat]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => ((ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_eq_nat @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1794_power__decreasing__iff)). 159.59/70.64 thf(27050,plain,((! [A:real,B:nat,C:nat]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ one_one_real) => ((ord_less_eq_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C)) = (ord_less_eq_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5674])). 159.59/70.64 thf(1544,axiom,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (uminus1351360451143612070nteger @ B)) = (plus_p5714425477246183910nteger @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4709_diff__minus__eq__add)). 159.59/70.64 thf(13272,plain,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (uminus1351360451143612070nteger @ B)) = (plus_p5714425477246183910nteger @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544])). 159.59/70.64 thf(6944,axiom,((! [A:nat]: ((((power_power_int @ zero_zero_int @ A) = one_one_int) <= (A = zero_zero_nat)) & ((A != zero_zero_nat) => ((power_power_int @ zero_zero_int @ A) = zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1814_power__0__left)). 159.59/70.64 thf(32022,plain,((! [A:nat]: ((((power_power_int @ zero_zero_int @ A) = one_one_int) | ~ (A = zero_zero_nat)) & ((~ (A = zero_zero_nat)) => ((power_power_int @ zero_zero_int @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6944])). 159.59/70.64 thf(3456,axiom,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ A @ (plus_plus_complex @ B @ C)) = (minus_minus_complex @ (minus_minus_complex @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1278_diff__add__eq__diff__diff__swap)). 159.59/70.64 thf(19357,plain,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ A @ (plus_plus_complex @ B @ C)) = (minus_minus_complex @ (minus_minus_complex @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3456])). 159.59/70.64 thf(2100,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (powr_real @ A @ C) @ B) = (ord_less_real @ C @ (log @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7264_powr__less__iff)). 159.59/70.64 thf(15015,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (powr_real @ A @ C) @ B) = (ord_less_real @ C @ (log @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2100])). 159.59/70.64 thf(1997,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6529_of__nat__add)). 159.59/70.64 thf(14706,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)],[1997])). 159.59/70.64 thf(4940,axiom,((~ (ord_less_eq_real @ one_one_real @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2049_not__one__le__zero)). 159.59/70.64 thf(24318,plain,((~ (ord_less_eq_real @ one_one_real @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4940])). 159.59/70.64 thf(1449,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((A = B) | (ord_less_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3073_order_Oorder__iff__strict)). 159.59/70.64 thf(12973,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((A = B) | (ord_less_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449])). 159.59/70.64 thf(5652,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((ord_less_eq_nat @ D @ C) <= (A @ D))) => (? [D:nat]: (! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E)) & (A @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_Nat_Oex__has__greatest__nat)). 159.59/70.64 thf(26944,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((! [D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (A @ D))) => (? [D:nat]: (! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E)) & (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5652])). 159.59/70.64 thf(6232,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1897_nat_Odistinct_I1_J)). 159.59/70.64 thf(29189,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6232])). 159.59/70.64 thf(6817,axiom,((! [A:nat]: ((bit_se2925701944663578781it_nat @ (suc @ zero_zero_nat) @ A) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4903_take__bit__Suc__0)). 159.59/70.64 thf(31498,plain,((! [A:nat]: ((bit_se2925701944663578781it_nat @ (suc @ zero_zero_nat) @ A) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6817])). 159.59/70.64 thf(2186,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((powr_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (powr_real @ A @ C) @ (powr_real @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7251_powr__mult)). 159.59/70.64 thf(15297,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((powr_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (powr_real @ A @ C) @ (powr_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2186])). 159.59/70.64 thf(4729,axiom,((((=) @ int) = (^ [A:int,B:int]: ((ord_less_eq_int @ B @ A) & (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2718_dual__order_Oeq__iff)). 159.59/70.64 thf(23589,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)],[4729])). 159.59/70.64 thf(329,axiom,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (times_times_int @ A @ (comm_s4660882817536571857er_int @ (plus_plus_int @ A @ one_one_int) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8267_pochhammer__rec)). 159.59/70.64 thf(9263,plain,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (times_times_int @ A @ (comm_s4660882817536571857er_int @ (plus_plus_int @ A @ one_one_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[329])). 159.59/70.64 thf(5621,axiom,((! [A:num,B:num]: (((~ (ord_less_num @ B @ A)) = (B = A)) <= (~ (ord_less_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2788_antisym__conv3)). 159.59/70.64 thf(26848,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)],[5621])). 159.59/70.64 thf(2542,axiom,((! [A:(nat > real),B:(nat > real)]: (((summable_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C)))) <= (summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (B @ C))))) <= (summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8900_summable__Cauchy__product)). 159.59/70.64 thf(16425,plain,((! [A:(nat > real),B:(nat > real)]: ((summable_real @ (^ [C:nat]: (groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C)))) | ~ (summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (B @ C)))) | ~ (summable_real @ (^ [C:nat]: (real_V7735802525324610683m_real @ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2542])). 159.59/70.64 thf(4490,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/sandbox/benchmark/theBenchmark.p',fact_873_nat__diff__add__eq2)). 159.59/70.64 thf(22693,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)],[4490])). 159.59/70.64 thf(5238,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_le__refl)). 159.59/70.64 thf(25400,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5238])). 159.59/70.64 thf(2332,axiom,((! [A:int,B:int,C:int,D:int]: ((((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) => ((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)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1343_add__le__add__imp__diff__le)). 159.59/70.64 thf(15745,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) => ((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)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2332])). 159.59/70.64 thf(161,axiom,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (semiri3624122377584611663nteger @ A) @ (semiri3624122377584611663nteger @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8090_fact__dvd)). 159.59/70.64 thf(8750,plain,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (semiri3624122377584611663nteger @ A) @ (semiri3624122377584611663nteger @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[161])). 159.59/70.64 thf(3793,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (cos_real @ A) @ (cos_real @ B))) <= (ord_less_eq_real @ A @ B)) <= (ord_less_eq_real @ (uminus_uminus_real @ pi) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7123_cos__monotone__minus__pi__0_H)). 159.59/70.64 thf(20458,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (cos_real @ A) @ (cos_real @ B))) | ~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ (uminus_uminus_real @ pi) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3793])). 159.59/70.64 thf(35,axiom,(((re @ one_one_complex) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9633_one__complex_Osimps_I1_J)). 159.59/70.64 thf(8355,plain,(((re @ one_one_complex) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 159.59/70.64 thf(1706,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/sandbox/benchmark/theBenchmark.p',fact_4819_neg__numeral__less__iff)). 159.59/70.64 thf(13766,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)],[1706])). 159.59/70.64 thf(7723,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/sandbox/benchmark/theBenchmark.p',fact_1636_div__mult__mult1__if)). 159.59/70.64 thf(34946,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)],[7723])). 159.59/70.64 thf(1159,axiom,((archim8280529875227126926d_real = (^ [A:real]: (archim6058952711729229775r_real @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8335_round__def)). 159.59/70.64 thf(11964,plain,(((archim8280529875227126926d_real) = (^ [A:real]: (archim6058952711729229775r_real @ (plus_plus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159])). 159.59/70.64 thf(3114,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/sandbox/benchmark/theBenchmark.p',fact_4230_even__iff__mod__2__eq__zero)). 159.59/70.64 thf(18270,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)],[3114])). 159.59/70.64 thf(3004,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2928_order__less__imp__not__eq2)). 159.59/70.64 thf(17914,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3004])). 159.59/70.64 thf(4172,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((times_times_int @ B @ A) = (times_times_int @ C @ A)) = (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4071_unit__mult__right__cancel)). 159.59/70.64 thf(21635,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((times_times_int @ B @ A) = (times_times_int @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4172])). 159.59/70.64 thf(2659,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 @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F))))) <= ((C @ B) = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2879_ord__less__eq__subst)). 159.59/70.64 thf(16819,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 @ E @ F) => (ord_less_real @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2659])). 159.59/70.64 thf(6790,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (sqrt @ B)) <= (ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6427_real__less__rsqrt)). 159.59/70.64 thf(31416,plain,((! [A:real,B:real]: ((ord_less_real @ A @ (sqrt @ B)) | ~ (ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6790])). 159.59/70.64 thf(7930,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1626_nonzero__mult__div__cancel__right)). 159.59/70.64 thf(35598,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)],[7930])). 159.59/70.64 thf(396,axiom,((! [A:complex,B:nat]: (((im @ A) = zero_zero_real) => ((re @ (power_power_complex @ A @ B)) = (power_power_real @ (re @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9646_Re__power__real)). 159.59/70.64 thf(9487,plain,((! [A:complex,B:nat]: (((im @ A) = zero_zero_real) => ((re @ (power_power_complex @ A @ B)) = (power_power_real @ (re @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])). 159.59/70.64 thf(5749,axiom,(((semiri2265585572941072030t_real @ one_one_nat) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8052_fact__1)). 159.59/70.64 thf(27293,plain,(((semiri2265585572941072030t_real @ one_one_nat) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5749])). 159.59/70.64 thf(6988,axiom,((! [A:(int > (int > $o)),B:set_nat,C:(nat > int),D:(nat > int)]: (((! [E:int,F:int,G:int,H:int]: ((A @ (times_times_int @ E @ F) @ (times_times_int @ G @ H)) <= ((A @ F @ H) & (A @ E @ G)))) => ((finite_finite_nat @ B) => ((A @ (groups705719431365010083at_int @ C @ B) @ (groups705719431365010083at_int @ D @ B)) <= (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E))))))) <= (A @ one_one_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8568_prod_Orelated)). 159.59/70.64 thf(32291,plain,((! [A:(int > (int > $o)),B:set_nat,C:(nat > int),D:(nat > int)]: (((! [E:int,F:int,G:int,H:int]: ((A @ (times_times_int @ E @ F) @ (times_times_int @ G @ H)) | ~ ((A @ F @ H) & (A @ E @ G)))) => ((finite_finite_nat @ B) => ((A @ (groups705719431365010083at_int @ (C) @ B) @ (groups705719431365010083at_int @ (D) @ B)) | ~ (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E))))))) | ~ (A @ one_one_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6988])). 159.59/70.64 thf(3401,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/sandbox/benchmark/theBenchmark.p',fact_7181_sin__diff__sin)). 159.59/70.64 thf(19185,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)],[3401])). 159.59/70.64 thf(3376,axiom,((! [A:complex,B:complex,C:nat]: ((comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ B) @ C) = (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ (binomial @ C @ D)) @ (comm_s2602460028002588243omplex @ A @ D)) @ (comm_s2602460028002588243omplex @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9152_pochhammer__binomial__sum)). 159.59/70.64 thf(19103,plain,((! [A:complex,B:complex,C:nat]: ((comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ B) @ C) = (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ (binomial @ C @ D)) @ (comm_s2602460028002588243omplex @ A @ D)) @ (comm_s2602460028002588243omplex @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3376])). 159.59/70.64 thf(6660,axiom,((! [A:int]: ~ (ord_less_int @ (power_power_int @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2511_power2__less__0)). 159.59/70.64 thf(30816,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)],[6660])). 159.59/70.64 thf(906,axiom,((! [A:real]: (((sin_real @ A) = zero_zero_real) <= ((cos_real @ A) = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7088_cos__one__sin__zero)). 159.59/70.64 thf(11158,plain,((! [A:real]: (((sin_real @ A) = zero_zero_real) | ~ ((cos_real @ A) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[906])). 159.59/70.64 thf(4311,axiom,((bit_se725231765392027082nd_int = (^ [A:int,B:int]: (bit_se725231765392027082nd_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6045_and_Ocommute)). 159.59/70.64 thf(22074,plain,(((bit_se725231765392027082nd_int) = (^ [A:int,B:int]: (bit_se725231765392027082nd_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4311])). 159.59/70.64 thf(4848,axiom,(((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1657_diff__numeral__special_I9_J)). 159.59/70.64 thf(24026,plain,(((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4848])). 159.59/70.64 thf(7216,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8092_fact__dvd)). 159.59/70.64 thf(33211,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)],[7216])). 159.59/70.64 thf(5424,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1918_bot__nat__0_Oextremum__unique)). 159.59/70.64 thf(26174,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5424])). 159.59/70.64 thf(414,axiom,((! [A:real]: ((plus_plus_real @ (cosh_real @ A) @ (sinh_real @ A)) = (exp_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9320_cosh__plus__sinh)). 159.59/70.64 thf(9553,plain,((! [A:real]: ((plus_plus_real @ (cosh_real @ A) @ (sinh_real @ A)) = (exp_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[414])). 159.59/70.64 thf(6054,axiom,((! [A:nat,B:nat]: ((ord_min_nat @ A @ (suc @ B)) = (case_nat_nat @ zero_zero_nat @ (^ [C:nat]: (suc @ (ord_min_nat @ C @ B))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10178_min__Suc2)). 159.59/70.64 thf(28612,plain,((! [A:nat,B:nat]: ((ord_min_nat @ A @ (suc @ B)) = (case_nat_nat @ zero_zero_nat @ (^ [C:nat]: (suc @ (ord_min_nat @ C @ B))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6054])). 159.59/70.64 thf(593,axiom,((! [A:real,B:real,C:real,D:real]: (((((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_eq_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2291_frac__less2)). 159.59/70.64 thf(10136,plain,((! [A:real,B:real,C:real,D:real]: ((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_eq_real @ A @ B) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[593])). 159.59/70.64 thf(4127,axiom,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (power_power_nat @ A @ B)) = (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6560_of__nat__power)). 159.59/70.64 thf(21488,plain,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (power_power_nat @ A @ B)) = (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4127])). 159.59/70.64 thf(334,axiom,((! [A:(nat > code_integer),B:nat,C:code_integer]: ((minus_8373710615458151222nteger @ (groups7501900531339628137nteger @ A @ (set_ord_lessThan_nat @ B)) @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ B) @ C)) = (groups7501900531339628137nteger @ (^ [D:nat]: (minus_8373710615458151222nteger @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7968_sumr__diff__mult__const2)). 159.59/70.64 thf(9280,plain,((! [A:(nat > code_integer),B:nat,C:code_integer]: ((minus_8373710615458151222nteger @ (groups7501900531339628137nteger @ (A) @ (set_ord_lessThan_nat @ B)) @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ B) @ C)) = (groups7501900531339628137nteger @ (^ [D:nat]: (minus_8373710615458151222nteger @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 159.59/70.64 thf(4242,axiom,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ B @ (plus_plus_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_add_Oleft__commute)). 159.59/70.64 thf(21869,plain,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ B @ (plus_plus_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4242])). 159.59/70.64 thf(5742,axiom,((! [A:nat,B:num]: ((ord_less_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (ord_less_nat @ A @ (pred_numeral @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5685_less__Suc__numeral)). 159.59/70.64 thf(27271,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)],[5742])). 159.59/70.64 thf(2711,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/sandbox/benchmark/theBenchmark.p',fact_6955_suminf__geometric)). 159.59/70.64 thf(16999,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)],[2711])). 159.59/70.64 thf(4991,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/sandbox/benchmark/theBenchmark.p',fact_4804_mult__neg__numeral__simps_I1_J)). 159.59/70.64 thf(24520,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)],[4991])). 159.59/70.64 thf(5624,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/sandbox/benchmark/theBenchmark.p',fact_5590_numeral__Bit1)). 159.59/70.64 thf(26861,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)],[5624])). 159.59/70.64 thf(3314,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (((ord_less_eq_real @ B @ A) <= (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))) & ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) => (ord_less_eq_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9087_inverse__le__iff)). 159.59/70.64 thf(18912,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (((ord_less_eq_real @ B @ A) | ~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))) & ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) => (ord_less_eq_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3314])). 159.59/70.64 thf(7959,axiom,((ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__C5_Ohyps_C_I8_J)). 159.59/70.64 thf(35694,plain,((ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7959])). 159.59/70.64 thf(7766,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/sandbox/benchmark/theBenchmark.p',fact_3893_even__plus__one__iff)). 159.59/70.64 thf(35091,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)],[7766])). 159.59/70.64 thf(5988,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/sandbox/benchmark/theBenchmark.p',fact_2535_vebt__pred_Osimps_I6_J)). 159.59/70.64 thf(28400,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)],[5988])). 159.59/70.64 thf(7735,axiom,((nat_triangle = (^ [A:nat]: (divide_divide_nat @ (times_times_nat @ A @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4304_triangle__def)). 159.59/70.64 thf(34990,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)],[7735])). 159.59/70.64 thf(3639,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ C @ A) => (ord_less_real @ C @ B)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2824_dual__order_Ostrict__trans)). 159.59/70.64 thf(19934,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ C @ A) => (ord_less_real @ C @ B)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3639])). 159.59/70.64 thf(2844,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) <= (vEBT_VEBT_valid @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9623_valid__eq2)). 159.59/70.64 thf(17396,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) | ~ (vEBT_VEBT_valid @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2844])). 159.59/70.64 thf(4739,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/sandbox/benchmark/theBenchmark.p',fact_318_power__increasing)). 159.59/70.64 thf(23620,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)],[4739])). 159.59/70.64 thf(4522,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/sandbox/benchmark/theBenchmark.p',fact_206_length__list__update)). 159.59/70.64 thf(22818,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)],[4522])). 159.59/70.64 thf(3351,axiom,((! [A:nat,B:nat]: ((member_nat @ A @ (set_ord_lessThan_nat @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7869_lessThan__iff)). 159.59/70.64 thf(19025,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)],[3351])). 159.59/70.64 thf(7631,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2821_not__less__iff__gr__or__eq)). 159.59/70.64 thf(34647,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((ord_less_nat @ B @ A) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7631])). 159.59/70.64 thf(2428,axiom,((! [A:(nat > nat),B:(nat > nat)]: (((summable_nat @ B) => ((plus_plus_nat @ (suminf_nat @ A) @ (suminf_nat @ B)) = (suminf_nat @ (^ [C:nat]: (plus_plus_nat @ (A @ C) @ (B @ C)))))) <= (summable_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7047_suminf__add)). 159.59/70.64 thf(16069,plain,((! [A:(nat > nat),B:(nat > nat)]: (((summable_nat @ (B)) => ((plus_plus_nat @ (suminf_nat @ (A)) @ (suminf_nat @ (B))) = (suminf_nat @ (^ [C:nat]: (plus_plus_nat @ (A @ C) @ (B @ C)))))) | ~ (summable_nat @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2428])). 159.59/70.64 thf(2795,axiom,((! [A:real,B:real]: ((((ln_ln_real @ (times_times_real @ A @ B)) = (plus_plus_real @ (ln_ln_real @ A) @ (ln_ln_real @ B))) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5233_ln__mult)). 159.59/70.64 thf(17248,plain,((! [A:real,B:real]: (((ln_ln_real @ (times_times_real @ A @ B)) = (plus_plus_real @ (ln_ln_real @ A) @ (ln_ln_real @ B))) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2795])). 159.59/70.64 thf(6402,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/sandbox/benchmark/theBenchmark.p',fact_4812_mult__neg__numeral__simps_I3_J)). 159.59/70.64 thf(29857,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)],[6402])). 159.59/70.64 thf(3051,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/sandbox/benchmark/theBenchmark.p',fact_2168_nonzero__divide__eq__eq)). 159.59/70.64 thf(18057,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)],[3051])). 159.59/70.64 thf(4288,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/sandbox/benchmark/theBenchmark.p',fact_3833_dvd__add__times__triv__right__iff)). 159.59/70.64 thf(22006,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)],[4288])). 159.59/70.64 thf(3759,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1198_add__strict__mono)). 159.59/70.64 thf(20342,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ C @ D) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3759])). 159.59/70.64 thf(5269,axiom,((! [A:int,B:int,C:(int > nat),D:nat]: ((ord_less_eq_int @ A @ B) => (((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:int,F:int]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_int @ E @ F)))) <= (ord_less_eq_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2681_order__subst2)). 159.59/70.64 thf(25501,plain,((! [A:int,B:int,C:(int > nat),D:nat]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:int,F:int]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_int @ E @ F))) | ~ (ord_less_eq_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5269])). 159.59/70.64 thf(6080,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/sandbox/benchmark/theBenchmark.p',fact_1211_diff__left__mono)). 159.59/70.64 thf(28688,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)],[6080])). 159.59/70.64 thf(7696,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/sandbox/benchmark/theBenchmark.p',fact_6792_of__nat__code__if)). 159.59/70.64 thf(34842,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)],[7696])). 159.59/70.64 thf(3270,axiom,((! [A:nat,B:nat,C:(nat > int),D:int]: ((((! [E:nat,F:nat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_int @ (C @ A) @ D)) <= (ord_less_int @ (C @ B) @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3231_order__le__less__subst2)). 159.59/70.64 thf(18780,plain,((! [A:nat,B:nat,C:(nat > int),D:int]: (((! [E:nat,F:nat]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_int @ (C @ A) @ D)) | ~ (ord_less_int @ (C @ B) @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3270])). 159.59/70.64 thf(1622,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/sandbox/benchmark/theBenchmark.p',fact_4200_is__unit__div__mult__cancel__right)). 159.59/70.64 thf(13518,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)],[1622])). 159.59/70.64 thf(4387,axiom,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ A @ B) @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3512_mod__div__mult__eq)). 159.59/70.64 thf(22305,plain,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ A @ B) @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4387])). 159.59/70.64 thf(1314,axiom,((! [A:real,B:real]: ((((((ord_less_eq_real @ (sin_real @ A) @ (sin_real @ B)) = (ord_less_eq_real @ A @ B)) <= (ord_less_eq_real @ B @ (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 @ 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/sandbox/benchmark/theBenchmark.p',fact_6864_sin__mono__le__eq)). 159.59/70.64 thf(12496,plain,((! [A:real,B:real]: (((ord_less_eq_real @ (sin_real @ A) @ (sin_real @ B)) = (ord_less_eq_real @ A @ B)) | ~ (ord_less_eq_real @ B @ (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 @ 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)],[1314])). 159.59/70.64 thf(5840,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6526_of__nat__le__iff)). 159.59/70.64 thf(27834,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)],[5840])). 159.59/70.64 thf(5288,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (ord_max_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_923_max_Ocobounded2)). 159.59/70.64 thf(25578,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (ord_max_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5288])). 159.59/70.64 thf(675,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ C) => (((divide6298287555418463151nteger @ B @ A) = (divide6298287555418463151nteger @ C @ A)) = (B = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4012_dvd__div__eq__iff)). 159.59/70.64 thf(10412,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ C) => (((divide6298287555418463151nteger @ B @ A) = (divide6298287555418463151nteger @ C @ A)) = (B = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[675])). 159.59/70.64 thf(2446,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_complex @ (A @ zero_zero_nat) @ (groups2073611262835488442omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7956_sum_OlessThan__Suc__shift)). 159.59/70.64 thf(16128,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (A) @ (set_ord_lessThan_nat @ (suc @ B))) = (plus_plus_complex @ (A @ zero_zero_nat) @ (groups2073611262835488442omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2446])). 159.59/70.64 thf(7415,axiom,((! [A:real,B:nat]: ((sqrt @ (power_power_real @ A @ B)) = (power_power_real @ (sqrt @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6371_real__sqrt__power)). 159.59/70.64 thf(33873,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)],[7415])). 159.59/70.64 thf(519,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((A != zero_z3403309356797280102nteger) => ((dvd_dvd_Code_integer @ A @ B) => (((divide6298287555418463151nteger @ B @ A) = C) = (B = (times_3573771949741848930nteger @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4141_dvd__div__eq__mult)). 159.59/70.64 thf(9905,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((dvd_dvd_Code_integer @ A @ B) => (((divide6298287555418463151nteger @ B @ A) = C) = (B = (times_3573771949741848930nteger @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])). 159.59/70.64 thf(6469,axiom,((! [A:num,B:num,C:complex]: ((real_V2046097035970521341omplex @ (numeral_numeral_real @ A) @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ C)) = (real_V2046097035970521341omplex @ (times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9204_scaleR__times)). 159.59/70.64 thf(30137,plain,((! [A:num,B:num,C:complex]: ((real_V2046097035970521341omplex @ (numeral_numeral_real @ A) @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ C)) = (real_V2046097035970521341omplex @ (times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6469])). 159.59/70.64 thf(4375,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/sandbox/benchmark/theBenchmark.p',fact_5836_numeral__power__eq__of__int__cancel__iff)). 159.59/70.64 thf(22263,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)],[4375])). 159.59/70.64 thf(7776,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/sandbox/benchmark/theBenchmark.p',fact_2512_exp__add__not__zero__imp__right)). 159.59/70.64 thf(35117,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)],[7776])). 159.59/70.64 thf(1169,axiom,((! [A:int]: ((ord_less_nat @ zero_zero_nat @ (nat2 @ A)) = (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9416_zero__less__nat__eq)). 159.59/70.64 thf(12000,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)],[1169])). 159.59/70.64 thf(2897,axiom,((! [A:real]: ((ord_less_real @ one_one_real @ (sqrt @ A)) = (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6320_real__sqrt__gt__1__iff)). 159.59/70.64 thf(17579,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)],[2897])). 159.59/70.64 thf(7338,axiom,((! [A:num]: ((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A)) = (uminus_uminus_int @ (numeral_numeral_int @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5706_diff__numeral__special_I5_J)). 159.59/70.64 thf(33628,plain,((! [A:num]: ((minus_minus_int @ (uminus_uminus_int @ one_one_int) @ (numeral_numeral_int @ A)) = (uminus_uminus_int @ (numeral_numeral_int @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7338])). 159.59/70.64 thf(7197,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((minus_minus_nat @ (suc @ B) @ A) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2480_Suc__diff__eq__diff__pred)). 159.59/70.64 thf(33133,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((minus_minus_nat @ (suc @ B) @ A) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7197])). 159.59/70.64 thf(7662,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/sandbox/benchmark/theBenchmark.p',fact_31__C4_C)). 159.59/70.64 thf(34736,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)],[7662])). 159.59/70.64 thf(7475,axiom,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ A @ C) <= (ord_less_eq_num @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2724_order__trans)). 159.59/70.64 thf(34078,plain,((! [A:num,B:num,C:num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ A @ C) | ~ (ord_less_eq_num @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7475])). 159.59/70.64 thf(3579,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/sandbox/benchmark/theBenchmark.p',fact_1227_combine__common__factor)). 159.59/70.64 thf(19747,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)],[3579])). 159.59/70.64 thf(4713,axiom,((! [A:num,B:num]: (((numera1916890842035813515d_enat @ A) = (numera1916890842035813515d_enat @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_numeral__eq__iff)). 159.59/70.64 thf(23541,plain,((! [A:num,B:num]: (((numera1916890842035813515d_enat @ A) = (numera1916890842035813515d_enat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4713])). 159.59/70.64 thf(1097,axiom,((! [A:(extended_enat > $o),B:(extended_enat > $o),C:(extended_enat > $o),D:(extended_enat > $o)]: (((? [E:extended_enat]: ! [F:extended_enat]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) <= (ord_le72135733267957522d_enat @ F @ E))) <= (? [E:extended_enat]: ! [F:extended_enat]: ((ord_le72135733267957522d_enat @ F @ E) => ((C @ F) = (D @ F))))) <= (? [E:extended_enat]: ! [F:extended_enat]: (((A @ F) = (B @ F)) <= (ord_le72135733267957522d_enat @ F @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4462_minf_I2_J)). 159.59/70.64 thf(11767,plain,((! [A:(extended_enat > $o),B:(extended_enat > $o),C:(extended_enat > $o),D:(extended_enat > $o)]: (? [E:extended_enat]: ! [F:extended_enat]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) | ~ (ord_le72135733267957522d_enat @ F @ E)) | ~ (? [E:extended_enat]: ! [F:extended_enat]: ((ord_le72135733267957522d_enat @ F @ E) => ((C @ F) = (D @ F)))) | ~ (? [E:extended_enat]: ! [F:extended_enat]: (((A @ F) = (B @ F)) | ~ (ord_le72135733267957522d_enat @ F @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097])). 159.59/70.64 thf(7192,axiom,((! [A:real,B:nat]: ((ord_less_eq_real @ (power_power_real @ A @ B) @ zero_zero_real) = ((((A = zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_real @ A @ zero_zero_real))) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4270_power__le__zero__eq)). 159.59/70.64 thf(33115,plain,((! [A:real,B:nat]: ((ord_less_eq_real @ (power_power_real @ A @ B) @ zero_zero_real) = ((((A = zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (ord_less_eq_real @ A @ zero_zero_real))) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7192])). 159.59/70.64 thf(3581,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = (~ (ord_less_eq_int @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3038_nless__le)). 159.59/70.64 thf(19753,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)],[3581])). 159.59/70.64 thf(2409,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1766_le__divide__eq__1__pos)). 159.59/70.64 thf(15993,plain,((! [A:real,B:real]: (((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2409])). 159.59/70.64 thf(3024,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/sandbox/benchmark/theBenchmark.p',fact_8299_floor__unique)). 159.59/70.64 thf(17974,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)],[3024])). 159.59/70.64 thf(3075,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3007_pos__zdiv__mult__2)). 159.59/70.64 thf(18131,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3075])). 159.59/70.64 thf(2304,axiom,((! [A:complex,B:complex]: ((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide_divide_real @ (real_V1022390504157884413omplex @ A) @ (real_V1022390504157884413omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6904_norm__divide)). 159.59/70.64 thf(15668,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)],[2304])). 159.59/70.64 thf(6168,axiom,((! [A:nat,B:(nat > real),C:real,D:real]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_real @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (B @ E) @ (power_power_real @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (B @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_real @ (minus_minus_real @ C @ D) @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (B @ F) @ (power_power_real @ D @ (minus_minus_nat @ (minus_minus_nat @ F @ E) @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ E) @ A)) @ (power_power_real @ C @ E))) @ (set_ord_lessThan_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8960_polyfun__diff)). 159.59/70.64 thf(28983,plain,((! [A:nat,B:(nat > real),C:real,D:real]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_real @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (B @ E) @ (power_power_real @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (B @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_real @ (minus_minus_real @ C @ D) @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (B @ F) @ (power_power_real @ D @ (minus_minus_nat @ (minus_minus_nat @ F @ E) @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ E) @ A)) @ (power_power_real @ C @ E))) @ (set_ord_lessThan_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6168])). 159.59/70.64 thf(4924,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ (power_power_nat @ A @ (suc @ B)) @ (power_power_nat @ C @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2361_power__le__imp__le__base)). 159.59/70.64 thf(24271,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ (power_power_nat @ A @ (suc @ B)) @ (power_power_nat @ C @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4924])). 159.59/70.64 thf(6675,axiom,((! [A:real]: ((power_power_real @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_power__one__right)). 159.59/70.64 thf(30871,plain,((! [A:real]: ((power_power_real @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6675])). 159.59/70.64 thf(7619,axiom,((! [A:nat,B:list_VEBT_VEBT,C:nat]: ((((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)) <= (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ B))) <= (ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_set__swap)). 159.59/70.64 thf(34610,plain,((! [A:nat,B:list_VEBT_VEBT,C:nat]: (((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)) | ~ (ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ B)) | ~ (ord_less_nat @ A @ (size_s6755466524823107622T_VEBT @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7619])). 159.59/70.64 thf(130,axiom,((! [A:int,B:real]: ((cos_real @ (times_times_real @ (ring_1_of_int_real @ A) @ (real_V1803761363581548252l_real @ B))) = (real_V1803761363581548252l_real @ (cos_real @ (times_times_real @ (ring_1_of_int_real @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7767_cos__int__times__real)). 159.59/70.64 thf(8652,plain,((! [A:int,B:real]: ((cos_real @ (times_times_real @ (ring_1_of_int_real @ A) @ (real_V1803761363581548252l_real @ B))) = (real_V1803761363581548252l_real @ (cos_real @ (times_times_real @ (ring_1_of_int_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 159.59/70.64 thf(1397,axiom,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1882_comm__monoid__add__class_Oadd__0)). 159.59/70.64 thf(12810,plain,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397])). 159.59/70.64 thf(8084,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ A) = (ord_less_nat @ B @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1606_add__less__same__cancel1)). 159.59/70.64 thf(36100,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)],[8084])). 159.59/70.64 thf(1627,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) <= (ord_less_real @ zero_zero_real @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2155_divide__strict__right__mono)). 159.59/70.64 thf(13535,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) | ~ (ord_less_real @ zero_zero_real @ C) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627])). 159.59/70.64 thf(5729,axiom,((! [A:(list_int > $o),B:list_int]: ((! [C:list_int]: ((A @ C) <= (! [D:list_int]: ((A @ D) <= (ord_less_nat @ (size_size_list_int @ D) @ (size_size_list_int @ C)))))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_length__induct)). 159.59/70.64 thf(27225,plain,((! [A:(list_int > $o),B:list_int]: ((! [C:list_int]: ((A @ C) | ~ (! [D:list_int]: ((A @ D) | ~ (ord_less_nat @ (size_size_list_int @ D) @ (size_size_list_int @ C)))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5729])). 159.59/70.64 thf(2035,axiom,((! [A:nat,B:complex]: ((exp_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ A) @ B)) = (power_power_complex @ (exp_complex @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6734_exp__of__nat__mult)). 159.59/70.64 thf(14824,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)],[2035])). 159.59/70.64 thf(6643,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/sandbox/benchmark/theBenchmark.p',fact_8910_sum__atLeastAtMost__code)). 159.59/70.64 thf(30764,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)],[6643])). 159.59/70.64 thf(1191,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ zero_zero_complex @ A) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1541_div__0)). 159.59/70.64 thf(12079,plain,((! [A:complex]: ((divide1717551699836669952omplex @ zero_zero_complex @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191])). 159.59/70.64 thf(3613,axiom,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D))) <= (A = (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1142_group__cancel_Oadd1)). 159.59/70.64 thf(19853,plain,((! [A:real,B:real,C:real,D:real]: (((plus_plus_real @ A @ D) = (plus_plus_real @ B @ (plus_plus_real @ C @ D))) | ~ (A = (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3613])). 159.59/70.64 thf(7642,axiom,(((ord_less_nat @ xa @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) & (mi != ma))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062)). 159.59/70.64 thf(34679,plain,(((ord_less_nat @ xa @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) & ~ (mi = ma))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7642])). 159.59/70.64 thf(2697,axiom,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => (((! [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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2904_order__less__subst2)). 159.59/70.64 thf(16952,plain,((! [A:real,B:real,C:(real > real),D:real]: ((ord_less_real @ A @ B) => (((! [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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2697])). 159.59/70.64 thf(2401,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (times_times_real @ C @ A)) => (ord_less_eq_real @ (divide_divide_real @ B @ A) @ C)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2429_mult__imp__div__pos__le)). 159.59/70.64 thf(15966,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (times_times_real @ C @ A)) => (ord_less_eq_real @ (divide_divide_real @ B @ A) @ C)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2401])). 159.59/70.64 thf(3576,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/sandbox/benchmark/theBenchmark.p',fact_6629_numeral__power__less__of__nat__cancel__iff)). 159.59/70.64 thf(19737,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)],[3576])). 159.59/70.64 thf(7746,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9112_binomial__le__pow2)). 159.59/70.64 thf(35033,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)],[7746])). 159.59/70.64 thf(10,axiom,((ord_max_int = (^ [A:int,B:int]: (if_int @ (ord_less_eq_int @ A @ B) @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3309_max__def)). 159.59/70.64 thf(8281,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)],[10])). 159.59/70.64 thf(5717,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/sandbox/benchmark/theBenchmark.p',fact_6599_real__of__nat__eq__numeral__power__cancel__iff)). 159.59/70.64 thf(27176,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)],[5717])). 159.59/70.64 thf(7912,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/sandbox/benchmark/theBenchmark.p',fact_5314_minus__power__mult__self)). 159.59/70.64 thf(35546,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)],[7912])). 159.59/70.64 thf(256,axiom,((! [A:code_integer,B:nat]: (((bit_se9216721137139052372nteger @ A @ B) = (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))) <= ((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6421_stable__imp__bit__iff__odd)). 159.59/70.64 thf(9030,plain,((! [A:code_integer,B:nat]: (((bit_se9216721137139052372nteger @ A @ B) = (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))) | ~ ((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 159.59/70.64 thf(5895,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/sandbox/benchmark/theBenchmark.p',fact_340_power__le__imp__le__exp)). 159.59/70.64 thf(28030,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)],[5895])). 159.59/70.64 thf(5493,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit1 @ A) @ (bit1 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5403_semiring__norm_I73_J)). 159.59/70.64 thf(26422,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)],[5493])). 159.59/70.64 thf(2662,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((plus_plus_int @ A @ (minus_minus_int @ B @ A)) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_le__add__diff__inverse)). 159.59/70.64 thf(16834,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((plus_plus_int @ A @ (minus_minus_int @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2662])). 159.59/70.64 thf(2125,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_le__add__diff__inverse)). 159.59/70.64 thf(15094,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => ((plus_plus_real @ A @ (minus_minus_real @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2125])). 159.59/70.64 thf(3874,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((arcsin @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (arcsin @ A))) <= (ord_less_eq_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7556_arcsin__minus)). 159.59/70.64 thf(20728,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => (((arcsin @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (arcsin @ A))) | ~ (ord_less_eq_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3874])). 159.59/70.64 thf(4746,axiom,(((bit_or_not_num_neg @ one @ one) = one)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6204_or__not__num__neg_Osimps_I1_J)). 159.59/70.64 thf(23638,plain,(((bit_or_not_num_neg @ one @ one) = one)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4746])). 159.59/70.64 thf(7513,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)) = zero_zero_int) <= (~ (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)) = (minus_minus_int @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat)))) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7775_sum__natinterval__diff)). 159.59/70.64 thf(34225,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)) = zero_zero_int) | (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)) = (minus_minus_int @ (C @ A) @ (C @ (plus_plus_nat @ B @ one_one_nat)))) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7513])). 159.59/70.64 thf(7991,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_less__not__refl3)). 159.59/70.64 thf(35789,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7991])). 159.59/70.64 thf(7182,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | (ord_less_num @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3254_linorder__le__less__linear)). 159.59/70.64 thf(33089,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | (ord_less_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7182])). 159.59/70.64 thf(7090,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/sandbox/benchmark/theBenchmark.p',fact_4808_mult__neg__numeral__simps_I2_J)). 159.59/70.64 thf(32704,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)],[7090])). 159.59/70.64 thf(1242,axiom,((neg_nu6511756317524482435omplex = (^ [A:complex]: (minus_minus_complex @ (plus_plus_complex @ A @ A) @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5734_dbl__dec__def)). 159.59/70.64 thf(12274,plain,(((neg_nu6511756317524482435omplex) = (^ [A:complex]: (minus_minus_complex @ (plus_plus_complex @ A @ A) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242])). 159.59/70.64 thf(1338,axiom,((! [A:real,B:real]: ((ord_less_real @ (arctan @ A) @ (arctan @ B)) = (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5883_arctan__less__iff)). 159.59/70.64 thf(12573,plain,((! [A:real,B:real]: ((ord_less_real @ (arctan @ A) @ (arctan @ B)) = (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338])). 159.59/70.64 thf(54,axiom,((cos_complex = (^ [A:complex]: (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (cos_coeff @ B) @ (power_power_complex @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9270_cos__def)). 159.59/70.64 thf(8413,plain,(((cos_complex) = (^ [A:complex]: (suminf_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (cos_coeff @ B) @ (power_power_complex @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 159.59/70.64 thf(1030,axiom,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_not__numeral__less__one)). 159.59/70.64 thf(11551,plain,((! [A:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030])). 159.59/70.64 thf(6066,axiom,((! [A:nat]: ((size_size_option_nat @ (some_nat @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2195_option_Osize_I4_J)). 159.59/70.64 thf(28648,plain,((! [A:nat]: ((size_size_option_nat @ (some_nat @ A)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6066])). 159.59/70.64 thf(6664,axiom,((! [A:nat]: ((bit_se2925701944663578781it_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4722_take__bit__0)). 159.59/70.64 thf(30829,plain,((! [A:nat]: ((bit_se2925701944663578781it_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6664])). 159.59/70.64 thf(2623,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/sandbox/benchmark/theBenchmark.p',fact_7966_sumr__diff__mult__const2)). 159.59/70.64 thf(16703,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)],[2623])). 159.59/70.64 thf(348,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1485227260804924795R_real @ A @ B) @ C) @ (plus_plus_real @ (real_V1485227260804924795R_real @ D @ B) @ E)) = (ord_less_eq_real @ (plus_plus_real @ (real_V1485227260804924795R_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9235_Real__Vector__Spaces_Ole__add__iff1)). 159.59/70.64 thf(9327,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1485227260804924795R_real @ A @ B) @ C) @ (plus_plus_real @ (real_V1485227260804924795R_real @ D @ B) @ E)) = (ord_less_eq_real @ (plus_plus_real @ (real_V1485227260804924795R_real @ (minus_minus_real @ A @ D) @ B) @ C) @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 159.59/70.64 thf(2521,axiom,((power_8040749407984259932d_enat = (^ [A:extended_enat,B:nat]: (if_Extended_enat @ (B = zero_zero_nat) @ one_on7984719198319812577d_enat @ (times_7803423173614009249d_enat @ A @ (power_8040749407984259932d_enat @ A @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2524_power__eq__if)). 159.59/70.64 thf(16366,plain,(((power_8040749407984259932d_enat) = (^ [A:extended_enat,B:nat]: (if_Extended_enat @ (B = zero_zero_nat) @ one_on7984719198319812577d_enat @ (times_7803423173614009249d_enat @ A @ (power_8040749407984259932d_enat @ A @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2521])). 159.59/70.64 thf(5916,axiom,((! [A:num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_numeral__le__one__iff)). 159.59/70.64 thf(28116,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)],[5916])). 159.59/70.64 thf(4684,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/sandbox/benchmark/theBenchmark.p',fact_4978_minus__diff__minus)). 159.59/70.64 thf(23448,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)],[4684])). 159.59/70.64 thf(2255,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2800_dual__order_Oasym)). 159.59/70.64 thf(15528,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2255])). 159.59/70.64 thf(8247,axiom,((? [A:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ summin) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062)). 159.59/70.64 thf(36769,plain,((? [A:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ summin) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8247])). 159.59/70.64 thf(7962,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/sandbox/benchmark/theBenchmark.p',fact_130_div__mult2__eq)). 159.59/70.64 thf(35701,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)],[7962])). 159.59/70.64 thf(4078,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/sandbox/benchmark/theBenchmark.p',fact_5230_real__add__le__0__iff)). 159.59/70.64 thf(21341,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)],[4078])). 159.59/70.64 thf(7399,axiom,((! [A:num]: ((ord_max_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1695_max__0__1_I4_J)). 159.59/70.64 thf(33829,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)],[7399])). 159.59/70.64 thf(7265,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/sandbox/benchmark/theBenchmark.p',fact_1272_diff__diff__eq)). 159.59/70.64 thf(33364,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)],[7265])). 159.59/70.64 thf(3959,axiom,((! [A:(real > $o),B:real]: ((? [C:real]: (A @ (times_times_real @ B @ C))) = (? [C:real]: ((A @ C) & (dvd_dvd_real @ B @ (plus_plus_real @ C @ zero_zero_real))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4301_unity__coeff__ex)). 159.59/70.64 thf(20992,plain,((! [A:(real > $o),B:real]: ((? [C:real]: (A @ (times_times_real @ B @ C))) = (? [C:real]: ((A @ C) & (dvd_dvd_real @ B @ (plus_plus_real @ C @ zero_zero_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3959])). 159.59/70.64 thf(5556,axiom,((! [A:nat,B:nat]: ((? [C:nat]: (A = (times_times_nat @ B @ C))) <= ((modulo_modulo_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3489_mod__eq__0D)). 159.59/70.64 thf(26619,plain,((! [A:nat,B:nat]: (? [C:nat]: (A = (times_times_nat @ B @ C)) | ~ ((modulo_modulo_nat @ A @ B) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5556])). 159.59/70.64 thf(4500,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/sandbox/benchmark/theBenchmark.p',fact_3464_power__mod)). 159.59/70.64 thf(22725,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)],[4500])). 159.59/70.64 thf(5710,axiom,((! [A:num]: ~ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1953_not__numeral__le__zero)). 159.59/70.64 thf(27157,plain,((! [A:num]: ~ (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5710])). 159.59/70.64 thf(7673,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => (((A @ B) <= (! [C:nat]: ((A @ C) => (A @ (plus_plus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))))) <= (A @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2523_nat__induct2)). 159.59/70.64 thf(34770,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ C) => (A @ (plus_plus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))))) | ~ (A @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7673])). 159.59/70.64 thf(5253,axiom,((! [A:nat,B:nat]: (((bit_se1148574629649215175it_nat @ (plus_plus_nat @ one_one_nat @ A) @ B) = ((B = zero_zero_nat) | (bit_se1148574629649215175it_nat @ A @ B))) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6451_even__bit__succ__iff)). 159.59/70.64 thf(25450,plain,((! [A:nat,B:nat]: (((bit_se1148574629649215175it_nat @ (plus_plus_nat @ one_one_nat @ A) @ B) = ((B = zero_zero_nat) | (bit_se1148574629649215175it_nat @ A @ B))) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5253])). 159.59/70.64 thf(672,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ one_one_real @ (powr_real @ A @ B))) <= (ord_less_eq_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7249_ge__one__powr__ge__zero)). 159.59/70.64 thf(10402,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ one_one_real @ (powr_real @ A @ B))) | ~ (ord_less_eq_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[672])). 159.59/70.64 thf(1364,axiom,((! [A:nat,B:nat]: (((modulo_modulo_int @ (semiri1406184849735516958ct_int @ B) @ (semiri1406184849735516958ct_int @ A)) = zero_zero_int) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8100_fact__mod)). 159.59/70.64 thf(12680,plain,((! [A:nat,B:nat]: (((modulo_modulo_int @ (semiri1406184849735516958ct_int @ B) @ (semiri1406184849735516958ct_int @ A)) = zero_zero_int) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364])). 159.59/70.64 thf(956,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (divide1717551699836669952omplex @ B @ C)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1382_times__divide__eq__right)). 159.59/70.64 thf(11310,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)],[956])). 159.59/70.64 thf(1059,axiom,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (((? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F))))) <= (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => ((C @ F) = (D @ F))))) <= (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4436_pinf_I2_J)). 159.59/70.64 thf(11643,plain,((! [A:(int > $o),B:(int > $o),C:(int > $o),D:(int > $o)]: (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F)))) | ~ (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => ((C @ F) = (D @ F)))) | ~ (? [E:int]: ! [F:int]: ((ord_less_int @ E @ F) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059])). 159.59/70.64 thf(3952,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/sandbox/benchmark/theBenchmark.p',fact_3557_divmod__digit__0_I2_J)). 159.59/70.64 thf(20968,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)],[3952])). 159.59/70.64 thf(2399,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/sandbox/benchmark/theBenchmark.p',fact_3381_mult__le__cancel__iff1)). 159.59/70.64 thf(15960,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)],[2399])). 159.59/70.64 thf(4149,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1236_comm__semiring__class_Odistrib)). 159.59/70.64 thf(21565,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4149])). 159.59/70.64 thf(7594,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/sandbox/benchmark/theBenchmark.p',fact_441_power4__eq__xxxx)). 159.59/70.64 thf(34541,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)],[7594])). 159.59/70.64 thf(4995,axiom,((! [A:vEBT_VEBT,B:nat]: (((~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT]: ((~ (((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))) & (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:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((C) <= (B = zero_zero_nat)) & ((B != zero_zero_nat) => ((B = one_one_nat) & ((B = one_one_nat) => (D))))))))) <= (vEBT_V5719532721284313246member @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2488_VEBT__internal_Onaive__member_Oelims_I2_J)). 159.59/70.64 thf(24531,plain,((! [A:vEBT_VEBT,B:nat]: (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT]: (~ (((vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))) | ~ (? [F:vEBT_VEBT]: (A = (vEBT_Node @ C @ (suc @ D) @ E @ F))))) | ~ (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((C) | ~ (B = zero_zero_nat)) & ((~ (B = zero_zero_nat)) => ((B = one_one_nat) & ((B = one_one_nat) => (D)))))))) | ~ (vEBT_V5719532721284313246member @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4995])). 159.59/70.64 thf(4609,axiom,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ A @ one_one_int) => (ord_less_int @ (power_power_int @ A @ (suc @ B)) @ one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2453_power__Suc__less__one)). 159.59/70.64 thf(23185,plain,((! [A:int,B:nat]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ A @ one_one_int) => (ord_less_int @ (power_power_int @ A @ (suc @ B)) @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4609])). 159.59/70.64 thf(7765,axiom,((! [A:$o]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (zero_n2687167440665602831ol_nat @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4369_odd__of__bool__self)). 159.59/70.64 thf(35086,plain,((! [A:$o]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (zero_n2687167440665602831ol_nat @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7765])). 159.59/70.64 thf(912,axiom,((! [A:int]: ((((cos_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = (uminus_uminus_real @ one_one_real)) <= (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) & ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((cos_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7016_cos__npi__int)). 159.59/70.64 thf(11173,plain,((! [A:int]: ((((cos_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = (uminus_uminus_real @ one_one_real)) | (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) & ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) => ((cos_real @ (times_times_real @ pi @ (ring_1_of_int_real @ A))) = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[912])). 159.59/70.64 thf(7376,axiom,((! [A:nat,B:real]: (((? [C:real]: (((power_power_real @ C @ A) = B) & (ord_less_real @ zero_zero_real @ C))) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3004_realpow__pos__nth)). 159.59/70.64 thf(33756,plain,((! [A:nat,B:real]: (? [C:real]: (((power_power_real @ C @ A) = B) & (ord_less_real @ zero_zero_real @ C)) | ~ (ord_less_real @ zero_zero_real @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7376])). 159.59/70.64 thf(6007,axiom,((! [A:nat]: ((binomial @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9019_choose__one)). 159.59/70.64 thf(28463,plain,((! [A:nat]: ((binomial @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6007])). 159.59/70.64 thf(8022,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4135_div2__even__ext__nat)). 159.59/70.64 thf(35885,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8022])). 159.59/70.64 thf(4979,axiom,(((abs_abs_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5487_abs__one)). 159.59/70.64 thf(24488,plain,(((abs_abs_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4979])). 159.59/70.64 thf(63,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/sandbox/benchmark/theBenchmark.p',fact_8321_gbinomial__rec)). 159.59/70.64 thf(8440,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)],[63])). 159.59/70.64 thf(2611,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ zero_zero_real @ B)) | ((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2143_zero__le__divide__iff)). 159.59/70.64 thf(16670,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ zero_zero_real @ B)) | ((ord_less_eq_real @ B @ zero_zero_real) & (ord_less_eq_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2611])). 159.59/70.64 thf(7220,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/sandbox/benchmark/theBenchmark.p',fact_7718_sum_Oub__add__nat)). 159.59/70.64 thf(33221,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)],[7220])). 159.59/70.64 thf(2413,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/sandbox/benchmark/theBenchmark.p',fact_7983_geometric__sum)). 159.59/70.64 thf(16005,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)],[2413])). 159.59/70.64 thf(2685,axiom,((! [A:(extended_enat > $o),B:(extended_enat > $o),C:(extended_enat > $o),D:(extended_enat > $o)]: (((? [E:extended_enat]: ! [F:extended_enat]: (((C @ F) = (D @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => (? [E:extended_enat]: ! [F:extended_enat]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) <= (ord_le72135733267957522d_enat @ E @ F)))) <= (? [E:extended_enat]: ! [F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4427_pinf_I1_J)). 159.59/70.64 thf(16904,plain,((! [A:(extended_enat > $o),B:(extended_enat > $o),C:(extended_enat > $o),D:(extended_enat > $o)]: (((? [E:extended_enat]: ! [F:extended_enat]: (((C @ F) = (D @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => (? [E:extended_enat]: ! [F:extended_enat]: ((((A @ F) & (C @ F)) = ((D @ F) & (B @ F))) | ~ (ord_le72135733267957522d_enat @ E @ F)))) | ~ (? [E:extended_enat]: ! [F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2685])). 159.59/70.64 thf(5648,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/sandbox/benchmark/theBenchmark.p',fact_5650_abs__square__le__1)). 159.59/70.64 thf(26928,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)],[5648])). 159.59/70.64 thf(926,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/sandbox/benchmark/theBenchmark.p',fact_4307_flip__bit__0)). 159.59/70.64 thf(11220,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)],[926])). 159.59/70.64 thf(4744,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/sandbox/benchmark/theBenchmark.p',fact_6355_bit__minus__numeral__int_I2_J)). 159.59/70.64 thf(23632,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)],[4744])). 159.59/70.64 thf(5265,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5406_abs__le__self__iff)). 159.59/70.64 thf(25486,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)],[5265])). 159.59/70.64 thf(4064,axiom,((arsinh_real = (^ [A:real]: (ln_ln_real @ (plus_plus_real @ A @ (sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6482_arsinh__real__def)). 159.59/70.64 thf(21296,plain,(((arsinh_real) = (^ [A:real]: (ln_ln_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)],[4064])). 159.59/70.64 thf(5669,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/sandbox/benchmark/theBenchmark.p',fact_575_Ex__less__Suc)). 159.59/70.64 thf(27013,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)],[5669])). 159.59/70.64 thf(6965,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) => ((ord_less_nat @ zero_zero_nat @ A) => (dvd_dvd_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4182_dvd__mult__cancel)). 159.59/70.64 thf(32099,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) => ((ord_less_nat @ zero_zero_nat @ A) => (dvd_dvd_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6965])). 159.59/70.64 thf(4050,axiom,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ A @ B)) = (dvd_dvd_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3791_dvd__add__triv__left__iff)). 159.59/70.64 thf(21254,plain,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ A @ B)) = (dvd_dvd_complex @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4050])). 159.59/70.64 thf(4095,axiom,((! [A:real,B:real]: ((A != B) => ((~ (ord_less_real @ A @ B)) => (ord_less_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1093_linorder__neqE__linordered__idom)). 159.59/70.64 thf(21392,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)],[4095])). 159.59/70.64 thf(7379,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_nat @ C @ one_one_nat) => (ord_less_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2455_power__strict__decreasing)). 159.59/70.64 thf(33766,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => ((ord_less_nat @ C @ one_one_nat) => (ord_less_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7379])). 159.59/70.64 thf(4466,axiom,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1252_comm__monoid__mult__class_Omult__1)). 159.59/70.64 thf(22612,plain,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4466])). 159.59/70.64 thf(4662,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/sandbox/benchmark/theBenchmark.p',fact_4183_nat__mult__dvd__cancel1)). 159.59/70.64 thf(23377,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)],[4662])). 159.59/70.64 thf(8127,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/sandbox/benchmark/theBenchmark.p',fact_4093_div__plus__div__distrib__dvd__right)). 159.59/70.64 thf(36234,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)],[8127])). 159.59/70.64 thf(6811,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/sandbox/benchmark/theBenchmark.p',fact_5330_power__minus1__odd)). 159.59/70.64 thf(31480,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)],[6811])). 159.59/70.64 thf(5697,axiom,((set_ord_atMost_nat = (^ [A:nat]: (set_nat2 @ (upt @ zero_zero_nat @ (suc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10139_atMost__upto)). 159.59/70.64 thf(27117,plain,(((set_ord_atMost_nat) = (^ [A:nat]: (set_nat2 @ (upt @ zero_zero_nat @ (suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5697])). 159.59/70.64 thf(5897,axiom,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1500_mult__zero__left)). 159.59/70.64 thf(28035,plain,((! [A:int]: ((times_times_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5897])). 159.59/70.64 thf(3252,axiom,((! [A:real]: ((ord_less_real @ (arctan @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5793_arctan__less__zero__iff)). 159.59/70.64 thf(18712,plain,((! [A:real]: ((ord_less_real @ (arctan @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3252])). 159.59/70.64 thf(2150,axiom,((set_ord_lessThan_nat = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7899_lessThan__def)). 159.59/70.64 thf(15188,plain,(((set_ord_lessThan_nat) = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2150])). 159.59/70.64 thf(1642,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ A @ (set_ord_atMost_nat @ B)) = (plus_plus_complex @ (A @ zero_zero_nat) @ (groups2073611262835488442omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8836_sum_OatMost__shift)). 159.59/70.64 thf(13578,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (A) @ (set_ord_atMost_nat @ B)) = (plus_plus_complex @ (A @ zero_zero_nat) @ (groups2073611262835488442omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642])). 159.59/70.64 thf(1882,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/sandbox/benchmark/theBenchmark.p',fact_6938_norm__triangle__ineq4)). 159.59/70.64 thf(14329,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)],[1882])). 159.59/70.64 thf(1263,axiom,((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2320_zero__less__two)). 159.59/70.64 thf(12336,plain,((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263])). 159.59/70.64 thf(2238,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/sandbox/benchmark/theBenchmark.p',fact_474_real__divide__square__eq)). 159.59/70.64 thf(15475,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)],[2238])). 159.59/70.64 thf(437,axiom,((! [A:num]: ~ (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5146_not__zero__less__neg__numeral)). 159.59/70.64 thf(9619,plain,((! [A:num]: ~ (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[437])). 159.59/70.64 thf(295,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ A @ (ord_max_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_max_Ostrict__coboundedI1)). 159.59/70.64 thf(9143,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ A @ (ord_max_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 159.59/70.64 thf(2292,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_top_real @ C) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9952_filterlim__pow__at__bot__even)). 159.59/70.64 thf(15635,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_top_real @ C) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2292])). 159.59/70.64 thf(2857,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((~ (member_nat @ zero_zero_nat @ A)) => (((groups6591440286371151544t_real @ B @ A) = (groups6591440286371151544t_real @ C @ A)) <= (! [D:nat]: (((B @ (suc @ D)) = (C @ (suc @ D))) <= (member_nat @ (suc @ D) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7449_sum__cong__Suc)). 159.59/70.64 thf(17444,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((~ (member_nat @ zero_zero_nat @ A)) => (((groups6591440286371151544t_real @ (B) @ A) = (groups6591440286371151544t_real @ (C) @ A)) | ~ (! [D:nat]: (((B @ (suc @ D)) = (C @ (suc @ D))) | ~ (member_nat @ (suc @ D) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2857])). 159.59/70.64 thf(5020,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/sandbox/benchmark/theBenchmark.p',fact_4145_dvd__div__iff__mult)). 159.59/70.64 thf(24625,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)],[5020])). 159.59/70.64 thf(2624,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/sandbox/benchmark/theBenchmark.p',fact_6926_norm__triangle__le)). 159.59/70.64 thf(16706,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)],[2624])). 159.59/70.64 thf(6563,axiom,((! [A:complex,B:complex,C:nat]: (((times_times_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C)) = one_one_complex) <= ((times_times_complex @ A @ B) = one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_left__right__inverse__power)). 159.59/70.64 thf(30469,plain,((! [A:complex,B:complex,C:nat]: (((times_times_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C)) = one_one_complex) | ~ ((times_times_complex @ A @ B) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6563])). 159.59/70.64 thf(4883,axiom,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (root @ A @ B) @ (root @ A @ C))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9508_real__root__le__mono)). 159.59/70.64 thf(24132,plain,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ (root @ A @ B) @ (root @ A @ C))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4883])). 159.59/70.64 thf(6355,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/sandbox/benchmark/theBenchmark.p',fact_2479_div__geq)). 159.59/70.64 thf(29658,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)],[6355])). 159.59/70.64 thf(1944,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1129_add_Oright__cancel)). 159.59/70.64 thf(14525,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)],[1944])). 159.59/70.64 thf(2578,axiom,((! [A:complex,B:complex,C:complex]: (((B = (divide1717551699836669952omplex @ C @ A)) = ((times_times_complex @ B @ A) = C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2167_nonzero__eq__divide__eq)). 159.59/70.64 thf(16538,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)],[2578])). 159.59/70.64 thf(7490,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/sandbox/benchmark/theBenchmark.p',fact_6596_numeral__power__eq__of__nat__cancel__iff)). 159.59/70.64 thf(34158,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)],[7490])). 159.59/70.64 thf(5507,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1557_less__nat__zero__code)). 159.59/70.64 thf(26480,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5507])). 159.59/70.64 thf(392,axiom,((sinh_real = (^ [A:real]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (numeral_numeral_real @ (bit0 @ one))) @ (minus_minus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9368_sinh__def)). 159.59/70.64 thf(9478,plain,(((sinh_real) = (^ [A:real]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (numeral_numeral_real @ (bit0 @ one))) @ (minus_minus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[392])). 159.59/70.64 thf(4200,axiom,((! [A:int,B:int]: ((ord_less_int @ (uminus_uminus_int @ A) @ B) = (ord_less_int @ (uminus_uminus_int @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4936_minus__less__iff)). 159.59/70.64 thf(21718,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)],[4200])). 159.59/70.64 thf(1763,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/sandbox/benchmark/theBenchmark.p',fact_7848_monoI1)). 159.59/70.64 thf(13944,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)],[1763])). 159.59/70.64 thf(1894,axiom,((! [A:(nat > real),B:real,C:(nat > real),D:real]: (((sums_real @ (^ [E:nat]: (plus_plus_real @ (A @ E) @ (C @ E))) @ (plus_plus_real @ B @ D)) <= (sums_real @ C @ D)) <= (sums_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7891_sums__add)). 159.59/70.64 thf(14370,plain,((! [A:(nat > real),B:real,C:(nat > real),D:real]: ((sums_real @ (^ [E:nat]: (plus_plus_real @ (A @ E) @ (C @ E))) @ (plus_plus_real @ B @ D)) | ~ (sums_real @ (C) @ D) | ~ (sums_real @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1894])). 159.59/70.64 thf(2679,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/sandbox/benchmark/theBenchmark.p',fact_4116_power__le__dvd)). 159.59/70.64 thf(16887,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)],[2679])). 159.59/70.64 thf(6808,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((((ord_less_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) <= ((modulo_modulo_nat @ B @ C) = zero_zero_nat)) <= ((modulo_modulo_nat @ A @ C) = zero_zero_nat)) <= (ord_less_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3586_div__less__mono)). 159.59/70.64 thf(31470,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) | ~ ((modulo_modulo_nat @ B @ C) = zero_zero_nat) | ~ ((modulo_modulo_nat @ A @ C) = zero_zero_nat) | ~ (ord_less_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6808])). 159.59/70.64 thf(4802,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_not__less__eq__eq)). 159.59/70.64 thf(23834,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)],[4802])). 159.59/70.64 thf(110,axiom,(((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = zero_z3403309356797280102nteger)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4748_diff__numeral__special_I12_J)). 159.59/70.64 thf(8588,plain,(((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = zero_z3403309356797280102nteger)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 159.59/70.64 thf(640,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((plus_plus_complex @ (times_times_complex @ A @ B) @ (plus_plus_complex @ (times_times_complex @ C @ B) @ D)) = (plus_plus_complex @ (times_times_complex @ (plus_plus_complex @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1224_combine__common__factor)). 159.59/70.64 thf(10301,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((plus_plus_complex @ (times_times_complex @ A @ B) @ (plus_plus_complex @ (times_times_complex @ C @ B) @ D)) = (plus_plus_complex @ (times_times_complex @ (plus_plus_complex @ A @ C) @ B) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[640])). 159.59/70.64 thf(5139,axiom,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (bit0 @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_semiring__norm_I13_J)). 159.59/70.64 thf(25032,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)],[5139])). 159.59/70.64 thf(6676,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/sandbox/benchmark/theBenchmark.p',fact_4827_divide__le__eq__numeral1_I2_J)). 159.59/70.64 thf(30874,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)],[6676])). 159.59/70.64 thf(6630,axiom,((! [A:nat,B:nat,C:(nat > num),D:num]: ((((! [E:nat,F:nat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2649_ord__le__eq__subst)). 159.59/70.64 thf(30704,plain,((! [A:nat,B:nat,C:(nat > num),D:num]: (((! [E:nat,F:nat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_num @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6630])). 159.59/70.64 thf(7343,axiom,((! [A:nat,B:code_integer]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (power_8256067586552552935nteger @ B @ A)) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4869_Parity_Oring__1__class_Opower__minus__even)). 159.59/70.64 thf(33645,plain,((! [A:nat,B:code_integer]: (((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (power_8256067586552552935nteger @ B @ A)) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7343])). 159.59/70.64 thf(6837,axiom,((! [A:num,B:num,C:(num > int),D:int]: (((ord_less_eq_int @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F)))) => (ord_less_eq_int @ (C @ A) @ D))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2676_order__subst2)). 159.59/70.64 thf(31567,plain,((! [A:num,B:num,C:(num > int),D:int]: (((ord_less_eq_int @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F)))) => (ord_less_eq_int @ (C @ A) @ D))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6837])). 159.59/70.64 thf(3900,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => ((dvd_dvd_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (dvd_dvd_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3823_dvd__times__right__cancel__iff)). 159.59/70.64 thf(20805,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => ((dvd_dvd_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (dvd_dvd_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3900])). 159.59/70.64 thf(8044,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/sandbox/benchmark/theBenchmark.p',fact_3492_nat__mod__eq__iff)). 159.59/70.64 thf(35967,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)],[8044])). 159.59/70.64 thf(3715,axiom,((! [A:num]: ((real_V7735802525324610683m_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6889_norm__neg__numeral)). 159.59/70.64 thf(20201,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)],[3715])). 159.59/70.64 thf(5617,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5951_and__zero__eq)). 159.59/70.64 thf(26837,plain,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5617])). 159.59/70.64 thf(5736,axiom,((! [A:num]: ((suc @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_Suc__numeral)). 159.59/70.64 thf(27246,plain,((! [A:num]: ((suc @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5736])). 159.59/70.64 thf(5430,axiom,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_less__numeral__extra_I4_J)). 159.59/70.64 thf(26200,plain,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5430])). 159.59/70.64 thf(1841,axiom,((! [A:nat,B:nat,C:nat]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6611_of__nat__power__less__of__nat__cancel__iff)). 159.59/70.64 thf(14207,plain,((! [A:nat,B:nat,C:nat]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1841])). 159.59/70.64 thf(2786,axiom,((! [A:num]: ((ring_1_of_int_real @ (numeral_numeral_int @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5762_of__int__numeral)). 159.59/70.64 thf(17223,plain,((! [A:num]: ((ring_1_of_int_real @ (numeral_numeral_int @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2786])). 159.59/70.64 thf(6018,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/sandbox/benchmark/theBenchmark.p',fact_2492_vebt__pred_Osimps_I5_J)). 159.59/70.64 thf(28496,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)],[6018])). 159.59/70.64 thf(7715,axiom,((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2472_pos2)). 159.59/70.64 thf(34922,plain,((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7715])). 159.59/70.64 thf(7076,axiom,((! [A:int,B:nat,C:int]: (((((ord_less_nat @ zero_zero_nat @ B) => (A = C)) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_eq_int @ zero_zero_int @ A)) <= ((power_power_int @ A @ B) = (power_power_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1930_power__eq__imp__eq__base)). 159.59/70.64 thf(32634,plain,((! [A:int,B:nat,C:int]: (((ord_less_nat @ zero_zero_nat @ B) => (A = C)) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_eq_int @ zero_zero_int @ A) | ~ ((power_power_int @ A @ B) = (power_power_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7076])). 159.59/70.64 thf(3940,axiom,((! [A:real,B:real]: (((inverse_inverse_real @ A) = B) <= ((times_times_real @ A @ B) = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9037_inverse__unique)). 159.59/70.64 thf(20924,plain,((! [A:real,B:real]: (((inverse_inverse_real @ A) = B) | ~ ((times_times_real @ A @ B) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3940])). 159.59/70.64 thf(2276,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = one_one_complex) = ((B != zero_zero_complex) & (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1675_divide__eq__1__iff)). 159.59/70.64 thf(15588,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = one_one_complex) = (~ (B = zero_zero_complex) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2276])). 159.59/70.64 thf(7236,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1898_old_Onat_Odistinct_I2_J)). 159.59/70.64 thf(33275,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7236])). 159.59/70.64 thf(2016,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3152_dual__order_Ostrict__implies__order)). 159.59/70.64 thf(14768,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2016])). 159.59/70.64 thf(2564,axiom,((! [A:set_nat]: ((ord_less_eq_nat @ (finite_card_nat @ A) @ (suc @ (lattic8265883725875713057ax_nat @ A))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10195_card__le__Suc__Max)). 159.59/70.64 thf(16493,plain,((! [A:set_nat]: ((ord_less_eq_nat @ (finite_card_nat @ A) @ (suc @ (lattic8265883725875713057ax_nat @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2564])). 159.59/70.64 thf(2053,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/sandbox/benchmark/theBenchmark.p',fact_6948_norm__diff__triangle__ineq)). 159.59/70.64 thf(14876,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)],[2053])). 159.59/70.64 thf(1921,axiom,((! [A:complex]: ((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)))) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6877_exp__bound__lemma)). 159.59/70.64 thf(14453,plain,((! [A:complex]: ((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)))) | ~ (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)],[1921])). 159.59/70.64 thf(3055,axiom,((! [A:real]: (((divide_divide_real @ A @ A) = one_one_real) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1660_div__self)). 159.59/70.64 thf(18071,plain,((! [A:real]: (((divide_divide_real @ A @ A) = one_one_real) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3055])). 159.59/70.64 thf(6531,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]: ((ord_less_num @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:num]: ! [F:num]: ((((C @ F) & (A @ F)) = ((B @ F) & (D @ F))) <= (ord_less_num @ F @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4459_minf_I1_J)). 159.59/70.64 thf(30361,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]: ((ord_less_num @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:num]: ! [F:num]: ((((C @ F) & (A @ F)) = ((B @ F) & (D @ F))) | ~ (ord_less_num @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6531])). 159.59/70.64 thf(7939,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4470_minf_I3_J)). 159.59/70.64 thf(35626,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7939])). 159.59/70.64 thf(5101,axiom,((! [A:nat,B:nat,C:(nat > real)]: (((groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (times_times_real @ (C @ (suc @ B)) @ (groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8737_prod_Onat__ivl__Suc_H)). 159.59/70.64 thf(24915,plain,((! [A:nat,B:nat,C:(nat > real)]: (((groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ (suc @ B))) = (times_times_real @ (C @ (suc @ B)) @ (groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ B)))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5101])). 159.59/70.64 thf(3753,axiom,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = zero_zero_int) = (dvd_dvd_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5302_take__bit__eq__0__iff)). 159.59/70.64 thf(20323,plain,((! [A:nat,B:int]: (((bit_se2923211474154528505it_int @ A @ B) = zero_zero_int) = (dvd_dvd_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3753])). 159.59/70.64 thf(5202,axiom,((! [A:nat]: (((semiri1408675320244567234ct_nat @ A) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ A @ one_one_nat)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8129_fact__reduce)). 159.59/70.64 thf(25280,plain,((! [A:nat]: (((semiri1408675320244567234ct_nat @ A) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ A @ one_one_nat)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5202])). 159.59/70.64 thf(6297,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((modulo_modulo_nat @ B @ A) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4179_unit__imp__mod__eq__0)). 159.59/70.64 thf(29482,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)],[6297])). 159.59/70.64 thf(6885,axiom,((! [A:int,B:nat]: (((ord_less_int @ A @ one_one_int) => (ord_less_int @ (times_times_int @ A @ (power_power_int @ A @ B)) @ (power_power_int @ A @ B))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2446_power__Suc__less)). 159.59/70.64 thf(31809,plain,((! [A:int,B:nat]: (((ord_less_int @ A @ one_one_int) => (ord_less_int @ (times_times_int @ A @ (power_power_int @ A @ B)) @ (power_power_int @ A @ B))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6885])). 159.59/70.64 thf(8118,axiom,((! [A:nat]: (((plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ one_one_nat) = A) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3914_odd__two__times__div__two__succ)). 159.59/70.64 thf(36199,plain,((! [A:nat]: (((plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) @ one_one_nat) = A) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8118])). 159.59/70.64 thf(7166,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/sandbox/benchmark/theBenchmark.p',fact_5834_numeral__power__eq__of__int__cancel__iff)). 159.59/70.64 thf(33011,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)],[7166])). 159.59/70.64 thf(3537,axiom,((! [A:real,B:int]: (((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)) <= (ord_less_real @ (minus_minus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (ring_1_of_int_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6146_round__unique)). 159.59/70.64 thf(19602,plain,((! [A:real,B:int]: (((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)) | ~ (ord_less_real @ (minus_minus_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) @ (ring_1_of_int_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3537])). 159.59/70.64 thf(184,axiom,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (real_V1485227260804924795R_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (real_V7735802525324610683m_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9201_norm__scaleR)). 159.59/70.64 thf(8821,plain,((! [A:real,B:real]: ((real_V7735802525324610683m_real @ (real_V1485227260804924795R_real @ A @ B)) = (times_times_real @ (abs_abs_real @ A) @ (real_V7735802525324610683m_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 159.59/70.64 thf(4945,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ C @ (suc @ (minus_minus_nat @ B @ A))) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_diff__Suc__diff__eq1)). 159.59/70.64 thf(24332,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ C @ (suc @ (minus_minus_nat @ B @ A))) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4945])). 159.59/70.64 thf(6087,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/sandbox/benchmark/theBenchmark.p',fact_7189_cos__one__2pi)). 159.59/70.64 thf(28711,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)],[6087])). 159.59/70.64 thf(2643,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/sandbox/benchmark/theBenchmark.p',fact_7012_cos__int__2pin)). 159.59/70.64 thf(16770,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)],[2643])). 159.59/70.64 thf(517,axiom,((! [A:complex,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (gbinomial_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ C)) @ C)) @ (set_ord_atMost_nat @ B)) = (gbinomial_complex @ (plus_plus_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8845_gbinomial__parallel__sum)). 159.59/70.64 thf(9899,plain,((! [A:complex,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (gbinomial_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ C)) @ C)) @ (set_ord_atMost_nat @ B)) = (gbinomial_complex @ (plus_plus_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ one_one_complex) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[517])). 159.59/70.64 thf(1816,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/sandbox/benchmark/theBenchmark.p',fact_306_power__gt1__lemma)). 159.59/70.64 thf(14115,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)],[1816])). 159.59/70.64 thf(7533,axiom,((! [A:num]: ((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ A)) = (uminus_uminus_real @ (numeral_numeral_real @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5705_diff__numeral__special_I5_J)). 159.59/70.64 thf(34289,plain,((! [A:num]: ((minus_minus_real @ (uminus_uminus_real @ one_one_real) @ (numeral_numeral_real @ A)) = (uminus_uminus_real @ (numeral_numeral_real @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7533])). 159.59/70.64 thf(8012,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/sandbox/benchmark/theBenchmark.p',fact_3551_unset__bit__Suc)). 159.59/70.64 thf(35853,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)],[8012])). 159.59/70.64 thf(4308,axiom,((! [A:nat]: ((one_one_complex = (semiri8010041392384452111omplex @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6548_of__nat__1__eq__iff)). 159.59/70.64 thf(22067,plain,((! [A:nat]: ((one_one_complex = (semiri8010041392384452111omplex @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4308])). 159.59/70.64 thf(2937,axiom,((! [A:nat]: (ord_less_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ A))) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6852_negative__zless__0)). 159.59/70.64 thf(17708,plain,((! [A:nat]: (ord_less_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ A))) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2937])). 159.59/70.64 thf(711,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ A @ C) @ (times_7803423173614009249d_enat @ B @ C)) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C)) <= (ord_le2932123472753598470d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1982_mult__right__mono)). 159.59/70.64 thf(10544,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ A @ C) @ (times_7803423173614009249d_enat @ B @ C)) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C) | ~ (ord_le2932123472753598470d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[711])). 159.59/70.64 thf(1304,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/sandbox/benchmark/theBenchmark.p',fact_296_power__one__over)). 159.59/70.64 thf(12465,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)],[1304])). 159.59/70.64 thf(3903,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/sandbox/benchmark/theBenchmark.p',fact_8294_pochhammer__product_H)). 159.59/70.64 thf(20815,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)],[3903])). 159.59/70.64 thf(784,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((cosh_real @ (ln_ln_real @ A)) = (divide_divide_real @ (plus_plus_real @ A @ (inverse_inverse_real @ A)) @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9367_cosh__ln__real)). 159.59/70.64 thf(10782,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((cosh_real @ (ln_ln_real @ A)) = (divide_divide_real @ (plus_plus_real @ A @ (inverse_inverse_real @ A)) @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[784])). 159.59/70.64 thf(7071,axiom,((! [A:nat,B:int]: (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = zero_zero_int) => (~ (bit_se1146084159140164899it_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6416_exp__eq__0__imp__not__bit)). 159.59/70.64 thf(32617,plain,((! [A:nat,B:int]: (((power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = zero_zero_int) => (~ (bit_se1146084159140164899it_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7071])). 159.59/70.64 thf(1270,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ one_on7984719198319812577d_enat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1246_mult_Ocomm__neutral)). 159.59/70.64 thf(12358,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ one_on7984719198319812577d_enat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270])). 159.59/70.64 thf(3422,axiom,((! [A:num]: ((neg_nu8804712462038260780nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (uminus1351360451143612070nteger @ (neg_nu8804712462038260780nteger @ (numera6620942414471956472nteger @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4736_dbl__simps_I1_J)). 159.59/70.64 thf(19257,plain,((! [A:num]: ((neg_nu8804712462038260780nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))) = (uminus1351360451143612070nteger @ (neg_nu8804712462038260780nteger @ (numera6620942414471956472nteger @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3422])). 159.59/70.64 thf(4104,axiom,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2715_dual__order_Oeq__iff)). 159.59/70.64 thf(21420,plain,((((=) @ set_nat) = (^ [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ B @ A) & (ord_less_eq_set_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4104])). 159.59/70.64 thf(1566,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/sandbox/benchmark/theBenchmark.p',fact_3441_mod__mult__right__eq)). 159.59/70.64 thf(13339,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)],[1566])). 159.59/70.64 thf(1672,axiom,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1878_add_Ocomm__neutral)). 159.59/70.64 thf(13666,plain,((! [A:real]: ((plus_plus_real @ A @ zero_zero_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1672])). 159.59/70.64 thf(2391,axiom,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1547_bits__div__0)). 159.59/70.64 thf(15933,plain,((! [A:int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2391])). 159.59/70.64 thf(1333,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2924_order__less__imp__not__eq)). 159.59/70.64 thf(12556,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333])). 159.59/70.64 thf(2224,axiom,((! [A:real,B:(num > real),C:num,D:num]: (((ord_less_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D)))) <= (ord_less_eq_real @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3217_order__le__less__subst1)). 159.59/70.64 thf(15432,plain,((! [A:real,B:(num > real),C:num,D:num]: (((ord_less_num @ C @ D) => ((! [E:num,F:num]: ((ord_less_num @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) => (ord_less_real @ A @ (B @ D)))) | ~ (ord_less_eq_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2224])). 159.59/70.64 thf(3384,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/sandbox/benchmark/theBenchmark.p',fact_2436_divide__le__eq)). 159.59/70.64 thf(19125,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)],[3384])). 159.59/70.64 thf(4890,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/sandbox/benchmark/theBenchmark.p',fact_6953_norm__power__diff)). 159.59/70.64 thf(24154,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)],[4890])). 159.59/70.64 thf(7314,axiom,((one_one_nat = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9638_one__natural_Orsp)). 159.59/70.64 thf(33551,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7314])). 159.59/70.64 thf(4818,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((B @ D) != one_one_complex) & (member_nat @ D @ A))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((times_times_complex @ (B @ D) @ (C @ D)) != one_one_complex) & (member_nat @ D @ A))))) <= (finite_finite_nat @ (collect_nat @ (^ [D:nat]: (((C @ D) != one_one_complex) & (member_nat @ D @ A))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3726_prod_Ofinite__Collect__op)). 159.59/70.64 thf(23926,plain,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((B @ D) = one_one_complex) & (member_nat @ D @ A))))) => ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((times_times_complex @ (B @ D) @ (C @ D)) = one_one_complex) & (member_nat @ D @ A))))) | ~ (finite_finite_nat @ (collect_nat @ (^ [D:nat]: (~ ((C @ D) = one_one_complex) & (member_nat @ D @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4818])). 159.59/70.64 thf(3575,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/sandbox/benchmark/theBenchmark.p',fact_5924_even__of__int__iff)). 159.59/70.64 thf(19734,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)],[3575])). 159.59/70.64 thf(5549,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1966_mult__nonneg__nonpos2)). 159.59/70.64 thf(26601,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5549])). 159.59/70.64 thf(7078,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_le__trans)). 159.59/70.64 thf(32640,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7078])). 159.59/70.64 thf(3875,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/sandbox/benchmark/theBenchmark.p',fact_5844_of__int__less__of__int__power__cancel__iff)). 159.59/70.64 thf(20731,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)],[3875])). 159.59/70.64 thf(4615,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) => ((groups3539618377306564664at_int @ (^ [E:nat]: (if_int @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_int @ (E = B) @ zero_zero_int @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups3539618377306564664at_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/sandbox/benchmark/theBenchmark.p',fact_8938_sum_Ozero__middle)). 159.59/70.64 thf(23202,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) => ((groups3539618377306564664at_int @ (^ [E:nat]: (if_int @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_int @ (E = B) @ zero_zero_int @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups3539618377306564664at_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)],[4615])). 159.59/70.64 thf(4968,axiom,((! [A:real,B:real]: (((sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = A) => (B = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6442_real__sqrt__sum__squares__eq__cancel)). 159.59/70.64 thf(24456,plain,((! [A:real,B:real]: (((sqrt @ (plus_plus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))))) = A) => (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4968])). 159.59/70.64 thf(7095,axiom,((! [A:list_VEBT_VEBT,B:list_int]: ((size_s3661962791536183091BT_int @ (produc7292646706713671643BT_int @ A @ B)) = (times_times_nat @ (size_s6755466524823107622T_VEBT @ A) @ (size_size_list_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3625_length__product)). 159.59/70.64 thf(32720,plain,((! [A:list_VEBT_VEBT,B:list_int]: ((size_s3661962791536183091BT_int @ (produc7292646706713671643BT_int @ A @ B)) = (times_times_nat @ (size_s6755466524823107622T_VEBT @ A) @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7095])). 159.59/70.64 thf(5776,axiom,((! [A:nat,B:real,C:real]: (((ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) <= (ord_less_eq_real @ B @ C)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4234_power__mono__odd)). 159.59/70.64 thf(27377,plain,((! [A:nat,B:real,C:real]: ((ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) | ~ (ord_less_eq_real @ B @ C) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5776])). 159.59/70.64 thf(5723,axiom,((! [A:num]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ one_one_complex)) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4751_numeral__eq__neg__one__iff)). 159.59/70.64 thf(27203,plain,((! [A:num]: (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) = (uminus1482373934393186551omplex @ one_one_complex)) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5723])). 159.59/70.64 thf(1489,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => ((arcosh_real @ A) = (ln_ln_real @ (plus_plus_real @ A @ (sqrt @ (minus_minus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6478_arcosh__real__def)). 159.59/70.64 thf(13112,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ A) => ((arcosh_real @ A) = (ln_ln_real @ (plus_plus_real @ A @ (sqrt @ (minus_minus_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1489])). 159.59/70.64 thf(8109,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/sandbox/benchmark/theBenchmark.p',fact_5451_abs__power2)). 159.59/70.64 thf(36174,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)],[8109])). 159.59/70.64 thf(4933,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1507_zero__eq__add__iff__both__eq__0)). 159.59/70.64 thf(24299,plain,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4933])). 159.59/70.64 thf(6645,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/sandbox/benchmark/theBenchmark.p',fact_5865_of__int__le__neg__numeral__power__cancel__iff)). 159.59/70.64 thf(30769,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)],[6645])). 159.59/70.64 thf(3340,axiom,(((arccos @ zero_zero_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7370_arccos__0)). 159.59/70.64 thf(18993,plain,(((arccos @ zero_zero_real) = (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3340])). 159.59/70.64 thf(978,axiom,((! [A:nat]: ((ring_1_of_int_int @ (bit_se2000444600071755411sk_int @ A)) = (bit_se2000444600071755411sk_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6034_of__int__mask__eq)). 159.59/70.64 thf(11380,plain,((! [A:nat]: ((ring_1_of_int_int @ (bit_se2000444600071755411sk_int @ A)) = (bit_se2000444600071755411sk_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[978])). 159.59/70.64 thf(4086,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/sandbox/benchmark/theBenchmark.p',fact_1170_add__left__mono)). 159.59/70.64 thf(21365,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)],[4086])). 159.59/70.64 thf(3854,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (((ord_less_int @ A @ C) <= (ord_less_eq_int @ zero_zero_int @ B)) & ((ord_less_int @ C @ A) <= (ord_less_eq_int @ B @ zero_zero_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2238_mult__less__cancel__right)). 159.59/70.64 thf(20660,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = (((ord_less_int @ A @ C) | ~ (ord_less_eq_int @ zero_zero_int @ B)) & ((ord_less_int @ C @ A) | ~ (ord_less_eq_int @ B @ zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3854])). 159.59/70.64 thf(5016,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_eq_real @ (times_times_real @ B @ A) @ A) <= (ord_less_eq_real @ B @ one_one_real)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2298_mult__left__le__one__le)). 159.59/70.64 thf(24611,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (times_times_real @ B @ A) @ A) | ~ (ord_less_eq_real @ B @ one_one_real) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5016])). 159.59/70.64 thf(4767,axiom,((! [A:num]: ((archim8280529875227126926d_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6182_round__neg__numeral)). 159.59/70.64 thf(23734,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)],[4767])). 159.59/70.64 thf(3399,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/sandbox/benchmark/theBenchmark.p',fact_1378_square__diff__one__factored)). 159.59/70.64 thf(19179,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)],[3399])). 159.59/70.64 thf(5901,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/sandbox/benchmark/theBenchmark.p',fact_8157_sin__coeff__def)). 159.59/70.64 thf(28052,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)],[5901])). 159.59/70.64 thf(5931,axiom,((! [A:real]: ((archim6058952711729229775r_real @ (minus_minus_real @ A @ one_one_real)) = (minus_minus_int @ (archim6058952711729229775r_real @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8195_floor__diff__one)). 159.59/70.64 thf(28163,plain,((! [A:real]: ((archim6058952711729229775r_real @ (minus_minus_real @ A @ one_one_real)) = (minus_minus_int @ (archim6058952711729229775r_real @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5931])). 159.59/70.64 thf(5763,axiom,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ A) @ B) = (times_3573771949741848930nteger @ A @ (uminus1351360451143612070nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4955_minus__mult__commute)). 159.59/70.64 thf(27335,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)],[5763])). 159.59/70.64 thf(7248,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/sandbox/benchmark/theBenchmark.p',fact_4899_neg__one__odd__power)). 159.59/70.64 thf(33317,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)],[7248])). 159.59/70.64 thf(7826,axiom,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_semiring__norm_I87_J)). 159.59/70.64 thf(35276,plain,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7826])). 159.59/70.64 thf(7646,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))) = (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) = zero_zero_nat) | ((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)))) & (ord_less_eq_nat @ B @ C)) | (ord_less_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4275_even__mult__exp__div__exp__iff)). 159.59/70.64 thf(34692,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))) = (((power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) = zero_zero_nat) | ((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)))) & (ord_less_eq_nat @ B @ C)) | (ord_less_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7646])). 159.59/70.64 thf(1983,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/sandbox/benchmark/theBenchmark.p',fact_6860_sin__gt__zero2)). 159.59/70.64 thf(14660,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)],[1983])). 159.59/70.64 thf(523,axiom,(((ord_max_int @ one_one_int @ zero_zero_int) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1713_max__0__1_I2_J)). 159.59/70.64 thf(9916,plain,(((ord_max_int @ one_one_int @ zero_zero_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[523])). 159.59/70.64 thf(306,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (real_V1485227260804924795R_real @ B @ C)) = (real_V1485227260804924795R_real @ B @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9185_mult__scaleR__right)). 159.59/70.64 thf(9197,plain,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (real_V1485227260804924795R_real @ B @ C)) = (real_V1485227260804924795R_real @ B @ (times_times_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[306])). 159.59/70.64 thf(3486,axiom,((! [A:num]: ((numeral_numeral_int @ (bit0 @ A)) = (plus_plus_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1428_numeral__code_I2_J)). 159.59/70.64 thf(19448,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)],[3486])). 159.59/70.64 thf(2818,axiom,((! [A:option_nat,B:option_nat]: ((if_option_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T)). 159.59/70.64 thf(17313,plain,((! [A:option_nat,B:option_nat]: ((if_option_nat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2818])). 159.59/70.64 thf(4583,axiom,((! [A:(int > $o),B:int]: (((((! [C:int]: (((A @ (plus_plus_int @ one_one_int @ (times_times_int @ C @ (numeral_numeral_int @ (bit0 @ one))))) <= (C != (uminus_uminus_int @ one_one_int))) <= (A @ C))) => (A @ B)) <= (! [C:int]: ((A @ C) => ((C != zero_zero_int) => (A @ (times_times_int @ C @ (numeral_numeral_int @ (bit0 @ one)))))))) <= (A @ (uminus_uminus_int @ one_one_int))) <= (A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5335_int__bit__induct)). 159.59/70.64 thf(23062,plain,((! [A:(int > $o),B:int]: (((! [C:int]: ((A @ (plus_plus_int @ one_one_int @ (times_times_int @ C @ (numeral_numeral_int @ (bit0 @ one))))) | (C = (uminus_uminus_int @ one_one_int)) | ~ (A @ C))) => (A @ B)) | ~ (! [C:int]: ((A @ C) => ((~ (C = zero_zero_int)) => (A @ (times_times_int @ C @ (numeral_numeral_int @ (bit0 @ one))))))) | ~ (A @ (uminus_uminus_int @ one_one_int)) | ~ (A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4583])). 159.59/70.64 thf(8193,axiom,((! [A:complex]: ((power_power_complex @ (csqrt @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9376_power2__csqrt)). 159.59/70.64 thf(36448,plain,((! [A:complex]: ((power_power_complex @ (csqrt @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8193])). 159.59/70.64 thf(846,axiom,((! [A:real,B:real,C:real]: ((((ord_less_real @ (log @ A @ B) @ C) = (ord_less_real @ B @ (powr_real @ A @ C))) <= (ord_less_real @ zero_zero_real @ B)) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7266_log__less__iff)). 159.59/70.64 thf(10979,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ (log @ A @ B) @ C) = (ord_less_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)],[846])). 159.59/70.64 thf(1868,axiom,((! [A:num]: ~ (ord_less_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5182_not__one__less__neg__numeral)). 159.59/70.64 thf(14287,plain,((! [A:num]: ~ (ord_less_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1868])). 159.59/70.64 thf(3707,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/sandbox/benchmark/theBenchmark.p',fact_3584_flip__bit__Suc)). 159.59/70.64 thf(20176,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)],[3707])). 159.59/70.64 thf(94,axiom,((! [A:nat]: (ord_le3102999989581377725nteger @ (semiri3624122377584611663nteger @ A) @ (semiri4939895301339042750nteger @ (power_power_nat @ A @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8102_fact__le__power)). 159.59/70.64 thf(8541,plain,((! [A:nat]: (ord_le3102999989581377725nteger @ (semiri3624122377584611663nteger @ A) @ (semiri4939895301339042750nteger @ (power_power_nat @ A @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[94])). 159.59/70.64 thf(7644,axiom,((! [A:nat,B:nat]: ((product_fst_nat_nat @ (divmod_nat @ A @ B)) = (divide_divide_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9749_fst__divmod__nat)). 159.59/70.64 thf(34686,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)],[7644])). 159.59/70.64 thf(7116,axiom,((! [A:vEBT_VEBT,B:$o]: (((vEBT_VEBT_minNull @ A) = B) => (((~ (B)) <= (A = (vEBT_Leaf @ ($false) @ ($false)))) => (((B) <= (? [C:$o]: (A = (vEBT_Leaf @ ($true) @ C)))) => ((((~ (B)) <= (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ ((? [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)))) <= ((? [C:$o]: (A = (vEBT_Leaf @ C @ ($true)))) => (B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2219_VEBT__internal_OminNull_Oelims_I1_J)). 159.59/70.64 thf(32794,plain,((! [A:vEBT_VEBT,B:$o]: (((vEBT_VEBT_minNull @ A) = B) => ((~ (B) | ~ (A = (vEBT_Leaf @ ($false) @ ($false)))) => (((B) | ~ (? [C:$o]: (A = (vEBT_Leaf @ ($true) @ C)))) => (((~ (B) | ~ (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ ((? [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F))) => (B)))) | ~ ((? [C:$o]: (A = (vEBT_Leaf @ C @ ($true)))) => (B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7116])). 159.59/70.64 thf(7291,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4469_minf_I3_J)). 159.59/70.64 thf(33451,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7291])). 159.59/70.64 thf(3006,axiom,((! [A:real,B:real,C:real]: ((powr_real @ A @ (plus_plus_real @ B @ C)) = (times_times_real @ (powr_real @ A @ B) @ (powr_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7258_powr__add)). 159.59/70.64 thf(17921,plain,((! [A:real,B:real,C:real]: ((powr_real @ A @ (plus_plus_real @ B @ C)) = (times_times_real @ (powr_real @ A @ B) @ (powr_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3006])). 159.59/70.64 thf(4791,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: (vEBT_VEBT_minNull @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2571_VEBT__internal_OminNull_Osimps_I4_J)). 159.59/70.64 thf(23801,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)],[4791])). 159.59/70.64 thf(7006,axiom,((! [A:real,B:real,C:nat]: (((((ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) = (ord_less_eq_real @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ C)) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1777_power__mono__iff)). 159.59/70.64 thf(32375,plain,((! [A:real,B:real,C:nat]: (((ord_less_eq_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) = (ord_less_eq_real @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ 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)],[7006])). 159.59/70.64 thf(3699,axiom,((! [A:int]: (((ring_1_of_int_int @ A) = one_one_int) = (A = one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5775_of__int__eq__1__iff)). 159.59/70.64 thf(20132,plain,((! [A:int]: (((ring_1_of_int_int @ A) = one_one_int) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3699])). 159.59/70.64 thf(7464,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/sandbox/benchmark/theBenchmark.p',fact_8153_fact__diff__Suc)). 159.59/70.64 thf(34042,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)],[7464])). 159.59/70.64 thf(1047,axiom,((! [A:real,B:real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1515_add__cancel__right__left)). 159.59/70.64 thf(11607,plain,((! [A:real,B:real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047])). 159.59/70.64 thf(2745,axiom,((bit_se2923211474154528505it_int = (^ [A:nat,B:int]: (bit_se725231765392027082nd_int @ B @ (bit_se2000444600071755411sk_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6035_take__bit__eq__mask)). 159.59/70.64 thf(17102,plain,(((bit_se2923211474154528505it_int) = (^ [A:nat,B:int]: (bit_se725231765392027082nd_int @ B @ (bit_se2000444600071755411sk_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2745])). 159.59/70.64 thf(584,axiom,((! [A:real]: (sums_real @ (^ [B:nat]: (uminus_uminus_real @ (real_V1485227260804924795R_real @ (sin_coeff @ B) @ (power_power_real @ (uminus_uminus_real @ A) @ B)))) @ (sin_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9289_sin__minus__converges)). 159.59/70.64 thf(10108,plain,((! [A:real]: (sums_real @ (^ [B:nat]: (uminus_uminus_real @ (real_V1485227260804924795R_real @ (sin_coeff @ B) @ (power_power_real @ (uminus_uminus_real @ A) @ B)))) @ (sin_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[584])). 159.59/70.64 thf(460,axiom,((! [A:real]: (((archim2898591450579166408c_real @ A) = A) = ((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9119_frac__eq)). 159.59/70.64 thf(9698,plain,((! [A:real]: (((archim2898591450579166408c_real @ A) = A) = ((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[460])). 159.59/70.64 thf(4019,axiom,((! [A:nat]: ((set_or4665077453230672383an_nat @ A @ (suc @ A)) = (insert_nat @ A @ bot_bot_set_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9576_atLeastLessThan__singleton)). 159.59/70.64 thf(21166,plain,((! [A:nat]: ((set_or4665077453230672383an_nat @ A @ (suc @ A)) = (insert_nat @ A @ bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4019])). 159.59/70.64 thf(3778,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ one_one_real @ C) => ((ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ D @ B)) <= (ord_less_eq_real @ C @ D)))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7248_powr__mono__both)). 159.59/70.64 thf(20403,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ one_one_real @ C) => ((ord_less_eq_real @ (powr_real @ C @ A) @ (powr_real @ D @ B)) | ~ (ord_less_eq_real @ C @ D)))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3778])). 159.59/70.64 thf(7795,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2911_order__less__not__sym)). 159.59/70.64 thf(35171,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7795])). 159.59/70.64 thf(282,axiom,((! [A:real,B:real]: ((sinh_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (sinh_real @ A) @ (cosh_real @ B)) @ (times_times_real @ (cosh_real @ A) @ (sinh_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9328_sinh__add)). 159.59/70.64 thf(9106,plain,((! [A:real,B:real]: ((sinh_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (times_times_real @ (sinh_real @ A) @ (cosh_real @ B)) @ (times_times_real @ (cosh_real @ A) @ (sinh_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 159.59/70.64 thf(6822,axiom,((! [A:num]: ((ord_less_eq_real @ (numeral_numeral_real @ A) @ one_one_real) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_numeral__le__one__iff)). 159.59/70.64 thf(31512,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)],[6822])). 159.59/70.64 thf(2274,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (nat_prod_encode @ (product_Pair_nat_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10206_le__prod__encode__1)). 159.59/70.64 thf(15583,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (nat_prod_encode @ (product_Pair_nat_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2274])). 159.59/70.64 thf(2371,axiom,((! [A:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4690_ab__left__minus)). 159.59/70.64 thf(15868,plain,((! [A:real]: ((plus_plus_real @ (uminus_uminus_real @ A) @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2371])). 159.59/70.64 thf(3229,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/sandbox/benchmark/theBenchmark.p',fact_1580_le__add__same__cancel2)). 159.59/70.64 thf(18637,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)],[3229])). 159.59/70.64 thf(7461,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/sandbox/benchmark/theBenchmark.p',fact_9417_diff__nat__numeral)). 159.59/70.64 thf(34023,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)],[7461])). 159.59/70.64 thf(6241,axiom,((! [A:num,B:num]: ((bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ B)) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ (pred_numeral @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6345_bit__numeral__simps_I2_J)). 159.59/70.64 thf(29217,plain,((! [A:num,B:num]: ((bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ B)) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6241])). 159.59/70.64 thf(1046,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/sandbox/benchmark/theBenchmark.p',fact_7152_cos__45)). 159.59/70.64 thf(11605,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)],[1046])). 159.59/70.64 thf(7155,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8148_fact__mono__nat)). 159.59/70.64 thf(32957,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)],[7155])). 159.59/70.64 thf(5696,axiom,((! [A:complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1497_mult__zero__left)). 159.59/70.64 thf(27114,plain,((! [A:complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5696])). 159.59/70.64 thf(569,axiom,((! [A:complex,B:nat]: ((times_times_complex @ A @ (gbinomial_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ B) @ (gbinomial_complex @ A @ B)) @ (times_times_complex @ (semiri8010041392384452111omplex @ (suc @ B)) @ (gbinomial_complex @ A @ (suc @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8255_gbinomial__mult__1)). 159.59/70.64 thf(10063,plain,((! [A:complex,B:nat]: ((times_times_complex @ A @ (gbinomial_complex @ A @ B)) = (plus_plus_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ B) @ (gbinomial_complex @ A @ B)) @ (times_times_complex @ (semiri8010041392384452111omplex @ (suc @ B)) @ (gbinomial_complex @ A @ (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[569])). 159.59/70.64 thf(1649,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/sandbox/benchmark/theBenchmark.p',fact_6942_norm__diff__ineq)). 159.59/70.64 thf(13598,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)],[1649])). 159.59/70.64 thf(7489,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/sandbox/benchmark/theBenchmark.p',fact_8282_pochhammer__of__nat__eq__0__iff)). 159.59/70.64 thf(34155,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)],[7489])). 159.59/70.64 thf(6706,axiom,((! [A:num,B:num,C:num]: (((((B = one) => (C != one)) <= (A = one)) => ((((((C != (bit0 @ one)) <= (B = one)) <= (? [D:num]: (A = (bit0 @ D)))) => (((! [D:num]: ((! [E:num]: ((B = (bit1 @ E)) => (C != (bit0 @ (bit_or_not_num_neg @ D @ E))))) <= (A = (bit0 @ D)))) => (((! [D:num]: ((! [E:num]: ((C != (bitM @ (bit_or_not_num_neg @ D @ E))) <= (B = (bit0 @ E)))) <= (A = (bit1 @ D)))) => (~ (! [D:num]: ((A = (bit1 @ D)) => (! [E:num]: ((B = (bit1 @ E)) => (C != (bitM @ (bit_or_not_num_neg @ D @ E))))))))) <= ((? [D:num]: (A = (bit1 @ D))) => ((C != one) <= (B = one))))) <= (! [D:num]: ((A = (bit0 @ D)) => (! [E:num]: ((B = (bit0 @ E)) => (C != (bitM @ (bit_or_not_num_neg @ D @ E))))))))) <= ((A = one) => (! [D:num]: ((C != (bit1 @ D)) <= (B = (bit1 @ D)))))) <= ((A = one) => (! [D:num]: ((B = (bit0 @ D)) => (C != (bit1 @ D))))))) <= ((bit_or_not_num_neg @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6289_or__not__num__neg_Oelims)). 159.59/70.64 thf(31028,plain,((! [A:num,B:num,C:num]: (((((B = one) => (~ (C = one))) | ~ (A = one)) => (((~ (C = (bit0 @ one)) | ~ (B = one) | ~ (? [D:num]: (A = (bit0 @ D)))) => (((! [D:num]: (! [E:num]: ((B = (bit1 @ E)) => (~ (C = (bit0 @ (bit_or_not_num_neg @ D @ E))))) | ~ (A = (bit0 @ D)))) => (((! [D:num]: (! [E:num]: (~ (C = (bitM @ (bit_or_not_num_neg @ D @ E))) | ~ (B = (bit0 @ E))) | ~ (A = (bit1 @ D)))) => (~ (! [D:num]: ((A = (bit1 @ D)) => (! [E:num]: ((B = (bit1 @ E)) => (~ (C = (bitM @ (bit_or_not_num_neg @ D @ E)))))))))) | ~ ((? [D:num]: (A = (bit1 @ D))) => (~ (C = one) | ~ (B = one))))) | ~ (! [D:num]: ((A = (bit0 @ D)) => (! [E:num]: ((B = (bit0 @ E)) => (~ (C = (bitM @ (bit_or_not_num_neg @ D @ E)))))))))) | ~ ((A = one) => (! [D:num]: (~ (C = (bit1 @ D)) | ~ (B = (bit1 @ D))))) | ~ ((A = one) => (! [D:num]: ((B = (bit0 @ D)) => (~ (C = (bit1 @ D)))))))) | ~ ((bit_or_not_num_neg @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6706])). 159.59/70.64 thf(3479,axiom,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ (plus_plus_int @ B @ A) @ C)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2039_add__decreasing2)). 159.59/70.64 thf(19426,plain,((! [A:int,B:int,C:int]: (((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ (plus_plus_int @ B @ A) @ C)) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3479])). 159.59/70.64 thf(4454,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/sandbox/benchmark/theBenchmark.p',fact_5538_abs__le__iff)). 159.59/70.64 thf(22518,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)],[4454])). 159.59/70.64 thf(3821,axiom,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6808_sin__pi__half)). 159.59/70.64 thf(20536,plain,(((sin_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3821])). 159.59/70.64 thf(3706,axiom,((! [A:(extended_enat > (extended_enat > $o)),B:set_nat,C:(nat > extended_enat),D:(nat > extended_enat)]: (((! [E:extended_enat,F:extended_enat,G:extended_enat,H:extended_enat]: ((A @ (times_7803423173614009249d_enat @ E @ F) @ (times_7803423173614009249d_enat @ G @ H)) <= ((A @ F @ H) & (A @ E @ G)))) => (((A @ (groups7961826882256487087d_enat @ C @ B) @ (groups7961826882256487087d_enat @ D @ B)) <= (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E))))) <= (finite_finite_nat @ B))) <= (A @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8559_prod_Orelated)). 159.59/70.64 thf(20154,plain,((! [A:(extended_enat > (extended_enat > $o)),B:set_nat,C:(nat > extended_enat),D:(nat > extended_enat)]: (((! [E:extended_enat,F:extended_enat,G:extended_enat,H:extended_enat]: ((A @ (times_7803423173614009249d_enat @ E @ F) @ (times_7803423173614009249d_enat @ G @ H)) | ~ ((A @ F @ H) & (A @ E @ G)))) => ((A @ (groups7961826882256487087d_enat @ (C) @ B) @ (groups7961826882256487087d_enat @ (D) @ B)) | ~ (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) | ~ (finite_finite_nat @ B))) | ~ (A @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3706])). 159.59/70.64 thf(249,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/sandbox/benchmark/theBenchmark.p',fact_944_max_OboundedE)). 159.59/70.64 thf(9011,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)],[249])). 159.59/70.64 thf(6784,axiom,((! [A:nat]: ? [B:list_int]: ((size_size_list_int @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_Ex__list__of__length)). 159.59/70.64 thf(31400,plain,((! [A:nat]: ? [B:list_int]: ((size_size_list_int @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6784])). 159.59/70.64 thf(3620,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le2932123472753598470d_enat @ A @ B)) = (ord_le72135733267957522d_enat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3167_linorder__not__le)). 159.59/70.64 thf(19880,plain,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le2932123472753598470d_enat @ A @ B)) = (ord_le72135733267957522d_enat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3620])). 159.59/70.64 thf(3562,axiom,((! [A:(code_integer > $o),B:code_integer]: (((A @ B) <= (! [C:code_integer,D:$o]: ((A @ C) => (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ (zero_n356916108424825756nteger @ D) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C)) @ (numera6620942414471956472nteger @ (bit0 @ one))) = C) => (A @ (plus_p5714425477246183910nteger @ (zero_n356916108424825756nteger @ D) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C))))))) <= (! [C:code_integer]: ((A @ C) <= ((divide6298287555418463151nteger @ C @ (numera6620942414471956472nteger @ (bit0 @ one))) = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4492_bits__induct)). 159.59/70.64 thf(19680,plain,((! [A:(code_integer > $o),B:code_integer]: ((A @ B) | ~ (! [C:code_integer,D:$o]: ((A @ C) => (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ (zero_n356916108424825756nteger @ D) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C)) @ (numera6620942414471956472nteger @ (bit0 @ one))) = C) => (A @ (plus_p5714425477246183910nteger @ (zero_n356916108424825756nteger @ D) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C)))))) | ~ (! [C:code_integer]: ((A @ C) | ~ ((divide6298287555418463151nteger @ C @ (numera6620942414471956472nteger @ (bit0 @ one))) = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3562])). 159.59/70.64 thf(1980,axiom,((! [A:int,B:int,C:nat,D:nat]: ((((((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) @ (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 @ A) = zero_zero_int) | (C = zero_zero_nat) | ((sgn_sgn_int @ B) = zero_zero_int)))) & ((((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/sandbox/benchmark/theBenchmark.p',fact_9407_modulo__int__unfold)). 159.59/70.64 thf(14639,plain,((! [A:int,B:int,C:nat,D:nat]: ((((((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) @ (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 @ A) = zero_zero_int) | (C = zero_zero_nat) | ((sgn_sgn_int @ B) = zero_zero_int)) & ((((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)],[1980])). 159.59/70.64 thf(4919,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/sandbox/benchmark/theBenchmark.p',fact_4885_signed__take__bit__Suc__minus__bit0)). 159.59/70.64 thf(24257,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)],[4919])). 159.59/70.64 thf(5313,axiom,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3789_nat__dvd__1__iff__1)). 159.59/70.64 thf(25694,plain,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5313])). 159.59/70.64 thf(7820,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: ((((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((((vEBT_VEBT_low @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F) => ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ G @ H) @ B) = (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ E)) = none_nat) @ A @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ E)))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ E @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ E)))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ G @ E @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ (vEBT_vebt_delete @ H @ E)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (plus_plus_nat @ (times_times_nat @ E @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ E @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ E)))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ G @ E @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ H))))) <= ((vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = E))) <= (A != C)) <= ((ord_less_nat @ A @ B) & (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1399_del__x__not__mia)). 159.59/70.64 thf(35244,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => ((((vEBT_VEBT_low @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F) => ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ G @ H) @ B) = (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ E)) = none_nat) @ A @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ E)))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ E @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ E)))))))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ G @ E @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ (vEBT_vebt_delete @ H @ E)) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (plus_plus_nat @ (times_times_nat @ E @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ E @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ E)))) @ C))) @ D @ (list_u1324408373059187874T_VEBT @ G @ E @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ E) @ F)) @ H))))) | ~ ((vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = E))) | (A = C) | ~ ((ord_less_nat @ A @ B) & (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7820])). 159.59/70.64 thf(966,axiom,((! [A:real]: (ord_less_eq_real @ one_one_real @ (cosh_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9337_cosh__real__ge__1)). 159.59/70.64 thf(11342,plain,((! [A:real]: (ord_less_eq_real @ one_one_real @ (cosh_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[966])). 159.59/70.64 thf(5959,axiom,((ord_less_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2130_zero__less__one)). 159.59/70.64 thf(28311,plain,((ord_less_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5959])). 159.59/70.64 thf(1744,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ C @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6076_AND__upper2_H)). 159.59/70.64 thf(13884,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ A @ B) => (ord_less_eq_int @ (bit_se725231765392027082nd_int @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744])). 159.59/70.64 thf(7895,axiom,((! [A:nat,B:nat]: (((bit_se2925701944663578781it_nat @ A @ B) = zero_zero_nat) = (dvd_dvd_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5303_take__bit__eq__0__iff)). 159.59/70.64 thf(35491,plain,((! [A:nat,B:nat]: (((bit_se2925701944663578781it_nat @ A @ B) = zero_zero_nat) = (dvd_dvd_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7895])). 159.59/70.64 thf(6406,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/sandbox/benchmark/theBenchmark.p',fact_854_Nat_Odiff__add__assoc)). 159.59/70.64 thf(29871,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)],[6406])). 159.59/70.64 thf(5451,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (binomial @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9009_zero__less__binomial__iff)). 159.59/70.64 thf(26271,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)],[5451])). 159.59/70.64 thf(7774,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/sandbox/benchmark/theBenchmark.p',fact_5313_minus__power__mult__self)). 159.59/70.64 thf(35112,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)],[7774])). 159.59/70.64 thf(4880,axiom,((! [A:list_int,B:list_int]: (((A = B) <= (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_int @ A)) => ((nth_int @ A @ C) = (nth_int @ B @ C))))) <= ((size_size_list_int @ A) = (size_size_list_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_nth__equalityI)). 159.59/70.64 thf(24122,plain,((! [A:list_int,B:list_int]: ((A = B) | ~ (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_int @ A)) => ((nth_int @ A @ C) = (nth_int @ B @ C)))) | ~ ((size_size_list_int @ A) = (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4880])). 159.59/70.64 thf(4904,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (minus_minus_nat @ B @ A) @ C) = (ord_less_nat @ B @ (plus_plus_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_867_less__diff__conv2)). 159.59/70.64 thf(24203,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (minus_minus_nat @ B @ A) @ C) = (ord_less_nat @ B @ (plus_plus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4904])). 159.59/70.64 thf(1988,axiom,((! [A:int,B:int]: ((bit_se1409905431419307370or_int @ (bit_se1409905431419307370or_int @ A @ B) @ B) = (bit_se1409905431419307370or_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5939_or_Oright__idem)). 159.59/70.64 thf(14675,plain,((! [A:int,B:int]: ((bit_se1409905431419307370or_int @ (bit_se1409905431419307370or_int @ A @ B) @ B) = (bit_se1409905431419307370or_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1988])). 159.59/70.64 thf(5561,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1908_Zero__not__Suc)). 159.59/70.64 thf(26636,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5561])). 159.59/70.64 thf(8245,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => (ord_less_nat @ B @ C)) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_power__less__imp__less__exp)). 159.59/70.64 thf(36762,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => (ord_less_nat @ B @ C)) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8245])). 159.59/70.64 thf(559,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (? [B:real]: ((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ A @ (tan_real @ B)) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7283_lemma__tan__total)). 159.59/70.64 thf(10031,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (? [B:real]: ((ord_less_real @ zero_zero_real @ B) & (ord_less_real @ A @ (tan_real @ B)) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[559])). 159.59/70.64 thf(3188,axiom,((! [A:int,B:int,C:int]: ((bit_se725231765392027082nd_int @ (bit_se725231765392027082nd_int @ A @ B) @ C) = (bit_se725231765392027082nd_int @ A @ (bit_se725231765392027082nd_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6049_and_Oassoc)). 159.59/70.64 thf(18505,plain,((! [A:int,B:int,C:int]: ((bit_se725231765392027082nd_int @ (bit_se725231765392027082nd_int @ A @ B) @ C) = (bit_se725231765392027082nd_int @ A @ (bit_se725231765392027082nd_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3188])). 159.59/70.64 thf(3546,axiom,((! [A:int,B:int]: ((ord_less_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4942_verit__negate__coefficient_I2_J)). 159.59/70.64 thf(19631,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)],[3546])). 159.59/70.64 thf(1837,axiom,((minus_minus_int = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5107_ab__group__add__class_Oab__diff__conv__add__uminus)). 159.59/70.64 thf(14194,plain,(((minus_minus_int) = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1837])). 159.59/70.64 thf(5821,axiom,(((('!') @ option_nat) = (^ [A:(option_nat > $o)]: ((A @ none_nat) & ! [B:nat]: (A @ (some_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_split__option__all)). 159.59/70.64 thf(27702,plain,(((('!') @ option_nat) = (^ [A:(option_nat > $o)]: ((A @ none_nat) & ! [B:nat]: (A @ (some_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5821])). 159.59/70.64 thf(900,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/sandbox/benchmark/theBenchmark.p',fact_7913_sums__mult2__iff)). 159.59/70.64 thf(11141,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)],[900])). 159.59/70.64 thf(525,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ (real_V1485227260804924795R_real @ A @ C)) = (ord_less_eq_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9226_scaleR__le__cancel__left__neg)). 159.59/70.64 thf(9921,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ (real_V1485227260804924795R_real @ A @ C)) = (ord_less_eq_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[525])). 159.59/70.64 thf(7724,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:nat,J:vEBT_VEBT,K:list_VEBT_VEBT]: ((((((((ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)) => (((((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (plus_plus_nat @ (times_times_nat @ F @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ F)))) @ C))) @ D @ K @ G)) <= (~ (vEBT_VEBT_minNull @ J))) <= (K = (list_u1324408373059187874T_VEBT @ H @ F @ J))) <= (J = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)))) <= ((vEBT_VEBT_low @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = I)) <= (E = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ G)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ H @ (the_nat @ (vEBT_vebt_mint @ G)))))))) <= ((vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) <= (B != C)) <= ((ord_less_nat @ A @ C) & (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_del__x__mi__lets__in__not__minNull)). 159.59/70.64 thf(34954,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:nat,J:vEBT_VEBT,K:list_VEBT_VEBT]: (((ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)) => (((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (plus_plus_nat @ (times_times_nat @ F @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ F)))) @ C))) @ D @ K @ G)) | (vEBT_VEBT_minNull @ J) | ~ (K = (list_u1324408373059187874T_VEBT @ H @ F @ J)) | ~ (J = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)))) | ~ ((vEBT_VEBT_low @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = I) | ~ (E = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ G)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ H @ (the_nat @ (vEBT_vebt_mint @ G))))))) | ~ ((vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) | (B = C) | ~ ((ord_less_nat @ A @ C) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7724])). 159.59/70.64 thf(1228,axiom,((! [A:num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2015_zero__less__numeral)). 159.59/70.64 thf(12224,plain,((! [A:num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228])). 159.59/70.64 thf(7507,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/sandbox/benchmark/theBenchmark.p',fact_4956_square__eq__iff)). 159.59/70.64 thf(34211,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)],[7507])). 159.59/70.64 thf(6989,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((groups708209901874060359at_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ B) @ (suc @ C))) = (groups708209901874060359at_nat @ (^ [D:nat]: (A @ (suc @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8540_prod_Oshift__bounds__cl__Suc__ivl)). 159.59/70.64 thf(32313,plain,((! [A:(nat > nat),B:nat,C:nat]: ((groups708209901874060359at_nat @ (A) @ (set_or1269000886237332187st_nat @ (suc @ B) @ (suc @ C))) = (groups708209901874060359at_nat @ (^ [D:nat]: (A @ (suc @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6989])). 159.59/70.64 thf(1563,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/sandbox/benchmark/theBenchmark.p',fact_6104_even__and__iff__int)). 159.59/70.64 thf(13330,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)],[1563])). 159.59/70.64 thf(13,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)) = (ord_less_eq_real @ C @ (real_V1485227260804924795R_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9253_neg__le__divideR__eq)). 159.59/70.64 thf(8291,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)) = (ord_less_eq_real @ C @ (real_V1485227260804924795R_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 159.59/70.64 thf(6899,axiom,((! [A:set_nat,B:nat]: (((? [C:nat]: ((ord_less_eq_nat @ C @ B) & ! [D:nat]: ((member_nat @ D @ A) => ((ord_less_eq_nat @ D @ C) => (C = D))) & (member_nat @ C @ A))) <= (member_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3755_finite__has__minimal2)). 159.59/70.64 thf(31851,plain,((! [A:set_nat,B:nat]: (? [C:nat]: ((ord_less_eq_nat @ C @ B) & ! [D:nat]: ((member_nat @ D @ A) => ((ord_less_eq_nat @ D @ C) => (C = D))) & (member_nat @ C @ A)) | ~ (member_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6899])). 159.59/70.64 thf(2195,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/sandbox/benchmark/theBenchmark.p',fact_2627_half__negative__int__iff)). 159.59/70.64 thf(15340,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)],[2195])). 159.59/70.64 thf(1524,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/sandbox/benchmark/theBenchmark.p',fact_4247_even__diff__iff)). 159.59/70.64 thf(13214,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)],[1524])). 159.59/70.64 thf(7421,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/sandbox/benchmark/theBenchmark.p',fact_4163_div__mult__unit2)). 159.59/70.64 thf(33891,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)],[7421])). 159.59/70.64 thf(2463,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) => ((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_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7302_tan__mono__le)). 159.59/70.64 thf(16181,plain,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) => ((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_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2463])). 159.59/70.64 thf(2475,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/sandbox/benchmark/theBenchmark.p',fact_5598_cong__exp__iff__simps_I13_J)). 159.59/70.64 thf(16217,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)],[2475])). 159.59/70.64 thf(1424,axiom,((! [A:(nat > complex),B:(nat > complex)]: ((summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C)))) => ((summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (B @ C)))) => ((times_times_complex @ (suminf_complex @ A) @ (suminf_complex @ B)) = (suminf_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8901_Cauchy__product)). 159.59/70.64 thf(12890,plain,((! [A:(nat > complex),B:(nat > complex)]: ((summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C)))) => ((summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (B @ C)))) => ((times_times_complex @ (suminf_complex @ (A)) @ (suminf_complex @ (B))) = (suminf_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (A @ D) @ (B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424])). 159.59/70.64 thf(4041,axiom,((! [A:extended_enat,B:extended_enat]: (((ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ zero_z5237406670263579293d_enat) <= (ord_le2932123472753598470d_enat @ B @ zero_z5237406670263579293d_enat)) <= (ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2275_add__neg__nonpos)). 159.59/70.64 thf(21230,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ zero_z5237406670263579293d_enat) | ~ (ord_le2932123472753598470d_enat @ B @ zero_z5237406670263579293d_enat) | ~ (ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4041])). 159.59/70.64 thf(2061,axiom,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3976_dvd__triv__right)). 159.59/70.64 thf(14898,plain,((! [A:real,B:real]: (dvd_dvd_real @ A @ (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2061])). 159.59/70.64 thf(7340,axiom,((! [A:complex,B:complex,C:real,D:nat]: ((A != zero_zero_complex) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ C) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6795_lemma__termdiff3)). 159.59/70.64 thf(33634,plain,((! [A:complex,B:complex,C:real,D:nat]: ((~ (A = zero_zero_complex)) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ C) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7340])). 159.59/70.64 thf(5649,axiom,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ B)) = (times_times_complex @ A @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_power__Suc)). 159.59/70.64 thf(26931,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)],[5649])). 159.59/70.64 thf(8165,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/sandbox/benchmark/theBenchmark.p',fact_2552_div__2__gt__zero)). 159.59/70.64 thf(36366,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)],[8165])). 159.59/70.64 thf(7980,axiom,((! [A:nat,B:list_o,C:list_o]: (((nth_Product_prod_o_o @ (product_o_o @ B @ C) @ A) = (product_Pair_o_o @ (nth_o @ B @ (divide_divide_nat @ A @ (size_size_list_o @ C))) @ (nth_o @ C @ (modulo_modulo_nat @ A @ (size_size_list_o @ C))))) <= (ord_less_nat @ A @ (times_times_nat @ (size_size_list_o @ B) @ (size_size_list_o @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3594_product__nth)). 159.59/70.64 thf(35753,plain,((! [A:nat,B:list_o,C:list_o]: (((nth_Product_prod_o_o @ (product_o_o @ B @ C) @ A) = (product_Pair_o_o @ (nth_o @ B @ (divide_divide_nat @ A @ (size_size_list_o @ C))) @ (nth_o @ C @ (modulo_modulo_nat @ A @ (size_size_list_o @ C))))) | ~ (ord_less_nat @ A @ (times_times_nat @ (size_size_list_o @ B) @ (size_size_list_o @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7980])). 159.59/70.64 thf(166,axiom,((! [A:code_integer]: ((! [B:nat]: ((bit_se9216721137139052372nteger @ A @ B) = (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))) => ((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6424_bit__iff__idd__imp__stable)). 159.59/70.64 thf(8763,plain,((! [A:code_integer]: ((! [B:nat]: ((bit_se9216721137139052372nteger @ A @ B) = (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))) => ((divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 159.59/70.64 thf(5666,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/sandbox/benchmark/theBenchmark.p',fact_5640_cong__exp__iff__simps_I11_J)). 159.59/70.64 thf(27004,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)],[5666])). 159.59/70.64 thf(6754,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (~ (ord_less_eq_num @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4495_pinf_I6_J)). 159.59/70.64 thf(31291,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)],[6754])). 159.59/70.64 thf(4777,axiom,((! [A:(int > (int > $o)),B:int,C:int]: ((! [D:int,E:int]: ((ord_less_eq_int @ D @ E) => (A @ D @ E))) => ((! [D:int,E:int]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2721_linorder__wlog)). 159.59/70.64 thf(23759,plain,((! [A:(int > (int > $o)),B:int,C:int]: ((! [D:int,E:int]: ((ord_less_eq_int @ D @ E) => (A @ D @ E))) => ((! [D:int,E:int]: ((A @ E @ D) => (A @ D @ E))) => (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4777])). 159.59/70.64 thf(6368,axiom,((! [A:nat]: ((power_power_complex @ zero_zero_complex @ (suc @ A)) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1680_power__0__Suc)). 159.59/70.64 thf(29698,plain,((! [A:nat]: ((power_power_complex @ zero_zero_complex @ (suc @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6368])). 159.59/70.64 thf(1692,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/sandbox/benchmark/theBenchmark.p',fact_7877_sum_OlessThan__Suc)). 159.59/70.64 thf(13727,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)],[1692])). 159.59/70.64 thf(2570,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [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)))) & (ord_less_eq_real @ C @ A) & (ord_less_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8145_Maclaurin__sin__expansion4)). 159.59/70.64 thf(16510,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ A) => (? [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)))) & (ord_less_eq_real @ C @ A) & (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2570])). 159.59/70.64 thf(8058,axiom,((! [A:num,B:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6007_and__numerals_I3_J)). 159.59/70.64 thf(36017,plain,((! [A:num,B:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8058])). 159.59/70.64 thf(2998,axiom,((! [A:real,B:real,C:complex]: ((real_V2046097035970521341omplex @ (plus_plus_real @ A @ B) @ C) = (plus_plus_complex @ (real_V2046097035970521341omplex @ A @ C) @ (real_V2046097035970521341omplex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9215_scaleR__left_Oadd)). 159.59/70.65 thf(17896,plain,((! [A:real,B:real,C:complex]: ((real_V2046097035970521341omplex @ (plus_plus_real @ A @ B) @ C) = (plus_plus_complex @ (real_V2046097035970521341omplex @ A @ C) @ (real_V2046097035970521341omplex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2998])). 159.59/70.65 thf(1695,axiom,((! [A:num]: ((archim8280529875227126926d_real @ (numeral_numeral_real @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6163_round__numeral)). 159.59/70.65 thf(13737,plain,((! [A:num]: ((archim8280529875227126926d_real @ (numeral_numeral_real @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695])). 159.59/70.65 thf(6133,axiom,((! [A:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5138_neg__numeral__le__zero)). 159.59/70.65 thf(28860,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)],[6133])). 159.59/70.65 thf(7780,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/sandbox/benchmark/theBenchmark.p',fact_3882_even__mod__2__iff)). 159.59/70.65 thf(35127,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)],[7780])). 159.59/70.65 thf(1977,axiom,((! [A:int,B:int,C:int]: ((bit_se725231765392027082nd_int @ A @ (bit_se1409905431419307370or_int @ B @ C)) = (bit_se1409905431419307370or_int @ (bit_se725231765392027082nd_int @ A @ B) @ (bit_se725231765392027082nd_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6040_bit_Oconj__disj__distrib)). 159.59/70.65 thf(14628,plain,((! [A:int,B:int,C:int]: ((bit_se725231765392027082nd_int @ A @ (bit_se1409905431419307370or_int @ B @ C)) = (bit_se1409905431419307370or_int @ (bit_se725231765392027082nd_int @ A @ B) @ (bit_se725231765392027082nd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1977])). 159.59/70.65 thf(1014,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ C) = (((ord_less_real @ A @ (times_times_real @ C @ B)) <= (ord_less_real @ zero_zero_real @ B)) & ((~ (ord_less_real @ zero_zero_real @ B)) => (((~ (ord_less_real @ B @ zero_zero_real)) => (ord_less_real @ zero_zero_real @ C)) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ C @ B) @ A)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2333_divide__less__eq)). 159.59/70.65 thf(11493,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ C) = (((ord_less_real @ A @ (times_times_real @ C @ B)) | ~ (ord_less_real @ zero_zero_real @ B)) & ((~ (ord_less_real @ zero_zero_real @ B)) => (((~ (ord_less_real @ B @ zero_zero_real)) => (ord_less_real @ zero_zero_real @ C)) & ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ C @ B) @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014])). 159.59/70.65 thf(2813,axiom,((! [A:real,B:int]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ B) = (ord_less_real @ A @ (ring_1_of_int_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8225_floor__less__iff)). 159.59/70.65 thf(17300,plain,((! [A:real,B:int]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ B) = (ord_less_real @ A @ (ring_1_of_int_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2813])). 159.59/70.65 thf(3474,axiom,(((inverse_inverse_real @ one_one_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8980_inverse__1)). 159.59/70.65 thf(19409,plain,(((inverse_inverse_real @ one_one_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3474])). 159.59/70.65 thf(701,axiom,((! [A:($o > $o),B:(nat > (nat > $o)),C:product_prod_nat_nat]: ((A @ (produc6081775807080527818_nat_o @ B @ C)) => (~ (! [D:nat,E:nat]: ((~ (A @ (B @ D @ E))) <= (C = (product_Pair_nat_nat @ D @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5012_case__prodE2)). 159.59/70.65 thf(10499,plain,((! [A:($o > $o),B:(nat > (nat > $o)),C:product_prod_nat_nat]: ((A @ (produc6081775807080527818_nat_o @ (B) @ C)) => (~ (! [D:nat,E:nat]: (~ (A @ (B @ D @ E)) | ~ (C = (product_Pair_nat_nat @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[701])). 159.59/70.65 thf(1797,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_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/sandbox/benchmark/theBenchmark.p',fact_2253_mult__le__cancel__right)). 159.59/70.65 thf(14049,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ (times_times_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)],[1797])). 159.59/70.65 thf(3934,axiom,((! [A:real]: (((ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) = A) = (? [B:int]: (A = (ring_1_of_int_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8169_of__int__floor__cancel)). 159.59/70.65 thf(20907,plain,((! [A:real]: (((ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) = A) = (? [B:int]: (A = (ring_1_of_int_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3934])). 159.59/70.65 thf(6388,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1344_diff__add)). 159.59/70.65 thf(29797,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6388])). 159.59/70.65 thf(7567,axiom,((! [A:vEBT_VEBT,B:nat,C:option_nat]: ((((((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((C = none_nat) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B)))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)))) => ((! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((C = none_nat) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F) @ B)))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ 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)) => ((((ord_less_nat @ B @ D) => (C = (some_nat @ D))) & ((~ (ord_less_nat @ B @ D)) => (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_maxt @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) != none_nat) & (vEBT_VEBT_less @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (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 @ 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_succ @ (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_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)))) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B))))))) <= (! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F) @ B))) <= (C = none_nat)) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F))))))) <= (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (! [F:nat]: ((B = (suc @ F)) => ((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ F)))) <= (C = none_nat))))))) <= (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((B = zero_zero_nat) => ((((C = none_nat) <= (~ (E))) & ((E) => (C = (some_nat @ one_one_nat)))) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ zero_zero_nat)))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ (produc738532404422230701BT_nat @ A @ B))) <= ((vEBT_vebt_succ @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2589_vebt__succ_Opelims)). 159.59/70.65 thf(34390,plain,((! [A:vEBT_VEBT,B:nat,C:option_nat]: (((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((C = none_nat) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_succ_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B)))) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)))) => ((! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((C = none_nat) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_succ_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ E @ F) @ B)))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ zero_zero_nat @ 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)) => ((((ord_less_nat @ B @ D) => (C = (some_nat @ D))) & ((~ (ord_less_nat @ B @ D)) => (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_maxt @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) & (vEBT_VEBT_less @ (some_nat @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (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 @ 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_succ @ (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_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) = none_nat) @ 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_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_succ @ H @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))))))))) @ none_nat)))) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_succ_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B)))))) | ~ (! [D:product_prod_nat_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_succ_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F) @ B)) | ~ (C = none_nat) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ D) @ (suc @ zero_zero_nat) @ E @ F))))))) | ~ (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (! [F:nat]: ((B = (suc @ F)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_succ_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ F))) | ~ (C = none_nat)))))) | ~ (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => ((B = zero_zero_nat) => ((((C = none_nat) | (E)) & ((E) => (C = (some_nat @ one_one_nat)))) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_succ_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ zero_zero_nat))))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_succ_rel) @ (produc738532404422230701BT_nat @ A @ B)) | ~ ((vEBT_vebt_succ @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7567])). 159.59/70.65 thf(1912,axiom,((! [A:nat,B:int]: (((bit_ri631733984087533419it_int @ A @ B) = B) = ((ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) & (ord_less_eq_int @ (uminus_uminus_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5320_signed__take__bit__int__eq__self__iff)). 159.59/70.65 thf(14427,plain,((! [A:nat,B:int]: (((bit_ri631733984087533419it_int @ A @ B) = B) = ((ord_less_int @ B @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) & (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)],[1912])). 159.59/70.65 thf(8014,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4480_minf_I5_J)). 159.59/70.65 thf(35860,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8014])). 159.59/70.65 thf(69,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/sandbox/benchmark/theBenchmark.p',fact_9610_and__not__numerals_I9_J)). 159.59/70.65 thf(8457,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)],[69])). 159.59/70.65 thf(424,axiom,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ A)) = (ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4679_neg__0__less__iff__less)). 159.59/70.65 thf(9582,plain,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ A)) = (ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])). 159.59/70.65 thf(2855,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) <= ((C = D) & (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_add__mono__thms__linordered__semiring_I3_J)). 159.59/70.65 thf(17430,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_eq_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D)) | ~ ((C = D) & (ord_less_eq_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2855])). 159.59/70.65 thf(3876,axiom,((exp_real = (^ [A:real]: (plus_plus_real @ (plus_plus_real @ one_one_real @ A) @ (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (plus_plus_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_real @ A @ (plus_plus_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9182_exp__first__two__terms)). 159.59/70.65 thf(20734,plain,(((exp_real) = (^ [A:real]: (plus_plus_real @ (plus_plus_real @ one_one_real @ A) @ (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (plus_plus_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_real @ A @ (plus_plus_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3876])). 159.59/70.65 thf(5294,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3255_linorder__le__less__linear)). 159.59/70.65 thf(25597,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5294])). 159.59/70.65 thf(6310,axiom,((! [A:num]: (ord_less_eq_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1957_zero__le__numeral)). 159.59/70.65 thf(29523,plain,((! [A:num]: (ord_less_eq_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6310])). 159.59/70.65 thf(3907,axiom,((bit_se2923211474154528505it_int = (^ [A:nat,B:int]: (if_int @ (A = zero_zero_nat) @ zero_zero_int @ (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ (minus_minus_nat @ A @ one_one_nat) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4599_take__bit__rec)). 159.59/70.65 thf(20828,plain,(((bit_se2923211474154528505it_int) = (^ [A:nat,B:int]: (if_int @ (A = zero_zero_nat) @ zero_zero_int @ (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ (minus_minus_nat @ A @ one_one_nat) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3907])). 159.59/70.65 thf(2922,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/sandbox/benchmark/theBenchmark.p',fact_4994_mod__minus__right)). 159.59/70.65 thf(17664,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)],[2922])). 159.59/70.65 thf(619,axiom,((! [A:complex,B:complex,C:complex]: (((A = zero_zero_complex) => ((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = C)) & (((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/sandbox/benchmark/theBenchmark.p',fact_2356_add__divide__eq__if__simps_I2_J)). 159.59/70.65 thf(10226,plain,((! [A:complex,B:complex,C:complex]: (((A = zero_zero_complex) => ((plus_plus_complex @ (divide1717551699836669952omplex @ B @ A) @ C) = C)) & (((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)],[619])). 159.59/70.65 thf(1729,axiom,((! [A:real,B:int]: ((archim7802044766580827645g_real @ (plus_plus_real @ A @ (ring_1_of_int_real @ B))) = (plus_plus_int @ (archim7802044766580827645g_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6971_ceiling__add__of__int)). 159.59/70.65 thf(13840,plain,((! [A:real,B:int]: ((archim7802044766580827645g_real @ (plus_plus_real @ A @ (ring_1_of_int_real @ B))) = (plus_plus_int @ (archim7802044766580827645g_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729])). 159.59/70.65 thf(5098,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2387_nat__mult__le__cancel1)). 159.59/70.65 thf(24905,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5098])). 159.59/70.65 thf(6412,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ zero_zero_nat)) => (? [C:nat]: ((A @ (suc @ C)) & ! [D:nat]: ((ord_less_eq_nat @ D @ C) => (~ (A @ D))) & (ord_less_nat @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2381_ex__least__nat__less)). 159.59/70.65 thf(29896,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ zero_zero_nat)) => (? [C:nat]: ((A @ (suc @ C)) & ! [D:nat]: ((ord_less_eq_nat @ D @ C) => (~ (A @ D))) & (ord_less_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6412])). 159.59/70.65 thf(144,axiom,((! [A:real]: ((archim2898591450579166408c_real @ (plus_plus_real @ A @ one_one_real)) = (archim2898591450579166408c_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9061_frac__1__eq)). 159.59/70.65 thf(8689,plain,((! [A:real]: ((archim2898591450579166408c_real @ (plus_plus_real @ A @ one_one_real)) = (archim2898591450579166408c_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 159.59/70.65 thf(3253,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ B @ C) => (ord_le72135733267957522d_enat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3081_order_Ostrict__trans1)). 159.59/70.65 thf(18715,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ B @ C) => (ord_le72135733267957522d_enat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3253])). 159.59/70.65 thf(1134,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) <= (ord_less_eq_set_nat @ B @ C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2728_order_Otrans)). 159.59/70.65 thf(11887,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (ord_less_eq_set_nat @ B @ C) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134])). 159.59/70.65 thf(7842,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/sandbox/benchmark/theBenchmark.p',fact_9168_binomial__r__part__sum)). 159.59/70.65 thf(35320,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)],[7842])). 159.59/70.65 thf(4259,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) = (? [B:nat]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B))) & (ord_less_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B)) @ A) & (B != zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9098_real__arch__inverse)). 159.59/70.65 thf(21918,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) = (? [B:nat]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B))) & (ord_less_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ B)) @ A) & ~ (B = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4259])). 159.59/70.65 thf(5798,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/sandbox/benchmark/theBenchmark.p',fact_4830_divide__eq__eq__numeral1_I2_J)). 159.59/70.65 thf(27526,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)],[5798])). 159.59/70.65 thf(2437,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_eq_real @ (minus_minus_real @ B @ C) @ A) & (ord_less_eq_real @ A @ (plus_plus_real @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5583_abs__diff__le__iff)). 159.59/70.65 thf(16094,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ A @ B)) @ C) = ((ord_less_eq_real @ (minus_minus_real @ B @ C) @ A) & (ord_less_eq_real @ A @ (plus_plus_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2437])). 159.59/70.65 thf(6596,axiom,((! [A:int,B:int]: (((times_times_int @ A @ A) = (times_times_int @ B @ B)) = ((A = B) | (A = (uminus_uminus_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4957_square__eq__iff)). 159.59/70.65 thf(30592,plain,((! [A:int,B:int]: (((times_times_int @ A @ A) = (times_times_int @ B @ B)) = ((A = B) | (A = (uminus_uminus_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6596])). 159.59/70.65 thf(1948,axiom,((! [A:(nat > real),B:real]: (((ord_less_real @ zero_zero_real @ B) => (~ (! [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)))))) <= (summable_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7781_summable__partial__sum__bound)). 159.59/70.65 thf(14535,plain,((! [A:(nat > real),B:real]: (((ord_less_real @ zero_zero_real @ B) => (~ (! [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)))))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1948])). 159.59/70.65 thf(535,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/sandbox/benchmark/theBenchmark.p',fact_959_max_Omono)). 159.59/70.65 thf(9958,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)],[535])). 159.59/70.65 thf(6028,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/sandbox/benchmark/theBenchmark.p',fact_6017_or__minus__numerals_I6_J)). 159.59/70.65 thf(28528,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)],[6028])). 159.59/70.65 thf(5108,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_minNull @ A) => (~ (vEBT_vebt_member @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_min__Null__member)). 159.59/70.65 thf(24937,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_minNull @ A) => (~ (vEBT_vebt_member @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5108])). 159.59/70.65 thf(4641,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (modulo_modulo_nat @ A @ B)) @ B) = (modulo_modulo_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3467_mod__Suc__eq)). 159.59/70.65 thf(23292,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)],[4641])). 159.59/70.65 thf(4293,axiom,((! [A:num]: ((neg_nu6511756317524482435omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu8557863876264182079omplex @ (numera6690914467698888265omplex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5759_dbl__dec__simps_I1_J)). 159.59/70.65 thf(22026,plain,((! [A:num]: ((neg_nu6511756317524482435omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu8557863876264182079omplex @ (numera6690914467698888265omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4293])). 159.59/70.65 thf(5225,axiom,(((minus_minus_real @ one_one_real @ (uminus_uminus_real @ one_one_real)) = (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4852_diff__numeral__special_I11_J)). 159.59/70.65 thf(25365,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)],[5225])). 159.59/70.65 thf(7501,axiom,((! [A:nat,B:nat,C:(nat > real),D:nat]: (((groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (times_times_real @ (groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups129246275422532515t_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/sandbox/benchmark/theBenchmark.p',fact_8807_prod_Oub__add__nat)). 159.59/70.65 thf(34190,plain,((! [A:nat,B:nat,C:(nat > real),D:nat]: (((groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (times_times_real @ (groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups129246275422532515t_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)],[7501])). 159.59/70.65 thf(1671,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/sandbox/benchmark/theBenchmark.p',fact_3572_divmod__digit__1_I2_J)). 159.59/70.65 thf(13662,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)],[1671])). 159.59/70.65 thf(5158,axiom,((! [A:(nat > $o),B:nat]: (((~ (A @ zero_zero_nat)) => (? [C:nat]: ((A @ C) & ! [D:nat]: ((ord_less_nat @ D @ C) => (~ (A @ D))) & (ord_less_eq_nat @ C @ B)))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2197_ex__least__nat__le)). 159.59/70.65 thf(25104,plain,((! [A:(nat > $o),B:nat]: (((~ (A @ zero_zero_nat)) => (? [C:nat]: ((A @ C) & ! [D:nat]: ((ord_less_nat @ D @ C) => (~ (A @ D))) & (ord_less_eq_nat @ C @ B)))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5158])). 159.59/70.65 thf(5855,axiom,((! [A:int,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (power_power_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3912_even__power)). 159.59/70.65 thf(27890,plain,((! [A:int,B:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (power_power_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5855])). 159.59/70.65 thf(4805,axiom,((! [A:nat]: (((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ one_one_real)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4898_neg__one__odd__power)). 159.59/70.65 thf(23851,plain,((! [A:nat]: (((power_power_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ one_one_real)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4805])). 159.59/70.65 thf(5637,axiom,((! [A:real]: ((log @ A @ one_one_real) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6323_log__one)). 159.59/70.65 thf(26899,plain,((! [A:real]: ((log @ A @ one_one_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5637])). 159.59/70.65 thf(7086,axiom,((! [A:$o,B:$o]: ((ord_less_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B)) = ((B) & ~ (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4317_of__bool__less__iff)). 159.59/70.65 thf(32685,plain,((! [A:$o,B:$o]: ((ord_less_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B)) = ((B) & ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7086])). 159.59/70.65 thf(2911,axiom,((! [A:int,B:int]: ((plus_plus_int @ (uminus_uminus_int @ A) @ (plus_plus_int @ A @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4640_minus__add__cancel)). 159.59/70.65 thf(17625,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)],[2911])). 159.59/70.65 thf(907,axiom,((! [A:complex,B:complex]: (sums_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (if_complex @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (times_times_complex @ (real_V2046097035970521341omplex @ (uminus_uminus_real @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C))) @ (power_power_complex @ A @ D)) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_complex)) @ (set_ord_atMost_nat @ C))) @ (times_times_complex @ (sin_complex @ A) @ (sin_complex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9177_sin__x__sin__y)). 159.59/70.65 thf(11161,plain,((! [A:complex,B:complex]: (sums_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (if_complex @ ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) @ (times_times_complex @ (real_V2046097035970521341omplex @ (uminus_uminus_real @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C))) @ (power_power_complex @ A @ D)) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_complex)) @ (set_ord_atMost_nat @ C))) @ (times_times_complex @ (sin_complex @ A) @ (sin_complex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[907])). 159.59/70.65 thf(2090,axiom,((! [A:real,B:real,C:nat]: (((((archim7802044766580827645g_real @ (log @ B @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int)) = ((ord_less_eq_real @ A @ (powr_real @ B @ (semiri5074537144036343181t_real @ (plus_plus_nat @ C @ one_one_nat)))) & (ord_less_real @ (powr_real @ B @ (semiri5074537144036343181t_real @ C)) @ A))) <= (ord_less_real @ one_one_real @ B)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7209_ceiling__log__eq__powr__iff)). 159.59/70.65 thf(14983,plain,((! [A:real,B:real,C:nat]: ((((archim7802044766580827645g_real @ (log @ B @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ C) @ one_one_int)) = ((ord_less_eq_real @ A @ (powr_real @ B @ (semiri5074537144036343181t_real @ (plus_plus_nat @ C @ one_one_nat)))) & (ord_less_real @ (powr_real @ B @ (semiri5074537144036343181t_real @ C)) @ A))) | ~ (ord_less_real @ one_one_real @ B) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2090])). 159.59/70.65 thf(7169,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/sandbox/benchmark/theBenchmark.p',fact_1994_mult__left__mono__neg)). 159.59/70.65 thf(33021,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)],[7169])). 159.59/70.65 thf(1432,axiom,((! [A:real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1665_one__divide__eq__0__iff)). 159.59/70.65 thf(12922,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)],[1432])). 159.59/70.65 thf(7987,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/sandbox/benchmark/theBenchmark.p',fact_360_power__commutes)). 159.59/70.65 thf(35772,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)],[7987])). 159.59/70.65 thf(6701,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3468_mod__less__eq__dividend)). 159.59/70.65 thf(31014,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6701])). 159.59/70.65 thf(5566,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_lift__Suc__mono__less__iff)). 159.59/70.65 thf(26651,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5566])). 159.59/70.65 thf(5679,axiom,((! [A:num]: ((one_one_int = (numeral_numeral_int @ A)) = (one = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_one__eq__numeral__iff)). 159.59/70.65 thf(27065,plain,((! [A:num]: ((one_one_int = (numeral_numeral_int @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5679])). 159.59/70.65 thf(4887,axiom,((! [A:nat,B:nat,C:complex]: (((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)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7784_sum__gp__multiplied)). 159.59/70.65 thf(24143,plain,((! [A:nat,B:nat,C:complex]: (((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)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4887])). 159.59/70.65 thf(7067,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) <= (ord_less_eq_nat @ D @ E))) => ((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2720_linorder__wlog)). 159.59/70.65 thf(32602,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) | ~ (ord_less_eq_nat @ D @ E))) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7067])). 159.59/70.65 thf(7130,axiom,((! [A:list_VEBT_VEBT,B:list_o]: ((size_s9168528473962070013VEBT_o @ (product_VEBT_VEBT_o @ A @ B)) = (times_times_nat @ (size_s6755466524823107622T_VEBT @ A) @ (size_size_list_o @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3623_length__product)). 159.59/70.65 thf(32878,plain,((! [A:list_VEBT_VEBT,B:list_o]: ((size_s9168528473962070013VEBT_o @ (product_VEBT_VEBT_o @ A @ B)) = (times_times_nat @ (size_s6755466524823107622T_VEBT @ A) @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7130])). 159.59/70.65 thf(7297,axiom,((! [A:(num > (num > $o)),B:num,C:num]: ((! [D:num,E:num]: ((A @ D @ E) <= (ord_less_eq_num @ D @ E))) => ((A @ B @ C) <= (! [D:num,E:num]: ((A @ D @ E) <= (A @ E @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2719_linorder__wlog)). 159.59/70.65 thf(33470,plain,((! [A:(num > (num > $o)),B:num,C:num]: ((! [D:num,E:num]: ((A @ D @ E) | ~ (ord_less_eq_num @ D @ E))) => ((A @ B @ C) | ~ (! [D:num,E:num]: ((A @ D @ E) | ~ (A @ E @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7297])). 159.59/70.65 thf(4832,axiom,((! [A:list_o,B:list_o]: ((A != B) <= ((size_size_list_o @ A) != (size_size_list_o @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_size__neq__size__imp__neq)). 159.59/70.65 thf(23975,plain,((! [A:list_o,B:list_o]: (~ (A = B) | ((size_size_list_o @ A) = (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4832])). 159.59/70.65 thf(8106,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/sandbox/benchmark/theBenchmark.p',fact_8117_square__fact__le__2__fact)). 159.59/70.65 thf(36167,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)],[8106])). 159.59/70.65 thf(429,axiom,((! [A:nat]: ((comm_s4660882817536571857er_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ A) = (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A) @ (semiri1406184849735516958ct_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8331_pochhammer__same)). 159.59/70.65 thf(9595,plain,((! [A:nat]: ((comm_s4660882817536571857er_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ A) = (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ A) @ (semiri1406184849735516958ct_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])). 159.59/70.65 thf(7229,axiom,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1247_mult_Ocomm__neutral)). 159.59/70.65 thf(33253,plain,((! [A:complex]: ((times_times_complex @ A @ one_one_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7229])). 159.59/70.65 thf(7933,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/sandbox/benchmark/theBenchmark.p',fact_372_power__mult)). 159.59/70.65 thf(35608,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)],[7933])). 159.59/70.65 thf(1546,axiom,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ one_one_int @ (semiri1314217659103216013at_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6583_of__nat__Suc)). 159.59/70.65 thf(13278,plain,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ one_one_int @ (semiri1314217659103216013at_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1546])). 159.59/70.65 thf(6401,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (ord_max_nat @ B @ C)) = ((ord_less_eq_nat @ A @ C) | (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_918_le__max__iff__disj)). 159.59/70.65 thf(29854,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (ord_max_nat @ B @ C)) = ((ord_less_eq_nat @ A @ C) | (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6401])). 159.59/70.65 thf(4555,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ A @ B) = (divide_divide_nat @ C @ B)) => ((dvd_dvd_nat @ B @ A) => ((dvd_dvd_nat @ B @ C) => (A = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4013_dvd__div__eq__cancel)). 159.59/70.65 thf(22984,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ A @ B) = (divide_divide_nat @ C @ B)) => ((dvd_dvd_nat @ B @ A) => ((dvd_dvd_nat @ B @ C) => (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4555])). 159.59/70.65 thf(2488,axiom,((! [A:set_nat,B:(nat > real),C:(nat > 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)))) & ((~ ((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7373_sum__zero__power_H)). 159.59/70.65 thf(16253,plain,((! [A:set_nat,B:(nat > real),C:(nat > 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)))) & ((~ ((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2488])). 159.59/70.65 thf(958,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/sandbox/benchmark/theBenchmark.p',fact_7450_complex__of__real__mult__Complex)). 159.59/70.65 thf(11316,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)],[958])). 159.59/70.65 thf(4419,axiom,((! [A:num,B:real,C:real]: ((ord_less_real @ (numeral_numeral_real @ A) @ (divide_divide_real @ B @ 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))))) & ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ (numeral_numeral_real @ A) @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2441_less__divide__eq__numeral_I1_J)). 159.59/70.65 thf(22414,plain,((! [A:num,B:real,C:real]: ((ord_less_real @ (numeral_numeral_real @ A) @ (divide_divide_real @ B @ 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))))) & ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ (numeral_numeral_real @ A) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4419])). 159.59/70.65 thf(3370,axiom,((! [A:real,B:real,C:real]: (((! [D:real]: (((ord_less_eq_real @ D @ C) <= (ord_less_real @ D @ B)) <= (ord_less_real @ A @ D))) => (ord_less_eq_real @ B @ C)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3103_dense__le__bounded)). 159.59/70.65 thf(19080,plain,((! [A:real,B:real,C:real]: (((! [D:real]: ((ord_less_eq_real @ D @ C) | ~ (ord_less_real @ D @ B) | ~ (ord_less_real @ A @ D))) => (ord_less_eq_real @ B @ C)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3370])). 159.59/70.65 thf(1259,axiom,((! [A:real,B:real]: (((divide_divide_real @ B @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (divide_divide_real @ B @ A))) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5116_dvd__div__neg)). 159.59/70.65 thf(12326,plain,((! [A:real,B:real]: (((divide_divide_real @ B @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (divide_divide_real @ B @ A))) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259])). 159.59/70.65 thf(3865,axiom,((! [A:$o]: (((zero_n356916108424825756nteger @ A) = one_one_Code_integer) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4331_of__bool__eq__1__iff)). 159.59/70.65 thf(20692,plain,((! [A:$o]: (((zero_n356916108424825756nteger @ A) = one_one_Code_integer) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3865])). 159.59/70.65 thf(7915,axiom,((! [A:num,B:num]: ((bit_se2925701944663578781it_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ (times_times_nat @ (bit_se2925701944663578781it_nat @ (pred_numeral @ A) @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5743_take__bit__numeral__bit1)). 159.59/70.65 thf(35555,plain,((! [A:num,B:num]: ((bit_se2925701944663578781it_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ (times_times_nat @ (bit_se2925701944663578781it_nat @ (pred_numeral @ A) @ (numeral_numeral_nat @ B)) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7915])). 159.59/70.65 thf(7191,axiom,((! [A:nat]: ((power_power_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1679_power__0__Suc)). 159.59/70.65 thf(33112,plain,((! [A:nat]: ((power_power_int @ zero_zero_int @ (suc @ A)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7191])). 159.59/70.65 thf(3141,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_eq_real @ (log @ A @ B) @ C) = (ord_less_eq_real @ B @ (powr_real @ A @ C))) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7272_log__le__iff)). 159.59/70.65 thf(18358,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_eq_real @ (log @ A @ B) @ C) = (ord_less_eq_real @ B @ (powr_real @ A @ C))) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3141])). 159.59/70.65 thf(5178,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/sandbox/benchmark/theBenchmark.p',fact_8094_choose__dvd)). 159.59/70.65 thf(25181,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)],[5178])). 159.59/70.65 thf(3550,axiom,((! [A:complex]: (ord_less_eq_real @ (uminus_uminus_real @ (real_V1022390504157884413omplex @ A)) @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6818_complex__mod__minus__le__complex__mod)). 159.59/70.65 thf(19641,plain,((! [A:complex]: (ord_less_eq_real @ (uminus_uminus_real @ (real_V1022390504157884413omplex @ A)) @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3550])). 159.59/70.65 thf(6551,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/sandbox/benchmark/theBenchmark.p',fact_466_div__exp__eq)). 159.59/70.65 thf(30434,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)],[6551])). 159.59/70.65 thf(1064,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/sandbox/benchmark/theBenchmark.p',fact_1244_ring__class_Oring__distribs_I2_J)). 159.59/70.65 thf(11665,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)],[1064])). 159.59/70.65 thf(2724,axiom,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ A @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_complex @ (groups6464643781859351333omplex @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8448_prod_OatMost__Suc)). 159.59/70.65 thf(17038,plain,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (times_times_complex @ (groups6464643781859351333omplex @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2724])). 159.59/70.65 thf(798,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/sandbox/benchmark/theBenchmark.p',fact_1368_ordered__ring__class_Ole__add__iff2)). 159.59/70.65 thf(10824,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)],[798])). 159.59/70.65 thf(3435,axiom,((! [A:int]: ((! [B:nat]: ((bit_se1146084159140164899it_int @ A @ B) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))) => ((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6425_bit__iff__idd__imp__stable)). 159.59/70.65 thf(19293,plain,((! [A:int]: ((! [B:nat]: ((bit_se1146084159140164899it_int @ A @ B) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))) => ((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3435])). 159.59/70.65 thf(6483,axiom,((! [A:real]: ((sqrt @ (times_times_real @ A @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6324_real__sqrt__abs2)). 159.59/70.65 thf(30191,plain,((! [A:real]: ((sqrt @ (times_times_real @ A @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6483])). 159.59/70.65 thf(2300,axiom,((! [A:int,B:int]: ((ord_less_int @ (plus_plus_int @ A @ B) @ B) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1604_add__less__same__cancel2)). 159.59/70.65 thf(15657,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)],[2300])). 159.59/70.65 thf(2958,axiom,((! [A:complex]: (((real_V1022390504157884413omplex @ (cos_complex @ A)) = one_one_real) <= ((sin_complex @ A) = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7115_sin__zero__norm__cos__one)). 159.59/70.65 thf(17781,plain,((! [A:complex]: (((real_V1022390504157884413omplex @ (cos_complex @ A)) = one_one_real) | ~ ((sin_complex @ A) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2958])). 159.59/70.65 thf(2214,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/sandbox/benchmark/theBenchmark.p',fact_1462_mint__corr__help__empty)). 159.59/70.65 thf(15400,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)],[2214])). 159.59/70.65 thf(5789,axiom,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_num @ (C @ A) @ D)) <= (ord_less_num @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3229_order__le__less__subst2)). 159.59/70.65 thf(27498,plain,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => (((! [E:nat,F:nat]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_num @ (C @ A) @ D)) | ~ (ord_less_num @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5789])). 159.59/70.65 thf(1371,axiom,((! [A:nat,B:real]: (((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))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8339_gbinomial__reduce__nat)). 159.59/70.65 thf(12708,plain,((! [A:nat,B:real]: (((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))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371])). 159.59/70.65 thf(4106,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/sandbox/benchmark/theBenchmark.p',fact_6911_power__eq__imp__eq__norm)). 159.59/70.65 thf(21425,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)],[4106])). 159.59/70.65 thf(4681,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)) = ((B = F) & (C = G) & (D = H) & (A = E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_VEBT_Oinject_I1_J)). 159.59/70.65 thf(23434,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)) = ((B = F) & (C = G) & (D = H) & (A = E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4681])). 159.59/70.65 thf(3307,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 @ C @ D)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1315_add__le__less__mono)). 159.59/70.65 thf(18891,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 @ C @ D) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3307])). 159.59/70.65 thf(1508,axiom,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (groups129246275422532515t_real @ (^ [C:nat]: (plus_plus_real @ A @ (semiri5074537144036343181t_real @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8919_pochhammer__Suc__prod__rev)). 159.59/70.65 thf(13168,plain,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (groups129246275422532515t_real @ (^ [C:nat]: (plus_plus_real @ A @ (semiri5074537144036343181t_real @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508])). 159.59/70.65 thf(3517,axiom,((! [A:extended_enat,B:(nat > extended_enat),C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((ord_le72135733267957522d_enat @ A @ (B @ D)) <= (! [E:nat,F:nat]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) <= (ord_less_nat @ E @ F))))) <= (ord_le72135733267957522d_enat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2891_order__less__subst1)). 159.59/70.65 thf(19542,plain,((! [A:extended_enat,B:(nat > extended_enat),C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((ord_le72135733267957522d_enat @ A @ (B @ D)) | ~ (! [E:nat,F:nat]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) | ~ (ord_less_nat @ E @ F))))) | ~ (ord_le72135733267957522d_enat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3517])). 159.59/70.65 thf(6048,axiom,((! [A:int,B:int,C:nat]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) <= (ord_less_eq_int @ zero_zero_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2153_power__mono)). 159.59/70.65 thf(28593,plain,((! [A:int,B:int,C:nat]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C)) | ~ (ord_less_eq_int @ zero_zero_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6048])). 159.59/70.65 thf(3442,axiom,((! [A:(nat > extended_enat),B:nat,C:nat]: ((! [D:nat]: (ord_le72135733267957522d_enat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_le72135733267957522d_enat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_lift__Suc__mono__less__iff)). 159.59/70.65 thf(19316,plain,((! [A:(nat > extended_enat),B:nat,C:nat]: ((! [D:nat]: (ord_le72135733267957522d_enat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_le72135733267957522d_enat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3442])). 159.59/70.65 thf(6038,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/sandbox/benchmark/theBenchmark.p',fact_5837_of__int__eq__numeral__power__cancel__iff)). 159.59/70.65 thf(28561,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)],[6038])). 159.59/70.65 thf(6011,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/sandbox/benchmark/theBenchmark.p',fact_1798_sum__power2__eq__zero__iff)). 159.59/70.65 thf(28475,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)],[6011])). 159.59/70.65 thf(1820,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/sandbox/benchmark/theBenchmark.p',fact_4122_le__imp__power__dvd)). 159.59/70.65 thf(14126,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)],[1820])). 159.59/70.65 thf(3348,axiom,((! [A:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (exp_real @ A)) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6867_exp__bound__half)). 159.59/70.65 thf(19018,plain,((! [A:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ A) @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (exp_real @ A)) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3348])). 159.59/70.65 thf(1176,axiom,((ord_less_real = (^ [A:real,B:real]: ((ord_less_eq_real @ A @ B) & ~ (ord_less_eq_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3096_order_Ostrict__iff__not)). 159.59/70.65 thf(12021,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)],[1176])). 159.59/70.65 thf(7658,axiom,(((ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) & (ord_less_eq_nat @ mi @ ma))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103__C6_C)). 159.59/70.65 thf(34724,plain,(((ord_less_nat @ ma @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) & (ord_less_eq_nat @ mi @ ma))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7658])). 159.59/70.65 thf(2736,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/sandbox/benchmark/theBenchmark.p',fact_2310_power__less__imp__less__base)). 159.59/70.65 thf(17070,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)],[2736])). 159.59/70.65 thf(1438,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/sandbox/benchmark/theBenchmark.p',fact_1174_add__mono__thms__linordered__semiring_I1_J)). 159.59/70.65 thf(12941,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)],[1438])). 159.59/70.65 thf(275,axiom,((! [A:complex,B:complex]: ((ord_less_real @ (im @ (divide1717551699836669952omplex @ A @ B)) @ zero_zero_real) = (ord_less_real @ (im @ (times_times_complex @ A @ (cnj @ B))) @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9695_Im__complex__div__lt__0)). 159.59/70.65 thf(9086,plain,((! [A:complex,B:complex]: ((ord_less_real @ (im @ (divide1717551699836669952omplex @ A @ B)) @ zero_zero_real) = (ord_less_real @ (im @ (times_times_complex @ A @ (cnj @ B))) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 159.59/70.65 thf(6128,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1566_mult__0__right)). 159.59/70.65 thf(28845,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6128])). 159.59/70.65 thf(5382,axiom,((zero_zero_complex != (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5070_zero__neq__neg__one)). 159.59/70.65 thf(25995,plain,((~ (zero_zero_complex = (uminus1482373934393186551omplex @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5382])). 159.59/70.65 thf(3758,axiom,((! [A:real,B:real,C:real]: ((B = C) <= ((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1116_add__left__imp__eq)). 159.59/70.65 thf(20338,plain,((! [A:real,B:real,C:real]: ((B = C) | ~ ((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3758])). 159.59/70.65 thf(5340,axiom,((! [A:$o,B:$o]: ((vEBT_vebt_delete @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = (vEBT_Leaf @ ($false) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1801_vebt__delete_Osimps_I1_J)). 159.59/70.65 thf(25803,plain,((! [A:$o,B:$o]: ((vEBT_vebt_delete @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = (vEBT_Leaf @ ($false) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5340])). 159.59/70.65 thf(2179,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/sandbox/benchmark/theBenchmark.p',fact_5822_of__int__less__numeral__iff)). 159.59/70.65 thf(15276,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)],[2179])). 159.59/70.65 thf(452,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ (semiri4939895301339042750nteger @ A)) @ B) = zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8281_pochhammer__of__nat__eq__0__lemma)). 159.59/70.65 thf(9673,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ (semiri4939895301339042750nteger @ A)) @ B) = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[452])). 159.59/70.65 thf(4733,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/sandbox/benchmark/theBenchmark.p',fact_3802_div__dvd__div)). 159.59/70.65 thf(23600,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)],[4733])). 159.59/70.65 thf(2032,axiom,((! [A:nat]: ((zero_z5237406670263579293d_enat = (semiri4216267220026989637d_enat @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6501_of__nat__0__eq__iff)). 159.59/70.65 thf(14813,plain,((! [A:nat]: ((zero_z5237406670263579293d_enat = (semiri4216267220026989637d_enat @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2032])). 159.59/70.65 thf(1247,axiom,((! [A:real]: (ord_less_real @ A @ (plus_plus_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8259_real__of__int__floor__add__one__gt)). 159.59/70.65 thf(12288,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)],[1247])). 159.59/70.65 thf(3564,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/sandbox/benchmark/theBenchmark.p',fact_6913_norm__mult__less)). 159.59/70.65 thf(19695,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)],[3564])). 159.59/70.65 thf(872,axiom,((! [A:nat,B:nat]: (((times_times_complex @ (semiri5044797733671781792omplex @ A) @ (semiri8010041392384452111omplex @ (binomial @ B @ A))) = (divide1717551699836669952omplex @ (semiri5044797733671781792omplex @ B) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ B @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9134_fact__binomial)). 159.59/70.65 thf(11062,plain,((! [A:nat,B:nat]: (((times_times_complex @ (semiri5044797733671781792omplex @ A) @ (semiri8010041392384452111omplex @ (binomial @ B @ A))) = (divide1717551699836669952omplex @ (semiri5044797733671781792omplex @ B) @ (semiri5044797733671781792omplex @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[872])). 159.59/70.65 thf(7682,axiom,((! [A:num]: ((num_of_nat @ (numeral_numeral_nat @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9785_num__of__nat__numeral__eq)). 159.59/70.65 thf(34802,plain,((! [A:num]: ((num_of_nat @ (numeral_numeral_nat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7682])). 159.59/70.65 thf(1784,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/sandbox/benchmark/theBenchmark.p',fact_7980_power__diff__1__eq)). 159.59/70.65 thf(14012,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)],[1784])). 159.59/70.65 thf(7011,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/sandbox/benchmark/theBenchmark.p',fact_1339_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2)). 159.59/70.65 thf(32390,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)],[7011])). 159.59/70.65 thf(7194,axiom,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (power_power_nat @ A @ B)) = (power_power_real @ (semiri5074537144036343181t_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6556_of__nat__power)). 159.59/70.65 thf(33121,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)],[7194])). 159.59/70.65 thf(5059,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) => ((divide_divide_nat @ B @ A) = (suc @ (divide_divide_nat @ (minus_minus_nat @ B @ A) @ A)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2534_le__div__geq)). 159.59/70.65 thf(24767,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) => ((divide_divide_nat @ B @ A) = (suc @ (divide_divide_nat @ (minus_minus_nat @ B @ A) @ A)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5059])). 159.59/70.65 thf(3248,axiom,((ord_less_real @ (ln_ln_real @ (numeral_numeral_real @ (bit0 @ one))) @ one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5345_ln__2__less__1)). 159.59/70.65 thf(18698,plain,((ord_less_real @ (ln_ln_real @ (numeral_numeral_real @ (bit0 @ one))) @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3248])). 159.59/70.65 thf(7487,axiom,((! [A:(nat > $o),B:(nat > $o)]: (((collect_nat @ A) = (collect_nat @ B)) <= (! [C:nat]: ((A @ C) = (B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Collect__cong)). 159.59/70.65 thf(34151,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)],[7487])). 159.59/70.65 thf(6195,axiom,((! [A:nat,B:real]: ((times_times_real @ (semiri5074537144036343181t_real @ A) @ B) = (times_times_real @ B @ (semiri5074537144036343181t_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6649_mult__of__nat__commute)). 159.59/70.65 thf(29078,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)],[6195])). 159.59/70.65 thf(3999,axiom,((! [A:set_nat,B:nat,C:(nat > complex)]: ((((~ (member_nat @ B @ A)) => ((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (D = B) @ (C @ D) @ one_one_complex)) @ A) = one_one_complex)) & (((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (D = B) @ (C @ D) @ one_one_complex)) @ A) = (C @ B)) <= (member_nat @ B @ A))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8420_prod_Odelta)). 159.59/70.65 thf(21103,plain,((! [A:set_nat,B:nat,C:(nat > complex)]: ((((~ (member_nat @ B @ A)) => ((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (D = B) @ (C @ D) @ one_one_complex)) @ A) = one_one_complex)) & (((groups6464643781859351333omplex @ (^ [D:nat]: (if_complex @ (D = B) @ (C @ D) @ one_one_complex)) @ A) = (C @ B)) | ~ (member_nat @ B @ A))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3999])). 159.59/70.65 thf(608,axiom,((! [A:complex]: ((times_times_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) = one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6093_exp__minus__inverse)). 159.59/70.65 thf(10191,plain,((! [A:complex]: ((times_times_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[608])). 159.59/70.65 thf(350,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/sandbox/benchmark/theBenchmark.p',fact_9605_or__not__numerals_I3_J)). 159.59/70.65 thf(9334,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)],[350])). 159.59/70.65 thf(1376,axiom,((! [A:list_o]: (ord_less_int @ (groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (size_size_list_o @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9539_horner__sum__of__bool__2__less)). 159.59/70.65 thf(12723,plain,((! [A:list_o]: (ord_less_int @ (groups9116527308978886569_o_int @ (zero_n2684676970156552555ol_int) @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ (size_size_list_o @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376])). 159.59/70.65 thf(4173,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/sandbox/benchmark/theBenchmark.p',fact_7156_cos__plus__cos)). 159.59/70.65 thf(21639,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)],[4173])). 159.59/70.65 thf(658,axiom,((! [A:nat,B:nat,C:list_int,D:int]: (((nth_int @ (list_update_int @ C @ A @ D) @ B) = (nth_int @ C @ B)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_nth__list__update__neq)). 159.59/70.65 thf(10354,plain,((! [A:nat,B:nat,C:list_int,D:int]: (((nth_int @ (list_update_int @ C @ A @ D) @ B) = (nth_int @ C @ B)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[658])). 159.59/70.65 thf(7439,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/sandbox/benchmark/theBenchmark.p',fact_3553_unique__euclidean__semiring__numeral__class_Omod__mult2__eq)). 159.59/70.65 thf(33947,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)],[7439])). 159.59/70.65 thf(8222,axiom,((! [A:nat,B:nat]: ((bit_se2925701944663578781it_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ (ord_less_nat @ B @ A)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4908_take__bit__of__exp)). 159.59/70.65 thf(36543,plain,((! [A:nat,B:nat]: ((bit_se2925701944663578781it_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ (ord_less_nat @ B @ A)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8222])). 159.59/70.65 thf(4673,axiom,((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4189_even__zero)). 159.59/70.65 thf(23413,plain,((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4673])). 159.59/70.65 thf(3851,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4467_minf_I3_J)). 159.59/70.65 thf(20650,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3851])). 159.59/70.65 thf(459,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/sandbox/benchmark/theBenchmark.p',fact_904_max_OcoboundedI1)). 159.59/70.65 thf(9695,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)],[459])). 159.59/70.65 thf(6632,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/sandbox/benchmark/theBenchmark.p',fact_8455_prod_Ocl__ivl__Suc)). 159.59/70.65 thf(30714,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)],[6632])). 159.59/70.65 thf(1186,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ C @ B) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ C @ A) @ (divide6298287555418463151nteger @ B @ A))) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4095_div__plus__div__distrib__dvd__right)). 159.59/70.65 thf(12048,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ C @ B) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ C @ A) @ (divide6298287555418463151nteger @ B @ A))) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186])). 159.59/70.65 thf(3913,axiom,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ B) = (minus_8373710615458151222nteger @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4713_uminus__add__conv__diff)). 159.59/70.65 thf(20843,plain,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ B) = (minus_8373710615458151222nteger @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3913])). 159.59/70.65 thf(7360,axiom,((! [A:int,B:num]: ((ord_less_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_int @ zero_zero_int @ A)) | ((A != zero_zero_int) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))) | ((numeral_numeral_nat @ B) = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3900_zero__less__power__eq__numeral)). 159.59/70.65 thf(33702,plain,((! [A:int,B:num]: ((ord_less_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_int @ zero_zero_int @ A)) | (~ (A = zero_zero_int) & (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)],[7360])). 159.59/70.65 thf(7605,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/sandbox/benchmark/theBenchmark.p',fact_6291_and__nat__unfold)). 159.59/70.65 thf(34573,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)],[7605])). 159.59/70.65 thf(6503,axiom,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1075_mult__1)). 159.59/70.65 thf(30255,plain,((! [A:complex]: ((times_times_complex @ one_one_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6503])). 159.59/70.65 thf(618,axiom,((! [A:real,B:real]: (((complex2 @ A @ B) = one_one_complex) = ((A = one_one_real) & (B = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7240_Complex__eq__1)). 159.59/70.65 thf(10223,plain,((! [A:real,B:real]: (((complex2 @ A @ B) = one_one_complex) = ((A = one_one_real) & (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[618])). 159.59/70.65 thf(238,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/sandbox/benchmark/theBenchmark.p',fact_9680_complex__abs__le__norm)). 159.59/70.65 thf(8979,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)],[238])). 159.59/70.65 thf(3025,axiom,((! [A:(nat > real),B:nat,C:real]: ? [D:(nat > real)]: ! [E:real]: ((groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (A @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ B)) = (plus_plus_real @ (times_times_real @ (minus_minus_real @ E @ C) @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (D @ F) @ (power_power_real @ E @ F))) @ (set_ord_lessThan_nat @ B))) @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (A @ F) @ (power_power_real @ C @ F))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8887_polyfun__linear__factor)). 159.59/70.65 thf(17977,plain,((! [A:(nat > real),B:nat,C:real]: ? [D:(nat > real)]: ! [E:real]: ((groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (A @ F) @ (power_power_real @ E @ F))) @ (set_ord_atMost_nat @ B)) = (plus_plus_real @ (times_times_real @ (minus_minus_real @ E @ C) @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (D @ F) @ (power_power_real @ E @ F))) @ (set_ord_lessThan_nat @ B))) @ (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (A @ F) @ (power_power_real @ C @ F))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3025])). 159.59/70.65 thf(2036,axiom,((ord_less_real @ zero_zero_real @ (plus_plus_real @ one_one_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2321_zero__less__two)). 159.59/70.65 thf(14827,plain,((ord_less_real @ zero_zero_real @ (plus_plus_real @ one_one_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2036])). 159.59/70.65 thf(809,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/sandbox/benchmark/theBenchmark.p',fact_2547_not__sum__power2__lt__zero)). 159.59/70.65 thf(10867,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)],[809])). 159.59/70.65 thf(5681,axiom,((nat_prod_encode = (produc6842872674320459806at_nat @ (^ [A:nat,B:nat]: (plus_plus_nat @ (nat_triangle @ (plus_plus_nat @ A @ B)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10207_prod__encode__def)). 159.59/70.65 thf(27072,plain,(((nat_prod_encode) = (produc6842872674320459806at_nat @ (^ [A:nat,B:nat]: (plus_plus_nat @ (nat_triangle @ (plus_plus_nat @ A @ B)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5681])). 159.59/70.65 thf(1347,axiom,((! [A:real]: (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ (nat2 @ (archim7802044766580827645g_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9442_real__nat__ceiling__ge)). 159.59/70.65 thf(12599,plain,((! [A:real]: (ord_less_eq_real @ A @ (semiri5074537144036343181t_real @ (nat2 @ (archim7802044766580827645g_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347])). 159.59/70.65 thf(1664,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/sandbox/benchmark/theBenchmark.p',fact_5846_of__int__power__less__of__int__cancel__iff)). 159.59/70.65 thf(13641,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)],[1664])). 159.59/70.65 thf(224,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B)) @ C) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ (real_V1485227260804924795R_real @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9276_pos__minus__divideR__le__eq)). 159.59/70.65 thf(8936,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ B)) @ C) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ (real_V1485227260804924795R_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 159.59/70.65 thf(4371,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 @ C @ zero_zero_real)) => (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ 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 @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5280_less__divide__eq__numeral_I2_J)). 159.59/70.65 thf(22251,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 @ C @ zero_zero_real)) => (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ 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 @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4371])). 159.59/70.65 thf(5643,axiom,((! [A:num]: (ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5165_neg__numeral__le__one)). 159.59/70.65 thf(26914,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)],[5643])). 159.59/70.65 thf(2229,axiom,((! [A:nat]: ((nat2 @ (bit_se2000444600071755411sk_int @ A)) = (bit_se2002935070580805687sk_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9431_nat__mask__eq)). 159.59/70.65 thf(15447,plain,((! [A:nat]: ((nat2 @ (bit_se2000444600071755411sk_int @ A)) = (bit_se2002935070580805687sk_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2229])). 159.59/70.65 thf(3033,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (uminus_uminus_int @ B)) = (ord_less_int @ B @ (uminus_uminus_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4939_less__minus__iff)). 159.59/70.65 thf(18000,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)],[3033])). 159.59/70.65 thf(1355,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/sandbox/benchmark/theBenchmark.p',fact_5730_even__abs__add__iff)). 159.59/70.65 thf(12627,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)],[1355])). 159.59/70.65 thf(5036,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/sandbox/benchmark/theBenchmark.p',fact_4925_minus__le__iff)). 159.59/70.65 thf(24674,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)],[5036])). 159.59/70.65 thf(2870,axiom,((! [A:real]: (((ord_less_real @ A @ one_one_real) => (ord_less_eq_real @ (ln_ln_real @ (minus_minus_real @ one_one_real @ A)) @ (uminus_uminus_real @ A))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5130_ln__one__minus__pos__upper__bound)). 159.59/70.65 thf(17487,plain,((! [A:real]: (((ord_less_real @ A @ one_one_real) => (ord_less_eq_real @ (ln_ln_real @ (minus_minus_real @ one_one_real @ A)) @ (uminus_uminus_real @ A))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2870])). 159.59/70.65 thf(2096,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/sandbox/benchmark/theBenchmark.p',fact_6290_round__diff__minimal)). 159.59/70.65 thf(15004,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)],[2096])). 159.59/70.65 thf(828,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/sandbox/benchmark/theBenchmark.p',fact_9364_cmod__unit__one)). 159.59/70.65 thf(10920,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)],[828])). 159.59/70.65 thf(2865,axiom,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ one_one_real) = (((ord_less_real @ B @ A) & (ord_less_real @ B @ zero_zero_real)) | (B = zero_zero_real) | ((ord_less_real @ A @ B) & (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2342_divide__less__eq__1)). 159.59/70.65 thf(17472,plain,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ one_one_real) = (((ord_less_real @ B @ A) & (ord_less_real @ B @ zero_zero_real)) | (B = zero_zero_real) | ((ord_less_real @ A @ B) & (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2865])). 159.59/70.65 thf(3164,axiom,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se1745604003318907178nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4874_even__take__bit__eq)). 159.59/70.65 thf(18434,plain,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se1745604003318907178nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3164])). 159.59/70.65 thf(1861,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/sandbox/benchmark/theBenchmark.p',fact_8118_cos__coeff__def)). 159.59/70.65 thf(14265,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)],[1861])). 159.59/70.65 thf(877,axiom,((! [A:extended_enat,B:extended_enat]: (((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B) => (((plus_p3455044024723400733d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((B = zero_z5237406670263579293d_enat) & (A = zero_z5237406670263579293d_enat)))) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2020_add__nonneg__eq__0__iff)). 159.59/70.65 thf(11077,plain,((! [A:extended_enat,B:extended_enat]: (((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B) => (((plus_p3455044024723400733d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((B = zero_z5237406670263579293d_enat) & (A = zero_z5237406670263579293d_enat)))) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[877])). 159.59/70.65 thf(7227,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/sandbox/benchmark/theBenchmark.p',fact_5732_take__bit__numeral__minus__bit1)). 159.59/70.65 thf(33243,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)],[7227])). 159.59/70.65 thf(7070,axiom,((! [A:num]: (zero_zero_int != (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5033_zero__neq__neg__numeral)). 159.59/70.65 thf(32613,plain,((! [A:num]: ~ (zero_zero_int = (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7070])). 159.59/70.65 thf(7928,axiom,(((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ xa @ ma)) @ deg @ treeList @ summary) @ xa) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma))) @ deg @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ summary))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_dsimp)). 159.59/70.65 thf(35594,plain,(((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ xa @ ma)) @ deg @ treeList @ summary) @ xa) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma))) @ deg @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ summary))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7928])). 159.59/70.65 thf(2388,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/sandbox/benchmark/theBenchmark.p',fact_3249_order__less__le__subst2)). 159.59/70.65 thf(15918,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)],[2388])). 159.59/70.65 thf(3598,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1874_add_Ogroup__left__neutral)). 159.59/70.65 thf(19806,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3598])). 159.59/70.65 thf(6494,axiom,((! [A:nat]: ((((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))))) & ((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/sandbox/benchmark/theBenchmark.p',fact_4525_vebt__buildup_Osimps_I3_J)). 159.59/70.65 thf(30223,plain,((! [A:nat]: ((((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)))) & ((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)],[6494])). 159.59/70.65 thf(688,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/sandbox/benchmark/theBenchmark.p',fact_8039_sum__bounds__lt__plus1)). 159.59/70.65 thf(10449,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)],[688])). 159.59/70.65 thf(5905,axiom,((! [A:nat,B:extended_enat]: ((dvd_dv3785147216227455552d_enat @ B @ (power_8040749407984259932d_enat @ B @ A)) <= ((B = one_on7984719198319812577d_enat) | (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4215_dvd__power)). 159.59/70.65 thf(28084,plain,((! [A:nat,B:extended_enat]: ((dvd_dv3785147216227455552d_enat @ B @ (power_8040749407984259932d_enat @ B @ A)) | ~ ((B = one_on7984719198319812577d_enat) | (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5905])). 159.59/70.65 thf(4099,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/sandbox/benchmark/theBenchmark.p',fact_2244_mult__right__less__imp__less)). 159.59/70.65 thf(21405,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)],[4099])). 159.59/70.65 thf(4199,axiom,((! [A:real,B:real,C: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)) <= (A != zero_zero_real)) & ((A = zero_zero_real) => ((plus_plus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5249_add__divide__eq__if__simps_I3_J)). 159.59/70.65 thf(21711,plain,((! [A:real,B:real,C: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)) | (A = zero_zero_real)) & ((A = zero_zero_real) => ((plus_plus_real @ (uminus_uminus_real @ (divide_divide_real @ B @ A)) @ C) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4199])). 159.59/70.65 thf(5910,axiom,((! [A:num]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5703_add__neg__numeral__special_I6_J)). 159.59/70.65 thf(28099,plain,((! [A:num]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5910])). 159.59/70.65 thf(2187,axiom,((! [A:int,B:int]: (((plus_plus_int @ A @ B) = zero_zero_int) = (B = (uminus_uminus_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5059_add__eq__0__iff)). 159.59/70.65 thf(15301,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)],[2187])). 159.59/70.65 thf(7205,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1724_diff__is__0__eq_H)). 159.59/70.65 thf(33157,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)],[7205])). 159.59/70.65 thf(6463,axiom,((! [A:set_nat,B:(set_nat > $o),C:(nat > num)]: ((finite_finite_nat @ A) => (((! [D:nat,E:set_nat]: (((! [F:nat]: ((member_nat @ F @ E) => (ord_less_eq_num @ (C @ F) @ (C @ D)))) => ((B @ E) => (B @ (insert_nat @ D @ E)))) <= (finite_finite_nat @ E))) => (B @ A)) <= (B @ bot_bot_set_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6223_finite__ranking__induct)). 159.59/70.65 thf(30100,plain,((! [A:set_nat,B:(set_nat > $o),C:(nat > num)]: ((finite_finite_nat @ A) => (((! [D:nat,E:set_nat]: (((! [F:nat]: ((member_nat @ F @ E) => (ord_less_eq_num @ (C @ F) @ (C @ D)))) => ((B @ E) => (B @ (insert_nat @ D @ E)))) | ~ (finite_finite_nat @ E))) => (B @ A)) | ~ (B @ bot_bot_set_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6463])). 159.59/70.65 thf(228,axiom,((! [A:real]: ((ord_less_eq_real @ (tanh_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5432_tanh__real__nonpos__iff)). 159.59/70.65 thf(8949,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)],[228])). 159.59/70.65 thf(4814,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/sandbox/benchmark/theBenchmark.p',fact_7797_mask__eq__sum__exp__nat)). 159.59/70.65 thf(23883,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)],[4814])). 159.59/70.65 thf(2097,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/sandbox/benchmark/theBenchmark.p',fact_6337_signed__take__bit__nonnegative__iff)). 159.59/70.65 thf(15006,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)],[2097])). 159.59/70.65 thf(175,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((A != zero_z3403309356797280102nteger) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ B @ A) @ C) @ A) = (plus_p5714425477246183910nteger @ B @ (divide6298287555418463151nteger @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1745_div__mult__self3)). 159.59/70.65 thf(8789,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ B @ A) @ C) @ A) = (plus_p5714425477246183910nteger @ B @ (divide6298287555418463151nteger @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[175])). 159.59/70.65 thf(667,axiom,((! [A:code_integer]: ((bit_se1080825931792720795nteger @ A @ one_one_Code_integer) = (plus_p5714425477246183910nteger @ A @ (zero_n356916108424825756nteger @ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6124_or__one__eq)). 159.59/70.65 thf(10384,plain,((! [A:code_integer]: ((bit_se1080825931792720795nteger @ A @ one_one_Code_integer) = (plus_p5714425477246183910nteger @ A @ (zero_n356916108424825756nteger @ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[667])). 159.59/70.65 thf(1906,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/sandbox/benchmark/theBenchmark.p',fact_4292_inf__period_I4_J)). 159.59/70.65 thf(14406,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)],[1906])). 159.59/70.65 thf(3391,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((B = C) => (ord_le72135733267957522d_enat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2779_ord__less__eq__trans)). 159.59/70.65 thf(19150,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((B = C) => (ord_le72135733267957522d_enat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3391])). 159.59/70.65 thf(2975,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/sandbox/benchmark/theBenchmark.p',fact_6562_of__nat__eq__of__nat__power__cancel__iff)). 159.59/70.65 thf(17826,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)],[2975])). 159.59/70.65 thf(3460,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ A) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3566_divmod__digit__0_I1_J)). 159.59/70.65 thf(19367,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (modulo_modulo_int @ B @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) @ A) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3460])). 159.59/70.65 thf(1233,axiom,((! [A:real]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ zero_zero_int) = (ord_less_real @ A @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8189_floor__le__zero)). 159.59/70.65 thf(12239,plain,((! [A:real]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ zero_zero_int) = (ord_less_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233])). 159.59/70.65 thf(7041,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/sandbox/benchmark/theBenchmark.p',fact_739_vebt__insert_Osimps_I4_J)). 159.59/70.65 thf(32489,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)],[7041])). 159.59/70.65 thf(7900,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1597_less__add__same__cancel2)). 159.59/70.65 thf(35508,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)],[7900])). 159.59/70.65 thf(6217,axiom,((! [A:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4701_mult__minus1)). 159.59/70.65 thf(29145,plain,((! [A:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) = (uminus1351360451143612070nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6217])). 159.59/70.65 thf(6275,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/sandbox/benchmark/theBenchmark.p',fact_3424_Suc__mod__mult__self3)). 159.59/70.65 thf(29393,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)],[6275])). 159.59/70.65 thf(6621,axiom,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2677_order__subst2)). 159.59/70.65 thf(30677,plain,((! [A:nat,B:nat,C:(nat > num),D:num]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_num @ (C @ B) @ D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_num @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6621])). 159.59/70.65 thf(2349,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_eq_real @ A @ C) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4499_pinf_I8_J)). 159.59/70.65 thf(15797,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)],[2349])). 159.59/70.65 thf(5282,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8072_fact__ge__zero)). 159.59/70.65 thf(25560,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5282])). 159.59/70.65 thf(442,axiom,((! [A:code_integer]: ((bit_ri6519982836138164636nteger @ zero_zero_nat @ A) = (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4904_signed__take__bit__0)). 159.59/70.65 thf(9639,plain,((! [A:code_integer]: ((bit_ri6519982836138164636nteger @ zero_zero_nat @ A) = (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[442])). 159.59/70.65 thf(1200,axiom,((! [A:(extended_enat > (extended_enat > $o)),B:extended_enat,C:extended_enat]: ((((A @ B @ C) <= (! [D:extended_enat,E:extended_enat]: ((A @ E @ D) => (A @ D @ E)))) <= (! [D:extended_enat]: (A @ D @ D))) <= (! [D:extended_enat,E:extended_enat]: ((A @ D @ E) <= (ord_le72135733267957522d_enat @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2808_linorder__less__wlog)). 159.59/70.65 thf(12107,plain,((! [A:(extended_enat > (extended_enat > $o)),B:extended_enat,C:extended_enat]: ((A @ B @ C) | ~ (! [D:extended_enat,E:extended_enat]: ((A @ E @ D) => (A @ D @ E))) | ~ (! [D:extended_enat]: (A @ D @ D)) | ~ (! [D:extended_enat,E:extended_enat]: ((A @ D @ E) | ~ (ord_le72135733267957522d_enat @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200])). 159.59/70.65 thf(4287,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/sandbox/benchmark/theBenchmark.p',fact_7263_powr__realpow)). 159.59/70.65 thf(22002,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)],[4287])). 159.59/70.65 thf(1294,axiom,((! [A:code_integer,B:code_integer]: ((divide6298287555418463151nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (divide6298287555418463151nteger @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4648_div__minus__minus)). 159.59/70.65 thf(12434,plain,((! [A:code_integer,B:code_integer]: ((divide6298287555418463151nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (divide6298287555418463151nteger @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294])). 159.59/70.65 thf(3745,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/sandbox/benchmark/theBenchmark.p',fact_8362_pochhammer__code)). 159.59/70.65 thf(20302,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)],[3745])). 159.59/70.65 thf(4081,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1194_add__strict__left__mono)). 159.59/70.65 thf(21350,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => (ord_less_int @ (plus_plus_int @ C @ A) @ (plus_plus_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4081])). 159.59/70.65 thf(6716,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/sandbox/benchmark/theBenchmark.p',fact_1584_le__add__same__cancel1)). 159.59/70.65 thf(31154,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)],[6716])). 159.59/70.65 thf(1073,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/sandbox/benchmark/theBenchmark.p',fact_1351_diff__le__eq)). 159.59/70.65 thf(11689,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)],[1073])). 159.59/70.65 thf(6340,axiom,((ord_max_nat = (^ [A:nat,B:nat]: (if_nat @ (ord_less_eq_nat @ A @ B) @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3711_max__def__raw)). 159.59/70.65 thf(29610,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)],[6340])). 159.59/70.65 thf(2838,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/sandbox/benchmark/theBenchmark.p',fact_7937_sums__zero__iff__shift)). 159.59/70.65 thf(17376,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)],[2838])). 159.59/70.65 thf(5528,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/sandbox/benchmark/theBenchmark.p',fact_6950_norm__triangle__ineq3)). 159.59/70.65 thf(26540,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)],[5528])). 159.59/70.65 thf(1040,axiom,((! [A:set_nat,B:(nat > extended_enat),C:nat]: (((! [D:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ D)) <= (member_nat @ D @ A))) => ((((B @ C) = zero_z5237406670263579293d_enat) <= (member_nat @ C @ A)) <= ((groups7108830773950497114d_enat @ B @ A) = zero_z5237406670263579293d_enat))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7527_sum__nonneg__0)). 159.59/70.65 thf(11579,plain,((! [A:set_nat,B:(nat > extended_enat),C:nat]: (((! [D:nat]: ((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ D)) | ~ (member_nat @ D @ A))) => (((B @ C) = zero_z5237406670263579293d_enat) | ~ (member_nat @ C @ A) | ~ ((groups7108830773950497114d_enat @ (B) @ A) = zero_z5237406670263579293d_enat))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040])). 159.59/70.65 thf(7427,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/sandbox/benchmark/theBenchmark.p',fact_1758_power__eq__0__iff)). 159.59/70.65 thf(33909,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)],[7427])). 159.59/70.65 thf(132,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((A != zero_z3403309356797280102nteger) => ((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = (divide6298287555418463151nteger @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1644_div__mult__mult1)). 159.59/70.65 thf(8657,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = (divide6298287555418463151nteger @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 159.59/70.65 thf(5732,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/sandbox/benchmark/theBenchmark.p',fact_8266_pochhammer__rec)). 159.59/70.65 thf(27235,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)],[5732])). 159.59/70.65 thf(7924,axiom,((! [A:num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2014_zero__less__numeral)). 159.59/70.65 thf(35582,plain,((! [A:num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7924])). 159.59/70.65 thf(4649,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1103_mult_Oassoc)). 159.59/70.65 thf(23321,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4649])). 159.59/70.65 thf(4484,axiom,((! [A:$o]: (ord_less_eq_nat @ zero_zero_nat @ (zero_n2687167440665602831ol_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4391_zero__less__eq__of__bool)). 159.59/70.65 thf(22676,plain,((! [A:$o]: (ord_less_eq_nat @ zero_zero_nat @ (zero_n2687167440665602831ol_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4484])). 159.59/70.65 thf(5068,axiom,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) <= (ord_less_nat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3225_order__le__less__subst2)). 159.59/70.65 thf(24806,plain,((! [A:num,B:num,C:(num > nat),D:nat]: ((ord_less_eq_num @ A @ B) => (((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_nat @ (C @ E) @ (C @ F)))) => (ord_less_nat @ (C @ A) @ D)) | ~ (ord_less_nat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5068])). 159.59/70.65 thf(6386,axiom,((! [A:vEBT_VEBT,B:nat]: ((((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((~ (((B != zero_zero_nat) => (((D) <= (B = one_one_nat)) & (B = one_one_nat))) & ((C) <= (B = zero_zero_nat)))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B))))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G) @ B)) => (~ ((B != C) => ((B != D) => ((((((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((vEBT_vebt_member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ (suc @ E)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)))) <= (~ (ord_less_nat @ D @ B))) & ~ (ord_less_nat @ D @ B)) <= (~ (ord_less_nat @ B @ C))) & ~ (ord_less_nat @ B @ C)))))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ (suc @ (suc @ E)) @ F @ G)))))) <= (accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ (produc738532404422230701BT_nat @ A @ B))) <= (vEBT_vebt_member @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3326_vebt__member_Opelims_I2_J)). 159.59/70.65 thf(29771,plain,((! [A:vEBT_VEBT,B:nat]: (((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((~ (B = zero_zero_nat)) => (((D) | ~ (B = one_one_nat)) & (B = one_one_nat))) & ((C) | ~ (B = zero_zero_nat))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_member_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B))))) => (~ (! [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)) => ((~ (B = D)) => ((((((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)))))) | ~ (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)],[6386])). 159.59/70.65 thf(7289,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = A) = ((B = one_one_real) | (A = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1621_mult__cancel__left2)). 159.59/70.65 thf(33445,plain,((! [A:real,B:real]: (((times_times_real @ A @ B) = A) = ((B = one_one_real) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7289])). 159.59/70.65 thf(5893,axiom,((ord_less_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2134_less__numeral__extra_I1_J)). 159.59/70.65 thf(28026,plain,((ord_less_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5893])). 159.59/70.65 thf(6883,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/sandbox/benchmark/theBenchmark.p',fact_9169_choose__linear__sum)). 159.59/70.65 thf(31804,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)],[6883])). 159.59/70.65 thf(7684,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/sandbox/benchmark/theBenchmark.p',fact_1032_double__not__eq__Suc__double)). 159.59/70.65 thf(34807,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)],[7684])). 159.59/70.65 thf(5025,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (vEBT_VEBT_lesseq @ (some_nat @ A) @ (some_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_lesseq__shift)). 159.59/70.65 thf(24642,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)],[5025])). 159.59/70.65 thf(5794,axiom,((! [A:num]: ((size_num @ (bit1 @ A)) = (plus_plus_nat @ (size_num @ A) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5636_num_Osize__gen_I3_J)). 159.59/70.65 thf(27513,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)],[5794])). 159.59/70.65 thf(6008,axiom,((! [A:nat]: (((num_of_nat @ A) = one) <= (ord_less_eq_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9788_num__of__nat__One)). 159.59/70.65 thf(28466,plain,((! [A:nat]: (((num_of_nat @ A) = one) | ~ (ord_less_eq_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6008])). 159.59/70.65 thf(4166,axiom,((! [A:complex]: (ord_less_eq_real @ (real_V1022390504157884413omplex @ (exp_complex @ A)) @ (exp_real @ (real_V1022390504157884413omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6843_norm__exp)). 159.59/70.65 thf(21616,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)],[4166])). 159.59/70.65 thf(3612,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5239_neg__minus__divide__less__eq)). 159.59/70.65 thf(19849,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3612])). 159.59/70.65 thf(2438,axiom,((! [A:real]: ((divide_divide_real @ A @ one_one_real) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1034_div__by__1)). 159.59/70.65 thf(16097,plain,((! [A:real]: ((divide_divide_real @ A @ one_one_real) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2438])). 159.59/70.65 thf(4586,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/sandbox/benchmark/theBenchmark.p',fact_4252_mod2__eq__if)). 159.59/70.65 thf(23087,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)],[4586])). 159.59/70.65 thf(1412,axiom,((ord_le72135733267957522d_enat = (^ [A:extended_enat,B:extended_enat]: ((A != B) & (ord_le2932123472753598470d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3074_order_Ostrict__iff__order)). 159.59/70.65 thf(12854,plain,(((ord_le72135733267957522d_enat) = (^ [A:extended_enat,B:extended_enat]: (~ (A = B) & (ord_le2932123472753598470d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412])). 159.59/70.65 thf(5571,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2610_order__refl)). 159.59/70.65 thf(26668,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5571])). 159.59/70.65 thf(3400,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2092_mult__pos__pos)). 159.59/70.65 thf(19182,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3400])). 159.59/70.65 thf(3944,axiom,((! [A:extended_enat,B:(int > extended_enat),C:int,D:int]: ((ord_le2932123472753598470d_enat @ A @ (B @ C)) => (((! [E:int,F:int]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) <= (ord_less_int @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) <= (ord_less_int @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3220_order__le__less__subst1)). 159.59/70.65 thf(20936,plain,((! [A:extended_enat,B:(int > extended_enat),C:int,D:int]: ((ord_le2932123472753598470d_enat @ A @ (B @ C)) => (((! [E:int,F:int]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) | ~ (ord_less_int @ E @ F))) => (ord_le72135733267957522d_enat @ A @ (B @ D))) | ~ (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3944])). 159.59/70.65 thf(1629,axiom,((! [A:real]: (((sin_real @ A) = zero_zero_real) = (? [B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) | ? [B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = (uminus_uminus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6880_sin__zero__iff)). 159.59/70.65 thf(13541,plain,((! [A:real]: (((sin_real @ A) = zero_zero_real) = (? [B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))) | ? [B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (A = (uminus_uminus_real @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629])). 159.59/70.65 thf(786,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/sandbox/benchmark/theBenchmark.p',fact_7158_sin__squared__eq)). 159.59/70.65 thf(10788,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)],[786])). 159.59/70.65 thf(318,axiom,((tanh_real = (^ [A:real]: (divide_divide_real @ (sinh_real @ A) @ (cosh_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9317_tanh__def)). 159.59/70.65 thf(9232,plain,(((tanh_real) = (^ [A:real]: (divide_divide_real @ (sinh_real @ A) @ (cosh_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 159.59/70.65 thf(4112,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_le72135733267957522d_enat @ (semiri4216267220026989637d_enat @ A) @ (semiri4216267220026989637d_enat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6686_of__nat__less__imp__less)). 159.59/70.65 thf(21442,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_le72135733267957522d_enat @ (semiri4216267220026989637d_enat @ A) @ (semiri4216267220026989637d_enat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4112])). 159.59/70.65 thf(1551,axiom,((! [A:real,B:real]: ((A != zero_zero_real) => ((B != zero_zero_real) => ((inverse_inverse_real @ (times_times_real @ A @ B)) = (times_times_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9031_nonzero__inverse__mult__distrib)). 159.59/70.65 thf(13292,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real)) => ((~ (B = zero_zero_real)) => ((inverse_inverse_real @ (times_times_real @ A @ B)) = (times_times_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551])). 159.59/70.65 thf(4066,axiom,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (bit_se2000444600071755411sk_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6083_mask__nonnegative__int)). 159.59/70.65 thf(21301,plain,((! [A:nat]: (ord_less_eq_int @ zero_zero_int @ (bit_se2000444600071755411sk_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4066])). 159.59/70.65 thf(2031,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/sandbox/benchmark/theBenchmark.p',fact_7539_complex__of__real__add__Complex)). 159.59/70.65 thf(14810,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)],[2031])). 159.59/70.65 thf(481,axiom,((! [A:nat,B:nat]: ((ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6626_of__nat__zero__less__power__iff)). 159.59/70.65 thf(9783,plain,((! [A:nat,B:nat]: ((ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B)) = ((ord_less_nat @ zero_zero_nat @ A) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])). 159.59/70.65 thf(1491,axiom,((! [A:real,B:real,C:real]: ((A = (minus_minus_real @ C @ B)) <= ((plus_plus_real @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1275_add__implies__diff)). 159.59/70.65 thf(13117,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)],[1491])). 159.59/70.65 thf(4053,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)) = (ord_less_eq_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4720_ln__le__cancel__iff)). 159.59/70.65 thf(21263,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ (ln_ln_real @ A) @ (ln_ln_real @ B)) = (ord_less_eq_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4053])). 159.59/70.65 thf(2113,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (power_power_nat @ A @ B)) = (power_power_int @ (semiri1314217659103216013at_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6557_of__nat__power)). 159.59/70.65 thf(15058,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)],[2113])). 159.59/70.65 thf(208,axiom,((! [A:int]: ((gbinomial_int @ A @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8178_gbinomial__0_I1_J)). 159.59/70.65 thf(8885,plain,((! [A:int]: ((gbinomial_int @ A @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 159.59/70.65 thf(5869,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ (modulo_modulo_nat @ C @ B) @ A) = (modulo_modulo_nat @ C @ A)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4030_mod__mod__cancel)). 159.59/70.65 thf(27933,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ (modulo_modulo_nat @ C @ B) @ A) = (modulo_modulo_nat @ C @ A)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5869])). 159.59/70.65 thf(7484,axiom,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_complex @ (C @ A) @ (groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8732_prod_OatLeast__Suc__atMost)). 159.59/70.65 thf(34141,plain,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_complex @ (C @ A) @ (groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7484])). 159.59/70.65 thf(8009,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/sandbox/benchmark/theBenchmark.p',fact_1639_div__mult__mult2)). 159.59/70.65 thf(35843,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)],[8009])). 159.59/70.65 thf(2219,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/sandbox/benchmark/theBenchmark.p',fact_4976_take__bit__diff)). 159.59/70.65 thf(15415,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)],[2219])). 159.59/70.65 thf(2553,axiom,((! [A:nat,B:nat]: ((((nat2 @ (abs_abs_int @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))) = (minus_minus_nat @ B @ A)) <= (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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9468_nat__abs__int__diff)). 159.59/70.65 thf(16457,plain,((! [A:nat,B:nat]: ((((nat2 @ (abs_abs_int @ (minus_minus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))) = (minus_minus_nat @ B @ A)) | ~ (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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2553])). 159.59/70.65 thf(5511,axiom,((! [A:num]: ((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (numeral_numeral_real @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5697_add__neg__numeral__special_I5_J)). 159.59/70.65 thf(26491,plain,((! [A:num]: ((plus_plus_real @ (uminus_uminus_real @ one_one_real) @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_real @ (numeral_numeral_real @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5511])). 159.59/70.65 thf(200,axiom,((bit_ri7919022796975470100ot_int = (^ [A:int]: (minus_minus_int @ (uminus_uminus_int @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9584_not__int__def)). 159.59/70.65 thf(8863,plain,(((bit_ri7919022796975470100ot_int) = (^ [A:int]: (minus_minus_int @ (uminus_uminus_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[200])). 159.59/70.65 thf(4473,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/sandbox/benchmark/theBenchmark.p',fact_1390_vebt__pred_Osimps_I4_J)). 159.59/70.65 thf(22638,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)],[4473])). 159.59/70.65 thf(7118,axiom,((! [A:num,B:num]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (numera6690914467698888265omplex @ B)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4790_diff__numeral__simps_I3_J)). 159.59/70.65 thf(32826,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)],[7118])). 159.59/70.65 thf(982,axiom,((! [A:int]: ~ (ord_less_int @ (times_times_int @ A @ A) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2104_not__square__less__zero)). 159.59/70.65 thf(11391,plain,((! [A:int]: ~ (ord_less_int @ (times_times_int @ A @ A) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[982])). 159.59/70.65 thf(6076,axiom,((! [A:num]: (zero_zero_int != (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1849_zero__neq__numeral)). 159.59/70.65 thf(28676,plain,((! [A:num]: ~ (zero_zero_int = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6076])). 159.59/70.65 thf(4443,axiom,((! [A:int,B:real]: ((((archim6058952711729229775r_real @ B) = A) <= (ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real))) <= (ord_less_real @ (ring_1_of_int_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8258_floor__eq)). 159.59/70.65 thf(22483,plain,((! [A:int,B:real]: (((archim6058952711729229775r_real @ B) = A) | ~ (ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real)) | ~ (ord_less_real @ (ring_1_of_int_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4443])). 159.59/70.65 thf(5278,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/sandbox/benchmark/theBenchmark.p',fact_9511_real__root__gt__zero)). 159.59/70.65 thf(25528,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)],[5278])). 159.59/70.65 thf(4566,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/sandbox/benchmark/theBenchmark.p',fact_2486_add__eq__if)). 159.59/70.65 thf(23016,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)],[4566])). 159.59/70.65 thf(7515,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/sandbox/benchmark/theBenchmark.p',fact_6632_of__nat__less__numeral__power__cancel__iff)). 159.59/70.65 thf(34237,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)],[7515])). 159.59/70.65 thf(1129,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/sandbox/benchmark/theBenchmark.p',fact_4996_mod__minus__cong)). 159.59/70.65 thf(11872,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)],[1129])). 159.59/70.65 thf(2270,axiom,((! [A:int]: (((divide_divide_int @ (plus_plus_int @ A @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) <= (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3908_even__succ__div__two)). 159.59/70.65 thf(15571,plain,((! [A:int]: (((divide_divide_int @ (plus_plus_int @ A @ one_one_int) @ (numeral_numeral_int @ (bit0 @ one))) = (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2270])). 159.59/70.65 thf(2687,axiom,((! [A:complex,B:nat]: ((((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_atMost_nat @ B)) = (semiri8010041392384452111omplex @ (plus_plus_nat @ B @ one_one_nat))) <= (A = one_one_complex)) & ((A != one_one_complex) => ((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_atMost_nat @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ (suc @ B))) @ (minus_minus_complex @ one_one_complex @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8947_sum__gp0)). 159.59/70.65 thf(16917,plain,((! [A:complex,B:nat]: ((((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_atMost_nat @ B)) = (semiri8010041392384452111omplex @ (plus_plus_nat @ B @ one_one_nat))) | ~ (A = one_one_complex)) & ((~ (A = one_one_complex)) => ((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_atMost_nat @ B)) = (divide1717551699836669952omplex @ (minus_minus_complex @ one_one_complex @ (power_power_complex @ A @ (suc @ B))) @ (minus_minus_complex @ one_one_complex @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2687])). 159.59/70.65 thf(4651,axiom,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_eq_real @ C @ B) => ((ord_less_eq_real @ zero_zero_real @ D) => ((ord_less_eq_real @ zero_zero_real @ E) => ((ord_less_eq_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 @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2439_convex__bound__le)). 159.59/70.65 thf(23328,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((ord_less_eq_real @ C @ B) => ((ord_less_eq_real @ zero_zero_real @ D) => ((ord_less_eq_real @ zero_zero_real @ E) => ((ord_less_eq_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 @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4651])). 159.59/70.65 thf(2953,axiom,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6024_and__numerals_I7_J)). 159.59/70.65 thf(17764,plain,((! [A:num,B:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ one_one_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se725231765392027082nd_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2953])). 159.59/70.65 thf(694,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/sandbox/benchmark/theBenchmark.p',fact_8134_Maclaurin__zero)). 159.59/70.65 thf(10471,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)],[694])). 159.59/70.65 thf(4383,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/sandbox/benchmark/theBenchmark.p',fact_2345_add__divide__eq__iff)). 159.59/70.65 thf(22292,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)],[4383])). 159.59/70.65 thf(5932,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_V5719532721284313246member @ A @ B) => (((! [C:$o,D:$o]: (((accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (~ (((C) <= (B = zero_zero_nat)) & (((B = one_one_nat) & ((B = one_one_nat) => (D))) <= (B != zero_zero_nat))))) <= (A = (vEBT_Leaf @ C @ D)))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ (suc @ D) @ E @ F)) => ((~ (((vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ E @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one))))) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E))) & (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ D) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ E)))) <= (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ (suc @ D) @ E @ F) @ B))))))) <= (accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ (produc738532404422230701BT_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3316_VEBT__internal_Onaive__member_Opelims_I2_J)). 159.59/70.65 thf(28166,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_V5719532721284313246member @ A @ B) => (((! [C:$o,D:$o]: (((accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (~ (((C) | ~ (B = zero_zero_nat)) & (((B = one_one_nat) & ((B = one_one_nat) => (D))) | (B = zero_zero_nat))))) | ~ (A = (vEBT_Leaf @ C @ D)))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ (suc @ D) @ E @ F)) => (~ (((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))) & (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 @ (vEBT_Node @ C @ (suc @ D) @ E @ F) @ B))))))) | ~ (accp_P2887432264394892906BT_nat @ (vEBT_V5765760719290551771er_rel) @ (produc738532404422230701BT_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5932])). 159.59/70.65 thf(2762,axiom,((! [A:int]: ((bit_se2923211474154528505it_int @ (suc @ zero_zero_nat) @ A) = (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4902_take__bit__Suc__0)). 159.59/70.65 thf(17151,plain,((! [A:int]: ((bit_se2923211474154528505it_int @ (suc @ zero_zero_nat) @ A) = (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2762])). 159.59/70.65 thf(6390,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/sandbox/benchmark/theBenchmark.p',fact_5299_signed__take__bit__int__less__eq__self__iff)). 159.59/70.65 thf(29803,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)],[6390])). 159.59/70.65 thf(7471,axiom,((! [A:complex,B:complex]: (((B != zero_zero_complex) & (A != zero_zero_complex)) <= ((times_times_complex @ A @ B) != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1869_mult__not__zero)). 159.59/70.65 thf(34064,plain,((! [A:complex,B:complex]: ((~ (B = zero_zero_complex) & ~ (A = zero_zero_complex)) | ((times_times_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7471])). 159.59/70.65 thf(1399,axiom,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = (ord_less_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3171_linorder__not__le)). 159.59/70.65 thf(12817,plain,((! [A:int,B:int]: ((~ (ord_less_eq_int @ A @ B)) = (ord_less_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399])). 159.59/70.65 thf(3203,axiom,((! [A:real]: ((ord_less_real @ (exp_real @ A) @ one_one_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5995_exp__less__one__iff)). 159.59/70.65 thf(18554,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)],[3203])). 159.59/70.65 thf(7809,axiom,(((ord_less_nat @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) & (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_hlbound)). 159.59/70.65 thf(35212,plain,(((ord_less_nat @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) & (ord_less_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7809])). 159.59/70.65 thf(5654,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_valid @ A @ B) => (((? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))) => (B != one_one_nat)) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((~ ((case_o184042715313410164at_nat @ (! [G:vEBT_VEBT]: ((member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E)) => (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H)))) & ~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) @ (produc6081775807080527818_nat_o @ (^ [G:nat,H:nat]: ((ord_less_eq_nat @ G @ H) & ((! [I:nat]: ((((ord_less_nat @ G @ I) & (ord_less_eq_nat @ I @ H)) <= (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ I)) <= (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) & (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ H)) <= (G != H)) & ((! [I:vEBT_VEBT]: ((~ (? [J:nat]: (vEBT_V8194947554948674370ptions @ I @ J))) <= (member_VEBT_VEBT @ I @ (set_VEBT_VEBT2 @ E)))) <= (G = H)) & ! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [J:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ E @ I) @ J)) = (vEBT_V8194947554948674370ptions @ F @ I))) & (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ C) & ((size_s6755466524823107622T_VEBT @ E) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) & (vEBT_VEBT_valid @ F @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) & ! [G:vEBT_VEBT]: ((vEBT_VEBT_valid @ G @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) <= (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E))) & (D = B))) <= (A = (vEBT_Node @ C @ D @ E @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10068_VEBT__internal_Ovalid_H_Oelims_I2_J)). 159.59/70.65 thf(26953,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_valid @ A @ B) => (((? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))) => (~ (B = one_one_nat))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ ((case_o184042715313410164at_nat @ (! [G:vEBT_VEBT]: ((member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E)) => (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H)))) & ~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) @ (produc6081775807080527818_nat_o @ (^ [G:nat,H:nat]: ((ord_less_eq_nat @ G @ H) & ((! [I:nat]: (((ord_less_nat @ G @ I) & (ord_less_eq_nat @ I @ H)) | ~ (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ I) | ~ (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) & (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ H)) | (G = H)) & (! [I:vEBT_VEBT]: (~ (? [J:nat]: (vEBT_V8194947554948674370ptions @ I @ J)) | ~ (member_VEBT_VEBT @ I @ (set_VEBT_VEBT2 @ E))) | ~ (G = H)) & ! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) => ((? [J:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ E @ I) @ J)) = (vEBT_V8194947554948674370ptions @ F @ I))) & (ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))) @ C) & ((size_s6755466524823107622T_VEBT @ E) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) & (vEBT_VEBT_valid @ F @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) & ! [G:vEBT_VEBT]: ((vEBT_VEBT_valid @ G @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E))) & (D = B)) | ~ (A = (vEBT_Node @ C @ D @ E @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5654])). 159.59/70.65 thf(2661,axiom,((! [A:nat]: ~ (ord_less_real @ (semiri5074537144036343181t_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6668_of__nat__less__0__iff)). 159.59/70.65 thf(16831,plain,((! [A:nat]: ~ (ord_less_real @ (semiri5074537144036343181t_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2661])). 159.59/70.65 thf(6838,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3158_order__le__less)). 159.59/70.65 thf(31571,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6838])). 159.59/70.65 thf(2459,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (! [D:code_integer,E:code_integer]: ((~ (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ C))) = (~ (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ (minus_8373710615458151222nteger @ D @ (times_3573771949741848930nteger @ E @ B)) @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4290_inf__period_I4_J)). 159.59/70.65 thf(16166,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (! [D:code_integer,E:code_integer]: ((~ (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ C))) = (~ (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ (minus_8373710615458151222nteger @ D @ (times_3573771949741848930nteger @ E @ B)) @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2459])). 159.59/70.65 thf(344,axiom,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5139_neg__numeral__le__zero)). 159.59/70.65 thf(9317,plain,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[344])). 159.59/70.65 thf(6789,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/sandbox/benchmark/theBenchmark.p',fact_239_power__add__numeral)). 159.59/70.65 thf(31413,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)],[6789])). 159.59/70.65 thf(7763,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_add__left__cancel)). 159.59/70.65 thf(35080,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)],[7763])). 159.59/70.65 thf(5686,axiom,((set_ord_atMost_nat = (^ [A:nat]: (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8490_atMost__def)). 159.59/70.65 thf(27085,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)],[5686])). 159.59/70.65 thf(5061,axiom,((! [A:num]: ~ (ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5141_not__zero__le__neg__numeral)). 159.59/70.65 thf(24774,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)],[5061])). 159.59/70.65 thf(5970,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/sandbox/benchmark/theBenchmark.p',fact_1335_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2)). 159.59/70.65 thf(28343,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)],[5970])). 159.59/70.65 thf(5826,axiom,((! [A:option_nat]: ((A != none_nat) = (? [B:nat]: (A = (some_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_not__None__eq)). 159.59/70.65 thf(27716,plain,((! [A:option_nat]: ((~ (A = none_nat)) = (? [B:nat]: (A = (some_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5826])). 159.59/70.65 thf(6539,axiom,((! [A:nat,B:nat,C:(nat > nat)]: ((((groups3542108847815614940at_nat @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_nat) <= (ord_less_nat @ (suc @ A) @ B)) & ((~ (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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7362_sum_Ocl__ivl__Suc)). 159.59/70.65 thf(30393,plain,((! [A:nat,B:nat,C:(nat > nat)]: ((((groups3542108847815614940at_nat @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_nat) | ~ (ord_less_nat @ (suc @ A) @ B)) & ((~ (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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6539])). 159.59/70.65 thf(742,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((((modulo_modulo_int @ (plus_plus_int @ A @ D) @ B) = (modulo_modulo_int @ (plus_plus_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/sandbox/benchmark/theBenchmark.p',fact_3457_mod__add__cong)). 159.59/70.65 thf(10653,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((modulo_modulo_int @ (plus_plus_int @ A @ D) @ B) = (modulo_modulo_int @ (plus_plus_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)],[742])). 159.59/70.65 thf(4543,axiom,((! [A:nat]: ((bit_se1745604003318907178nteger @ (suc @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (suc @ A)) @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5223_take__bit__Suc__minus__1__eq)). 159.59/70.65 thf(22949,plain,((! [A:nat]: ((bit_se1745604003318907178nteger @ (suc @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (minus_8373710615458151222nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (suc @ A)) @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4543])). 159.59/70.65 thf(6496,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/sandbox/benchmark/theBenchmark.p',fact_179_list__update__beyond)). 159.59/70.65 thf(30233,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)],[6496])). 159.59/70.65 thf(5662,axiom,((((=) @ num) = (^ [A:num,B:num]: ((ord_less_eq_num @ B @ A) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2696_Orderings_Oorder__eq__iff)). 159.59/70.65 thf(26989,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)],[5662])). 159.59/70.65 thf(7562,axiom,((! [A:int,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_int @ one_one_int @ (power_power_int @ A @ B))) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2470_one__less__power)). 159.59/70.65 thf(34375,plain,((! [A:int,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_int @ one_one_int @ (power_power_int @ A @ B))) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7562])). 159.59/70.65 thf(4827,axiom,((! [A:set_nat,B:(nat > int),C:(nat > int),D:int,E:int]: ((((! [F:nat]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (C @ F) @ D)) @ E) <= (member_nat @ F @ A))) => (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (C @ F) @ (B @ F))) @ A) @ D)) @ E)) <= ((groups3539618377306564664at_int @ B @ A) = one_one_int)) <= (! [F:nat]: ((member_nat @ F @ A) => (ord_less_eq_int @ zero_zero_int @ (B @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7758_convex__sum__bound__le)). 159.59/70.65 thf(23954,plain,((! [A:set_nat,B:(nat > int),C:(nat > int),D:int,E:int]: (((! [F:nat]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (C @ F) @ D)) @ E) | ~ (member_nat @ F @ A))) => (ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (C @ F) @ (B @ F))) @ A) @ D)) @ E)) | ~ ((groups3539618377306564664at_int @ (B) @ A) = one_one_int) | ~ (! [F:nat]: ((member_nat @ F @ A) => (ord_less_eq_int @ zero_zero_int @ (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4827])). 159.59/70.65 thf(5933,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1907_Zero__neq__Suc)). 159.59/70.65 thf(28183,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5933])). 159.59/70.65 thf(2764,axiom,((! [A:int]: ((modulo_modulo_int @ A @ one_one_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3407_bits__mod__by__1)). 159.59/70.65 thf(17156,plain,((! [A:int]: ((modulo_modulo_int @ A @ one_one_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2764])). 159.59/70.65 thf(5339,axiom,((! [A:nat]: ~ (ord_less_eq_int @ (power_power_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3000_not__exp__less__eq__0__int)). 159.59/70.65 thf(25800,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)],[5339])). 159.59/70.65 thf(4579,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/sandbox/benchmark/theBenchmark.p',fact_3498_cong__exp__iff__simps_I2_J)). 159.59/70.65 thf(23052,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)],[4579])). 159.59/70.65 thf(5990,axiom,((! [A:nat,B:nat]: (((some_nat @ A) = (some_nat @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_option_Oinject)). 159.59/70.65 thf(28406,plain,((! [A:nat,B:nat]: (((some_nat @ A) = (some_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5990])). 159.59/70.65 thf(2372,axiom,((! [A:real,B:real,C:int]: (((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))))))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8350_floor__log__eq__powr__iff)). 159.59/70.65 thf(15871,plain,((! [A:real,B:real,C:int]: (((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))))))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2372])). 159.59/70.65 thf(1087,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/sandbox/benchmark/theBenchmark.p',fact_9507_real__root__less__mono)). 159.59/70.65 thf(11738,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)],[1087])). 159.59/70.65 thf(2102,axiom,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ A @ (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4646_add__minus__cancel)). 159.59/70.65 thf(15021,plain,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ A @ (plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2102])). 159.59/70.65 thf(6150,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/sandbox/benchmark/theBenchmark.p',fact_5460_power__even__abs__numeral)). 159.59/70.65 thf(28916,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)],[6150])). 159.59/70.65 thf(4935,axiom,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_mult__numeral__1)). 159.59/70.65 thf(24304,plain,((! [A:real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4935])). 159.59/70.65 thf(7919,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/sandbox/benchmark/theBenchmark.p',fact_3516_div__mult__mod__eq)). 159.59/70.65 thf(35567,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)],[7919])). 159.59/70.65 thf(7524,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ A @ B) = C) = ((vEBT_VEBT_power @ (some_nat @ A) @ (some_nat @ B)) = (some_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_power__shift)). 159.59/70.65 thf(34262,plain,((! [A:nat,B:nat,C:nat]: (((power_power_nat @ A @ B) = C) = ((vEBT_VEBT_power @ (some_nat @ A) @ (some_nat @ B)) = (some_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7524])). 159.59/70.65 thf(2573,axiom,((! [A:int,B:int,C:int]: ((! [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))))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4293_inf__period_I4_J)). 159.59/70.65 thf(16521,plain,((! [A:int,B:int,C:int]: (! [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)))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2573])). 159.59/70.65 thf(4376,axiom,((! [A:complex,B:nat,C:nat]: ((((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))) <= (A != one_one_complex)) & (((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7833_sum__gp__offset)). 159.59/70.65 thf(22266,plain,((! [A:complex,B:nat,C:nat]: ((((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))) | (A = one_one_complex)) & (((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4376])). 159.59/70.65 thf(5021,axiom,((! [A:nat,B:nat,C:(nat > extended_enat),D:(nat > extended_enat)]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ A) => ((groups7108830773950497114d_enat @ (^ [E:nat]: (if_Extended_enat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_Extended_enat @ (E = B) @ zero_z5237406670263579293d_enat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups7108830773950497114d_enat @ (^ [E:nat]: (if_Extended_enat @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8936_sum_Ozero__middle)). 159.59/70.65 thf(24629,plain,((! [A:nat,B:nat,C:(nat > extended_enat),D:(nat > extended_enat)]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ A) => ((groups7108830773950497114d_enat @ (^ [E:nat]: (if_Extended_enat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_Extended_enat @ (E = B) @ zero_z5237406670263579293d_enat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups7108830773950497114d_enat @ (^ [E:nat]: (if_Extended_enat @ (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)],[5021])). 159.59/70.65 thf(4317,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/sandbox/benchmark/theBenchmark.p',fact_7541_sum_OatLeastAtMost__rev)). 159.59/70.65 thf(22091,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)],[4317])). 159.59/70.65 thf(6430,axiom,((! [A:int,B:nat,C:nat]: ((A != zero_zero_int) => ((((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)))) <= (~ (ord_less_eq_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2519_power__diff__power__eq)). 159.59/70.65 thf(29973,plain,((! [A:int,B:nat,C:nat]: ((~ (A = zero_zero_int)) => ((((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)))) | (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6430])). 159.59/70.65 thf(2529,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/sandbox/benchmark/theBenchmark.p',fact_606_lift__Suc__mono__less__iff)). 159.59/70.65 thf(16389,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)],[2529])). 159.59/70.65 thf(5968,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/sandbox/benchmark/theBenchmark.p',fact_7674_sum__Suc__diff)). 159.59/70.65 thf(28336,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)],[5968])). 159.59/70.65 thf(4663,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1924_mult__0)). 159.59/70.65 thf(23381,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4663])). 159.59/70.65 thf(112,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/sandbox/benchmark/theBenchmark.p',fact_9595_or__not__numerals_I2_J)). 159.59/70.65 thf(8593,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)],[112])). 159.59/70.65 thf(7316,axiom,((! [A:real]: ((power_power_real @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_real @ (times_times_real @ A @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5624_power3__eq__cube)). 159.59/70.65 thf(33556,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)],[7316])). 159.59/70.65 thf(789,axiom,((! [A:real]: (sums_real @ (^ [B:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)) @ zero_zero_real)) @ (cosh_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9302_cosh__converges)). 159.59/70.65 thf(10797,plain,((! [A:real]: (sums_real @ (^ [B:nat]: (if_real @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B)) @ zero_zero_real)) @ (cosh_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[789])). 159.59/70.65 thf(253,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 @ (real_V1485227260804924795R_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9242_scaleR__nonneg__nonneg)). 159.59/70.65 thf(9022,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 @ (real_V1485227260804924795R_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 159.59/70.65 thf(5657,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/sandbox/benchmark/theBenchmark.p',fact_1266_right__diff__distrib)). 159.59/70.65 thf(26972,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)],[5657])). 159.59/70.65 thf(3480,axiom,((! [A:real,B:num]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ (numeral_numeral_int @ B)) = (ord_less_eq_real @ A @ (minus_minus_real @ (numeral_numeral_real @ B) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6996_ceiling__less__numeral)). 159.59/70.65 thf(19429,plain,((! [A:real,B:num]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ (numeral_numeral_int @ B)) = (ord_less_eq_real @ A @ (minus_minus_real @ (numeral_numeral_real @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3480])). 159.59/70.65 thf(7870,axiom,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = zero_zero_nat) = ((ord_less_nat @ zero_zero_nat @ B) & (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1756_power__eq__0__iff)). 159.59/70.65 thf(35403,plain,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = zero_zero_nat) = ((ord_less_nat @ zero_zero_nat @ B) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7870])). 159.59/70.65 thf(4524,axiom,((! [A:nat]: (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3713_finite__Collect__le__nat)). 159.59/70.65 thf(22825,plain,((! [A:nat]: (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (ord_less_eq_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4524])). 159.59/70.65 thf(1874,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 @ B @ C) | ~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8437_Icc__subset__Iic__iff)). 159.59/70.65 thf(14304,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 @ B @ C) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1874])). 159.59/70.65 thf(2843,axiom,((! [A:real,B:real,C:nat,D:nat]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ D)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4110_dvd__power__le)). 159.59/70.65 thf(17393,plain,((! [A:real,B:real,C:nat,D:nat]: ((dvd_dvd_real @ A @ B) => ((dvd_dvd_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ D)) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2843])). 159.59/70.65 thf(3956,axiom,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5167_neg__one__le__numeral)). 159.59/70.65 thf(20983,plain,((! [A:num]: (ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3956])). 159.59/70.65 thf(2780,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2758_lt__ex)). 159.59/70.65 thf(17208,plain,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2780])). 159.59/70.65 thf(4862,axiom,((! [A:int,B: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)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3705_neg__zmod__mult__2)). 159.59/70.65 thf(24066,plain,((! [A:int,B: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)) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4862])). 159.59/70.65 thf(1600,axiom,((! [A:real,B:real]: ((ord_less_real @ (sqrt @ A) @ (sqrt @ B)) = (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6311_real__sqrt__less__iff)). 159.59/70.65 thf(13450,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)],[1600])). 159.59/70.65 thf(636,axiom,((! [A:code_integer,B:code_integer]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ A @ B))) = ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) != (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3875_odd__add)). 159.59/70.65 thf(10290,plain,((! [A:code_integer,B:code_integer]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ 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)],[636])). 159.59/70.65 thf(1839,axiom,((! [A:nat]: ((zero_zero_complex = (semiri8010041392384452111omplex @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6505_of__nat__0__eq__iff)). 159.59/70.65 thf(14201,plain,((! [A:nat]: ((zero_zero_complex = (semiri8010041392384452111omplex @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1839])). 159.59/70.65 thf(2784,axiom,((! [A:code_integer,B:code_integer]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) => ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ A @ B)) <= (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4202_odd__even__add)). 159.59/70.65 thf(17217,plain,((! [A:code_integer,B:code_integer]: ((~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) => ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ A @ B)) | (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2784])). 159.59/70.65 thf(867,axiom,((! [A:num,B:real]: ((ord_less_int @ (numeral_numeral_int @ A) @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8198_numeral__less__floor)). 159.59/70.65 thf(11045,plain,((! [A:num,B:real]: ((ord_less_int @ (numeral_numeral_int @ A) @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[867])). 159.59/70.65 thf(5254,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/sandbox/benchmark/theBenchmark.p',fact_4130_less__eq__dvd__minus)). 159.59/70.65 thf(25454,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)],[5254])). 159.59/70.65 thf(2892,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3695_verit__comp__simplify1_I3_J)). 159.59/70.65 thf(17564,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2892])). 159.59/70.65 thf(5342,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat]: ((! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ F @ B))) => ((vEBT_invar_vebt @ C @ D) => (((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((D = B) => ((E = (plus_plus_nat @ B @ D)) => ((~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ C @ F))) => ((! [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)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_invar__vebt_Ointros_I2_J)). 159.59/70.65 thf(25815,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT,D:nat,E:nat]: ((! [F:vEBT_VEBT]: ((member_VEBT_VEBT @ F @ (set_VEBT_VEBT2 @ A)) => (vEBT_invar_vebt @ F @ B))) => ((vEBT_invar_vebt @ C @ D) => (((size_s6755466524823107622T_VEBT @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((D = B) => ((E = (plus_plus_nat @ B @ D)) => ((~ (? [F:nat]: (vEBT_V8194947554948674370ptions @ C @ F))) => ((! [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)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5342])). 159.59/70.65 thf(6816,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2149_zero__le__power)). 159.59/70.65 thf(31495,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ zero_zero_nat @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6816])). 159.59/70.65 thf(6130,axiom,((! [A:nat]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6660_not__bit__Suc__0__Suc)). 159.59/70.65 thf(28851,plain,((! [A:nat]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6130])). 159.59/70.65 thf(1972,axiom,((! [A:nat,B:nat,C:(nat > complex)]: (((ord_less_nat @ (suc @ A) @ B) => ((groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7360_sum_Ocl__ivl__Suc)). 159.59/70.65 thf(14609,plain,((! [A:nat,B:nat,C:(nat > complex)]: (((ord_less_nat @ (suc @ A) @ B) => ((groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1972])). 159.59/70.65 thf(1311,axiom,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ A @ B) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2224_mult__le__less__imp__less)). 159.59/70.65 thf(12487,plain,((! [A:real,B:real,C:real,D:real]: ((ord_less_eq_real @ A @ B) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311])). 159.59/70.65 thf(103,axiom,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ one_one_real) => ((artanh_real @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (artanh_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5444_artanh__minus__real)). 159.59/70.65 thf(8569,plain,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ one_one_real) => ((artanh_real @ (uminus_uminus_real @ A)) = (uminus_uminus_real @ (artanh_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 159.59/70.65 thf(5369,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2910_order__less__not__sym)). 159.59/70.65 thf(25946,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5369])). 159.59/70.65 thf(4463,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/sandbox/benchmark/theBenchmark.p',fact_9081_binomial__Suc__Suc__eq__times)). 159.59/70.65 thf(22587,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)],[4463])). 159.59/70.65 thf(2889,axiom,((! [A:complex,B:(nat > complex),C:complex]: (((sums_complex @ (^ [D:nat]: (times_times_complex @ (B @ D) @ A)) @ (times_times_complex @ C @ A)) = (sums_complex @ B @ C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7912_sums__mult2__iff)). 159.59/70.65 thf(17551,plain,((! [A:complex,B:(nat > complex),C:complex]: (((sums_complex @ (^ [D:nat]: (times_times_complex @ (B @ D) @ A)) @ (times_times_complex @ C @ A)) = (sums_complex @ (B) @ C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2889])). 159.59/70.65 thf(4631,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D)))) => ((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/sandbox/benchmark/theBenchmark.p',fact_7921_sum__subtractf__nat)). 159.59/70.65 thf(23260,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D)))) => ((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)],[4631])). 159.59/70.65 thf(5522,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (B = A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2712_dual__order_Oantisym)). 159.59/70.65 thf(26523,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)],[5522])). 159.59/70.65 thf(2640,axiom,((! [A:complex]: ((uminus1482373934393186551omplex @ (sin_complex @ A)) = (cos_complex @ (plus_plus_complex @ A @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7800_minus__sin__cos__eq)). 159.59/70.65 thf(16759,plain,((! [A:complex]: ((uminus1482373934393186551omplex @ (sin_complex @ A)) = (cos_complex @ (plus_plus_complex @ A @ (divide1717551699836669952omplex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2640])). 159.59/70.65 thf(7335,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/sandbox/benchmark/theBenchmark.p',fact_7779_sum__telescope_H_H)). 159.59/70.65 thf(33617,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)],[7335])). 159.59/70.65 thf(3779,axiom,((! [A:num,B:num]: ((ord_less_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_numeral__less__iff)). 159.59/70.65 thf(20406,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)],[3779])). 159.59/70.65 thf(4775,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/sandbox/benchmark/theBenchmark.p',fact_287_one__le__power)). 159.59/70.65 thf(23754,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)],[4775])). 159.59/70.65 thf(4334,axiom,((! [A:real]: ~ (ord_less_real @ (exp_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6065_not__exp__less__zero)). 159.59/70.65 thf(22142,plain,((! [A:real]: ~ (ord_less_real @ (exp_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4334])). 159.59/70.65 thf(4591,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/sandbox/benchmark/theBenchmark.p',fact_6459_sqrt__sum__squares__le__sum__abs)). 159.59/70.65 thf(23106,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)],[4591])). 159.59/70.65 thf(6913,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/sandbox/benchmark/theBenchmark.p',fact_3568_mult__exp__mod__exp__eq)). 159.59/70.65 thf(31900,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)],[6913])). 159.59/70.65 thf(3824,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/sandbox/benchmark/theBenchmark.p',fact_2370_divide__diff__eq__iff)). 159.59/70.65 thf(20545,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)],[3824])). 159.59/70.65 thf(4970,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/sandbox/benchmark/theBenchmark.p',fact_4920_le__minus__iff)). 159.59/70.65 thf(24460,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)],[4970])). 159.59/70.65 thf(5887,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/sandbox/benchmark/theBenchmark.p',fact_7257_Complex__eq__neg__numeral)). 159.59/70.65 thf(28011,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)],[5887])). 159.59/70.65 thf(1005,axiom,((ord_le2932123472753598470d_enat = (^ [A:extended_enat,B:extended_enat]: ((A = B) | (ord_le72135733267957522d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3067_order_Oorder__iff__strict)). 159.59/70.65 thf(11461,plain,(((ord_le2932123472753598470d_enat) = (^ [A:extended_enat,B:extended_enat]: ((A = B) | (ord_le72135733267957522d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005])). 159.59/70.65 thf(4029,axiom,((! [A:real]: (((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (cot_real @ A) @ zero_zero_real)) <= (ord_less_real @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9384_cot__less__zero)). 159.59/70.65 thf(21195,plain,((! [A:real]: (((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (cot_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)],[4029])). 159.59/70.65 thf(5861,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (~ (ord_less_eq_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3037_nless__le)). 159.59/70.65 thf(27908,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)],[5861])). 159.59/70.65 thf(7040,axiom,((! [A:nat,B:nat,C:product_prod_nat_nat]: ((((ord_less_eq_nat @ B @ A) => (C = (product_Pair_nat_nat @ B @ (minus_minus_nat @ A @ B)))) & ((C = (nat_prod_decode_aux @ (suc @ A) @ (minus_minus_nat @ B @ (suc @ A)))) <= (~ (ord_less_eq_nat @ B @ A)))) <= ((nat_prod_decode_aux @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9744_prod__decode__aux_Oelims)). 159.59/70.65 thf(32482,plain,((! [A:nat,B:nat,C:product_prod_nat_nat]: ((((ord_less_eq_nat @ B @ A) => (C = (product_Pair_nat_nat @ B @ (minus_minus_nat @ A @ B)))) & ((C = (nat_prod_decode_aux @ (suc @ A) @ (minus_minus_nat @ B @ (suc @ A)))) | (ord_less_eq_nat @ B @ A))) | ~ ((nat_prod_decode_aux @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7040])). 159.59/70.65 thf(5877,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4926_le__imp__neg__le)). 159.59/70.65 thf(27962,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5877])). 159.59/70.65 thf(8037,axiom,((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ ma @ na)) @ (vEBT_VEBT_low @ ma @ na))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__092_060open_062both__member__options_A_ItreeList_A_B_Ahigh_Ama_An_J_A_Ilow_Ama_An_J_092_060close_062)). 159.59/70.65 thf(35948,plain,((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ ma @ na)) @ (vEBT_VEBT_low @ ma @ na))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8037])). 159.59/70.65 thf(3017,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/sandbox/benchmark/theBenchmark.p',fact_4835_less__divide__eq__numeral1_I2_J)). 159.59/70.65 thf(17953,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)],[3017])). 159.59/70.65 thf(7108,axiom,((! [A:nat]: (((groups2073611262835488442omplex @ (^ [B:nat]: (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (semiri8010041392384452111omplex @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_complex) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9171_choose__alternating__sum)). 159.59/70.65 thf(32762,plain,((! [A:nat]: (((groups2073611262835488442omplex @ (^ [B:nat]: (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (semiri8010041392384452111omplex @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_complex) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7108])). 159.59/70.65 thf(3867,axiom,((! [A:real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1534_div__by__0)). 159.59/70.65 thf(20702,plain,((! [A:real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3867])). 159.59/70.65 thf(1979,axiom,((! [A:nat,B:nat,C:(nat > extended_enat),D:extended_enat]: ((ord_less_eq_nat @ A @ B) => (((ord_le72135733267957522d_enat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le2932123472753598470d_enat @ (C @ E) @ (C @ F))))) <= (ord_le72135733267957522d_enat @ (C @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3227_order__le__less__subst2)). 159.59/70.65 thf(14635,plain,((! [A:nat,B:nat,C:(nat > extended_enat),D:extended_enat]: ((ord_less_eq_nat @ A @ B) => ((ord_le72135733267957522d_enat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le2932123472753598470d_enat @ (C @ E) @ (C @ F)))) | ~ (ord_le72135733267957522d_enat @ (C @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1979])). 159.59/70.65 thf(549,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((A != zero_z3403309356797280102nteger) => ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ C @ (divide6298287555418463151nteger @ B @ A)) = (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ C @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4147_dvd__div__iff__mult)). 159.59/70.65 thf(10001,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ C @ (divide6298287555418463151nteger @ B @ A)) = (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ C @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[549])). 159.59/70.65 thf(5693,axiom,((! [A:(int > $o),B:int,C:(int > $o)]: (((! [D:int,E:int]: ((C @ D) = (C @ (minus_minus_int @ D @ (times_times_int @ E @ B))))) => (! [D:int,E:int]: (((C @ D) | (A @ D)) = ((A @ (minus_minus_int @ D @ (times_times_int @ E @ B))) | (C @ (minus_minus_int @ D @ (times_times_int @ E @ B))))))) <= (! [D:int,E:int]: ((A @ D) = (A @ (minus_minus_int @ D @ (times_times_int @ E @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4521_inf__period_I2_J)). 159.59/70.65 thf(27105,plain,((! [A:(int > $o),B:int,C:(int > $o)]: (((! [D:int,E:int]: ((C @ D) = (C @ (minus_minus_int @ D @ (times_times_int @ E @ B))))) => (! [D:int,E:int]: (((C @ D) | (A @ D)) = ((A @ (minus_minus_int @ D @ (times_times_int @ E @ B))) | (C @ (minus_minus_int @ D @ (times_times_int @ E @ B))))))) | ~ (! [D:int,E:int]: ((A @ D) = (A @ (minus_minus_int @ D @ (times_times_int @ E @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5693])). 159.59/70.65 thf(4597,axiom,((! [A:nat]: ((semiri1316708129612266289at_nat @ (suc @ A)) != zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6675_of__nat__neq__0)). 159.59/70.65 thf(23136,plain,((! [A:nat]: ~ ((semiri1316708129612266289at_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4597])). 159.59/70.65 thf(1038,axiom,((! [A:real,B:real]: (ord_less_eq_int @ (plus_plus_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) @ (archim6058952711729229775r_real @ (plus_plus_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8226_le__floor__add)). 159.59/70.65 thf(11575,plain,((! [A:real,B:real]: (ord_less_eq_int @ (plus_plus_int @ (archim6058952711729229775r_real @ A) @ (archim6058952711729229775r_real @ B)) @ (archim6058952711729229775r_real @ (plus_plus_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038])). 159.59/70.65 thf(1770,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((produc6081775807080527818_nat_o @ A @ (product_Pair_nat_nat @ B @ C)) = (A @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4989_old_Oprod_Ocase)). 159.59/70.65 thf(13967,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((produc6081775807080527818_nat_o @ (A) @ (product_Pair_nat_nat @ B @ C)) = (A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770])). 159.59/70.65 thf(6652,axiom,(((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one)) = (uminus1351360451143612070nteger @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5214_uminus__numeral__One)). 159.59/70.65 thf(30791,plain,(((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ one)) = (uminus1351360451143612070nteger @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6652])). 159.59/70.65 thf(1194,axiom,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ A @ (set_ord_atMost_nat @ B)) = (times_times_complex @ (A @ zero_zero_nat) @ (groups6464643781859351333omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8522_prod_OatMost__shift)). 159.59/70.65 thf(12088,plain,((! [A:(nat > complex),B:nat]: ((groups6464643781859351333omplex @ (A) @ (set_ord_atMost_nat @ B)) = (times_times_complex @ (A @ zero_zero_nat) @ (groups6464643781859351333omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194])). 159.59/70.65 thf(695,axiom,((! [A:real,B:(nat > complex),C:nat]: ((? [D:real]: ! [E:complex]: ((ord_less_eq_real @ D @ (real_V1022390504157884413omplex @ E)) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (B @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ A @ (power_power_real @ (real_V1022390504157884413omplex @ E) @ (suc @ C)))))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8956_polyfun__extremal__lemma)). 159.59/70.65 thf(10476,plain,((! [A:real,B:(nat > complex),C:nat]: (? [D:real]: ! [E:complex]: ((ord_less_eq_real @ D @ (real_V1022390504157884413omplex @ E)) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (B @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ C))) @ (times_times_real @ A @ (power_power_real @ (real_V1022390504157884413omplex @ E) @ (suc @ C))))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[695])). 159.59/70.65 thf(8153,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/sandbox/benchmark/theBenchmark.p',fact_5450_abs__power2)). 159.59/70.65 thf(36327,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)],[8153])). 159.59/70.65 thf(7796,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/sandbox/benchmark/theBenchmark.p',fact_9111_binomial__maximum)). 159.59/70.65 thf(35173,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)],[7796])). 159.59/70.65 thf(1513,axiom,((! [A:code_integer]: ((zero_n356916108424825756nteger @ (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))) = (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4489_of__bool__odd__eq__mod__2)). 159.59/70.65 thf(13181,plain,((! [A:code_integer]: ((zero_n356916108424825756nteger @ (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))) = (modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513])). 159.59/70.65 thf(7571,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit0 @ A) @ (bit1 @ B)) = (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5425_semiring__norm_I72_J)). 159.59/70.65 thf(34464,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)],[7571])). 159.59/70.65 thf(2262,axiom,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ B) => (ord_less_int @ (bit_se725231765392027082nd_int @ A @ C) @ B)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6090_AND__upper1_H_H)). 159.59/70.65 thf(15549,plain,((! [A:int,B:int,C:int]: (((ord_less_int @ A @ B) => (ord_less_int @ (bit_se725231765392027082nd_int @ A @ C) @ B)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2262])). 159.59/70.65 thf(7504,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/sandbox/benchmark/theBenchmark.p',fact_2570_vebt__member_Osimps_I2_J)). 159.59/70.65 thf(34201,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)],[7504])). 159.59/70.65 thf(8004,axiom,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3602_verit__eq__simplify_I8_J)). 159.59/70.65 thf(35828,plain,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8004])). 159.59/70.65 thf(5062,axiom,((! [A:num]: ((bit_se2925701944663578781it_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4729_take__bit__numeral__1)). 159.59/70.65 thf(24777,plain,((! [A:num]: ((bit_se2925701944663578781it_nat @ (numeral_numeral_nat @ A) @ one_one_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5062])). 159.59/70.65 thf(4601,axiom,((! [A:(nat > num),B:nat,C:nat]: (((ord_less_eq_num @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C)) <= (! [D:nat]: (ord_less_eq_num @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_lift__Suc__mono__le)). 159.59/70.65 thf(23149,plain,((! [A:(nat > num),B:nat,C:nat]: ((ord_less_eq_num @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C) | ~ (! [D:nat]: (ord_less_eq_num @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4601])). 159.59/70.65 thf(7717,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/sandbox/benchmark/theBenchmark.p',fact_2482_less__eq__div__iff__mult__less__eq)). 159.59/70.65 thf(34926,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)],[7717])). 159.59/70.65 thf(3372,axiom,((! [A:code_integer,B:code_integer,C:nat]: ((groups7501900531339628137nteger @ (^ [D:nat]: (plus_p5714425477246183910nteger @ A @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ C) @ one_one_Code_integer) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ C) @ B))) @ (numera6620942414471956472nteger @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7822_arith__series)). 159.59/70.65 thf(19089,plain,((! [A:code_integer,B:code_integer,C:nat]: ((groups7501900531339628137nteger @ (^ [D:nat]: (plus_p5714425477246183910nteger @ A @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ (plus_p5714425477246183910nteger @ (semiri4939895301339042750nteger @ C) @ one_one_Code_integer) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ C) @ B))) @ (numera6620942414471956472nteger @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3372])). 159.59/70.65 thf(4911,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/sandbox/benchmark/theBenchmark.p',fact_5129_take__bit__Suc__minus__bit0)). 159.59/70.65 thf(24228,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)],[4911])). 159.59/70.65 thf(5495,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/sandbox/benchmark/theBenchmark.p',fact_4763_minus__one__mult__self)). 159.59/70.65 thf(26427,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)],[5495])). 159.59/70.65 thf(6209,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ A))) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6003_and__numerals_I1_J)). 159.59/70.65 thf(29120,plain,((! [A:num]: ((bit_se727722235901077358nd_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ A))) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6209])). 159.59/70.65 thf(8236,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/sandbox/benchmark/theBenchmark.p',fact_7783_mask__eq__sum__exp)). 159.59/70.65 thf(36652,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)],[8236])). 159.59/70.65 thf(3411,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/sandbox/benchmark/theBenchmark.p',fact_3453_mod__add__right__eq)). 159.59/70.65 thf(19221,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)],[3411])). 159.59/70.65 thf(6057,axiom,((! [A:real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ A)) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4668_less__eq__neg__nonpos)). 159.59/70.65 thf(28624,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)],[6057])). 159.59/70.65 thf(3022,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ (times_times_int @ B @ C)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3953_dvd__mult2)). 159.59/70.65 thf(17968,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)],[3022])). 159.59/70.65 thf(5047,axiom,((! [A:nat,B:vEBT_VEBT]: (((((~ (! [C:nat]: ((A = (suc @ (suc @ C))) => ((~ (accp_nat @ vEBT_v4011308405150292612up_rel @ (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)))))) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C))))))))) <= (((~ (accp_nat @ vEBT_v4011308405150292612up_rel @ (suc @ zero_zero_nat))) <= (B = (vEBT_Leaf @ ($false) @ ($false)))) <= (A = (suc @ zero_zero_nat)))) <= (((~ (accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat)) <= (B = (vEBT_Leaf @ ($false) @ ($false)))) <= (A = zero_zero_nat))) <= (accp_nat @ vEBT_v4011308405150292612up_rel @ A)) <= ((vEBT_vebt_buildup @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4546_vebt__buildup_Opelims)). 159.59/70.65 thf(24706,plain,((! [A:nat,B:vEBT_VEBT]: (~ (! [C:nat]: ((A = (suc @ (suc @ C))) => (~ (accp_nat @ (vEBT_v4011308405150292612up_rel) @ (suc @ (suc @ C))) | ~ (((B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (suc @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))))) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C)))) & ((B = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ C)) @ (replicate_VEBT_VEBT @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_vebt_buildup @ (divide_divide_nat @ (suc @ (suc @ C)) @ (numeral_numeral_nat @ (bit0 @ one)))))) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ C)))))))) | ~ (~ (accp_nat @ (vEBT_v4011308405150292612up_rel) @ (suc @ zero_zero_nat)) | ~ (B = (vEBT_Leaf @ ($false) @ ($false))) | ~ (A = (suc @ zero_zero_nat))) | ~ (~ (accp_nat @ (vEBT_v4011308405150292612up_rel) @ zero_zero_nat) | ~ (B = (vEBT_Leaf @ ($false) @ ($false))) | ~ (A = zero_zero_nat)) | ~ (accp_nat @ (vEBT_v4011308405150292612up_rel) @ A) | ~ ((vEBT_vebt_buildup @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5047])). 159.59/70.65 thf(6245,axiom,((! [A:complex,B:complex]: ((A = (times_times_complex @ B @ A)) = ((B = one_one_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1617_mult__cancel__right1)). 159.59/70.65 thf(29229,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)],[6245])). 159.59/70.65 thf(6287,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_le__add__diff__inverse)). 159.59/70.65 thf(29450,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)],[6287])). 159.59/70.65 thf(150,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9243_scaleR__nonneg__nonpos)). 159.59/70.65 thf(8707,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 159.59/70.65 thf(4811,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ B) @ B) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3402_mod__mult__self2__is__0)). 159.59/70.65 thf(23875,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)],[4811])). 159.59/70.65 thf(1075,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_VEBT_valid @ (vEBT_Leaf @ A @ B) @ C) = (C = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9624_VEBT__internal_Ovalid_H_Osimps_I1_J)). 159.59/70.65 thf(11694,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_VEBT_valid @ (vEBT_Leaf @ A @ B) @ C) = (C = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075])). 159.59/70.65 thf(2732,axiom,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3963_dvd__triv__left)). 159.59/70.65 thf(17060,plain,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2732])). 159.59/70.65 thf(5085,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1559_bot__nat__0_Onot__eq__extremum)). 159.59/70.65 thf(24866,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5085])). 159.59/70.65 thf(6862,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ (power_power_int @ A @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_power__Suc2)). 159.59/70.65 thf(31740,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)],[6862])). 159.59/70.65 thf(3747,axiom,((! [A:complex,B:real,C:complex]: ((times_times_complex @ A @ (real_V2046097035970521341omplex @ B @ C)) = (real_V2046097035970521341omplex @ B @ (times_times_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9186_mult__scaleR__right)). 159.59/70.65 thf(20306,plain,((! [A:complex,B:real,C:complex]: ((times_times_complex @ A @ (real_V2046097035970521341omplex @ B @ C)) = (real_V2046097035970521341omplex @ B @ (times_times_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3747])). 159.59/70.65 thf(5095,axiom,((! [A:int]: ((times_times_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4703_mult__minus1__right)). 159.59/70.65 thf(24896,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)],[5095])). 159.59/70.65 thf(2094,axiom,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6840_int__ops_I4_J)). 159.59/70.65 thf(14998,plain,((! [A:nat]: ((semiri1314217659103216013at_int @ (suc @ A)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2094])). 159.59/70.65 thf(4695,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/sandbox/benchmark/theBenchmark.p',fact_3805_nat__mult__dvd__cancel__disj)). 159.59/70.65 thf(23485,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)],[4695])). 159.59/70.65 thf(2602,axiom,((minus_minus_int = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5103_diff__conv__add__uminus)). 159.59/70.65 thf(16621,plain,(((minus_minus_int) = (^ [A:int,B:int]: (plus_plus_int @ A @ (uminus_uminus_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2602])). 159.59/70.65 thf(5584,axiom,((! [A:nat]: (((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)))) = (numeral_numeral_nat @ (bit1 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = one_one_nat) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5630_mod__exhaust__less__4)). 159.59/70.65 thf(26707,plain,((! [A:nat]: (((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)))) = (numeral_numeral_nat @ (bit1 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = one_one_nat) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5584])). 159.59/70.65 thf(1884,axiom,((artanh_real = (^ [A:real]: (divide_divide_real @ (ln_ln_real @ (divide_divide_real @ (plus_plus_real @ one_one_real @ A) @ (minus_minus_real @ one_one_real @ A))) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4593_artanh__def)). 159.59/70.65 thf(14336,plain,(((artanh_real) = (^ [A:real]: (divide_divide_real @ (ln_ln_real @ (divide_divide_real @ (plus_plus_real @ one_one_real @ A) @ (minus_minus_real @ one_one_real @ A))) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1884])). 159.59/70.65 thf(1682,axiom,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1836_not__less__zero)). 159.59/70.65 thf(13698,plain,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682])). 159.59/70.65 thf(72,axiom,((! [A:nat,B:nat,C:complex]: ((ord_less_eq_nat @ A @ B) => ((times_times_complex @ (gbinomial_complex @ C @ B) @ (gbinomial_complex @ (semiri8010041392384452111omplex @ B) @ A)) = (times_times_complex @ (gbinomial_complex @ C @ A) @ (gbinomial_complex @ (minus_minus_complex @ C @ (semiri8010041392384452111omplex @ A)) @ (minus_minus_nat @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8311_gbinomial__trinomial__revision)). 159.59/70.65 thf(8466,plain,((! [A:nat,B:nat,C:complex]: ((ord_less_eq_nat @ A @ B) => ((times_times_complex @ (gbinomial_complex @ C @ B) @ (gbinomial_complex @ (semiri8010041392384452111omplex @ B) @ A)) = (times_times_complex @ (gbinomial_complex @ C @ A) @ (gbinomial_complex @ (minus_minus_complex @ C @ (semiri8010041392384452111omplex @ A)) @ (minus_minus_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 159.59/70.65 thf(3594,axiom,((~ (ord_less_int @ one_one_int @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2127_not__one__less__zero)). 159.59/70.65 thf(19793,plain,((~ (ord_less_int @ one_one_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3594])). 159.59/70.65 thf(8062,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((? [C:nat]: ((ord_less_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))) & (ord_less_eq_nat @ (power_power_nat @ A @ C) @ B))) <= (ord_less_eq_nat @ one_one_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_ex__power__ivl1)). 159.59/70.65 thf(36030,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (? [C:nat]: ((ord_less_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))) & (ord_less_eq_nat @ (power_power_nat @ A @ C) @ B)) | ~ (ord_less_eq_nat @ one_one_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8062])). 159.59/70.65 thf(4193,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/sandbox/benchmark/theBenchmark.p',fact_843_mult__diff__mult)). 159.59/70.65 thf(21696,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)],[4193])). 159.59/70.65 thf(2759,axiom,(((cos_real @ zero_zero_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6964_cos__zero)). 159.59/70.65 thf(17144,plain,(((cos_real @ zero_zero_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2759])). 159.59/70.65 thf(1933,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/sandbox/benchmark/theBenchmark.p',fact_2142_divide__nonneg__nonneg)). 159.59/70.65 thf(14485,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)],[1933])). 159.59/70.65 thf(1108,axiom,((! [A:int,B:(extended_enat > int),C:extended_enat,D:extended_enat]: (((ord_le72135733267957522d_enat @ C @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_int @ (B @ E) @ (B @ F)))) => (ord_less_int @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2867_ord__eq__less__subst)). 159.59/70.65 thf(11808,plain,((! [A:int,B:(extended_enat > int),C:extended_enat,D:extended_enat]: (((ord_le72135733267957522d_enat @ C @ D) => ((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_int @ (B @ E) @ (B @ F)))) => (ord_less_int @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108])). 159.59/70.65 thf(5989,axiom,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ B)) = (B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_mem__Collect__eq)). 159.59/70.65 thf(28403,plain,((! [A:nat,B:(nat > $o)]: ((member_nat @ A @ (collect_nat @ (B))) = (B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5989])). 159.59/70.65 thf(6590,axiom,((! [A:int,B:nat]: (((ord_less_eq_int @ A @ one_one_int) => (ord_less_eq_int @ (power_power_int @ A @ (suc @ B)) @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2450_power__Suc__le__self)). 159.59/70.65 thf(30573,plain,((! [A:int,B:nat]: (((ord_less_eq_int @ A @ one_one_int) => (ord_less_eq_int @ (power_power_int @ A @ (suc @ B)) @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6590])). 159.59/70.65 thf(1199,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((~ (member_nat @ A @ B)) => ((ord_less_eq_set_nat @ B @ (insert_nat @ A @ C)) = (ord_less_eq_set_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6200_subset__insert)). 159.59/70.65 thf(12103,plain,((! [A:nat,B:set_nat,C:set_nat]: ((~ (member_nat @ A @ B)) => ((ord_less_eq_set_nat @ B @ (insert_nat @ A @ C)) = (ord_less_eq_set_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199])). 159.59/70.65 thf(4635,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/sandbox/benchmark/theBenchmark.p',fact_5818_of__int__numeral__le__iff)). 159.59/70.65 thf(23273,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)],[4635])). 159.59/70.65 thf(7663,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2886_order__less__irrefl)). 159.59/70.65 thf(34739,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7663])). 159.59/70.65 thf(7072,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) <= (dvd_dvd_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4032_dvd__diff__nat)). 159.59/70.65 thf(32621,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C)) | ~ (dvd_dvd_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7072])). 159.59/70.65 thf(3381,axiom,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ pi) => (((sin_real @ A) = zero_zero_real) = (A = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6845_sin__zero__pi__iff)). 159.59/70.65 thf(19118,plain,((! [A:real]: ((ord_less_real @ (abs_abs_real @ A) @ pi) => (((sin_real @ A) = zero_zero_real) = (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3381])). 159.59/70.65 thf(1488,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/sandbox/benchmark/theBenchmark.p',fact_1646_nonzero__mult__divide__mult__cancel__right2)). 159.59/70.65 thf(13108,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)],[1488])). 159.59/70.65 thf(1212,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ (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_eq_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C)) <= (ord_less_real @ C @ zero_zero_real)))) & ((ord_less_eq_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B)) <= (ord_less_real @ zero_zero_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5279_le__minus__divide__eq)). 159.59/70.65 thf(12174,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ (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_eq_real @ (uminus_uminus_real @ B) @ (times_times_real @ A @ C)) | ~ (ord_less_real @ C @ zero_zero_real)))) & ((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)],[1212])). 159.59/70.65 thf(2805,axiom,((! [A:nat,B:real]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B) => (ord_less_eq_nat @ A @ (nat2 @ (archim6058952711729229775r_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9458_le__nat__floor)). 159.59/70.65 thf(17276,plain,((! [A:nat,B:real]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B) => (ord_less_eq_nat @ A @ (nat2 @ (archim6058952711729229775r_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2805])). 159.59/70.65 thf(5163,axiom,((! [A:num]: ~ (ord_less_num @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2885_order__less__irrefl)). 159.59/70.65 thf(25129,plain,((! [A:num]: ~ (ord_less_num @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5163])). 159.59/70.65 thf(6228,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ C))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1941_power__strict__mono)). 159.59/70.65 thf(29177,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ C))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6228])). 159.59/70.65 thf(1241,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/sandbox/benchmark/theBenchmark.p',fact_1053_mul__shift)). 159.59/70.65 thf(12271,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)],[1241])). 159.59/70.65 thf(6163,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/sandbox/benchmark/theBenchmark.p',fact_5638_power__even__abs)). 159.59/70.65 thf(28966,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)],[6163])). 159.59/70.65 thf(7492,axiom,((! [A:nat,B:list_int,C:int]: ((ord_less_nat @ A @ (size_size_list_int @ B)) => ((nth_int @ (list_update_int @ B @ A @ C) @ A) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_nth__list__update__eq)). 159.59/70.65 thf(34162,plain,((! [A:nat,B:list_int,C:int]: ((ord_less_nat @ A @ (size_size_list_int @ B)) => ((nth_int @ (list_update_int @ B @ A @ C) @ A) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7492])). 159.59/70.65 thf(1918,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/sandbox/benchmark/theBenchmark.p',fact_5790_of__int__power)). 159.59/70.65 thf(14444,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)],[1918])). 159.59/70.65 thf(7349,axiom,((! [A:complex,B:nat]: (((power_power_complex @ A @ B) = one_one_complex) => ((B = zero_zero_nat) | ((real_V1022390504157884413omplex @ A) = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6946_power__eq__1__iff)). 159.59/70.65 thf(33666,plain,((! [A:complex,B:nat]: (((power_power_complex @ A @ B) = one_one_complex) => ((B = zero_zero_nat) | ((real_V1022390504157884413omplex @ A) = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7349])). 159.59/70.65 thf(5256,axiom,((! [A:num]: ((ord_less_eq_num @ A @ one) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_le__num__One__iff)). 159.59/70.65 thf(25461,plain,((! [A:num]: ((ord_less_eq_num @ A @ one) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5256])). 159.59/70.65 thf(1361,axiom,((! [A:num,B:nat,C:nat]: ((ord_le6747313008572928689nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ A) @ B) @ (semiri4939895301339042750nteger @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6631_numeral__power__less__of__nat__cancel__iff)). 159.59/70.65 thf(12648,plain,((! [A:num,B:nat,C:nat]: ((ord_le6747313008572928689nteger @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ A) @ B) @ (semiri4939895301339042750nteger @ C)) = (ord_less_nat @ (power_power_nat @ (numeral_numeral_nat @ A) @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361])). 159.59/70.65 thf(2109,axiom,((! [A:set_nat,B:(nat > extended_enat),C:extended_enat,D:nat]: ((finite_finite_nat @ A) => ((! [E:nat]: ((member_nat @ E @ A) => (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ E)))) => (((member_nat @ D @ A) => (ord_le2932123472753598470d_enat @ (B @ D) @ C)) <= ((groups7108830773950497114d_enat @ B @ A) = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7517_sum__nonneg__leq__bound)). 159.59/70.65 thf(15043,plain,((! [A:set_nat,B:(nat > extended_enat),C:extended_enat,D:nat]: ((finite_finite_nat @ A) => ((! [E:nat]: ((member_nat @ E @ A) => (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ (B @ E)))) => (((member_nat @ D @ A) => (ord_le2932123472753598470d_enat @ (B @ D) @ C)) | ~ ((groups7108830773950497114d_enat @ (B) @ A) = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2109])). 159.59/70.65 thf(8244,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1631_nonzero__mult__div__cancel__left)). 159.59/70.65 thf(36758,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)],[8244])). 159.59/70.65 thf(3490,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/sandbox/benchmark/theBenchmark.p',fact_3526_cancel__div__mod__rules_I2_J)). 159.59/70.65 thf(19460,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)],[3490])). 159.59/70.65 thf(6482,axiom,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1538_div__0)). 159.59/70.65 thf(30188,plain,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6482])). 159.59/70.65 thf(568,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C))) = (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ (uminus_uminus_real @ C))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9275_pos__le__minus__divideR__eq)). 159.59/70.65 thf(10059,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (uminus_uminus_real @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C))) = (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ (uminus_uminus_real @ C))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[568])). 159.59/70.65 thf(5830,axiom,((! [A:nat]: ((bit_se1412395901928357646or_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5955_or_Oleft__neutral)). 159.59/70.65 thf(27727,plain,((! [A:nat]: ((bit_se1412395901928357646or_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5830])). 159.59/70.65 thf(4425,axiom,((! [A:nat,B:code_integer]: ((bit_se1345352211410354436nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se1345352211410354436nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3583_flip__bit__Suc)). 159.59/70.65 thf(22431,plain,((! [A:nat,B:code_integer]: ((bit_se1345352211410354436nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se1345352211410354436nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4425])). 159.59/70.65 thf(258,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/sandbox/benchmark/theBenchmark.p',fact_8040_sumr__cos__zero__one)). 159.59/70.65 thf(9037,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)],[258])). 159.59/70.65 thf(3325,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => ((((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 @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7837_arcsin__le__iff)). 159.59/70.65 thf(18947,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => (((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 @ (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3325])). 159.59/70.65 thf(6946,axiom,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat)]: ((finite_finite_nat @ A) => (((dvd_dvd_nat @ (groups708209901874060359at_nat @ C @ B) @ (groups708209901874060359at_nat @ D @ A)) <= (! [E:nat]: ((member_nat @ E @ B) => (dvd_dvd_nat @ (C @ E) @ (D @ E))))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8598_prod__dvd__prod__subset2)). 159.59/70.65 thf(32033,plain,((! [A:set_nat,B:set_nat,C:(nat > nat),D:(nat > nat)]: ((finite_finite_nat @ A) => ((dvd_dvd_nat @ (groups708209901874060359at_nat @ (C) @ B) @ (groups708209901874060359at_nat @ (D) @ A)) | ~ (! [E:nat]: ((member_nat @ E @ B) => (dvd_dvd_nat @ (C @ E) @ (D @ E)))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6946])). 159.59/70.65 thf(4049,axiom,((! [A:set_nat,B:(nat > extended_enat)]: ((! [C:nat]: ((ord_le2932123472753598470d_enat @ (B @ C) @ zero_z5237406670263579293d_enat) <= (member_nat @ C @ A))) => (ord_le2932123472753598470d_enat @ (groups7108830773950497114d_enat @ B @ A) @ zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7428_sum__nonpos)). 159.59/70.65 thf(21251,plain,((! [A:set_nat,B:(nat > extended_enat)]: ((! [C:nat]: ((ord_le2932123472753598470d_enat @ (B @ C) @ zero_z5237406670263579293d_enat) | ~ (member_nat @ C @ A))) => (ord_le2932123472753598470d_enat @ (groups7108830773950497114d_enat @ (B) @ A) @ zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4049])). 159.59/70.65 thf(7097,axiom,((! [A:num,B:num]: (ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ (numeral_numeral_real @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5029_neg__numeral__le__numeral)). 159.59/70.65 thf(32725,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)],[7097])). 159.59/70.65 thf(4753,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/sandbox/benchmark/theBenchmark.p',fact_6604_of__nat__less__of__nat__power__cancel__iff)). 159.59/70.65 thf(23683,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)],[4753])). 159.59/70.65 thf(1492,axiom,(((exp_real @ zero_zero_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5964_exp__zero)). 159.59/70.65 thf(13121,plain,(((exp_real @ zero_zero_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1492])). 159.59/70.65 thf(7551,axiom,((! [A:num,B:num]: ((ord_less_num @ B @ A) | (A = B) | (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2920_linorder__less__linear)). 159.59/70.65 thf(34343,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)],[7551])). 159.59/70.65 thf(3645,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3958_dvd__mult__left)). 159.59/70.65 thf(19954,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3645])). 159.59/70.65 thf(2704,axiom,((! [A:int]: (((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)) & (((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) <= (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4253_mod2__eq__if)). 159.59/70.65 thf(16974,plain,((! [A:int]: (((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = one_one_int)) & (((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) | ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2704])). 159.59/70.65 thf(3328,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ A @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3909_even__succ__div__two)). 159.59/70.65 thf(18957,plain,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => ((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ A @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3328])). 159.59/70.65 thf(722,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/sandbox/benchmark/theBenchmark.p',fact_1444_diff__divide__distrib)). 159.59/70.65 thf(10581,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)],[722])). 159.59/70.65 thf(7485,axiom,(((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = one_one_Code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4859_minus__1__mod__2__eq)). 159.59/70.65 thf(34145,plain,(((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7485])). 159.59/70.65 thf(1443,axiom,((! [A:nat,B:nat,C:real]: ((dvd_dvd_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4120_le__imp__power__dvd)). 159.59/70.65 thf(12954,plain,((! [A:nat,B:nat,C:real]: ((dvd_dvd_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1443])). 159.59/70.65 thf(7829,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/sandbox/benchmark/theBenchmark.p',fact_2085_zero__less__mult__pos)). 159.59/70.65 thf(35283,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)],[7829])). 159.59/70.65 thf(3183,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/sandbox/benchmark/theBenchmark.p',fact_6474_set__bit__eq)). 159.59/70.65 thf(18490,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)],[3183])). 159.59/70.65 thf(3432,axiom,((! [A:real,B:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ A) = (ord_less_real @ B @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1605_add__less__same__cancel1)). 159.59/70.65 thf(19284,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)],[3432])). 159.59/70.65 thf(4622,axiom,((ord_less_num = (^ [A:num,B:num]: ((A != B) & (ord_less_eq_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3078_order_Ostrict__iff__order)). 159.59/70.65 thf(23228,plain,(((ord_less_num) = (^ [A:num,B:num]: (~ (A = B) & (ord_less_eq_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4622])). 159.59/70.65 thf(7758,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/sandbox/benchmark/theBenchmark.p',fact_536_misiz)). 159.59/70.65 thf(35068,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)],[7758])). 159.59/70.65 thf(6799,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3170_linorder__not__le)). 159.59/70.65 thf(31441,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6799])). 159.59/70.65 thf(5764,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/sandbox/benchmark/theBenchmark.p',fact_1258_right__diff__distrib_H)). 159.59/70.65 thf(27338,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)],[5764])). 159.59/70.65 thf(1165,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/sandbox/benchmark/theBenchmark.p',fact_8337_gbinomial__minus)). 159.59/70.65 thf(11989,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)],[1165])). 159.59/70.65 thf(4851,axiom,((! [A:nat]: (ord_less_eq_nat @ one_one_nat @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8081_fact__ge__1)). 159.59/70.65 thf(24035,plain,((! [A:nat]: (ord_less_eq_nat @ one_one_nat @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4851])). 159.59/70.65 thf(6465,axiom,((! [A:nat,B:nat,C:nat]: ((A = (plus_plus_nat @ B @ C)) => ((suc @ A) = (plus_plus_nat @ B @ (suc @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_nat__arith_Osuc1)). 159.59/70.65 thf(30123,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)],[6465])). 159.59/70.65 thf(7104,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/sandbox/benchmark/theBenchmark.p',fact_3093_order_Ostrict__trans2)). 159.59/70.65 thf(32745,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)],[7104])). 159.59/70.65 thf(4905,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1911_gr__implies__not0)). 159.59/70.65 thf(24207,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4905])). 159.59/70.65 thf(1156,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_int @ A @ zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2122_add__less__zeroD)). 159.59/70.65 thf(11956,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_int @ A @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156])). 159.59/70.65 thf(5129,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/sandbox/benchmark/theBenchmark.p',fact_9573_sum__power2)). 159.59/70.65 thf(25001,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)],[5129])). 159.59/70.65 thf(7154,axiom,((! [A:nat,B:nat,C:int]: (((groups3539618377306564664at_int @ (power_power_int @ C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_int @ (power_power_int @ C @ A) @ (groups3539618377306564664at_int @ (power_power_int @ C) @ (set_ord_atMost_nat @ (minus_minus_nat @ B @ A))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8889_sum__power__shift)). 159.59/70.65 thf(32953,plain,((! [A:nat,B:nat,C:int]: (((groups3539618377306564664at_int @ (power_power_int @ C) @ (set_or1269000886237332187st_nat @ A @ B)) = (times_times_int @ (power_power_int @ C @ A) @ (groups3539618377306564664at_int @ (power_power_int @ C) @ (set_ord_atMost_nat @ (minus_minus_nat @ B @ A))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7154])). 159.59/70.65 thf(6762,axiom,((! [A:num]: ((one_on7984719198319812577d_enat = (numera1916890842035813515d_enat @ A)) = (one = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_one__eq__numeral__iff)). 159.59/70.65 thf(31317,plain,((! [A:num]: ((one_on7984719198319812577d_enat = (numera1916890842035813515d_enat @ A)) = (one = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6762])). 159.59/70.65 thf(5594,axiom,((! [A:real]: ((times_times_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ one))) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5205_mult__1s__ring__1_I2_J)). 159.59/70.65 thf(26739,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)],[5594])). 159.59/70.65 thf(4410,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((? [C:real]: ((B = (cos_real @ C)) & (A = (sin_real @ C)) & (ord_less_eq_real @ C @ pi) & (ord_less_eq_real @ zero_zero_real @ C))) <= ((plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7193_sincos__total__pi)). 159.59/70.65 thf(22376,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (? [C:real]: ((B = (cos_real @ C)) & (A = (sin_real @ C)) & (ord_less_eq_real @ C @ pi) & (ord_less_eq_real @ zero_zero_real @ C)) | ~ ((plus_plus_real @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4410])). 159.59/70.65 thf(3443,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/sandbox/benchmark/theBenchmark.p',fact_6846_sin__zero__iff__int2)). 159.59/70.65 thf(19320,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)],[3443])). 159.59/70.65 thf(664,axiom,((! [A:complex,B:nat]: ((((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))) <= (A != one_one_complex)) & (((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)) = (semiri8010041392384452111omplex @ B)) <= (A = one_one_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7991_sum__gp__strict)). 159.59/70.65 thf(10371,plain,((! [A:complex,B:nat]: ((((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))) | (A = one_one_complex)) & (((groups2073611262835488442omplex @ (power_power_complex @ A) @ (set_ord_lessThan_nat @ B)) = (semiri8010041392384452111omplex @ B)) | ~ (A = one_one_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[664])). 159.59/70.65 thf(1618,axiom,((! [A:int]: ? [B:int]: (ord_less_int @ A @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2762_gt__ex)). 159.59/70.65 thf(13508,plain,((! [A:int]: ? [B:int]: (ord_less_int @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618])). 159.59/70.65 thf(4225,axiom,((! [A:complex,B:complex,C:complex]: ((A = (divide1717551699836669952omplex @ B @ C)) = (((C != zero_zero_complex) => ((times_times_complex @ A @ C) = B)) & ((C = zero_zero_complex) => (A = zero_zero_complex)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2175_eq__divide__eq)). 159.59/70.65 thf(21818,plain,((! [A:complex,B:complex,C:complex]: ((A = (divide1717551699836669952omplex @ B @ C)) = (((~ (C = zero_zero_complex)) => ((times_times_complex @ A @ C) = B)) & ((C = zero_zero_complex) => (A = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4225])). 159.59/70.65 thf(2730,axiom,((one_one_nat = (nat2 @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9429_nat__one__as__int)). 159.59/70.65 thf(17055,plain,((one_one_nat = (nat2 @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2730])). 159.59/70.65 thf(5086,axiom,((! [A:nat]: (dvd_dvd_nat @ one_one_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4004_one__dvd)). 159.59/70.65 thf(24869,plain,((! [A:nat]: (dvd_dvd_nat @ one_one_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5086])). 159.59/70.65 thf(6423,axiom,((! [A:nat,B:real,C:real]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (((power_power_real @ B @ A) = C) => ((root @ A @ C) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9522_odd__real__root__unique)). 159.59/70.65 thf(29941,plain,((! [A:nat,B:real,C:real]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (((power_power_real @ B @ A) = C) => ((root @ A @ C) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6423])). 159.59/70.65 thf(1597,axiom,((! [A:$o,B:$o]: ((ord_less_eq_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B)) = ((A) => (B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4313_of__bool__less__eq__iff)). 159.59/70.65 thf(13435,plain,((! [A:$o,B:$o]: ((ord_less_eq_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B)) = ((A) => (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597])). 159.59/70.65 thf(6236,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_old_Onat_Oinject)). 159.59/70.65 thf(29202,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6236])). 159.59/70.65 thf(1743,axiom,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1844_less__numeral__extra_I3_J)). 159.59/70.65 thf(13882,plain,((~ (ord_less_int @ zero_zero_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743])). 159.59/70.65 thf(2431,axiom,((ord_less_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6743_pi__less__4)). 159.59/70.65 thf(16079,plain,((ord_less_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2431])). 159.59/70.65 thf(7790,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/sandbox/benchmark/theBenchmark.p',fact_674_power__odd__eq)). 159.59/70.65 thf(35156,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)],[7790])). 159.59/70.65 thf(747,axiom,((! [A:(extended_enat > $o),B:extended_enat]: ((A @ B) <= (! [C:extended_enat]: ((! [D:extended_enat]: ((A @ D) <= (ord_le72135733267957522d_enat @ D @ C))) => (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_enat__less__induct)). 159.59/70.65 thf(10667,plain,((! [A:(extended_enat > $o),B:extended_enat]: ((A @ B) | ~ (! [C:extended_enat]: ((! [D:extended_enat]: ((A @ D) | ~ (ord_le72135733267957522d_enat @ D @ C))) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[747])). 159.59/70.65 thf(1083,axiom,((! [A:nat,B:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6692_of__nat__mono)). 159.59/70.65 thf(11726,plain,((! [A:nat,B:nat]: ((ord_le3102999989581377725nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083])). 159.59/70.65 thf(2592,axiom,((! [A:real,B:real,C:(real > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((! [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 @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3245_order__less__le__subst2)). 159.59/70.65 thf(16579,plain,((! [A:real,B:real,C:(real > real),D:real]: (((ord_less_eq_real @ (C @ B) @ D) => ((! [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 @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2592])). 159.59/70.65 thf(7292,axiom,((! [A:num,B:(num > num),C:num,D:num]: ((ord_less_num @ A @ (B @ C)) => (((! [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_eq_num @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3234_order__less__le__subst1)). 159.59/70.65 thf(33455,plain,((! [A:num,B:(num > num),C:num,D:num]: ((ord_less_num @ A @ (B @ C)) => (((! [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_eq_num @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7292])). 159.59/70.65 thf(4952,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (((ord_less_nat @ B @ C) => (A @ zero_zero_nat)) & ! [D:nat]: ((A @ D) <= (B = (plus_plus_nat @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2398_nat__diff__split)). 159.59/70.65 thf(24357,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (((ord_less_nat @ B @ C) => (A @ zero_zero_nat)) & ! [D:nat]: ((A @ D) | ~ (B = (plus_plus_nat @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4952])). 159.59/70.65 thf(1540,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/sandbox/benchmark/theBenchmark.p',fact_1313_add__le__less__mono)). 159.59/70.65 thf(13261,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)],[1540])). 159.59/70.65 thf(4482,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/sandbox/benchmark/theBenchmark.p',fact_568_nat__mult__max__right)). 159.59/70.65 thf(22670,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)],[4482])). 159.59/70.65 thf(5228,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/sandbox/benchmark/theBenchmark.p',fact_2360_power__le__imp__le__base)). 159.59/70.65 thf(25372,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)],[5228])). 159.59/70.65 thf(1418,axiom,((! [A:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ zero_zero_real) => ((ord_less_real @ A @ zero_zero_real) <= (A != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9027_inverse__negative__imp__negative)). 159.59/70.65 thf(12873,plain,((! [A:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ zero_zero_real) => ((ord_less_real @ A @ zero_zero_real) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1418])). 159.59/70.65 thf(4132,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C) => ((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 @ B @ D)) @ E))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6935_norm__diff__triangle__le)). 159.59/70.65 thf(21501,plain,((! [A:real,B:real,C:real,D:real,E:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ A @ B)) @ C) => ((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 @ B @ D)) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4132])). 159.59/70.65 thf(5099,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((B = one_one_nat) & (A = one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_nat__mult__eq__1__iff)). 159.59/70.65 thf(24909,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)],[5099])). 159.59/70.65 thf(5579,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/sandbox/benchmark/theBenchmark.p',fact_6265_or__not__num__neg_Osimps_I8_J)). 159.59/70.65 thf(26694,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)],[5579])). 159.59/70.65 thf(476,axiom,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A) => ((ord_le6747313008572928689nteger @ A @ B) => ((divide6298287555418463151nteger @ A @ B) = zero_z3403309356797280102nteger))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2283_unique__euclidean__semiring__numeral__class_Odiv__less)). 159.59/70.65 thf(9766,plain,((! [A:code_integer,B:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A) => ((ord_le6747313008572928689nteger @ A @ B) => ((divide6298287555418463151nteger @ A @ B) = zero_z3403309356797280102nteger))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[476])). 159.59/70.65 thf(247,axiom,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ zero_z3403309356797280102nteger) = (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4666_neg__le__0__iff__le)). 159.59/70.65 thf(9005,plain,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ A) @ zero_z3403309356797280102nteger) = (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 159.59/70.65 thf(2747,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/sandbox/benchmark/theBenchmark.p',fact_8349_gbinomial__sum__up__index)). 159.59/70.65 thf(17105,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)],[2747])). 159.59/70.65 thf(8032,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/sandbox/benchmark/theBenchmark.p',fact_1230_distrib__right)). 159.59/70.65 thf(35925,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)],[8032])). 159.59/70.65 thf(3608,axiom,((~ (ord_less_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5076_less__minus__one__simps_I4_J)). 159.59/70.65 thf(19838,plain,((~ (ord_less_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3608])). 159.59/70.65 thf(3036,axiom,((! [A:nat]: ((semiri8010041392384452111omplex @ (suc @ A)) = (plus_plus_complex @ one_one_complex @ (semiri8010041392384452111omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6585_of__nat__Suc)). 159.59/70.65 thf(18009,plain,((! [A:nat]: ((semiri8010041392384452111omplex @ (suc @ A)) = (plus_plus_complex @ one_one_complex @ (semiri8010041392384452111omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3036])). 159.59/70.65 thf(2940,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/sandbox/benchmark/theBenchmark.p',fact_7155_cos__times__cos)). 159.59/70.65 thf(17717,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)],[2940])). 159.59/70.65 thf(1754,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 @ 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) => (ord_less_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5242_less__minus__divide__eq)). 159.59/70.65 thf(13916,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 @ 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) => (ord_less_real @ (times_times_real @ A @ C) @ (uminus_uminus_real @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754])). 159.59/70.65 thf(5264,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/sandbox/benchmark/theBenchmark.p',fact_1338_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc)). 159.59/70.65 thf(25482,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)],[5264])). 159.59/70.65 thf(2674,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/sandbox/benchmark/theBenchmark.p',fact_4297_inf__period_I3_J)). 159.59/70.65 thf(16870,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)],[2674])). 159.59/70.65 thf(3513,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5519_abs__of__pos)). 159.59/70.65 thf(19531,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3513])). 159.59/70.65 thf(400,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((gbinomial_complex @ (semiri8010041392384452111omplex @ B) @ A) = (gbinomial_complex @ (semiri8010041392384452111omplex @ B) @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8238_gbinomial__of__nat__symmetric)). 159.59/70.65 thf(9499,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((gbinomial_complex @ (semiri8010041392384452111omplex @ B) @ A) = (gbinomial_complex @ (semiri8010041392384452111omplex @ B) @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[400])). 159.59/70.65 thf(895,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((ord_less_int @ A @ B) | (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3110_dual__order_Oorder__iff__strict)). 159.59/70.65 thf(11126,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((ord_less_int @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[895])). 159.59/70.65 thf(1776,axiom,((! [A:int,B:int,C:int]: (((((divide_divide_int @ B @ A) = C) = (B = (times_times_int @ C @ A))) <= (dvd_dvd_int @ A @ B)) <= (A != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4140_dvd__div__eq__mult)). 159.59/70.65 thf(13990,plain,((! [A:int,B:int,C:int]: ((((divide_divide_int @ B @ A) = C) = (B = (times_times_int @ C @ A))) | ~ (dvd_dvd_int @ A @ B) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776])). 159.59/70.65 thf(7509,axiom,((! [A:num]: ((plus_plus_real @ one_one_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_one__plus__numeral)). 159.59/70.65 thf(34215,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)],[7509])). 159.59/70.65 thf(33,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/sandbox/benchmark/theBenchmark.p',fact_7290_tan__minus__45)). 159.59/70.65 thf(8350,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)],[33])). 159.59/70.65 thf(3976,axiom,(((zero_n356916108424825756nteger @ ($true)) = one_one_Code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4325_of__bool__eq_I2_J)). 159.59/70.65 thf(21039,plain,(((zero_n356916108424825756nteger @ ($true)) = one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3976])). 159.59/70.65 thf(7341,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/sandbox/benchmark/theBenchmark.p',fact_5593_power__minus__Bit1)). 159.59/70.65 thf(33638,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)],[7341])). 159.59/70.65 thf(4265,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/sandbox/benchmark/theBenchmark.p',fact_7455_sum_Oshift__bounds__cl__nat__ivl)). 159.59/70.65 thf(21941,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)],[4265])). 159.59/70.65 thf(4005,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/sandbox/benchmark/theBenchmark.p',fact_1347_add__le__imp__le__diff)). 159.59/70.65 thf(21126,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)],[4005])). 159.59/70.65 thf(7704,axiom,((! [A:nat]: ((divide_divide_nat @ (plus_plus_nat @ A @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_add__self__div__2)). 159.59/70.65 thf(34866,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)],[7704])). 159.59/70.65 thf(4475,axiom,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1033_div__by__1)). 159.59/70.65 thf(22644,plain,((! [A:nat]: ((divide_divide_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4475])). 159.59/70.65 thf(38,axiom,((! [A:set_nat,B:set_nat,C:(nat > real)]: ((ord_less_eq_set_nat @ A @ B) => ((finite_finite_nat @ B) => ((groups129246275422532515t_real @ C @ B) = (times_times_real @ (groups129246275422532515t_real @ C @ (minus_minus_set_nat @ B @ A)) @ (groups129246275422532515t_real @ C @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8667_prod_Osubset__diff)). 159.59/70.65 thf(8364,plain,((! [A:set_nat,B:set_nat,C:(nat > real)]: ((ord_less_eq_set_nat @ A @ B) => ((finite_finite_nat @ B) => ((groups129246275422532515t_real @ (C) @ B) = (times_times_real @ (groups129246275422532515t_real @ (C) @ (minus_minus_set_nat @ B @ A)) @ (groups129246275422532515t_real @ (C) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[38])). 159.59/70.65 thf(14,axiom,((! [A:real,B:real]: ((sinh_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ (times_times_real @ (sinh_real @ A) @ (cosh_real @ B)) @ (times_times_real @ (cosh_real @ A) @ (sinh_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9332_sinh__diff)). 159.59/70.65 thf(8295,plain,((! [A:real,B:real]: ((sinh_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ (times_times_real @ (sinh_real @ A) @ (cosh_real @ B)) @ (times_times_real @ (cosh_real @ A) @ (sinh_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[14])). 159.59/70.65 thf(533,axiom,((! [A:nat,B:nat,C:int]: (((ord_less_eq_nat @ A @ B) => ((bit_se2923211474154528505it_int @ A @ (bit_se2159334234014336723it_int @ B @ C)) = (bit_se2923211474154528505it_int @ A @ C))) & (((bit_se2923211474154528505it_int @ A @ (bit_se2159334234014336723it_int @ B @ C)) = (bit_se2159334234014336723it_int @ B @ (bit_se2923211474154528505it_int @ A @ C))) <= (~ (ord_less_eq_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5114_take__bit__flip__bit__eq)). 159.59/70.65 thf(9948,plain,((! [A:nat,B:nat,C:int]: (((ord_less_eq_nat @ A @ B) => ((bit_se2923211474154528505it_int @ A @ (bit_se2159334234014336723it_int @ B @ C)) = (bit_se2923211474154528505it_int @ A @ C))) & (((bit_se2923211474154528505it_int @ A @ (bit_se2159334234014336723it_int @ B @ C)) = (bit_se2159334234014336723it_int @ B @ (bit_se2923211474154528505it_int @ A @ C))) | (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[533])). 159.59/70.65 thf(3365,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ B @ C) => (~ (ord_less_eq_int @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4497_pinf_I6_J)). 159.59/70.65 thf(19067,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)],[3365])). 159.59/70.65 thf(2716,axiom,((bit_se1409905431419307370or_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_se1409905431419307370or_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6131_or__int__rec)). 159.59/70.65 thf(17013,plain,(((bit_se1409905431419307370or_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_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)],[2716])). 159.59/70.65 thf(2774,axiom,((! [A:real]: (((((sin_real @ (arcsin @ A)) = A) & (ord_less_eq_real @ (arcsin @ 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)))) @ (arcsin @ A))) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7835_arcsin)). 159.59/70.65 thf(17187,plain,((! [A:real]: ((((sin_real @ (arcsin @ A)) = A) & (ord_less_eq_real @ (arcsin @ 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)))) @ (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)],[2774])). 159.59/70.65 thf(5839,axiom,((! [A:int,B:nat,C:nat]: ((A != zero_zero_int) => ((dvd_dvd_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = ((ord_less_eq_nat @ B @ C) | (dvd_dvd_int @ A @ one_one_int)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4213_dvd__power__iff)). 159.59/70.65 thf(27830,plain,((! [A:int,B:nat,C:nat]: ((~ (A = zero_zero_int)) => ((dvd_dvd_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C)) = ((ord_less_eq_nat @ B @ C) | (dvd_dvd_int @ A @ one_one_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5839])). 159.59/70.65 thf(181,axiom,((! [A:num]: ((real_V1803761363581548252l_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7329_of__real__numeral)). 159.59/70.65 thf(8813,plain,((! [A:num]: ((real_V1803761363581548252l_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 159.59/70.65 thf(2281,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/sandbox/benchmark/theBenchmark.p',fact_1149_ab__semigroup__add__class_Oadd__ac_I1_J)). 159.59/70.65 thf(15603,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)],[2281])). 159.59/70.65 thf(3891,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (plus_plus_real @ A @ C)) <= (ord_less_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2257_add__strict__increasing2)). 159.59/70.65 thf(20779,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ B @ (plus_plus_real @ A @ C)) | ~ (ord_less_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3891])). 159.59/70.65 thf(4794,axiom,(((code_integer_of_num @ one) = one_one_Code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9813_integer__of__num__triv_I1_J)). 159.59/70.65 thf(23808,plain,(((code_integer_of_num @ one) = one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4794])). 159.59/70.65 thf(3287,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (? [B:nat]: (ord_less_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ (suc @ B))) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9093_reals__Archimedean)). 159.59/70.65 thf(18835,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => (? [B:nat]: (ord_less_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ (suc @ B))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3287])). 159.59/70.65 thf(331,axiom,((! [A:real]: ((power_power_real @ (sinh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_real @ (power_power_real @ (cosh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9348_sinh__square__eq)). 159.59/70.65 thf(9270,plain,((! [A:real]: ((power_power_real @ (sinh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_real @ (power_power_real @ (cosh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 159.59/70.65 thf(2712,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/sandbox/benchmark/theBenchmark.p',fact_1312_add__less__le__mono)). 159.59/70.65 thf(17002,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)],[2712])). 159.59/70.65 thf(7585,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1922_plus__nat_Oadd__0)). 159.59/70.65 thf(34509,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7585])). 159.59/70.65 thf(1730,axiom,((! [A:set_nat,B:(nat > complex)]: (((groups6464643781859351333omplex @ B @ A) = one_one_complex) <= (~ (finite_finite_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8390_prod_Oinfinite)). 159.59/70.65 thf(13843,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)],[1730])). 159.59/70.65 thf(6213,axiom,((! [A:num]: (zero_zero_complex != (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5034_zero__neq__neg__numeral)). 159.59/70.65 thf(29133,plain,((! [A:num]: ~ (zero_zero_complex = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6213])). 159.59/70.65 thf(6107,axiom,(((numera6690914467698888265omplex @ one) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_numeral__One)). 159.59/70.65 thf(28777,plain,(((numera6690914467698888265omplex @ one) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6107])). 159.59/70.65 thf(2515,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))) & (((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = B) <= (A = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2353_add__divide__eq__if__simps_I1_J)). 159.59/70.65 thf(16345,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))) & (((plus_plus_real @ B @ (divide_divide_real @ C @ A)) = B) | ~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2515])). 159.59/70.65 thf(2886,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) => ((C @ F) = (D @ F)))) => (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4466_minf_I2_J)). 159.59/70.65 thf(17536,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) => ((C @ F) = (D @ F)))) => (? [E:int]: ! [F:int]: ((ord_less_int @ F @ E) => (((C @ F) | (A @ F)) = ((B @ F) | (D @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2886])). 159.59/70.65 thf(1529,axiom,((! [A:complex,B:complex,C:num]: (((divide1717551699836669952omplex @ A @ B) = (numera6690914467698888265omplex @ C)) = (((B != zero_zero_complex) => (A = (times_times_complex @ (numera6690914467698888265omplex @ C) @ B))) & (((numera6690914467698888265omplex @ C) = zero_zero_complex) <= (B = zero_zero_complex)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2340_divide__eq__eq__numeral_I1_J)). 159.59/70.65 thf(13229,plain,((! [A:complex,B:complex,C:num]: (((divide1717551699836669952omplex @ A @ B) = (numera6690914467698888265omplex @ C)) = (((~ (B = zero_zero_complex)) => (A = (times_times_complex @ (numera6690914467698888265omplex @ C) @ B))) & (((numera6690914467698888265omplex @ C) = zero_zero_complex) | ~ (B = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529])). 159.59/70.65 thf(7344,axiom,((! [A:num,B:num]: ((times_times_num @ (bit0 @ A) @ (bit1 @ B)) = (bit0 @ (times_times_num @ A @ (bit1 @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5423_semiring__norm_I14_J)). 159.59/70.65 thf(33649,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)],[7344])). 159.59/70.65 thf(6046,axiom,(((bit_se2002935070580805687sk_nat @ (suc @ zero_zero_nat)) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5992_mask__Suc__0)). 159.59/70.65 thf(28589,plain,(((bit_se2002935070580805687sk_nat @ (suc @ zero_zero_nat)) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6046])). 159.59/70.65 thf(3869,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/sandbox/benchmark/theBenchmark.p',fact_6402_le__real__sqrt__sumsq)). 159.59/70.65 thf(20714,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)],[3869])). 159.59/70.65 thf(1844,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/sandbox/benchmark/theBenchmark.p',fact_9462_divide__int__def)). 159.59/70.65 thf(14215,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)],[1844])). 159.59/70.65 thf(2930,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ (times_times_int @ A @ C)) = (dvd_dvd_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4062_dvd__mult__unit__iff_H)). 159.59/70.65 thf(17689,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => ((dvd_dvd_int @ B @ (times_times_int @ A @ C)) = (dvd_dvd_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2930])). 159.59/70.65 thf(3482,axiom,((! [A:complex,B:complex]: (dvd_dvd_complex @ A @ (times_times_complex @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3975_dvd__triv__right)). 159.59/70.65 thf(19436,plain,((! [A:complex,B:complex]: (dvd_dvd_complex @ A @ (times_times_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3482])). 159.59/70.65 thf(7711,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/sandbox/benchmark/theBenchmark.p',fact_9174_binomial__code)). 159.59/70.65 thf(34909,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)],[7711])). 159.59/70.65 thf(7353,axiom,((! [A:nat,B:nat,C:(nat > int),D:int]: ((((ord_less_eq_int @ (C @ A) @ D) => ((ord_less_eq_int @ D @ (C @ B)) => (? [E:nat]: ((ord_less_eq_nat @ E @ B) & ((C @ E) = D) & (ord_less_eq_nat @ A @ E))))) <= (ord_less_eq_nat @ A @ B)) <= (! [E:nat]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (C @ (suc @ E)) @ (C @ E))) @ one_one_int) <= ((ord_less_nat @ E @ B) & (ord_less_eq_nat @ A @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5733_nat__intermed__int__val)). 159.59/70.65 thf(33677,plain,((! [A:nat,B:nat,C:(nat > int),D:int]: (((ord_less_eq_int @ (C @ A) @ D) => ((ord_less_eq_int @ D @ (C @ B)) => (? [E:nat]: ((ord_less_eq_nat @ E @ B) & ((C @ E) = D) & (ord_less_eq_nat @ A @ E))))) | ~ (ord_less_eq_nat @ A @ B) | ~ (! [E:nat]: ((ord_less_eq_int @ (abs_abs_int @ (minus_minus_int @ (C @ (suc @ E)) @ (C @ E))) @ one_one_int) | ~ ((ord_less_nat @ E @ B) & (ord_less_eq_nat @ A @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7353])). 159.59/70.65 thf(3994,axiom,((! [A:(nat > complex),B:nat,C:nat]: ((groups2073611262835488442omplex @ A @ (set_ord_atMost_nat @ (plus_plus_nat @ B @ C))) = (plus_plus_complex @ (groups2073611262835488442omplex @ A @ (set_ord_atMost_nat @ B)) @ (groups2073611262835488442omplex @ A @ (set_or1269000886237332187st_nat @ (suc @ B) @ (plus_plus_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8840_sum__up__index__split)). 159.59/70.65 thf(21090,plain,((! [A:(nat > complex),B:nat,C:nat]: ((groups2073611262835488442omplex @ (A) @ (set_ord_atMost_nat @ (plus_plus_nat @ B @ C))) = (plus_plus_complex @ (groups2073611262835488442omplex @ (A) @ (set_ord_atMost_nat @ B)) @ (groups2073611262835488442omplex @ (A) @ (set_or1269000886237332187st_nat @ (suc @ B) @ (plus_plus_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3994])). 159.59/70.65 thf(5204,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/sandbox/benchmark/theBenchmark.p',fact_6566_of__nat__power__eq__of__nat__cancel__iff)). 159.59/70.65 thf(25287,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)],[5204])). 159.59/70.65 thf(4788,axiom,((! [A:num]: ((pred_numeral @ (bit0 @ A)) = (numeral_numeral_nat @ (bitM @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5809_pred__numeral__simps_I2_J)). 159.59/70.65 thf(23791,plain,((! [A:num]: ((pred_numeral @ (bit0 @ A)) = (numeral_numeral_nat @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4788])). 159.59/70.65 thf(5954,axiom,((! [A:num,B:num]: ((modulo_modulo_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) != zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5622_cong__exp__iff__simps_I3_J)). 159.59/70.65 thf(28294,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)],[5954])). 159.59/70.65 thf(5439,axiom,(((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one)) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5213_uminus__numeral__One)). 159.59/70.65 thf(26232,plain,(((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one)) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5439])). 159.59/70.65 thf(994,axiom,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ A @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_real @ (A @ zero_zero_nat) @ (groups6591440286371151544t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8751_sum_OatMost__Suc__shift)). 159.59/70.65 thf(11428,plain,((! [A:(nat > real),B:nat]: ((groups6591440286371151544t_real @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_real @ (A @ zero_zero_nat) @ (groups6591440286371151544t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[994])). 159.59/70.65 thf(5790,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/sandbox/benchmark/theBenchmark.p',fact_6642_of__nat__le__numeral__power__cancel__iff)). 159.59/70.65 thf(27502,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)],[5790])). 159.59/70.65 thf(8130,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/sandbox/benchmark/theBenchmark.p',fact_1317_add__mono__thms__linordered__field_I3_J)). 159.59/70.65 thf(36245,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)],[8130])). 159.59/70.65 thf(7222,axiom,(((^ [A:real]: (A)) = (times_times_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1414_lambda__one)). 159.59/70.65 thf(33229,plain,(((^ [A:real]: (A)) = (times_times_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7222])). 159.59/70.65 thf(5460,axiom,((! [A:list_VEBT_VEBT,B:set_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((ord_le4337996190870823476T_VEBT @ (set_VEBT_VEBT2 @ A) @ B) => ((ord_le4337996190870823476T_VEBT @ (set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ A @ D @ C)) @ B) <= (member_VEBT_VEBT @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_set__update__subsetI)). 159.59/70.65 thf(26309,plain,((! [A:list_VEBT_VEBT,B:set_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((ord_le4337996190870823476T_VEBT @ (set_VEBT_VEBT2 @ A) @ B) => ((ord_le4337996190870823476T_VEBT @ (set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ A @ D @ C)) @ B) | ~ (member_VEBT_VEBT @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5460])). 159.59/70.65 thf(5116,axiom,((! [A:num]: ((sqr @ (bit1 @ A)) = (bit1 @ (bit0 @ (plus_plus_num @ (sqr @ A) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9800_sqr_Osimps_I3_J)). 159.59/70.65 thf(24960,plain,((! [A:num]: ((sqr @ (bit1 @ A)) = (bit1 @ (bit0 @ (plus_plus_num @ (sqr @ A) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5116])). 159.59/70.65 thf(1792,axiom,((ord_le72135733267957522d_enat = (^ [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) & ~ (ord_le2932123472753598470d_enat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3055_less__le__not__le)). 159.59/70.65 thf(14036,plain,(((ord_le72135733267957522d_enat) = (^ [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) & ~ (ord_le2932123472753598470d_enat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1792])). 159.59/70.65 thf(3267,axiom,((! [A:complex,B:complex]: ((A = (uminus1482373934393186551omplex @ B)) = ((plus_plus_complex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5048_eq__neg__iff__add__eq__0)). 159.59/70.65 thf(18771,plain,((! [A:complex,B:complex]: ((A = (uminus1482373934393186551omplex @ B)) = ((plus_plus_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3267])). 159.59/70.65 thf(3642,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ D) = (plus_plus_int @ B @ (plus_plus_int @ C @ D))) <= (A = (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1144_group__cancel_Oadd1)). 159.59/70.65 thf(19944,plain,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ D) = (plus_plus_int @ B @ (plus_plus_int @ C @ D))) | ~ (A = (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3642])). 159.59/70.65 thf(826,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ B @ A)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2908_order__less__not__sym)). 159.59/70.65 thf(10915,plain,((! [A:extended_enat,B:extended_enat]: (~ (ord_le72135733267957522d_enat @ B @ A) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[826])). 159.59/70.65 thf(2296,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/sandbox/benchmark/theBenchmark.p',fact_7965_sum__lessThan__telescope)). 159.59/70.65 thf(15645,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)],[2296])). 159.59/70.65 thf(616,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/sandbox/benchmark/theBenchmark.p',fact_1380_real__average__minus__second)). 159.59/70.65 thf(10218,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)],[616])). 159.59/70.65 thf(6281,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/sandbox/benchmark/theBenchmark.p',fact_3470_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend)). 159.59/70.65 thf(29432,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)],[6281])). 159.59/70.65 thf(5089,axiom,((! [A:$o]: ((ord_less_nat @ (zero_n2687167440665602831ol_nat @ A) @ one_one_nat) = (~ (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4345_of__bool__less__one__iff)). 159.59/70.65 thf(24876,plain,((! [A:$o]: ((ord_less_nat @ (zero_n2687167440665602831ol_nat @ A) @ one_one_nat) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5089])). 159.59/70.65 thf(6344,axiom,((! [A:nat]: ((ord_max_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1571_max__nat_Oleft__neutral)). 159.59/70.65 thf(29623,plain,((! [A:nat]: ((ord_max_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6344])). 159.59/70.65 thf(8029,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2099_mult__neg__pos)). 159.59/70.65 thf(35916,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8029])). 159.59/70.65 thf(7624,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/sandbox/benchmark/theBenchmark.p',fact_6595_numeral__power__eq__of__nat__cancel__iff)). 159.59/70.65 thf(34628,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)],[7624])). 159.59/70.65 thf(3484,axiom,((! [A:extended_enat,B:extended_enat,C:nat]: (((times_7803423173614009249d_enat @ (power_8040749407984259932d_enat @ A @ C) @ (power_8040749407984259932d_enat @ B @ C)) = one_on7984719198319812577d_enat) <= ((times_7803423173614009249d_enat @ A @ B) = one_on7984719198319812577d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_left__right__inverse__power)). 159.59/70.65 thf(19441,plain,((! [A:extended_enat,B:extended_enat,C:nat]: (((times_7803423173614009249d_enat @ (power_8040749407984259932d_enat @ A @ C) @ (power_8040749407984259932d_enat @ B @ C)) = one_on7984719198319812577d_enat) | ~ ((times_7803423173614009249d_enat @ A @ B) = one_on7984719198319812577d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3484])). 159.59/70.65 thf(7425,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2609_order__refl)). 159.59/70.65 thf(33904,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7425])). 159.59/70.65 thf(1753,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_int @ B @ A) => ((divide_divide_int @ A @ B) = zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2621_div__neg__neg__trivial)). 159.59/70.65 thf(13912,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_int @ B @ A) => ((divide_divide_int @ A @ B) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753])). 159.59/70.65 thf(7329,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/sandbox/benchmark/theBenchmark.p',fact_6563_of__nat__eq__of__nat__power__cancel__iff)). 159.59/70.65 thf(33598,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)],[7329])). 159.59/70.65 thf(1217,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((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 @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7235_powr__mono2)). 159.59/70.65 thf(12187,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((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 @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217])). 159.59/70.65 thf(3198,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/sandbox/benchmark/theBenchmark.p',fact_5300_signed__take__bit__int__greater__self__iff)). 159.59/70.65 thf(18537,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)],[3198])). 159.59/70.65 thf(2797,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/sandbox/benchmark/theBenchmark.p',fact_2500_half__gt__zero)). 159.59/70.65 thf(17255,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)],[2797])). 159.59/70.65 thf(387,axiom,((! [A:nat,B:real]: ((sin_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ B)) = (im @ (power_power_complex @ (cis @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9664_sin__n__Im__cis__pow__n)). 159.59/70.65 thf(9462,plain,((! [A:nat,B:real]: ((sin_real @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ B)) = (im @ (power_power_complex @ (cis @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[387])). 159.59/70.65 thf(1112,axiom,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ B) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6365_bit__numeral__iff)). 159.59/70.65 thf(11823,plain,((! [A:num,B:nat]: ((bit_se1146084159140164899it_int @ (numeral_numeral_int @ A) @ B) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112])). 159.59/70.65 thf(1707,axiom,((! [A:real]: ((ord_less_eq_real @ (inverse_inverse_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8989_inverse__nonpositive__iff__nonpositive)). 159.59/70.65 thf(13769,plain,((! [A:real]: ((ord_less_eq_real @ (inverse_inverse_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707])). 159.59/70.65 thf(4768,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/sandbox/benchmark/theBenchmark.p',fact_9104_sum__choose__lower)). 159.59/70.65 thf(23737,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)],[4768])). 159.59/70.65 thf(4403,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/sandbox/benchmark/theBenchmark.p',fact_5841_of__int__power__le__of__int__cancel__iff)). 159.59/70.65 thf(22355,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)],[4403])). 159.59/70.65 thf(6779,axiom,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (C @ (suc @ D)) @ (C @ D))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_complex @ (C @ (suc @ B)) @ (C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7672_sum__Suc__diff)). 159.59/70.65 thf(31381,plain,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ (suc @ B)) => ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (C @ (suc @ D)) @ (C @ D))) @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_complex @ (C @ (suc @ B)) @ (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6779])). 159.59/70.65 thf(3050,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/sandbox/benchmark/theBenchmark.p',fact_7415_sum__divide__distrib)). 159.59/70.65 thf(18054,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)],[3050])). 159.59/70.65 thf(4683,axiom,((! [A:int,B:(nat > int),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) <= (ord_less_eq_nat @ E @ F))) => (ord_less_eq_int @ A @ (B @ D)))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2661_ord__eq__le__subst)). 159.59/70.65 thf(23440,plain,((! [A:int,B:(nat > int),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_int @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_nat @ E @ F))) => (ord_less_eq_int @ A @ (B @ D)))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4683])). 159.59/70.65 thf(5154,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/sandbox/benchmark/theBenchmark.p',fact_4816_neg__numeral__le__iff)). 159.59/70.65 thf(25092,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)],[5154])). 159.59/70.65 thf(2833,axiom,((! [A:int,B:int,C:int]: (((divide_divide_int @ B @ (times_times_int @ C @ A)) = (divide_divide_int @ (divide_divide_int @ B @ C) @ A)) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2319_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq)). 159.59/70.65 thf(17356,plain,((! [A:int,B:int,C:int]: (((divide_divide_int @ B @ (times_times_int @ C @ A)) = (divide_divide_int @ (divide_divide_int @ B @ C) @ A)) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2833])). 159.59/70.65 thf(6403,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ A @ C) <= (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2741_ord__le__eq__trans)). 159.59/70.65 thf(29860,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_eq_int @ A @ C) | ~ (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6403])). 159.59/70.65 thf(6558,axiom,((bit_se2161824704523386999it_nat = (^ [A:nat,B:nat]: (if_nat_nat_nat @ (bit_se1148574629649215175it_nat @ B @ A) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6410_flip__bit__eq__if)). 159.59/70.65 thf(30454,plain,(((bit_se2161824704523386999it_nat) = (^ [A:nat,B:nat]: (if_nat_nat_nat @ (bit_se1148574629649215175it_nat @ B @ A) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6558])). 159.59/70.65 thf(81,axiom,((! [A:set_nat,B:set_nat,C:(nat > extended_enat)]: (((((groups7108830773950497114d_enat @ C @ B) = (groups7108830773950497114d_enat @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = zero_z5237406670263579293d_enat)))) <= (ord_less_eq_set_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7610_sum_Omono__neutral__left)). 159.59/70.65 thf(8498,plain,((! [A:set_nat,B:set_nat,C:(nat > extended_enat)]: (((groups7108830773950497114d_enat @ (C) @ B) = (groups7108830773950497114d_enat @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ (minus_minus_set_nat @ A @ B)) => ((C @ D) = zero_z5237406670263579293d_enat))) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 159.59/70.65 thf(6550,axiom,((! [A:nat]: ((binomial @ A @ A) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8987_binomial__n__n)). 159.59/70.65 thf(30431,plain,((! [A:nat]: ((binomial @ A @ A) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6550])). 159.59/70.65 thf(4717,axiom,((! [A:real]: ((times_times_real @ A @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4702_mult__minus1__right)). 159.59/70.65 thf(23553,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)],[4717])). 159.59/70.65 thf(5743,axiom,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_power__one__right)). 159.59/70.65 thf(27274,plain,((! [A:nat]: ((power_power_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5743])). 159.59/70.65 thf(8123,axiom,((((((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) != ma) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma)) & (((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))))) <= ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma))) => (! [A:vEBT_VEBT]: ((member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) => (~ (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26__C112_C)). 159.59/70.65 thf(36221,plain,(((((~ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma)) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma)) & (((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))))) | ~ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma))) => (! [A:vEBT_VEBT]: ((member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) => (~ (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8123])). 159.59/70.65 thf(4077,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_real @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2880_ord__less__eq__subst)). 159.59/70.65 thf(21333,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_real @ E @ F) => (ord_less_num @ (C @ E) @ (C @ F)))))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4077])). 159.59/70.65 thf(6584,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (sqrt @ A) @ (sqrt @ B)) = (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6312_real__sqrt__le__iff)). 159.59/70.65 thf(30541,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)],[6584])). 159.59/70.65 thf(7750,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4450_pinf_I5_J)). 159.59/70.65 thf(35042,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7750])). 159.59/70.65 thf(5913,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1998_zero__le__square)). 159.59/70.65 thf(28108,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5913])). 159.59/70.65 thf(649,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/sandbox/benchmark/theBenchmark.p',fact_4300_unity__coeff__ex)). 159.59/70.65 thf(10328,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)],[649])). 159.59/70.65 thf(7273,axiom,((! [A:num,B:num]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (numera6690914467698888265omplex @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4806_mult__neg__numeral__simps_I1_J)). 159.59/70.65 thf(33387,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)],[7273])). 159.59/70.65 thf(546,axiom,((! [A:real]: ((tan_real @ (minus_minus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ A)) = (cot_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9405_tan__cot_H)). 159.59/70.65 thf(9991,plain,((! [A:real]: ((tan_real @ (minus_minus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ A)) = (cot_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[546])). 159.59/70.65 thf(685,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((A != one_one_real) => ((log @ A @ (powr_real @ A @ B)) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7221_log__powr__cancel)). 159.59/70.65 thf(10439,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((~ (A = one_one_real)) => ((log @ A @ (powr_real @ A @ B)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[685])). 159.59/70.65 thf(5149,axiom,((! [A:num]: ((plus_plus_num @ A @ one) = (inc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5721_add__One)). 159.59/70.65 thf(25076,plain,((! [A:num]: ((plus_plus_num @ A @ one) = (inc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5149])). 159.59/70.65 thf(1576,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/sandbox/benchmark/theBenchmark.p',fact_3926_dvd__productE)). 159.59/70.65 thf(13369,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)],[1576])). 159.59/70.65 thf(5333,axiom,((! [A:$o]: ((ord_less_nat @ zero_zero_nat @ (zero_n2687167440665602831ol_nat @ A)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4341_zero__less__of__bool__iff)). 159.59/70.65 thf(25758,plain,((! [A:$o]: ((ord_less_nat @ zero_zero_nat @ (zero_n2687167440665602831ol_nat @ A)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5333])). 159.59/70.65 thf(1119,axiom,((! [A:int,B:int]: ((bit_se725231765392027082nd_int @ A @ (bit_se725231765392027082nd_int @ A @ B)) = (bit_se725231765392027082nd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5935_and_Oleft__idem)). 159.59/70.65 thf(11842,plain,((! [A:int,B:int]: ((bit_se725231765392027082nd_int @ A @ (bit_se725231765392027082nd_int @ A @ B)) = (bit_se725231765392027082nd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119])). 159.59/70.65 thf(7099,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se727722235901077358nd_nat @ A @ (bit_se727722235901077358nd_nat @ B @ C)) = (bit_se727722235901077358nd_nat @ B @ (bit_se727722235901077358nd_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6042_and_Oleft__commute)). 159.59/70.65 thf(32730,plain,((! [A:nat,B:nat,C:nat]: ((bit_se727722235901077358nd_nat @ A @ (bit_se727722235901077358nd_nat @ B @ C)) = (bit_se727722235901077358nd_nat @ B @ (bit_se727722235901077358nd_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7099])). 159.59/70.65 thf(3983,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/sandbox/benchmark/theBenchmark.p',fact_3520_mod__div__decomp)). 159.59/70.65 thf(21058,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)],[3983])). 159.59/70.65 thf(6857,axiom,((! [A:real,B:num]: ((archim7802044766580827645g_real @ (minus_minus_real @ A @ (numeral_numeral_real @ B))) = (minus_minus_int @ (archim7802044766580827645g_real @ A) @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6988_ceiling__diff__numeral)). 159.59/70.65 thf(31726,plain,((! [A:real,B:num]: ((archim7802044766580827645g_real @ (minus_minus_real @ A @ (numeral_numeral_real @ B))) = (minus_minus_int @ (archim7802044766580827645g_real @ A) @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6857])). 159.59/70.65 thf(6805,axiom,((! [A:real]: (((sqrt @ A) = zero_zero_real) = (A = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6309_real__sqrt__eq__zero__cancel__iff)). 159.59/70.65 thf(31460,plain,((! [A:real]: (((sqrt @ A) = zero_zero_real) = (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6805])). 159.59/70.65 thf(2213,axiom,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) = (divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ A))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5085_nonzero__minus__divide__right)). 159.59/70.65 thf(15396,plain,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)) = (divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ A))) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2213])). 159.59/70.65 thf(1499,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ A) @ (uminus5710092332889474511et_nat @ B)) = (ord_less_eq_set_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4615_compl__le__compl__iff)). 159.59/70.65 thf(13140,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ A) @ (uminus5710092332889474511et_nat @ B)) = (ord_less_eq_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499])). 159.59/70.65 thf(3194,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/sandbox/benchmark/theBenchmark.p',fact_7206_sin__tan)). 159.59/70.65 thf(18526,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)],[3194])). 159.59/70.65 thf(42,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ (ord_max_int @ C @ B)) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_max_Ostrict__coboundedI2)). 159.59/70.65 thf(8377,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)],[42])). 159.59/70.65 thf(5977,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/sandbox/benchmark/theBenchmark.p',fact_6619_of__nat__power__le__of__nat__cancel__iff)). 159.59/70.65 thf(28371,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)],[5977])). 159.59/70.65 thf(1676,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/sandbox/benchmark/theBenchmark.p',fact_5722_abs__mod__less)). 159.59/70.65 thf(13677,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)],[1676])). 159.59/70.65 thf(4197,axiom,((! [A:(nat > complex),B:complex]: ((sums_complex @ A @ (plus_plus_complex @ B @ (A @ zero_zero_nat))) <= (sums_complex @ (^ [C:nat]: (A @ (suc @ C))) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7931_sums__Suc)). 159.59/70.65 thf(21706,plain,((! [A:(nat > complex),B:complex]: ((sums_complex @ (A) @ (plus_plus_complex @ B @ (A @ zero_zero_nat))) | ~ (sums_complex @ (^ [C:nat]: (A @ (suc @ C))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4197])). 159.59/70.65 thf(6599,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/sandbox/benchmark/theBenchmark.p',fact_5631_abs__le__square__iff)). 159.59/70.65 thf(30600,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)],[6599])). 159.59/70.65 thf(4198,axiom,((! [A:real]: (((nat2 @ (archim6058952711729229775r_real @ A)) = zero_zero_nat) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9454_nat__floor__neg)). 159.59/70.65 thf(21708,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)],[4198])). 159.59/70.65 thf(6026,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/sandbox/benchmark/theBenchmark.p',fact_1346_add__le__imp__le__diff)). 159.59/70.65 thf(28524,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)],[6026])). 159.59/70.65 thf(5433,axiom,((! [A:list_o,B:list_VEBT_VEBT]: ((size_s4313452262239582901T_VEBT @ (product_o_VEBT_VEBT @ A @ B)) = (times_times_nat @ (size_size_list_o @ A) @ (size_s6755466524823107622T_VEBT @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3626_length__product)). 159.59/70.65 thf(26207,plain,((! [A:list_o,B:list_VEBT_VEBT]: ((size_s4313452262239582901T_VEBT @ (product_o_VEBT_VEBT @ A @ B)) = (times_times_nat @ (size_size_list_o @ A) @ (size_s6755466524823107622T_VEBT @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5433])). 159.59/70.65 thf(2539,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/sandbox/benchmark/theBenchmark.p',fact_5751_of__int__code__if)). 159.59/70.65 thf(16416,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)],[2539])). 159.59/70.65 thf(6190,axiom,((! [A:complex]: ((power_power_complex @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1689_power__Suc0__right)). 159.59/70.65 thf(29061,plain,((! [A:complex]: ((power_power_complex @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6190])). 159.59/70.65 thf(5425,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1567_mult__is__0)). 159.59/70.65 thf(26177,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)],[5425])). 159.59/70.65 thf(4672,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:$o,F:$o]: ((vEBT_Node @ A @ B @ C @ D) != (vEBT_Leaf @ E @ F)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1821_VEBT_Odistinct_I1_J)). 159.59/70.65 thf(23409,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:$o,F:$o]: ~ ((vEBT_Node @ A @ B @ C @ D) = (vEBT_Leaf @ E @ F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4672])). 159.59/70.65 thf(1375,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)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2098_mult__neg__pos)). 159.59/70.65 thf(12720,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)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375])). 159.59/70.65 thf(2991,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ C @ (times_3573771949741848930nteger @ A @ B)) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ C @ A) @ B)) <= (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4083_dvd__div__mult2__eq)). 159.59/70.65 thf(17877,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ C @ (times_3573771949741848930nteger @ A @ B)) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ C @ A) @ B)) | ~ (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2991])). 159.59/70.65 thf(5410,axiom,((ord_less_eq_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2059_zero__less__one__class_Ozero__le__one)). 159.59/70.65 thf(26095,plain,((ord_less_eq_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5410])). 159.59/70.65 thf(1272,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/sandbox/benchmark/theBenchmark.p',fact_2163_zero__less__power)). 159.59/70.65 thf(12364,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)],[1272])). 159.59/70.65 thf(5119,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_Suc__less__eq)). 159.59/70.65 thf(24969,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)],[5119])). 159.59/70.65 thf(4389,axiom,((bit_se1409905431419307370or_int = (^ [A:int,B:int]: (bit_se1409905431419307370or_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6047_or_Ocommute)). 159.59/70.65 thf(22312,plain,(((bit_se1409905431419307370or_int) = (^ [A:int,B:int]: (bit_se1409905431419307370or_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4389])). 159.59/70.65 thf(5246,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/sandbox/benchmark/theBenchmark.p',fact_5596_power__minus__Bit1)). 159.59/70.65 thf(25422,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)],[5246])). 159.59/70.65 thf(5919,axiom,((! [A:num]: (zero_z5237406670263579293d_enat != (numera1916890842035813515d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1845_zero__neq__numeral)). 159.59/70.65 thf(28126,plain,((! [A:num]: ~ (zero_z5237406670263579293d_enat = (numera1916890842035813515d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5919])). 159.59/70.65 thf(4732,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1833_zero__less__iff__neq__zero)). 159.59/70.65 thf(23597,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4732])). 159.59/70.65 thf(268,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/sandbox/benchmark/theBenchmark.p',fact_9591_even__not__iff__int)). 159.59/70.65 thf(9065,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)],[268])). 159.59/70.65 thf(7486,axiom,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((times_times_complex @ (groups6464643781859351333omplex @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (times_times_complex @ (C @ A) @ (groups6464643781859351333omplex @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8744_prod_OSuc__reindex__ivl)). 159.59/70.65 thf(34147,plain,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((times_times_complex @ (groups6464643781859351333omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (times_times_complex @ (C @ A) @ (groups6464643781859351333omplex @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7486])). 159.59/70.65 thf(3571,axiom,((ord_less_real = (^ [A:real,B:real]: (~ (ord_less_eq_real @ B @ A) & (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3056_less__le__not__le)). 159.59/70.65 thf(19724,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)],[3571])). 159.59/70.65 thf(7654,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/sandbox/benchmark/theBenchmark.p',fact_167_in__children__def)). 159.59/70.65 thf(34714,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)],[7654])). 159.59/70.65 thf(600,axiom,((! [A:real,B:real,C:(real > extended_enat),D:extended_enat]: ((ord_less_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2878_ord__less__eq__subst)). 159.59/70.65 thf(10162,plain,((! [A:real,B:real,C:(real > extended_enat),D:extended_enat]: ((ord_less_real @ A @ B) => (((C @ B) = D) => ((! [E:real,F:real]: ((ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[600])). 159.59/70.65 thf(5240,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ A) = (times_times_complex @ B @ B)) = ((A = B) | (A = (uminus1482373934393186551omplex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4958_square__eq__iff)). 159.59/70.65 thf(25405,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ A) = (times_times_complex @ B @ B)) = ((A = B) | (A = (uminus1482373934393186551omplex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5240])). 159.59/70.65 thf(6104,axiom,((! [A:num]: ((plus_plus_num @ one @ (bit0 @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5443_semiring__norm_I3_J)). 159.59/70.65 thf(28760,plain,((! [A:num]: ((plus_plus_num @ one @ (bit0 @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6104])). 159.59/70.65 thf(3671,axiom,((! [A:nat,B:nat]: (((semiri1314217659103216013at_int @ A) = (semiri1314217659103216013at_int @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6488_of__nat__eq__iff)). 159.59/70.65 thf(20044,plain,((! [A:nat,B:nat]: (((semiri1314217659103216013at_int @ A) = (semiri1314217659103216013at_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3671])). 159.59/70.65 thf(5145,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) | (dvd_dvd_nat @ A @ one_one_nat))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4212_dvd__power__iff)). 159.59/70.65 thf(25057,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) | (dvd_dvd_nat @ A @ one_one_nat))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5145])). 159.59/70.65 thf(3545,axiom,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ A @ (set_ord_atMost_nat @ (plus_plus_nat @ B @ C))) = (plus_plus_real @ (groups6591440286371151544t_real @ A @ (set_ord_atMost_nat @ B)) @ (groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ (suc @ B) @ (plus_plus_nat @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8843_sum__up__index__split)). 159.59/70.65 thf(19628,plain,((! [A:(nat > real),B:nat,C:nat]: ((groups6591440286371151544t_real @ (A) @ (set_ord_atMost_nat @ (plus_plus_nat @ B @ C))) = (plus_plus_real @ (groups6591440286371151544t_real @ (A) @ (set_ord_atMost_nat @ B)) @ (groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ (suc @ B) @ (plus_plus_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3545])). 159.59/70.65 thf(7440,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/sandbox/benchmark/theBenchmark.p',fact_1340_le__add__diff)). 159.59/70.65 thf(33951,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)],[7440])). 159.59/70.65 thf(2973,axiom,((! [A:real]: (ord_less_eq_real @ (minus_minus_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A)) @ one_one_real) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7117_of__int__ceiling__diff__one__le)). 159.59/70.65 thf(17822,plain,((! [A:real]: (ord_less_eq_real @ (minus_minus_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A)) @ one_one_real) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2973])). 159.59/70.65 thf(2183,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/sandbox/benchmark/theBenchmark.p',fact_7351_sum__abs__ge__zero)). 159.59/70.65 thf(15288,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)],[2183])). 159.59/70.65 thf(4714,axiom,((! [A:nat]: ((ord_less_real @ zero_zero_real @ (semiri5074537144036343181t_real @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6588_of__nat__0__less__iff)). 159.59/70.65 thf(23544,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)],[4714])). 159.59/70.65 thf(5979,axiom,((! [A:nat,B:nat]: ((ord_min_nat @ (suc @ A) @ (suc @ B)) = (suc @ (ord_min_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10166_min__Suc__Suc)). 159.59/70.65 thf(28376,plain,((! [A:nat,B:nat]: ((ord_min_nat @ (suc @ A) @ (suc @ B)) = (suc @ (ord_min_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5979])). 159.59/70.65 thf(7068,axiom,(((plus_plus_int @ one_one_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_one__add__one)). 159.59/70.65 thf(32608,plain,(((plus_plus_int @ one_one_int @ one_one_int) = (numeral_numeral_int @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7068])). 159.59/70.65 thf(1482,axiom,((! [A:real,B:real,C:(real > extended_enat),D:extended_enat]: ((ord_less_real @ A @ B) => ((ord_le72135733267957522d_enat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2903_order__less__subst2)). 159.59/70.65 thf(13089,plain,((! [A:real,B:real,C:(real > extended_enat),D:extended_enat]: ((ord_less_real @ A @ B) => ((ord_le72135733267957522d_enat @ (C @ B) @ D) => ((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482])). 159.59/70.65 thf(3977,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 @ B @ (powr_real @ A @ C)) = (ord_less_eq_real @ (log @ A @ B) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7273_le__powr__iff)). 159.59/70.65 thf(21041,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 @ B @ (powr_real @ A @ C)) = (ord_less_eq_real @ (log @ A @ B) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3977])). 159.59/70.65 thf(6936,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (bit_se2002935070580805687sk_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5945_mask__nat__positive__iff)). 159.59/70.65 thf(31986,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)],[6936])). 159.59/70.65 thf(5978,axiom,(((numeral_numeral_int @ one) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_numeral__One)). 159.59/70.65 thf(28374,plain,(((numeral_numeral_int @ one) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5978])). 159.59/70.65 thf(6220,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/sandbox/benchmark/theBenchmark.p',fact_650_power__gt1)). 159.59/70.65 thf(29152,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)],[6220])). 159.59/70.65 thf(3694,axiom,((! [A:(nat > real),B:(nat > real)]: ((! [C:nat]: (ord_less_eq_real @ (A @ C) @ (B @ C))) => (((ord_less_eq_real @ (suminf_real @ A) @ (suminf_real @ B)) <= (summable_real @ B)) <= (summable_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7033_suminf__le)). 159.59/70.65 thf(20115,plain,((! [A:(nat > real),B:(nat > real)]: ((! [C:nat]: (ord_less_eq_real @ (A @ C) @ (B @ C))) => ((ord_less_eq_real @ (suminf_real @ (A)) @ (suminf_real @ (B))) | ~ (summable_real @ (B)) | ~ (summable_real @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3694])). 159.59/70.65 thf(4201,axiom,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) <= (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2047_add__decreasing)). 159.59/70.65 thf(21721,plain,((! [A:int,B:int,C:int]: ((ord_less_eq_int @ A @ zero_zero_int) => ((ord_less_eq_int @ (plus_plus_int @ A @ B) @ C) | ~ (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4201])). 159.59/70.65 thf(1723,axiom,((! [A:extended_enat,B:extended_enat]: ((A != B) = ((ord_le72135733267957522d_enat @ B @ A) | (ord_le72135733267957522d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2848_linorder__neq__iff)). 159.59/70.65 thf(13823,plain,((! [A:extended_enat,B:extended_enat]: ((~ (A = B)) = ((ord_le72135733267957522d_enat @ B @ A) | (ord_le72135733267957522d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723])). 159.59/70.65 thf(3790,axiom,((! [A:nat,B:int]: ((ord_less_nat @ A @ (nat2 @ B)) = (ord_less_int @ (semiri1314217659103216013at_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9433_zless__nat__eq__int__zless)). 159.59/70.65 thf(20438,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)],[3790])). 159.59/70.65 thf(3840,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/sandbox/benchmark/theBenchmark.p',fact_1350_diff__le__eq)). 159.59/70.65 thf(20613,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)],[3840])). 159.59/70.65 thf(1656,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/sandbox/benchmark/theBenchmark.p',fact_6144_take__bit__eq__mask__iff__exp__dvd)). 159.59/70.65 thf(13617,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)],[1656])). 159.59/70.65 thf(263,axiom,((! [A:int,B:int]: ((ord_max_int @ A @ (ord_max_int @ A @ B)) = (ord_max_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_771_max_Oleft__idem)). 159.59/70.65 thf(9050,plain,((! [A:int,B:int]: ((ord_max_int @ A @ (ord_max_int @ A @ B)) = (ord_max_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 159.59/70.65 thf(4691,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/sandbox/benchmark/theBenchmark.p',fact_8975_choose__even__sum)). 159.59/70.65 thf(23472,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)],[4691])). 159.59/70.65 thf(2792,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/sandbox/benchmark/theBenchmark.p',fact_7242_complex__add)). 159.59/70.65 thf(17240,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)],[2792])). 159.59/70.65 thf(2902,axiom,((! [A:real,B:int]: (((archim6058952711729229775r_real @ A) = B) = ((ord_less_eq_real @ (ring_1_of_int_real @ B) @ A) & (ord_less_real @ A @ (plus_plus_real @ (ring_1_of_int_real @ B) @ one_one_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8298_floor__eq__iff)). 159.59/70.65 thf(17600,plain,((! [A:real,B:int]: (((archim6058952711729229775r_real @ A) = B) = ((ord_less_eq_real @ (ring_1_of_int_real @ B) @ A) & (ord_less_real @ A @ (plus_plus_real @ (ring_1_of_int_real @ B) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2902])). 159.59/70.65 thf(2253,axiom,((! [A:nat,B:nat,C:(nat > real)]: (((~ (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))))) & (((groups6591440286371151544t_real @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_real) <= (ord_less_nat @ (suc @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7363_sum_Ocl__ivl__Suc)). 159.59/70.65 thf(15519,plain,((! [A:nat,B:nat,C:(nat > real)]: (((~ (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))))) & (((groups6591440286371151544t_real @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = zero_zero_real) | ~ (ord_less_nat @ (suc @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2253])). 159.59/70.65 thf(6739,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_le__cube)). 159.59/70.65 thf(31227,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)],[6739])). 159.59/70.65 thf(4839,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ B) = (((ord_less_eq_real @ one_one_real @ A) <= (ord_less_real @ B @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ one_one_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2418_mult__le__cancel__right2)). 159.59/70.65 thf(23998,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ B) = (((ord_less_eq_real @ one_one_real @ A) | ~ (ord_less_real @ B @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_eq_real @ A @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4839])). 159.59/70.65 thf(3015,axiom,((cosh_complex = (^ [A:complex]: (divide1717551699836669952omplex @ (plus_plus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9359_cosh__field__def)). 159.59/70.65 thf(17948,plain,(((cosh_complex) = (^ [A:complex]: (divide1717551699836669952omplex @ (plus_plus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3015])). 159.59/70.65 thf(5728,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ one_one_nat) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5991_or__numerals_I8_J)). 159.59/70.65 thf(27222,plain,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ one_one_nat) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5728])). 159.59/70.65 thf(1143,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/sandbox/benchmark/theBenchmark.p',fact_3541_minus__div__mult__eq__mod)). 159.59/70.65 thf(11915,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)],[1143])). 159.59/70.65 thf(4988,axiom,((! [A:(nat > real),B:nat]: ((! [C:real]: ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ C @ D))) @ (set_ord_atMost_nat @ B)) = zero_zero_real)) = (! [C:nat]: (((A @ C) = zero_zero_real) <= (ord_less_eq_nat @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8835_polyfun__eq__0)). 159.59/70.65 thf(24511,plain,((! [A:(nat > real),B:nat]: ((! [C:real]: ((groups6591440286371151544t_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ C @ D))) @ (set_ord_atMost_nat @ B)) = zero_zero_real)) = (! [C:nat]: (((A @ C) = zero_zero_real) | ~ (ord_less_eq_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4988])). 159.59/70.65 thf(122,axiom,((! [A:code_integer,B:nat,C:nat]: (((((divide6298287555418463151nteger @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ A @ B)) = (power_8256067586552552935nteger @ A @ (minus_minus_nat @ C @ B))) <= (ord_less_eq_nat @ B @ C)) & (((divide6298287555418463151nteger @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ A @ B)) = (divide6298287555418463151nteger @ one_one_Code_integer @ (power_8256067586552552935nteger @ A @ (minus_minus_nat @ B @ C)))) <= (~ (ord_less_eq_nat @ B @ C)))) <= (A != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2520_power__diff__power__eq)). 159.59/70.65 thf(8625,plain,((! [A:code_integer,B:nat,C:nat]: (((((divide6298287555418463151nteger @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ A @ B)) = (power_8256067586552552935nteger @ A @ (minus_minus_nat @ C @ B))) | ~ (ord_less_eq_nat @ B @ C)) & (((divide6298287555418463151nteger @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ A @ B)) = (divide6298287555418463151nteger @ one_one_Code_integer @ (power_8256067586552552935nteger @ A @ (minus_minus_nat @ B @ C)))) | (ord_less_eq_nat @ B @ C))) | (A = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 159.59/70.65 thf(3770,axiom,((! [A:nat,B:nat]: ((ord_le72135733267957522d_enat @ (semiri4216267220026989637d_enat @ A) @ (semiri4216267220026989637d_enat @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6519_of__nat__less__iff)). 159.59/70.65 thf(20379,plain,((! [A:nat,B:nat]: ((ord_le72135733267957522d_enat @ (semiri4216267220026989637d_enat @ A) @ (semiri4216267220026989637d_enat @ B)) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3770])). 159.59/70.65 thf(2899,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > extended_enat),D:extended_enat]: ((((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)) <= ((C @ B) = D)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2873_ord__less__eq__subst)). 159.59/70.65 thf(17586,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > extended_enat),D:extended_enat]: (((! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)))) => (ord_le72135733267957522d_enat @ (C @ A) @ D)) | ~ ((C @ B) = D) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2899])). 159.59/70.65 thf(4355,axiom,((! [A:nat,B:list_nat]: ((member_nat @ A @ (set_nat2 @ B)) = (? [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ B)) & ((nth_nat @ B @ C) = A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_in__set__conv__nth)). 159.59/70.65 thf(22205,plain,((! [A:nat,B:list_nat]: ((member_nat @ A @ (set_nat2 @ B)) = (? [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ B)) & ((nth_nat @ B @ C) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4355])). 159.59/70.65 thf(301,axiom,((! [A:real,B:real,C:real]: ((real_V1485227260804924795R_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9216_scaleR__left__distrib)). 159.59/70.65 thf(9182,plain,((! [A:real,B:real,C:real]: ((real_V1485227260804924795R_real @ (plus_plus_real @ A @ B) @ C) = (plus_plus_real @ (real_V1485227260804924795R_real @ A @ C) @ (real_V1485227260804924795R_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 159.59/70.65 thf(1581,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/sandbox/benchmark/theBenchmark.p',fact_7173_sin__times__sin)). 159.59/70.65 thf(13384,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)],[1581])). 159.59/70.65 thf(3311,axiom,((! [A:real]: (((real_V4546457046886955230omplex @ A) = one_one_complex) = (A = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7326_of__real__eq__1__iff)). 159.59/70.65 thf(18903,plain,((! [A:real]: (((real_V4546457046886955230omplex @ A) = one_one_complex) = (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3311])). 159.59/70.65 thf(1636,axiom,((! [A:real,B:real]: ((((ord_less_eq_real @ (cos_real @ B) @ (cos_real @ A)) <= (ord_less_eq_real @ B @ pi)) <= (ord_less_eq_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7105_cos__monotone__0__pi__le)). 159.59/70.65 thf(13560,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (cos_real @ B) @ (cos_real @ A)) | ~ (ord_less_eq_real @ B @ pi) | ~ (ord_less_eq_real @ A @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1636])). 159.59/70.65 thf(951,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((A != one_one_real) => ((ord_less_real @ zero_zero_real @ B) => ((log @ A @ (inverse_inverse_real @ B)) = (uminus_uminus_real @ (log @ A @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9120_log__inverse)). 159.59/70.65 thf(11295,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((~ (A = one_one_real)) => ((ord_less_real @ zero_zero_real @ B) => ((log @ A @ (inverse_inverse_real @ B)) = (uminus_uminus_real @ (log @ A @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[951])). 159.59/70.65 thf(2279,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/sandbox/benchmark/theBenchmark.p',fact_2364_div__add__self2)). 159.59/70.65 thf(15598,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)],[2279])). 159.59/70.65 thf(4799,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/sandbox/benchmark/theBenchmark.p',fact_3202_order__le__less__trans)). 159.59/70.65 thf(23824,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)],[4799])). 159.59/70.65 thf(5475,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ one_one_nat @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5989_or__numerals_I2_J)). 159.59/70.65 thf(26355,plain,((! [A:num]: ((bit_se1412395901928357646or_nat @ one_one_nat @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5475])). 159.59/70.65 thf(3377,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/sandbox/benchmark/theBenchmark.p',fact_5784_of__int__power__eq__of__int__cancel__iff)). 159.59/70.65 thf(19106,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)],[3377])). 159.59/70.65 thf(4039,axiom,((! [A:complex,B:real,C:real,D:complex]: ((A = (real_V2046097035970521341omplex @ (divide_divide_real @ B @ C) @ D)) = (((C = zero_zero_real) => (A = zero_zero_complex)) & (((real_V2046097035970521341omplex @ C @ A) = (real_V2046097035970521341omplex @ B @ D)) <= (C != zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9233_eq__vector__fraction__iff)). 159.59/70.65 thf(21225,plain,((! [A:complex,B:real,C:real,D:complex]: ((A = (real_V2046097035970521341omplex @ (divide_divide_real @ B @ C) @ D)) = (((C = zero_zero_real) => (A = zero_zero_complex)) & (((real_V2046097035970521341omplex @ C @ A) = (real_V2046097035970521341omplex @ B @ D)) | (C = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4039])). 159.59/70.65 thf(403,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ (times_3573771949741848930nteger @ C @ A)) @ A) = (plus_p5714425477246183910nteger @ C @ (divide6298287555418463151nteger @ B @ A))) <= (A != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1751_div__mult__self1)). 159.59/70.65 thf(9518,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ (times_3573771949741848930nteger @ C @ A)) @ A) = (plus_p5714425477246183910nteger @ C @ (divide6298287555418463151nteger @ B @ A))) | (A = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[403])). 159.59/70.65 thf(2527,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ B) @ A) <= (ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4934_compl__le__swap2)). 159.59/70.65 thf(16384,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ B) @ A) | ~ (ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2527])). 159.59/70.65 thf(693,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((A = B) => ((ord_le72135733267957522d_enat @ A @ C) <= (ord_le72135733267957522d_enat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2774_ord__eq__less__trans)). 159.59/70.65 thf(10466,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((A = B) => ((ord_le72135733267957522d_enat @ A @ C) | ~ (ord_le72135733267957522d_enat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[693])). 159.59/70.65 thf(5639,axiom,((! [A:real,B:nat,C:real]: ((ord_less_real @ (power_power_real @ A @ B) @ C) => ((ord_less_real @ (semiri5074537144036343181t_real @ B) @ (log @ A @ C)) <= (ord_less_real @ one_one_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6749_less__log__of__power)). 159.59/70.65 thf(26904,plain,((! [A:real,B:nat,C:real]: ((ord_less_real @ (power_power_real @ A @ B) @ C) => ((ord_less_real @ (semiri5074537144036343181t_real @ B) @ (log @ A @ C)) | ~ (ord_less_real @ one_one_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5639])). 159.59/70.65 thf(766,axiom,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ B) = ((B = zero_zero_nat) & ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6357_bit__mod__2__iff)). 159.59/70.65 thf(10724,plain,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ B) = ((B = zero_zero_nat) & ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[766])). 159.59/70.65 thf(2913,axiom,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1502_add__0)). 159.59/70.65 thf(17632,plain,((! [A:complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2913])). 159.59/70.65 thf(5856,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_538_add__Suc__right)). 159.59/70.65 thf(27893,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)],[5856])). 159.59/70.65 thf(8116,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/sandbox/benchmark/theBenchmark.p',fact_440_power4__eq__xxxx)). 159.59/70.65 thf(36193,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)],[8116])). 159.59/70.65 thf(6279,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ A)) = ((ord_less_nat @ B @ A) | (dvd_dvd_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4127_dvd__minus__self)). 159.59/70.65 thf(29425,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (minus_minus_nat @ B @ A)) = ((ord_less_nat @ B @ A) | (dvd_dvd_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6279])). 159.59/70.65 thf(1759,axiom,((! [A:nat,B:real,C:real,D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (times_times_real @ (gbinomial_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ B) @ E) @ (power_power_real @ C @ E)) @ (power_power_real @ D @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A)) = (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (times_times_real @ (gbinomial_real @ (uminus_uminus_real @ B) @ E) @ (power_power_real @ (uminus_uminus_real @ C) @ E)) @ (power_power_real @ (plus_plus_real @ C @ D) @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8942_gbinomial__partial__sum__poly)). 159.59/70.65 thf(13931,plain,((! [A:nat,B:real,C:real,D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (times_times_real @ (gbinomial_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ B) @ E) @ (power_power_real @ C @ E)) @ (power_power_real @ D @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A)) = (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (times_times_real @ (gbinomial_real @ (uminus_uminus_real @ B) @ E) @ (power_power_real @ (uminus_uminus_real @ C) @ E)) @ (power_power_real @ (plus_plus_real @ C @ D) @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759])). 159.59/70.65 thf(5483,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (minus_minus_complex @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_atMost_nat @ B)) = (minus_minus_complex @ (A @ zero_zero_nat) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8752_sum__telescope)). 159.59/70.65 thf(26386,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (minus_minus_complex @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_atMost_nat @ B)) = (minus_minus_complex @ (A @ zero_zero_nat) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5483])). 159.59/70.65 thf(413,axiom,((! [A:code_integer]: ((divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1542_div__0)). 159.59/70.65 thf(9550,plain,((! [A:code_integer]: ((divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])). 159.59/70.65 thf(5961,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) = (dvd_dvd_nat @ B @ C)) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4064_mult__unit__dvd__iff_H)). 159.59/70.65 thf(28315,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) = (dvd_dvd_nat @ B @ C)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5961])). 159.59/70.65 thf(4444,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ C) <= (ord_le72135733267957522d_enat @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4452_pinf_I7_J)). 159.59/70.65 thf(22486,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ C) | ~ (ord_le72135733267957522d_enat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4444])). 159.59/70.65 thf(3723,axiom,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1510_add__cancel__right__right)). 159.59/70.65 thf(20225,plain,((! [A:complex,B:complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3723])). 159.59/70.65 thf(7056,axiom,((ord_less_eq_num = (^ [A:num,B:num]: ((A = B) | (ord_less_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3157_order__le__less)). 159.59/70.65 thf(32546,plain,(((ord_less_eq_num) = (^ [A:num,B:num]: ((A = B) | (ord_less_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7056])). 159.59/70.65 thf(596,axiom,((! [A:int,B:nat]: (((bit_se1146084159140164899it_int @ A @ B) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) <= ((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6422_stable__imp__bit__iff__odd)). 159.59/70.65 thf(10144,plain,((! [A:int,B:nat]: (((bit_se1146084159140164899it_int @ A @ B) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))) | ~ ((divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[596])). 159.59/70.65 thf(807,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 @ (powr_real @ B @ A) @ (powr_real @ C @ A)) <= (ord_less_real @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7244_powr__less__mono2)). 159.59/70.65 thf(10861,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 @ (powr_real @ B @ A) @ (powr_real @ C @ A)) | ~ (ord_less_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[807])). 159.59/70.65 thf(7701,axiom,(((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1781_bits__1__div__2)). 159.59/70.65 thf(34856,plain,(((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7701])). 159.59/70.65 thf(7396,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (~ ((~ (A @ zero_zero_nat) & (ord_less_nat @ B @ C)) | ? [D:nat]: ((B = (plus_plus_nat @ C @ D)) & ~ (A @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2397_nat__diff__split__asm)). 159.59/70.65 thf(33820,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (~ ((~ (A @ zero_zero_nat) & (ord_less_nat @ B @ C)) | ? [D:nat]: ((B = (plus_plus_nat @ C @ D)) & ~ (A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7396])). 159.59/70.65 thf(4083,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((((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)) <= (ord_less_eq_int @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2223_mult__less__le__imp__less)). 159.59/70.65 thf(21356,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((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) | ~ (ord_less_eq_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4083])). 159.59/70.65 thf(2977,axiom,((! [A:real]: ((real_V1022390504157884413omplex @ (plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ one_one_complex)) = (abs_abs_real @ (plus_plus_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7367_norm__of__real__add1)). 159.59/70.65 thf(17832,plain,((! [A:real]: ((real_V1022390504157884413omplex @ (plus_plus_complex @ (real_V4546457046886955230omplex @ A) @ one_one_complex)) = (abs_abs_real @ (plus_plus_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2977])). 159.59/70.65 thf(2614,axiom,((! [A:num,B:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5036_not__numeral__less__neg__numeral)). 159.59/70.65 thf(16678,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)],[2614])). 159.59/70.65 thf(4974,axiom,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ one_one_nat) = (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1468_deg1Leaf)). 159.59/70.65 thf(24471,plain,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ one_one_nat) = (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4974])). 159.59/70.65 thf(7158,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ zero_zero_real @ (sqrt @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6388_real__sqrt__ge__zero)). 159.59/70.65 thf(32965,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_eq_real @ zero_zero_real @ (sqrt @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7158])). 159.59/70.65 thf(3653,axiom,((! [A:num,B:num]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (ord_less_num @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4821_neg__numeral__less__iff)). 159.59/70.65 thf(19983,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)],[3653])). 159.59/70.65 thf(4564,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((modulo_modulo_nat @ B @ C) = (modulo_modulo_nat @ A @ C)) = (dvd_dvd_nat @ C @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4185_mod__eq__dvd__iff__nat)). 159.59/70.65 thf(23009,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((modulo_modulo_nat @ B @ C) = (modulo_modulo_nat @ A @ C)) = (dvd_dvd_nat @ C @ (minus_minus_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4564])). 159.59/70.65 thf(193,axiom,((! [A:real]: (sums_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (sin_coeff @ B) @ (power_power_real @ A @ B))) @ (sin_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9263_sin__converges)). 159.59/70.65 thf(8845,plain,((! [A:real]: (sums_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (sin_coeff @ B) @ (power_power_real @ A @ B))) @ (sin_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 159.59/70.65 thf(358,axiom,((! [A:real]: (ord_less_real @ (tanh_real @ A) @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5551_tanh__real__lt__1)). 159.59/70.65 thf(9358,plain,((! [A:real]: (ord_less_real @ (tanh_real @ A) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])). 159.59/70.65 thf(1502,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ C) <= (dvd_dvd_real @ (times_times_real @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3971_dvd__mult__right)). 159.59/70.65 thf(13149,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ B @ C) | ~ (dvd_dvd_real @ (times_times_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1502])). 159.59/70.65 thf(5783,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/sandbox/benchmark/theBenchmark.p',fact_339_power__le__imp__le__exp)). 159.59/70.65 thf(27481,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)],[5783])). 159.59/70.65 thf(2173,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = one_one_complex) => ((invers8013647133539491842omplex @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9038_inverse__unique)). 159.59/70.65 thf(15256,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = one_one_complex) => ((invers8013647133539491842omplex @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2173])). 159.59/70.65 thf(5041,axiom,((! [A:num]: ((archim6058952711729229775r_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8193_floor__neg__numeral)). 159.59/70.65 thf(24689,plain,((! [A:num]: ((archim6058952711729229775r_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5041])). 159.59/70.65 thf(1067,axiom,((ord_less_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5156_less__minus__one__simps_I1_J)). 159.59/70.65 thf(11674,plain,((ord_less_real @ (uminus_uminus_real @ one_one_real) @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067])). 159.59/70.65 thf(1223,axiom,((! [A:nat]: ((abs_abs_int @ (semiri1314217659103216013at_int @ A)) = (semiri1314217659103216013at_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6493_abs__of__nat)). 159.59/70.65 thf(12202,plain,((! [A:nat]: ((abs_abs_int @ (semiri1314217659103216013at_int @ A)) = (semiri1314217659103216013at_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223])). 159.59/70.65 thf(84,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 @ (real_V1485227260804924795R_real @ C @ B) @ (real_V1485227260804924795R_real @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9228_scaleR__left__mono__neg)). 159.59/70.65 thf(8509,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 @ (real_V1485227260804924795R_real @ C @ B) @ (real_V1485227260804924795R_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 159.59/70.65 thf(3074,axiom,((! [A:code_integer,B:code_integer]: ((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4652_mod__minus__minus)). 159.59/70.65 thf(18128,plain,((! [A:code_integer,B:code_integer]: ((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3074])). 159.59/70.65 thf(2524,axiom,((! [A:real,B:(num > real),C:num,D:num]: ((ord_less_real @ A @ (B @ C)) => ((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))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2895_order__less__subst1)). 159.59/70.65 thf(16374,plain,((! [A:real,B:(num > real),C:num,D:num]: ((ord_less_real @ A @ (B @ C)) => ((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))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2524])). 159.59/70.65 thf(6653,axiom,((! [A:nat]: ((modulo_modulo_nat @ A @ (suc @ zero_zero_nat)) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3422_mod__by__Suc__0)). 159.59/70.65 thf(30793,plain,((! [A:nat]: ((modulo_modulo_nat @ A @ (suc @ zero_zero_nat)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6653])). 159.59/70.65 thf(6610,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2192_add__is__1)). 159.59/70.65 thf(30636,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((B = (suc @ zero_zero_nat)) & (A = zero_zero_nat)) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6610])). 159.59/70.65 thf(4130,axiom,((! [A:nat,B:nat]: ((ord_less_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B)) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6687_of__nat__less__imp__less)). 159.59/70.65 thf(21496,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)],[4130])). 159.59/70.65 thf(2620,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/sandbox/benchmark/theBenchmark.p',fact_9617_not__int__rec)). 159.59/70.65 thf(16695,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)],[2620])). 159.59/70.65 thf(8070,axiom,((! [A:list_nat,B:list_o]: ((size_s6491369823275344609_nat_o @ (product_nat_o @ A @ B)) = (times_times_nat @ (size_size_list_nat @ A) @ (size_size_list_o @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3631_length__product)). 159.59/70.65 thf(36058,plain,((! [A:list_nat,B:list_o]: ((size_s6491369823275344609_nat_o @ (product_nat_o @ A @ B)) = (times_times_nat @ (size_size_list_nat @ A) @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8070])). 159.59/70.65 thf(1456,axiom,((! [A:nat]: ((bit_se2923211474154528505it_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4653_take__bit__of__0)). 159.59/70.65 thf(12995,plain,((! [A:nat]: ((bit_se2923211474154528505it_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456])). 159.59/70.65 thf(7541,axiom,((! [A:real]: ((one_one_real = A) = (A = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154_one__reorient)). 159.59/70.65 thf(34311,plain,((! [A:real]: ((one_one_real = A) = (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7541])). 159.59/70.65 thf(8250,axiom,(((numeral_numeral_nat @ one) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_numeral__One)). 159.59/70.65 thf(36779,plain,(((numeral_numeral_nat @ one) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8250])). 159.59/70.65 thf(6976,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => (((C @ A) <= (! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))))) <= (C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_inc__induct)). 159.59/70.65 thf(32236,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) | ~ (! [D:nat]: ((ord_less_eq_nat @ A @ D) => ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D))))) | ~ (C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6976])). 159.59/70.65 thf(2481,axiom,((! [A:real,B:real]: ((A = (uminus_uminus_real @ B)) = ((plus_plus_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5046_eq__neg__iff__add__eq__0)). 159.59/70.65 thf(16234,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)],[2481])). 159.59/70.65 thf(6015,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/sandbox/benchmark/theBenchmark.p',fact_5665_divmod__divmod__step)). 159.59/70.65 thf(28488,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)],[6015])). 159.59/70.65 thf(1052,axiom,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (times_times_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ (comm_s2602460028002588243omplex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8276_pochhammer__rec_H)). 159.59/70.65 thf(11622,plain,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (times_times_complex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ (comm_s2602460028002588243omplex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052])). 159.59/70.65 thf(2083,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/sandbox/benchmark/theBenchmark.p',fact_3550_unset__bit__Suc)). 159.59/70.65 thf(14962,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)],[2083])). 159.59/70.65 thf(2559,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2909_order__less__not__sym)). 159.59/70.65 thf(16478,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2559])). 159.59/70.65 thf(7361,axiom,((! [A:nat]: ((finite_finite_nat @ (collect_nat @ (^ [B:nat]: (dvd_dvd_nat @ B @ A)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4134_finite__divisors__nat)). 159.59/70.65 thf(33705,plain,((! [A:nat]: ((finite_finite_nat @ (collect_nat @ (^ [B:nat]: (dvd_dvd_nat @ B @ A)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7361])). 159.59/70.65 thf(3922,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 @ A) @ (cos_real @ B)) = (ord_less_eq_real @ B @ A))) <= (ord_less_eq_real @ zero_zero_real @ B)) <= (ord_less_eq_real @ A @ pi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7104_cos__mono__le__eq)). 159.59/70.65 thf(20868,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 @ A) @ (cos_real @ B)) = (ord_less_eq_real @ B @ A))) | ~ (ord_less_eq_real @ zero_zero_real @ B) | ~ (ord_less_eq_real @ A @ pi))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3922])). 159.59/70.65 thf(91,axiom,((! [A:set_nat,B:set_nat]: (ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2997_Diff__subset)). 159.59/70.65 thf(8528,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)],[91])). 159.59/70.65 thf(3130,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ A @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups2073611262835488442omplex @ (^ [C:nat]: (plus_plus_complex @ (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/sandbox/benchmark/theBenchmark.p',fact_8912_sum_Oin__pairs__0)). 159.59/70.65 thf(18318,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (A) @ (set_ord_atMost_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) = (groups2073611262835488442omplex @ (^ [C:nat]: (plus_plus_complex @ (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)],[3130])). 159.59/70.65 thf(1940,axiom,((! [A:real]: (ord_less_real @ zero_zero_real @ (plus_plus_real @ one_one_real @ (abs_abs_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5613_abs__add__one__gt__zero)). 159.59/70.65 thf(14513,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)],[1940])). 159.59/70.65 thf(7769,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((divide_divide_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1722_div__less)). 159.59/70.65 thf(35100,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)],[7769])). 159.59/70.65 thf(6037,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C)) <= (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_832_eq__diff__iff)). 159.59/70.65 thf(28557,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C)) | ~ (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6037])). 159.59/70.65 thf(4756,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/sandbox/benchmark/theBenchmark.p',fact_5652_abs__square__less__1)). 159.59/70.65 thf(23690,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)],[4756])). 159.59/70.65 thf(4177,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/sandbox/benchmark/theBenchmark.p',fact_5861_neg__numeral__power__eq__of__int__cancel__iff)). 159.59/70.65 thf(21650,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)],[4177])). 159.59/70.65 thf(889,axiom,((! [A:nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (insert_nat @ A @ B) @ C) = ((ord_less_eq_set_nat @ B @ C) & (member_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6156_insert__subset)). 159.59/70.65 thf(11109,plain,((! [A:nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ (insert_nat @ A @ B) @ C) = ((ord_less_eq_set_nat @ B @ C) & (member_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[889])). 159.59/70.65 thf(2376,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/sandbox/benchmark/theBenchmark.p',fact_2084_zero__less__mult__pos)). 159.59/70.65 thf(15883,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)],[2376])). 159.59/70.65 thf(6159,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_max_nat @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_max_Oabsorb2)). 159.59/70.65 thf(28944,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)],[6159])). 159.59/70.65 thf(24,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/sandbox/benchmark/theBenchmark.p',fact_9658_cmod__Re__le__iff)). 159.59/70.65 thf(8327,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)],[24])). 159.59/70.65 thf(191,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ B @ A) <= (A = (ord_max_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_max_OorderI)). 159.59/70.65 thf(8840,plain,((! [A:int,B:int]: ((ord_less_eq_int @ B @ A) | ~ (A = (ord_max_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 159.59/70.65 thf(913,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ B @ zero_zero_int) => (ord_less_int @ (times_times_int @ B @ A) @ zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2091_mult__pos__neg2)). 159.59/70.65 thf(11180,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ B @ zero_zero_int) => (ord_less_int @ (times_times_int @ B @ A) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[913])). 159.59/70.65 thf(8211,axiom,((! [A:nat]: (((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) & (A != (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) => ((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ A) = (nth_VEBT_VEBT @ treeList @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_nothprolist)). 159.59/70.65 thf(36513,plain,((! [A:nat]: (((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) & ~ (A = (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) => ((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ A) = (nth_VEBT_VEBT @ treeList @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8211])). 159.59/70.65 thf(8100,axiom,(((some_nat @ lx) = (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ summin)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501__092_060open_062Some_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_092_060close_062)). 159.59/70.65 thf(36144,plain,(((some_nat @ lx) = (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ summin)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8100])). 159.59/70.65 thf(4339,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3139_order_Ostrict__implies__order)). 159.59/70.65 thf(22157,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4339])). 159.59/70.65 thf(47,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => ((ord_max_int @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_max_Oabsorb3)). 159.59/70.65 thf(8391,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => ((ord_max_int @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[47])). 159.59/70.65 thf(6511,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/sandbox/benchmark/theBenchmark.p',fact_3925_dvd__productE)). 159.59/70.65 thf(30278,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)],[6511])). 159.59/70.65 thf(878,axiom,((! [A:complex]: (summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (real_V2046097035970521341omplex @ (sin_coeff @ B) @ (power_power_complex @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9272_summable__norm__sin)). 159.59/70.65 thf(11081,plain,((! [A:complex]: (summable_real @ (^ [B:nat]: (real_V1022390504157884413omplex @ (real_V2046097035970521341omplex @ (sin_coeff @ B) @ (power_power_complex @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[878])). 159.59/70.65 thf(7589,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_nat @ zero_zero_nat @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2204_mult__less__mono2)). 159.59/70.65 thf(34528,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7589])). 159.59/70.65 thf(3126,axiom,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5192_neg__numeral__less__one)). 159.59/70.65 thf(18307,plain,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3126])). 159.59/70.65 thf(2707,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/sandbox/benchmark/theBenchmark.p',fact_6903_norm__divide)). 159.59/70.65 thf(16987,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)],[2707])). 159.59/70.65 thf(5330,axiom,((! [A:nat,B:(int > nat),C:int,D:int]: (((ord_less_eq_int @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) <= (ord_less_eq_nat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2689_order__subst1)). 159.59/70.65 thf(25747,plain,((! [A:nat,B:(int > nat),C:int,D:int]: (((ord_less_eq_int @ C @ D) => ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_eq_int @ E @ F) => (ord_less_eq_nat @ (B @ E) @ (B @ F)))))) | ~ (ord_less_eq_nat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5330])). 159.59/70.65 thf(2402,axiom,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3699_verit__sum__simplify)). 159.59/70.65 thf(15969,plain,((! [A:complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2402])). 159.59/70.65 thf(343,axiom,((! [A:code_integer,B:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ A) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ B @ A) @ one_one_Code_integer)) <= (A != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2365_div__add__self2)). 159.59/70.65 thf(9313,plain,((! [A:code_integer,B:code_integer]: (((divide6298287555418463151nteger @ (plus_p5714425477246183910nteger @ B @ A) @ A) = (plus_p5714425477246183910nteger @ (divide6298287555418463151nteger @ B @ A) @ one_one_Code_integer)) | (A = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 159.59/70.65 thf(7318,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/sandbox/benchmark/theBenchmark.p',fact_249_power__increasing__iff)). 159.59/70.65 thf(33561,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)],[7318])). 159.59/70.65 thf(4790,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_V8194947554948674370ptions @ A @ B) <= ((vEBT_vebt_maxt @ A) = (some_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_maxbmo)). 159.59/70.65 thf(23798,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)],[4790])). 159.59/70.65 thf(4639,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C))) <= (! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) <= (ord_less_nat @ D @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_less__mono__imp__le__mono)). 159.59/70.65 thf(23285,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ 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)],[4639])). 159.59/70.65 thf(127,axiom,((real_V1485227260804924795R_real = (^ [A:real]: (times_times_real @ (real_V1803761363581548252l_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9218_scaleR__conv__of__real)). 159.59/70.65 thf(8644,plain,(((real_V1485227260804924795R_real) = (^ [A:real]: (times_times_real @ (real_V1803761363581548252l_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 159.59/70.65 thf(8227,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/sandbox/benchmark/theBenchmark.p',fact_3873_even__mult__iff)). 159.59/70.65 thf(36557,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)],[8227])). 159.59/70.65 thf(4833,axiom,((! [A:num,B:num]: (((numeral_numeral_int @ A) = (numeral_numeral_int @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_numeral__eq__iff)). 159.59/70.65 thf(23979,plain,((! [A:num,B:num]: (((numeral_numeral_int @ A) = (numeral_numeral_int @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4833])). 159.59/70.65 thf(4585,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/sandbox/benchmark/theBenchmark.p',fact_9567_push__bit__minus__one)). 159.59/70.65 thf(23084,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)],[4585])). 159.59/70.65 thf(1324,axiom,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1503_add__0)). 159.59/70.65 thf(12529,plain,((! [A:real]: ((plus_plus_real @ zero_zero_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324])). 159.59/70.65 thf(7442,axiom,((! [A:num]: ((size_size_num @ (bit1 @ A)) = (plus_plus_nat @ (size_size_num @ A) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5635_num_Osize_I6_J)). 159.59/70.65 thf(33958,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)],[7442])). 159.59/70.65 thf(7263,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((~ (ord_less_eq_num @ A @ C)) <= (ord_less_num @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4510_minf_I8_J)). 159.59/70.65 thf(33359,plain,((! [A:num]: ? [B:num]: ! [C:num]: (~ (ord_less_eq_num @ A @ C) | ~ (ord_less_num @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7263])). 159.59/70.65 thf(2039,axiom,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (times_times_nat @ A @ B)) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6537_of__nat__mult)). 159.59/70.65 thf(14832,plain,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (times_times_nat @ A @ B)) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2039])). 159.59/70.65 thf(1935,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) => (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_add__right__imp__eq)). 159.59/70.65 thf(14498,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)],[1935])). 159.59/70.65 thf(1588,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_int @ (B @ E) @ (B @ F)) <= (ord_less_real @ E @ F))))) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2872_ord__eq__less__subst)). 159.59/70.65 thf(13403,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_int @ (B @ E) @ (B @ F)) | ~ (ord_less_real @ E @ F))))) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588])). 159.59/70.65 thf(4109,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((A != zero_zero_complex) => ((B != zero_zero_complex) => (((divide1717551699836669952omplex @ C @ A) = (divide1717551699836669952omplex @ D @ B)) = ((times_times_complex @ C @ B) = (times_times_complex @ D @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2179_frac__eq__eq)). 159.59/70.65 thf(21432,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((~ (A = zero_zero_complex)) => ((~ (B = zero_zero_complex)) => (((divide1717551699836669952omplex @ C @ A) = (divide1717551699836669952omplex @ D @ B)) = ((times_times_complex @ C @ B) = (times_times_complex @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4109])). 159.59/70.65 thf(5078,axiom,((! [A:num,B:num]: ((bit0 @ A) != (bit1 @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5386_semiring__norm_I88_J)). 159.59/70.65 thf(24844,plain,((! [A:num,B:num]: ~ ((bit0 @ A) = (bit1 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5078])). 159.59/70.65 thf(3938,axiom,((! [A:int]: (((ring_1_of_int_real @ A) = one_one_real) = (A = one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5776_of__int__eq__1__iff)). 159.59/70.65 thf(20919,plain,((! [A:int]: (((ring_1_of_int_real @ A) = one_one_real) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3938])). 159.59/70.65 thf(5205,axiom,((! [A:nat,B:nat]: ((((ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat) <= (ord_less_eq_nat @ B @ one_one_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2304_mult__le__one)). 159.59/70.65 thf(25290,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat) | ~ (ord_less_eq_nat @ 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)],[5205])). 159.59/70.65 thf(6304,axiom,((! [A:int,B:nat]: ((times_times_int @ (minus_minus_int @ one_one_int @ A) @ (groups3539618377306564664at_int @ (power_power_int @ A) @ (set_ord_atMost_nat @ B))) = (minus_minus_int @ one_one_int @ (power_power_int @ A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8871_sum__gp__basic)). 159.59/70.65 thf(29506,plain,((! [A:int,B:nat]: ((times_times_int @ (minus_minus_int @ one_one_int @ A) @ (groups3539618377306564664at_int @ (power_power_int @ A) @ (set_ord_atMost_nat @ B))) = (minus_minus_int @ one_one_int @ (power_power_int @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6304])). 159.59/70.65 thf(2284,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ A)) => ((A != zero_zero_real) => (ord_less_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9028_inverse__positive__imp__positive)). 159.59/70.65 thf(15613,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (inverse_inverse_real @ A)) => ((~ (A = zero_zero_real)) => (ord_less_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2284])). 159.59/70.65 thf(5449,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (times_times_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ one_one_real @ B)) & ((ord_less_real @ B @ one_one_real) <= (ord_less_eq_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2416_mult__less__cancel__left1)). 159.59/70.65 thf(26264,plain,((! [A:real,B:real]: ((ord_less_real @ A @ (times_times_real @ A @ B)) = (((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ one_one_real @ B)) & ((ord_less_real @ B @ one_one_real) | ~ (ord_less_eq_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5449])). 159.59/70.65 thf(3500,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/sandbox/benchmark/theBenchmark.p',fact_6919_norm__add__less)). 159.59/70.65 thf(19492,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)],[3500])). 159.59/70.65 thf(553,axiom,((! [A:num]: ((ord_max_int @ zero_zero_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1701_max__0__1_I3_J)). 159.59/70.65 thf(10012,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)],[553])). 159.59/70.65 thf(521,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ (real_V1485227260804924795R_real @ A @ C)) = (((ord_less_eq_real @ B @ C) <= (ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ C @ B) <= (ord_less_real @ A @ zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9225_scaleR__le__cancel__left)). 159.59/70.65 thf(9911,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ (real_V1485227260804924795R_real @ A @ C)) = (((ord_less_eq_real @ B @ C) | ~ (ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ C @ B) | ~ (ord_less_real @ A @ zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[521])). 159.59/70.65 thf(1057,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/sandbox/benchmark/theBenchmark.p',fact_5275_pos__le__minus__divide__eq)). 159.59/70.65 thf(11637,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)],[1057])). 159.59/70.65 thf(164,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((ord_max_int @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_914_max_Oabsorb__iff1)). 159.59/70.65 thf(8757,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((ord_max_int @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[164])). 159.59/70.65 thf(1848,axiom,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2801_dual__order_Oirrefl)). 159.59/70.65 thf(14226,plain,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1848])). 159.59/70.65 thf(537,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/sandbox/benchmark/theBenchmark.p',fact_8357_gbinomial__code)). 159.59/70.65 thf(9963,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)],[537])). 159.59/70.65 thf(1832,axiom,((! [A:extended_enat,B:extended_enat]: (((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B) => (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ A @ B))) <= (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2113_add__pos__pos)). 159.59/70.65 thf(14179,plain,((! [A:extended_enat,B:extended_enat]: (((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B) => (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (plus_p3455044024723400733d_enat @ A @ B))) | ~ (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1832])). 159.59/70.65 thf(2944,axiom,((! [A:extended_enat,B:(num > extended_enat),C:num,D:num]: ((ord_le2932123472753598470d_enat @ A @ (B @ C)) => ((ord_less_num @ C @ D) => ((ord_le72135733267957522d_enat @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) <= (ord_less_num @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3216_order__le__less__subst1)). 159.59/70.65 thf(17730,plain,((! [A:extended_enat,B:(num > extended_enat),C:num,D:num]: ((ord_le2932123472753598470d_enat @ A @ (B @ C)) => ((ord_less_num @ C @ D) => ((ord_le72135733267957522d_enat @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_le72135733267957522d_enat @ (B @ E) @ (B @ F)) | ~ (ord_less_num @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2944])). 159.59/70.65 thf(1340,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/sandbox/benchmark/theBenchmark.p',fact_2546_not__sum__power2__lt__zero)). 159.59/70.65 thf(12580,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)],[1340])). 159.59/70.65 thf(7185,axiom,((((=) @ list_o) = (^ [A:list_o,B:list_o]: (((size_size_list_o @ A) = (size_size_list_o @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_o @ A)) => ((nth_o @ A @ C) = (nth_o @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_list__eq__iff__nth__eq)). 159.59/70.65 thf(33097,plain,((((=) @ list_o) = (^ [A:list_o,B:list_o]: (((size_size_list_o @ A) = (size_size_list_o @ B)) & ! [C:nat]: ((ord_less_nat @ C @ (size_size_list_o @ A)) => ((nth_o @ A @ C) = (nth_o @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7185])). 159.59/70.65 thf(5195,axiom,((! [A:nat]: ((ord_min_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10168_min__0R)). 159.59/70.65 thf(25234,plain,((! [A:nat]: ((ord_min_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5195])). 159.59/70.65 thf(2378,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (dvd_dvd_Code_integer @ (divide6298287555418463151nteger @ one_one_Code_integer @ A) @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3851_unit__div__1__unit)). 159.59/70.65 thf(15888,plain,((! [A:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (dvd_dvd_Code_integer @ (divide6298287555418463151nteger @ one_one_Code_integer @ A) @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2378])). 159.59/70.65 thf(3380,axiom,((! [A:complex,B:real,C:complex,D:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ B) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ C)) @ (plus_plus_real @ B @ D)) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ C) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6930_norm__triangle__mono)). 159.59/70.65 thf(19115,plain,((! [A:complex,B:real,C:complex,D:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ B) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ C)) @ (plus_plus_real @ B @ D)) | ~ (ord_less_eq_real @ (real_V1022390504157884413omplex @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3380])). 159.59/70.65 thf(4330,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/sandbox/benchmark/theBenchmark.p',fact_6303_signed__take__bit__eq__take__bit__minus)). 159.59/70.65 thf(22131,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)],[4330])). 159.59/70.65 thf(1959,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/sandbox/benchmark/theBenchmark.p',fact_7299_tan__pos__pi2__le)). 159.59/70.65 thf(14567,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)],[1959])). 159.59/70.65 thf(805,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]: (((divide_divide_int @ C @ (numeral_numeral_int @ (bit0 @ one))) = C) => (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4491_bits__induct)). 159.59/70.65 thf(10846,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]: (((divide_divide_int @ C @ (numeral_numeral_int @ (bit0 @ one))) = C) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[805])). 159.59/70.65 thf(1452,axiom,((! [A:real,B:real]: ((powr_real @ A @ (uminus_uminus_real @ B)) = (divide_divide_real @ one_one_real @ (powr_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7268_powr__minus__divide)). 159.59/70.65 thf(12983,plain,((! [A:real,B:real]: ((powr_real @ A @ (uminus_uminus_real @ B)) = (divide_divide_real @ one_one_real @ (powr_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452])). 159.59/70.65 thf(315,axiom,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se2793503036327961859nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) & (A != zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4241_even__set__bit__iff)). 159.59/70.65 thf(9220,plain,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_se2793503036327961859nteger @ A @ B)) = ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) & ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 159.59/70.65 thf(771,axiom,((! [A:num]: ((real_V1022390504157884413omplex @ (numera6690914467698888265omplex @ A)) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6896_norm__numeral)). 159.59/70.65 thf(10739,plain,((! [A:num]: ((real_V1022390504157884413omplex @ (numera6690914467698888265omplex @ A)) = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[771])). 159.59/70.65 thf(2841,axiom,((! [A:set_nat]: (inj_on_nat_nat @ suc @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10111_inj__Suc)). 159.59/70.65 thf(17388,plain,((! [A:set_nat]: (inj_on_nat_nat @ (suc) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2841])). 159.59/70.65 thf(2362,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/sandbox/benchmark/theBenchmark.p',fact_5544_abs__less__iff)). 159.59/70.65 thf(15836,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)],[2362])). 159.59/70.65 thf(3452,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (vEBT_invar_vebt @ (vEBT_vebt_buildup @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2573_buildup__gives__valid)). 159.59/70.65 thf(19348,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (vEBT_invar_vebt @ (vEBT_vebt_buildup @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3452])). 159.59/70.65 thf(8072,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/sandbox/benchmark/theBenchmark.p',fact_6634_of__nat__less__numeral__power__cancel__iff)). 159.59/70.65 thf(36063,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)],[8072])). 159.59/70.65 thf(7256,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/sandbox/benchmark/theBenchmark.p',fact_8626_prod_OatLeastAtMost__rev)). 159.59/70.65 thf(33339,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)],[7256])). 159.59/70.65 thf(4386,axiom,((! [A:real]: (((plus_plus_real @ one_one_real @ (power_power_real @ (tan_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_real @ (inverse_inverse_real @ (cos_real @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))) <= ((cos_real @ A) != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9162_tan__sec)). 159.59/70.65 thf(22302,plain,((! [A:real]: (((plus_plus_real @ one_one_real @ (power_power_real @ (tan_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = (power_power_real @ (inverse_inverse_real @ (cos_real @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))) | ((cos_real @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4386])). 159.59/70.65 thf(6860,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/sandbox/benchmark/theBenchmark.p',fact_582_less__trans__Suc)). 159.59/70.65 thf(31735,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)],[6860])). 159.59/70.65 thf(5757,axiom,((one_one_int = (abs_Integ @ (product_Pair_nat_nat @ one_one_nat @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9777_one__int__def)). 159.59/70.65 thf(27317,plain,((one_one_int = (abs_Integ @ (product_Pair_nat_nat @ one_one_nat @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5757])). 159.59/70.65 thf(4512,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/sandbox/benchmark/theBenchmark.p',fact_5862_neg__numeral__power__eq__of__int__cancel__iff)). 159.59/70.65 thf(22764,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)],[4512])). 159.59/70.65 thf(7036,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((A @ (minus_minus_nat @ B @ C)) <= (! [D:nat]: ((A @ D) <= (A @ (suc @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_zero__induct__lemma)). 159.59/70.65 thf(32464,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((A @ (minus_minus_nat @ B @ C)) | ~ (! [D:nat]: ((A @ D) | ~ (A @ (suc @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7036])). 159.59/70.65 thf(6261,axiom,((! [A:num,B:num]: ((uminus_uminus_real @ (numeral_numeral_real @ A)) != (numeral_numeral_real @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4948_neg__numeral__neq__numeral)). 159.59/70.65 thf(29332,plain,((! [A:num,B:num]: ~ ((uminus_uminus_real @ (numeral_numeral_real @ A)) = (numeral_numeral_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6261])). 159.59/70.65 thf(7435,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3060_less__le__not__le)). 159.59/70.65 thf(33936,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)],[7435])). 159.59/70.65 thf(5577,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/sandbox/benchmark/theBenchmark.p',fact_4881_diff__numeral__special_I3_J)). 159.59/70.65 thf(26688,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)],[5577])). 159.59/70.65 thf(4617,axiom,((! [A:nat,B:nat,C:nat]: ((A != zero_zero_nat) => ((((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))) <= (ord_less_eq_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2518_power__diff__power__eq)). 159.59/70.65 thf(23209,plain,((! [A:nat,B:nat,C:nat]: ((~ (A = zero_zero_nat)) => ((((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))) | ~ (ord_less_eq_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4617])). 159.59/70.65 thf(8034,axiom,((! [A:nat]: ((ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) => ((A = zero_zero_nat) | (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2522_less__2__cases)). 159.59/70.65 thf(35931,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)],[8034])). 159.59/70.65 thf(4116,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/sandbox/benchmark/theBenchmark.p',fact_7878_sum_OlessThan__Suc)). 159.59/70.65 thf(21457,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)],[4116])). 159.59/70.65 thf(1910,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/sandbox/benchmark/theBenchmark.p',fact_5757_dbl__dec__simps_I1_J)). 159.59/70.65 thf(14421,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)],[1910])). 159.59/70.65 thf(2122,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/sandbox/benchmark/theBenchmark.p',fact_5585_abs__diff__less__iff)). 159.59/70.65 thf(15085,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)],[2122])). 159.59/70.65 thf(3363,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ A @ B)) = ((ord_less_int @ B @ A) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2822_not__less__iff__gr__or__eq)). 159.59/70.65 thf(19061,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)],[3363])). 159.59/70.65 thf(5027,axiom,(((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4850_diff__numeral__special_I10_J)). 159.59/70.65 thf(24646,plain,(((minus_minus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5027])). 159.59/70.65 thf(3805,axiom,((! [A:int,B:int]: (((uminus_uminus_int @ A) = B) = ((plus_plus_int @ A @ B) = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5043_neg__eq__iff__add__eq__0)). 159.59/70.65 thf(20489,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)],[3805])). 159.59/70.65 thf(2656,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/sandbox/benchmark/theBenchmark.p',fact_9099_sqrt__divide__self__eq)). 159.59/70.65 thf(16811,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)],[2656])). 159.59/70.65 thf(7199,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/sandbox/benchmark/theBenchmark.p',fact_700_trans__le__add1)). 159.59/70.65 thf(33140,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)],[7199])). 159.59/70.65 thf(6744,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((((dvd_dvd_nat @ A @ C) => ((((divide_divide_nat @ C @ A) = (divide_divide_nat @ D @ B)) = ((times_times_nat @ C @ B) = (times_times_nat @ A @ D))) <= (dvd_dvd_nat @ B @ D))) <= (B != zero_zero_nat)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4148_dvd__div__div__eq__mult)). 159.59/70.65 thf(31242,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((dvd_dvd_nat @ A @ C) => ((((divide_divide_nat @ C @ A) = (divide_divide_nat @ D @ B)) = ((times_times_nat @ C @ B) = (times_times_nat @ A @ D))) | ~ (dvd_dvd_nat @ B @ D))) | (B = zero_zero_nat) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6744])). 159.59/70.65 thf(1781,axiom,((! [A:nat,B:int,C:int]: (((bit_ri631733984087533419it_int @ A @ B) = (bit_ri631733984087533419it_int @ A @ C)) = ((bit_se2923211474154528505it_int @ (suc @ A) @ B) = (bit_se2923211474154528505it_int @ (suc @ A) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5020_signed__take__bit__eq__iff__take__bit__eq)). 159.59/70.65 thf(14005,plain,((! [A:nat,B:int,C:int]: (((bit_ri631733984087533419it_int @ A @ B) = (bit_ri631733984087533419it_int @ A @ C)) = ((bit_se2923211474154528505it_int @ (suc @ A) @ B) = (bit_se2923211474154528505it_int @ (suc @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1781])). 159.59/70.65 thf(5200,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/sandbox/benchmark/theBenchmark.p',fact_898_max_OcoboundedI2)). 159.59/70.65 thf(25273,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)],[5200])). 159.59/70.65 thf(7581,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/sandbox/benchmark/theBenchmark.p',fact_3910_even__power)). 159.59/70.65 thf(34497,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)],[7581])). 159.59/70.65 thf(4080,axiom,((! [A:real]: ((times_times_real @ (exp_real @ A) @ A) = (times_times_real @ A @ (exp_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6059_exp__times__arg__commute)). 159.59/70.65 thf(21347,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)],[4080])). 159.59/70.65 thf(2682,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4984_minus__divide__left)). 159.59/70.65 thf(16895,plain,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ A @ B)) = (divide1717551699836669952omplex @ (uminus1482373934393186551omplex @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2682])). 159.59/70.65 thf(4243,axiom,((! [A:complex,B:nat,C:nat]: ((comm_s2602460028002588243omplex @ A @ (plus_plus_nat @ B @ C)) = (times_times_complex @ (comm_s2602460028002588243omplex @ A @ B) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8295_pochhammer__product_H)). 159.59/70.65 thf(21872,plain,((! [A:complex,B:nat,C:nat]: ((comm_s2602460028002588243omplex @ A @ (plus_plus_nat @ B @ C)) = (times_times_complex @ (comm_s2602460028002588243omplex @ A @ B) @ (comm_s2602460028002588243omplex @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4243])). 159.59/70.65 thf(2188,axiom,((! [A:real,B:real,C:$o]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ A) => (C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2914_order__less__imp__triv)). 159.59/70.65 thf(15304,plain,((! [A:real,B:real,C:$o]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ A) => (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2188])). 159.59/70.65 thf(1897,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (minus_8373710615458151222nteger @ B @ C)) = (dvd_dvd_Code_integer @ A @ (minus_8373710615458151222nteger @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4006_dvd__diff__commute)). 159.59/70.65 thf(14378,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (minus_8373710615458151222nteger @ B @ C)) = (dvd_dvd_Code_integer @ A @ (minus_8373710615458151222nteger @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1897])). 159.59/70.65 thf(6956,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/sandbox/benchmark/theBenchmark.p',fact_5291_neg__one__power__add__eq__neg__one__power__diff)). 159.59/70.65 thf(32061,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)],[6956])). 159.59/70.65 thf(2731,axiom,((! [A:real,B:real]: (((~ (ord_less_real @ A @ B)) = (A = B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3047_antisym__conv2)). 159.59/70.65 thf(17057,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)],[2731])). 159.59/70.65 thf(305,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/sandbox/benchmark/theBenchmark.p',fact_3378_unset__bit__0)). 159.59/70.65 thf(9194,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)],[305])). 159.59/70.65 thf(283,axiom,((! [A:nat]: ((bit_ri6519982836138164636nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4731_signed__take__bit__of__minus__1)). 159.59/70.65 thf(9109,plain,((! [A:nat]: ((bit_ri6519982836138164636nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 159.59/70.65 thf(514,axiom,((bit_se7879613467334960850it_int = (^ [A:nat,B:int]: (bit_se1409905431419307370or_int @ B @ (bit_se545348938243370406it_int @ A @ one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9564_set__bit__int__def)). 159.59/70.65 thf(9891,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)],[514])). 159.59/70.65 thf(2265,axiom,((! [A:extended_enat,B:extended_enat]: ? [C:extended_enat]: ! [D:extended_enat]: ((ord_le72135733267957522d_enat @ C @ D) => ((dvd_dv3785147216227455552d_enat @ A @ (plus_p3455044024723400733d_enat @ D @ B)) = (dvd_dv3785147216227455552d_enat @ A @ (plus_p3455044024723400733d_enat @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4527_pinf_I9_J)). 159.59/70.65 thf(15557,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2265])). 159.59/70.65 thf(7268,axiom,((zero_n2687167440665602831ol_nat = (^ [A:$o]: (if_nat @ A @ one_one_nat @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4401_of__bool__def)). 159.59/70.65 thf(33373,plain,(((zero_n2687167440665602831ol_nat) = (^ [A:$o]: (if_nat @ A @ one_one_nat @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7268])). 159.59/70.65 thf(8200,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/sandbox/benchmark/theBenchmark.p',fact_4891_power__minus1__even)). 159.59/70.65 thf(36472,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)],[8200])). 159.59/70.65 thf(970,axiom,((! [A:real,B:(extended_enat > real),C:extended_enat,D:extended_enat]: ((((ord_less_real @ A @ (B @ D)) <= (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F))))) <= (ord_le72135733267957522d_enat @ C @ D)) <= (ord_less_real @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2893_order__less__subst1)). 159.59/70.65 thf(11354,plain,((! [A:real,B:(extended_enat > real),C:extended_enat,D:extended_enat]: ((ord_less_real @ A @ (B @ D)) | ~ (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F)))) | ~ (ord_le72135733267957522d_enat @ C @ D) | ~ (ord_less_real @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[970])). 159.59/70.65 thf(590,axiom,((! [A:complex]: (ord_less_eq_real @ (abs_abs_real @ (re @ A)) @ (real_V1022390504157884413omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9636_abs__Re__le__cmod)). 159.59/70.65 thf(10129,plain,((! [A:complex]: (ord_less_eq_real @ (abs_abs_real @ (re @ A)) @ (real_V1022390504157884413omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[590])). 159.59/70.65 thf(3255,axiom,((! [A:int,B:(nat > int),C:nat,D:nat]: ((ord_less_int @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))) => (ord_less_int @ A @ (B @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3241_order__less__le__subst1)). 159.59/70.65 thf(18720,plain,((! [A:int,B:(nat > int),C:nat,D:nat]: ((ord_less_int @ A @ (B @ C)) => ((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_int @ (B @ E) @ (B @ F)))) => (ord_less_int @ A @ (B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3255])). 159.59/70.65 thf(8071,axiom,(((size_s6755466524823107622T_VEBT @ treeList) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__C2_C)). 159.59/70.65 thf(36061,plain,(((size_s6755466524823107622T_VEBT @ treeList) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8071])). 159.59/70.65 thf(8087,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1117_add__left__imp__eq)). 159.59/70.65 thf(36110,plain,((! [A:nat,B:nat,C:nat]: ((B = C) | ~ ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8087])). 159.59/70.65 thf(5133,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2702_antisym)). 159.59/70.65 thf(25013,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)],[5133])). 159.59/70.65 thf(1289,axiom,(((exp_complex @ (times_times_complex @ imaginary_unit @ (times_times_complex @ (real_V4546457046886955230omplex @ pi) @ (numera6690914467698888265omplex @ (bit0 @ one))))) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9304_exp__two__pi__i_H)). 159.59/70.65 thf(12416,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)],[1289])). 159.59/70.65 thf(2505,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ one_on7984719198319812577d_enat) @ (plus_p3455044024723400733d_enat @ B @ one_on7984719198319812577d_enat)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1325_add__mono1)). 159.59/70.65 thf(16318,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ one_on7984719198319812577d_enat) @ (plus_p3455044024723400733d_enat @ B @ one_on7984719198319812577d_enat)) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2505])). 159.59/70.65 thf(1603,axiom,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5189_neg__one__less__numeral)). 159.59/70.65 thf(13461,plain,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603])). 159.59/70.65 thf(5620,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/sandbox/benchmark/theBenchmark.p',fact_7880_powser__sums__zero__iff)). 159.59/70.65 thf(26845,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)],[5620])). 159.59/70.65 thf(5022,axiom,((! [A:num]: ((minus_minus_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ one_one_complex) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (plus_plus_num @ A @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4879_diff__numeral__special_I4_J)). 159.59/70.65 thf(24633,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)],[5022])). 159.59/70.65 thf(7374,axiom,((! [A:num]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ one_one_int) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_numeral__le__one__iff)). 159.59/70.65 thf(33748,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)],[7374])). 159.59/70.65 thf(8121,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4435_pinf_I2_J)). 159.59/70.65 thf(36208,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((A @ F) | (C @ F)) = ((D @ F) | (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8121])). 159.59/70.65 thf(2168,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)) | ((ord_less_int @ B @ C) & (ord_less_int @ zero_zero_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2071_mult__less__cancel__left__disj)). 159.59/70.65 thf(15241,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)) | ((ord_less_int @ B @ C) & (ord_less_int @ zero_zero_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2168])). 159.59/70.65 thf(3644,axiom,((! [A:list_nat]: (finite_finite_nat @ (set_nat2 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3615_List_Ofinite__set)). 159.59/70.65 thf(19952,plain,((! [A:list_nat]: (finite_finite_nat @ (set_nat2 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3644])). 159.59/70.65 thf(7069,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/sandbox/benchmark/theBenchmark.p',fact_1590_add__le__same__cancel1)). 159.59/70.65 thf(32610,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)],[7069])). 159.59/70.65 thf(7503,axiom,((! [A:nat,B:complex]: (((times_times_complex @ (power_power_complex @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_complex @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2529_power__minus__mult)). 159.59/70.65 thf(34197,plain,((! [A:nat,B:complex]: (((times_times_complex @ (power_power_complex @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_complex @ B @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7503])). 159.59/70.65 thf(3358,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/sandbox/benchmark/theBenchmark.p',fact_5162_take__bit__decr__eq)). 159.59/70.65 thf(19046,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)],[3358])). 159.59/70.65 thf(4102,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/sandbox/benchmark/theBenchmark.p',fact_8268_pochhammer__Suc)). 159.59/70.65 thf(21414,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)],[4102])). 159.59/70.65 thf(2894,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/sandbox/benchmark/theBenchmark.p',fact_9150_real__inv__sqrt__pow2)). 159.59/70.65 thf(17570,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)],[2894])). 159.59/70.65 thf(4523,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/sandbox/benchmark/theBenchmark.p',fact_1334_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right)). 159.59/70.65 thf(22821,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)],[4523])). 159.59/70.65 thf(4344,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((((ord_less_nat @ (groups3542108847815614940at_nat @ A @ (set_ord_lessThan_nat @ B)) @ (suminf_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ (A @ C))) <= (ord_less_eq_nat @ B @ C)) <= (! [D:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (A @ D)) <= (ord_less_eq_nat @ B @ D)))) <= (summable_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8010_sum__less__suminf2)). 159.59/70.65 thf(22171,plain,((! [A:(nat > nat),B:nat,C:nat]: ((ord_less_nat @ (groups3542108847815614940at_nat @ (A) @ (set_ord_lessThan_nat @ B)) @ (suminf_nat @ (A))) | ~ (ord_less_nat @ zero_zero_nat @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C) | ~ (! [D:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (A @ D)) | ~ (ord_less_eq_nat @ B @ D))) | ~ (summable_nat @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4344])). 159.59/70.65 thf(66,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/sandbox/benchmark/theBenchmark.p',fact_4242_even__set__bit__iff)). 159.59/70.65 thf(8448,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)],[66])). 159.59/70.65 thf(7960,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/sandbox/benchmark/theBenchmark.p',fact_1226_combine__common__factor)). 159.59/70.65 thf(35695,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)],[7960])). 159.59/70.65 thf(5714,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1499_mult__zero__left)). 159.59/70.65 thf(27167,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5714])). 159.59/70.65 thf(6078,axiom,((! [A:real,B:nat,C:real]: ((ord_less_eq_real @ (power_power_real @ A @ B) @ C) => ((ord_less_eq_real @ (semiri5074537144036343181t_real @ B) @ (log @ A @ C)) <= (ord_less_real @ one_one_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6764_le__log__of__power)). 159.59/70.65 thf(28683,plain,((! [A:real,B:nat,C:real]: ((ord_less_eq_real @ (power_power_real @ A @ B) @ C) => ((ord_less_eq_real @ (semiri5074537144036343181t_real @ B) @ (log @ A @ C)) | ~ (ord_less_real @ one_one_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6078])). 159.59/70.65 thf(6416,axiom,((! [A:(nat > real),B:nat]: (((A @ zero_zero_nat) = zero_zero_real) => ((groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups6591440286371151544t_real @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7655_sum__shift__lb__Suc0__0)). 159.59/70.65 thf(29919,plain,((! [A:(nat > real),B:nat]: (((A @ zero_zero_nat) = zero_zero_real) => ((groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups6591440286371151544t_real @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6416])). 159.59/70.65 thf(6452,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat))) => ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ D)))) => ((((~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G)))) <= (! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E)))) <= (! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E)))) <= (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2216_vebt__succ_Ocases)). 159.59/70.65 thf(30066,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat))) => ((! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ 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: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: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: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)],[6452])). 159.59/70.65 thf(3937,axiom,((! [A:code_integer,B:nat]: ((comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ (minus_8373710615458151222nteger @ A @ (semiri4939895301339042750nteger @ B)) @ one_one_Code_integer) @ B) = (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8343_pochhammer__minus_H)). 159.59/70.65 thf(20916,plain,((! [A:code_integer,B:nat]: ((comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ (minus_8373710615458151222nteger @ A @ (semiri4939895301339042750nteger @ B)) @ one_one_Code_integer) @ B) = (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3937])). 159.59/70.65 thf(3122,axiom,((! [A:nat,B:num,C:nat]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6635_of__nat__less__numeral__power__cancel__iff)). 159.59/70.65 thf(18295,plain,((! [A:nat,B:num,C:nat]: ((ord_le6747313008572928689nteger @ (semiri4939895301339042750nteger @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3122])). 159.59/70.65 thf(1356,axiom,((! [A:complex]: ((A != zero_zero_complex) => ((divide1717551699836669952omplex @ A @ A) = one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1662_div__self)). 159.59/70.65 thf(12630,plain,((! [A:complex]: ((~ (A = zero_zero_complex)) => ((divide1717551699836669952omplex @ A @ A) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356])). 159.59/70.65 thf(1116,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 @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4540_minf_I9_J)). 159.59/70.65 thf(11835,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116])). 159.59/70.65 thf(3920,axiom,((ord_less_int = (^ [A:int,B:int]: (~ (ord_less_eq_int @ B @ A) & (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3101_order_Ostrict__iff__not)). 159.59/70.65 thf(20863,plain,(((ord_less_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)],[3920])). 159.59/70.65 thf(8185,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/sandbox/benchmark/theBenchmark.p',fact_170_valid__insert__both__member__options__add)). 159.59/70.65 thf(36423,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)],[8185])). 159.59/70.65 thf(5733,axiom,((! [A:nat,B:nat,C:int]: ((((ord_less_int @ (power_power_int @ C @ B) @ (power_power_int @ C @ A)) <= (ord_less_int @ C @ one_one_int)) <= (ord_less_int @ zero_zero_int @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2456_power__strict__decreasing)). 159.59/70.65 thf(27238,plain,((! [A:nat,B:nat,C:int]: ((ord_less_int @ (power_power_int @ C @ B) @ (power_power_int @ C @ A)) | ~ (ord_less_int @ C @ one_one_int) | ~ (ord_less_int @ zero_zero_int @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5733])). 159.59/70.65 thf(6826,axiom,((! [A:num,B:(int > num),C:int,D:int]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_int @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) <= (ord_less_eq_int @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2686_order__subst1)). 159.59/70.65 thf(31531,plain,((! [A:num,B:(int > num),C:int,D:int]: ((ord_less_eq_num @ A @ (B @ C)) => ((ord_less_eq_int @ C @ D) => ((ord_less_eq_num @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_eq_num @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_int @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6826])). 159.59/70.65 thf(1239,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (B @ D)) @ one_one_real))) => ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (groups129246275422532515t_real @ B @ A) @ (groups129246275422532515t_real @ C @ A))) @ (groups6591440286371151544t_real @ (^ [D:nat]: (real_V7735802525324610683m_real @ (minus_minus_real @ (B @ D) @ (C @ D)))) @ A)) <= (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (C @ D)) @ one_one_real))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8830_norm__prod__diff)). 159.59/70.65 thf(12262,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (B @ D)) @ one_one_real))) => ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (minus_minus_real @ (groups129246275422532515t_real @ (B) @ A) @ (groups129246275422532515t_real @ (C) @ A))) @ (groups6591440286371151544t_real @ (^ [D:nat]: (real_V7735802525324610683m_real @ (minus_minus_real @ (B @ D) @ (C @ D)))) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V7735802525324610683m_real @ (C @ D)) @ one_one_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239])). 159.59/70.65 thf(1384,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/sandbox/benchmark/theBenchmark.p',fact_2296_sum__squares__le__zero__iff)). 159.59/70.65 thf(12771,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)],[1384])). 159.59/70.65 thf(2816,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ A @ C)) = ((A = zero_zero_complex) | (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1554_divide__cancel__left)). 159.59/70.65 thf(17308,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ A @ C)) = ((A = zero_zero_complex) | (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2816])). 159.59/70.65 thf(6175,axiom,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_num @ A @ C) <= (ord_less_num @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2860_order__less__trans)). 159.59/70.65 thf(29008,plain,((! [A:num,B:num,C:num]: ((ord_less_num @ A @ B) => ((ord_less_num @ A @ C) | ~ (ord_less_num @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6175])). 159.59/70.65 thf(6760,axiom,((! [A:nat]: ((bit_se1148574629649215175it_nat @ A @ zero_zero_nat) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6352_bit__0)). 159.59/70.65 thf(31311,plain,((! [A:nat]: ((bit_se1148574629649215175it_nat @ A @ zero_zero_nat) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6760])). 159.59/70.65 thf(3032,axiom,((! [A:int,B:int]: ((plus_plus_int @ A @ (plus_plus_int @ (uminus_uminus_int @ A) @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4644_add__minus__cancel)). 159.59/70.65 thf(17997,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)],[3032])). 159.59/70.65 thf(2783,axiom,((plus_plus_complex = (^ [A:complex,B:complex]: (plus_plus_complex @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_add_Ocommute)). 159.59/70.65 thf(17215,plain,(((plus_plus_complex) = (^ [A:complex,B:complex]: (plus_plus_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2783])). 159.59/70.65 thf(2558,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/sandbox/benchmark/theBenchmark.p',fact_1438_divide__divide__times__eq)). 159.59/70.65 thf(16475,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)],[2558])). 159.59/70.65 thf(707,axiom,((! [A:real,B:real,C:num]: ((ord_less_real @ (divide_divide_real @ A @ B) @ (numeral_numeral_real @ C)) = (((((~ (ord_less_real @ B @ zero_zero_real)) => (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ C))) & ((ord_less_real @ (times_times_real @ (numeral_numeral_real @ C) @ B) @ A) <= (ord_less_real @ B @ zero_zero_real))) <= (~ (ord_less_real @ zero_zero_real @ B))) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ C) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2442_divide__less__eq__numeral_I1_J)). 159.59/70.65 thf(10531,plain,((! [A:real,B:real,C:num]: ((ord_less_real @ (divide_divide_real @ A @ B) @ (numeral_numeral_real @ C)) = (((((~ (ord_less_real @ B @ zero_zero_real)) => (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ C))) & ((ord_less_real @ (times_times_real @ (numeral_numeral_real @ C) @ B) @ A) | ~ (ord_less_real @ B @ zero_zero_real))) | (ord_less_real @ zero_zero_real @ B)) & ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ A @ (times_times_real @ (numeral_numeral_real @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[707])). 159.59/70.65 thf(5904,axiom,((! [A:(nat > (nat > $o)),B:set_nat,C:(nat > nat),D:(nat > nat)]: (((((A @ (groups708209901874060359at_nat @ C @ B) @ (groups708209901874060359at_nat @ D @ B)) <= (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E))))) <= (finite_finite_nat @ B)) <= (! [E:nat,F:nat,G:nat,H:nat]: (((A @ F @ H) & (A @ E @ G)) => (A @ (times_times_nat @ E @ F) @ (times_times_nat @ G @ H))))) <= (A @ one_one_nat @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8567_prod_Orelated)). 159.59/70.65 thf(28058,plain,((! [A:(nat > (nat > $o)),B:set_nat,C:(nat > nat),D:(nat > nat)]: ((A @ (groups708209901874060359at_nat @ (C) @ B) @ (groups708209901874060359at_nat @ (D) @ B)) | ~ (! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) | ~ (finite_finite_nat @ B) | ~ (! [E:nat,F:nat,G:nat,H:nat]: (((A @ F @ H) & (A @ E @ G)) => (A @ (times_times_nat @ E @ F) @ (times_times_nat @ G @ H)))) | ~ (A @ one_one_nat @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5904])). 159.59/70.65 thf(5058,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_Suc__le__lessD)). 159.59/70.65 thf(24765,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)],[5058])). 159.59/70.65 thf(1012,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => (((divide_divide_int @ A @ B) = (uminus_uminus_int @ one_one_int)) <= (ord_less_eq_int @ (plus_plus_int @ A @ B) @ zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5323_div__pos__neg__trivial)). 159.59/70.65 thf(11486,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => (((divide_divide_int @ A @ B) = (uminus_uminus_int @ one_one_int)) | ~ (ord_less_eq_int @ (plus_plus_int @ A @ B) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012])). 159.59/70.65 thf(2517,axiom,((! [A:code_integer,B:nat]: (((bit_se9216721137139052372nteger @ (plus_p5714425477246183910nteger @ one_one_Code_integer @ A) @ B) = ((B = zero_zero_nat) | (bit_se9216721137139052372nteger @ A @ B))) <= (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6449_even__bit__succ__iff)). 159.59/70.65 thf(16354,plain,((! [A:code_integer,B:nat]: (((bit_se9216721137139052372nteger @ (plus_p5714425477246183910nteger @ one_one_Code_integer @ A) @ B) = ((B = zero_zero_nat) | (bit_se9216721137139052372nteger @ A @ B))) | ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2517])). 159.59/70.65 thf(3200,axiom,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5191_neg__numeral__less__one)). 159.59/70.65 thf(18547,plain,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3200])). 159.59/70.65 thf(4052,axiom,((! [A:nat,B:nat]: ((semiri8010041392384452111omplex @ (plus_plus_nat @ A @ B)) = (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ (semiri8010041392384452111omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6531_of__nat__add)). 159.59/70.65 thf(21260,plain,((! [A:nat,B:nat]: ((semiri8010041392384452111omplex @ (plus_plus_nat @ A @ B)) = (plus_plus_complex @ (semiri8010041392384452111omplex @ A) @ (semiri8010041392384452111omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4052])). 159.59/70.65 thf(7566,axiom,((! [A:num,B:num]: ((plus_plus_num @ (bit0 @ A) @ (bit0 @ B)) = (bit0 @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_semiring__norm_I6_J)). 159.59/70.65 thf(34387,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)],[7566])). 159.59/70.65 thf(2619,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/sandbox/benchmark/theBenchmark.p',fact_8548_prod_Oshift__bounds__cl__nat__ivl)). 159.59/70.65 thf(16692,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)],[2619])). 159.59/70.65 thf(97,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (tanh_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5431_tanh__real__nonneg__iff)). 159.59/70.65 thf(8547,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)],[97])). 159.59/70.65 thf(3633,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/sandbox/benchmark/theBenchmark.p',fact_5434_divide__le__0__abs__iff)). 159.59/70.65 thf(19920,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)],[3633])). 159.59/70.65 thf(6620,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ A @ (semiri1408675320244567234ct_nat @ B)) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8152_dvd__fact)). 159.59/70.65 thf(30674,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (semiri1408675320244567234ct_nat @ B)) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6620])). 159.59/70.65 thf(7031,axiom,((bot_bot_nat = zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2628_bot__nat__def)). 159.59/70.65 thf(32449,plain,((bot_bot_nat = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7031])). 159.59/70.65 thf(506,axiom,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (times_times_int @ (plus_plus_int @ A @ (semiri1314217659103216013at_int @ B)) @ (comm_s4660882817536571857er_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8274_pochhammer__rec_H)). 159.59/70.65 thf(9863,plain,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (times_times_int @ (plus_plus_int @ A @ (semiri1314217659103216013at_int @ B)) @ (comm_s4660882817536571857er_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])). 159.59/70.65 thf(5881,axiom,((! [A:(nat > complex),B:nat,C:(nat > complex)]: ((! [D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (A @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ B)) = (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (C @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ B)))) = (! [D:nat]: (((A @ D) = (C @ D)) <= (ord_less_eq_nat @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8755_polyfun__eq__coeffs)). 159.59/70.65 thf(27982,plain,((! [A:(nat > complex),B:nat,C:(nat > complex)]: ((! [D:complex]: ((groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (A @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ B)) = (groups2073611262835488442omplex @ (^ [E:nat]: (times_times_complex @ (C @ E) @ (power_power_complex @ D @ E))) @ (set_ord_atMost_nat @ B)))) = (! [D:nat]: (((A @ D) = (C @ D)) | ~ (ord_less_eq_nat @ D @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5881])). 159.59/70.65 thf(3519,axiom,((! [A:real,B:real]: ((A != zero_zero_real) => ((abs_abs_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (abs_abs_real @ B) @ (abs_abs_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5531_nonzero__abs__divide)). 159.59/70.65 thf(19549,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real)) => ((abs_abs_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (abs_abs_real @ B) @ (abs_abs_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3519])). 159.59/70.65 thf(6090,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/sandbox/benchmark/theBenchmark.p',fact_3437_not__mod2__eq__Suc__0__eq__0)). 159.59/70.65 thf(28719,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)],[6090])). 159.59/70.65 thf(4859,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se2925701944663578781it_nat @ A @ (bit_se1412395901928357646or_nat @ B @ C)) = (bit_se1412395901928357646or_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ (bit_se2925701944663578781it_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5962_take__bit__or)). 159.59/70.65 thf(24057,plain,((! [A:nat,B:nat,C:nat]: ((bit_se2925701944663578781it_nat @ A @ (bit_se1412395901928357646or_nat @ B @ C)) = (bit_se1412395901928357646or_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ (bit_se2925701944663578781it_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4859])). 159.59/70.65 thf(6884,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/sandbox/benchmark/theBenchmark.p',fact_6444_real__sqrt__sum__squares__ge2)). 159.59/70.65 thf(31807,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)],[6884])). 159.59/70.65 thf(6413,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => (((divide_divide_nat @ A @ (times_times_nat @ A @ B)) = (divide_divide_nat @ one_one_nat @ B)) <= (dvd_dvd_nat @ B @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4196_is__unit__div__mult__cancel__left)). 159.59/70.65 thf(29909,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => (((divide_divide_nat @ A @ (times_times_nat @ A @ B)) = (divide_divide_nat @ one_one_nat @ B)) | ~ (dvd_dvd_nat @ B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6413])). 159.59/70.65 thf(2139,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ (times_times_complex @ B @ A)) = (divide1717551699836669952omplex @ one_one_complex @ B)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1753_nonzero__divide__mult__cancel__right)). 159.59/70.65 thf(15154,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ (times_times_complex @ B @ A)) = (divide1717551699836669952omplex @ one_one_complex @ B)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2139])). 159.59/70.65 thf(2363,axiom,((set_ord_lessThan_nat = (^ [A:nat]: (set_nat2 @ (upt @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10131_atLeast__upt)). 159.59/70.65 thf(15839,plain,(((set_ord_lessThan_nat) = (^ [A:nat]: (set_nat2 @ (upt @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2363])). 159.59/70.65 thf(2012,axiom,((! [A:set_nat]: (((! [B:nat]: ((? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ B @ C))) <= (member_nat @ B @ A))) => (~ (finite_finite_nat @ A))) <= (A != bot_bot_set_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4281_infinite__growing)). 159.59/70.65 thf(14755,plain,((! [A:set_nat]: (((! [B:nat]: (? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ B @ C)) | ~ (member_nat @ B @ A))) => (~ (finite_finite_nat @ A))) | (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2012])). 159.59/70.65 thf(3557,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_eq_real @ C @ (log @ A @ B)) = (ord_less_eq_real @ (powr_real @ A @ C) @ B)) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7271_le__log__iff)). 159.59/70.65 thf(19665,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => (((ord_less_eq_real @ C @ (log @ A @ B)) = (ord_less_eq_real @ (powr_real @ A @ C) @ B)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3557])). 159.59/70.65 thf(6587,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = A) = ((divide_divide_nat @ A @ B) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3477_mod__eq__self__iff__div__eq__0)). 159.59/70.65 thf(30550,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)],[6587])). 159.59/70.65 thf(3866,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/sandbox/benchmark/theBenchmark.p',fact_7113_cos__add)). 159.59/70.65 thf(20699,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)],[3866])). 159.59/70.65 thf(2390,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arctan @ A)) & ((tan_real @ (arctan @ A)) = A) & (ord_less_real @ (arctan @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7307_arctan)). 159.59/70.65 thf(15925,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ (arctan @ A)) & ((tan_real @ (arctan @ A)) = A) & (ord_less_real @ (arctan @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2390])). 159.59/70.65 thf(6180,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1889_zero__neq__one)). 159.59/70.65 thf(29023,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6180])). 159.59/70.65 thf(2721,axiom,((! [A:int,B:int,C:int,D:int,E:int]: ((A != zero_zero_int) => (((D != E) & (B = C)) => ((plus_plus_int @ B @ (times_times_int @ A @ D)) != (plus_plus_int @ C @ (times_times_int @ A @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4560_add__scale__eq__noteq)). 159.59/70.65 thf(17027,plain,((! [A:int,B:int,C:int,D:int,E:int]: ((~ (A = zero_zero_int)) => ((~ (D = E) & (B = C)) => (~ ((plus_plus_int @ B @ (times_times_int @ A @ D)) = (plus_plus_int @ C @ (times_times_int @ A @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2721])). 159.59/70.65 thf(5499,axiom,((! [A:num,B:num,C:(num > int),D:int]: ((ord_less_eq_num @ A @ B) => (((C @ B) = D) => ((ord_less_eq_int @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2648_ord__le__eq__subst)). 159.59/70.65 thf(26450,plain,((! [A:num,B:num,C:(num > int),D:int]: ((ord_less_eq_num @ A @ B) => (((C @ B) = D) => ((ord_less_eq_int @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5499])). 159.59/70.65 thf(4612,axiom,((! [A:nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3801_dvd__1__left)). 159.59/70.65 thf(23193,plain,((! [A:nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4612])). 159.59/70.65 thf(3555,axiom,((! [A:int,B:int]: (((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) <= (ord_less_int @ B @ zero_zero_int)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2097_mult__pos__neg)). 159.59/70.65 thf(19656,plain,((! [A:int,B:int]: ((ord_less_int @ (times_times_int @ A @ B) @ zero_zero_int) | ~ (ord_less_int @ B @ zero_zero_int) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3555])). 159.59/70.65 thf(1553,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/sandbox/benchmark/theBenchmark.p',fact_7153_sin__cos__le1)). 159.59/70.65 thf(13299,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)],[1553])). 159.59/70.65 thf(1691,axiom,((! [A:real,B:(nat > real)]: ((summable_real @ (^ [C:nat]: (times_times_real @ A @ (B @ C)))) => ((summable_real @ B) <= (A != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7037_summable__mult__D)). 159.59/70.65 thf(13724,plain,((! [A:real,B:(nat > real)]: ((summable_real @ (^ [C:nat]: (times_times_real @ A @ (B @ C)))) => ((summable_real @ (B)) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691])). 159.59/70.65 thf(3343,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C))) <= (A = (plus_plus_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_group__cancel_Oadd2)). 159.59/70.65 thf(19001,plain,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ D @ A) = (plus_plus_int @ B @ (plus_plus_int @ D @ C))) | ~ (A = (plus_plus_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3343])). 159.59/70.65 thf(5963,axiom,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) <= ((vEBT_vebt_mint @ A) = none_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_minminNull)). 159.59/70.65 thf(28321,plain,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) | ~ ((vEBT_vebt_mint @ A) = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5963])). 159.59/70.65 thf(2379,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/sandbox/benchmark/theBenchmark.p',fact_4024_dvd__power__same)). 159.59/70.65 thf(15890,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)],[2379])). 159.59/70.65 thf(6393,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((root @ A @ (power_power_real @ B @ A)) = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9525_real__root__power__cancel)). 159.59/70.65 thf(29818,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((root @ A @ (power_power_real @ B @ A)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6393])). 159.59/70.65 thf(360,axiom,((! [A:$o,B:$o]: ((zero_n2684676970156552555ol_int @ ((A) | (B))) = (ord_max_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4338_of__bool__or__iff)). 159.59/70.65 thf(9363,plain,((! [A:$o,B:$o]: ((zero_n2684676970156552555ol_int @ ((A) | (B))) = (ord_max_int @ (zero_n2684676970156552555ol_int @ A) @ (zero_n2684676970156552555ol_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])). 159.59/70.65 thf(1610,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ (divide_divide_int @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3868_unit__div__mult__self)). 159.59/70.65 thf(13481,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => ((times_times_int @ (divide_divide_int @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610])). 159.59/70.65 thf(4450,axiom,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => (((~ (member_nat @ B @ A)) => ((groups129246275422532515t_real @ C @ (insert_nat @ B @ A)) = (times_times_real @ (C @ B) @ (groups129246275422532515t_real @ C @ A)))) & (((groups129246275422532515t_real @ C @ (insert_nat @ B @ A)) = (groups129246275422532515t_real @ C @ A)) <= (member_nat @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8575_prod_Oinsert__if)). 159.59/70.65 thf(22501,plain,((! [A:set_nat,B:nat,C:(nat > real)]: ((finite_finite_nat @ A) => (((~ (member_nat @ B @ A)) => ((groups129246275422532515t_real @ (C) @ (insert_nat @ B @ A)) = (times_times_real @ (C @ B) @ (groups129246275422532515t_real @ (C) @ A)))) & (((groups129246275422532515t_real @ (C) @ (insert_nat @ B @ A)) = (groups129246275422532515t_real @ (C) @ A)) | ~ (member_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4450])). 159.59/70.65 thf(5375,axiom,((! [A:nat,B:(nat > int),C:int]: ((! [D:nat]: ((ord_less_nat @ D @ A) => (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_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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5741_nat0__intermed__int__val)). 159.59/70.65 thf(25969,plain,((! [A:nat,B:(nat > int),C:int]: ((! [D:nat]: ((ord_less_nat @ D @ A) => (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_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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5375])). 159.59/70.65 thf(3636,axiom,((ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2323_zero__less__two)). 159.59/70.65 thf(19929,plain,((ord_less_int @ zero_zero_int @ (plus_plus_int @ one_one_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3636])). 159.59/70.65 thf(7606,axiom,((bit_se2925701944663578781it_nat = (^ [A:nat,B:nat]: (modulo_modulo_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5271_take__bit__nat__def)). 159.59/70.65 thf(34575,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)],[7606])). 159.59/70.65 thf(2273,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/sandbox/benchmark/theBenchmark.p',fact_7182_sin__diff__sin)). 159.59/70.65 thf(15580,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)],[2273])). 159.59/70.65 thf(3361,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/sandbox/benchmark/theBenchmark.p',fact_7275_ln__powr__bound)). 159.59/70.65 thf(19055,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)],[3361])). 159.59/70.65 thf(5974,axiom,((! [A:$o,B:$o]: ((vEBT_vebt_delete @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (vEBT_Leaf @ A @ ($false))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1807_vebt__delete_Osimps_I2_J)). 159.59/70.65 thf(28357,plain,((! [A:$o,B:$o]: ((vEBT_vebt_delete @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (vEBT_Leaf @ A @ ($false))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5974])). 159.59/70.65 thf(6918,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_eq__imp__le)). 159.59/70.65 thf(31921,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6918])). 159.59/70.65 thf(4186,axiom,(((ring_17405671764205052669omplex @ one_one_int) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5771_of__int__1)). 159.59/70.65 thf(21676,plain,(((ring_17405671764205052669omplex @ one_one_int) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4186])). 159.59/70.65 thf(6132,axiom,((! [A:num]: ((plus_plus_complex @ (numera6690914467698888265omplex @ A) @ one_one_complex) = (numera6690914467698888265omplex @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_numeral__plus__one)). 159.59/70.65 thf(28857,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)],[6132])). 159.59/70.65 thf(6634,axiom,((! [A:real]: (((sqrt @ A) = one_one_real) = (A = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6314_real__sqrt__eq__1__iff)). 159.59/70.65 thf(30725,plain,((! [A:real]: (((sqrt @ A) = one_one_real) = (A = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6634])). 159.59/70.65 thf(8046,axiom,((! [A:nat,B:nat,C:nat]: ((((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) <= (A = 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/sandbox/benchmark/theBenchmark.p',fact_1727_nat__mult__div__cancel__disj)). 159.59/70.65 thf(35973,plain,((! [A:nat,B:nat,C:nat]: ((((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) | ~ (A = 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)],[8046])). 159.59/70.65 thf(7173,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/sandbox/benchmark/theBenchmark.p',fact_3534_minus__mod__eq__mult__div)). 159.59/70.65 thf(33033,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)],[7173])). 159.59/70.65 thf(1174,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (((plus_plus_real @ A @ B) = zero_zero_real) = ((B = zero_zero_real) & (A = zero_zero_real)))) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2017_add__nonpos__eq__0__iff)). 159.59/70.65 thf(12014,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => (((plus_plus_real @ A @ B) = zero_zero_real) = ((B = zero_zero_real) & (A = zero_zero_real)))) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174])). 159.59/70.65 thf(4770,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1912_less__zeroE)). 159.59/70.65 thf(23742,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4770])). 159.59/70.65 thf(4999,axiom,((! [A:int]: ((power_power_int @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1688_power__Suc0__right)). 159.59/70.65 thf(24555,plain,((! [A:int]: ((power_power_int @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4999])). 159.59/70.65 thf(2153,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/sandbox/benchmark/theBenchmark.p',fact_4782_semiring__norm_I168_J)). 159.59/70.65 thf(15196,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)],[2153])). 159.59/70.65 thf(4133,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (minus_minus_complex @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_complex @ (A @ zero_zero_nat) @ (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7960_sum__lessThan__telescope_H)). 159.59/70.65 thf(21504,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (minus_minus_complex @ (A @ C) @ (A @ (suc @ C)))) @ (set_ord_lessThan_nat @ B)) = (minus_minus_complex @ (A @ zero_zero_nat) @ (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4133])). 159.59/70.65 thf(2347,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/sandbox/benchmark/theBenchmark.p',fact_3813_dvd__mult__cancel__left)). 159.59/70.65 thf(15790,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)],[2347])). 159.59/70.65 thf(2050,axiom,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ A @ C) | (bit_se1146084159140164899it_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6380_bit__or__int__iff)). 159.59/70.65 thf(14868,plain,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ A @ C) | (bit_se1146084159140164899it_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2050])). 159.59/70.65 thf(2329,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) <= (ord_less_real @ zero_zero_real @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2065_mult__strict__right__mono)). 159.59/70.65 thf(15736,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) | ~ (ord_less_real @ zero_zero_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2329])). 159.59/70.65 thf(4141,axiom,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: ((if_Pro6206227464963214023at_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T)). 159.59/70.65 thf(21537,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)],[4141])). 159.59/70.65 thf(6359,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/sandbox/benchmark/theBenchmark.p',fact_1757_power__eq__0__iff)). 159.59/70.65 thf(29671,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)],[6359])). 159.59/70.65 thf(8021,axiom,((~ (! [A:nat]: ((some_nat @ A) != (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ summin)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lx_O_ASome_Alx_A_061_Avebt__mint_A_ItreeList_A_B_Asummin_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)). 159.59/70.65 thf(35880,plain,((~ (! [A:nat]: ~ ((some_nat @ A) = (vEBT_vebt_mint @ (nth_VEBT_VEBT @ treeList @ summin)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8021])). 159.59/70.65 thf(3606,axiom,((! [A:nat,B:int]: ((bit_se547839408752420682it_nat @ A @ (nat2 @ B)) = (nat2 @ (bit_se545348938243370406it_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9555_push__bit__nat__eq)). 159.59/70.65 thf(19833,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)],[3606])). 159.59/70.65 thf(558,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/sandbox/benchmark/theBenchmark.p',fact_9639_cmod__plus__Re__le__0__iff)). 159.59/70.65 thf(10028,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)],[558])). 159.59/70.65 thf(1978,axiom,((! [A:real,B:real,C:real]: (((((divide_divide_real @ B @ A) = (divide_divide_real @ C @ A)) = (B = C)) <= (dvd_dvd_real @ A @ C)) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4009_dvd__div__eq__iff)). 159.59/70.65 thf(14631,plain,((! [A:real,B:real,C:real]: ((((divide_divide_real @ B @ A) = (divide_divide_real @ C @ A)) = (B = C)) | ~ (dvd_dvd_real @ A @ C) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1978])). 159.59/70.65 thf(2800,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)) & ((ord_less_int @ B @ zero_zero_int) => (ord_less_eq_int @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2254_mult__le__cancel__right)). 159.59/70.65 thf(17262,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)) & ((ord_less_int @ B @ zero_zero_int) => (ord_less_eq_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2800])). 159.59/70.65 thf(115,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((((dvd_dvd_Code_integer @ (divide6298287555418463151nteger @ B @ A) @ C) = (dvd_dvd_Code_integer @ B @ (times_3573771949741848930nteger @ C @ A))) <= (dvd_dvd_Code_integer @ A @ B)) <= (A != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4144_div__dvd__iff__mult)). 159.59/70.65 thf(8602,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((dvd_dvd_Code_integer @ (divide6298287555418463151nteger @ B @ A) @ C) = (dvd_dvd_Code_integer @ B @ (times_3573771949741848930nteger @ C @ A))) | ~ (dvd_dvd_Code_integer @ A @ B) | (A = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[115])). 159.59/70.65 thf(6294,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (power_power_nat @ A @ B)) = (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6558_of__nat__power)). 159.59/70.65 thf(29474,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)],[6294])). 159.59/70.65 thf(5212,axiom,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Collect__mem__eq)). 159.59/70.65 thf(25310,plain,((! [A:set_nat]: ((collect_nat @ (^ [B:nat]: (member_nat @ B @ A))) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5212])). 159.59/70.65 thf(6552,axiom,((! [A:real,B:num]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_eq_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6998_ceiling__le__neg__numeral)). 159.59/70.65 thf(30437,plain,((! [A:real,B:num]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_eq_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6552])). 159.59/70.65 thf(7454,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/sandbox/benchmark/theBenchmark.p',fact_5864_of__int__le__neg__numeral__power__cancel__iff)). 159.59/70.65 thf(34002,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)],[7454])). 159.59/70.65 thf(3667,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((C != A) <= (ord_le72135733267957522d_enat @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4472_minf_I4_J)). 159.59/70.65 thf(20030,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: (~ (C = A) | ~ (ord_le72135733267957522d_enat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3667])). 159.59/70.65 thf(6910,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/sandbox/benchmark/theBenchmark.p',fact_4154_unit__div__eq__0__iff)). 159.59/70.65 thf(31888,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)],[6910])). 159.59/70.65 thf(3210,axiom,((! [A:num]: ((neg_nu8557863876264182079omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5803_dbl__inc__simps_I5_J)). 159.59/70.65 thf(18574,plain,((! [A:num]: ((neg_nu8557863876264182079omplex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3210])). 159.59/70.65 thf(3246,axiom,((! [A:real,B:real,C:real,D:real]: (((((ord_less_eq_real @ C @ D) => (ord_less_real @ (divide_divide_real @ A @ D) @ (divide_divide_real @ B @ C))) <= (ord_less_real @ zero_zero_real @ C)) <= (ord_less_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2292_frac__less)). 159.59/70.65 thf(18692,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => (ord_less_real @ (divide_divide_real @ A @ D) @ (divide_divide_real @ B @ C))) | ~ (ord_less_real @ zero_zero_real @ C) | ~ (ord_less_real @ A @ B) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3246])). 159.59/70.65 thf(440,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/sandbox/benchmark/theBenchmark.p',fact_4556_diff__shunt__var)). 159.59/70.65 thf(9632,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)],[440])). 159.59/70.65 thf(7357,axiom,((! [A:num,B:real,C:real]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (divide_divide_real @ B @ C)) = (((C = zero_zero_real) => ((uminus_uminus_real @ (numeral_numeral_real @ A)) = zero_zero_real)) & (((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) = B) <= (C != zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5243_eq__divide__eq__numeral_I2_J)). 159.59/70.65 thf(33694,plain,((! [A:num,B:real,C:real]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (divide_divide_real @ B @ C)) = (((C = zero_zero_real) => ((uminus_uminus_real @ (numeral_numeral_real @ A)) = zero_zero_real)) & (((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) = B) | (C = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7357])). 159.59/70.65 thf(6981,axiom,(((semiri5044797733671781792omplex @ one_one_nat) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8050_fact__1)). 159.59/70.65 thf(32271,plain,(((semiri5044797733671781792omplex @ one_one_nat) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6981])). 159.59/70.65 thf(5297,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/sandbox/benchmark/theBenchmark.p',fact_1484_mult__cancel__left)). 159.59/70.65 thf(25606,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)],[5297])). 159.59/70.65 thf(6770,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/sandbox/benchmark/theBenchmark.p',fact_3434_not__mod__2__eq__1__eq__0)). 159.59/70.65 thf(31353,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)],[6770])). 159.59/70.65 thf(969,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ C)) = (((ord_less_eq_real @ (times_times_real @ A @ C) @ B) <= (ord_less_real @ zero_zero_real @ 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 @ B @ (times_times_real @ A @ C)))) <= (~ (ord_less_real @ zero_zero_real @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2435_le__divide__eq)). 159.59/70.65 thf(11351,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ (divide_divide_real @ B @ C)) = (((ord_less_eq_real @ (times_times_real @ A @ C) @ B) | ~ (ord_less_real @ zero_zero_real @ 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 @ B @ (times_times_real @ A @ C)))) | (ord_less_real @ zero_zero_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[969])). 159.59/70.65 thf(4370,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2670_order__eq__refl)). 159.59/70.65 thf(22247,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4370])). 159.59/70.65 thf(1986,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/sandbox/benchmark/theBenchmark.p',fact_9530_log__root)). 159.59/70.65 thf(14668,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)],[1986])). 159.59/70.65 thf(5862,axiom,((! [A:option4927543243414619207at_nat]: ((! [B:product_prod_nat_nat]: (A != (some_P7363390416028606310at_nat @ B))) = (A = none_P5556105721700978146at_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_not__Some__eq)). 159.59/70.65 thf(27911,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)],[5862])). 159.59/70.65 thf(5323,axiom,((! [A:nat,B:nat,C:(nat > nat),D:(nat > nat)]: (((ord_less_eq_nat @ B @ A) => ((groups3542108847815614940at_nat @ (^ [E:nat]: (if_nat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_nat @ (E = B) @ zero_zero_nat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups3542108847815614940at_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 @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8939_sum_Ozero__middle)). 159.59/70.65 thf(25723,plain,((! [A:nat,B:nat,C:(nat > nat),D:(nat > nat)]: (((ord_less_eq_nat @ B @ A) => ((groups3542108847815614940at_nat @ (^ [E:nat]: (if_nat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_nat @ (E = B) @ zero_zero_nat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups3542108847815614940at_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 @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5323])). 159.59/70.65 thf(7897,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A) => ((bit_se1148574629649215175it_nat @ A @ B) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6423_stable__imp__bit__iff__odd)). 159.59/70.65 thf(35497,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A) => ((bit_se1148574629649215175it_nat @ A @ B) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7897])). 159.59/70.65 thf(438,axiom,((! [A:code_integer]: ((((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger) <= (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) & (((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = one_one_Code_integer) <= (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4251_mod2__eq__if)). 159.59/70.65 thf(9622,plain,((! [A:code_integer]: ((((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger) | ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) & (((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = one_one_Code_integer) | (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])). 159.59/70.65 thf(6131,axiom,((! [A:complex,B:complex,C:num]: (((divide1717551699836669952omplex @ A @ B) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = (((B = zero_zero_complex) => ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex)) & ((B != zero_zero_complex) => (A = (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5246_divide__eq__eq__numeral_I2_J)). 159.59/70.65 thf(28854,plain,((! [A:complex,B:complex,C:num]: (((divide1717551699836669952omplex @ A @ B) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = (((B = zero_zero_complex) => ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex)) & ((~ (B = zero_zero_complex)) => (A = (times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6131])). 159.59/70.65 thf(803,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((minus_minus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ D)) = (plus_plus_complex @ (times_times_complex @ A @ (minus_minus_complex @ B @ D)) @ (times_times_complex @ (minus_minus_complex @ A @ C) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_842_mult__diff__mult)). 159.59/70.65 thf(10841,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((minus_minus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ D)) = (plus_plus_complex @ (times_times_complex @ A @ (minus_minus_complex @ B @ D)) @ (times_times_complex @ (minus_minus_complex @ A @ C) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[803])). 159.59/70.65 thf(371,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/sandbox/benchmark/theBenchmark.p',fact_9596_bit__minus__int__iff)). 159.59/70.65 thf(9406,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)],[371])). 159.59/70.65 thf(6161,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => (ord_less_nat @ B @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2386_power__gt__expt)). 159.59/70.65 thf(28950,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => (ord_less_nat @ B @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6161])). 159.59/70.65 thf(7798,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/sandbox/benchmark/theBenchmark.p',fact_3575_set__bit__Suc)). 159.59/70.65 thf(35177,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)],[7798])). 159.59/70.65 thf(4964,axiom,((! [A:real,B:real]: (((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))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2300_mult__right__le__one__le)). 159.59/70.65 thf(24443,plain,((! [A:real,B:real]: (((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))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4964])). 159.59/70.65 thf(7748,axiom,((! [A:num]: ((divide_divide_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5615_numeral__Bit1__div__2)). 159.59/70.65 thf(35036,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)],[7748])). 159.59/70.65 thf(8099,axiom,(((semiri5044797733671781792omplex @ (numeral_numeral_nat @ (bit0 @ one))) = (numera6690914467698888265omplex @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8066_fact__2)). 159.59/70.65 thf(36142,plain,(((semiri5044797733671781792omplex @ (numeral_numeral_nat @ (bit0 @ one))) = (numera6690914467698888265omplex @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8099])). 159.59/70.65 thf(5363,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/sandbox/benchmark/theBenchmark.p',fact_5863_neg__numeral__power__eq__of__int__cancel__iff)). 159.59/70.65 thf(25927,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)],[5363])). 159.59/70.65 thf(6004,axiom,(((nat2 @ (numeral_numeral_int @ (bit0 @ one))) = (suc @ (suc @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9464_nat__2)). 159.59/70.65 thf(28456,plain,(((nat2 @ (numeral_numeral_int @ (bit0 @ one))) = (suc @ (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6004])). 159.59/70.65 thf(3394,axiom,((! [A:code_integer,B:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => (((modulo364778990260209775nteger @ (plus_p5714425477246183910nteger @ one_one_Code_integer @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (plus_p5714425477246183910nteger @ one_one_Code_integer @ (modulo364778990260209775nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3786_even__succ__mod__exp)). 159.59/70.65 thf(19164,plain,((! [A:code_integer,B:nat]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => (((modulo364778990260209775nteger @ (plus_p5714425477246183910nteger @ one_one_Code_integer @ A) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) = (plus_p5714425477246183910nteger @ one_one_Code_integer @ (modulo364778990260209775nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3394])). 159.59/70.65 thf(4682,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/sandbox/benchmark/theBenchmark.p',fact_380_power__add)). 159.59/70.65 thf(23437,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)],[4682])). 159.59/70.65 thf(7777,axiom,((! [A:num]: ((pow @ A @ one) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5131_pow_Osimps_I1_J)). 159.59/70.65 thf(35120,plain,((! [A:num]: ((pow @ A @ one) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7777])). 159.59/70.65 thf(815,axiom,((! [A:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2000444600071755411sk_int @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6123_semiring__bit__operations__class_Oeven__mask__iff)). 159.59/70.65 thf(10884,plain,((! [A:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se2000444600071755411sk_int @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[815])). 159.59/70.65 thf(1577,axiom,((! [A:int,B:real]: ((ord_less_int @ A @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8301_less__floor__iff)). 159.59/70.65 thf(13374,plain,((! [A:int,B:real]: ((ord_less_int @ A @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577])). 159.59/70.65 thf(2041,axiom,((! [A:num]: ((numeral_numeral_real @ (bit0 @ A)) = (plus_plus_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_numeral__Bit0)). 159.59/70.65 thf(14838,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)],[2041])). 159.59/70.65 thf(7845,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/sandbox/benchmark/theBenchmark.p',fact_189_power2__sum)). 159.59/70.65 thf(35328,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)],[7845])). 159.59/70.65 thf(4677,axiom,((ord_less_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6411_sqrt2__less__2)). 159.59/70.65 thf(23424,plain,((ord_less_real @ (sqrt @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4677])). 159.59/70.65 thf(2434,axiom,((! [A:nat,B:complex]: ((times_times_complex @ (invers8013647133539491842omplex @ (semiri8010041392384452111omplex @ A)) @ B) = (times_times_complex @ B @ (invers8013647133539491842omplex @ (semiri8010041392384452111omplex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9055_mult__inverse__of__nat__commute)). 159.59/70.65 thf(16085,plain,((! [A:nat,B:complex]: ((times_times_complex @ (invers8013647133539491842omplex @ (semiri8010041392384452111omplex @ A)) @ B) = (times_times_complex @ B @ (invers8013647133539491842omplex @ (semiri8010041392384452111omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2434])). 159.59/70.65 thf(7734,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2772_order_Oasym)). 159.59/70.65 thf(34988,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7734])). 159.59/70.65 thf(7251,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/sandbox/benchmark/theBenchmark.p',fact_7823_arith__series)). 159.59/70.65 thf(33325,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)],[7251])). 159.59/70.65 thf(2449,axiom,((! [A:complex,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (gbinomial_complex @ A @ C) @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ C))) @ (set_ord_atMost_nat @ B)) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (gbinomial_complex @ (minus_minus_complex @ A @ one_one_complex) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8926_gbinomial__sum__lower__neg)). 159.59/70.65 thf(16138,plain,((! [A:complex,B:nat]: ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (gbinomial_complex @ A @ C) @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ C))) @ (set_ord_atMost_nat @ B)) = (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (gbinomial_complex @ (minus_minus_complex @ A @ one_one_complex) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2449])). 159.59/70.65 thf(1413,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/sandbox/benchmark/theBenchmark.p',fact_1741_div__mult__self4)). 159.59/70.65 thf(12856,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)],[1413])). 159.59/70.65 thf(2241,axiom,((! [A:real,B:real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1602_add__less__same__cancel2)). 159.59/70.65 thf(15483,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)],[2241])). 159.59/70.65 thf(6870,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/sandbox/benchmark/theBenchmark.p',fact_1763_mult__le__cancel2)). 159.59/70.65 thf(31764,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)],[6870])). 159.59/70.65 thf(7459,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/sandbox/benchmark/theBenchmark.p',fact_2825_dual__order_Ostrict__trans)). 159.59/70.65 thf(34017,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)],[7459])). 159.59/70.65 thf(7804,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/sandbox/benchmark/theBenchmark.p',fact_890_nat__less__add__iff2)). 159.59/70.65 thf(35196,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)],[7804])). 159.59/70.65 thf(684,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_real @ zero_zero_real @ (arccos @ A)) & (ord_less_real @ (arccos @ A) @ pi)) <= (ord_less_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7764_arccos__lt__bounded)). 159.59/70.65 thf(10436,plain,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ one_one_real) @ A) => (((ord_less_real @ zero_zero_real @ (arccos @ A)) & (ord_less_real @ (arccos @ A) @ pi)) | ~ (ord_less_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[684])). 159.59/70.65 thf(3353,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6694_of__nat__mono)). 159.59/70.65 thf(19031,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3353])). 159.59/70.65 thf(3815,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/sandbox/benchmark/theBenchmark.p',fact_1282_diff__add__eq)). 159.59/70.65 thf(20519,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)],[3815])). 159.59/70.65 thf(2364,axiom,((cos_real = (^ [A:real]: (sin_real @ (minus_minus_real @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7793_cos__sin__eq)). 159.59/70.65 thf(15841,plain,(((cos_real) = (^ [A:real]: (sin_real @ (minus_minus_real @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2364])). 159.59/70.65 thf(5888,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/sandbox/benchmark/theBenchmark.p',fact_8544_power__sum)). 159.59/70.65 thf(28014,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)],[5888])). 159.59/70.65 thf(6421,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/sandbox/benchmark/theBenchmark.p',fact_1480_mult__cancel__right)). 159.59/70.65 thf(29936,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)],[6421])). 159.59/70.65 thf(2871,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/sandbox/benchmark/theBenchmark.p',fact_4121_le__imp__power__dvd)). 159.59/70.65 thf(17489,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)],[2871])). 159.59/70.65 thf(1726,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/sandbox/benchmark/theBenchmark.p',fact_4051_is__unit__mult__iff)). 159.59/70.65 thf(13831,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)],[1726])). 159.59/70.65 thf(3261,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/sandbox/benchmark/theBenchmark.p',fact_101_numeral__plus__numeral)). 159.59/70.65 thf(18747,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)],[3261])). 159.59/70.65 thf(6461,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1509_add__eq__0__iff__both__eq__0)). 159.59/70.65 thf(30094,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)],[6461])). 159.59/70.65 thf(4188,axiom,((! [A:real]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ one_one_int) = (ord_less_real @ A @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8192_floor__less__one)). 159.59/70.65 thf(21681,plain,((! [A:real]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ one_one_int) = (ord_less_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4188])). 159.59/70.65 thf(5809,axiom,((! [A:num,B:num]: ((power_power_int @ (numeral_numeral_int @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_int @ (pow @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4606_power__numeral)). 159.59/70.65 thf(27612,plain,((! [A:num,B:num]: ((power_power_int @ (numeral_numeral_int @ A) @ (numeral_numeral_nat @ B)) = (numeral_numeral_int @ (pow @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5809])). 159.59/70.65 thf(7109,axiom,((! [A:nat,B:num]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5661_take__bit__Suc__bit1)). 159.59/70.65 thf(32765,plain,((! [A:nat,B:num]: ((bit_se2923211474154528505it_int @ (suc @ A) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ A @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7109])). 159.59/70.65 thf(7838,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/sandbox/benchmark/theBenchmark.p',fact_8811_fold__atLeastAtMost__nat_Osimps)). 159.59/70.65 thf(35309,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)],[7838])). 159.59/70.65 thf(3602,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/sandbox/benchmark/theBenchmark.p',fact_9420_nat__ceiling__le__eq)). 159.59/70.65 thf(19820,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)],[3602])). 159.59/70.65 thf(1283,axiom,((cosh_complex = (^ [A:complex]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (numeral_numeral_real @ (bit0 @ one))) @ (plus_plus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9366_cosh__def)). 159.59/70.65 thf(12402,plain,(((cosh_complex) = (^ [A:complex]: (real_V2046097035970521341omplex @ (inverse_inverse_real @ (numeral_numeral_real @ (bit0 @ one))) @ (plus_plus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283])). 159.59/70.65 thf(4226,axiom,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ A @ one_one_Code_integer)) = (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3892_even__plus__one__iff)). 159.59/70.65 thf(21821,plain,((! [A:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ A @ one_one_Code_integer)) = (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4226])). 159.59/70.65 thf(7385,axiom,((! [A:code_integer]: ((~ (! [B:code_integer]: (A != (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))) <= (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4190_evenE)). 159.59/70.65 thf(33785,plain,((! [A:code_integer]: (~ (! [B:code_integer]: ~ (A = (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))) | ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7385])). 159.59/70.65 thf(5629,axiom,((! [A:nat,B:nat,C:int,D:int]: ((bit_se2923211474154528505it_int @ A @ (bit_concat_bit @ B @ C @ D)) = (bit_concat_bit @ (ord_min_nat @ A @ B) @ C @ (bit_se2923211474154528505it_int @ (minus_minus_nat @ A @ B) @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10176_take__bit__concat__bit__eq)). 159.59/70.65 thf(26877,plain,((! [A:nat,B:nat,C:int,D:int]: ((bit_se2923211474154528505it_int @ A @ (bit_concat_bit @ B @ C @ D)) = (bit_concat_bit @ (ord_min_nat @ A @ B) @ C @ (bit_se2923211474154528505it_int @ (minus_minus_nat @ A @ B) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5629])). 159.59/70.65 thf(1819,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/sandbox/benchmark/theBenchmark.p',fact_7995_lemma__termdiff1)). 159.59/70.65 thf(14123,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)],[1819])). 159.59/70.65 thf(8220,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (power_power_nat @ A @ B) @ (times_times_nat @ A @ (power_power_nat @ A @ B))) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_power__less__power__Suc)). 159.59/70.65 thf(36538,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (power_power_nat @ A @ B) @ (times_times_nat @ A @ (power_power_nat @ A @ B))) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8220])). 159.59/70.65 thf(4302,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 @ (powr_real @ A @ C) @ B) = (ord_less_eq_real @ C @ (log @ A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7274_powr__le__iff)). 159.59/70.65 thf(22050,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 @ (powr_real @ A @ C) @ B) = (ord_less_eq_real @ C @ (log @ A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4302])). 159.59/70.65 thf(7603,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/sandbox/benchmark/theBenchmark.p',fact_1323_less__1__mult)). 159.59/70.65 thf(34568,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)],[7603])). 159.59/70.65 thf(4696,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/sandbox/benchmark/theBenchmark.p',fact_9505_sgn__power__root)). 159.59/70.65 thf(23488,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)],[4696])). 159.59/70.65 thf(7659,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_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4237_dvd__power__iff__le)). 159.59/70.65 thf(34727,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_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7659])). 159.59/70.65 thf(447,axiom,((! [A:nat]: (((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ (^ [B:nat]: (if_Code_integer @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri4939895301339042750nteger @ (binomial @ A @ B)) @ zero_z3403309356797280102nteger)) @ (set_ord_atMost_nat @ A))) = (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8974_choose__even__sum)). 159.59/70.65 thf(9654,plain,((! [A:nat]: (((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ (^ [B:nat]: (if_Code_integer @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (semiri4939895301339042750nteger @ (binomial @ A @ B)) @ zero_z3403309356797280102nteger)) @ (set_ord_atMost_nat @ A))) = (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[447])). 159.59/70.65 thf(7055,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 @ C @ B)) <= (ord_less_int @ A @ one_one_int)) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1796_power__decreasing__iff)). 159.59/70.65 thf(32542,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 @ C @ B)) | ~ (ord_less_int @ A @ one_one_int) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7055])). 159.59/70.65 thf(946,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/sandbox/benchmark/theBenchmark.p',fact_4059_mult__unit__dvd__iff)). 159.59/70.65 thf(11280,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)],[946])). 159.59/70.65 thf(101,axiom,(((plus_p5714425477246183910nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = zero_z3403309356797280102nteger)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4740_add__neg__numeral__special_I7_J)). 159.59/70.65 thf(8565,plain,(((plus_p5714425477246183910nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = zero_z3403309356797280102nteger)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 159.59/70.65 thf(7536,axiom,(((minus_8373710615458151222nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (numera6620942414471956472nteger @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4855_diff__numeral__special_I11_J)). 159.59/70.65 thf(34298,plain,(((minus_8373710615458151222nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (numera6620942414471956472nteger @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7536])). 159.59/70.65 thf(6283,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (times_times_real @ B @ C) @ (times_times_real @ A @ C)) <= (ord_less_eq_real @ C @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1986_mult__right__mono__neg)). 159.59/70.65 thf(29438,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (times_times_real @ B @ C) @ (times_times_real @ A @ C)) | ~ (ord_less_eq_real @ C @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6283])). 159.59/70.66 thf(1817,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/sandbox/benchmark/theBenchmark.p',fact_6866_sin__60)). 159.59/70.66 thf(14118,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)],[1817])). 159.59/70.66 thf(6179,axiom,((! [A:nat]: ((modulo_modulo_nat @ A @ one_one_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3406_bits__mod__by__1)). 159.59/70.66 thf(29020,plain,((! [A:nat]: ((modulo_modulo_nat @ A @ one_one_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6179])). 159.59/70.66 thf(2668,axiom,((! [A:int,B:int,C:int]: ((bit_se1409905431419307370or_int @ A @ (bit_se725231765392027082nd_int @ B @ C)) = (bit_se725231765392027082nd_int @ (bit_se1409905431419307370or_int @ A @ B) @ (bit_se1409905431419307370or_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6039_bit_Odisj__conj__distrib)). 159.59/70.66 thf(16852,plain,((! [A:int,B:int,C:int]: ((bit_se1409905431419307370or_int @ A @ (bit_se725231765392027082nd_int @ B @ C)) = (bit_se725231765392027082nd_int @ (bit_se1409905431419307370or_int @ A @ B) @ (bit_se1409905431419307370or_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2668])). 159.59/70.66 thf(6565,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/sandbox/benchmark/theBenchmark.p',fact_3092_order_Ostrict__trans2)). 159.59/70.66 thf(30477,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)],[6565])). 159.59/70.66 thf(7691,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2799_dual__order_Oasym)). 159.59/70.66 thf(34828,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7691])). 159.59/70.66 thf(781,axiom,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ B) = (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4937_minus__less__iff)). 159.59/70.66 thf(10769,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)],[781])). 159.59/70.66 thf(6669,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1917_less__eq__nat_Osimps_I1_J)). 159.59/70.66 thf(30845,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6669])). 159.59/70.66 thf(1567,axiom,((minus_minus_complex = (^ [A:complex,B:complex]: (plus_plus_complex @ A @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5104_diff__conv__add__uminus)). 159.59/70.66 thf(13342,plain,(((minus_minus_complex) = (^ [A:complex,B:complex]: (plus_plus_complex @ A @ (uminus1482373934393186551omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567])). 159.59/70.66 thf(6501,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = none_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2536_vebt__succ_Osimps_I5_J)). 159.59/70.66 thf(30250,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6501])). 159.59/70.66 thf(5994,axiom,((! [A:num]: ((numeral_numeral_real @ A) != (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5086_numeral__neq__neg__one)). 159.59/70.66 thf(28416,plain,((! [A:num]: ~ ((numeral_numeral_real @ A) = (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5994])). 159.59/70.66 thf(7217,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/sandbox/benchmark/theBenchmark.p',fact_4897_neg__one__even__power)). 159.59/70.66 thf(33213,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)],[7217])). 159.59/70.66 thf(1932,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = ((B = zero_zero_int) | (dvd_dvd_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3817_dvd__mult__cancel__right)). 159.59/70.66 thf(14482,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ (times_times_int @ C @ B)) = ((B = zero_zero_int) | (dvd_dvd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1932])). 159.59/70.66 thf(2951,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) => ((C @ F) = (D @ F)))) => (? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => (((C @ F) | (A @ F)) = ((D @ F) | (B @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4463_minf_I2_J)). 159.59/70.66 thf(17750,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) => ((C @ F) = (D @ F)))) => (? [E:real]: ! [F:real]: ((ord_less_real @ F @ E) => (((C @ F) | (A @ F)) = ((D @ F) | (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2951])). 159.59/70.66 thf(2193,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/sandbox/benchmark/theBenchmark.p',fact_121_div__mult2__numeral__eq)). 159.59/70.66 thf(15319,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)],[2193])). 159.59/70.66 thf(1648,axiom,((! [A:num,B:num]: ((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (plus_plus_num @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4791_diff__numeral__simps_I3_J)). 159.59/70.66 thf(13595,plain,((! [A:num,B:num]: ((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (numera6620942414471956472nteger @ B)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (plus_plus_num @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648])). 159.59/70.66 thf(6012,axiom,((! [A:num,B:nat]: ((archim6058952711729229775r_real @ (power_power_real @ (numeral_numeral_real @ A) @ B)) = (power_power_int @ (numeral_numeral_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8196_floor__numeral__power)). 159.59/70.66 thf(28478,plain,((! [A:num,B:nat]: ((archim6058952711729229775r_real @ (power_power_real @ (numeral_numeral_real @ A) @ B)) = (power_power_int @ (numeral_numeral_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6012])). 159.59/70.66 thf(7436,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/sandbox/benchmark/theBenchmark.p',fact_2542_sum__power2__ge__zero)). 159.59/70.66 thf(33938,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)],[7436])). 159.59/70.66 thf(7948,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/sandbox/benchmark/theBenchmark.p',fact_3589_product__nth)). 159.59/70.66 thf(35663,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)],[7948])). 159.59/70.66 thf(749,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ one) @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_mult__numeral__1)). 159.59/70.66 thf(10674,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ one) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[749])). 159.59/70.66 thf(2327,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/sandbox/benchmark/theBenchmark.p',fact_5931_and__int__unfold)). 159.59/70.66 thf(15731,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)],[2327])). 159.59/70.66 thf(4912,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ one_one_nat @ (numeral_numeral_nat @ (bit1 @ A))) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5985_and__numerals_I2_J)). 159.59/70.66 thf(24231,plain,((! [A:num]: ((bit_se727722235901077358nd_nat @ one_one_nat @ (numeral_numeral_nat @ (bit1 @ A))) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4912])). 159.59/70.66 thf(751,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/sandbox/benchmark/theBenchmark.p',fact_5789_of__int__power)). 159.59/70.66 thf(10680,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)],[751])). 159.59/70.66 thf(6492,axiom,((! [A:num,B:num]: ((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) != (numera6620942414471956472nteger @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4951_neg__numeral__neq__numeral)). 159.59/70.66 thf(30218,plain,((! [A:num,B:num]: ~ ((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (numera6620942414471956472nteger @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6492])). 159.59/70.66 thf(1777,axiom,((! [A:real,B:real]: ? [C:real]: ! [D:real]: ((ord_less_real @ D @ C) => ((~ (dvd_dvd_real @ A @ (plus_plus_real @ D @ B))) = (~ (dvd_dvd_real @ A @ (plus_plus_real @ D @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4543_minf_I10_J)). 159.59/70.66 thf(13994,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777])). 159.59/70.66 thf(3332,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5986_and__numerals_I8_J)). 159.59/70.66 thf(18969,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ (numeral_numeral_int @ (bit1 @ A)) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3332])). 159.59/70.66 thf(6686,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/sandbox/benchmark/theBenchmark.p',fact_4757_left__minus__one__mult__self)). 159.59/70.66 thf(30922,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)],[6686])). 159.59/70.66 thf(7009,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/sandbox/benchmark/theBenchmark.p',fact_3874_even__mult__iff)). 159.59/70.66 thf(32384,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)],[7009])). 159.59/70.66 thf(7664,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/sandbox/benchmark/theBenchmark.p',fact_1717_nat__0__less__mult__iff)). 159.59/70.66 thf(34742,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)],[7664])). 159.59/70.66 thf(2601,axiom,((! [A:num,B:real]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6999_neg__numeral__less__ceiling)). 159.59/70.66 thf(16618,plain,((! [A:num,B:real]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2601])). 159.59/70.66 thf(431,axiom,((! [A:set_nat,B:nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (insert_nat @ B @ C)) = (((~ (member_nat @ B @ A)) => (ord_less_eq_set_nat @ A @ C)) & ((ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)) @ C) <= (member_nat @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6256_subset__insert__iff)). 159.59/70.66 thf(9601,plain,((! [A:set_nat,B:nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ (insert_nat @ B @ C)) = (((~ (member_nat @ B @ A)) => (ord_less_eq_set_nat @ A @ C)) & ((ord_less_eq_set_nat @ (minus_minus_set_nat @ A @ (insert_nat @ B @ bot_bot_set_nat)) @ C) | ~ (member_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])). 159.59/70.66 thf(4816,axiom,((! [A:num]: ((neg_numeral_sub_int @ (bitM @ A) @ one) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (neg_numeral_sub_int @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9769_sub__BitM__One__eq)). 159.59/70.66 thf(23920,plain,((! [A:num]: ((neg_numeral_sub_int @ (bitM @ A) @ one) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (neg_numeral_sub_int @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4816])). 159.59/70.66 thf(1538,axiom,((~ (ord_le6747313008572928689nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5078_less__minus__one__simps_I4_J)). 159.59/70.66 thf(13256,plain,((~ (ord_le6747313008572928689nteger @ one_one_Code_integer @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538])). 159.59/70.66 thf(857,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/sandbox/benchmark/theBenchmark.p',fact_7932_sums__Suc)). 159.59/70.66 thf(11017,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)],[857])). 159.59/70.66 thf(4085,axiom,((! [A:int,B:nat]: ((ord_less_int @ (power_power_int @ A @ B) @ (times_times_int @ A @ (power_power_int @ A @ B))) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_power__less__power__Suc)). 159.59/70.66 thf(21362,plain,((! [A:int,B:nat]: ((ord_less_int @ (power_power_int @ A @ B) @ (times_times_int @ A @ (power_power_int @ A @ B))) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4085])). 159.59/70.66 thf(7417,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ (divide_divide_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_Suc__div__le__mono)). 159.59/70.66 thf(33879,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)],[7417])). 159.59/70.66 thf(6433,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3210_order__less__le__trans)). 159.59/70.66 thf(29987,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6433])). 159.59/70.66 thf(60,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/sandbox/benchmark/theBenchmark.p',fact_7310_tan__diff)). 159.59/70.66 thf(8431,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)],[60])). 159.59/70.66 thf(518,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/sandbox/benchmark/theBenchmark.p',fact_9590_not__int__div__2)). 159.59/70.66 thf(9902,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)],[518])). 159.59/70.66 thf(2735,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (times_times_nat @ A @ B)) = (times_times_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6828_int__ops_I7_J)). 159.59/70.66 thf(17067,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)],[2735])). 159.59/70.66 thf(2181,axiom,((! [A:real]: ? [B:int]: (ord_less_real @ (ring_1_of_int_real @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6138_ex__of__int__less)). 159.59/70.66 thf(15283,plain,((! [A:real]: ? [B:int]: (ord_less_real @ (ring_1_of_int_real @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2181])). 159.59/70.66 thf(1145,axiom,((semiri1314217659103216013at_int = (^ [A:nat]: (abs_Integ @ (product_Pair_nat_nat @ A @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9775_int__def)). 159.59/70.66 thf(11921,plain,(((semiri1314217659103216013at_int) = (^ [A:nat]: (abs_Integ @ (product_Pair_nat_nat @ A @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145])). 159.59/70.66 thf(6825,axiom,((! [A:option_nat,B:(option_nat > (option_nat > $o)),C:option_nat]: (((B @ A @ C) <= (A = none_nat)) => (((B @ A @ C) <= (! [D:nat,E:nat]: (((B @ A @ C) <= (C = (some_nat @ E))) <= (A = (some_nat @ D))))) <= ((C = none_nat) => (B @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_combine__options__cases)). 159.59/70.66 thf(31518,plain,((! [A:option_nat,B:(option_nat > (option_nat > $o)),C:option_nat]: (((B @ A @ C) | ~ (A = none_nat)) => ((B @ A @ C) | ~ (! [D:nat,E:nat]: ((B @ A @ C) | ~ (C = (some_nat @ E)) | ~ (A = (some_nat @ D)))) | ~ ((C = none_nat) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6825])). 159.59/70.66 thf(4237,axiom,((abs_abs_int = (^ [A:int]: (if_int @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_int @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5571_abs__if__raw)). 159.59/70.66 thf(21850,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)],[4237])). 159.59/70.66 thf(477,axiom,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se4203085406695923979it_int @ A @ B) @ C) = ((A != C) & (bit_se1146084159140164899it_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6378_bit__unset__bit__iff)). 159.59/70.66 thf(9770,plain,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se4203085406695923979it_int @ A @ B) @ C) = (~ (A = C) & (bit_se1146084159140164899it_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])). 159.59/70.66 thf(2548,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8089_fact__dvd)). 159.59/70.66 thf(16443,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (dvd_dvd_int @ (semiri1406184849735516958ct_int @ A) @ (semiri1406184849735516958ct_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2548])). 159.59/70.66 thf(7784,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (modulo_modulo_nat @ B @ C)) = (((A @ B) <= (C = zero_zero_nat)) & ((C != zero_zero_nat) => (! [D:nat,E:nat]: (((A @ E) <= (B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E))) <= (ord_less_nat @ E @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3548_split__mod)). 159.59/70.66 thf(35139,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (modulo_modulo_nat @ B @ C)) = (((A @ B) | ~ (C = zero_zero_nat)) & ((~ (C = zero_zero_nat)) => (! [D:nat,E:nat]: ((A @ E) | ~ (B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)) | ~ (ord_less_nat @ E @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7784])). 159.59/70.66 thf(2024,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1240_ring__class_Oring__distribs_I1_J)). 159.59/70.66 thf(14791,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2024])). 159.59/70.66 thf(6274,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/sandbox/benchmark/theBenchmark.p',fact_5342_ln__one__plus__pos__lower__bound)). 159.59/70.66 thf(29391,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)],[6274])). 159.59/70.66 thf(141,axiom,((! [A:complex]: (sums_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (cos_coeff @ B) @ (power_power_complex @ (uminus1482373934393186551omplex @ A) @ B))) @ (cos_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9292_cos__minus__converges)). 159.59/70.66 thf(8681,plain,((! [A:complex]: (sums_complex @ (^ [B:nat]: (real_V2046097035970521341omplex @ (cos_coeff @ B) @ (power_power_complex @ (uminus1482373934393186551omplex @ A) @ B))) @ (cos_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 159.59/70.66 thf(5536,axiom,((! [A:nat]: ((~ (! [B:nat]: (A != (plus_plus_nat @ B @ (suc @ B))))) <= (! [B:nat]: (A != (plus_plus_nat @ B @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_even__odd__cases)). 159.59/70.66 thf(26561,plain,((! [A:nat]: (~ (! [B:nat]: ~ (A = (plus_plus_nat @ B @ (suc @ B)))) | ~ (! [B:nat]: ~ (A = (plus_plus_nat @ B @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5536])). 159.59/70.66 thf(3509,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/sandbox/benchmark/theBenchmark.p',fact_7199_cos__expansion__lemma)). 159.59/70.66 thf(19517,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)],[3509])). 159.59/70.66 thf(6238,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/sandbox/benchmark/theBenchmark.p',fact_6614_of__nat__le__of__nat__power__cancel__iff)). 159.59/70.66 thf(29209,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)],[6238])). 159.59/70.66 thf(37,axiom,((! [A:nat,B:code_integer,C:code_integer]: ((((power_8256067586552552935nteger @ B @ A) = C) = ((groups7501900531339628137nteger @ (^ [D:nat]: (times_3573771949741848930nteger @ (if_Code_integer @ (D = zero_zero_nat) @ (uminus1351360451143612070nteger @ C) @ (if_Code_integer @ (D = A) @ one_one_Code_integer @ zero_z3403309356797280102nteger)) @ (power_8256067586552552935nteger @ B @ D))) @ (set_ord_atMost_nat @ A)) = zero_z3403309356797280102nteger)) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8945_root__polyfun)). 159.59/70.66 thf(8360,plain,((! [A:nat,B:code_integer,C:code_integer]: ((((power_8256067586552552935nteger @ B @ A) = C) = ((groups7501900531339628137nteger @ (^ [D:nat]: (times_3573771949741848930nteger @ (if_Code_integer @ (D = zero_zero_nat) @ (uminus1351360451143612070nteger @ C) @ (if_Code_integer @ (D = A) @ one_one_Code_integer @ zero_z3403309356797280102nteger)) @ (power_8256067586552552935nteger @ B @ D))) @ (set_ord_atMost_nat @ A)) = zero_z3403309356797280102nteger)) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 159.59/70.66 thf(6593,axiom,((! [A:num,B:num]: (((ord_less_num @ A @ B) <= (ord_less_eq_num @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3195_order__neq__le__trans)). 159.59/70.66 thf(30582,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)],[6593])). 159.59/70.66 thf(6290,axiom,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (times_times_real @ (groups129246275422532515t_real @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8729_prod_OatLeast0__atMost__Suc)). 159.59/70.66 thf(29459,plain,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (times_times_real @ (groups129246275422532515t_real @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6290])). 159.59/70.66 thf(3318,axiom,((! [A:nat,B:code_integer]: ((bit_se1745604003318907178nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (bit_se1745604003318907178nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))) @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5332_take__bit__Suc)). 159.59/70.66 thf(18926,plain,((! [A:nat,B:code_integer]: ((bit_se1745604003318907178nteger @ (suc @ A) @ B) = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (bit_se1745604003318907178nteger @ A @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))) @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3318])). 159.59/70.66 thf(3403,axiom,((! [A:real,B:complex]: ((plus_plus_complex @ (real_V2046097035970521341omplex @ (minus_minus_real @ one_one_real @ A) @ B) @ (real_V2046097035970521341omplex @ A @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9200_scaleR__collapse)). 159.59/70.66 thf(19192,plain,((! [A:real,B:complex]: ((plus_plus_complex @ (real_V2046097035970521341omplex @ (minus_minus_real @ one_one_real @ A) @ B) @ (real_V2046097035970521341omplex @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3403])). 159.59/70.66 thf(187,axiom,((bit_se9216721137139052372nteger = (^ [A:code_integer,B:nat]: ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6433_bit__iff__odd)). 159.59/70.66 thf(8830,plain,(((bit_se9216721137139052372nteger) = (^ [A:code_integer,B:nat]: ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 159.59/70.66 thf(1505,axiom,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) => (summable_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7074_powser__split__head_I3_J)). 159.59/70.66 thf(13160,plain,((! [A:(nat > real),B:real]: ((summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C)))) => (summable_real @ (^ [C:nat]: (times_times_real @ (A @ (suc @ C)) @ (power_power_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505])). 159.59/70.66 thf(7613,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/sandbox/benchmark/theBenchmark.p',fact_2561_VEBT__internal_Oexp__split__high__low_I2_J)). 159.59/70.66 thf(34594,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)],[7613])). 159.59/70.66 thf(4906,axiom,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1926_minus__nat_Odiff__0)). 159.59/70.66 thf(24211,plain,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4906])). 159.59/70.66 thf(6903,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1725_diff__is__0__eq)). 159.59/70.66 thf(31866,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)],[6903])). 159.59/70.66 thf(3928,axiom,((! [A:code_integer,B:code_integer]: ? [C:code_integer]: ! [D:code_integer]: (((~ (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ B))) = (~ (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ B)))) <= (ord_le6747313008572928689nteger @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4541_minf_I10_J)). 159.59/70.66 thf(20888,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3928])). 159.59/70.66 thf(1919,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ (bit0 @ one)))) => ((((ord_less_eq_real @ zero_zero_real @ C) => (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 @ A)) <= (ord_less_real @ C @ (divide_divide_real @ B @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6480_sqrt__sum__squares__half__less)). 159.59/70.66 thf(14447,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ (divide_divide_real @ B @ (numeral_numeral_real @ (bit0 @ one)))) => (((ord_less_eq_real @ zero_zero_real @ C) => (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 @ A) | ~ (ord_less_real @ C @ (divide_divide_real @ B @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1919])). 159.59/70.66 thf(7643,axiom,((! [A:num,B:num]: (((numeral_numeral_nat @ A) = (numeral_numeral_nat @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_numeral__eq__iff)). 159.59/70.66 thf(34683,plain,((! [A:num,B:num]: (((numeral_numeral_nat @ A) = (numeral_numeral_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7643])). 159.59/70.66 thf(6718,axiom,((! [A:int]: ((one_one_int = A) = (A = one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_one__reorient)). 159.59/70.66 thf(31159,plain,((! [A:int]: ((one_one_int = A) = (A = one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6718])). 159.59/70.66 thf(1585,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/sandbox/benchmark/theBenchmark.p',fact_1183_add__less__imp__less__right)). 159.59/70.66 thf(13396,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)],[1585])). 159.59/70.66 thf(2130,axiom,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (uminus1351360451143612070nteger @ (minus_8373710615458151222nteger @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4980_minus__diff__minus)). 159.59/70.66 thf(15131,plain,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (uminus1351360451143612070nteger @ (minus_8373710615458151222nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2130])). 159.59/70.66 thf(1472,axiom,((! [A:complex,B:nat,C:nat]: (((comm_s2602460028002588243omplex @ A @ B) != zero_zero_complex) => ((ord_less_eq_nat @ C @ B) => ((comm_s2602460028002588243omplex @ A @ C) != zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8217_pochhammer__neq__0__mono)). 159.59/70.66 thf(13057,plain,((! [A:complex,B:nat,C:nat]: ((~ ((comm_s2602460028002588243omplex @ A @ B) = zero_zero_complex)) => ((ord_less_eq_nat @ C @ B) => (~ ((comm_s2602460028002588243omplex @ A @ C) = zero_zero_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472])). 159.59/70.66 thf(6895,axiom,((! [A:option_nat,B:nat]: ((A != none_nat) <= (A = (some_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_option_OdiscI)). 159.59/70.66 thf(31839,plain,((! [A:option_nat,B:nat]: (~ (A = none_nat) | ~ (A = (some_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6895])). 159.59/70.66 thf(7212,axiom,((! [A:vEBT_VEBT,B:nat,C:$o]: (((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (C = (~ ((((B = one_one_nat) & ((E) <= (B = one_one_nat))) <= (B != zero_zero_nat)) & ((B = zero_zero_nat) => (D))))))) => ((~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT]: ((C = (~ ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) & ((ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ F)) => (vEBT_V5719532721284313246member @ (nth_VEBT_VEBT @ F @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ B @ (divide_divide_nat @ (suc @ E) @ (numeral_numeral_nat @ (bit0 @ one))))))))) <= (? [G:vEBT_VEBT]: (A = (vEBT_Node @ D @ (suc @ E) @ F @ G)))))) <= ((C) <= (? [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ D @ zero_zero_nat @ E @ F)))))) <= ((vEBT_V5719532721284313246member @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2487_VEBT__internal_Onaive__member_Oelims_I1_J)). 159.59/70.66 thf(33181,plain,((! [A:vEBT_VEBT,B:nat,C:$o]: (((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (C = (~ ((((B = one_one_nat) & ((E) | ~ (B = one_one_nat))) | (B = zero_zero_nat)) & ((B = zero_zero_nat) => (D))))))) => (~ (! [D:option4927543243414619207at_nat,E:nat,F:list_VEBT_VEBT]: ((C = (~ ((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_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))))))))) | ~ (? [G:vEBT_VEBT]: (A = (vEBT_Node @ D @ (suc @ E) @ F @ G))))) | ~ ((C) | ~ (? [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ D @ zero_zero_nat @ E @ F)))))) | ~ ((vEBT_V5719532721284313246member @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7212])). 159.59/70.66 thf(2185,axiom,((! [A:complex]: ((power_power_complex @ (sinh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_complex @ (power_power_complex @ (cosh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9347_sinh__square__eq)). 159.59/70.66 thf(15294,plain,((! [A:complex]: ((power_power_complex @ (sinh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (minus_minus_complex @ (power_power_complex @ (cosh_complex @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2185])). 159.59/70.66 thf(7893,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/sandbox/benchmark/theBenchmark.p',fact_4378_one__div__2__pow__eq)). 159.59/70.66 thf(35484,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)],[7893])). 159.59/70.66 thf(6576,axiom,((! [A:code_integer,B:$o,C:code_integer,D:$o]: ((~ ((A = C) => (B = (~ (D))))) <= ((produc6677183202524767010eger_o @ A @ B) = (produc6677183202524767010eger_o @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3672_Pair__inject)). 159.59/70.66 thf(30509,plain,((! [A:code_integer,B:$o,C:code_integer,D:$o]: (~ ((A = C) => (B = (~ (D)))) | ~ ((produc6677183202524767010eger_o @ A @ B) = (produc6677183202524767010eger_o @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6576])). 159.59/70.66 thf(7478,axiom,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((vEBT_vebt_insert @ A @ B) = C) => ((! [D:$o,E:$o]: ((~ (((B != zero_zero_nat) => (((B != one_one_nat) => (C = (vEBT_Leaf @ D @ E))) & ((B = one_one_nat) => (C = (vEBT_Leaf @ D @ ($true)))))) & ((B = zero_zero_nat) => (C = (vEBT_Leaf @ ($true) @ E))))) <= (A = (vEBT_Leaf @ D @ E)))) => ((((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F)) => (C != (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ (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]: ((A = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)) => (C != (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F))))) <= (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((C != (vEBT_Node @ D @ zero_zero_nat @ E @ F)) <= (A = (vEBT_Node @ D @ zero_zero_nat @ E @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2566_vebt__insert_Oelims)). 159.59/70.66 thf(34087,plain,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((vEBT_vebt_insert @ A @ B) = C) => ((! [D:$o,E:$o]: (~ (((~ (B = zero_zero_nat)) => (((~ (B = one_one_nat)) => (C = (vEBT_Leaf @ D @ E))) & ((B = one_one_nat) => (C = (vEBT_Leaf @ D @ ($true)))))) & ((B = zero_zero_nat) => (C = (vEBT_Leaf @ ($true) @ E)))) | ~ (A = (vEBT_Leaf @ D @ E)))) => (((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ D)) @ E @ F)) => (~ (C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ (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]: ((A = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F)) => (~ (C = (vEBT_Node @ D @ (suc @ zero_zero_nat) @ E @ F))))) | ~ (! [D:option4927543243414619207at_nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ (C = (vEBT_Node @ D @ zero_zero_nat @ E @ F)) | ~ (A = (vEBT_Node @ D @ zero_zero_nat @ E @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7478])). 159.59/70.66 thf(1638,axiom,((! [A:code_integer,B:nat,C:nat]: ((divide6298287555418463151nteger @ A @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ B) @ (semiri4939895301339042750nteger @ C))) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ A @ (semiri4939895301339042750nteger @ B)) @ (semiri4939895301339042750nteger @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6680_div__mult2__eq_H)). 159.59/70.66 thf(13566,plain,((! [A:code_integer,B:nat,C:nat]: ((divide6298287555418463151nteger @ A @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ B) @ (semiri4939895301339042750nteger @ C))) = (divide6298287555418463151nteger @ (divide6298287555418463151nteger @ A @ (semiri4939895301339042750nteger @ B)) @ (semiri4939895301339042750nteger @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638])). 159.59/70.66 thf(700,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/sandbox/benchmark/theBenchmark.p',fact_5788_of__int__eq__of__int__power__cancel__iff)). 159.59/70.66 thf(10496,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)],[700])). 159.59/70.66 thf(236,axiom,((! [A:code_integer]: (((divide6298287555418463151nteger @ A @ A) = one_one_Code_integer) <= (A != zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1663_div__self)). 159.59/70.66 thf(8973,plain,((! [A:code_integer]: (((divide6298287555418463151nteger @ A @ A) = one_one_Code_integer) | (A = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 159.59/70.66 thf(6982,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 @ A @ zero_zero_int) & (ord_less_eq_int @ B @ zero_zero_int))) => (ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1997_split__mult__pos__le)). 159.59/70.66 thf(32273,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 @ A @ zero_zero_int) & (ord_less_eq_int @ B @ zero_zero_int))) => (ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6982])). 159.59/70.66 thf(4084,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) => (ord_less_real @ A @ B)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3192_order__neq__le__trans)). 159.59/70.66 thf(21359,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)],[4084])). 159.59/70.66 thf(1800,axiom,((! [A:real,B:real,C:real]: (((A != one_one_real) => ((ord_less_real @ zero_zero_real @ B) => ((plus_plus_real @ (log @ A @ B) @ C) = (log @ A @ (times_times_real @ B @ (powr_real @ A @ C)))))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7278_log__add__eq__powr)). 159.59/70.66 thf(14058,plain,((! [A:real,B:real,C:real]: (((~ (A = one_one_real)) => ((ord_less_real @ zero_zero_real @ B) => ((plus_plus_real @ (log @ A @ B) @ C) = (log @ A @ (times_times_real @ B @ (powr_real @ A @ C)))))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1800])). 159.59/70.66 thf(6964,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2644_linorder__le__cases)). 159.59/70.66 thf(32097,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)],[6964])). 159.59/70.66 thf(3547,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/sandbox/benchmark/theBenchmark.p',fact_3455_mod__add__left__eq)). 159.59/70.66 thf(19633,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)],[3547])). 159.59/70.66 thf(2831,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/sandbox/benchmark/theBenchmark.p',fact_4085_dvd__mult__imp__div)). 159.59/70.66 thf(17352,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)],[2831])). 159.59/70.66 thf(261,axiom,((ord_less_eq_int = (^ [A:int,B:int]: ((ord_max_int @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_max_Oabsorb__iff2)). 159.59/70.66 thf(9046,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: ((ord_max_int @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[261])). 159.59/70.66 thf(6704,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/sandbox/benchmark/theBenchmark.p',fact_6361_real__sqrt__sum__squares__mult__squared__eq)). 159.59/70.66 thf(31022,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)],[6704])). 159.59/70.66 thf(6234,axiom,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1546_bits__div__0)). 159.59/70.66 thf(29196,plain,((! [A:nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6234])). 159.59/70.66 thf(6851,axiom,((! [A:nat,B:nat,C:(nat > real)]: ((((groups129246275422532515t_real @ C @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_real) <= (ord_less_nat @ (suc @ A) @ B)) & ((~ (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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8454_prod_Ocl__ivl__Suc)). 159.59/70.66 thf(31704,plain,((! [A:nat,B:nat,C:(nat > real)]: ((((groups129246275422532515t_real @ (C) @ (set_or1269000886237332187st_nat @ B @ (suc @ A))) = one_one_real) | ~ (ord_less_nat @ (suc @ A) @ B)) & ((~ (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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6851])). 159.59/70.66 thf(4275,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/sandbox/benchmark/theBenchmark.p',fact_7993_lemma__termdiff1)). 159.59/70.66 thf(21968,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)],[4275])). 159.59/70.66 thf(2198,axiom,((! [A:nat,B:int]: ((bit_se2923211474154528505it_int @ (suc @ A) @ B) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5333_take__bit__Suc)). 159.59/70.66 thf(15347,plain,((! [A:nat,B:int]: ((bit_se2923211474154528505it_int @ (suc @ A) @ B) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ A @ (divide_divide_int @ B @ (numeral_numeral_int @ (bit0 @ one)))) @ (numeral_numeral_int @ (bit0 @ one))) @ (modulo_modulo_int @ B @ (numeral_numeral_int @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2198])). 159.59/70.66 thf(1760,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((sinh_real @ (ln_ln_real @ A)) = (divide_divide_real @ (minus_minus_real @ A @ (inverse_inverse_real @ A)) @ (numeral_numeral_real @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9370_sinh__ln__real)). 159.59/70.66 thf(13934,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((sinh_real @ (ln_ln_real @ A)) = (divide_divide_real @ (minus_minus_real @ A @ (inverse_inverse_real @ A)) @ (numeral_numeral_real @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760])). 159.59/70.66 thf(1703,axiom,((! [A:complex]: (sums_complex @ (^ [B:nat]: (if_complex @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B)) @ zero_zero_complex)) @ (cosh_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9303_cosh__converges)). 159.59/70.66 thf(13756,plain,((! [A:complex]: (sums_complex @ (^ [B:nat]: (if_complex @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B)) @ zero_zero_complex)) @ (cosh_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703])). 159.59/70.66 thf(8078,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/sandbox/benchmark/theBenchmark.p',fact_685_add__less__mono)). 159.59/70.66 thf(36082,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)],[8078])). 159.59/70.66 thf(7020,axiom,(((^ [A:complex]: (zero_zero_complex)) = (times_times_complex @ zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1935_lambda__zero)). 159.59/70.66 thf(32414,plain,(((^ [A:complex]: (zero_zero_complex)) = (times_times_complex @ zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7020])). 159.59/70.66 thf(2540,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/sandbox/benchmark/theBenchmark.p',fact_7304_tan__30)). 159.59/70.66 thf(16418,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)],[2540])). 159.59/70.66 thf(7496,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/sandbox/benchmark/theBenchmark.p',fact_3086_order_Ostrict__trans1)). 159.59/70.66 thf(34175,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)],[7496])). 159.59/70.66 thf(767,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/sandbox/benchmark/theBenchmark.p',fact_8260_real__of__int__floor__add__one__ge)). 159.59/70.66 thf(10727,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)],[767])). 159.59/70.66 thf(6349,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5938_and_Oidem)). 159.59/70.66 thf(29639,plain,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6349])). 159.59/70.66 thf(4363,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((plus_p5714425477246183910nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ A @ (divide6298287555418463151nteger @ B @ A)) @ (modulo364778990260209775nteger @ B @ A)) @ C) = (plus_p5714425477246183910nteger @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3524_cancel__div__mod__rules_I2_J)). 159.59/70.66 thf(22226,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((plus_p5714425477246183910nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ A @ (divide6298287555418463151nteger @ B @ A)) @ (modulo364778990260209775nteger @ B @ A)) @ C) = (plus_p5714425477246183910nteger @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4363])). 159.59/70.66 thf(1266,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => (~ (! [C:code_integer]: (B != (times_3573771949741848930nteger @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3929_dvdE)). 159.59/70.66 thf(12343,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)],[1266])). 159.59/70.66 thf(6890,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((B @ D) != zero_zero_complex))))) => ((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/sandbox/benchmark/theBenchmark.p',fact_3736_sum_Ofinite__Collect__op)). 159.59/70.66 thf(31824,plain,((! [A:set_nat,B:(nat > complex),C:(nat > complex)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((B @ D) = zero_zero_complex))))) => ((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)],[6890])). 159.59/70.66 thf(5481,axiom,((! [A:nat,B:real,C:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) <= (ord_less_eq_real @ (abs_abs_real @ B) @ (abs_abs_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5657_power__mono__even)). 159.59/70.66 thf(26380,plain,((! [A:nat,B:real,C:real]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_eq_real @ (power_power_real @ B @ A) @ (power_power_real @ C @ A)) | ~ (ord_less_eq_real @ (abs_abs_real @ B) @ (abs_abs_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5481])). 159.59/70.66 thf(4607,axiom,((! [A:(complex > $o),B:complex,C:(complex > $o)]: ((! [D:complex,E:complex]: ((A @ D) = (A @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))))) => ((! [D:complex,E:complex]: ((C @ D) = (C @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))))) => (! [D:complex,E:complex]: (((A @ D) & (C @ D)) = ((A @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))) & (C @ (minus_minus_complex @ D @ (times_times_complex @ E @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4516_inf__period_I1_J)). 159.59/70.66 thf(23178,plain,((! [A:(complex > $o),B:complex,C:(complex > $o)]: ((! [D:complex,E:complex]: ((A @ D) = (A @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))))) => ((! [D:complex,E:complex]: ((C @ D) = (C @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))))) => (! [D:complex,E:complex]: (((A @ D) & (C @ D)) = ((A @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))) & (C @ (minus_minus_complex @ D @ (times_times_complex @ E @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4607])). 159.59/70.66 thf(4292,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (? [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) & ! [C:real]: ((C = B) <= (((cos_real @ C) = A) & (ord_less_eq_real @ C @ pi) & (ord_less_eq_real @ zero_zero_real @ C))) & ((cos_real @ B) = A) & (ord_less_eq_real @ B @ pi)))) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7149_cos__total)). 159.59/70.66 thf(22018,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (? [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) & ! [C:real]: ((C = B) | ~ (((cos_real @ C) = A) & (ord_less_eq_real @ C @ pi) & (ord_less_eq_real @ zero_zero_real @ C))) & ((cos_real @ B) = A) & (ord_less_eq_real @ B @ pi)))) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4292])). 159.59/70.66 thf(2852,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/sandbox/benchmark/theBenchmark.p',fact_6907_norm__uminus__minus)). 159.59/70.66 thf(17421,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)],[2852])). 159.59/70.66 thf(7021,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4506_minf_I6_J)). 159.59/70.66 thf(32416,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7021])). 159.59/70.66 thf(7498,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/sandbox/benchmark/theBenchmark.p',fact_6628_numeral__power__less__of__nat__cancel__iff)). 159.59/70.66 thf(34182,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)],[7498])). 159.59/70.66 thf(1989,axiom,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (modulo364778990260209775nteger @ A @ B)) = (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3536_minus__mod__eq__div__mult)). 159.59/70.66 thf(14678,plain,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (modulo364778990260209775nteger @ A @ B)) = (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1989])). 159.59/70.66 thf(4992,axiom,(((semiri2265585572941072030t_real @ zero_zero_nat) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8047_fact__0)). 159.59/70.66 thf(24523,plain,(((semiri2265585572941072030t_real @ zero_zero_nat) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4992])). 159.59/70.66 thf(4754,axiom,((~ (ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5153_le__minus__one__simps_I3_J)). 159.59/70.66 thf(23686,plain,((~ (ord_less_eq_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4754])). 159.59/70.66 thf(4573,axiom,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) => (ord_less_eq_num @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2643_linorder__le__cases)). 159.59/70.66 thf(23035,plain,((! [A:num,B:num]: ((~ (ord_less_eq_num @ A @ B)) => (ord_less_eq_num @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4573])). 159.59/70.66 thf(1931,axiom,((! [A:real,B:nat]: ((power_power_real @ (inverse_inverse_real @ A) @ B) = (inverse_inverse_real @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9015_power__inverse)). 159.59/70.66 thf(14479,plain,((! [A:real,B:nat]: ((power_power_real @ (inverse_inverse_real @ A) @ B) = (inverse_inverse_real @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1931])). 159.59/70.66 thf(6009,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/sandbox/benchmark/theBenchmark.p',fact_2400_div__le__mono2)). 159.59/70.66 thf(28469,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)],[6009])). 159.59/70.66 thf(4884,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/sandbox/benchmark/theBenchmark.p',fact_9175_central__binomial__lower__bound)). 159.59/70.66 thf(24135,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)],[4884])). 159.59/70.66 thf(6147,axiom,((! [A:code_integer,B:nat,C:nat]: ((divide6298287555418463151nteger @ (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C)) = (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_div__exp__eq)). 159.59/70.66 thf(28906,plain,((! [A:code_integer,B:nat,C:nat]: ((divide6298287555418463151nteger @ (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C)) = (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6147])). 159.59/70.66 thf(5947,axiom,((! [A:nat]: ~ (bit_se1148574629649215175it_nat @ one_one_nat @ (suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6382_not__bit__1__Suc)). 159.59/70.66 thf(28272,plain,((! [A:nat]: ~ (bit_se1148574629649215175it_nat @ one_one_nat @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5947])). 159.59/70.66 thf(6315,axiom,((! [A:num,B:num]: (((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4622_neg__numeral__eq__iff)). 159.59/70.66 thf(29536,plain,((! [A:num,B:num]: (((uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6315])). 159.59/70.66 thf(8002,axiom,((! [A:nat,B:nat]: ((bit_se1148574629649215175it_nat @ A @ (suc @ B)) = (bit_se1148574629649215175it_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6420_bit__Suc)). 159.59/70.66 thf(35822,plain,((! [A:nat,B:nat]: ((bit_se1148574629649215175it_nat @ A @ (suc @ B)) = (bit_se1148574629649215175it_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8002])). 159.59/70.66 thf(241,axiom,((semiri3624122377584611663nteger = (^ [A:nat]: (semiri4939895301339042750nteger @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8764_fact__prod)). 159.59/70.66 thf(8987,plain,(((semiri3624122377584611663nteger) = (^ [A:nat]: (semiri4939895301339042750nteger @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 159.59/70.66 thf(7323,axiom,((! [A:nat,B:list_o,C:$o,D:nat]: (((nth_o @ (list_update_o @ B @ A @ C) @ D) = (((nth_o @ B @ D) <= (A != D)) & ((C) <= (A = D)))) <= (ord_less_nat @ A @ (size_size_list_o @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_nth__list__update)). 159.59/70.66 thf(33578,plain,((! [A:nat,B:list_o,C:$o,D:nat]: (((nth_o @ (list_update_o @ B @ A @ C) @ D) = (((nth_o @ B @ D) | (A = D)) & ((C) | ~ (A = D)))) | ~ (ord_less_nat @ A @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7323])). 159.59/70.66 thf(4071,axiom,((ord_le72135733267957522d_enat = (^ [A:extended_enat,B:extended_enat]: (~ (ord_le2932123472753598470d_enat @ B @ A) & (ord_le2932123472753598470d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3095_order_Ostrict__iff__not)). 159.59/70.66 thf(21315,plain,(((ord_le72135733267957522d_enat) = (^ [A:extended_enat,B:extended_enat]: (~ (ord_le2932123472753598470d_enat @ B @ A) & (ord_le2932123472753598470d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4071])). 159.59/70.66 thf(1716,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ zero_zero_int @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5947_bit_Oconj__zero__left)). 159.59/70.66 thf(13797,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ zero_zero_int @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716])). 159.59/70.66 thf(7770,axiom,((! [A:num,B:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6031_or__numerals_I7_J)). 159.59/70.66 thf(35103,plain,((! [A:num,B:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7770])). 159.59/70.66 thf(3684,axiom,((! [A:int]: ((? [B:nat]: ((ord_less_nat @ zero_zero_nat @ B) & (A = (semiri1314217659103216013at_int @ B)))) <= (ord_less_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6847_zero__less__imp__eq__int)). 159.59/70.66 thf(20082,plain,((! [A:int]: (? [B:nat]: ((ord_less_nat @ zero_zero_nat @ B) & (A = (semiri1314217659103216013at_int @ B))) | ~ (ord_less_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3684])). 159.59/70.66 thf(2247,axiom,((! [A:num]: ~ (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5180_not__neg__one__less__neg__numeral)). 159.59/70.66 thf(15501,plain,((! [A:num]: ~ (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2247])). 159.59/70.66 thf(7936,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/sandbox/benchmark/theBenchmark.p',fact_1746_div__mult__self2)). 159.59/70.66 thf(35616,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)],[7936])). 159.59/70.66 thf(5004,axiom,((! [A:num,B:real]: ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7014_neg__numeral__le__ceiling)). 159.59/70.66 thf(24570,plain,((! [A:num,B:real]: ((ord_less_eq_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (archim7802044766580827645g_real @ B)) = (ord_less_real @ (minus_minus_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ one_one_real) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5004])). 159.59/70.66 thf(4035,axiom,((! [A:real,B:real,C: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))) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5240_neg__less__minus__divide__eq)). 159.59/70.66 thf(21212,plain,((! [A:real,B:real,C: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))) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4035])). 159.59/70.66 thf(5917,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/sandbox/benchmark/theBenchmark.p',fact_5641_cong__exp__iff__simps_I7_J)). 159.59/70.66 thf(28119,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)],[5917])). 159.59/70.66 thf(661,axiom,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5148_neg__numeral__less__zero)). 159.59/70.66 thf(10364,plain,((! [A:num]: (ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[661])). 159.59/70.66 thf(811,axiom,((sinh_complex = (^ [A:complex]: (divide1717551699836669952omplex @ (minus_minus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9361_sinh__field__def)). 159.59/70.66 thf(10873,plain,(((sinh_complex) = (^ [A:complex]: (divide1717551699836669952omplex @ (minus_minus_complex @ (exp_complex @ A) @ (exp_complex @ (uminus1482373934393186551omplex @ A))) @ (numera6690914467698888265omplex @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[811])). 159.59/70.66 thf(2875,axiom,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ A @ B) => (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4943_verit__negate__coefficient_I2_J)). 159.59/70.66 thf(17501,plain,((! [A:code_integer,B:code_integer]: ((ord_le6747313008572928689nteger @ A @ B) => (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ B) @ (uminus1351360451143612070nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2875])). 159.59/70.66 thf(7916,axiom,((! [A:complex]: (((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_complex) = (A = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1776_zero__eq__power2)). 159.59/70.66 thf(35558,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)],[7916])). 159.59/70.66 thf(7468,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2667_linorder__linear)). 159.59/70.66 thf(34055,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)],[7468])). 159.59/70.66 thf(2516,axiom,((ord_le2932123472753598470d_enat = (^ [A:extended_enat,B:extended_enat]: ((A = B) | (ord_le72135733267957522d_enat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3153_order__le__less)). 159.59/70.66 thf(16352,plain,(((ord_le2932123472753598470d_enat) = (^ [A:extended_enat,B:extended_enat]: ((A = B) | (ord_le72135733267957522d_enat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2516])). 159.59/70.66 thf(7558,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/sandbox/benchmark/theBenchmark.p',fact_520_deg__SUcn__Node)). 159.59/70.66 thf(34366,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)],[7558])). 159.59/70.66 thf(4438,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/sandbox/benchmark/theBenchmark.p',fact_5133_ln__gt__zero__imp__gt__one)). 159.59/70.66 thf(22469,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)],[4438])). 159.59/70.66 thf(7995,axiom,((! [A:nat,B:nat,C:nat]: ((((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)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9110_binomial__antimono)). 159.59/70.66 thf(35801,plain,((! [A:nat,B:nat,C:nat]: ((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) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7995])). 159.59/70.66 thf(3308,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ A @ B) <= (A != B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3190_order__le__neq__trans)). 159.59/70.66 thf(18894,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_less_int @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3308])). 159.59/70.66 thf(7383,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/sandbox/benchmark/theBenchmark.p',fact_8124_fact__num__eq__if)). 159.59/70.66 thf(33780,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)],[7383])). 159.59/70.66 thf(2754,axiom,((! [A:nat,B:real]: ((root @ A @ (inverse_inverse_real @ B)) = (inverse_inverse_real @ (root @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9501_real__root__inverse)). 159.59/70.66 thf(17127,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)],[2754])). 159.59/70.66 thf(4875,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((A = zero_zero_nat) | (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1866_divisors__zero)). 159.59/70.66 thf(24105,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)],[4875])). 159.59/70.66 thf(7760,axiom,(((finite_card_o @ top_top_set_o) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9820_card__UNIV__bool)). 159.59/70.66 thf(35075,plain,(((finite_card_o @ top_top_set_o) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7760])). 159.59/70.66 thf(4501,axiom,((! [A:num]: ((divide_divide_int @ (numeral_numeral_int @ (bit1 @ A)) @ (numeral_numeral_int @ (bit0 @ one))) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5616_numeral__Bit1__div__2)). 159.59/70.66 thf(22728,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)],[4501])). 159.59/70.66 thf(510,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/sandbox/benchmark/theBenchmark.p',fact_4775_max__number__of_I2_J)). 159.59/70.66 thf(9876,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)],[510])). 159.59/70.66 thf(2799,axiom,((! [A:extended_enat]: ((plus_p3455044024723400733d_enat @ zero_z5237406670263579293d_enat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1501_add__0)). 159.59/70.66 thf(17259,plain,((! [A:extended_enat]: ((plus_p3455044024723400733d_enat @ zero_z5237406670263579293d_enat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2799])). 159.59/70.66 thf(5555,axiom,((! [A:nat]: ((abs_abs_real @ (semiri5074537144036343181t_real @ A)) = (semiri5074537144036343181t_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6492_abs__of__nat)). 159.59/70.66 thf(26616,plain,((! [A:nat]: ((abs_abs_real @ (semiri5074537144036343181t_real @ A)) = (semiri5074537144036343181t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5555])). 159.59/70.66 thf(8169,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3556_divmod__digit__0_I2_J)). 159.59/70.66 thf(36376,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8169])). 159.59/70.66 thf(474,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/sandbox/benchmark/theBenchmark.p',fact_8308_gbinomial__absorption)). 159.59/70.66 thf(9760,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)],[474])). 159.59/70.66 thf(1481,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/sandbox/benchmark/theBenchmark.p',fact_2086_zero__less__mult__pos)). 159.59/70.66 thf(13087,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)],[1481])). 159.59/70.66 thf(7909,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/sandbox/benchmark/theBenchmark.p',fact_6768_bit__nat__def)). 159.59/70.66 thf(35537,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)],[7909])). 159.59/70.66 thf(4210,axiom,((! [A:nat,B:real]: (((ord_less_real @ B @ zero_zero_real) => (? [C:real]: ((ord_less_real @ B @ C) & ((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_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8141_Maclaurin__minus__cos__expansion)). 159.59/70.66 thf(21749,plain,((! [A:nat,B:real]: (((ord_less_real @ B @ zero_zero_real) => (? [C:real]: ((ord_less_real @ B @ C) & ((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_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4210])). 159.59/70.66 thf(3730,axiom,((! [A:complex,B:complex,C:nat]: (((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)))))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7844_lemma__termdiff2)). 159.59/70.66 thf(20251,plain,((! [A:complex,B:complex,C:nat]: (((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)))))) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3730])). 159.59/70.66 thf(1026,axiom,((! [A:(nat > complex),B:complex,C:(nat > complex),D:complex]: (((sums_complex @ (^ [E:nat]: (plus_plus_complex @ (A @ E) @ (C @ E))) @ (plus_plus_complex @ B @ D)) <= (sums_complex @ C @ D)) <= (sums_complex @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7890_sums__add)). 159.59/70.66 thf(11530,plain,((! [A:(nat > complex),B:complex,C:(nat > complex),D:complex]: ((sums_complex @ (^ [E:nat]: (plus_plus_complex @ (A @ E) @ (C @ E))) @ (plus_plus_complex @ B @ D)) | ~ (sums_complex @ (C) @ D) | ~ (sums_complex @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026])). 159.59/70.66 thf(6738,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/sandbox/benchmark/theBenchmark.p',fact_2318_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq)). 159.59/70.66 thf(31223,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)],[6738])). 159.59/70.66 thf(3544,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ C @ A)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ C) @ A)) <= (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4171_unit__div__mult__swap)). 159.59/70.66 thf(19624,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ C @ A)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ C) @ A)) | ~ (dvd_dvd_Code_integer @ A @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3544])). 159.59/70.66 thf(2208,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ (plus_plus_complex @ A @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4641_minus__add__cancel)). 159.59/70.66 thf(15377,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ A) @ (plus_plus_complex @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2208])). 159.59/70.66 thf(3118,axiom,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: (((dvd_dvd_Code_integer @ C @ D) => ((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ D @ C)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ D) @ (times_3573771949741848930nteger @ A @ C)))) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4089_div__mult__div__if__dvd)). 159.59/70.66 thf(18281,plain,((! [A:code_integer,B:code_integer,C:code_integer,D:code_integer]: (((dvd_dvd_Code_integer @ C @ D) => ((times_3573771949741848930nteger @ (divide6298287555418463151nteger @ B @ A) @ (divide6298287555418463151nteger @ D @ C)) = (divide6298287555418463151nteger @ (times_3573771949741848930nteger @ B @ D) @ (times_3573771949741848930nteger @ A @ C)))) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3118])). 159.59/70.66 thf(6573,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/sandbox/benchmark/theBenchmark.p',fact_841_diff__mult__distrib2)). 159.59/70.66 thf(30500,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)],[6573])). 159.59/70.66 thf(4256,axiom,((! [A:real,B:real,C:real]: ((A = (uminus_uminus_real @ (divide_divide_real @ B @ C))) = (((C != zero_zero_real) => ((times_times_real @ A @ C) = (uminus_uminus_real @ B))) & ((C = zero_zero_real) => (A = zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5199_eq__minus__divide__eq)). 159.59/70.66 thf(21910,plain,((! [A:real,B:real,C:real]: ((A = (uminus_uminus_real @ (divide_divide_real @ B @ C))) = (((~ (C = zero_zero_real)) => ((times_times_real @ A @ C) = (uminus_uminus_real @ B))) & ((C = zero_zero_real) => (A = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4256])). 159.59/70.66 thf(5607,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_707_mult__le__mono2)). 159.59/70.66 thf(26803,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5607])). 159.59/70.66 thf(7808,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/sandbox/benchmark/theBenchmark.p',fact_3414_mod__mult__self4)). 159.59/70.66 thf(35209,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)],[7808])). 159.59/70.66 thf(5915,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ A @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_power__Suc)). 159.59/70.66 thf(28113,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)],[5915])). 159.59/70.66 thf(3582,axiom,(((archim8280529875227126926d_real @ one_one_real) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6164_round__1)). 159.59/70.66 thf(19756,plain,(((archim8280529875227126926d_real @ one_one_real) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3582])). 159.59/70.66 thf(480,axiom,((! [A:real]: ((power_power_real @ (cosh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_real @ (power_power_real @ (sinh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9343_cosh__square__eq)). 159.59/70.66 thf(9780,plain,((! [A:real]: ((power_power_real @ (cosh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (plus_plus_real @ (power_power_real @ (sinh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[480])). 159.59/70.66 thf(1833,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/sandbox/benchmark/theBenchmark.p',fact_6876_exp__bound__lemma)). 159.59/70.66 thf(14182,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)],[1833])). 159.59/70.66 thf(3719,axiom,((! [A:int,B:int]: (((ord_less_eq_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/sandbox/benchmark/theBenchmark.p',fact_2266_add__pos__nonneg)). 159.59/70.66 thf(20214,plain,((! [A:int,B:int]: (((ord_less_eq_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)],[3719])). 159.59/70.66 thf(1102,axiom,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ (modulo_modulo_int @ C @ B) @ A) = (modulo_modulo_int @ C @ A)) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4031_mod__mod__cancel)). 159.59/70.66 thf(11789,plain,((! [A:int,B:int,C:int]: (((modulo_modulo_int @ (modulo_modulo_int @ C @ B) @ A) = (modulo_modulo_int @ C @ A)) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102])). 159.59/70.66 thf(7761,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2503_power2__le__imp__le)). 159.59/70.66 thf(35077,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ B)) | ~ (ord_less_eq_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)],[7761])). 159.59/70.66 thf(5818,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/sandbox/benchmark/theBenchmark.p',fact_1565_mult__cancel1)). 159.59/70.66 thf(27693,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)],[5818])). 159.59/70.66 thf(381,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = zero_z3403309356797280102nteger) <= (A = zero_z3403309356797280102nteger)) & (((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = (divide6298287555418463151nteger @ B @ C)) <= (A != zero_z3403309356797280102nteger))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1638_div__mult__mult1__if)). 159.59/70.66 thf(9438,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = zero_z3403309356797280102nteger) | ~ (A = zero_z3403309356797280102nteger)) & (((divide6298287555418463151nteger @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = (divide6298287555418463151nteger @ B @ C)) | (A = zero_z3403309356797280102nteger))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[381])). 159.59/70.66 thf(6109,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (~ (ord_less_num @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4449_pinf_I5_J)). 159.59/70.66 thf(28782,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (~ (ord_less_num @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6109])). 159.59/70.66 thf(2162,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C) => (ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ C @ A) @ (times_7803423173614009249d_enat @ C @ B))) <= (ord_le2932123472753598470d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1988_mult__left__mono)). 159.59/70.66 thf(15223,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C) => (ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ C @ A) @ (times_7803423173614009249d_enat @ C @ B))) | ~ (ord_le2932123472753598470d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2162])). 159.59/70.66 thf(6719,axiom,((xa = mi)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_xmi)). 159.59/70.66 thf(31162,plain,((xa = mi)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6719])). 159.59/70.66 thf(5973,axiom,((! [A:int,B:int,C:int]: ((A = B) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2746_ord__eq__le__trans)). 159.59/70.66 thf(28352,plain,((! [A:int,B:int,C:int]: ((A = B) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5973])). 159.59/70.66 thf(6376,axiom,((! [A:complex]: (((real_V1022390504157884413omplex @ A) = one_one_real) <= ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6952_square__norm__one)). 159.59/70.66 thf(29720,plain,((! [A:complex]: (((real_V1022390504157884413omplex @ A) = one_one_real) | ~ ((power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6376])). 159.59/70.66 thf(4864,axiom,((! [A:nat,B:nat]: ((ord_max_nat @ (ord_max_nat @ A @ B) @ B) = (ord_max_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_765_max_Oright__idem)). 159.59/70.66 thf(24073,plain,((! [A:nat,B:nat]: ((ord_max_nat @ (ord_max_nat @ A @ B) @ B) = (ord_max_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4864])). 159.59/70.66 thf(2657,axiom,((! [A:nat]: (((semiri1314217659103216013at_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6509_of__nat__eq__0__iff)). 159.59/70.66 thf(16814,plain,((! [A:nat]: (((semiri1314217659103216013at_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2657])). 159.59/70.66 thf(797,axiom,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ C @ B)) = ((B = zero_zero_complex) | (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1552_divide__cancel__right)). 159.59/70.66 thf(10821,plain,((! [A:complex,B:complex,C:complex]: (((divide1717551699836669952omplex @ A @ B) = (divide1717551699836669952omplex @ C @ B)) = ((B = zero_zero_complex) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[797])). 159.59/70.66 thf(7013,axiom,(((pred_numeral @ one) = zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5680_pred__numeral__simps_I1_J)). 159.59/70.66 thf(32397,plain,(((pred_numeral @ one) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7013])). 159.59/70.66 thf(4024,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((A != one_one_real) => ((ord_less_real @ zero_zero_real @ B) => ((powr_real @ A @ (log @ A @ B)) = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7222_powr__log__cancel)). 159.59/70.66 thf(21180,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((~ (A = one_one_real)) => ((ord_less_real @ zero_zero_real @ B) => ((powr_real @ A @ (log @ A @ B)) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4024])). 159.59/70.66 thf(5491,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/sandbox/benchmark/theBenchmark.p',fact_816_diff__commute)). 159.59/70.66 thf(26416,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)],[5491])). 159.59/70.66 thf(4,axiom,((! [A:real,B:real]: ((A != zero_zero_real) => ((real_V1803761363581548252l_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (real_V1803761363581548252l_real @ B) @ (real_V1803761363581548252l_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7513_nonzero__of__real__divide)). 159.59/70.66 thf(8260,plain,((! [A:real,B:real]: ((~ (A = zero_zero_real)) => ((real_V1803761363581548252l_real @ (divide_divide_real @ B @ A)) = (divide_divide_real @ (real_V1803761363581548252l_real @ B) @ (real_V1803761363581548252l_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 159.59/70.66 thf(5927,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/sandbox/benchmark/theBenchmark.p',fact_1793_zero__less__power2)). 159.59/70.66 thf(28151,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)],[5927])). 159.59/70.66 thf(3052,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/sandbox/benchmark/theBenchmark.p',fact_3855_div__diff)). 159.59/70.66 thf(18061,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)],[3052])). 159.59/70.66 thf(4737,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/sandbox/benchmark/theBenchmark.p',fact_1090_add__diff__cancel__right)). 159.59/70.66 thf(23614,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)],[4737])). 159.59/70.66 thf(3618,axiom,((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1828_le__numeral__extra_I3_J)). 159.59/70.66 thf(19876,plain,((ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3618])). 159.59/70.66 thf(6319,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((abs_abs_real @ (root @ A @ (power_power_real @ B @ A))) = (abs_abs_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9515_root__abs__power)). 159.59/70.66 thf(29553,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((abs_abs_real @ (root @ A @ (power_power_real @ B @ A))) = (abs_abs_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6319])). 159.59/70.66 thf(376,axiom,((! [A:code_integer,B:code_integer]: (((plus_p5714425477246183910nteger @ A @ B) = zero_z3403309356797280102nteger) => ((uminus1351360451143612070nteger @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5053_add_Oinverse__unique)). 159.59/70.66 thf(9417,plain,((! [A:code_integer,B:code_integer]: (((plus_p5714425477246183910nteger @ A @ B) = zero_z3403309356797280102nteger) => ((uminus1351360451143612070nteger @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[376])). 159.59/70.66 thf(6111,axiom,((! [A:real,B:real]: (((B != zero_zero_real) => ((minus_minus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (uminus_uminus_real @ (times_times_real @ (times_times_real @ (inverse_inverse_real @ A) @ (minus_minus_real @ A @ B)) @ (inverse_inverse_real @ B))))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9091_inverse__diff__inverse)). 159.59/70.66 thf(28787,plain,((! [A:real,B:real]: (((~ (B = zero_zero_real)) => ((minus_minus_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (uminus_uminus_real @ (times_times_real @ (times_times_real @ (inverse_inverse_real @ A) @ (minus_minus_real @ A @ B)) @ (inverse_inverse_real @ B))))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6111])). 159.59/70.66 thf(3892,axiom,((! [A:nat,B:nat]: (((comm_s2602460028002588243omplex @ (uminus1482373934393186551omplex @ (semiri8010041392384452111omplex @ A)) @ B) = zero_zero_complex) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8284_pochhammer__of__nat__eq__0__iff)). 159.59/70.66 thf(20782,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)],[3892])). 159.59/70.66 thf(7608,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:vEBT_VEBT]: (((list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ C @ A @ D) @ B @ E) = (list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ C @ B @ E) @ A @ D)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_list__update__swap)). 159.59/70.66 thf(34579,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:vEBT_VEBT]: (((list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ C @ A @ D) @ B @ E) = (list_u1324408373059187874T_VEBT @ (list_u1324408373059187874T_VEBT @ C @ B @ E) @ A @ D)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7608])). 159.59/70.66 thf(491,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/sandbox/benchmark/theBenchmark.p',fact_9594_or__not__numerals_I4_J)). 159.59/70.66 thf(9819,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)],[491])). 159.59/70.66 thf(1858,axiom,((! [A:code_integer,B:code_integer]: ? [C:code_integer]: ! [D:code_integer]: ((ord_le6747313008572928689nteger @ D @ C) => ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ B)) = (dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4536_minf_I9_J)). 159.59/70.66 thf(14257,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1858])). 159.59/70.66 thf(1433,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/sandbox/benchmark/theBenchmark.p',fact_9461_bit__nat__iff)). 159.59/70.66 thf(12925,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)],[1433])). 159.59/70.66 thf(1357,axiom,((! [A:set_nat]: ((finite_finite_nat @ A) => ((A != bot_bot_set_nat) => (? [B:nat]: (~ (? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ B))) & (member_nat @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4286_ex__min__if__finite)). 159.59/70.66 thf(12633,plain,((! [A:set_nat]: ((finite_finite_nat @ A) => ((~ (A = bot_bot_set_nat)) => (? [B:nat]: (~ (? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ B))) & (member_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357])). 159.59/70.66 thf(6896,axiom,(((neg_numeral_dbl_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4886_dbl__simps_I4_J)). 159.59/70.66 thf(31844,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)],[6896])). 159.59/70.66 thf(4476,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((sin_real @ (arccos @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7321_sin__arccos__abs)). 159.59/70.66 thf(22647,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => ((sin_real @ (arccos @ A)) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4476])). 159.59/70.66 thf(551,axiom,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5149_neg__numeral__less__zero)). 159.59/70.66 thf(10008,plain,((! [A:num]: (ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[551])). 159.59/70.66 thf(1461,axiom,((! [A:real]: ((ord_less_real @ (uminus_uminus_real @ A) @ A) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4680_neg__less__pos)). 159.59/70.66 thf(13021,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)],[1461])). 159.59/70.66 thf(6777,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (ord_max_nat @ A @ B)) = (ord_max_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6710_of__nat__max)). 159.59/70.66 thf(31375,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)],[6777])). 159.59/70.66 thf(2333,axiom,((! [A:nat]: (((semiri4216267220026989637d_enat @ A) = zero_z5237406670263579293d_enat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6507_of__nat__eq__0__iff)). 159.59/70.66 thf(15749,plain,((! [A:nat]: (((semiri4216267220026989637d_enat @ A) = zero_z5237406670263579293d_enat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2333])). 159.59/70.66 thf(1772,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ pi) @ A) => (((ord_less_real @ (cos_real @ A) @ (cos_real @ B)) <= (ord_less_eq_real @ B @ zero_zero_real)) <= (ord_less_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7148_cos__monotone__minus__pi__0)). 159.59/70.66 thf(13974,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (uminus_uminus_real @ pi) @ A) => ((ord_less_real @ (cos_real @ A) @ (cos_real @ B)) | ~ (ord_less_eq_real @ B @ zero_zero_real) | ~ (ord_less_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772])). 159.59/70.66 thf(7958,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1765_div__mult__self__is__m)). 159.59/70.66 thf(35690,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (times_times_nat @ B @ A) @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7958])). 159.59/70.66 thf(2686,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/sandbox/benchmark/theBenchmark.p',fact_6995_ceiling__divide__eq__div__numeral)). 159.59/70.66 thf(16914,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)],[2686])). 159.59/70.66 thf(1070,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ A) @ B @ C) = ((ord_less_nat @ C @ B) & ! [D:nat]: (((ord_less_nat @ D @ B) & (vEBT_vebt_member @ A @ D)) => (ord_less_eq_nat @ D @ C)) & (vEBT_vebt_member @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_pred__member)). 159.59/70.66 thf(11681,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_is_pred_in_set @ (vEBT_VEBT_set_vebt @ A) @ B @ C) = ((ord_less_nat @ C @ B) & ! [D:nat]: (((ord_less_nat @ D @ B) & (vEBT_vebt_member @ A @ D)) => (ord_less_eq_nat @ D @ C)) & (vEBT_vebt_member @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070])). 159.59/70.66 thf(5709,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/sandbox/benchmark/theBenchmark.p',fact_7832_double__gauss__sum__from__Suc__0)). 159.59/70.66 thf(27154,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)],[5709])). 159.59/70.66 thf(2410,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) => ((ord_le2932123472753598470d_enat @ A @ B) = (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3039_antisym__conv1)). 159.59/70.66 thf(15997,plain,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) => ((ord_le2932123472753598470d_enat @ A @ B) = (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2410])). 159.59/70.66 thf(5942,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6174_or__nat__numerals_I3_J)). 159.59/70.66 thf(28257,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)],[5942])). 159.59/70.66 thf(6935,axiom,((! [A:nat]: (ord_less_eq_real @ zero_zero_real @ (semiri5074537144036343181t_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6663_of__nat__0__le__iff)). 159.59/70.66 thf(31984,plain,((! [A:nat]: (ord_less_eq_real @ zero_zero_real @ (semiri5074537144036343181t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6935])). 159.59/70.66 thf(4139,axiom,((! [A:real]: ((ord_less_real @ A @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4683_less__neg__neg)). 159.59/70.66 thf(21524,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)],[4139])). 159.59/70.66 thf(2952,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/sandbox/benchmark/theBenchmark.p',fact_7661_sum_Onat__ivl__Suc_H)). 159.59/70.66 thf(17760,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)],[2952])). 159.59/70.66 thf(5587,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/sandbox/benchmark/theBenchmark.p',fact_9133_binomial__addition__formula)). 159.59/70.66 thf(26720,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)],[5587])). 159.59/70.66 thf(6429,axiom,((! [A:nat,B:complex]: ((dvd_dvd_complex @ B @ (power_power_complex @ B @ A)) <= ((B = one_one_complex) | (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4219_dvd__power)). 159.59/70.66 thf(29968,plain,((! [A:nat,B:complex]: ((dvd_dvd_complex @ B @ (power_power_complex @ B @ A)) | ~ ((B = one_one_complex) | (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6429])). 159.59/70.66 thf(2878,axiom,((! [A:real,B:real]: (ord_less_eq_int @ (archim7802044766580827645g_real @ (plus_plus_real @ A @ B)) @ (plus_plus_int @ (archim7802044766580827645g_real @ A) @ (archim7802044766580827645g_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7102_ceiling__add__le)). 159.59/70.66 thf(17508,plain,((! [A:real,B:real]: (ord_less_eq_int @ (archim7802044766580827645g_real @ (plus_plus_real @ A @ B)) @ (plus_plus_int @ (archim7802044766580827645g_real @ A) @ (archim7802044766580827645g_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2878])). 159.59/70.66 thf(5319,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/sandbox/benchmark/theBenchmark.p',fact_4613_neg__le__iff__le)). 159.59/70.66 thf(25711,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)],[5319])). 159.59/70.66 thf(6427,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/sandbox/benchmark/theBenchmark.p',fact_2148_zero__le__power)). 159.59/70.66 thf(29955,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)],[6427])). 159.59/70.66 thf(1203,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/sandbox/benchmark/theBenchmark.p',fact_7297_powr__neg__numeral)). 159.59/70.66 thf(12130,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)],[1203])). 159.59/70.66 thf(2752,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) => ((ord_le2932123472753598470d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ C) <= (ord_le2932123472753598470d_enat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2044_add__decreasing)). 159.59/70.66 thf(17120,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) => ((ord_le2932123472753598470d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ C) | ~ (ord_le2932123472753598470d_enat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2752])). 159.59/70.66 thf(4965,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int)) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1970_mult__nonpos__nonneg)). 159.59/70.66 thf(24446,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => (ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int)) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4965])). 159.59/70.66 thf(4871,axiom,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1083_mult_Oright__neutral)). 159.59/70.66 thf(24092,plain,((! [A:int]: ((times_times_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4871])). 159.59/70.66 thf(6937,axiom,((! [A:nat,B:(num > nat),C:num,D:num]: ((((ord_less_eq_nat @ A @ (B @ D)) <= (! [E:num,F:num]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_less_eq_num @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2657_ord__eq__le__subst)). 159.59/70.66 thf(31989,plain,((! [A:nat,B:(num > nat),C:num,D:num]: ((ord_less_eq_nat @ A @ (B @ D)) | ~ (! [E:num,F:num]: ((ord_less_eq_nat @ (B @ E) @ (B @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_less_eq_num @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6937])). 159.59/70.66 thf(7039,axiom,((ord_less_eq_real @ zero_zero_real @ one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2057_zero__less__one__class_Ozero__le__one)). 159.59/70.66 thf(32481,plain,((ord_less_eq_real @ zero_zero_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7039])). 159.59/70.66 thf(1886,axiom,((! [A:real,B:real]: ((((divide_divide_real @ B @ A) = one_one_real) = (B = A)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2180_right__inverse__eq)). 159.59/70.66 thf(14344,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)],[1886])). 159.59/70.66 thf(1310,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/sandbox/benchmark/theBenchmark.p',fact_9437_nat__abs__mult__distrib)). 159.59/70.66 thf(12484,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)],[1310])). 159.59/70.66 thf(7597,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((A = B) <= (ord_less_eq_nat @ zero_zero_nat @ B))) <= ((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2506_power2__eq__imp__eq)). 159.59/70.66 thf(34551,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((A = B) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))) | ~ ((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)],[7597])). 159.59/70.66 thf(2948,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/sandbox/benchmark/theBenchmark.p',fact_4528_pinf_I9_J)). 159.59/70.66 thf(17743,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2948])). 159.59/70.66 thf(6505,axiom,(((size_s170228958280169651at_nat @ none_P5556105721700978146at_nat) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2199_option_Osize_I3_J)). 159.59/70.66 thf(30261,plain,(((size_s170228958280169651at_nat @ none_P5556105721700978146at_nat) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6505])). 159.59/70.66 thf(2383,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ one_one_real @ C) => (ord_less_real @ (powr_real @ C @ A) @ (powr_real @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7236_powr__less__mono)). 159.59/70.66 thf(15903,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ one_one_real @ C) => (ord_less_real @ (powr_real @ C @ A) @ (powr_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2383])). 159.59/70.66 thf(710,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/sandbox/benchmark/theBenchmark.p',fact_5852_numeral__power__less__of__int__cancel__iff)). 159.59/70.66 thf(10541,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)],[710])). 159.59/70.66 thf(7355,axiom,(((semiri4449623510593786356d_enat @ zero_zero_nat) = one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8044_fact__0)). 159.59/70.66 thf(33689,plain,(((semiri4449623510593786356d_enat @ zero_zero_nat) = one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7355])). 159.59/70.66 thf(5519,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10118_atLeastLessThan__add__Un)). 159.59/70.66 thf(26514,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5519])). 159.59/70.66 thf(5767,axiom,((ord_less_num = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3115_dual__order_Ostrict__iff__order)). 159.59/70.66 thf(27347,plain,(((ord_less_num) = (^ [A:num,B:num]: ((ord_less_eq_num @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5767])). 159.59/70.66 thf(1661,axiom,((! [A:int]: ~ (ord_less_int @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2887_order__less__irrefl)). 159.59/70.66 thf(13632,plain,((! [A:int]: ~ (ord_less_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661])). 159.59/70.66 thf(8115,axiom,(((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_z5237406670263579293d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2457_zero__power2)). 159.59/70.66 thf(36191,plain,(((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_z5237406670263579293d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8115])). 159.59/70.66 thf(6845,axiom,((! [A:real]: (((topolo6980174941875973593q_real @ (power_power_real @ A)) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6857_monoseq__realpow)). 159.59/70.66 thf(31687,plain,((! [A:real]: ((topolo6980174941875973593q_real @ (power_power_real @ 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)],[6845])). 159.59/70.66 thf(6432,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)) @ A) != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2515_exp__add__not__zero__imp__left)). 159.59/70.66 thf(29983,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)) @ A) = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6432])). 159.59/70.66 thf(822,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (nat2 @ (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9439_nat__plus__as__int)). 159.59/70.66 thf(10905,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)],[822])). 159.59/70.66 thf(607,axiom,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_bits__div__by__1)). 159.59/70.66 thf(10188,plain,((! [A:int]: ((divide_divide_int @ A @ one_one_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[607])). 159.59/70.66 thf(3310,axiom,((! [A:complex,B:nat]: ((power_power_complex @ (invers8013647133539491842omplex @ A) @ B) = (invers8013647133539491842omplex @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9016_power__inverse)). 159.59/70.66 thf(18900,plain,((! [A:complex,B:nat]: ((power_power_complex @ (invers8013647133539491842omplex @ A) @ B) = (invers8013647133539491842omplex @ (power_power_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3310])). 159.59/70.66 thf(1512,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = one_one_real) = ((A = B) & (B != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1674_divide__eq__1__iff)). 159.59/70.66 thf(13178,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = one_one_real) = ((A = B) & ~ (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512])). 159.59/70.66 thf(6153,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/sandbox/benchmark/theBenchmark.p',fact_3436_not__mod__2__eq__0__eq__1)). 159.59/70.66 thf(28925,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)],[6153])). 159.59/70.66 thf(6042,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/sandbox/benchmark/theBenchmark.p',fact_7410_sum_Odistrib)). 159.59/70.66 thf(28574,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)],[6042])). 159.59/70.66 thf(1785,axiom,((! [A:num,B:num]: ((minus_8373710615458151222nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (numera6620942414471956472nteger @ (plus_plus_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4787_diff__numeral__simps_I2_J)). 159.59/70.66 thf(14015,plain,((! [A:num,B:num]: ((minus_8373710615458151222nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (numera6620942414471956472nteger @ (plus_plus_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1785])). 159.59/70.66 thf(4101,axiom,((! [A:num,B:num,C:complex]: ((real_V2046097035970521341omplex @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A)) @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ C)) = (real_V2046097035970521341omplex @ (divide_divide_real @ (numeral_numeral_real @ B) @ (numeral_numeral_real @ A)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9206_inverse__scaleR__times)). 159.59/70.66 thf(21411,plain,((! [A:num,B:num,C:complex]: ((real_V2046097035970521341omplex @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A)) @ (times_times_complex @ (numera6690914467698888265omplex @ B) @ C)) = (real_V2046097035970521341omplex @ (divide_divide_real @ (numeral_numeral_real @ B) @ (numeral_numeral_real @ A)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4101])). 159.59/70.66 thf(1229,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/sandbox/benchmark/theBenchmark.p',fact_5827_of__int__1__le__iff)). 159.59/70.66 thf(12226,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)],[1229])). 159.59/70.66 thf(6443,axiom,((! [A:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one))) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5207_mult__1s__ring__1_I2_J)). 159.59/70.66 thf(30034,plain,((! [A:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one))) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6443])). 159.59/70.66 thf(7080,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/sandbox/benchmark/theBenchmark.p',fact_705_mult__le__mono)). 159.59/70.66 thf(32645,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)],[7080])). 159.59/70.66 thf(2785,axiom,((! [A:int,B:int]: ((A = (plus_plus_int @ B @ A)) = (B = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1517_add__cancel__right__left)). 159.59/70.66 thf(17220,plain,((! [A:int,B:int]: ((A = (plus_plus_int @ B @ A)) = (B = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2785])). 159.59/70.66 thf(5478,axiom,((! [A:num,B:num]: (((~ (ord_less_num @ A @ B)) => ((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit1 @ B)) = (unique5026877609467782581ep_nat @ (bit1 @ B) @ (unique5055182867167087721od_nat @ (bit1 @ A) @ (bit0 @ (bit1 @ B)))))) & (((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit1 @ B)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit1 @ A)))) <= (ord_less_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5470_divmod__algorithm__code_I8_J)). 159.59/70.66 thf(26368,plain,((! [A:num,B:num]: (((~ (ord_less_num @ A @ B)) => ((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit1 @ B)) = (unique5026877609467782581ep_nat @ (bit1 @ B) @ (unique5055182867167087721od_nat @ (bit1 @ A) @ (bit0 @ (bit1 @ B)))))) & (((unique5055182867167087721od_nat @ (bit1 @ A) @ (bit1 @ B)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit1 @ A)))) | ~ (ord_less_num @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5478])). 159.59/70.66 thf(7129,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_delete @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = (vEBT_Leaf @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1927_vebt__delete_Osimps_I3_J)). 159.59/70.66 thf(32865,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_delete @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = (vEBT_Leaf @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7129])). 159.59/70.66 thf(2688,axiom,((! [A:real,B:(real > real),C:(nat > real),D:nat]: ((? [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)))))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8135_Maclaurin__lemma)). 159.59/70.66 thf(16925,plain,((! [A:real,B:(real > real),C:(nat > real),D:nat]: (? [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))))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2688])). 159.59/70.66 thf(4309,axiom,((dvd_dvd_complex = (^ [A:complex,B:complex]: ? [C:complex]: (B = (times_times_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3940_dvd__def)). 159.59/70.66 thf(22070,plain,(((dvd_dvd_complex) = (^ [A:complex,B:complex]: ? [C:complex]: (B = (times_times_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4309])). 159.59/70.66 thf(5018,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (((ord_less_eq_nat @ B @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) => ((minus_minus_nat @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ B) = (modulo_modulo_nat @ A @ B))) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3571_divmod__digit__1_I2_J)). 159.59/70.66 thf(24618,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (((ord_less_eq_nat @ B @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) => ((minus_minus_nat @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ B) = (modulo_modulo_nat @ A @ B))) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5018])). 159.59/70.66 thf(507,axiom,((! [A:set_nat,B:set_nat,C:nat,D:(nat > nat)]: ((((member_nat @ C @ (minus_minus_set_nat @ A @ B)) => (((! [E:nat]: ((member_nat @ E @ A) => (ord_less_eq_nat @ zero_zero_nat @ (D @ E)))) => (ord_less_nat @ (groups3542108847815614940at_nat @ D @ B) @ (groups3542108847815614940at_nat @ D @ A))) <= (ord_less_nat @ zero_zero_nat @ (D @ C)))) <= (ord_less_eq_set_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7743_sum__strict__mono2)). 159.59/70.66 thf(9866,plain,((! [A:set_nat,B:set_nat,C:nat,D:(nat > nat)]: (((member_nat @ C @ (minus_minus_set_nat @ A @ B)) => (((! [E:nat]: ((member_nat @ E @ A) => (ord_less_eq_nat @ zero_zero_nat @ (D @ E)))) => (ord_less_nat @ (groups3542108847815614940at_nat @ (D) @ B) @ (groups3542108847815614940at_nat @ (D) @ A))) | ~ (ord_less_nat @ zero_zero_nat @ (D @ C)))) | ~ (ord_less_eq_set_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])). 159.59/70.66 thf(2616,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/sandbox/benchmark/theBenchmark.p',fact_6812_sin__int__2pin)). 159.59/70.66 thf(16685,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)],[2616])). 159.59/70.66 thf(7877,axiom,((! [A:num,B:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6029_or__numerals_I6_J)). 159.59/70.66 thf(35431,plain,((! [A:num,B:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7877])). 159.59/70.66 thf(7634,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_trans__less__add1)). 159.59/70.66 thf(34656,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)],[7634])). 159.59/70.66 thf(5303,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/sandbox/benchmark/theBenchmark.p',fact_1720_nat__power__eq__Suc__0__iff)). 159.59/70.66 thf(25638,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)],[5303])). 159.59/70.66 thf(135,axiom,((~ (dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4043_not__is__unit__0)). 159.59/70.66 thf(8666,plain,((~ (dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 159.59/70.66 thf(1814,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (((divide6298287555418463151nteger @ B @ A) = (divide6298287555418463151nteger @ C @ A)) = (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4098_unit__div__cancel)). 159.59/70.66 thf(14108,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => (((divide6298287555418463151nteger @ B @ A) = (divide6298287555418463151nteger @ C @ A)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1814])). 159.59/70.66 thf(1269,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/sandbox/benchmark/theBenchmark.p',fact_3082_order_Ostrict__trans1)). 159.59/70.66 thf(12355,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)],[1269])). 159.59/70.66 thf(107,axiom,((! [A:real,B:real]: ((((tanh_real @ (plus_plus_real @ A @ B)) = (divide_divide_real @ (plus_plus_real @ (tanh_real @ A) @ (tanh_real @ B)) @ (plus_plus_real @ one_one_real @ (times_times_real @ (tanh_real @ A) @ (tanh_real @ B))))) <= ((cosh_real @ B) != zero_zero_real)) <= ((cosh_real @ A) != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9354_tanh__add)). 159.59/70.66 thf(8579,plain,((! [A:real,B:real]: (((tanh_real @ (plus_plus_real @ A @ B)) = (divide_divide_real @ (plus_plus_real @ (tanh_real @ A) @ (tanh_real @ B)) @ (plus_plus_real @ one_one_real @ (times_times_real @ (tanh_real @ A) @ (tanh_real @ B))))) | ((cosh_real @ B) = zero_zero_real) | ((cosh_real @ A) = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 159.59/70.66 thf(5845,axiom,((! [A:num,B:num]: (((uminus_uminus_real @ (numeral_numeral_real @ A)) = (uminus_uminus_real @ (numeral_numeral_real @ B))) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4619_neg__numeral__eq__iff)). 159.59/70.66 thf(27856,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)],[5845])). 159.59/70.66 thf(3379,axiom,((! [A:set_nat,B:nat,C:(nat > int)]: (((((ord_less_int @ one_one_int @ (groups705719431365010083at_int @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_int @ one_one_int @ (C @ D))))) <= (ord_less_int @ one_one_int @ (C @ B))) <= (member_nat @ B @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8646_less__1__prod2)). 159.59/70.66 thf(19111,plain,((! [A:set_nat,B:nat,C:(nat > int)]: ((ord_less_int @ one_one_int @ (groups705719431365010083at_int @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_int @ one_one_int @ (C @ D)))) | ~ (ord_less_int @ one_one_int @ (C @ B)) | ~ (member_nat @ B @ A) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3379])). 159.59/70.66 thf(8191,axiom,((! [A:nat]: (((power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1773_zero__eq__power2)). 159.59/70.66 thf(36442,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)],[8191])). 159.59/70.66 thf(6171,axiom,((! [A:real]: ((ord_less_eq_real @ (sqrt @ A) @ one_one_real) = (ord_less_eq_real @ A @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6322_real__sqrt__le__1__iff)). 159.59/70.66 thf(28998,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)],[6171])). 159.59/70.66 thf(6560,axiom,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((nat2 @ (power_power_int @ A @ B)) = (power_power_nat @ (nat2 @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9453_nat__power__eq)). 159.59/70.66 thf(30460,plain,((! [A:int,B:nat]: ((ord_less_eq_int @ zero_zero_int @ A) => ((nat2 @ (power_power_int @ A @ B)) = (power_power_nat @ (nat2 @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6560])). 159.59/70.66 thf(979,axiom,((! [A:complex]: (sums_complex @ (^ [B:nat]: (if_complex @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ zero_zero_complex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B)))) @ (sinh_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9301_sinh__converges)). 159.59/70.66 thf(11383,plain,((! [A:complex]: (sums_complex @ (^ [B:nat]: (if_complex @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ zero_zero_complex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_complex @ A @ B)))) @ (sinh_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[979])). 159.59/70.66 thf(4690,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/sandbox/benchmark/theBenchmark.p',fact_5476_signed__take__bit__Suc__bit1)). 159.59/70.66 thf(23469,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)],[4690])). 159.59/70.66 thf(3915,axiom,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (cos_real @ A)) @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7107_abs__cos__le__one)). 159.59/70.66 thf(20849,plain,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (cos_real @ A)) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3915])). 159.59/70.66 thf(6898,axiom,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1415_lambda__one)). 159.59/70.66 thf(31849,plain,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6898])). 159.59/70.66 thf(6881,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) <= (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2671_order__eq__refl)). 159.59/70.66 thf(31796,plain,((! [A:num,B:num]: ((ord_less_eq_num @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6881])). 159.59/70.66 thf(721,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/sandbox/benchmark/theBenchmark.p',fact_5608_numeral__code_I3_J)). 159.59/70.66 thf(10578,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)],[721])). 159.59/70.66 thf(4434,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/sandbox/benchmark/theBenchmark.p',fact_6813_sin__3over2__pi)). 159.59/70.66 thf(22458,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)],[4434])). 159.59/70.66 thf(3497,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (bit_se1412395901928357646or_nat @ A @ B)) = (bit_se1409905431419307370or_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6719_of__nat__or__eq)). 159.59/70.66 thf(19482,plain,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (bit_se1412395901928357646or_nat @ A @ B)) = (bit_se1409905431419307370or_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3497])). 159.59/70.66 thf(2135,axiom,((! [A:int,B:int,C:int]: ((bit_se1409905431419307370or_int @ (bit_se725231765392027082nd_int @ A @ B) @ C) = (bit_se725231765392027082nd_int @ (bit_se1409905431419307370or_int @ A @ C) @ (bit_se1409905431419307370or_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6037_bit_Odisj__conj__distrib2)). 159.59/70.66 thf(15144,plain,((! [A:int,B:int,C:int]: ((bit_se1409905431419307370or_int @ (bit_se725231765392027082nd_int @ A @ B) @ C) = (bit_se725231765392027082nd_int @ (bit_se1409905431419307370or_int @ A @ C) @ (bit_se1409905431419307370or_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2135])). 159.59/70.66 thf(2741,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((~ (finite_finite_nat @ A)) => (~ (finite_finite_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3762_infinite__super)). 159.59/70.66 thf(17088,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((~ (finite_finite_nat @ A)) => (~ (finite_finite_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2741])). 159.59/70.66 thf(2698,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/sandbox/benchmark/theBenchmark.p',fact_9160_real__le__x__sinh)). 159.59/70.66 thf(16956,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)],[2698])). 159.59/70.66 thf(445,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/sandbox/benchmark/theBenchmark.p',fact_9551_xor__negative__int__iff)). 159.59/70.66 thf(9647,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)],[445])). 159.59/70.66 thf(3727,axiom,((! [A:real]: ((plus_plus_int @ (archim6058952711729229775r_real @ A) @ one_one_int) = (archim6058952711729229775r_real @ (plus_plus_real @ A @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8247_one__add__floor)). 159.59/70.66 thf(20242,plain,((! [A:real]: ((plus_plus_int @ (archim6058952711729229775r_real @ A) @ one_one_int) = (archim6058952711729229775r_real @ (plus_plus_real @ A @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3727])). 159.59/70.66 thf(4491,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_div__le__dividend)). 159.59/70.66 thf(22697,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4491])). 159.59/70.66 thf(1632,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/sandbox/benchmark/theBenchmark.p',fact_6475_unset__bit__eq)). 159.59/70.66 thf(13549,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)],[1632])). 159.59/70.66 thf(2791,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/sandbox/benchmark/theBenchmark.p',fact_5831_of__int__1__less__iff)). 159.59/70.66 thf(17237,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)],[2791])). 159.59/70.66 thf(3491,axiom,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ A @ B))) = (modulo364778990260209775nteger @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3530_minus__mult__div__eq__mod)). 159.59/70.66 thf(19463,plain,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ A @ B))) = (modulo364778990260209775nteger @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3491])). 159.59/70.66 thf(3418,axiom,((! [A:real]: (ord_less_eq_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A)) @ (plus_plus_real @ A @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7116_of__int__ceiling__le__add__one)). 159.59/70.66 thf(19243,plain,((! [A:real]: (ord_less_eq_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A)) @ (plus_plus_real @ A @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3418])). 159.59/70.66 thf(3700,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/sandbox/benchmark/theBenchmark.p',fact_5782_of__int__add)). 159.59/70.66 thf(20135,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)],[3700])). 159.59/70.66 thf(3596,axiom,((! [A:int]: ((ord_less_int @ zero_zero_int @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4678_neg__0__less__iff__less)). 159.59/70.66 thf(19798,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)],[3596])). 159.59/70.66 thf(696,axiom,((! [A:nat,B:(extended_enat > nat),C:extended_enat,D:extended_enat]: ((((! [E:extended_enat,F:extended_enat]: ((ord_less_nat @ (B @ E) @ (B @ F)) <= (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_nat @ A @ (B @ D))) <= (ord_le72135733267957522d_enat @ C @ D)) <= (A = (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2866_ord__eq__less__subst)). 159.59/70.66 thf(10479,plain,((! [A:nat,B:(extended_enat > nat),C:extended_enat,D:extended_enat]: (((! [E:extended_enat,F:extended_enat]: ((ord_less_nat @ (B @ E) @ (B @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) => (ord_less_nat @ A @ (B @ D))) | ~ (ord_le72135733267957522d_enat @ C @ D) | ~ (A = (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[696])). 159.59/70.66 thf(7426,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) = B) = ((A = one_one_real) | (B = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1615_mult__cancel__right2)). 159.59/70.66 thf(33906,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)],[7426])). 159.59/70.66 thf(2598,axiom,((! [A:int,B:int]: ((! [C:nat]: (~ (bit_se1146084159140164899it_int @ A @ C) | ~ (bit_se1146084159140164899it_int @ B @ C))) => ((plus_plus_int @ A @ B) = (bit_se1409905431419307370or_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6390_disjunctive__add)). 159.59/70.66 thf(16603,plain,((! [A:int,B:int]: ((! [C:nat]: (~ (bit_se1146084159140164899it_int @ A @ C) | ~ (bit_se1146084159140164899it_int @ B @ C))) => ((plus_plus_int @ A @ B) = (bit_se1409905431419307370or_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2598])). 159.59/70.66 thf(8096,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2856_order__less__asym_H)). 159.59/70.66 thf(36135,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8096])). 159.59/70.66 thf(7587,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) <= (ord_less_nat @ F @ E))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F))))) <= (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4465_minf_I2_J)). 159.59/70.66 thf(34515,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) | ~ (ord_less_nat @ F @ E))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((A @ F) | (C @ F)) = ((B @ F) | (D @ F)))) | ~ (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7587])). 159.59/70.66 thf(3804,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/sandbox/benchmark/theBenchmark.p',fact_6484_machin)). 159.59/70.66 thf(20487,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)],[3804])). 159.59/70.66 thf(3534,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/sandbox/benchmark/theBenchmark.p',fact_6862_sin__30)). 159.59/70.66 thf(19593,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)],[3534])). 159.59/70.66 thf(6071,axiom,((! [A:nat]: ((zero_zero_real = (semiri5074537144036343181t_real @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6502_of__nat__0__eq__iff)). 159.59/70.66 thf(28662,plain,((! [A:nat]: ((zero_zero_real = (semiri5074537144036343181t_real @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6071])). 159.59/70.66 thf(6366,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se1412395901928357646or_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ C) | (bit_se1148574629649215175it_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6376_bit__or__iff)). 159.59/70.66 thf(29692,plain,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se1412395901928357646or_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ C) | (bit_se1148574629649215175it_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6366])). 159.59/70.66 thf(1444,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/sandbox/benchmark/theBenchmark.p',fact_8236_gbinomial__Suc__Suc)). 159.59/70.66 thf(12957,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)],[1444])). 159.59/70.66 thf(3257,axiom,((! [A:nat,B:nat,C:nat]: ((((image_nat_nat @ (^ [D:nat]: (minus_minus_nat @ D @ A)) @ (set_or4665077453230672383an_nat @ C @ B)) = (set_or4665077453230672383an_nat @ (minus_minus_nat @ C @ A) @ (minus_minus_nat @ B @ A))) <= (ord_less_nat @ A @ B)) & ((~ (ord_less_nat @ A @ B)) => ((((image_nat_nat @ (^ [D:nat]: (minus_minus_nat @ D @ A)) @ (set_or4665077453230672383an_nat @ C @ B)) = bot_bot_set_nat) <= (~ (ord_less_nat @ C @ B))) & ((ord_less_nat @ C @ B) => ((image_nat_nat @ (^ [D:nat]: (minus_minus_nat @ D @ A)) @ (set_or4665077453230672383an_nat @ C @ B)) = (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9802_image__minus__const__atLeastLessThan__nat)). 159.59/70.66 thf(18727,plain,((! [A:nat,B:nat,C:nat]: ((((image_nat_nat @ (^ [D:nat]: (minus_minus_nat @ D @ A)) @ (set_or4665077453230672383an_nat @ C @ B)) = (set_or4665077453230672383an_nat @ (minus_minus_nat @ C @ A) @ (minus_minus_nat @ B @ A))) | ~ (ord_less_nat @ A @ B)) & ((~ (ord_less_nat @ A @ B)) => ((((image_nat_nat @ (^ [D:nat]: (minus_minus_nat @ D @ A)) @ (set_or4665077453230672383an_nat @ C @ B)) = bot_bot_set_nat) | (ord_less_nat @ C @ B)) & ((ord_less_nat @ C @ B) => ((image_nat_nat @ (^ [D:nat]: (minus_minus_nat @ D @ A)) @ (set_or4665077453230672383an_nat @ C @ B)) = (insert_nat @ zero_zero_nat @ bot_bot_set_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3257])). 159.59/70.66 thf(2400,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)) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6868_exp__bound__half)). 159.59/70.66 thf(15964,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)) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2400])). 159.59/70.66 thf(3352,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/sandbox/benchmark/theBenchmark.p',fact_7196_cos__zero__iff__int)). 159.59/70.66 thf(19028,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)],[3352])). 159.59/70.66 thf(6951,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/sandbox/benchmark/theBenchmark.p',fact_9127_sum__choose__diagonal)). 159.59/70.66 thf(32048,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)],[6951])). 159.59/70.66 thf(3914,axiom,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1039_add__diff__cancel)). 159.59/70.66 thf(20846,plain,((! [A:real,B:real]: ((minus_minus_real @ (plus_plus_real @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3914])). 159.59/70.66 thf(28,axiom,((! [A:int,B:int]: (ord_less_eq_int @ A @ (ord_max_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_max_Ocobounded1)). 159.59/70.66 thf(8337,plain,((! [A:int,B:int]: (ord_less_eq_int @ A @ (ord_max_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 159.59/70.66 thf(3009,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 @ B @ C) & (ord_less_real @ zero_zero_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2070_mult__less__cancel__left__disj)). 159.59/70.66 thf(17930,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 @ B @ C) & (ord_less_real @ zero_zero_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3009])). 159.59/70.66 thf(3222,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_real @ zero_zero_real @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1596_less__add__same__cancel2)). 159.59/70.66 thf(18611,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)],[3222])). 159.59/70.66 thf(6876,axiom,((! [A:nat]: ((power_power_real @ zero_zero_real @ (suc @ A)) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1678_power__0__Suc)). 159.59/70.66 thf(31783,plain,((! [A:nat]: ((power_power_real @ zero_zero_real @ (suc @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6876])). 159.59/70.66 thf(3946,axiom,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: ((? [E:real]: ! [F:real]: (((A @ F) = (B @ F)) <= (ord_less_real @ E @ F))) => ((? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) <= (ord_less_real @ E @ F))) => (? [E:real]: ! [F:real]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) <= (ord_less_real @ E @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4433_pinf_I2_J)). 159.59/70.66 thf(20942,plain,((! [A:(real > $o),B:(real > $o),C:(real > $o),D:(real > $o)]: ((? [E:real]: ! [F:real]: (((A @ F) = (B @ F)) | ~ (ord_less_real @ E @ F))) => ((? [E:real]: ! [F:real]: (((C @ F) = (D @ F)) | ~ (ord_less_real @ E @ F))) => (? [E:real]: ! [F:real]: ((((A @ F) | (C @ F)) = ((B @ F) | (D @ F))) | ~ (ord_less_real @ E @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3946])). 159.59/70.66 thf(2506,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/sandbox/benchmark/theBenchmark.p',fact_5352_abs__ln__one__plus__x__minus__x__bound)). 159.59/70.66 thf(16320,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)],[2506])). 159.59/70.66 thf(6325,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) <= (ord_less_eq_int @ (abs_abs_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5483_abs__le__D1)). 159.59/70.66 thf(29568,plain,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) | ~ (ord_less_eq_int @ (abs_abs_int @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6325])). 159.59/70.66 thf(1329,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/sandbox/benchmark/theBenchmark.p',fact_7187_cos__gt__zero__pi)). 159.59/70.66 thf(12544,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)],[1329])). 159.59/70.66 thf(4990,axiom,((! [A:num]: (((numera6690914467698888265omplex @ A) = one_one_complex) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_numeral__eq__one__iff)). 159.59/70.66 thf(24517,plain,((! [A:num]: (((numera6690914467698888265omplex @ A) = one_one_complex) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4990])). 159.59/70.66 thf(572,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/sandbox/benchmark/theBenchmark.p',fact_8325_gbinomial__index__swap)). 159.59/70.66 thf(10072,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)],[572])). 159.59/70.66 thf(6859,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/sandbox/benchmark/theBenchmark.p',fact_8849_fact__eq__fact__times)). 159.59/70.66 thf(31732,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)],[6859])). 159.59/70.66 thf(7937,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/sandbox/benchmark/theBenchmark.p',fact_5462_Suc__div__eq__add3__div__numeral)). 159.59/70.66 thf(35620,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)],[7937])). 159.59/70.66 thf(7253,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((ord_max_nat @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_800_max_Oabsorb3)). 159.59/70.66 thf(33331,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((ord_max_nat @ B @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7253])). 159.59/70.66 thf(6053,axiom,((! [A:num,B:num]: ((ord_less_eq_num @ (bit1 @ A) @ (bit0 @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5447_semiring__norm_I74_J)). 159.59/70.66 thf(28609,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)],[6053])). 159.59/70.66 thf(6827,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/sandbox/benchmark/theBenchmark.p',fact_4259_zero__le__odd__power)). 159.59/70.66 thf(31535,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)],[6827])). 159.59/70.66 thf(5473,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1563_add__is__0)). 159.59/70.66 thf(26349,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)],[5473])). 159.59/70.66 thf(5312,axiom,((! [A:int,B:nat]: ((abs_abs_int @ (power_power_int @ A @ B)) = (power_power_int @ (abs_abs_int @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5490_power__abs)). 159.59/70.66 thf(25691,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)],[5312])). 159.59/70.66 thf(1209,axiom,((! [A:set_Pr1261947904930325089at_nat,B:(product_prod_nat_nat > real),C:(product_prod_nat_nat > real),D:real,E:real]: ((((groups4567486121110086003t_real @ B @ A) = one_one_real) => ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (groups4567486121110086003t_real @ (^ [F:product_prod_nat_nat]: (times_times_real @ (C @ F) @ (B @ F))) @ A) @ D)) @ E) <= (! [F:product_prod_nat_nat]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (C @ F) @ D)) @ E) <= (member8440522571783428010at_nat @ F @ A))))) <= (! [F:product_prod_nat_nat]: ((ord_less_eq_real @ zero_zero_real @ (B @ F)) <= (member8440522571783428010at_nat @ F @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7757_convex__sum__bound__le)). 159.59/70.66 thf(12157,plain,((! [A:set_Pr1261947904930325089at_nat,B:(product_prod_nat_nat > real),C:(product_prod_nat_nat > real),D:real,E:real]: ((((groups4567486121110086003t_real @ (B) @ A) = one_one_real) => ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (groups4567486121110086003t_real @ (^ [F:product_prod_nat_nat]: (times_times_real @ (C @ F) @ (B @ F))) @ A) @ D)) @ E) | ~ (! [F:product_prod_nat_nat]: ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (C @ F) @ D)) @ E) | ~ (member8440522571783428010at_nat @ F @ A))))) | ~ (! [F:product_prod_nat_nat]: ((ord_less_eq_real @ zero_zero_real @ (B @ F)) | ~ (member8440522571783428010at_nat @ F @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209])). 159.59/70.66 thf(1173,axiom,((! [A:complex,B:complex]: (((cos_complex @ A) != 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 @ B) != zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7313_lemma__tan__add1)). 159.59/70.66 thf(12010,plain,((! [A:complex,B:complex]: ((~ ((cos_complex @ A) = 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 @ B) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173])). 159.59/70.66 thf(5143,axiom,((! [A:num,B:num]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))) = (numera6620942414471956472nteger @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4807_mult__neg__numeral__simps_I1_J)). 159.59/70.66 thf(25051,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)],[5143])). 159.59/70.66 thf(6472,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/sandbox/benchmark/theBenchmark.p',fact_8612_prod_Oin__pairs__0)). 159.59/70.66 thf(30148,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)],[6472])). 159.59/70.66 thf(3709,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ A @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_complex @ (A @ zero_zero_nat) @ (groups2073611262835488442omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8748_sum_OatMost__Suc__shift)). 159.59/70.66 thf(20182,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_complex @ (A @ zero_zero_nat) @ (groups2073611262835488442omplex @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3709])). 159.59/70.66 thf(3597,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (? [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((tan_real @ B) = A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7298_tan__total__pos)). 159.59/70.66 thf(19801,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (? [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) & (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) & ((tan_real @ B) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3597])). 159.59/70.66 thf(2819,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2602_dual__order_Orefl)). 159.59/70.66 thf(17316,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2819])). 159.59/70.66 thf(1085,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = ((A = zero_zero_real) | (dvd_dvd_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3812_dvd__mult__cancel__left)). 159.59/70.66 thf(11732,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = ((A = zero_zero_real) | (dvd_dvd_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085])). 159.59/70.66 thf(757,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((A = (plus_plus_complex @ B @ C)) => ((plus_plus_complex @ D @ A) = (plus_plus_complex @ B @ (plus_plus_complex @ D @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1137_group__cancel_Oadd2)). 159.59/70.66 thf(10697,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((A = (plus_plus_complex @ B @ C)) => ((plus_plus_complex @ D @ A) = (plus_plus_complex @ B @ (plus_plus_complex @ D @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[757])). 159.59/70.66 thf(7976,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ B @ C)) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_power__strict__increasing__iff)). 159.59/70.66 thf(35741,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ B @ C)) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7976])). 159.59/70.66 thf(3673,axiom,(((archim6058952711729229775r_real @ one_one_real) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8179_floor__one)). 159.59/70.66 thf(20050,plain,(((archim6058952711729229775r_real @ one_one_real) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3673])). 159.59/70.66 thf(250,axiom,((! [A:nat]: ((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ (semiri4939895301339042750nteger @ A)) @ A) = (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) @ (semiri3624122377584611663nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8333_pochhammer__same)). 159.59/70.66 thf(9014,plain,((! [A:nat]: ((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ (semiri4939895301339042750nteger @ A)) @ A) = (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ A) @ (semiri3624122377584611663nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 159.59/70.66 thf(7638,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ A @ B)) = ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6102_even__or__iff)). 159.59/70.66 thf(34669,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_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)],[7638])). 159.59/70.66 thf(2311,axiom,((! [A:nat,B:nat]: ((unique6322359934112328802ux_nat @ (product_Pair_nat_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3385_divides__aux__eq)). 159.59/70.66 thf(15685,plain,((! [A:nat,B:nat]: ((unique6322359934112328802ux_nat @ (product_Pair_nat_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2311])). 159.59/70.66 thf(8213,axiom,(((size_s6755466524823107622T_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_newlistlength)). 159.59/70.66 thf(36518,plain,(((size_s6755466524823107622T_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)))) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8213])). 159.59/70.66 thf(3070,axiom,((! [A:complex]: (((times_times_complex @ (invers8013647133539491842omplex @ A) @ A) = one_one_complex) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9075_field__class_Ofield__inverse)). 159.59/70.66 thf(18117,plain,((! [A:complex]: (((times_times_complex @ (invers8013647133539491842omplex @ A) @ A) = one_one_complex) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3070])). 159.59/70.66 thf(4003,axiom,((! [A:int,B:num]: (((ring_1_of_int_real @ A) = (numeral_numeral_real @ B)) = (A = (numeral_numeral_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5765_of__int__eq__numeral__iff)). 159.59/70.66 thf(21120,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)],[4003])). 159.59/70.66 thf(5362,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((ord_less_eq_nat @ (groups708209901874060359at_nat @ B @ A) @ (groups708209901874060359at_nat @ C @ A)) <= (! [D:nat]: (((ord_less_eq_nat @ (B @ D) @ (C @ D)) & (ord_less_eq_nat @ zero_zero_nat @ (B @ D))) <= (member_nat @ D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8503_prod__mono)). 159.59/70.66 thf(25924,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((ord_less_eq_nat @ (groups708209901874060359at_nat @ (B) @ A) @ (groups708209901874060359at_nat @ (C) @ A)) | ~ (! [D:nat]: (((ord_less_eq_nat @ (B @ D) @ (C @ D)) & (ord_less_eq_nat @ zero_zero_nat @ (B @ D))) | ~ (member_nat @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5362])). 159.59/70.66 thf(7647,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/sandbox/benchmark/theBenchmark.p',fact_3904_odd__succ__div__two)). 159.59/70.66 thf(34695,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)],[7647])). 159.59/70.66 thf(7868,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2816_order_Ostrict__trans)). 159.59/70.66 thf(35397,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ C) | ~ (ord_less_nat @ B @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7868])). 159.59/70.66 thf(4843,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_lift__Suc__mono__less)). 159.59/70.66 thf(24010,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4843])). 159.59/70.66 thf(6194,axiom,((! [A:num]: ((plus_plus_complex @ one_one_complex @ (numera6690914467698888265omplex @ A)) = (numera6690914467698888265omplex @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_one__plus__numeral)). 159.59/70.66 thf(29075,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)],[6194])). 159.59/70.66 thf(3107,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/sandbox/benchmark/theBenchmark.p',fact_5586_abs__diff__less__iff)). 159.59/70.66 thf(18249,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)],[3107])). 159.59/70.66 thf(3949,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (divide_divide_real @ C @ A)) <= (ord_less_eq_real @ (times_times_real @ B @ A) @ C)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2428_mult__imp__le__div__pos)). 159.59/70.66 thf(20959,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ (divide_divide_real @ C @ A)) | ~ (ord_less_eq_real @ (times_times_real @ B @ A) @ C) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3949])). 159.59/70.66 thf(319,axiom,((! [A:real]: ((sinh_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sinh_real @ A)) @ (cosh_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9339_sinh__double)). 159.59/70.66 thf(9234,plain,((! [A:real]: ((sinh_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (sinh_real @ A)) @ (cosh_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 159.59/70.66 thf(6414,axiom,((! [A:complex,B:complex,C:complex]: ((((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = (B = C)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1854_mult__left__cancel)). 159.59/70.66 thf(29913,plain,((! [A:complex,B:complex,C:complex]: ((((times_times_complex @ A @ B) = (times_times_complex @ A @ C)) = (B = C)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6414])). 159.59/70.66 thf(8134,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/sandbox/benchmark/theBenchmark.p',fact_238_power__add__numeral)). 159.59/70.66 thf(36267,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)],[8134])). 159.59/70.66 thf(5523,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sin_real @ A)) => ((sin_real @ A) = (sqrt @ (minus_minus_real @ one_one_real @ (power_power_real @ (cos_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7194_sin__cos__sqrt)). 159.59/70.66 thf(26526,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sin_real @ A)) => ((sin_real @ A) = (sqrt @ (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)],[5523])). 159.59/70.66 thf(7132,axiom,((! [A:(real > (real > $o)),B:real]: ((A @ (abs_abs_real @ B) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) <= (! [C:real]: ((ord_less_eq_real @ zero_zero_real @ C) => (A @ C @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5645_abs__sqrt__wlog)). 159.59/70.66 thf(32884,plain,((! [A:(real > (real > $o)),B:real]: ((A @ (abs_abs_real @ B) @ (power_power_real @ B @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (! [C:real]: ((ord_less_eq_real @ zero_zero_real @ C) => (A @ C @ (power_power_real @ C @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7132])). 159.59/70.66 thf(1021,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/sandbox/benchmark/theBenchmark.p',fact_3463_mod__diff__eq)). 159.59/70.66 thf(11514,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)],[1021])). 159.59/70.66 thf(1768,axiom,((! [A:nat,B:(nat > real),C:real]: ((! [D:nat]: (((B @ D) = zero_zero_real) <= (ord_less_nat @ D @ A))) => ((sums_real @ (^ [D:nat]: (B @ (plus_plus_nat @ D @ A))) @ C) = (sums_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7938_sums__zero__iff__shift)). 159.59/70.66 thf(13959,plain,((! [A:nat,B:(nat > real),C:real]: ((! [D:nat]: (((B @ D) = zero_zero_real) | ~ (ord_less_nat @ D @ A))) => ((sums_real @ (^ [D:nat]: (B @ (plus_plus_nat @ D @ A))) @ C) = (sums_real @ (B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768])). 159.59/70.66 thf(8086,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/sandbox/benchmark/theBenchmark.p',fact_1642_div__mult__mult1)). 159.59/70.66 thf(36106,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)],[8086])). 159.59/70.66 thf(6614,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3998_unit__imp__dvd)). 159.59/70.66 thf(30649,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)],[6614])). 159.59/70.66 thf(3289,axiom,((! [A:nat]: ((gbinomial_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8177_gbinomial__0_I1_J)). 159.59/70.66 thf(18840,plain,((! [A:nat]: ((gbinomial_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3289])). 159.59/70.66 thf(74,axiom,((! [A:nat,B:nat,C:int]: ((((bit_se2923211474154528505it_int @ A @ (bit_se4203085406695923979it_int @ B @ C)) = (bit_se4203085406695923979it_int @ B @ (bit_se2923211474154528505it_int @ A @ C))) <= (~ (ord_less_eq_nat @ A @ B))) & ((ord_less_eq_nat @ A @ B) => ((bit_se2923211474154528505it_int @ A @ (bit_se4203085406695923979it_int @ B @ C)) = (bit_se2923211474154528505it_int @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5110_take__bit__unset__bit__eq)). 159.59/70.66 thf(8474,plain,((! [A:nat,B:nat,C:int]: ((((bit_se2923211474154528505it_int @ A @ (bit_se4203085406695923979it_int @ B @ C)) = (bit_se4203085406695923979it_int @ B @ (bit_se2923211474154528505it_int @ A @ C))) | (ord_less_eq_nat @ A @ B)) & ((ord_less_eq_nat @ A @ B) => ((bit_se2923211474154528505it_int @ A @ (bit_se4203085406695923979it_int @ B @ C)) = (bit_se2923211474154528505it_int @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 159.59/70.66 thf(3123,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/sandbox/benchmark/theBenchmark.p',fact_5545_abs__less__iff)). 159.59/70.66 thf(18298,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)],[3123])). 159.59/70.66 thf(1389,axiom,((ord_less_eq_real @ zero_zero_real @ pi)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6703_pi__ge__zero)). 159.59/70.66 thf(12786,plain,((ord_less_eq_real @ zero_zero_real @ pi)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389])). 159.59/70.66 thf(487,axiom,((! [A:code_integer]: (((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => ((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) != zero_z3403309356797280102nteger)) => (~ (((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) != one_one_Code_integer) <= (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4254_parity__cases)). 159.59/70.66 thf(9802,plain,((! [A:code_integer]: (((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) => (~ ((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger))) => (~ (~ ((modulo364778990260209775nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) = one_one_Code_integer) | (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[487])). 159.59/70.66 thf(3256,axiom,((! [A:set_nat,B:(nat > complex),C:(nat > real)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (B @ D)) @ (C @ D)))) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (groups2073611262835488442omplex @ B @ A)) @ (groups6591440286371151544t_real @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7385_sum__norm__le)). 159.59/70.66 thf(18724,plain,((! [A:set_nat,B:(nat > complex),C:(nat > real)]: ((! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (B @ D)) @ (C @ D)))) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (groups2073611262835488442omplex @ (B) @ A)) @ (groups6591440286371151544t_real @ (C) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3256])). 159.59/70.66 thf(959,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/sandbox/benchmark/theBenchmark.p',fact_5878_mult__of__int__commute)). 159.59/70.66 thf(11319,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)],[959])). 159.59/70.66 thf(3984,axiom,((real_V4546457046886955230omplex = (^ [A:real]: (real_V2046097035970521341omplex @ A @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9221_of__real__def)). 159.59/70.66 thf(21061,plain,(((real_V4546457046886955230omplex) = (^ [A:real]: (real_V2046097035970521341omplex @ A @ one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3984])). 159.59/70.66 thf(4263,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/sandbox/benchmark/theBenchmark.p',fact_8332_pochhammer__same)). 159.59/70.66 thf(21936,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)],[4263])). 159.59/70.66 thf(6723,axiom,((! [A:nat]: ((set_or4665077453230672383an_nat @ zero_zero_nat @ (suc @ A)) = (insert_nat @ A @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9587_atLeast0__lessThan__Suc)). 159.59/70.66 thf(31174,plain,((! [A:nat]: ((set_or4665077453230672383an_nat @ zero_zero_nat @ (suc @ A)) = (insert_nat @ A @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6723])). 159.59/70.66 thf(6444,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_eq_int @ B @ zero_zero_int) => (ord_less_int @ one_one_int @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2411_mult__less__cancel__right2)). 159.59/70.66 thf(30037,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_eq_int @ B @ zero_zero_int) => (ord_less_int @ one_one_int @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6444])). 159.59/70.66 thf(6633,axiom,((! [A:nat,B:code_integer]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4873_power__minus__odd)). 159.59/70.66 thf(30721,plain,((! [A:nat,B:code_integer]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6633])). 159.59/70.66 thf(7483,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/sandbox/benchmark/theBenchmark.p',fact_4272_even__mask__div__iff)). 159.59/70.66 thf(34138,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)],[7483])). 159.59/70.66 thf(4953,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/sandbox/benchmark/theBenchmark.p',fact_3123_dual__order_Ostrict__trans1)). 159.59/70.66 thf(24360,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)],[4953])). 159.59/70.66 thf(281,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((A != zero_z3403309356797280102nteger) => ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = (dvd_dvd_Code_integer @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3818_dvd__times__left__cancel__iff)). 159.59/70.66 thf(9102,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((~ (A = zero_z3403309356797280102nteger)) => ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ A @ B) @ (times_3573771949741848930nteger @ A @ C)) = (dvd_dvd_Code_integer @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 159.59/70.66 thf(5820,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = (! [C:nat]: ((B @ (suc @ C)) <= (ord_less_nat @ C @ A)) & (B @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2189_All__less__Suc2)). 159.59/70.66 thf(27699,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_nat @ C @ (suc @ A)) => (B @ C))) = (! [C:nat]: ((B @ (suc @ C)) | ~ (ord_less_nat @ C @ A)) & (B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5820])). 159.59/70.66 thf(5367,axiom,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o),C:vEBT_VEBT]: (((B @ C) <= (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A))) <= (! [D:nat]: ((ord_less_nat @ D @ (size_s6755466524823107622T_VEBT @ A)) => (B @ (nth_VEBT_VEBT @ A @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_all__nth__imp__all__set)). 159.59/70.66 thf(25939,plain,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o),C:vEBT_VEBT]: ((B @ C) | ~ (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A)) | ~ (! [D:nat]: ((ord_less_nat @ D @ (size_s6755466524823107622T_VEBT @ A)) => (B @ (nth_VEBT_VEBT @ A @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5367])). 159.59/70.66 thf(7172,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: (B != (times_times_nat @ A @ C)))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3932_dvdE)). 159.59/70.66 thf(33029,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)],[7172])). 159.59/70.66 thf(4831,axiom,((! [A:real,B:nat]: ((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)) <= (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6775_Bernoulli__inequality)). 159.59/70.66 thf(23972,plain,((! [A:real,B:nat]: ((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)) | ~ (ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4831])). 159.59/70.66 thf(4516,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1520_add__cancel__left__right)). 159.59/70.66 thf(22775,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4516])). 159.59/70.66 thf(5641,axiom,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ B)) = (times_times_complex @ (power_power_complex @ A @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_power__Suc2)). 159.59/70.66 thf(26908,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)],[5641])). 159.59/70.66 thf(167,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/sandbox/benchmark/theBenchmark.p',fact_9598_int__numeral__not__or__num__neg)). 159.59/70.66 thf(8766,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)],[167])). 159.59/70.66 thf(6726,axiom,((! [A:real]: (((abs_abs_real @ A) = A) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5408_abs__of__nonneg)). 159.59/70.66 thf(31187,plain,((! [A:real]: (((abs_abs_real @ A) = A) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6726])). 159.59/70.66 thf(5853,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/sandbox/benchmark/theBenchmark.p',fact_7230_square__powr__half)). 159.59/70.66 thf(27884,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)],[5853])). 159.59/70.66 thf(1755,axiom,((! [A:(nat > complex),B:nat,C:complex]: ? [D:(nat > complex)]: ! [E:complex]: ((groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (A @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ B)) = (plus_plus_complex @ (times_times_complex @ (minus_minus_complex @ E @ C) @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (D @ F) @ (power_power_complex @ E @ F))) @ (set_ord_lessThan_nat @ B))) @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (A @ F) @ (power_power_complex @ C @ F))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8885_polyfun__linear__factor)). 159.59/70.66 thf(13919,plain,((! [A:(nat > complex),B:nat,C:complex]: ? [D:(nat > complex)]: ! [E:complex]: ((groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (A @ F) @ (power_power_complex @ E @ F))) @ (set_ord_atMost_nat @ B)) = (plus_plus_complex @ (times_times_complex @ (minus_minus_complex @ E @ C) @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (D @ F) @ (power_power_complex @ E @ F))) @ (set_ord_lessThan_nat @ B))) @ (groups2073611262835488442omplex @ (^ [F:nat]: (times_times_complex @ (A @ F) @ (power_power_complex @ C @ F))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755])). 159.59/70.66 thf(1564,axiom,((! [A:code_integer]: (((plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))) @ one_one_Code_integer) = A) <= (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3916_odd__two__times__div__two__succ)). 159.59/70.66 thf(13333,plain,((! [A:code_integer]: (((plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))) @ one_one_Code_integer) = A) | (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564])). 159.59/70.66 thf(3893,axiom,((! [A:real]: (ord_less_eq_real @ (abs_abs_real @ (sin_real @ A)) @ (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6816_abs__sin__x__le__abs__x)). 159.59/70.66 thf(20785,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)],[3893])). 159.59/70.66 thf(1750,axiom,((! [A:int,B:real]: ((ord_less_real @ (abs_abs_real @ (ring_1_of_int_real @ A)) @ B) => ((ord_less_real @ one_one_real @ B) | (A = zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5903_of__int__lessD)). 159.59/70.66 thf(13902,plain,((! [A:int,B:real]: ((ord_less_real @ (abs_abs_real @ (ring_1_of_int_real @ A)) @ B) => ((ord_less_real @ one_one_real @ B) | (A = zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750])). 159.59/70.66 thf(1332,axiom,((! [A:code_integer,B:code_integer,C:nat]: ((! [D:nat]: ~ (bit_se9216721137139052372nteger @ A @ (suc @ D))) => ((bit_se9216721137139052372nteger @ (plus_p5714425477246183910nteger @ A @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) @ C) = (((C = zero_zero_nat) => (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))) & ((bit_se9216721137139052372nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) @ C) <= (C != zero_zero_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6463_bit__sum__mult__2__cases)). 159.59/70.66 thf(12552,plain,((! [A:code_integer,B:code_integer,C:nat]: ((! [D:nat]: ~ (bit_se9216721137139052372nteger @ A @ (suc @ D))) => ((bit_se9216721137139052372nteger @ (plus_p5714425477246183910nteger @ A @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) @ C) = (((C = zero_zero_nat) => (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))) & ((bit_se9216721137139052372nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) @ C) | (C = zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332])). 159.59/70.66 thf(5233,axiom,((! [A:int]: (ord_less_eq_int @ (uminus_uminus_int @ (abs_abs_int @ A)) @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5566_abs__minus__le__zero)). 159.59/70.66 thf(25386,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)],[5233])). 159.59/70.66 thf(4632,axiom,((! [A:num]: ((plus_plus_num @ (bit1 @ A) @ one) = (bit0 @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5440_semiring__norm_I8_J)). 159.59/70.66 thf(23265,plain,((! [A:num]: ((plus_plus_num @ (bit1 @ A) @ one) = (bit0 @ (plus_plus_num @ A @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4632])). 159.59/70.66 thf(6922,axiom,((! [A:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) = (plus_plus_complex @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_mult__2)). 159.59/70.66 thf(31933,plain,((! [A:complex]: ((times_times_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A) = (plus_plus_complex @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6922])). 159.59/70.66 thf(865,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_real @ (times_times_real @ B @ A) @ (uminus_uminus_real @ C))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5238_pos__less__minus__divide__eq)). 159.59/70.66 thf(11039,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ (uminus_uminus_real @ (divide_divide_real @ C @ A))) = (ord_less_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)],[865])). 159.59/70.66 thf(5543,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((groups708209901874060359at_nat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo2584398358068434914at_nat @ (^ [D:nat]: (times_times_nat @ (A @ D))) @ B @ C @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8520_prod__atLeastAtMost__code)). 159.59/70.66 thf(26584,plain,((! [A:(nat > nat),B:nat,C:nat]: ((groups708209901874060359at_nat @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo2584398358068434914at_nat @ (^ [D:nat]: (times_times_nat @ (A @ D))) @ B @ C @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5543])). 159.59/70.66 thf(7337,axiom,((! [A:nat]: ((set_or4665077453230672383an_nat @ zero_zero_nat @ (suc @ A)) = (insert_nat @ zero_zero_nat @ (image_nat_nat @ suc @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9810_atLeast0__lessThan__Suc__eq__insert__0)). 159.59/70.66 thf(33625,plain,((! [A:nat]: ((set_or4665077453230672383an_nat @ zero_zero_nat @ (suc @ A)) = (insert_nat @ zero_zero_nat @ (image_nat_nat @ (suc) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7337])). 159.59/70.66 thf(6517,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (B != (suc @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_Suc__lessE)). 159.59/70.66 thf(30299,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (~ (B = (suc @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6517])). 159.59/70.66 thf(2854,axiom,((! [A:list_o,B:nat,C:$o]: ((size_size_list_o @ (list_update_o @ A @ B @ C)) = (size_size_list_o @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_length__list__update)). 159.59/70.66 thf(17427,plain,((! [A:list_o,B:nat,C:$o]: ((size_size_list_o @ (list_update_o @ A @ B @ C)) = (size_size_list_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2854])). 159.59/70.66 thf(3100,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ B)) = ((B = zero_zero_complex) | (dvd_dvd_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3815_dvd__mult__cancel__right)). 159.59/70.66 thf(18224,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ B)) = ((B = zero_zero_complex) | (dvd_dvd_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3100])). 159.59/70.66 thf(5792,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_Suc__mono)). 159.59/70.66 thf(27508,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)],[5792])). 159.59/70.66 thf(2414,axiom,((! [A:int,B:int,C: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/sandbox/benchmark/theBenchmark.p',fact_1643_div__mult__mult1)). 159.59/70.66 thf(16009,plain,((! [A:int,B:int,C: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)],[2414])). 159.59/70.66 thf(3218,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ C) => (dvd_dvd_int @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3973_dvd__mult__right)). 159.59/70.66 thf(18598,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)],[3218])). 159.59/70.66 thf(2116,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ A @ B)) = ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B) & (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6101_even__or__iff)). 159.59/70.66 thf(15067,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_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)],[2116])). 159.59/70.66 thf(7325,axiom,((! [A:complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2186_power__0)). 159.59/70.66 thf(33585,plain,((! [A:complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7325])). 159.59/70.66 thf(6866,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/sandbox/benchmark/theBenchmark.p',fact_7842_gauss__sum__from__Suc__0)). 159.59/70.66 thf(31751,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)],[6866])). 159.59/70.66 thf(1611,axiom,((! [A:$o]: ((semiri1314217659103216013at_int @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n2684676970156552555ol_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6574_of__nat__of__bool)). 159.59/70.66 thf(13485,plain,((! [A:$o]: ((semiri1314217659103216013at_int @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n2684676970156552555ol_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1611])). 159.59/70.66 thf(1803,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le2932123472753598470d_enat @ A @ B)) = (ord_le72135733267957522d_enat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3694_verit__comp__simplify1_I3_J)). 159.59/70.66 thf(14069,plain,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le2932123472753598470d_enat @ A @ B)) = (ord_le72135733267957522d_enat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1803])). 159.59/70.66 thf(3044,axiom,((! [A:extended_enat,B:extended_enat]: (((plus_p3455044024723400733d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((A = zero_z5237406670263579293d_enat) & (B = zero_z5237406670263579293d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2632_iadd__is__0)). 159.59/70.66 thf(18034,plain,((! [A:extended_enat,B:extended_enat]: (((plus_p3455044024723400733d_enat @ A @ B) = zero_z5237406670263579293d_enat) = ((A = zero_z5237406670263579293d_enat) & (B = zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3044])). 159.59/70.66 thf(2225,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6823_nat__int__comparison_I3_J)). 159.59/70.66 thf(15436,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)],[2225])). 159.59/70.66 thf(3713,axiom,((! [A:(nat > real),B:(nat > real),C:real,D:real]: ((((sums_real @ B @ D) => (ord_less_eq_real @ C @ D)) <= (sums_real @ A @ C)) <= (! [E:nat]: (ord_less_eq_real @ (A @ E) @ (B @ E)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7883_sums__le)). 159.59/70.66 thf(20195,plain,((! [A:(nat > real),B:(nat > real),C:real,D:real]: (((sums_real @ (B) @ D) => (ord_less_eq_real @ C @ D)) | ~ (sums_real @ (A) @ C) | ~ (! [E:nat]: (ord_less_eq_real @ (A @ E) @ (B @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3713])). 159.59/70.66 thf(394,axiom,((arctan = (^ [A:real]: (the_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)))) & ((tan_real @ B) = A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9386_arctan__def)). 159.59/70.66 thf(9482,plain,(((arctan) = (^ [A:real]: (the_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)))) & ((tan_real @ B) = A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])). 159.59/70.66 thf(1041,axiom,((! [A:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) = (A != zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1832_zero__less__iff__neq__zero)). 159.59/70.66 thf(11585,plain,((! [A:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) = (~ (A = zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041])). 159.59/70.66 thf(4709,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/sandbox/benchmark/theBenchmark.p',fact_5485_abs__mult)). 159.59/70.66 thf(23529,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)],[4709])). 159.59/70.66 thf(7264,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/sandbox/benchmark/theBenchmark.p',fact_1262_left__diff__distrib_H)). 159.59/70.66 thf(33361,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)],[7264])). 159.59/70.66 thf(2862,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/sandbox/benchmark/theBenchmark.p',fact_4571_even__signed__take__bit__iff)). 159.59/70.66 thf(17464,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)],[2862])). 159.59/70.66 thf(2123,axiom,((! [A:nat,B:nat,C:nat]: ((ord_le6747313008572928689nteger @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B) @ (semiri4939895301339042750nteger @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6607_of__nat__less__of__nat__power__cancel__iff)). 159.59/70.66 thf(15088,plain,((! [A:nat,B:nat,C:nat]: ((ord_le6747313008572928689nteger @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B) @ (semiri4939895301339042750nteger @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2123])). 159.59/70.66 thf(4422,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ A)) <= (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2081_zero__less__mult__pos2)). 159.59/70.66 thf(22423,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ A)) | ~ (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4422])). 159.59/70.66 thf(8031,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/sandbox/benchmark/theBenchmark.p',fact_6630_numeral__power__less__of__nat__cancel__iff)). 159.59/70.66 thf(35922,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)],[8031])). 159.59/70.66 thf(1274,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/sandbox/benchmark/theBenchmark.p',fact_9459_nat__take__bit__eq)). 159.59/70.66 thf(12370,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)],[1274])). 159.59/70.66 thf(4406,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)) | ((ord_less_real @ A @ zero_zero_real) & (ord_less_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2158_divide__less__0__iff)). 159.59/70.66 thf(22366,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)) | ((ord_less_real @ A @ zero_zero_real) & (ord_less_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4406])). 159.59/70.66 thf(5760,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/sandbox/benchmark/theBenchmark.p',fact_7958_sum_OlessThan__Suc__shift)). 159.59/70.66 thf(27326,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)],[5760])). 159.59/70.66 thf(7945,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/sandbox/benchmark/theBenchmark.p',fact_1238_comm__semiring__class_Odistrib)). 159.59/70.66 thf(35652,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)],[7945])). 159.59/70.66 thf(2719,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((((divide6298287555418463151nteger @ C @ (divide6298287555418463151nteger @ B @ A)) = (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ C @ B) @ A)) <= (dvd_dvd_Code_integer @ B @ C)) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4080_div__div__eq__right)). 159.59/70.66 thf(17020,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((divide6298287555418463151nteger @ C @ (divide6298287555418463151nteger @ B @ A)) = (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ C @ B) @ A)) | ~ (dvd_dvd_Code_integer @ B @ C) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2719])). 159.59/70.66 thf(6006,axiom,((! [A:nat]: (((bit_se2925701944663578781it_nat @ A @ one_one_nat) = zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4777_take__bit__of__1__eq__0__iff)). 159.59/70.66 thf(28460,plain,((! [A:nat]: (((bit_se2925701944663578781it_nat @ A @ one_one_nat) = zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6006])). 159.59/70.66 thf(2933,axiom,((! [A:(nat > real)]: ((topolo6980174941875973593q_real @ A) <= (! [B:nat]: (ord_less_eq_real @ (A @ (suc @ B)) @ (A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8026_mono__SucI2)). 159.59/70.66 thf(17698,plain,((! [A:(nat > real)]: ((topolo6980174941875973593q_real @ (A)) | ~ (! [B:nat]: (ord_less_eq_real @ (A @ (suc @ B)) @ (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2933])). 159.59/70.66 thf(843,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/sandbox/benchmark/theBenchmark.p',fact_8445_prod_OlessThan__Suc)). 159.59/70.66 thf(10969,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)],[843])). 159.59/70.66 thf(1794,axiom,((! [A:real,B:real]: ((if_real @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_001t__Real__Oreal_T)). 159.59/70.66 thf(14041,plain,((! [A:real,B:real]: ((if_real @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1794])). 159.59/70.66 thf(7963,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/sandbox/benchmark/theBenchmark.p',fact_1031_Suc__double__not__eq__double)). 159.59/70.66 thf(35704,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)],[7963])). 159.59/70.66 thf(7745,axiom,((vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ summin) @ lx)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462__092_060open_062vebt__member_A_ItreeList_A_B_Asummin_J_Alx_092_060close_062)). 159.59/70.66 thf(35032,plain,((vEBT_vebt_member @ (nth_VEBT_VEBT @ treeList @ summin) @ lx)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7745])). 159.59/70.66 thf(1190,axiom,((! [A:(int > (int > $o)),B:int,C:int]: ((! [D:int,E:int]: ((ord_less_int @ D @ E) => (A @ D @ E))) => (((A @ B @ C) <= (! [D:int,E:int]: ((A @ E @ D) => (A @ D @ E)))) <= (! [D:int]: (A @ D @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2812_linorder__less__wlog)). 159.59/70.66 thf(12061,plain,((! [A:(int > (int > $o)),B:int,C:int]: ((! [D:int,E:int]: ((ord_less_int @ D @ E) => (A @ D @ E))) => ((A @ B @ C) | ~ (! [D:int,E:int]: ((A @ E @ D) => (A @ D @ E))) | ~ (! [D:int]: (A @ D @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190])). 159.59/70.66 thf(1495,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/sandbox/benchmark/theBenchmark.p',fact_1166_add__right__mono)). 159.59/70.66 thf(13129,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)],[1495])). 159.59/70.66 thf(5373,axiom,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: (((? [E:num]: ! [F:num]: ((((C @ F) | (A @ F)) = ((B @ F) | (D @ F))) <= (ord_less_num @ E @ F))) <= (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => ((C @ F) = (D @ F))))) <= (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4434_pinf_I2_J)). 159.59/70.66 thf(25956,plain,((! [A:(num > $o),B:(num > $o),C:(num > $o),D:(num > $o)]: (? [E:num]: ! [F:num]: ((((C @ F) | (A @ F)) = ((B @ F) | (D @ F))) | ~ (ord_less_num @ E @ F)) | ~ (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => ((C @ F) = (D @ F)))) | ~ (? [E:num]: ! [F:num]: ((ord_less_num @ E @ F) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5373])). 159.59/70.66 thf(1105,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/sandbox/benchmark/theBenchmark.p',fact_1441_add__divide__distrib)). 159.59/70.66 thf(11800,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)],[1105])). 159.59/70.66 thf(1366,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/sandbox/benchmark/theBenchmark.p',fact_1588_add__le__same__cancel2)). 159.59/70.66 thf(12685,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)],[1366])). 159.59/70.66 thf(7857,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]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_VEBT_VEBT @ C @ D))) & ((size_s6755466524823107622T_VEBT @ C) = A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_Skolem__list__nth)). 159.59/70.66 thf(35361,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]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_VEBT_VEBT @ C @ D))) & ((size_s6755466524823107622T_VEBT @ C) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7857])). 159.59/70.66 thf(3301,axiom,((! [A:real,B:real,C:real,D:real]: (((dvd_dvd_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) <= (dvd_dvd_real @ C @ D)) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3966_mult__dvd__mono)). 159.59/70.66 thf(18875,plain,((! [A:real,B:real,C:real,D:real]: ((dvd_dvd_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D)) | ~ (dvd_dvd_real @ C @ D) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3301])). 159.59/70.66 thf(3529,axiom,((! [A:(extended_enat > $o),B:extended_enat]: ((A @ B) <= (! [C:extended_enat]: ((A @ C) <= (! [D:extended_enat]: ((ord_le72135733267957522d_enat @ D @ C) => (A @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2784_less__induct)). 159.59/70.66 thf(19581,plain,((! [A:(extended_enat > $o),B:extended_enat]: ((A @ B) | ~ (! [C:extended_enat]: ((A @ C) | ~ (! [D:extended_enat]: ((ord_le72135733267957522d_enat @ D @ C) => (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3529])). 159.59/70.66 thf(744,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/sandbox/benchmark/theBenchmark.p',fact_5857_of__int__eq__neg__numeral__power__cancel__iff)). 159.59/70.66 thf(10659,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)],[744])). 159.59/70.66 thf(8019,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((hd_nat @ (upt @ A @ B)) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10156_hd__upt)). 159.59/70.66 thf(35874,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((hd_nat @ (upt @ A @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8019])). 159.59/70.66 thf(4667,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/sandbox/benchmark/theBenchmark.p',fact_893_power2__diff)). 159.59/70.66 thf(23392,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)],[4667])). 159.59/70.66 thf(3385,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > nat),D:nat]: ((((ord_less_nat @ (C @ A) @ D) <= (! [E:extended_enat,F:extended_enat]: ((ord_less_nat @ (C @ E) @ (C @ F)) <= (ord_le72135733267957522d_enat @ E @ F)))) <= ((C @ B) = D)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2876_ord__less__eq__subst)). 159.59/70.66 thf(19128,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > nat),D:nat]: ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:extended_enat,F:extended_enat]: ((ord_less_nat @ (C @ E) @ (C @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F))) | ~ ((C @ B) = D) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3385])). 159.59/70.66 thf(3345,axiom,((! [A:num]: ((inverse_inverse_real @ (numeral_numeral_real @ A)) = (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9007_inverse__eq__divide__numeral)). 159.59/70.66 thf(19009,plain,((! [A:num]: ((inverse_inverse_real @ (numeral_numeral_real @ A)) = (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3345])). 159.59/70.66 thf(6625,axiom,((! [A:num]: ((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ (numeral_numeral_nat @ A)) = zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1681_power__zero__numeral)). 159.59/70.66 thf(30689,plain,((! [A:num]: ((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ (numeral_numeral_nat @ A)) = zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6625])). 159.59/70.66 thf(3320,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((((vEBT_vebt_pred @ A @ C) = (some_nat @ D)) = (vEBT_is_pred_in_set @ (vEBT_set_vebt @ A) @ C @ D)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_pred__correct)). 159.59/70.66 thf(18932,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((((vEBT_vebt_pred @ A @ C) = (some_nat @ D)) = (vEBT_is_pred_in_set @ (vEBT_set_vebt @ A) @ C @ D)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3320])). 159.59/70.66 thf(2473,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1160_add__le__imp__le__left)). 159.59/70.66 thf(16213,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ B @ C) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2473])). 159.59/70.66 thf(4888,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ A) = (B = one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4220_dvd__mult__cancel1)). 159.59/70.66 thf(24147,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ A) = (B = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4888])). 159.59/70.66 thf(648,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (bit1 @ A)) = (plus_plus_complex @ (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A)) @ one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5588_numeral__Bit1)). 159.59/70.66 thf(10325,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)],[648])). 159.59/70.66 thf(6540,axiom,((! [A:num,B:num]: (((bit1 @ A) = (bit1 @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5353_semiring__norm_I90_J)). 159.59/70.66 thf(30400,plain,((! [A:num,B:num]: (((bit1 @ A) = (bit1 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6540])). 159.59/70.66 thf(7863,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/sandbox/benchmark/theBenchmark.p',fact_4534_pinf_I10_J)). 159.59/70.66 thf(35382,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7863])). 159.59/70.66 thf(5882,axiom,((! [A:vEBT_VEBT,B:nat]: ((~ (vEBT_VEBT_valid @ A @ B)) => ((accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ (produc738532404422230701BT_nat @ A @ B)) => ((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (B = one_one_nat)))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ D @ E @ F)) => ((accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ D @ E @ F) @ B)) => ((D = B) & (case_o184042715313410164at_nat @ (! [G:vEBT_VEBT]: ((~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H))) <= (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E))) & ~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) @ (produc6081775807080527818_nat_o @ (^ [G:nat,H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [I:nat]: (((? [J:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ E @ I) @ J)) = (vEBT_V8194947554948674370ptions @ F @ I)) <= (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))))) & ((! [I:vEBT_VEBT]: ((~ (? [J:nat]: (vEBT_V8194947554948674370ptions @ I @ J))) <= (member_VEBT_VEBT @ I @ (set_VEBT_VEBT2 @ E)))) <= (G = H)) & ((G != H) => (! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ I) => ((ord_less_eq_nat @ I @ H) & (ord_less_nat @ G @ I)))) & (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ H))) & (ord_less_eq_nat @ G @ H)))) @ C) & ((size_s6755466524823107622T_VEBT @ E) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) & (vEBT_VEBT_valid @ F @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) & ! [G:vEBT_VEBT]: ((member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E)) => (vEBT_VEBT_valid @ G @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10071_VEBT__internal_Ovalid_H_Opelims_I3_J)). 159.59/70.66 thf(27985,plain,((! [A:vEBT_VEBT,B:nat]: ((~ (vEBT_VEBT_valid @ A @ B)) => ((accp_P2887432264394892906BT_nat @ (vEBT_VEBT_valid_rel) @ (produc738532404422230701BT_nat @ A @ B)) => ((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((accp_P2887432264394892906BT_nat @ (vEBT_VEBT_valid_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ C @ D) @ B)) => (B = one_one_nat)))) => (~ (! [C:option4927543243414619207at_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((A = (vEBT_Node @ C @ D @ E @ F)) => ((accp_P2887432264394892906BT_nat @ (vEBT_VEBT_valid_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ C @ D @ E @ F) @ B)) => ((D = B) & (case_o184042715313410164at_nat @ (! [G:vEBT_VEBT]: (~ (? [H:nat]: (vEBT_V8194947554948674370ptions @ G @ H)) | ~ (member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E))) & ~ (? [G:nat]: (vEBT_V8194947554948674370ptions @ F @ G))) @ (produc6081775807080527818_nat_o @ (^ [G:nat,H:nat]: ((ord_less_nat @ H @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) & ! [I:nat]: (((? [J:nat]: (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ E @ I) @ J)) = (vEBT_V8194947554948674370ptions @ F @ I)) | ~ (ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))))) & (! [I:vEBT_VEBT]: (~ (? [J:nat]: (vEBT_V8194947554948674370ptions @ I @ J)) | ~ (member_VEBT_VEBT @ I @ (set_VEBT_VEBT2 @ E))) | ~ (G = H)) & ((~ (G = H)) => (! [I:nat]: ((ord_less_nat @ I @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ I) => ((ord_less_eq_nat @ I @ H) & (ord_less_nat @ G @ I)))) & (vEBT_V5917875025757280293ildren @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))) @ E @ H))) & (ord_less_eq_nat @ G @ H)))) @ C) & ((size_s6755466524823107622T_VEBT @ E) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))))) & (vEBT_VEBT_valid @ F @ (minus_minus_nat @ D @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) & ! [G:vEBT_VEBT]: ((member_VEBT_VEBT @ G @ (set_VEBT_VEBT2 @ E)) => (vEBT_VEBT_valid @ G @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5882])). 159.59/70.66 thf(2925,axiom,((! [A:int]: ((bit_se1409905431419307370or_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5954_or_Oleft__neutral)). 159.59/70.66 thf(17672,plain,((! [A:int]: ((bit_se1409905431419307370or_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2925])). 159.59/70.66 thf(5560,axiom,((! [A:num,B:num]: ((bit1 @ A) != (bit0 @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5385_semiring__norm_I89_J)). 159.59/70.66 thf(26632,plain,((! [A:num,B:num]: ~ ((bit1 @ A) = (bit0 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5560])). 159.59/70.66 thf(7007,axiom,(((semiri1406184849735516958ct_int @ one_one_nat) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8051_fact__1)). 159.59/70.66 thf(32379,plain,(((semiri1406184849735516958ct_int @ one_one_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7007])). 159.59/70.66 thf(5153,axiom,((! [A:nat,B:(real > real),C:filter_real]: (((filterlim_real_real @ B @ at_bot_real @ C) => ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (filterlim_real_real @ (^ [D:real]: (power_power_real @ (B @ D) @ A)) @ at_bot_real @ C))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9951_filterlim__pow__at__bot__odd)). 159.59/70.66 thf(25089,plain,((! [A:nat,B:(real > real),C:filter_real]: (((filterlim_real_real @ (B) @ at_bot_real @ C) => ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (filterlim_real_real @ (^ [D:real]: (power_power_real @ (B @ D) @ A)) @ at_bot_real @ C))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5153])). 159.59/70.66 thf(5383,axiom,(((neg_nu6511756317524482435omplex @ zero_zero_complex) = (uminus1482373934393186551omplex @ one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5695_dbl__dec__simps_I2_J)). 159.59/70.66 thf(25998,plain,(((neg_nu6511756317524482435omplex @ zero_zero_complex) = (uminus1482373934393186551omplex @ one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5383])). 159.59/70.66 thf(7100,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_real @ A @ one_one_real) <= (ord_less_eq_real @ zero_zero_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2410_mult__less__cancel__right2)). 159.59/70.66 thf(32733,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_real @ A @ one_one_real) | ~ (ord_less_eq_real @ zero_zero_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7100])). 159.59/70.66 thf(7592,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 @ C @ D) & (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1206_add__mono__thms__linordered__field_I5_J)). 159.59/70.66 thf(34536,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 @ C @ D) & (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7592])). 159.59/70.66 thf(7282,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/sandbox/benchmark/theBenchmark.p',fact_6561_of__nat__eq__of__nat__power__cancel__iff)). 159.59/70.66 thf(33415,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)],[7282])). 159.59/70.66 thf(116,axiom,((! [A:real,B:nat]: ((power_power_complex @ (cis @ A) @ B) = (cis @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9380_DeMoivre)). 159.59/70.66 thf(8606,plain,((! [A:real,B:nat]: ((power_power_complex @ (cis @ A) @ B) = (cis @ (times_times_real @ (semiri5074537144036343181t_real @ B) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 159.59/70.66 thf(4076,axiom,((! [A:real,B:real]: ((if_real @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_001t__Real__Oreal_T)). 159.59/70.66 thf(21330,plain,((! [A:real,B:real]: ((if_real @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4076])). 159.59/70.66 thf(3397,axiom,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se725231765392027082nd_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ B @ C) & (bit_se1146084159140164899it_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6373_bit__and__iff)). 159.59/70.66 thf(19173,plain,((! [A:int,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se725231765392027082nd_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ B @ C) & (bit_se1146084159140164899it_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3397])). 159.59/70.66 thf(5632,axiom,((one_one_nat = (suc @ zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2208_One__nat__def)). 159.59/70.66 thf(26885,plain,((one_one_nat = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5632])). 159.59/70.66 thf(4010,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/sandbox/benchmark/theBenchmark.p',fact_4209_bit__eq__rec)). 159.59/70.66 thf(21140,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)],[4010])). 159.59/70.66 thf(3290,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = (uminus_uminus_real @ one_one_real)) = ((A = (uminus_uminus_real @ B)) & (B != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5209_divide__eq__minus__1__iff)). 159.59/70.66 thf(18843,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = (uminus_uminus_real @ one_one_real)) = ((A = (uminus_uminus_real @ B)) & ~ (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3290])). 159.59/70.66 thf(1235,axiom,((! [A:real,B:int]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ B) = (ord_less_eq_real @ A @ (ring_1_of_int_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7099_ceiling__le__iff)). 159.59/70.66 thf(12245,plain,((! [A:real,B:int]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ B) = (ord_less_eq_real @ A @ (ring_1_of_int_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235])). 159.59/70.66 thf(3039,axiom,((! [A:int,B:int]: (((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))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5893_real__of__int__div)). 159.59/70.66 thf(18019,plain,((! [A:int,B:int]: (((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))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3039])). 159.59/70.66 thf(680,axiom,((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5066_le__minus__one__simps_I2_J)). 159.59/70.66 thf(10428,plain,((ord_le3102999989581377725nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ one_one_Code_integer)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[680])). 159.59/70.66 thf(4971,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/sandbox/benchmark/theBenchmark.p',fact_8307_gbinomial__absorption)). 159.59/70.66 thf(24463,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)],[4971])). 159.59/70.66 thf(4772,axiom,((~ (ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5062_le__minus__one__simps_I4_J)). 159.59/70.66 thf(23746,plain,((~ (ord_less_eq_real @ one_one_real @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4772])). 159.59/70.66 thf(3369,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/sandbox/benchmark/theBenchmark.p',fact_1068_add__less__cancel__right)). 159.59/70.66 thf(19077,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)],[3369])). 159.59/70.66 thf(1840,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/sandbox/benchmark/theBenchmark.p',fact_5469_zmod__numeral__Bit1)). 159.59/70.66 thf(14204,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)],[1840])). 159.59/70.66 thf(386,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/sandbox/benchmark/theBenchmark.p',fact_9554_bit__xor__int__iff)). 159.59/70.66 thf(9459,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)],[386])). 159.59/70.66 thf(2817,axiom,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3978_dvd__triv__right)). 159.59/70.66 thf(17311,plain,((! [A:int,B:int]: (dvd_dvd_int @ A @ (times_times_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2817])). 159.59/70.66 thf(4148,axiom,((! [A:int]: ((modulo_modulo_int @ A @ (uminus_uminus_int @ one_one_int)) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4765_mod__minus1__right)). 159.59/70.66 thf(21562,plain,((! [A:int]: ((modulo_modulo_int @ A @ (uminus_uminus_int @ one_one_int)) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4148])). 159.59/70.66 thf(5196,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_nat__less__le)). 159.59/70.66 thf(25237,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5196])). 159.59/70.66 thf(2673,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/sandbox/benchmark/theBenchmark.p',fact_7961_sum__lessThan__telescope_H)). 159.59/70.66 thf(16867,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)],[2673])). 159.59/70.66 thf(1659,axiom,((! [A:num,B:num]: ~ (ord_less_int @ (numeral_numeral_int @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5037_not__numeral__less__neg__numeral)). 159.59/70.66 thf(13625,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)],[1659])). 159.59/70.66 thf(5097,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ (plus_plus_nat @ C @ B)) = (dvd_dvd_nat @ A @ C)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3987_dvd__add__left__iff)). 159.59/70.66 thf(24901,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ (plus_plus_nat @ C @ B)) = (dvd_dvd_nat @ A @ C)) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5097])). 159.59/70.66 thf(7880,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/sandbox/benchmark/theBenchmark.p',fact_2551_Suc__n__div__2__gt__zero)). 159.59/70.66 thf(35441,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)],[7880])). 159.59/70.66 thf(7037,axiom,((! [A:nat,B:nat]: ((((divide_divide_nat @ A @ B) = A) = (B = one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2403_div__eq__dividend__iff)). 159.59/70.66 thf(32474,plain,((! [A:nat,B:nat]: ((((divide_divide_nat @ A @ B) = A) = (B = one_one_nat)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7037])). 159.59/70.66 thf(124,axiom,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => (((groups3539618377306564664at_int @ C @ (minus_minus_set_nat @ A @ B)) = (minus_minus_int @ (groups3539618377306564664at_int @ C @ A) @ (groups3539618377306564664at_int @ C @ B))) <= (ord_less_eq_set_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7647_sum__diff)). 159.59/70.66 thf(8634,plain,((! [A:set_nat,B:set_nat,C:(nat > int)]: ((finite_finite_nat @ A) => (((groups3539618377306564664at_int @ (C) @ (minus_minus_set_nat @ A @ B)) = (minus_minus_int @ (groups3539618377306564664at_int @ (C) @ A) @ (groups3539618377306564664at_int @ (C) @ B))) | ~ (ord_less_eq_set_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 159.59/70.66 thf(4929,axiom,((! [A:nat,B:nat,C:int]: ((ord_less_eq_nat @ A @ B) => (((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2464_power__decreasing)). 159.59/70.66 thf(24287,plain,((! [A:nat,B:nat,C:int]: ((ord_less_eq_nat @ A @ B) => (((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4929])). 159.59/70.66 thf(5318,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/sandbox/benchmark/theBenchmark.p',fact_5639_cong__exp__iff__simps_I11_J)). 159.59/70.66 thf(25708,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)],[5318])). 159.59/70.66 thf(5387,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/sandbox/benchmark/theBenchmark.p',fact_5449_zero__less__power__abs__iff)). 159.59/70.66 thf(26013,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)],[5387])). 159.59/70.66 thf(5261,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/sandbox/benchmark/theBenchmark.p',fact_2243_mult__right__less__imp__less)). 159.59/70.66 thf(25475,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)],[5261])). 159.59/70.66 thf(2089,axiom,((! [A:int,B:real]: ((sin_complex @ (times_times_complex @ (ring_17405671764205052669omplex @ A) @ (real_V4546457046886955230omplex @ B))) = (real_V4546457046886955230omplex @ (sin_real @ (times_times_real @ (ring_1_of_int_real @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7770_sin__int__times__real)). 159.59/70.66 thf(14980,plain,((! [A:int,B:real]: ((sin_complex @ (times_times_complex @ (ring_17405671764205052669omplex @ A) @ (real_V4546457046886955230omplex @ B))) = (real_V4546457046886955230omplex @ (sin_real @ (times_times_real @ (ring_1_of_int_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2089])). 159.59/70.66 thf(4415,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)) & (((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/sandbox/benchmark/theBenchmark.p',fact_1637_div__mult__mult1__if)). 159.59/70.66 thf(22398,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)) & (((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)],[4415])). 159.59/70.66 thf(4540,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (((archim6058952711729229775r_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))) = (semiri1314217659103216013at_int @ C)) = ((ord_less_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))) & (ord_less_eq_nat @ (power_power_nat @ A @ C) @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8158_floor__log__nat__eq__powr__iff)). 159.59/70.66 thf(22926,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (((archim6058952711729229775r_real @ (log @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))) = (semiri1314217659103216013at_int @ C)) = ((ord_less_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))) & (ord_less_eq_nat @ (power_power_nat @ A @ C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4540])). 159.59/70.66 thf(7791,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/sandbox/benchmark/theBenchmark.p',fact_465_div__exp__eq)). 159.59/70.66 thf(35159,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)],[7791])). 159.59/70.66 thf(3991,axiom,((! [A:nat]: (((bit_se2000444600071755411sk_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5976_mask__eq__0__iff)). 159.59/70.66 thf(21081,plain,((! [A:nat]: (((bit_se2000444600071755411sk_int @ A) = zero_zero_int) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3991])). 159.59/70.66 thf(605,axiom,((! [A:int,B:int]: ((modulo_modulo_int @ (plus_plus_int @ A @ B) @ A) = (modulo_modulo_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3395_mod__add__self1)). 159.59/70.66 thf(10182,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)],[605])). 159.59/70.66 thf(212,axiom,((! [A:nat]: (((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ (^ [B:nat]: (if_Code_integer @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri4939895301339042750nteger @ (binomial @ A @ B)) @ zero_z3403309356797280102nteger)) @ (set_ord_atMost_nat @ A))) = (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8970_choose__odd__sum)). 159.59/70.66 thf(8897,plain,((! [A:nat]: (((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (groups7501900531339628137nteger @ (^ [B:nat]: (if_Code_integer @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (semiri4939895301339042750nteger @ (binomial @ A @ B)) @ zero_z3403309356797280102nteger)) @ (set_ord_atMost_nat @ A))) = (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 159.59/70.66 thf(3423,axiom,((~ (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1841_less__numeral__extra_I3_J)). 159.59/70.66 thf(19260,plain,((~ (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3423])). 159.59/70.66 thf(4488,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/sandbox/benchmark/theBenchmark.p',fact_6623_of__nat__zero__less__power__iff)). 159.59/70.66 thf(22687,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)],[4488])). 159.59/70.66 thf(6711,axiom,((! [A:real,B:real]: ((times_times_real @ (uminus_uminus_real @ A) @ B) = (times_times_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4952_minus__mult__commute)). 159.59/70.66 thf(31120,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)],[6711])). 159.59/70.66 thf(5965,axiom,((! [A:complex]: ((^ [B:complex]: (times_times_complex @ B @ A)) = (times_times_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1408_mult__commute__abs)). 159.59/70.66 thf(28328,plain,((! [A:complex]: ((^ [B:complex]: (times_times_complex @ B @ A)) = (times_times_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5965])). 159.59/70.66 thf(3563,axiom,((! [A:num]: ((plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ (numera1916890842035813515d_enat @ A)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_one__plus__numeral__commute)). 159.59/70.66 thf(19692,plain,((! [A:num]: ((plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ (numera1916890842035813515d_enat @ A)) = (plus_p3455044024723400733d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3563])). 159.59/70.66 thf(2856,axiom,((! [A:(extended_enat > $o),B:(extended_enat > $o),C:(extended_enat > $o),D:(extended_enat > $o)]: ((? [E:extended_enat]: ! [F:extended_enat]: (((A @ F) = (B @ F)) <= (ord_le72135733267957522d_enat @ F @ E))) => ((? [E:extended_enat]: ! [F:extended_enat]: (((C @ F) = (D @ F)) <= (ord_le72135733267957522d_enat @ F @ E))) => (? [E:extended_enat]: ! [F:extended_enat]: ((((C @ F) & (A @ F)) = ((D @ F) & (B @ F))) <= (ord_le72135733267957522d_enat @ F @ E))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4457_minf_I1_J)). 159.59/70.66 thf(17434,plain,((! [A:(extended_enat > $o),B:(extended_enat > $o),C:(extended_enat > $o),D:(extended_enat > $o)]: ((? [E:extended_enat]: ! [F:extended_enat]: (((A @ F) = (B @ F)) | ~ (ord_le72135733267957522d_enat @ F @ E))) => ((? [E:extended_enat]: ! [F:extended_enat]: (((C @ F) = (D @ F)) | ~ (ord_le72135733267957522d_enat @ F @ E))) => (? [E:extended_enat]: ! [F:extended_enat]: ((((C @ F) & (A @ F)) = ((D @ F) & (B @ F))) | ~ (ord_le72135733267957522d_enat @ F @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2856])). 159.59/70.66 thf(6172,axiom,(((bit_se2002935070580805687sk_nat @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5977_mask__0)). 159.59/70.66 thf(29001,plain,(((bit_se2002935070580805687sk_nat @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6172])). 159.59/70.66 thf(1690,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ (plus_plus_int @ B @ A)) = (ord_less_int @ zero_zero_int @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1598_less__add__same__cancel2)). 159.59/70.66 thf(13721,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)],[1690])). 159.59/70.66 thf(3974,axiom,((! [A:complex,B:num]: ((real_V1022390504157884413omplex @ (divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ B))) = (divide_divide_real @ (real_V1022390504157884413omplex @ A) @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6884_norm__divide__numeral)). 159.59/70.66 thf(21032,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)],[3974])). 159.59/70.66 thf(172,axiom,(((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ one_one_int)) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9585_and__not__numerals_I1_J)). 159.59/70.66 thf(8781,plain,(((bit_se725231765392027082nd_int @ one_one_int @ (bit_ri7919022796975470100ot_int @ one_one_int)) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[172])). 159.59/70.66 thf(7179,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/sandbox/benchmark/theBenchmark.p',fact_8150_fact__less__mono__nat)). 159.59/70.66 thf(33052,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)],[7179])). 159.59/70.66 thf(2773,axiom,(((neg_nu8557863876264182079omplex @ zero_zero_complex) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5796_dbl__inc__simps_I2_J)). 159.59/70.66 thf(17185,plain,(((neg_nu8557863876264182079omplex @ zero_zero_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2773])). 159.59/70.66 thf(493,axiom,((! [A:int,B:nat]: ((times_times_int @ (minus_minus_int @ A @ (semiri1314217659103216013at_int @ B)) @ (comm_s4660882817536571857er_int @ (uminus_uminus_int @ A) @ B)) = (times_times_int @ A @ (comm_s4660882817536571857er_int @ (plus_plus_int @ (uminus_uminus_int @ A) @ one_one_int) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8327_pochhammer__absorb__comp)). 159.59/70.66 thf(9824,plain,((! [A:int,B:nat]: ((times_times_int @ (minus_minus_int @ A @ (semiri1314217659103216013at_int @ B)) @ (comm_s4660882817536571857er_int @ (uminus_uminus_int @ A) @ B)) = (times_times_int @ A @ (comm_s4660882817536571857er_int @ (plus_plus_int @ (uminus_uminus_int @ A) @ one_one_int) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])). 159.59/70.66 thf(4856,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/sandbox/benchmark/theBenchmark.p',fact_2557_odd__0__le__power__imp__0__le)). 159.59/70.66 thf(24048,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)],[4856])). 159.59/70.66 thf(7310,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/sandbox/benchmark/theBenchmark.p',fact_2528_power__eq__if)). 159.59/70.66 thf(33542,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)],[7310])). 159.59/70.66 thf(7386,axiom,((! [A:int]: ((times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ A) = (plus_plus_int @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_mult__2)). 159.59/70.66 thf(33789,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)],[7386])). 159.59/70.66 thf(810,axiom,((! [A:nat,B:complex]: ((times_times_complex @ (semiri8010041392384452111omplex @ A) @ B) = (times_times_complex @ B @ (semiri8010041392384452111omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6652_mult__of__nat__commute)). 159.59/70.66 thf(10870,plain,((! [A:nat,B:complex]: ((times_times_complex @ (semiri8010041392384452111omplex @ A) @ B) = (times_times_complex @ B @ (semiri8010041392384452111omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[810])). 159.59/70.66 thf(6979,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/sandbox/benchmark/theBenchmark.p',fact_6620_numeral__less__real__of__nat__iff)). 159.59/70.66 thf(32264,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)],[6979])). 159.59/70.66 thf(2776,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ B @ C) @ (times_times_real @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2068_mult__strict__right__mono__neg)). 159.59/70.66 thf(17195,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ B @ C) @ (times_times_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2776])). 159.59/70.66 thf(6586,axiom,((! [A:nat]: ((power_power_complex @ one_one_complex @ A) = one_one_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_power__one)). 159.59/70.66 thf(30547,plain,((! [A:nat]: ((power_power_complex @ one_one_complex @ A) = one_one_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6586])). 159.59/70.66 thf(4783,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/sandbox/benchmark/theBenchmark.p',fact_4799_semiring__norm_I171_J)). 159.59/70.66 thf(23778,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)],[4783])). 159.59/70.66 thf(627,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2598_empty__subsetI)). 159.59/70.66 thf(10254,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ bot_bot_set_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[627])). 159.59/70.66 thf(3766,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/sandbox/benchmark/theBenchmark.p',fact_106_distrib__right__numeral)). 159.59/70.66 thf(20365,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)],[3766])). 159.59/70.66 thf(383,axiom,((! [A:num]: ((ord_max_int @ (numeral_numeral_int @ A) @ zero_zero_int) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1696_max__0__1_I4_J)). 159.59/70.66 thf(9449,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)],[383])). 159.59/70.66 thf(3855,axiom,((! [A:complex,B:complex,C:nat,D:nat]: ((dvd_dvd_complex @ A @ B) => ((ord_less_eq_nat @ C @ D) => (dvd_dvd_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4112_dvd__power__le)). 159.59/70.66 thf(20663,plain,((! [A:complex,B:complex,C:nat,D:nat]: ((dvd_dvd_complex @ A @ B) => ((ord_less_eq_nat @ C @ D) => (dvd_dvd_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3855])). 159.61/70.66 thf(2267,axiom,((! [A:complex,B:nat]: (((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))) <= (A != one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7982_geometric__sum)). 159.61/70.66 thf(15561,plain,((! [A:complex,B:nat]: (((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))) | (A = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2267])). 159.61/70.66 thf(4244,axiom,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ one_one_real @ one_one_real)) @ B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1452_gt__half__sum)). 159.61/70.66 thf(21875,plain,((! [A:real,B:real]: ((ord_less_real @ (divide_divide_real @ (plus_plus_real @ A @ B) @ (plus_plus_real @ one_one_real @ one_one_real)) @ B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4244])). 159.61/70.66 thf(1694,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((C != A) <= (ord_less_real @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4443_pinf_I4_J)). 159.61/70.66 thf(13733,plain,((! [A:real]: ? [B:real]: ! [C:real]: (~ (C = A) | ~ (ord_less_real @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694])). 159.61/70.66 thf(4986,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ A @ B)) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3793_dvd__add__triv__left__iff)). 159.61/70.66 thf(24506,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)],[4986])). 159.61/70.66 thf(4815,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_mint @ A) = B) => ((accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ A) => ((! [C:$o,D:$o]: (((((C) => (B = (some_nat @ zero_zero_nat))) & ((((D) => (B = (some_nat @ one_one_nat))) & ((~ (D)) => (B = none_nat))) <= (~ (C)))) => (~ (accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ (vEBT_Leaf @ C @ D)))) <= (A = (vEBT_Leaf @ C @ D)))) => ((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => ((B = none_nat) => (~ (accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((~ (accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))) <= (B = (some_nat @ C))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9748_vebt__mint_Opelims)). 159.61/70.66 thf(23886,plain,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_mint @ A) = B) => ((accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ A) => ((! [C:$o,D:$o]: (((((C) => (B = (some_nat @ zero_zero_nat))) & ((((D) => (B = (some_nat @ one_one_nat))) & ((~ (D)) => (B = none_nat))) | (C))) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ (vEBT_Leaf @ C @ D)))) | ~ (A = (vEBT_Leaf @ C @ D)))) => ((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => ((B = none_nat) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (~ (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)) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4815])). 159.61/70.66 thf(1643,axiom,(((arg @ (uminus1482373934393186551omplex @ imaginary_unit)) = (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9371_Arg__minus__ii)). 159.61/70.66 thf(13581,plain,(((arg @ (uminus1482373934393186551omplex @ imaginary_unit)) = (divide_divide_real @ (uminus_uminus_real @ pi) @ (numeral_numeral_real @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643])). 159.61/70.66 thf(2964,axiom,((! [A:nat]: (((semiri1314217659103216013at_int @ A) = one_one_int) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6540_of__nat__eq__1__iff)). 159.61/70.66 thf(17797,plain,((! [A:nat]: (((semiri1314217659103216013at_int @ A) = one_one_int) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2964])). 159.61/70.66 thf(4391,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (sin_real @ A)) <= (ord_less_real @ A @ pi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6833_sin__gt__zero)). 159.61/70.66 thf(22317,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (sin_real @ A)) | ~ (ord_less_real @ A @ pi))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4391])). 159.61/70.66 thf(6564,axiom,((! [A:set_nat,B:nat]: ((member_nat @ zero_zero_nat @ A) => ((suc @ (finite_card_nat @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ B) & (member_nat @ (suc @ C) @ A)))))) = (finite_card_nat @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ (suc @ B)) & (member_nat @ C @ A))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9714_card__less__Suc)). 159.61/70.66 thf(30473,plain,((! [A:set_nat,B:nat]: ((member_nat @ zero_zero_nat @ A) => ((suc @ (finite_card_nat @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ B) & (member_nat @ (suc @ C) @ A)))))) = (finite_card_nat @ (collect_nat @ (^ [C:nat]: ((ord_less_nat @ C @ (suc @ B)) & (member_nat @ C @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6564])). 159.61/70.66 thf(1240,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ zero_z5237406670263579293d_enat) = zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1491_mult__zero__right)). 159.61/70.66 thf(12268,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ A @ zero_z5237406670263579293d_enat) = zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240])). 159.61/70.66 thf(856,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1769_divide__le__eq__1__neg)). 159.61/70.66 thf(11013,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[856])). 159.61/70.66 thf(1779,axiom,((! [A:nat]: ((one_one_int = (semiri1314217659103216013at_int @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6546_of__nat__1__eq__iff)). 159.61/70.66 thf(13998,plain,((! [A:nat]: ((one_one_int = (semiri1314217659103216013at_int @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1779])). 159.61/70.66 thf(3782,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3199_order__le__less__trans)). 159.61/70.66 thf(20414,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3782])). 159.61/70.66 thf(5695,axiom,((! [A:product_prod_nat_nat]: (none_P5556105721700978146at_nat != (some_P7363390416028606310at_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1011_option_Odistinct_I1_J)). 159.61/70.66 thf(27110,plain,((! [A:product_prod_nat_nat]: ~ (none_P5556105721700978146at_nat = (some_P7363390416028606310at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5695])). 159.61/70.66 thf(458,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/sandbox/benchmark/theBenchmark.p',fact_939_max_OboundedI)). 159.61/70.66 thf(9692,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)],[458])). 159.61/70.66 thf(5222,axiom,((! [A:int]: ((ord_less_eq_int @ (abs_abs_int @ A) @ zero_zero_int) = (A = zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5405_abs__le__zero__iff)). 159.61/70.66 thf(25342,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)],[5222])). 159.61/70.66 thf(5189,axiom,((! [A:nat,B:nat,C:(nat > int),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (times_times_int @ (groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8809_prod_Oub__add__nat)). 159.61/70.66 thf(25210,plain,((! [A:nat,B:nat,C:(nat > int),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (times_times_int @ (groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5189])). 159.61/70.66 thf(3187,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_real @ B @ (times_times_real @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2329_pos__divide__less__eq)). 159.61/70.66 thf(18501,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_real @ B @ (times_times_real @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3187])). 159.61/70.66 thf(882,axiom,(((bit_se2000444600071755411sk_int @ zero_zero_nat) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5978_mask__0)). 159.61/70.66 thf(11091,plain,(((bit_se2000444600071755411sk_int @ zero_zero_nat) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[882])). 159.61/70.66 thf(2636,axiom,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ A @ B) & (C = D)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1201_add__mono__thms__linordered__field_I1_J)). 159.61/70.66 thf(16746,plain,((! [A:int,B:int,C:int,D:int]: (((ord_less_int @ A @ B) & (C = D)) => (ord_less_int @ (plus_plus_int @ A @ C) @ (plus_plus_int @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2636])). 159.61/70.66 thf(901,axiom,((comm_s3181272606743183617d_enat = (^ [A:extended_enat,B:nat]: (if_Extended_enat @ (B = zero_zero_nat) @ one_on7984719198319812577d_enat @ (set_fo2538466533108834004d_enat @ (^ [C:nat]: (times_7803423173614009249d_enat @ (plus_p3455044024723400733d_enat @ A @ (semiri4216267220026989637d_enat @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_on7984719198319812577d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8361_pochhammer__code)). 159.61/70.66 thf(11145,plain,(((comm_s3181272606743183617d_enat) = (^ [A:extended_enat,B:nat]: (if_Extended_enat @ (B = zero_zero_nat) @ one_on7984719198319812577d_enat @ (set_fo2538466533108834004d_enat @ (^ [C:nat]: (times_7803423173614009249d_enat @ (plus_p3455044024723400733d_enat @ A @ (semiri4216267220026989637d_enat @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_on7984719198319812577d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[901])). 159.61/70.66 thf(7834,axiom,((vEBT_invar_vebt @ (nth_VEBT_VEBT @ treeList @ summin) @ na)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72__092_060open_062invar__vebt_A_ItreeList_A_B_Asummin_J_An_092_060close_062)). 159.61/70.66 thf(35298,plain,((vEBT_invar_vebt @ (nth_VEBT_VEBT @ treeList @ summin) @ na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7834])). 159.61/70.66 thf(3740,axiom,((! [A:real,B:real,C:(real > int),D:int]: ((((C @ B) = D) => ((ord_less_int @ (C @ A) @ D) <= (! [E:real,F:real]: ((ord_less_int @ (C @ E) @ (C @ F)) <= (ord_less_real @ E @ F))))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2882_ord__less__eq__subst)). 159.61/70.66 thf(20282,plain,((! [A:real,B:real,C:(real > int),D:int]: ((((C @ B) = D) => ((ord_less_int @ (C @ A) @ D) | ~ (! [E:real,F:real]: ((ord_less_int @ (C @ E) @ (C @ F)) | ~ (ord_less_real @ E @ F))))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3740])). 159.61/70.66 thf(300,axiom,((! [A:code_integer,B:code_integer]: ((A = (uminus1351360451143612070nteger @ B)) = ((plus_p5714425477246183910nteger @ A @ B) = zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5049_eq__neg__iff__add__eq__0)). 159.61/70.66 thf(9179,plain,((! [A:code_integer,B:code_integer]: ((A = (uminus1351360451143612070nteger @ B)) = ((plus_p5714425477246183910nteger @ A @ B) = zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 159.61/70.66 thf(3771,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/sandbox/benchmark/theBenchmark.p',fact_1319_add__mono__thms__linordered__field_I4_J)). 159.61/70.66 thf(20382,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)],[3771])). 159.61/70.66 thf(5628,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_mint @ A) = (some_nat @ C)) => (vEBT_vebt_member @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_mint__member)). 159.61/70.66 thf(26873,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_mint @ A) = (some_nat @ C)) => (vEBT_vebt_member @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5628])). 159.61/70.66 thf(1908,axiom,((! [A:int,B:int]: ((bit_se1409905431419307370or_int @ A @ (bit_se1409905431419307370or_int @ A @ B)) = (bit_se1409905431419307370or_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5941_or_Oleft__idem)). 159.61/70.66 thf(14415,plain,((! [A:int,B:int]: ((bit_se1409905431419307370or_int @ A @ (bit_se1409905431419307370or_int @ A @ B)) = (bit_se1409905431419307370or_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1908])). 159.61/70.66 thf(2017,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ (modulo364778990260209775nteger @ B @ C)) <= (dvd_dvd_Code_integer @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4026_dvd__mod)). 159.61/70.66 thf(14770,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ (modulo364778990260209775nteger @ B @ C)) | ~ (dvd_dvd_Code_integer @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2017])). 159.61/70.66 thf(7521,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/sandbox/benchmark/theBenchmark.p',fact_6772_linear__plus__1__le__power)). 159.61/70.66 thf(34255,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)],[7521])). 159.61/70.66 thf(7352,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ B) @ B) = (modulo_modulo_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3392_mod__add__self2)). 159.61/70.66 thf(33674,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)],[7352])). 159.61/70.66 thf(2962,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/sandbox/benchmark/theBenchmark.p',fact_2338_eq__divide__eq__numeral_I1_J)). 159.61/70.66 thf(17792,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)],[2962])). 159.61/70.66 thf(6479,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ A))) = (numeral_numeral_int @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6010_or__numerals_I1_J)). 159.61/70.66 thf(30180,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ A))) = (numeral_numeral_int @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6479])). 159.61/70.66 thf(3705,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/sandbox/benchmark/theBenchmark.p',fact_5247_minus__divide__add__eq__iff)). 159.61/70.66 thf(20150,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)],[3705])). 159.61/70.66 thf(7817,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/sandbox/benchmark/theBenchmark.p',fact_460_post__member__pre__member)). 159.61/70.66 thf(35233,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)],[7817])). 159.61/70.66 thf(6246,axiom,((! [A:num,B:num]: ((pow @ A @ (bit0 @ B)) = (sqr @ (pow @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9799_pow_Osimps_I2_J)). 159.61/70.66 thf(29232,plain,((! [A:num,B:num]: ((pow @ A @ (bit0 @ B)) = (sqr @ (pow @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6246])). 159.61/70.66 thf(8174,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/sandbox/benchmark/theBenchmark.p',fact_3379_unset__bit__0)). 159.61/70.66 thf(36391,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)],[8174])). 159.61/70.66 thf(1144,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/sandbox/benchmark/theBenchmark.p',fact_5829_of__int__le__1__iff)). 159.61/70.66 thf(11918,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)],[1144])). 159.61/70.66 thf(6731,axiom,((! [A:real]: ((^ [B:real]: (times_times_real @ B @ A)) = (times_times_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1409_mult__commute__abs)). 159.61/70.66 thf(31202,plain,((! [A:real]: ((^ [B:real]: (times_times_real @ B @ A)) = (times_times_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6731])). 159.61/70.66 thf(5080,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/sandbox/benchmark/theBenchmark.p',fact_7782_mask__eq__sum__exp)). 159.61/70.66 thf(24851,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)],[5080])). 159.61/70.66 thf(5997,axiom,((semiri5044797733671781792omplex = (^ [A:nat]: (semiri8010041392384452111omplex @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8763_fact__prod)). 159.61/70.66 thf(28433,plain,(((semiri5044797733671781792omplex) = (^ [A:nat]: (semiri8010041392384452111omplex @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5997])). 159.61/70.66 thf(6543,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ (suc @ zero_zero_nat)) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6184_and__Suc__0__eq)). 159.61/70.66 thf(30409,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)],[6543])). 159.61/70.66 thf(3417,axiom,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (groups6464643781859351333omplex @ (^ [C:nat]: (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8878_pochhammer__Suc__prod)). 159.61/70.66 thf(19240,plain,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (groups6464643781859351333omplex @ (^ [C:nat]: (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3417])). 159.61/70.66 thf(3688,axiom,((! [A:extended_enat,B:extended_enat,C:nat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (groups7108830773950497114d_enat @ (^ [D:nat]: (plus_p3455044024723400733d_enat @ A @ (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_7803423173614009249d_enat @ (plus_p3455044024723400733d_enat @ (semiri4216267220026989637d_enat @ C) @ one_on7984719198319812577d_enat) @ (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ A) @ (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7801_double__arith__series)). 159.61/70.66 thf(20094,plain,((! [A:extended_enat,B:extended_enat,C:nat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ (groups7108830773950497114d_enat @ (^ [D:nat]: (plus_p3455044024723400733d_enat @ A @ (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ D) @ B))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ C))) = (times_7803423173614009249d_enat @ (plus_p3455044024723400733d_enat @ (semiri4216267220026989637d_enat @ C) @ one_on7984719198319812577d_enat) @ (plus_p3455044024723400733d_enat @ (times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ A) @ (times_7803423173614009249d_enat @ (semiri4216267220026989637d_enat @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3688])). 159.61/70.66 thf(2215,axiom,((! [A:(nat > real),B:real]: ((sums_real @ (^ [C:nat]: (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ (A @ C)) @ (power_power_real @ B @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))) @ (suminf_real @ (^ [C:nat]: (times_times_real @ (diffs_real @ A @ C) @ (power_power_real @ B @ C))))) <= (summable_real @ (^ [C:nat]: (times_times_real @ (diffs_real @ A @ C) @ (power_power_real @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8041_diffs__equiv)). 159.61/70.66 thf(15404,plain,((! [A:(nat > real),B:real]: ((sums_real @ (^ [C:nat]: (times_times_real @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ (A @ C)) @ (power_power_real @ B @ (minus_minus_nat @ C @ (suc @ zero_zero_nat))))) @ (suminf_real @ (^ [C:nat]: (times_times_real @ (diffs_real @ A @ C) @ (power_power_real @ B @ C))))) | ~ (summable_real @ (^ [C:nat]: (times_times_real @ (diffs_real @ A @ C) @ (power_power_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2215])). 159.61/70.66 thf(2507,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/sandbox/benchmark/theBenchmark.p',fact_6403_bit__not__int__iff_H)). 159.61/70.66 thf(16322,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)],[2507])). 159.61/70.66 thf(5174,axiom,((! [A:real]: (((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))) <= (ord_less_eq_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5297_ln__one__minus__pos__lower__bound)). 159.61/70.66 thf(25163,plain,((! [A:real]: ((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))) | ~ (ord_less_eq_real @ A @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5174])). 159.61/70.66 thf(5537,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/sandbox/benchmark/theBenchmark.p',fact_8971_choose__odd__sum)). 159.61/70.66 thf(26565,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)],[5537])). 159.61/70.66 thf(4557,axiom,((vEBT_is_pred_in_set = (^ [A:set_nat,B:nat,C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ B) & ! [D:nat]: ((member_nat @ D @ A) => ((ord_less_nat @ D @ B) => (ord_less_eq_nat @ D @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1448_is__pred__in__set__def)). 159.61/70.66 thf(22990,plain,(((vEBT_is_pred_in_set) = (^ [A:set_nat,B:nat,C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ B) & ! [D:nat]: ((member_nat @ D @ A) => ((ord_less_nat @ D @ B) => (ord_less_eq_nat @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4557])). 159.61/70.66 thf(4562,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = A) = ((B = one_one_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1620_mult__cancel__left2)). 159.61/70.66 thf(23003,plain,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = A) = ((B = one_one_complex) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4562])). 159.61/70.66 thf(1957,axiom,((! [A:int,B:nat,C:nat]: ((((power_power_int @ A @ B) = (power_power_int @ A @ C)) = (B = C)) <= (ord_less_int @ one_one_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_power__inject__exp)). 159.61/70.66 thf(14560,plain,((! [A:int,B:nat,C:nat]: ((((power_power_int @ A @ B) = (power_power_int @ A @ C)) = (B = C)) | ~ (ord_less_int @ one_one_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1957])). 159.61/70.66 thf(1044,axiom,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3168_linorder__not__le)). 159.61/70.66 thf(11599,plain,((! [A:real,B:real]: ((~ (ord_less_eq_real @ A @ B)) = (ord_less_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044])). 159.61/70.66 thf(3191,axiom,(((cosh_real @ zero_zero_real) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9313_cosh__0)). 159.61/70.66 thf(18518,plain,(((cosh_real @ zero_zero_real) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3191])). 159.61/70.66 thf(7882,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/sandbox/benchmark/theBenchmark.p',fact_4838_power2__minus)). 159.61/70.66 thf(35446,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)],[7882])). 159.61/70.66 thf(718,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/sandbox/benchmark/theBenchmark.p',fact_2064_mult__less__cancel__right__disj)). 159.61/70.66 thf(10563,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)],[718])). 159.61/70.66 thf(201,axiom,((! [A:(code_integer > $o),B:$o]: ((A @ (zero_n356916108424825756nteger @ B)) = (~ ((~ (A @ one_one_Code_integer) & (B)) | (~ (B) & ~ (A @ zero_z3403309356797280102nteger))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4415_split__of__bool__asm)). 159.61/70.66 thf(8865,plain,((! [A:(code_integer > $o),B:$o]: ((A @ (zero_n356916108424825756nteger @ B)) = (~ ((~ (A @ one_one_Code_integer) & (B)) | (~ (B) & ~ (A @ zero_z3403309356797280102nteger))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[201])). 159.61/70.66 thf(3718,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (log @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ one_one_real))) <= (ord_less_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6332_log__less__zero__cancel__iff)). 159.61/70.66 thf(20210,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (log @ A @ B) @ zero_zero_real) = (ord_less_real @ B @ one_one_real))) | ~ (ord_less_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3718])). 159.61/70.66 thf(1745,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ A @ B)) = (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3790_dvd__add__triv__left__iff)). 159.61/70.66 thf(13887,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ A @ B)) = (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745])). 159.61/70.66 thf(6187,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1795_power__decreasing__iff)). 159.61/70.66 thf(29052,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6187])). 159.61/70.66 thf(7506,axiom,((! [A:real,B:real,C:nat]: (((log @ B @ (power_power_real @ A @ C)) = (times_times_real @ (semiri5074537144036343181t_real @ C) @ (log @ B @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6767_log__nat__power)). 159.61/70.66 thf(34207,plain,((! [A:real,B:real,C:nat]: (((log @ B @ (power_power_real @ A @ C)) = (times_times_real @ (semiri5074537144036343181t_real @ C) @ (log @ B @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7506])). 159.61/70.66 thf(833,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_eq_real @ (powr_real @ A @ B) @ (powr_real @ A @ C)) = (ord_less_eq_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7219_powr__le__cancel__iff)). 159.61/70.66 thf(10937,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ one_one_real @ A) => ((ord_less_eq_real @ (powr_real @ A @ B) @ (powr_real @ A @ C)) = (ord_less_eq_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[833])). 159.61/70.66 thf(1969,axiom,((~ (ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_less__numeral__extra_I4_J)). 159.61/70.66 thf(14596,plain,((~ (ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1969])). 159.61/70.66 thf(7260,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/sandbox/benchmark/theBenchmark.p',fact_6445_real__sqrt__sum__squares__ge1)). 159.61/70.66 thf(33351,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)],[7260])). 159.61/70.66 thf(5834,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6176_and__nat__numerals_I2_J)). 159.61/70.66 thf(27783,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)],[5834])). 159.61/70.66 thf(6894,axiom,(((semiri1408675320244567234ct_nat @ one_one_nat) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8053_fact__1)). 159.61/70.66 thf(31837,plain,(((semiri1408675320244567234ct_nat @ one_one_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6894])). 159.61/70.66 thf(2043,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/sandbox/benchmark/theBenchmark.p',fact_99_numeral__plus__numeral)). 159.61/70.66 thf(14845,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)],[2043])). 159.61/70.66 thf(8229,axiom,(((power_power_int @ one_one_int @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_one__power2)). 159.61/70.66 thf(36563,plain,(((power_power_int @ one_one_int @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8229])). 159.61/70.66 thf(467,axiom,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ (semiri3624122377584611663nteger @ A) @ (semiri3624122377584611663nteger @ (minus_minus_nat @ B @ A))) @ (semiri3624122377584611663nteger @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8093_choose__dvd)). 159.61/70.66 thf(9718,plain,((! [A:nat,B:nat]: ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ (semiri3624122377584611663nteger @ A) @ (semiri3624122377584611663nteger @ (minus_minus_nat @ B @ A))) @ (semiri3624122377584611663nteger @ B)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])). 159.61/70.66 thf(3059,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ A @ B) = (A = B)) <= (~ (ord_less_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3040_antisym__conv1)). 159.61/70.66 thf(18083,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)],[3059])). 159.61/70.66 thf(4012,axiom,((! [A:nat,B:real,C:real,D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (times_times_real @ (gbinomial_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ B) @ E) @ (power_power_real @ C @ E)) @ (power_power_real @ D @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A)) = (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (times_times_real @ (gbinomial_real @ (minus_minus_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ E) @ B) @ one_one_real) @ E) @ (power_power_real @ C @ E)) @ (power_power_real @ (plus_plus_real @ C @ D) @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8952_gbinomial__partial__sum__poly__xpos)). 159.61/70.66 thf(21145,plain,((! [A:nat,B:real,C:real,D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (times_times_real @ (gbinomial_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ B) @ E) @ (power_power_real @ C @ E)) @ (power_power_real @ D @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A)) = (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (times_times_real @ (gbinomial_real @ (minus_minus_real @ (plus_plus_real @ (semiri5074537144036343181t_real @ E) @ B) @ one_one_real) @ E) @ (power_power_real @ C @ E)) @ (power_power_real @ (plus_plus_real @ C @ D) @ (minus_minus_nat @ A @ E)))) @ (set_ord_atMost_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4012])). 159.61/70.66 thf(2000,axiom,((! [A:int,B:int]: ((ord_less_int @ B @ A) | (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3256_linorder__le__less__linear)). 159.61/70.66 thf(14715,plain,((! [A:int,B:int]: ((ord_less_int @ B @ A) | (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2000])). 159.61/70.66 thf(1427,axiom,((! [A:num,B:(real > num),C:real,D:real]: ((A = (B @ C)) => (((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_num @ (B @ E) @ (B @ F)))) => (ord_less_num @ A @ (B @ D))) <= (ord_less_real @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2870_ord__eq__less__subst)). 159.61/70.66 thf(12900,plain,((! [A:num,B:(real > num),C:real,D:real]: ((A = (B @ C)) => (((! [E:real,F:real]: ((ord_less_real @ E @ F) => (ord_less_num @ (B @ E) @ (B @ F)))) => (ord_less_num @ A @ (B @ D))) | ~ (ord_less_real @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1427])). 159.61/70.66 thf(3522,axiom,((! [A:int,B:real]: (((ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real)) => ((archim6058952711729229775r_real @ B) = A)) <= (ord_less_eq_real @ (ring_1_of_int_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8304_floor__eq2)). 159.61/70.66 thf(19559,plain,((! [A:int,B:real]: (((ord_less_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real)) => ((archim6058952711729229775r_real @ B) = A)) | ~ (ord_less_eq_real @ (ring_1_of_int_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3522])). 159.61/70.66 thf(6561,axiom,((divmod_nat = (^ [A:nat,B:nat]: (if_Pro6206227464963214023at_nat @ ((B = zero_zero_nat) | (ord_less_nat @ A @ B)) @ (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/sandbox/benchmark/theBenchmark.p',fact_5350_divmod__nat__if)). 159.61/70.66 thf(30464,plain,(((divmod_nat) = (^ [A:nat,B:nat]: (if_Pro6206227464963214023at_nat @ ((B = zero_zero_nat) | (ord_less_nat @ A @ B)) @ (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)],[6561])). 159.61/70.66 thf(2905,axiom,((! [A:real]: (ord_less_eq_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8210_of__int__floor__le)). 159.61/70.66 thf(17608,plain,((! [A:real]: (ord_less_eq_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2905])). 159.61/70.66 thf(3260,axiom,((! [A:$o]: (ord_less_eq_int @ zero_zero_int @ (zero_n2684676970156552555ol_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4392_zero__less__eq__of__bool)). 159.61/70.66 thf(18744,plain,((! [A:$o]: (ord_less_eq_int @ zero_zero_int @ (zero_n2684676970156552555ol_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3260])). 159.61/70.66 thf(7730,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A)) <= (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2841_linorder__neqE)). 159.61/70.66 thf(34976,plain,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A)) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7730])). 159.61/70.66 thf(3350,axiom,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7000_cos__pi__half)). 159.61/70.66 thf(19023,plain,(((cos_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3350])). 159.61/70.66 thf(5455,axiom,((! [A:(nat > complex),B:nat]: (((A @ zero_zero_nat) = zero_zero_complex) => ((groups2073611262835488442omplex @ A @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups2073611262835488442omplex @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7652_sum__shift__lb__Suc0__0)). 159.61/70.66 thf(26288,plain,((! [A:(nat > complex),B:nat]: (((A @ zero_zero_nat) = zero_zero_complex) => ((groups2073611262835488442omplex @ (A) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups2073611262835488442omplex @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5455])). 159.61/70.66 thf(7012,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7973_sum_OatLeast1__atMost__eq)). 159.61/70.66 thf(32394,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ (suc @ zero_zero_nat) @ B)) = (groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7012])). 159.61/70.66 thf(3412,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/sandbox/benchmark/theBenchmark.p',fact_6297_of__int__round__le)). 159.61/70.66 thf(19224,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)],[3412])). 159.61/70.66 thf(562,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/sandbox/benchmark/theBenchmark.p',fact_8844_atLeast1__atMost__eq__remove0)). 159.61/70.66 thf(10040,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)],[562])). 159.61/70.66 thf(2947,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (exp_complex @ A) @ (exp_complex @ B)) = (exp_complex @ (plus_plus_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6079_mult__exp__exp)). 159.61/70.66 thf(17740,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)],[2947])). 159.61/70.66 thf(5844,axiom,((! [A:(complex > $o),B:complex,C:(complex > $o)]: ((! [D:complex,E:complex]: ((A @ D) = (A @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))))) => ((! [D:complex,E:complex]: ((C @ D) = (C @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))))) => (! [D:complex,E:complex]: (((A @ D) | (C @ D)) = ((A @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))) | (C @ (minus_minus_complex @ D @ (times_times_complex @ E @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4519_inf__period_I2_J)). 159.61/70.66 thf(27852,plain,((! [A:(complex > $o),B:complex,C:(complex > $o)]: ((! [D:complex,E:complex]: ((A @ D) = (A @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))))) => ((! [D:complex,E:complex]: ((C @ D) = (C @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))))) => (! [D:complex,E:complex]: (((A @ D) | (C @ D)) = ((A @ (minus_minus_complex @ D @ (times_times_complex @ E @ B))) | (C @ (minus_minus_complex @ D @ (times_times_complex @ E @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5844])). 159.61/70.66 thf(4167,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (((ln_ln_real @ A) = (ln_ln_real @ B)) = (A = B))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4650_ln__inj__iff)). 159.61/70.66 thf(21618,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => (((ln_ln_real @ A) = (ln_ln_real @ B)) = (A = B))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4167])). 159.61/70.66 thf(7202,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/sandbox/benchmark/theBenchmark.p',fact_8288_pochhammer__of__nat__eq__0__lemma_H)). 159.61/70.66 thf(33149,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)],[7202])). 159.61/70.66 thf(7617,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (A = B) | (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2921_linorder__less__linear)). 159.61/70.66 thf(34604,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (A = B) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7617])). 159.61/70.66 thf(6611,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/sandbox/benchmark/theBenchmark.p',fact_2007_mult__mono)). 159.61/70.66 thf(30639,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)],[6611])). 159.61/70.66 thf(7476,axiom,((! [A:num,B:nat]: ((bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ B)) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6327_bit__numeral__Bit0__Suc__iff)). 159.61/70.66 thf(34081,plain,((! [A:num,B:nat]: ((bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ B)) = (bit_se1148574629649215175it_nat @ (numeral_numeral_nat @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7476])). 159.61/70.66 thf(6405,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/sandbox/benchmark/theBenchmark.p',fact_1215_diff__eq__diff__less__eq)). 159.61/70.66 thf(29868,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)],[6405])). 159.61/70.66 thf(3228,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/sandbox/benchmark/theBenchmark.p',fact_4733_dbl__simps_I1_J)). 159.61/70.66 thf(18634,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)],[3228])). 159.61/70.66 thf(6930,axiom,((! [A:real]: ((times_times_real @ (sqrt @ A) @ (sqrt @ A)) = (abs_abs_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6325_real__sqrt__mult__self)). 159.61/70.66 thf(31961,plain,((! [A:real]: ((times_times_real @ (sqrt @ A) @ (sqrt @ A)) = (abs_abs_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6930])). 159.61/70.66 thf(4458,axiom,((! [A:num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_one__le__numeral)). 159.61/70.66 thf(22531,plain,((! [A:num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4458])). 159.61/70.66 thf(7350,axiom,(((abs_abs_int @ (uminus_uminus_int @ one_one_int)) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5416_abs__neg__one)). 159.61/70.66 thf(33669,plain,(((abs_abs_int @ (uminus_uminus_int @ one_one_int)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7350])). 159.61/70.66 thf(6703,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4439_pinf_I3_J)). 159.61/70.66 thf(31018,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6703])). 159.61/70.66 thf(461,axiom,((! [A:int,B:nat]: (ord_less_eq_int @ A @ (bit_se7879613467334960850it_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3325_set__bit__greater__eq)). 159.61/70.66 thf(9701,plain,((! [A:int,B:nat]: (ord_less_eq_int @ A @ (bit_se7879613467334960850it_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[461])). 159.61/70.66 thf(3329,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((((powr_real @ A @ B) = (powr_real @ A @ C)) = (B = C)) <= (A != one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7245_powr__inj)). 159.61/70.66 thf(18960,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ zero_zero_real @ A) => ((((powr_real @ A @ B) = (powr_real @ A @ C)) = (B = C)) | (A = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3329])). 159.61/70.66 thf(7951,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_less__add__Suc1)). 159.61/70.66 thf(35672,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7951])). 159.61/70.66 thf(2453,axiom,((topolo4055970368930404560y_real = (^ [A:(nat > real)]: ! [B:nat]: ? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (! [E:nat]: ((ord_less_eq_nat @ C @ E) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ (A @ D) @ (A @ E))) @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ (suc @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9546_Cauchy__iff2)). 159.61/70.66 thf(16149,plain,(((topolo4055970368930404560y_real) = (^ [A:(nat > real)]: ! [B:nat]: ? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (! [E:nat]: ((ord_less_eq_nat @ C @ E) => (ord_less_real @ (abs_abs_real @ (minus_minus_real @ (A @ D) @ (A @ E))) @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ (suc @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2453])). 159.61/70.66 thf(4274,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/sandbox/benchmark/theBenchmark.p',fact_4091_div__plus__div__distrib__dvd__left)). 159.61/70.66 thf(21964,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)],[4274])). 159.61/70.66 thf(3169,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1189_add__strict__right__mono)). 159.61/70.66 thf(18447,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3169])). 159.61/70.66 thf(4878,axiom,((! [A:set_nat,B:(nat > nat)]: ((~ (finite_finite_nat @ A)) => ((groups708209901874060359at_nat @ B @ A) = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8396_prod_Oinfinite)). 159.61/70.66 thf(24115,plain,((! [A:set_nat,B:(nat > nat)]: ((~ (finite_finite_nat @ A)) => ((groups708209901874060359at_nat @ (B) @ A) = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4878])). 159.61/70.66 thf(3049,axiom,((! [A:real,B:real]: (((A = B) | (ord_less_real @ A @ B)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3258_order__le__imp__less__or__eq)). 159.61/70.66 thf(18051,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)],[3049])). 159.61/70.66 thf(2970,axiom,((! [A:int]: ((~ (! [B:nat]: ((A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ B))) => (~ (ord_less_nat @ zero_zero_nat @ B))))) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6855_neg__int__cases)). 159.61/70.66 thf(17814,plain,((! [A:int]: (~ (! [B:nat]: ((A = (uminus_uminus_int @ (semiri1314217659103216013at_int @ B))) => (~ (ord_less_nat @ zero_zero_nat @ B)))) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2970])). 159.61/70.66 thf(5497,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((modulo_modulo_nat @ B @ A) = (modulo_modulo_nat @ (minus_minus_nat @ B @ A) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3493_le__mod__geq)). 159.61/70.66 thf(26433,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((modulo_modulo_nat @ B @ A) = (modulo_modulo_nat @ (minus_minus_nat @ B @ A) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5497])). 159.61/70.66 thf(419,axiom,((filterlim_real_real @ tanh_real @ (topolo2815343760600316023s_real @ (uminus_uminus_real @ one_one_real)) @ at_bot_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9948_tanh__real__at__bot)). 159.61/70.66 thf(9569,plain,((filterlim_real_real @ (tanh_real) @ (topolo2815343760600316023s_real @ (uminus_uminus_real @ one_one_real)) @ at_bot_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])). 159.61/70.66 thf(6840,axiom,((! [A:nat,B:nat,C:nat]: ((! [D:nat]: ~ (bit_se1148574629649215175it_nat @ A @ (suc @ D))) => ((bit_se1148574629649215175it_nat @ (plus_plus_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ C) = (((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) <= (C = zero_zero_nat)) & ((bit_se1148574629649215175it_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) <= (C != zero_zero_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6465_bit__sum__mult__2__cases)). 159.61/70.66 thf(31576,plain,((! [A:nat,B:nat,C:nat]: ((! [D:nat]: ~ (bit_se1148574629649215175it_nat @ A @ (suc @ D))) => ((bit_se1148574629649215175it_nat @ (plus_plus_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ C) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) | ~ (C = zero_zero_nat)) & ((bit_se1148574629649215175it_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) | (C = zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6840])). 159.61/70.66 thf(3472,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ A) => (ord_less_int @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2827_dual__order_Ostrict__trans)). 159.61/70.66 thf(19403,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ A) => (ord_less_int @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3472])). 159.61/70.66 thf(7119,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ (sqrt @ B)) => (ord_less_eq_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6446_sqrt__ge__absD)). 159.61/70.66 thf(32829,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_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)],[7119])). 159.61/70.66 thf(6420,axiom,((! [A:nat,B:nat,C:nat]: ((((dvd_dvd_nat @ (divide_divide_nat @ B @ A) @ C) = (dvd_dvd_nat @ B @ (times_times_nat @ C @ A))) <= (dvd_dvd_nat @ A @ B)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4142_div__dvd__iff__mult)). 159.61/70.66 thf(29932,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (divide_divide_nat @ B @ A) @ C) = (dvd_dvd_nat @ B @ (times_times_nat @ C @ A))) | ~ (dvd_dvd_nat @ A @ B) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6420])). 159.61/70.66 thf(3303,axiom,((! [A:extended_enat,B:extended_enat]: ? [C:extended_enat]: ! [D:extended_enat]: (((dvd_dv3785147216227455552d_enat @ A @ (plus_p3455044024723400733d_enat @ D @ B)) = (dvd_dv3785147216227455552d_enat @ A @ (plus_p3455044024723400733d_enat @ D @ B))) <= (ord_le72135733267957522d_enat @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4537_minf_I9_J)). 159.61/70.66 thf(18881,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3303])). 159.61/70.66 thf(5889,axiom,((ord_less_eq_real @ (exp_real @ one_one_real) @ (numeral_numeral_real @ (bit1 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6112_exp__le)). 159.61/70.66 thf(28017,plain,((ord_less_eq_real @ (exp_real @ one_one_real) @ (numeral_numeral_real @ (bit1 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5889])). 159.61/70.66 thf(190,axiom,((! [A:nat]: (((semiri3624122377584611663nteger @ A) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (semiri3624122377584611663nteger @ (minus_minus_nat @ A @ one_one_nat)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8127_fact__reduce)). 159.61/70.66 thf(8837,plain,((! [A:nat]: (((semiri3624122377584611663nteger @ A) = (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ (semiri3624122377584611663nteger @ (minus_minus_nat @ A @ one_one_nat)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[190])). 159.61/70.66 thf(4997,axiom,((zero_zero_real != (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5068_zero__neq__neg__one)). 159.61/70.66 thf(24549,plain,((~ (zero_zero_real = (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4997])). 159.61/70.66 thf(46,axiom,((! [A:real,B:real]: ((plus_plus_real @ (real_V1485227260804924795R_real @ (minus_minus_real @ one_one_real @ A) @ B) @ (real_V1485227260804924795R_real @ A @ B)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9199_scaleR__collapse)). 159.61/70.66 thf(8388,plain,((! [A:real,B:real]: ((plus_plus_real @ (real_V1485227260804924795R_real @ (minus_minus_real @ one_one_real @ A) @ B) @ (real_V1485227260804924795R_real @ A @ B)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[46])). 159.61/70.66 thf(1835,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => (((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))) <= (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1341_add__le__add__imp__diff__le)). 159.61/70.66 thf(14187,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ (plus_plus_real @ D @ B)) => ((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))) | ~ (ord_less_eq_real @ (plus_plus_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1835])). 159.61/70.66 thf(6041,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ (suc @ A)) = (B = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_le__less__Suc__eq)). 159.61/70.66 thf(28571,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ (suc @ A)) = (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6041])). 159.61/70.66 thf(6216,axiom,((! [A:real]: (ord_less_eq_real @ (uminus_uminus_real @ (abs_abs_real @ A)) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5564_abs__minus__le__zero)). 159.61/70.66 thf(29143,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)],[6216])). 159.61/70.66 thf(7508,axiom,((ord_less_eq_int @ zero_zero_int @ one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2055_linordered__nonzero__semiring__class_Ozero__le__one)). 159.61/70.66 thf(34214,plain,((ord_less_eq_int @ zero_zero_int @ one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7508])). 159.61/70.66 thf(6211,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/sandbox/benchmark/theBenchmark.p',fact_2502_power2__le__imp__le)). 159.61/70.66 thf(29126,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)],[6211])). 159.61/70.66 thf(5227,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/sandbox/benchmark/theBenchmark.p',fact_565_nat__add__max__left)). 159.61/70.66 thf(25369,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)],[5227])). 159.61/70.66 thf(3603,axiom,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_real @ (A @ zero_zero_nat) @ (groups129246275422532515t_real @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8741_prod_OlessThan__Suc__shift)). 159.61/70.66 thf(19823,plain,((! [A:(nat > real),B:nat]: ((groups129246275422532515t_real @ (A) @ (set_ord_lessThan_nat @ (suc @ 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)],[3603])). 159.61/70.66 thf(4289,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4717_divide__minus1)). 159.61/70.66 thf(22009,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ (uminus1482373934393186551omplex @ one_one_complex)) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4289])). 159.61/70.66 thf(367,axiom,((! [A:code_integer,B:nat]: ((comm_s8582702949713902594nteger @ A @ (suc @ B)) = (times_3573771949741848930nteger @ (comm_s8582702949713902594nteger @ A @ B) @ (plus_p5714425477246183910nteger @ A @ (semiri4939895301339042750nteger @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8272_pochhammer__Suc)). 159.61/70.66 thf(9393,plain,((! [A:code_integer,B:nat]: ((comm_s8582702949713902594nteger @ A @ (suc @ B)) = (times_3573771949741848930nteger @ (comm_s8582702949713902594nteger @ A @ B) @ (plus_p5714425477246183910nteger @ A @ (semiri4939895301339042750nteger @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[367])). 159.61/70.66 thf(3935,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/sandbox/benchmark/theBenchmark.p',fact_1273_diff__diff__eq)). 159.61/70.66 thf(20910,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)],[3935])). 159.61/70.66 thf(6707,axiom,(((divide6298287555418463151nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (uminus1351360451143612070nteger @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4857_minus__1__div__2__eq)). 159.61/70.66 thf(31110,plain,(((divide6298287555418463151nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (uminus1351360451143612070nteger @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6707])). 159.61/70.66 thf(3499,axiom,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (groups129246275422532515t_real @ (^ [C:nat]: (plus_plus_real @ A @ (semiri5074537144036343181t_real @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8877_pochhammer__Suc__prod)). 159.61/70.66 thf(19489,plain,((! [A:real,B:nat]: ((comm_s7457072308508201937r_real @ A @ (suc @ B)) = (groups129246275422532515t_real @ (^ [C:nat]: (plus_plus_real @ A @ (semiri5074537144036343181t_real @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3499])). 159.61/70.66 thf(6535,axiom,((! [A:nat,B:nat]: ((B != zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1835_gr__implies__not__zero)). 159.61/70.66 thf(30381,plain,((! [A:nat,B:nat]: (~ (B = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6535])). 159.61/70.66 thf(4065,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/sandbox/benchmark/theBenchmark.p',fact_7824_gauss__sum)). 159.61/70.66 thf(21298,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)],[4065])). 159.61/70.66 thf(6997,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/sandbox/benchmark/theBenchmark.p',fact_5637_power__even__abs)). 159.61/70.66 thf(32347,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)],[6997])). 159.61/70.66 thf(6850,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/sandbox/benchmark/theBenchmark.p',fact_510_insert__simp__norm)). 159.61/70.66 thf(31700,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)],[6850])). 159.61/70.66 thf(484,axiom,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ A)) = (ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4663_neg__0__le__iff__le)). 159.61/70.66 thf(9792,plain,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ A)) = (ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])). 159.61/70.66 thf(6399,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1884_comm__monoid__add__class_Oadd__0)). 159.61/70.66 thf(29848,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6399])). 159.61/70.66 thf(6059,axiom,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ C @ B)) = ((A = C) | (B = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1478_mult__cancel__right)). 159.61/70.66 thf(28630,plain,((! [A:complex,B:complex,C:complex]: (((times_times_complex @ A @ B) = (times_times_complex @ C @ B)) = ((A = C) | (B = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6059])). 159.61/70.66 thf(129,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/sandbox/benchmark/theBenchmark.p',fact_8235_gbinomial__Suc__Suc)). 159.61/70.66 thf(8649,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)],[129])). 159.61/70.66 thf(7788,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/sandbox/benchmark/theBenchmark.p',fact_1718_mult__less__cancel2)). 159.61/70.66 thf(35150,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)],[7788])). 159.61/70.66 thf(125,axiom,((! [A:nat,B:(nat > code_integer),C:code_integer,D:nat]: (((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C) => (ord_le3102999989581377725nteger @ (groups7501900531339628137nteger @ B @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ C))) <= (! [E:nat]: ((ord_less_nat @ E @ A) => (ord_le3102999989581377725nteger @ (B @ E) @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8005_real__sum__nat__ivl__bounded2)). 159.61/70.66 thf(8638,plain,((! [A:nat,B:(nat > code_integer),C:code_integer,D:nat]: (((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C) => (ord_le3102999989581377725nteger @ (groups7501900531339628137nteger @ (B) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ C))) | ~ (! [E:nat]: ((ord_less_nat @ E @ A) => (ord_le3102999989581377725nteger @ (B @ E) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 159.61/70.66 thf(2777,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/sandbox/benchmark/theBenchmark.p',fact_4998_mod__minus__eq)). 159.61/70.66 thf(17198,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)],[2777])). 159.61/70.66 thf(1909,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/sandbox/benchmark/theBenchmark.p',fact_1245_ring__class_Oring__distribs_I2_J)). 159.61/70.66 thf(14418,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)],[1909])). 159.61/70.66 thf(4618,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/sandbox/benchmark/theBenchmark.p',fact_4382_one__mod__2__pow__eq)). 159.61/70.66 thf(23216,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)],[4618])). 159.61/70.66 thf(5611,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ A)) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3798_dvd__add__triv__right__iff)). 159.61/70.66 thf(26817,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)],[5611])). 159.61/70.66 thf(5357,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) = (A = B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3044_antisym__conv1)). 159.61/70.66 thf(25910,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)],[5357])). 159.61/70.66 thf(4467,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (sqrt @ A)) = (ord_less_eq_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6321_real__sqrt__ge__1__iff)). 159.61/70.66 thf(22615,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)],[4467])). 159.61/70.66 thf(5237,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/sandbox/benchmark/theBenchmark.p',fact_5687_le__Suc__numeral)). 159.61/70.66 thf(25397,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)],[5237])). 159.61/70.66 thf(7627,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2767_less__imp__neq)). 159.61/70.66 thf(34636,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7627])). 159.61/70.66 thf(7865,axiom,(((plus_plus_num @ one @ one) = (bit0 @ one))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_semiring__norm_I2_J)). 159.61/70.66 thf(35388,plain,(((plus_plus_num @ one @ one) = (bit0 @ one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7865])). 159.61/70.66 thf(4708,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6793_monoseq__arctan__series)). 159.61/70.66 thf(23527,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4708])). 159.61/70.66 thf(6682,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (ord_max_nat @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_max_Ostrict__coboundedI2)). 159.61/70.66 thf(30899,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)],[6682])). 159.61/70.66 thf(6721,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/sandbox/benchmark/theBenchmark.p',fact_2307_mult__left__le)). 159.61/70.66 thf(31168,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)],[6721])). 159.61/70.66 thf(7872,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => (ord_less_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2209_nat__power__less__imp__less)). 159.61/70.66 thf(35409,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => (ord_less_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7872])). 159.61/70.66 thf(1968,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/sandbox/benchmark/theBenchmark.p',fact_7214_powr__less__cancel__iff)). 159.61/70.66 thf(14592,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)],[1968])). 159.61/70.66 thf(4643,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/sandbox/benchmark/theBenchmark.p',fact_3458_mod__add__eq)). 159.61/70.66 thf(23298,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)],[4643])). 159.61/70.66 thf(2534,axiom,((abs_abs_real = (^ [A:real]: (if_real @ (ord_less_real @ A @ zero_zero_real) @ (uminus_uminus_real @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5576_abs__if)). 159.61/70.66 thf(16403,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)],[2534])). 159.61/70.66 thf(5072,axiom,((! [A:num]: ((power_power_real @ zero_zero_real @ (numeral_numeral_nat @ A)) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1683_power__zero__numeral)). 159.61/70.66 thf(24820,plain,((! [A:num]: ((power_power_real @ zero_zero_real @ (numeral_numeral_nat @ A)) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5072])). 159.61/70.66 thf(6306,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_nat__le__add__iff2)). 159.61/70.66 thf(29511,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6306])). 159.61/70.66 thf(7557,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_num @ A @ (B @ D))) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_num @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3239_order__less__le__subst1)). 159.61/70.66 thf(34362,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_num @ A @ (B @ D))) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_num @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7557])). 159.61/70.66 thf(316,axiom,((! [A:set_nat,B:set_nat,C:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => ((! [D:nat]: (((C @ D) = zero_z5237406670263579293d_enat) <= (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups7108830773950497114d_enat @ C @ A) = (groups7108830773950497114d_enat @ C @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7600_sum_Omono__neutral__right)). 159.61/70.66 thf(9223,plain,((! [A:set_nat,B:set_nat,C:(nat > extended_enat)]: ((finite_finite_nat @ A) => ((ord_less_eq_set_nat @ B @ A) => ((! [D:nat]: (((C @ D) = zero_z5237406670263579293d_enat) | ~ (member_nat @ D @ (minus_minus_set_nat @ A @ B)))) => ((groups7108830773950497114d_enat @ (C) @ A) = (groups7108830773950497114d_enat @ (C) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 159.61/70.66 thf(5575,axiom,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ A @ (set_ord_lessThan_nat @ (suc @ B))) = (times_times_nat @ (A @ zero_zero_nat) @ (groups708209901874060359at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_lessThan_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8742_prod_OlessThan__Suc__shift)). 159.61/70.66 thf(26681,plain,((! [A:(nat > nat),B:nat]: ((groups708209901874060359at_nat @ (A) @ (set_ord_lessThan_nat @ (suc @ 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)],[5575])). 159.61/70.66 thf(3731,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B)) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2272_add__nonneg__pos)). 159.61/70.66 thf(20255,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B)) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3731])). 159.61/70.66 thf(4125,axiom,((! [A:real,B:(int > real),C:int,D:int]: ((ord_less_eq_real @ A @ (B @ C)) => (((ord_less_real @ A @ (B @ D)) <= (! [E:int,F:int]: ((ord_less_real @ (B @ E) @ (B @ F)) <= (ord_less_int @ E @ F)))) <= (ord_less_int @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3221_order__le__less__subst1)). 159.61/70.66 thf(21481,plain,((! [A:real,B:(int > real),C:int,D:int]: ((ord_less_eq_real @ A @ (B @ C)) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:int,F:int]: ((ord_less_real @ (B @ E) @ (B @ F)) | ~ (ord_less_int @ E @ F))) | ~ (ord_less_int @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4125])). 159.61/70.66 thf(7819,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/sandbox/benchmark/theBenchmark.p',fact_4078_div__div__eq__right)). 159.61/70.66 thf(35240,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)],[7819])). 159.61/70.66 thf(5581,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/sandbox/benchmark/theBenchmark.p',fact_8965_fact__code)). 159.61/70.66 thf(26701,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)],[5581])). 159.61/70.66 thf(4834,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/sandbox/benchmark/theBenchmark.p',fact_153_left__add__twice)). 159.61/70.66 thf(23982,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)],[4834])). 159.61/70.66 thf(7030,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/sandbox/benchmark/theBenchmark.p',fact_4262_zero__le__even__power)). 159.61/70.66 thf(32446,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)],[7030])). 159.61/70.66 thf(2133,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (arctan @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5795_zero__le__arctan__iff)). 159.61/70.66 thf(15139,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)],[2133])). 159.61/70.66 thf(2396,axiom,((! [A:num,B:num,C:(num > int),D:int]: ((((ord_less_int @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_less_int @ (C @ B) @ D)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3226_order__le__less__subst2)). 159.61/70.66 thf(15950,plain,((! [A:num,B:num,C:(num > int),D:int]: ((ord_less_int @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_less_eq_int @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_less_int @ (C @ B) @ D) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2396])). 159.61/70.66 thf(5610,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8310_gbinomial__trinomial__revision)). 159.61/70.66 thf(26813,plain,((! [A:nat,B:nat,C:real]: ((ord_less_eq_nat @ A @ B) => ((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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5610])). 159.61/70.66 thf(987,axiom,((! [A:num,B:num,C:(num > extended_enat),D:extended_enat]: ((((ord_le72135733267957522d_enat @ (C @ A) @ D) <= (! [E:num,F:num]: ((ord_le2932123472753598470d_enat @ (C @ E) @ (C @ F)) <= (ord_less_eq_num @ E @ F)))) <= (ord_le72135733267957522d_enat @ (C @ B) @ D)) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3222_order__le__less__subst2)). 159.61/70.66 thf(11405,plain,((! [A:num,B:num,C:(num > extended_enat),D:extended_enat]: ((ord_le72135733267957522d_enat @ (C @ A) @ D) | ~ (! [E:num,F:num]: ((ord_le2932123472753598470d_enat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_num @ E @ F))) | ~ (ord_le72135733267957522d_enat @ (C @ B) @ D) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[987])). 159.61/70.66 thf(5502,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (suc @ A) @ B) = (times_times_nat @ (suc @ A) @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_Suc__mult__cancel1)). 159.61/70.66 thf(26465,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)],[5502])). 159.61/70.66 thf(409,axiom,((! [A:complex,B:complex]: ((ord_less_eq_real @ (im @ (divide1717551699836669952omplex @ A @ B)) @ zero_zero_real) = (ord_less_eq_real @ (im @ (times_times_complex @ A @ (cnj @ B))) @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9697_Im__complex__div__le__0)). 159.61/70.66 thf(9537,plain,((! [A:complex,B:complex]: ((ord_less_eq_real @ (im @ (divide1717551699836669952omplex @ A @ B)) @ zero_zero_real) = (ord_less_eq_real @ (im @ (times_times_complex @ A @ (cnj @ B))) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[409])). 159.61/70.66 thf(7126,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2018_add__nonpos__eq__0__iff)). 159.61/70.66 thf(32852,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ zero_zero_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)],[7126])). 159.61/70.66 thf(3887,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ B @ A) @ C)) = (dvd_dvd_Code_integer @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3824_dvd__add__times__triv__left__iff)). 159.61/70.66 thf(20768,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ B @ A) @ C)) = (dvd_dvd_Code_integer @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3887])). 159.61/70.66 thf(6392,axiom,((! [A:set_nat,B:(nat > complex)]: ((((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (B @ C) @ (power_power_complex @ zero_zero_complex @ 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))) => ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (B @ C) @ (power_power_complex @ zero_zero_complex @ C))) @ A) = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7364_sum__zero__power)). 159.61/70.66 thf(29808,plain,((! [A:set_nat,B:(nat > complex)]: ((((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (B @ C) @ (power_power_complex @ zero_zero_complex @ 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))) => ((groups2073611262835488442omplex @ (^ [C:nat]: (times_times_complex @ (B @ C) @ (power_power_complex @ zero_zero_complex @ C))) @ A) = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6392])). 159.61/70.66 thf(7438,axiom,((! [A:produc9072475918466114483BT_nat]: (((((! [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:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E)))) <= (! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1944_vebt__member_Ocases)). 159.61/70.66 thf(33943,plain,((! [A:produc9072475918466114483BT_nat]: (((! [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:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ 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)],[7438])). 159.61/70.66 thf(5926,axiom,(((neg_nu7009210354673126013omplex @ one_one_complex) = (numera6690914467698888265omplex @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3783_dbl__simps_I3_J)). 159.61/70.66 thf(28149,plain,(((neg_nu7009210354673126013omplex @ one_one_complex) = (numera6690914467698888265omplex @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5926])). 159.61/70.66 thf(7625,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/sandbox/benchmark/theBenchmark.p',fact_2109_pos__add__strict)). 159.61/70.66 thf(34631,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)],[7625])). 159.61/70.66 thf(1002,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2773_order_Oasym)). 159.61/70.66 thf(11454,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002])). 159.61/70.66 thf(7164,axiom,((! [A:(real > (real > $o)),B:set_nat,C:(nat > real),D:(nat > real)]: ((A @ one_one_real @ one_one_real) => (((finite_finite_nat @ B) => ((! [E:nat]: ((A @ (C @ E) @ (D @ E)) <= (member_nat @ E @ B))) => (A @ (groups129246275422532515t_real @ C @ B) @ (groups129246275422532515t_real @ D @ B)))) <= (! [E:real,F:real,G:real,H:real]: ((A @ (times_times_real @ E @ F) @ (times_times_real @ G @ H)) <= ((A @ F @ H) & (A @ E @ G)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8563_prod_Orelated)). 159.61/70.66 thf(32984,plain,((! [A:(real > (real > $o)),B:set_nat,C:(nat > real),D:(nat > real)]: ((A @ one_one_real @ one_one_real) => (((finite_finite_nat @ B) => ((! [E:nat]: ((A @ (C @ E) @ (D @ E)) | ~ (member_nat @ E @ B))) => (A @ (groups129246275422532515t_real @ (C) @ B) @ (groups129246275422532515t_real @ (D) @ B)))) | ~ (! [E:real,F:real,G:real,H:real]: ((A @ (times_times_real @ E @ F) @ (times_times_real @ G @ H)) | ~ ((A @ F @ H) & (A @ E @ G)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7164])). 159.61/70.66 thf(6035,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:nat,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => (((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ C)) @ A @ D @ F) @ B) = none_nat) <= (ord_less_eq_nat @ (size_s6755466524823107622T_VEBT @ D) @ (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/sandbox/benchmark/theBenchmark.p',fact_735_pred__list__to__short)). 159.61/70.66 thf(28549,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:nat,F:vEBT_VEBT]: (((ord_less_eq_nat @ B @ C) => (((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ C)) @ A @ D @ F) @ B) = none_nat) | ~ (ord_less_eq_nat @ (size_s6755466524823107622T_VEBT @ D) @ (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)],[6035])). 159.61/70.66 thf(5711,axiom,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2185_power__0)). 159.61/70.66 thf(27160,plain,((! [A:int]: ((power_power_int @ A @ zero_zero_nat) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5711])). 159.61/70.66 thf(6806,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_div__le__mono)). 159.61/70.66 thf(31463,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6806])). 159.61/70.66 thf(2467,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/sandbox/benchmark/theBenchmark.p',fact_2260_add__strict__increasing)). 159.61/70.66 thf(16193,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)],[2467])). 159.61/70.66 thf(2373,axiom,((! [A:code_integer,B:code_integer,C:nat]: ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ B @ C)) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4021_dvd__power__same)). 159.61/70.66 thf(15875,plain,((! [A:code_integer,B:code_integer,C:nat]: ((dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ A @ C) @ (power_8256067586552552935nteger @ B @ C)) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2373])). 159.61/70.66 thf(534,axiom,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sinh_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9311_sinh__real__nonneg__iff)). 159.61/70.66 thf(9955,plain,((! [A:real]: ((ord_less_eq_real @ zero_zero_real @ (sinh_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[534])). 159.61/70.66 thf(6222,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/sandbox/benchmark/theBenchmark.p',fact_6788_of__nat__code__if)). 159.61/70.66 thf(29158,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)],[6222])). 159.61/70.66 thf(7609,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/sandbox/benchmark/theBenchmark.p',fact_6679_div__mult2__eq_H)). 159.61/70.66 thf(34583,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)],[7609])). 159.61/70.66 thf(6939,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/sandbox/benchmark/theBenchmark.p',fact_958_max_Omono)). 159.61/70.66 thf(31999,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)],[6939])). 159.61/70.66 thf(4333,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/sandbox/benchmark/theBenchmark.p',fact_3858_concat__bit__negative__iff)). 159.61/70.66 thf(22139,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)],[4333])). 159.61/70.66 thf(1827,axiom,((! [A:complex,B:complex,C:complex]: ((A = (minus_minus_complex @ B @ C)) = ((plus_plus_complex @ A @ C) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1290_eq__diff__eq)). 159.61/70.66 thf(14165,plain,((! [A:complex,B:complex,C:complex]: ((A = (minus_minus_complex @ B @ C)) = ((plus_plus_complex @ A @ C) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1827])). 159.61/70.66 thf(4907,axiom,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ A @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_nat @ (A @ zero_zero_nat) @ (groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8750_sum_OatMost__Suc__shift)). 159.61/70.66 thf(24214,plain,((! [A:(nat > nat),B:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_nat @ (A @ zero_zero_nat) @ (groups3542108847815614940at_nat @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4907])). 159.61/70.66 thf(7560,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/sandbox/benchmark/theBenchmark.p',fact_8366_pochhammer__code)). 159.61/70.66 thf(34372,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)],[7560])). 159.61/70.66 thf(1298,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/sandbox/benchmark/theBenchmark.p',fact_5227_real__0__less__add__iff)). 159.61/70.66 thf(12448,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)],[1298])). 159.61/70.66 thf(176,axiom,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (bit_se1412395901928357646or_nat @ A @ B)) = (bit_se1080825931792720795nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6718_of__nat__or__eq)). 159.61/70.66 thf(8793,plain,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (bit_se1412395901928357646or_nat @ A @ B)) = (bit_se1080825931792720795nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[176])). 159.61/70.66 thf(8035,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_nat @ zero_zero_nat @ B) => ((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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3787_even__succ__mod__exp)). 159.61/70.66 thf(35934,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((ord_less_nat @ zero_zero_nat @ B) => ((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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8035])). 159.61/70.66 thf(3995,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/sandbox/benchmark/theBenchmark.p',fact_114_le__divide__eq__numeral1_I1_J)). 159.61/70.66 thf(21093,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)],[3995])). 159.61/70.66 thf(1220,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/sandbox/benchmark/theBenchmark.p',fact_8624_prod_Onat__diff__reindex)). 159.61/70.66 thf(12194,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)],[1220])). 159.61/70.66 thf(2765,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/sandbox/benchmark/theBenchmark.p',fact_4082_dvd__div__mult2__eq)). 159.61/70.66 thf(17159,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)],[2765])). 159.61/70.66 thf(3430,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real) <= (ord_less_real @ B @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2095_mult__pos__neg)). 159.61/70.66 thf(19278,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real) | ~ (ord_less_real @ B @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3430])). 159.61/70.66 thf(2709,axiom,((! [A:nat]: ((bit_ri631733984087533419it_int @ (suc @ A) @ one_one_int) = one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4562_signed__take__bit__Suc__1)). 159.61/70.66 thf(16993,plain,((! [A:nat]: ((bit_ri631733984087533419it_int @ (suc @ A) @ one_one_int) = one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2709])). 159.61/70.66 thf(6529,axiom,((! [A:num,B:num]: ((bit0 @ A) != (bit1 @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5501_verit__eq__simplify_I14_J)). 159.61/70.66 thf(30354,plain,((! [A:num,B:num]: ~ ((bit0 @ A) = (bit1 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6529])). 159.61/70.66 thf(4509,axiom,((! [A:real,B:nat]: ((times_times_real @ (minus_minus_real @ one_one_real @ A) @ (groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_atMost_nat @ B))) = (minus_minus_real @ one_one_real @ (power_power_real @ A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8872_sum__gp__basic)). 159.61/70.66 thf(22756,plain,((! [A:real,B:nat]: ((times_times_real @ (minus_minus_real @ one_one_real @ A) @ (groups6591440286371151544t_real @ (power_power_real @ A) @ (set_ord_atMost_nat @ B))) = (minus_minus_real @ one_one_real @ (power_power_real @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4509])). 159.61/70.66 thf(7123,axiom,((! [A:product_prod_num_num]: ~ (! [B:num,C:num]: (A != (product_Pair_num_num @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3688_old_Oprod_Oexhaust)). 159.61/70.66 thf(32841,plain,((! [A:product_prod_num_num]: ~ (! [B:num,C:num]: ~ (A = (product_Pair_num_num @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7123])). 159.61/70.66 thf(3799,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (ord_le72135733267957522d_enat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2796_dual__order_Oasym)). 159.61/70.66 thf(20474,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (~ (ord_le72135733267957522d_enat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3799])). 159.61/70.66 thf(5235,axiom,((! [A:real]: ((root @ zero_zero_nat @ A) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9478_root__0)). 159.61/70.66 thf(25390,plain,((! [A:real]: ((root @ zero_zero_nat @ A) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5235])). 159.61/70.66 thf(3461,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (finite_finite_nat @ (vEBT_VEBT_set_vebt @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3599_set__vebt__finite)). 159.61/70.66 thf(19371,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)],[3461])). 159.61/70.66 thf(7401,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_Suc__leI)). 159.61/70.66 thf(33834,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)],[7401])). 159.61/70.66 thf(298,axiom,((! [A:real]: ((real_V1485227260804924795R_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9197_scaleR__minus1__left)). 159.61/70.66 thf(9173,plain,((! [A:real]: ((real_V1485227260804924795R_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 159.61/70.66 thf(1180,axiom,((! [A:real]: ~ (ord_less_real @ (abs_abs_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5517_abs__not__less__zero)). 159.61/70.66 thf(12031,plain,((! [A:real]: ~ (ord_less_real @ (abs_abs_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180])). 159.61/70.66 thf(1796,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2854_order__less__asym_H)). 159.61/70.66 thf(14047,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1796])). 159.61/70.66 thf(416,axiom,((! [A:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ A) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5057_ab__group__add__class_Oab__left__minus)). 159.61/70.66 thf(9559,plain,((! [A:code_integer]: ((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ A) @ A) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])). 159.61/70.66 thf(2287,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => (dvd_dvd_complex @ A @ (times_times_complex @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3945_dvd__mult)). 159.61/70.66 thf(15621,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ B) => (dvd_dvd_complex @ A @ (times_times_complex @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2287])). 159.61/70.66 thf(3808,axiom,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ A) @ (uminus5710092332889474511et_nat @ B)) = (ord_less_eq_set_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4610_Compl__subset__Compl__iff)). 159.61/70.66 thf(20498,plain,((! [A:set_nat,B:set_nat]: ((ord_less_eq_set_nat @ (uminus5710092332889474511et_nat @ A) @ (uminus5710092332889474511et_nat @ B)) = (ord_less_eq_set_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3808])). 159.61/70.66 thf(3930,axiom,((! [A:int,B:num]: (((ring_1_of_int_int @ A) = (numeral_numeral_int @ B)) = (A = (numeral_numeral_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5766_of__int__eq__numeral__iff)). 159.61/70.66 thf(20891,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)],[3930])). 159.61/70.66 thf(7393,axiom,((! [A:set_nat]: ((vimage_nat_nat @ suc @ (insert_nat @ zero_zero_nat @ A)) = (vimage_nat_nat @ suc @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10191_vimage__Suc__insert__0)). 159.61/70.66 thf(33812,plain,((! [A:set_nat]: ((vimage_nat_nat @ (suc) @ (insert_nat @ zero_zero_nat @ A)) = (vimage_nat_nat @ (suc) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7393])). 159.61/70.66 thf(577,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/sandbox/benchmark/theBenchmark.p',fact_8319_gbinomial__factors)). 159.61/70.66 thf(10087,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)],[577])). 159.61/70.66 thf(6677,axiom,((! [A:complex,B:complex,C:complex]: (((A = zero_zero_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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5256_add__divide__eq__if__simps_I6_J)). 159.61/70.66 thf(30877,plain,((! [A:complex,B:complex,C:complex]: (((A = zero_zero_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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6677])). 159.61/70.66 thf(840,axiom,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1544_bits__div__by__0)). 159.61/70.66 thf(10960,plain,((! [A:int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[840])). 159.61/70.66 thf(3373,axiom,((! [A:set_nat,B:(nat > int)]: (((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups705719431365010083at_int @ B @ A)) = (? [C:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (B @ C)) & (member_nat @ C @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8784_even__prod__iff)). 159.61/70.66 thf(19092,plain,((! [A:set_nat,B:(nat > int)]: (((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (groups705719431365010083at_int @ (B) @ A)) = (? [C:nat]: ((dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (B @ C)) & (member_nat @ C @ A)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3373])). 159.61/70.66 thf(8237,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (ord_min_nat @ B @ C)) = (ord_min_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10172_nat__mult__min__right)). 159.61/70.66 thf(36655,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (ord_min_nat @ B @ C)) = (ord_min_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8237])). 159.61/70.66 thf(1292,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/sandbox/benchmark/theBenchmark.p',fact_5589_numeral__Bit1)). 159.61/70.66 thf(12427,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)],[1292])). 159.61/70.66 thf(5185,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/sandbox/benchmark/theBenchmark.p',fact_1106_mult_Oassoc)). 159.61/70.66 thf(25198,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)],[5185])). 159.61/70.66 thf(7087,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/sandbox/benchmark/theBenchmark.p',fact_868_nat__eq__add__iff1)). 159.61/70.66 thf(32694,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)],[7087])). 159.61/70.66 thf(2823,axiom,((! [A:code_integer,B:code_integer]: ((modulo364778990260209775nteger @ A @ (uminus1351360451143612070nteger @ B)) = (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4995_mod__minus__right)). 159.61/70.66 thf(17329,plain,((! [A:code_integer,B:code_integer]: ((modulo364778990260209775nteger @ A @ (uminus1351360451143612070nteger @ B)) = (uminus1351360451143612070nteger @ (modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2823])). 159.61/70.66 thf(1348,axiom,((! [A:complex,B:complex,C:complex,D:complex,E:complex]: ((((plus_plus_complex @ B @ (times_times_complex @ A @ D)) != (plus_plus_complex @ C @ (times_times_complex @ A @ E))) <= ((B = C) & (D != E))) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4557_add__scale__eq__noteq)). 159.61/70.66 thf(12601,plain,((! [A:complex,B:complex,C:complex,D:complex,E:complex]: (~ ((plus_plus_complex @ B @ (times_times_complex @ A @ D)) = (plus_plus_complex @ C @ (times_times_complex @ A @ E))) | ~ ((B = C) & ~ (D = E)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348])). 159.61/70.66 thf(8215,axiom,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ C @ (times_times_nat @ A @ B)) = (divide_divide_nat @ (divide_divide_nat @ C @ A) @ B)) <= (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4081_dvd__div__mult2__eq)). 159.61/70.66 thf(36523,plain,((! [A:nat,B:nat,C:nat]: (((divide_divide_nat @ C @ (times_times_nat @ A @ B)) = (divide_divide_nat @ (divide_divide_nat @ C @ A) @ B)) | ~ (dvd_dvd_nat @ (times_times_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8215])). 159.61/70.66 thf(3196,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/sandbox/benchmark/theBenchmark.p',fact_6071_or__greater__eq)). 159.61/70.66 thf(18532,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)],[3196])). 159.61/70.66 thf(1164,axiom,((! [A:complex]: (((real_V1022390504157884413omplex @ A) = one_one_real) => (~ (! [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) => ((A != (complex2 @ (cos_real @ B) @ (sin_real @ B))) <= (ord_less_real @ B @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7208_complex__unimodular__polar)). 159.61/70.66 thf(11982,plain,((! [A:complex]: (((real_V1022390504157884413omplex @ A) = one_one_real) => (~ (! [B:real]: ((ord_less_eq_real @ zero_zero_real @ B) => (~ (A = (complex2 @ (cos_real @ B) @ (sin_real @ B))) | ~ (ord_less_real @ B @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164])). 159.61/70.66 thf(5432,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/sandbox/benchmark/theBenchmark.p',fact_3542_mod__le__divisor)). 159.61/70.66 thf(26204,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)],[5432])). 159.61/70.66 thf(1500,axiom,((ord_less_int = (^ [A:int,B:int]: ? [C:nat]: (B = (plus_plus_int @ A @ (semiri1314217659103216013at_int @ (suc @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6841_zless__iff__Suc__zadd)). 159.61/70.66 thf(13143,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)],[1500])). 159.61/70.66 thf(486,axiom,((! [A:code_integer]: ((plus_p5714425477246183910nteger @ A @ (uminus1351360451143612070nteger @ A)) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4689_add_Oright__inverse)). 159.61/70.66 thf(9799,plain,((! [A:code_integer]: ((plus_p5714425477246183910nteger @ A @ (uminus1351360451143612070nteger @ A)) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])). 159.61/70.66 thf(3532,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 @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4545_minf_I10_J)). 159.61/70.66 thf(19590,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3532])). 159.61/70.66 thf(449,axiom,((! [A:complex,B:complex]: (((ord_less_real @ zero_zero_real @ (re @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_real @ zero_zero_real @ (re @ (times_times_complex @ A @ (cnj @ B))))) & ((ord_less_real @ zero_zero_real @ (im @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_real @ zero_zero_real @ (im @ (times_times_complex @ A @ (cnj @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9699_complex__div__gt__0)). 159.61/70.66 thf(9660,plain,((! [A:complex,B:complex]: (((ord_less_real @ zero_zero_real @ (re @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_real @ zero_zero_real @ (re @ (times_times_complex @ A @ (cnj @ B))))) & ((ord_less_real @ zero_zero_real @ (im @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_real @ zero_zero_real @ (im @ (times_times_complex @ A @ (cnj @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[449])). 159.61/70.66 thf(3232,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/sandbox/benchmark/theBenchmark.p',fact_4376_bits__1__div__exp)). 159.61/70.66 thf(18647,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)],[3232])). 159.61/70.66 thf(5469,axiom,((! [A:num]: ((numeral_numeral_int @ (bitM @ A)) = (minus_minus_int @ (numeral_numeral_int @ (bit0 @ A)) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5917_numeral__BitM)). 159.61/70.66 thf(26336,plain,((! [A:num]: ((numeral_numeral_int @ (bitM @ A)) = (minus_minus_int @ (numeral_numeral_int @ (bit0 @ A)) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5469])). 159.61/70.66 thf(7855,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/sandbox/benchmark/theBenchmark.p',fact_443_power4__eq__xxxx)). 159.61/70.66 thf(35356,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)],[7855])). 159.61/70.66 thf(6638,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_diff__add__inverse)). 159.61/70.66 thf(30738,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6638])). 159.61/70.66 thf(3515,axiom,((! [A:num]: (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (numera1916890842035813515d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2012_zero__less__numeral)). 159.61/70.66 thf(19537,plain,((! [A:num]: (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (numera1916890842035813515d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3515])). 159.61/70.66 thf(7965,axiom,((! [A:nat]: ((! [B:nat]: ((bit_se1148574629649215175it_nat @ A @ B) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))) => ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6426_bit__iff__idd__imp__stable)). 159.61/70.66 thf(35710,plain,((! [A:nat]: ((! [B:nat]: ((bit_se1148574629649215175it_nat @ A @ B) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))) => ((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7965])). 159.61/70.66 thf(6548,axiom,(((abs_abs_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5397_abs__1)). 159.61/70.66 thf(30426,plain,(((abs_abs_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6548])). 159.61/70.66 thf(3558,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/sandbox/benchmark/theBenchmark.p',fact_2952_Collect__mono__iff)). 159.61/70.66 thf(19669,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)],[3558])). 159.61/70.66 thf(6549,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2378_vebt__delete_Osimps_I5_J)). 159.61/70.66 thf(30428,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6549])). 159.61/70.66 thf(8122,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_not__add__less2)). 159.61/70.66 thf(36218,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8122])). 159.61/70.66 thf(1860,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/sandbox/benchmark/theBenchmark.p',fact_226_power__inject__exp)). 159.61/70.66 thf(14261,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)],[1860])). 159.61/70.66 thf(155,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (ord_max_nat @ A @ B)) = (ord_max_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6709_of__nat__max)). 159.61/70.66 thf(8721,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)],[155])). 159.61/70.66 thf(6102,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/sandbox/benchmark/theBenchmark.p',fact_8043_sin__paired)). 159.61/70.66 thf(28755,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)],[6102])). 159.61/70.66 thf(1915,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ A @ C) <= (ord_less_int @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4456_pinf_I7_J)). 159.61/70.66 thf(14435,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)],[1915])). 159.61/70.66 thf(6926,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/sandbox/benchmark/theBenchmark.p',fact_5658_power__mono__even)). 159.61/70.66 thf(31944,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)],[6926])). 159.61/70.66 thf(3941,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/sandbox/benchmark/theBenchmark.p',fact_3449_mod__mult__cong)). 159.61/70.66 thf(20927,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)],[3941])). 159.61/70.66 thf(2478,axiom,((! [A:code_integer]: ((bit_se1345352211410354436nteger @ zero_zero_nat @ A) = (plus_p5714425477246183910nteger @ (zero_n356916108424825756nteger @ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4306_flip__bit__0)). 159.61/70.66 thf(16225,plain,((! [A:code_integer]: ((bit_se1345352211410354436nteger @ zero_zero_nat @ A) = (plus_p5714425477246183910nteger @ (zero_n356916108424825756nteger @ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2478])). 159.61/70.66 thf(4817,axiom,((! [A:nat,B:set_nat]: ((! [C:nat]: ((ord_less_nat @ A @ C) => (? [D:nat]: ((ord_less_nat @ C @ D) & (member_nat @ D @ B))))) => (~ (finite_finite_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9764_unbounded__k__infinite)). 159.61/70.66 thf(23923,plain,((! [A:nat,B:set_nat]: ((! [C:nat]: ((ord_less_nat @ A @ C) => (? [D:nat]: ((ord_less_nat @ C @ D) & (member_nat @ D @ B))))) => (~ (finite_finite_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4817])). 159.61/70.66 thf(6,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 @ 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)) <= (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7287_tan__monotone_H)). 159.61/70.66 thf(8267,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 @ 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) | ~ (ord_less_real @ A @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 159.61/70.66 thf(3570,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/sandbox/benchmark/theBenchmark.p',fact_7978_one__diff__power__eq)). 159.61/70.66 thf(19721,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)],[3570])). 159.61/70.66 thf(6882,axiom,((! [A:nat,B:(nat > int),C:int,D:int]: (((minus_minus_int @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (B @ E) @ (power_power_int @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (B @ E) @ (power_power_int @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_int @ (minus_minus_int @ C @ D) @ (groups3539618377306564664at_int @ (^ [E:nat]: (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (times_times_int @ (B @ (plus_plus_nat @ (plus_plus_nat @ E @ F) @ one_one_nat)) @ (power_power_int @ D @ F)) @ (power_power_int @ C @ E))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ E)))) @ (set_ord_lessThan_nat @ A)))) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8954_polyfun__diff__alt)). 159.61/70.66 thf(31800,plain,((! [A:nat,B:(nat > int),C:int,D:int]: (((minus_minus_int @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (B @ E) @ (power_power_int @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups3539618377306564664at_int @ (^ [E:nat]: (times_times_int @ (B @ E) @ (power_power_int @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_int @ (minus_minus_int @ C @ D) @ (groups3539618377306564664at_int @ (^ [E:nat]: (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (times_times_int @ (B @ (plus_plus_nat @ (plus_plus_nat @ E @ F) @ one_one_nat)) @ (power_power_int @ D @ F)) @ (power_power_int @ C @ E))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ E)))) @ (set_ord_lessThan_nat @ A)))) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6882])). 159.61/70.66 thf(7685,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (ord_min_nat @ A @ B) @ C) = (ord_min_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10171_nat__mult__min__left)). 159.61/70.66 thf(34811,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (ord_min_nat @ A @ B) @ C) = (ord_min_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7685])). 159.61/70.66 thf(3586,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int)) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2278_add__neg__nonpos)). 159.61/70.66 thf(19766,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int)) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3586])). 159.61/70.66 thf(3538,axiom,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (modulo_modulo_nat @ A @ B)) = (modulo364778990260209775nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6706_of__nat__mod)). 159.61/70.66 thf(19605,plain,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (modulo_modulo_nat @ A @ B)) = (modulo364778990260209775nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3538])). 159.61/70.66 thf(1060,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/sandbox/benchmark/theBenchmark.p',fact_4836_divide__less__eq__numeral1_I2_J)). 159.61/70.66 thf(11653,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)],[1060])). 159.61/70.66 thf(960,axiom,((! [A:code_integer,B:nat,C:nat]: ((modulo364778990260209775nteger @ (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C)) = (divide6298287555418463151nteger @ (modulo364778990260209775nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_plus_nat @ B @ C))) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3561_div__exp__mod__exp__eq)). 159.61/70.66 thf(11322,plain,((! [A:code_integer,B:nat,C:nat]: ((modulo364778990260209775nteger @ (divide6298287555418463151nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ C)) = (divide6298287555418463151nteger @ (modulo364778990260209775nteger @ A @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_plus_nat @ B @ C))) @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[960])). 159.61/70.66 thf(4765,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/sandbox/benchmark/theBenchmark.p',fact_2490_mult__eq__if)). 159.61/70.66 thf(23729,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)],[4765])). 159.61/70.66 thf(2501,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ B @ A) @ C) = (dvd_dvd_Code_integer @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4057_mult__unit__dvd__iff)). 159.61/70.66 thf(16303,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ one_one_Code_integer) => ((dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ B @ A) @ C) = (dvd_dvd_Code_integer @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2501])). 159.61/70.66 thf(6114,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/sandbox/benchmark/theBenchmark.p',fact_1096_mult_Oleft__commute)). 159.61/70.66 thf(28797,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)],[6114])). 159.61/70.66 thf(8074,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/sandbox/benchmark/theBenchmark.p',fact_2516_exp__not__zero__imp__exp__diff__not__zero)). 159.61/70.66 thf(36069,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)],[8074])). 159.61/70.66 thf(5985,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_le__add1)). 159.61/70.66 thf(28393,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5985])). 159.61/70.66 thf(8205,axiom,(((ord_less_nat @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) & (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__C114_C)). 159.61/70.66 thf(36496,plain,(((ord_less_nat @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)) & (ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8205])). 159.61/70.66 thf(3843,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (ord_less_eq_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3382_mult__le__cancel__iff1)). 159.61/70.66 thf(20622,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ B @ A) @ (times_times_int @ C @ A)) = (ord_less_eq_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3843])). 159.61/70.66 thf(4152,axiom,((! [A:complex,B:nat]: ((gbinomial_complex @ A @ (suc @ B)) = (divide1717551699836669952omplex @ (groups6464643781859351333omplex @ (^ [C:nat]: (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (semiri5044797733671781792omplex @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8931_gbinomial__Suc)). 159.61/70.66 thf(21574,plain,((! [A:complex,B:nat]: ((gbinomial_complex @ A @ (suc @ B)) = (divide1717551699836669952omplex @ (groups6464643781859351333omplex @ (^ [C:nat]: (minus_minus_complex @ A @ (semiri8010041392384452111omplex @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (semiri5044797733671781792omplex @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4152])). 159.61/70.66 thf(1028,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/sandbox/benchmark/theBenchmark.p',fact_3928_division__decomp)). 159.61/70.66 thf(11537,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)],[1028])). 159.61/70.66 thf(3998,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 @ (divide_divide_real @ (times_times_real @ C @ (minus_minus_real @ B @ A)) @ D)) @ B)) <= (ord_less_eq_real @ zero_zero_real @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2501_scaling__mono)). 159.61/70.66 thf(21100,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 @ (divide_divide_real @ (times_times_real @ C @ (minus_minus_real @ B @ A)) @ D)) @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3998])). 159.61/70.66 thf(4352,axiom,((! [A:num]: ((ring_1_of_int_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5763_of__int__numeral)). 159.61/70.66 thf(22198,plain,((! [A:num]: ((ring_1_of_int_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4352])). 159.61/70.66 thf(6819,axiom,((! [A:num,B:num]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ B))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4814_mult__neg__numeral__simps_I3_J)). 159.61/70.66 thf(31503,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)],[6819])). 159.61/70.66 thf(8091,axiom,((! [A:set_nat]: ((nat_set_encode @ (vimage_nat_nat @ suc @ A)) = (divide_divide_nat @ (nat_set_encode @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10194_set__encode__vimage__Suc)). 159.61/70.66 thf(36121,plain,((! [A:set_nat]: ((nat_set_encode @ (vimage_nat_nat @ (suc) @ A)) = (divide_divide_nat @ (nat_set_encode @ A) @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8091])). 159.61/70.66 thf(2717,axiom,((! [A:real]: ? [B:int]: (ord_less_real @ A @ (ring_1_of_int_real @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6139_ex__less__of__int)). 159.61/70.66 thf(17015,plain,((! [A:real]: ? [B:int]: (ord_less_real @ A @ (ring_1_of_int_real @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2717])). 159.61/70.66 thf(3066,axiom,((! [A:real,B:int]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ B) <= (ord_less_eq_real @ A @ (ring_1_of_int_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7100_ceiling__le)). 159.61/70.66 thf(18106,plain,((! [A:real,B:int]: ((ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ B) | ~ (ord_less_eq_real @ A @ (ring_1_of_int_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3066])). 159.61/70.66 thf(4494,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3175_linorder__not__less)). 159.61/70.66 thf(22707,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4494])). 159.61/70.66 thf(1583,axiom,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4476_minf_I4_J)). 159.61/70.66 thf(13389,plain,((! [A:int]: ? [B:int]: ! [C:int]: ((ord_less_int @ C @ B) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583])). 159.61/70.66 thf(6904,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ one_one_nat @ (power_power_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2469_one__less__power)). 159.61/70.66 thf(31869,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ one_one_nat @ (power_power_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6904])). 159.61/70.66 thf(5075,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/sandbox/benchmark/theBenchmark.p',fact_5094_square__eq__1__iff)). 159.61/70.66 thf(24836,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)],[5075])). 159.61/70.66 thf(2885,axiom,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => (((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/sandbox/benchmark/theBenchmark.p',fact_2881_ord__less__eq__subst)). 159.61/70.66 thf(17528,plain,((! [A:real,B:real,C:(real > nat),D:nat]: ((ord_less_real @ A @ B) => (((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)],[2885])). 159.61/70.66 thf(1251,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) = ((A = B) | ~ (ord_less_eq_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3033_nless__le)). 159.61/70.66 thf(12298,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)],[1251])). 159.61/70.66 thf(3627,axiom,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ C) => ((divide_divide_int @ (divide_divide_int @ C @ A) @ (divide_divide_int @ B @ A)) = (divide_divide_int @ C @ B))) <= (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4019_div__div__div__same)). 159.61/70.66 thf(19901,plain,((! [A:int,B:int,C:int]: (((dvd_dvd_int @ B @ C) => ((divide_divide_int @ (divide_divide_int @ C @ A) @ (divide_divide_int @ B @ A)) = (divide_divide_int @ C @ B))) | ~ (dvd_dvd_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3627])). 159.61/70.66 thf(2342,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/sandbox/benchmark/theBenchmark.p',fact_8265_pochhammer__rec)). 159.61/70.66 thf(15775,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)],[2342])). 159.61/70.66 thf(5774,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1989_mult__left__mono)). 159.61/70.66 thf(27371,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5774])). 159.61/70.66 thf(3111,axiom,(((neg_nu6511756317524482435omplex @ one_one_complex) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5677_dbl__dec__simps_I3_J)). 159.61/70.66 thf(18263,plain,(((neg_nu6511756317524482435omplex @ one_one_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3111])). 159.61/70.66 thf(4027,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/sandbox/benchmark/theBenchmark.p',fact_1271_diff__diff__eq)). 159.61/70.66 thf(21189,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)],[4027])). 159.61/70.66 thf(6868,axiom,((! [A:num]: ((plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5702_add__neg__numeral__special_I6_J)). 159.61/70.66 thf(31758,plain,((! [A:num]: ((plus_plus_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ (numeral_numeral_int @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6868])). 159.61/70.66 thf(3378,axiom,((set_or1269000886237332187st_nat = (^ [A:nat,B:nat]: (set_nat2 @ (upt @ A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10133_atLeastAtMost__upt)). 159.61/70.66 thf(19109,plain,(((set_or1269000886237332187st_nat) = (^ [A:nat,B:nat]: (set_nat2 @ (upt @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3378])). 159.61/70.66 thf(4436,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/sandbox/benchmark/theBenchmark.p',fact_1652_nonzero__mult__divide__mult__cancel__left)). 159.61/70.66 thf(22462,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)],[4436])). 159.61/70.66 thf(1201,axiom,((! [A:int]: ((dvd_dvd_int @ (divide_divide_int @ one_one_int @ A) @ one_one_int) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3850_unit__div__1__unit)). 159.61/70.66 thf(12125,plain,((! [A:int]: ((dvd_dvd_int @ (divide_divide_int @ one_one_int @ A) @ one_one_int) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201])). 159.61/70.66 thf(1673,axiom,((! [A:num]: ((neg_nu3811975205180677377ec_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bitM @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5808_dbl__dec__simps_I5_J)). 159.61/70.66 thf(13669,plain,((! [A:num]: ((neg_nu3811975205180677377ec_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673])). 159.61/70.66 thf(4568,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/sandbox/benchmark/theBenchmark.p',fact_9489_real__root__le__0__iff)). 159.61/70.66 thf(23020,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)],[4568])). 159.61/70.66 thf(3587,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/sandbox/benchmark/theBenchmark.p',fact_1062_add__le__cancel__right)). 159.61/70.66 thf(19769,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)],[3587])). 159.61/70.66 thf(5044,axiom,((! [A:nat,B:num]: (((suc @ A) = (numeral_numeral_nat @ B)) = (A = (pred_numeral @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5681_Suc__eq__numeral)). 159.61/70.66 thf(24697,plain,((! [A:nat,B:num]: (((suc @ A) = (numeral_numeral_nat @ B)) = (A = (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5044])). 159.61/70.66 thf(499,axiom,((! [A:nat,B:code_integer]: (((bit_se1745604003318907178nteger @ A @ B) = zero_z3403309356797280102nteger) = (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5301_take__bit__eq__0__iff)). 159.61/70.66 thf(9839,plain,((! [A:nat,B:code_integer]: (((bit_se1745604003318907178nteger @ A @ B) = zero_z3403309356797280102nteger) = (dvd_dvd_Code_integer @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])). 159.61/70.66 thf(5570,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/sandbox/benchmark/theBenchmark.p',fact_811_Nat_Oadd__diff__assoc2)). 159.61/70.66 thf(26664,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)],[5570])). 159.61/70.66 thf(2161,axiom,((! [A:real]: ((ord_less_eq_real @ A @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A))) & (ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A)) @ one_one_real) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7136_ceiling__correct)). 159.61/70.66 thf(15218,plain,((! [A:real]: ((ord_less_eq_real @ A @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A))) & (ord_less_real @ (minus_minus_real @ (ring_1_of_int_real @ (archim7802044766580827645g_real @ A)) @ one_one_real) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2161])). 159.61/70.66 thf(5615,axiom,((! [A:complex,B:complex]: ((times_times_complex @ A @ (uminus1482373934393186551omplex @ B)) = (uminus1482373934393186551omplex @ (times_times_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4625_mult__minus__right)). 159.61/70.66 thf(26830,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)],[5615])). 159.61/70.66 thf(5779,axiom,((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4207_odd__one)). 159.61/70.66 thf(27386,plain,((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5779])). 159.61/70.66 thf(6773,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/sandbox/benchmark/theBenchmark.p',fact_1608_diff__ge__0__iff__ge)). 159.61/70.66 thf(31363,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)],[6773])). 159.61/70.66 thf(151,axiom,(((divide6298287555418463151nteger @ one_one_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1783_bits__1__div__2)). 159.61/70.66 thf(8710,plain,(((divide6298287555418463151nteger @ one_one_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one))) = zero_z3403309356797280102nteger)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 159.61/70.66 thf(3317,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/sandbox/benchmark/theBenchmark.p',fact_5248_minus__divide__add__eq__iff)). 159.61/70.66 thf(18922,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)],[3317])). 159.61/70.66 thf(2420,axiom,((! [A:nat,B:nat]: ((ord_less_eq_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6822_zle__int)). 159.61/70.66 thf(16038,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)],[2420])). 159.61/70.66 thf(8064,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/sandbox/benchmark/theBenchmark.p',fact_2198_less__imp__add__positive)). 159.61/70.66 thf(36037,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)],[8064])). 159.61/70.66 thf(3504,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/sandbox/benchmark/theBenchmark.p',fact_6947_norm__diff__triangle__ineq)). 159.61/70.66 thf(19505,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)],[3504])). 159.61/70.66 thf(7793,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/sandbox/benchmark/theBenchmark.p',fact_677_power__odd__eq)). 159.61/70.66 thf(35165,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)],[7793])). 159.61/70.66 thf(1273,axiom,((! [A:int,B:real]: ((ord_less_real @ (ring_1_of_int_real @ A) @ B) => (((archim7802044766580827645g_real @ B) = (plus_plus_int @ A @ one_one_int)) <= (ord_less_eq_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7163_ceiling__eq)). 159.61/70.66 thf(12367,plain,((! [A:int,B:real]: ((ord_less_real @ (ring_1_of_int_real @ A) @ B) => (((archim7802044766580827645g_real @ B) = (plus_plus_int @ A @ one_one_int)) | ~ (ord_less_eq_real @ B @ (plus_plus_real @ (ring_1_of_int_real @ A) @ one_one_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273])). 159.61/70.66 thf(3675,axiom,((! [A:(nat > real),B:set_nat,C:(nat > real),D:nat]: (((groups6591440286371151544t_real @ A @ B) = (groups6591440286371151544t_real @ C @ B)) => ((((finite_finite_nat @ B) => ((A @ D) = (C @ D))) <= (member_nat @ D @ B)) <= (! [E:nat]: ((ord_less_eq_real @ (A @ E) @ (C @ E)) <= (member_nat @ E @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7445_sum__mono__inv)). 159.61/70.66 thf(20054,plain,((! [A:(nat > real),B:set_nat,C:(nat > real),D:nat]: (((groups6591440286371151544t_real @ (A) @ B) = (groups6591440286371151544t_real @ (C) @ B)) => (((finite_finite_nat @ B) => ((A @ D) = (C @ D))) | ~ (member_nat @ D @ B) | ~ (! [E:nat]: ((ord_less_eq_real @ (A @ E) @ (C @ E)) | ~ (member_nat @ E @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3675])). 159.61/70.66 thf(5260,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1076_mult__1)). 159.61/70.66 thf(25472,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5260])). 159.61/70.66 thf(4758,axiom,((! [A:set_nat,B:(nat > real)]: ((! [C:nat]: (((ord_less_eq_real @ zero_zero_real @ (B @ C)) & (ord_less_eq_real @ (B @ C) @ one_one_real)) <= (member_nat @ C @ A))) => (ord_less_eq_real @ (groups129246275422532515t_real @ B @ A) @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8553_prod__le__1)). 159.61/70.66 thf(23697,plain,((! [A:set_nat,B:(nat > real)]: ((! [C:nat]: (((ord_less_eq_real @ zero_zero_real @ (B @ C)) & (ord_less_eq_real @ (B @ C) @ one_one_real)) | ~ (member_nat @ C @ A))) => (ord_less_eq_real @ (groups129246275422532515t_real @ (B) @ A) @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4758])). 159.61/70.66 thf(8235,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((A @ C) <= (! [D:nat]: ((A @ D) <= (ord_less_nat @ D @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_nat__less__induct)). 159.61/70.66 thf(36648,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((A @ C) | ~ (! [D:nat]: ((A @ D) | ~ (ord_less_nat @ D @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8235])). 159.61/70.66 thf(2492,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: (((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ A) @ B) = (modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ C) @ B)) <= ((modulo364778990260209775nteger @ A @ B) = (modulo364778990260209775nteger @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4997_mod__minus__cong)). 159.61/70.66 thf(16271,plain,((! [A:code_integer,B:code_integer,C:code_integer]: (((modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ A) @ B) = (modulo364778990260209775nteger @ (uminus1351360451143612070nteger @ C) @ B)) | ~ ((modulo364778990260209775nteger @ A @ B) = (modulo364778990260209775nteger @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2492])). 159.61/70.66 thf(1089,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/sandbox/benchmark/theBenchmark.p',fact_9736_max__Suc1)). 159.61/70.66 thf(11744,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)],[1089])). 159.61/70.66 thf(5217,axiom,((! [A:set_nat,B:(nat > extended_enat),C:(nat > extended_enat)]: (((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((plus_p3455044024723400733d_enat @ (B @ D) @ (C @ D)) != zero_z5237406670263579293d_enat))))) <= (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((C @ D) != zero_z5237406670263579293d_enat)))))) <= (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ((B @ D) != zero_z5237406670263579293d_enat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3732_sum_Ofinite__Collect__op)). 159.61/70.66 thf(25323,plain,((! [A:set_nat,B:(nat > extended_enat),C:(nat > extended_enat)]: ((finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((plus_p3455044024723400733d_enat @ (B @ D) @ (C @ D)) = zero_z5237406670263579293d_enat))))) | ~ (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((C @ D) = zero_z5237406670263579293d_enat))))) | ~ (finite_finite_nat @ (collect_nat @ (^ [D:nat]: ((member_nat @ D @ A) & ~ ((B @ D) = zero_z5237406670263579293d_enat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5217])). 159.61/70.66 thf(6568,axiom,((finite_finite_nat = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ B) <= (member_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3635_finite__nat__set__iff__bounded__le)). 159.61/70.66 thf(30485,plain,(((finite_finite_nat) = (^ [A:set_nat]: ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ B) | ~ (member_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6568])). 159.61/70.66 thf(7462,axiom,((! [A:$o,B:$o]: ((((vEBT_vebt_succ @ (vEBT_Leaf @ B @ A) @ zero_zero_nat) = none_nat) <= (~ (A))) & ((A) => ((vEBT_vebt_succ @ (vEBT_Leaf @ B @ A) @ zero_zero_nat) = (some_nat @ one_one_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1950_vebt__succ_Osimps_I1_J)). 159.61/70.66 thf(34026,plain,((! [A:$o,B:$o]: ((((vEBT_vebt_succ @ (vEBT_Leaf @ B @ A) @ zero_zero_nat) = none_nat) | (A)) & ((A) => ((vEBT_vebt_succ @ (vEBT_Leaf @ B @ A) @ zero_zero_nat) = (some_nat @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7462])). 159.61/70.66 thf(2222,axiom,((! [A:nat,B:(nat > int),C:int,D:nat]: ((! [E:nat]: ((ord_less_nat @ E @ A) => (ord_less_eq_int @ (B @ E) @ C))) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8006_real__sum__nat__ivl__bounded2)). 159.61/70.66 thf(15425,plain,((! [A:nat,B:(nat > int),C:int,D:nat]: ((! [E:nat]: ((ord_less_nat @ E @ A) => (ord_less_eq_int @ (B @ E) @ C))) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2222])). 159.61/70.66 thf(5512,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => ((? [D:nat]: (A = (plus_plus_nat @ C @ (times_times_nat @ B @ D)))) <= (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3543_nat__mod__eq__lemma)). 159.61/70.66 thf(26494,plain,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) => (? [D:nat]: (A = (plus_plus_nat @ C @ (times_times_nat @ B @ D))) | ~ (ord_less_eq_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5512])). 159.61/70.66 thf(3176,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ (archim7802044766580827645g_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7062_ceiling__mono)). 159.61/70.66 thf(18470,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_int @ (archim7802044766580827645g_real @ A) @ (archim7802044766580827645g_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3176])). 159.61/70.66 thf(1813,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/sandbox/benchmark/theBenchmark.p',fact_9726_drop__bit__negative__int__iff)). 159.61/70.66 thf(14105,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)],[1813])). 159.61/70.66 thf(5192,axiom,((! [A:nat]: ((((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = 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) = (uminus1482373934393186551omplex @ one_one_complex)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5318_minus__one__power__iff)). 159.61/70.66 thf(25222,plain,((! [A:nat]: ((((power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ A) = 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) = (uminus1482373934393186551omplex @ one_one_complex)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5192])). 159.61/70.66 thf(8234,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/sandbox/benchmark/theBenchmark.p',fact_4084_dvd__mult__imp__div)). 159.61/70.66 thf(36646,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)],[8234])). 159.61/70.66 thf(2355,axiom,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1519_add__cancel__left__right)). 159.61/70.66 thf(15813,plain,((! [A:real,B:real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2355])). 159.61/70.66 thf(2976,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/sandbox/benchmark/theBenchmark.p',fact_7195_sin__expansion__lemma)). 159.61/70.66 thf(17829,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)],[2976])). 159.61/70.66 thf(1849,axiom,((! [A:$o]: (ord_less_eq_int @ (zero_n2684676970156552555ol_int @ A) @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4396_of__bool__less__eq__one)). 159.61/70.66 thf(14229,plain,((! [A:$o]: (ord_less_eq_int @ (zero_n2684676970156552555ol_int @ A) @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1849])). 159.61/70.66 thf(6360,axiom,(((^ [A:int]: (A)) = (times_times_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1416_lambda__one)). 159.61/70.66 thf(29674,plain,(((^ [A:int]: (A)) = (times_times_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6360])). 159.61/70.66 thf(6206,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/sandbox/benchmark/theBenchmark.p',fact_8476_mod__prod__eq)). 159.61/70.66 thf(29111,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)],[6206])). 159.61/70.66 thf(3649,axiom,((! [A:nat]: ((semiri4216267220026989637d_enat @ (suc @ A)) = (plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ (semiri4216267220026989637d_enat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6581_of__nat__Suc)). 159.61/70.66 thf(19970,plain,((! [A:nat]: ((semiri4216267220026989637d_enat @ (suc @ A)) = (plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ (semiri4216267220026989637d_enat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3649])). 159.61/70.66 thf(2421,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/sandbox/benchmark/theBenchmark.p',fact_6727_of__nat__diff)). 159.61/70.66 thf(16041,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)],[2421])). 159.61/70.66 thf(1281,axiom,((! [A:nat,B:nat,C:real]: (((ord_less_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) <= (ord_less_real @ one_one_real @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_power__strict__increasing)). 159.61/70.66 thf(12391,plain,((! [A:nat,B:nat,C:real]: ((ord_less_real @ (power_power_real @ C @ A) @ (power_power_real @ C @ B)) | ~ (ord_less_real @ one_one_real @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281])). 159.61/70.66 thf(3948,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((powr_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ (powr_real @ A @ C) @ (powr_real @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7250_powr__divide)). 159.61/70.66 thf(20955,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((powr_real @ (divide_divide_real @ A @ B) @ C) = (divide_divide_real @ (powr_real @ A @ C) @ (powr_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3948])). 159.61/70.66 thf(4090,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/sandbox/benchmark/theBenchmark.p',fact_1583_le__add__same__cancel1)). 159.61/70.66 thf(21378,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)],[4090])). 159.61/70.66 thf(3807,axiom,((! [A:code_integer,B:nat]: ((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ A) @ B) = (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ (minus_8373710615458151222nteger @ A @ (semiri4939895301339042750nteger @ B)) @ one_one_Code_integer) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8347_pochhammer__minus)). 159.61/70.66 thf(20495,plain,((! [A:code_integer,B:nat]: ((comm_s8582702949713902594nteger @ (uminus1351360451143612070nteger @ A) @ B) = (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (comm_s8582702949713902594nteger @ (plus_p5714425477246183910nteger @ (minus_8373710615458151222nteger @ A @ (semiri4939895301339042750nteger @ B)) @ one_one_Code_integer) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3807])). 159.61/70.66 thf(5395,axiom,((! [A:nat,B:nat,C:real]: ((((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (root @ A @ C) @ (root @ B @ C)) <= (ord_less_real @ C @ one_one_real))) <= (ord_less_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9518_real__root__strict__increasing)). 159.61/70.66 thf(26045,plain,((! [A:nat,B:nat,C:real]: (((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (root @ A @ C) @ (root @ B @ C)) | ~ (ord_less_real @ C @ one_one_real))) | ~ (ord_less_nat @ A @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5395])). 159.61/70.66 thf(4553,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat) = ((dvd_dvd_nat @ A @ one_one_nat) & (dvd_dvd_nat @ B @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4052_is__unit__mult__iff)). 159.61/70.66 thf(22978,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat) = ((dvd_dvd_nat @ A @ one_one_nat) & (dvd_dvd_nat @ B @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4553])). 159.61/70.66 thf(1831,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))) <= (ord_less_eq_real @ zero_zero_real @ A))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2221_mult__less__le__imp__less)). 159.61/70.66 thf(14176,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_eq_real @ C @ D) => (((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))) | ~ (ord_less_eq_real @ zero_zero_real @ A))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1831])). 159.61/70.66 thf(3094,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/sandbox/benchmark/theBenchmark.p',fact_1648_nonzero__mult__divide__mult__cancel__right)). 159.61/70.66 thf(18206,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)],[3094])). 159.61/70.66 thf(7698,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/sandbox/benchmark/theBenchmark.p',fact_850_less__diff__conv)). 159.61/70.66 thf(34847,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)],[7698])). 159.61/70.66 thf(8195,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/sandbox/benchmark/theBenchmark.p',fact_6295_and__nat__rec)). 159.61/70.66 thf(36454,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)],[8195])). 159.61/70.66 thf(1208,axiom,((! [A:num,B:num]: (((size_size_num @ A) != (size_size_num @ B)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_size__neq__size__imp__neq)). 159.61/70.66 thf(12153,plain,((! [A:num,B:num]: ((~ ((size_size_num @ A) = (size_size_num @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208])). 159.61/70.66 thf(5273,axiom,((~ (ord_less_eq_int @ one_one_int @ (uminus_uminus_int @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5064_le__minus__one__simps_I4_J)). 159.61/70.66 thf(25513,plain,((~ (ord_less_eq_int @ one_one_int @ (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5273])). 159.61/70.66 thf(354,axiom,((! [A:code_integer]: ((divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1548_bits__div__0)). 159.61/70.66 thf(9346,plain,((! [A:code_integer]: ((divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 159.61/70.66 thf(8090,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/sandbox/benchmark/theBenchmark.p',fact_5452_power2__abs)). 159.61/70.66 thf(36118,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)],[8090])). 159.61/70.66 thf(7832,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/sandbox/benchmark/theBenchmark.p',fact_634_Suc__mult__less__cancel1)). 159.61/70.66 thf(35292,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)],[7832])). 159.61/70.66 thf(4070,axiom,((! [A:num,B:num]: ((ord_le2932123472753598470d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_enat__ord__number_I1_J)). 159.61/70.66 thf(21312,plain,((! [A:num,B:num]: ((ord_le2932123472753598470d_enat @ (numera1916890842035813515d_enat @ A) @ (numera1916890842035813515d_enat @ B)) = (ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4070])). 159.61/70.66 thf(6043,axiom,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & (((minus_minus_nat @ (times_times_nat @ B @ D) @ (times_times_nat @ A @ E)) = C) | ((minus_minus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ B @ E)) = C)) & (dvd_dvd_nat @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4036_bezout1__nat)). 159.61/70.66 thf(28577,plain,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & (((minus_minus_nat @ (times_times_nat @ B @ D) @ (times_times_nat @ A @ E)) = C) | ((minus_minus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ B @ E)) = C)) & (dvd_dvd_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6043])). 159.61/70.66 thf(7546,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/sandbox/benchmark/theBenchmark.p',fact_6458_sqrt__even__pow2)). 159.61/70.66 thf(34325,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)],[7546])). 159.61/70.66 thf(6164,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/sandbox/benchmark/theBenchmark.p',fact_7658_sum_OatLeast0__atMost__Suc)). 159.61/70.66 thf(28970,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)],[6164])). 159.61/70.66 thf(2080,axiom,((! [A:real,B:real,C:real]: (((((B != one_one_real) => ((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))))) <= (ord_less_real @ zero_zero_real @ B)) <= (A != one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6447_log__eq__div__ln__mult__log)). 159.61/70.66 thf(14952,plain,((! [A:real,B:real,C:real]: (((~ (B = one_one_real)) => ((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))))) | ~ (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)],[2080])). 159.61/70.66 thf(4184,axiom,((! [A:int,B:int]: ((archim7802044766580827645g_real @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))) = (uminus_uminus_int @ (divide_divide_int @ (uminus_uminus_int @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7124_ceiling__divide__eq__div)). 159.61/70.66 thf(21670,plain,((! [A:int,B:int]: ((archim7802044766580827645g_real @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))) = (uminus_uminus_int @ (divide_divide_int @ (uminus_uminus_int @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4184])). 159.61/70.66 thf(6553,axiom,((! [A:int]: (((abs_abs_int @ A) = A) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5409_abs__of__nonneg)). 159.61/70.66 thf(30440,plain,((! [A:int]: (((abs_abs_int @ A) = A) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6553])). 159.61/70.66 thf(2530,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((A @ B @ C) => (produc6081775807080527818_nat_o @ A @ (product_Pair_nat_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5358_case__prodI)). 159.61/70.66 thf(16393,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((A @ B @ C) => (produc6081775807080527818_nat_o @ (A) @ (product_Pair_nat_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2530])). 159.61/70.66 thf(23,axiom,((! [A:complex,B:real]: ((re @ (divide1717551699836669952omplex @ A @ (real_V4546457046886955230omplex @ B))) = (divide_divide_real @ (re @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9629_Re__divide__of__real)). 159.61/70.66 thf(8324,plain,((! [A:complex,B:real]: ((re @ (divide1717551699836669952omplex @ A @ (real_V4546457046886955230omplex @ B))) = (divide_divide_real @ (re @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 159.61/70.66 thf(3294,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (exp_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6068_exp__ge__zero)). 159.61/70.66 thf(18855,plain,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (exp_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3294])). 159.61/70.66 thf(4407,axiom,((ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_le__numeral__extra_I4_J)). 159.61/70.66 thf(22369,plain,((ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4407])). 159.61/70.66 thf(3604,axiom,((! [A:real]: ((ord_less_int @ zero_zero_int @ (archim7802044766580827645g_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6978_zero__less__ceiling)). 159.61/70.66 thf(19826,plain,((! [A:real]: ((ord_less_int @ zero_zero_int @ (archim7802044766580827645g_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3604])). 159.61/70.66 thf(7473,axiom,((! [A:real,B:real]: (((A = zero_zero_real) | (B = zero_zero_real)) <= ((times_times_real @ A @ B) = zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1865_divisors__zero)). 159.61/70.66 thf(34073,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)],[7473])). 159.61/70.66 thf(1709,axiom,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (divide_divide_nat @ A @ B)) = (divide6298287555418463151nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6697_unique__euclidean__semiring__with__nat__class_Oof__nat__div)). 159.61/70.66 thf(13775,plain,((! [A:nat,B:nat]: ((semiri4939895301339042750nteger @ (divide_divide_nat @ A @ B)) = (divide6298287555418463151nteger @ (semiri4939895301339042750nteger @ A) @ (semiri4939895301339042750nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709])). 159.61/70.66 thf(7896,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/sandbox/benchmark/theBenchmark.p',fact_3582_div__mod__decomp)). 159.61/70.66 thf(35494,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)],[7896])). 159.61/70.66 thf(7578,axiom,((! [A:num]: ((ord_max_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_max__0__1_I5_J)). 159.61/70.66 thf(34487,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)],[7578])). 159.61/70.66 thf(3356,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2912_order__less__not__sym)). 159.61/70.66 thf(19040,plain,((! [A:int,B:int]: ((ord_less_int @ A @ B) => (~ (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3356])). 159.61/70.66 thf(7245,axiom,((! [A:nat,B:nat]: ((((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))) <= (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9600_atLeastLessThanSuc)). 159.61/70.66 thf(33303,plain,((! [A:nat,B:nat]: ((((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))) | ~ (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7245])). 159.61/70.66 thf(2801,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/sandbox/benchmark/theBenchmark.p',fact_5892_real__of__int__div4)). 159.61/70.66 thf(17265,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)],[2801])). 159.61/70.66 thf(2115,axiom,((! [A:num,B:num,C:num,D:complex]: ((real_V2046097035970521341omplex @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) @ (times_times_complex @ (numera6690914467698888265omplex @ C) @ D)) = (real_V2046097035970521341omplex @ (divide_divide_real @ (times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ C)) @ (numeral_numeral_real @ B)) @ D)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9208_fraction__scaleR__times)). 159.61/70.66 thf(15064,plain,((! [A:num,B:num,C:num,D:complex]: ((real_V2046097035970521341omplex @ (divide_divide_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) @ (times_times_complex @ (numera6690914467698888265omplex @ C) @ D)) = (real_V2046097035970521341omplex @ (divide_divide_real @ (times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ C)) @ (numeral_numeral_real @ B)) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2115])). 159.61/70.66 thf(4863,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/sandbox/benchmark/theBenchmark.p',fact_7416_mod__sum__eq)). 159.61/70.66 thf(24070,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)],[4863])). 159.61/70.66 thf(257,axiom,((! [A:real]: ((tan_real @ (plus_plus_real @ A @ pi)) = (tan_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7215_tan__periodic__pi)). 159.61/70.66 thf(9034,plain,((! [A:real]: ((tan_real @ (plus_plus_real @ A @ pi)) = (tan_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[257])). 159.61/70.66 thf(2268,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (divide_divide_nat @ A @ B)) = (divide_divide_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6695_unique__euclidean__semiring__with__nat__class_Oof__nat__div)). 159.61/70.66 thf(15565,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)],[2268])). 159.61/70.66 thf(1790,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/sandbox/benchmark/theBenchmark.p',fact_6089_and__less__eq)). 159.61/70.66 thf(14030,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)],[1790])). 159.61/70.66 thf(1601,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/sandbox/benchmark/theBenchmark.p',fact_5100_group__cancel_Osub2)). 159.61/70.66 thf(13453,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)],[1601])). 159.61/70.66 thf(7688,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2851_linorder__neq__iff)). 159.61/70.66 thf(34820,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)],[7688])). 159.61/70.66 thf(7140,axiom,((! [A:num]: ((unique5055182867167087721od_nat @ A @ one) = (product_Pair_nat_nat @ (numeral_numeral_nat @ A) @ zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5457_divmod__algorithm__code_I2_J)). 159.61/70.66 thf(32909,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)],[7140])). 159.61/70.66 thf(3859,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) | (A = B) | (ord_le72135733267957522d_enat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2918_linorder__less__linear)). 159.61/70.66 thf(20676,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) | (A = B) | (ord_le72135733267957522d_enat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3859])). 159.61/70.66 thf(5002,axiom,((! [A:nat,B:nat]: (((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))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8896_fact__div__fact)). 159.61/70.66 thf(24564,plain,((! [A:nat,B:nat]: (((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))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5002])). 159.61/70.66 thf(6794,axiom,((! [A:num,B:num]: ((times_times_num @ A @ (inc @ B)) = (plus_plus_num @ (times_times_num @ A @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5723_mult__inc)). 159.61/70.66 thf(31427,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)],[6794])). 159.61/70.66 thf(2608,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) => ((A != B) => (ord_le72135733267957522d_enat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2791_linorder__cases)). 159.61/70.66 thf(16639,plain,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ A @ B)) => ((~ (A = B)) => (ord_le72135733267957522d_enat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2608])). 159.61/70.66 thf(4304,axiom,((! [A:nat]: (ord_less_real @ zero_zero_real @ (semiri2265585572941072030t_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8077_fact__gt__zero)). 159.61/70.66 thf(22057,plain,((! [A:nat]: (ord_less_real @ zero_zero_real @ (semiri2265585572941072030t_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4304])). 159.61/70.66 thf(3701,axiom,((! [A:int,B:complex]: ((times_times_complex @ (ring_17405671764205052669omplex @ A) @ B) = (times_times_complex @ B @ (ring_17405671764205052669omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5876_mult__of__int__commute)). 159.61/70.66 thf(20138,plain,((! [A:int,B:complex]: ((times_times_complex @ (ring_17405671764205052669omplex @ A) @ B) = (times_times_complex @ B @ (ring_17405671764205052669omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3701])). 159.61/70.66 thf(3102,axiom,((ln_ln_real = (log @ (exp_real @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6404_log__ln)). 159.61/70.66 thf(18231,plain,(((ln_ln_real) = (log @ (exp_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3102])). 159.61/70.66 thf(2496,axiom,((! [A:vEBT_VEBT,B:nat]: (((vEBT_set_vebt @ A) = (vEBT_VEBT_set_vebt @ A)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_set__vebt__set__vebt_H__valid)). 159.61/70.66 thf(16289,plain,((! [A:vEBT_VEBT,B:nat]: (((vEBT_set_vebt @ A) = (vEBT_VEBT_set_vebt @ A)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2496])). 159.61/70.66 thf(6547,axiom,((! [A:int,B:int,C:(int > nat),D:nat]: ((((C @ B) = D) => ((ord_less_eq_nat @ (C @ A) @ D) <= (! [E:int,F:int]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_int @ E @ F))))) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2653_ord__le__eq__subst)). 159.61/70.66 thf(30418,plain,((! [A:int,B:int,C:(int > nat),D:nat]: ((((C @ B) = D) => ((ord_less_eq_nat @ (C @ A) @ D) | ~ (! [E:int,F:int]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_int @ E @ F))))) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6547])). 159.61/70.66 thf(1369,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/sandbox/benchmark/theBenchmark.p',fact_1242_ring__class_Oring__distribs_I1_J)). 159.61/70.66 thf(12702,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)],[1369])). 159.61/70.66 thf(6941,axiom,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option_nat > $o)),C:option_nat]: ((((B @ A @ C) <= (! [D:product_prod_nat_nat,E:nat]: (((C = (some_nat @ E)) => (B @ A @ C)) <= (A = (some_P7363390416028606310at_nat @ D))))) <= ((B @ A @ C) <= (C = none_nat))) <= ((B @ A @ C) <= (A = none_P5556105721700978146at_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_combine__options__cases)). 159.61/70.66 thf(32004,plain,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option_nat > $o)),C:option_nat]: ((B @ A @ C) | ~ (! [D:product_prod_nat_nat,E:nat]: (((C = (some_nat @ E)) => (B @ A @ C)) | ~ (A = (some_P7363390416028606310at_nat @ D)))) | ~ ((B @ A @ C) | ~ (C = none_nat)) | ~ ((B @ A @ C) | ~ (A = none_P5556105721700978146at_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6941])). 159.61/70.66 thf(6990,axiom,((! [A:(nat > int),B:nat,C:nat]: ((groups705719431365010083at_int @ A @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups705719431365010083at_int @ (^ [D:nat]: (times_times_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/sandbox/benchmark/theBenchmark.p',fact_8906_prod_Oin__pairs)). 159.61/70.66 thf(32316,plain,((! [A:(nat > int),B:nat,C:nat]: ((groups705719431365010083at_int @ (A) @ (set_or1269000886237332187st_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))) = (groups705719431365010083at_int @ (^ [D:nat]: (times_times_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)],[6990])). 159.61/70.66 thf(1352,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_eq_real @ C @ (times_times_real @ B @ A))) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2432_neg__le__divide__eq)). 159.61/70.66 thf(12615,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ (divide_divide_real @ C @ A)) = (ord_less_eq_real @ C @ (times_times_real @ B @ A))) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352])). 159.61/70.66 thf(4761,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C))) <= (! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_lift__Suc__mono__le)). 159.61/70.66 thf(23710,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C))) | ~ (! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4761])). 159.61/70.66 thf(4711,axiom,((! [A:num,B:nat]: ((minus_minus_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (minus_minus_nat @ (pred_numeral @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5690_diff__numeral__Suc)). 159.61/70.66 thf(23535,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)],[4711])). 159.61/70.66 thf(7450,axiom,((ord_less_eq_real @ zero_zero_real @ one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2053_linordered__nonzero__semiring__class_Ozero__le__one)). 159.61/70.66 thf(33992,plain,((ord_less_eq_real @ zero_zero_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7450])). 159.61/70.66 thf(4694,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1906_Suc__neq__Zero)). 159.61/70.66 thf(23481,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4694])). 159.61/70.66 thf(7218,axiom,((! [A:real,B:num]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ zero_zero_real) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_real @ A @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3890_power__less__zero__eq__numeral)). 159.61/70.66 thf(33216,plain,((! [A:real,B:num]: ((ord_less_real @ (power_power_real @ A @ (numeral_numeral_nat @ B)) @ zero_zero_real) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_real @ A @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7218])). 159.61/70.66 thf(6509,axiom,((! [A:complex,B:complex,C:nat]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ one_one_real) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ 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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6954_norm__power__diff)). 159.61/70.66 thf(30272,plain,((! [A:complex,B:complex,C:nat]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ A) @ one_one_real) => ((ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ 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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6509])). 159.61/70.66 thf(4433,axiom,((! [A:nat,B:nat]: ((dvd_dvd_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)) = (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6698_of__nat__dvd__iff)). 159.61/70.66 thf(22455,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)],[4433])). 159.61/70.66 thf(5286,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_add__Suc__shift)). 159.61/70.66 thf(25571,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)],[5286])). 159.61/70.66 thf(1900,axiom,((cosh_real = (^ [A:real]: (divide_divide_real @ (plus_plus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))) @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9358_cosh__field__def)). 159.61/70.66 thf(14386,plain,(((cosh_real) = (^ [A:real]: (divide_divide_real @ (plus_plus_real @ (exp_real @ A) @ (exp_real @ (uminus_uminus_real @ A))) @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1900])). 159.61/70.66 thf(7295,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/sandbox/benchmark/theBenchmark.p',fact_7203_ceiling__log2__div2)). 159.61/70.66 thf(33465,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)],[7295])). 159.61/70.66 thf(317,axiom,((! [A:num,B:num,C:real]: ((real_V1485227260804924795R_real @ (numeral_numeral_real @ A) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (real_V1485227260804924795R_real @ (times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9203_scaleR__times)). 159.61/70.66 thf(9229,plain,((! [A:num,B:num,C:real]: ((real_V1485227260804924795R_real @ (numeral_numeral_real @ A) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (real_V1485227260804924795R_real @ (times_times_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 159.61/70.66 thf(4074,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_complex @ (groups2073611262835488442omplex @ A @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7656_sum_OatLeast0__atMost__Suc)). 159.61/70.66 thf(21323,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ (suc @ B))) = (plus_plus_complex @ (groups2073611262835488442omplex @ (A) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4074])). 159.61/70.66 thf(3512,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/sandbox/benchmark/theBenchmark.p',fact_2170_eq__divide__imp)). 159.61/70.66 thf(19526,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)],[3512])). 159.61/70.66 thf(942,axiom,((! [A:complex,B:complex,C:complex,D:complex,E:complex]: (((plus_plus_complex @ (times_times_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ D @ B) @ E)) = ((plus_plus_complex @ (times_times_complex @ (minus_minus_complex @ A @ D) @ B) @ C) = E)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1365_eq__add__iff1)). 159.61/70.66 thf(11271,plain,((! [A:complex,B:complex,C:complex,D:complex,E:complex]: (((plus_plus_complex @ (times_times_complex @ A @ B) @ C) = (plus_plus_complex @ (times_times_complex @ D @ B) @ E)) = ((plus_plus_complex @ (times_times_complex @ (minus_minus_complex @ A @ D) @ B) @ C) = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[942])). 159.61/70.66 thf(5091,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ bot_bot_nat) = (A = bot_bot_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3273_bot_Oextremum__unique)). 159.61/70.66 thf(24884,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ bot_bot_nat) = (A = bot_bot_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5091])). 159.61/70.66 thf(7850,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 @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4072_dvd__div__mult)). 159.61/70.66 thf(35341,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 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7850])). 159.61/70.66 thf(8188,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:nat,J:vEBT_VEBT,K:list_VEBT_VEBT,L:vEBT_VEBT]: (((B != C) => ((((E = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ G)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ H @ (the_nat @ (vEBT_vebt_mint @ G))))))) => (((vEBT_VEBT_low @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = I) => ((ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)) => ((J = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) => (((vEBT_VEBT_minNull @ J) => ((L = (vEBT_vebt_delete @ G @ F)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (if_nat @ ((vEBT_vebt_maxt @ L) = none_nat) @ E @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ L))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ (the_nat @ (vEBT_vebt_maxt @ L))))))) @ C))) @ D @ K @ L)))) <= (K = (list_u1324408373059187874T_VEBT @ H @ F @ J))))))) <= ((vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) <= ((A = B) & (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1403_del__x__mi__lets__in__minNull)). 159.61/70.66 thf(36432,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:nat,J:vEBT_VEBT,K:list_VEBT_VEBT,L:vEBT_VEBT]: (((~ (B = C)) => (((E = (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ G)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ H @ (the_nat @ (vEBT_vebt_mint @ G))))))) => (((vEBT_VEBT_low @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = I) => ((ord_less_nat @ (vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)) => ((J = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ F) @ I)) => (((vEBT_VEBT_minNull @ J) => ((L = (vEBT_vebt_delete @ G @ F)) => ((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ H @ G) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ E @ (if_nat @ (E = C) @ (if_nat @ ((vEBT_vebt_maxt @ L) = none_nat) @ E @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ L))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ (the_nat @ (vEBT_vebt_maxt @ L))))))) @ C))) @ D @ K @ L)))) | ~ (K = (list_u1324408373059187874T_VEBT @ H @ F @ J))))))) | ~ ((vEBT_VEBT_high @ E @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))) | ~ ((A = B) & (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8188])). 159.61/70.66 thf(4853,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/sandbox/benchmark/theBenchmark.p',fact_8351_gbinomial__absorption_H)). 159.61/70.66 thf(24039,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)],[4853])). 159.61/70.66 thf(3567,axiom,((divide_divide_real = (^ [A:real,B:real]: (times_times_real @ A @ (inverse_inverse_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9041_divide__inverse)). 159.61/70.66 thf(19709,plain,(((divide_divide_real) = (^ [A:real,B:real]: (times_times_real @ A @ (inverse_inverse_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3567])). 159.61/70.66 thf(1829,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/sandbox/benchmark/theBenchmark.p',fact_8523_prod_OatMost__shift)). 159.61/70.66 thf(14170,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)],[1829])). 159.61/70.66 thf(1148,axiom,((! [A:nat,B:nat,C:(nat > complex),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_complex @ (groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups2073611262835488442omplex @ C @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7716_sum_Oub__add__nat)). 159.61/70.66 thf(11928,plain,((! [A:nat,B:nat,C:(nat > complex),D:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ one_one_nat)) => ((groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ (plus_plus_nat @ B @ D))) = (plus_plus_complex @ (groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (groups2073611262835488442omplex @ (C) @ (set_or1269000886237332187st_nat @ (plus_plus_nat @ B @ one_one_nat) @ (plus_plus_nat @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148])). 159.61/70.66 thf(2720,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ one_on7984719198319812577d_enat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1251_comm__monoid__mult__class_Omult__1)). 159.61/70.66 thf(17024,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ one_on7984719198319812577d_enat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2720])). 159.61/70.66 thf(7598,axiom,((! [A:num]: ((times_times_num @ (bit0 @ one) @ A) = (bit0 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_num__double)). 159.61/70.66 thf(34554,plain,((! [A:num]: ((times_times_num @ (bit0 @ one) @ A) = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7598])). 159.61/70.66 thf(7479,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/sandbox/benchmark/theBenchmark.p',fact_9724_drop__bit__numeral__minus__bit1)). 159.61/70.66 thf(34124,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)],[7479])). 159.61/70.66 thf(4262,axiom,((! [A:list_nat,B:(nat > $o),C:nat]: (((ord_less_nat @ C @ (size_size_list_nat @ A)) => (B @ (nth_nat @ A @ C))) <= (! [D:nat]: ((member_nat @ D @ (set_nat2 @ A)) => (B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_inthall)). 159.61/70.66 thf(21932,plain,((! [A:list_nat,B:(nat > $o),C:nat]: (((ord_less_nat @ C @ (size_size_list_nat @ A)) => (B @ (nth_nat @ A @ C))) | ~ (! [D:nat]: ((member_nat @ D @ (set_nat2 @ A)) => (B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4262])). 159.61/70.66 thf(2075,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/sandbox/benchmark/theBenchmark.p',fact_7943_powser__sums__if)). 159.61/70.66 thf(14939,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)],[2075])). 159.61/70.66 thf(1746,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ A) <= (ord_less_real @ B @ zero_zero_real)) <= (ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9064_inverse__le__imp__le__neg)). 159.61/70.66 thf(13890,plain,((! [A:real,B:real]: ((ord_less_eq_real @ B @ A) | ~ (ord_less_real @ B @ zero_zero_real) | ~ (ord_less_eq_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746])). 159.61/70.66 thf(6030,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) = (dvd_dvd_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3992_dvd__add__right__iff)). 159.61/70.66 thf(28534,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) = (dvd_dvd_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6030])). 159.61/70.66 thf(4511,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/sandbox/benchmark/theBenchmark.p',fact_1268_left__diff__distrib)). 159.61/70.66 thf(22761,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)],[4511])). 159.61/70.66 thf(7200,axiom,((! [A:nat,B:(nat > (int > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:int]: (B @ C @ D)))) = (? [C:list_int]: (! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_int @ C @ D))) & ((size_size_list_int @ C) = A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_Skolem__list__nth)). 159.61/70.66 thf(33143,plain,((! [A:nat,B:(nat > (int > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:int]: (B @ C @ D)))) = (? [C:list_int]: (! [D:nat]: ((ord_less_nat @ D @ A) => (B @ D @ (nth_int @ C @ D))) & ((size_size_list_int @ C) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7200])). 159.61/70.66 thf(8139,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_less__iff__Suc__add)). 159.61/70.66 thf(36282,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)],[8139])). 159.61/70.66 thf(2758,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((A != zero_zero_complex) => ((B != zero_zero_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))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2352_add__frac__eq)). 159.61/70.66 thf(17140,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((~ (A = zero_zero_complex)) => ((~ (B = zero_zero_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))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2758])). 159.61/70.66 thf(1521,axiom,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_not__numeral__less__one)). 159.61/70.66 thf(13207,plain,((! [A:num]: ~ (ord_less_real @ (numeral_numeral_real @ A) @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521])). 159.61/70.66 thf(4546,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1827_zero__le)). 159.61/70.66 thf(22958,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4546])). 159.61/70.66 thf(5754,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/sandbox/benchmark/theBenchmark.p',fact_9477_real__root__eq__iff)). 159.61/70.66 thf(27307,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)],[5754])). 159.61/70.66 thf(423,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/sandbox/benchmark/theBenchmark.p',fact_7224_tan__periodic__n)). 159.61/70.66 thf(9579,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)],[423])). 159.61/70.66 thf(3093,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/sandbox/benchmark/theBenchmark.p',fact_6134_mask__half__int)). 159.61/70.66 thf(18203,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)],[3093])). 159.61/70.66 thf(2471,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/sandbox/benchmark/theBenchmark.p',fact_2264_add__pos__nonneg)). 159.61/70.66 thf(16207,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)],[2471])). 159.61/70.66 thf(1275,axiom,(((neg_nu5851722552734809277nc_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5800_dbl__inc__simps_I4_J)). 159.61/70.66 thf(12374,plain,(((neg_nu5851722552734809277nc_int @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275])). 159.61/70.66 thf(4873,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/sandbox/benchmark/theBenchmark.p',fact_383_power__add)). 159.61/70.66 thf(24099,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)],[4873])). 159.61/70.66 thf(5401,axiom,((! [A:int,B:int]: (((abs_abs_int @ A) = B) = ((ord_less_eq_int @ zero_zero_int @ B) & ((A = B) | (A = (uminus_uminus_int @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5560_abs__eq__iff_H)). 159.61/70.66 thf(26067,plain,((! [A:int,B:int]: (((abs_abs_int @ A) = B) = ((ord_less_eq_int @ zero_zero_int @ B) & ((A = B) | (A = (uminus_uminus_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5401])). 159.61/70.66 thf(1419,axiom,((! [A:nat,B:nat]: ((semiri1314217659103216013at_int @ (plus_plus_nat @ A @ B)) = (plus_plus_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6826_int__plus)). 159.61/70.66 thf(12876,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)],[1419])). 159.61/70.66 thf(8085,axiom,((! [A:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (suc @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_add__2__eq__Suc)). 159.61/70.66 thf(36103,plain,((! [A:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (suc @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8085])). 159.61/70.66 thf(2119,axiom,((! [A:real,B:num]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8203_floor__less__neg__numeral)). 159.61/70.66 thf(15076,plain,((! [A:real,B:num]: ((ord_less_int @ (archim6058952711729229775r_real @ A) @ (uminus_uminus_int @ (numeral_numeral_int @ B))) = (ord_less_real @ A @ (uminus_uminus_real @ (numeral_numeral_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2119])). 159.61/70.66 thf(8028,axiom,(((! [A:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => (! [B:nat]: (((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ B) & (ord_less_eq_nat @ B @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma))) <= ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ A) @ (vEBT_VEBT_low @ B @ na)) & ((vEBT_VEBT_high @ B @ na) = A))) & (((vEBT_VEBT_high @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma) @ na) = A) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ A) @ (vEBT_VEBT_low @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma) @ na)))))) <= (~ ((((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))))) & (((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) != ma) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__C115_C)). 159.61/70.66 thf(35901,plain,((! [A:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => (! [B:nat]: (((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ B) & (ord_less_eq_nat @ B @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma))) | ~ ((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ A) @ (vEBT_VEBT_low @ B @ na)) & ((vEBT_VEBT_high @ B @ na) = A))) & (((vEBT_VEBT_high @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma) @ na) = A) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ A) @ (vEBT_VEBT_low @ (if_nat @ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))) @ ma) @ na))))) | ((((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ deg @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ treeList @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na)) @ (vEBT_VEBT_low @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))) @ (vEBT_VEBT_high @ (plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) @ na))))))) & ((~ ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma)) => ((plus_plus_nat @ (times_times_nat @ summin @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ na)) @ lx) = ma))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8028])). 159.61/70.66 thf(2569,axiom,((! [A:real]: ((divide_divide_real @ A @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4716_divide__minus1)). 159.61/70.66 thf(16507,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)],[2569])). 159.61/70.66 thf(168,axiom,((bit_se2159334234014336723it_int = (^ [A:nat,B:int]: (bit_se6526347334894502574or_int @ B @ (bit_se545348938243370406it_int @ A @ one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9553_flip__bit__int__def)). 159.61/70.66 thf(8769,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)],[168])). 159.61/70.66 thf(4867,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_less__eq__Suc__le)). 159.61/70.66 thf(24082,plain,(((ord_less_nat) = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4867])). 159.61/70.66 thf(3117,axiom,((! [A:$o]: (ord_le3102999989581377725nteger @ (zero_n356916108424825756nteger @ A) @ one_one_Code_integer))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4397_of__bool__less__eq__one)). 159.61/70.66 thf(18278,plain,((! [A:$o]: (ord_le3102999989581377725nteger @ (zero_n356916108424825756nteger @ A) @ one_one_Code_integer))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3117])). 159.61/70.66 thf(6324,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (A = B)) <= (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_less__SucE)). 159.61/70.66 thf(29565,plain,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (A = B)) | ~ (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6324])). 159.61/70.66 thf(5929,axiom,((! [A:num]: ((pred_numeral @ (bit1 @ A)) = (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5686_pred__numeral__simps_I3_J)). 159.61/70.66 thf(28157,plain,((! [A:num]: ((pred_numeral @ (bit1 @ A)) = (numeral_numeral_nat @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5929])). 159.61/70.66 thf(6125,axiom,((! [A:(list_nat > $o),B:list_nat]: ((! [C:list_nat]: ((! [D:list_nat]: ((A @ D) <= (ord_less_nat @ (size_size_list_nat @ D) @ (size_size_list_nat @ C)))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_length__induct)). 159.61/70.66 thf(28833,plain,((! [A:(list_nat > $o),B:list_nat]: ((! [C:list_nat]: ((! [D:list_nat]: ((A @ D) | ~ (ord_less_nat @ (size_size_list_nat @ D) @ (size_size_list_nat @ C)))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6125])). 159.61/70.66 thf(8223,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/sandbox/benchmark/theBenchmark.p',fact_9826_nat__of__char__less__256)). 159.61/70.66 thf(36546,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)],[8223])). 159.61/70.66 thf(5660,axiom,((! [A:num]: (zero_zero_real != (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1847_zero__neq__numeral)). 159.61/70.66 thf(26982,plain,((! [A:num]: ~ (zero_zero_real = (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5660])). 159.61/70.66 thf(2457,axiom,((! [A:real]: ~ (ord_less_eq_real @ (exp_real @ A) @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6069_not__exp__le__zero)). 159.61/70.66 thf(16160,plain,((! [A:real]: ~ (ord_less_eq_real @ (exp_real @ A) @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2457])). 159.61/70.66 thf(1751,axiom,((! [A:code_integer,B:code_integer]: ((divide6298287555418463151nteger @ A @ (uminus1351360451143612070nteger @ B)) = (divide6298287555418463151nteger @ (uminus1351360451143612070nteger @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4982_div__minus__right)). 159.61/70.66 thf(13905,plain,((! [A:code_integer,B:code_integer]: ((divide6298287555418463151nteger @ A @ (uminus1351360451143612070nteger @ B)) = (divide6298287555418463151nteger @ (uminus1351360451143612070nteger @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751])). 159.61/70.66 thf(644,axiom,((dvd_dvd_Code_integer = (^ [A:code_integer,B:code_integer]: ? [C:code_integer]: (B = (times_3573771949741848930nteger @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3939_dvd__def)). 159.61/70.66 thf(10312,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)],[644])). 159.61/70.66 thf(3425,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) => ((ord_le2932123472753598470d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ zero_z5237406670263579293d_enat) <= (ord_le2932123472753598470d_enat @ B @ zero_z5237406670263579293d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2024_add__nonpos__nonpos)). 159.61/70.66 thf(19266,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) => ((ord_le2932123472753598470d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ zero_z5237406670263579293d_enat) | ~ (ord_le2932123472753598470d_enat @ B @ zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3425])). 159.61/70.66 thf(3806,axiom,((! [A:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8991_inverse__negative__iff__negative)). 159.61/70.66 thf(20492,plain,((! [A:real]: ((ord_less_real @ (inverse_inverse_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3806])). 159.61/70.66 thf(7932,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/sandbox/benchmark/theBenchmark.p',fact_1135_add_Oassoc)). 159.61/70.66 thf(35605,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)],[7932])). 159.61/70.66 thf(2931,axiom,((! [A:nat]: ((semiri8010041392384452111omplex @ (suc @ A)) != zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6676_of__nat__neq__0)). 159.61/70.66 thf(17693,plain,((! [A:nat]: ~ ((semiri8010041392384452111omplex @ (suc @ A)) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2931])). 159.61/70.66 thf(5023,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/sandbox/benchmark/theBenchmark.p',fact_1609_diff__ge__0__iff__ge)). 159.61/70.66 thf(24636,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)],[5023])). 159.61/70.66 thf(6449,axiom,((! [A:num]: ((real_V4546457046886955230omplex @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7354_of__real__neg__numeral)). 159.61/70.66 thf(30052,plain,((! [A:num]: ((real_V4546457046886955230omplex @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6449])). 159.61/70.66 thf(1558,axiom,((! [A:num]: ((numera6690914467698888265omplex @ (bit0 @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_numeral__Bit0)). 159.61/70.66 thf(13314,plain,((! [A:num]: ((numera6690914467698888265omplex @ (bit0 @ A)) = (plus_plus_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558])). 159.61/70.66 thf(3481,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1736_less__divide__eq__1__neg)). 159.61/70.66 thf(19432,plain,((! [A:real,B:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3481])). 159.61/70.66 thf(4654,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/sandbox/benchmark/theBenchmark.p',fact_5866_of__int__le__neg__numeral__power__cancel__iff)). 159.61/70.66 thf(23339,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)],[4654])). 159.61/70.66 thf(5703,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/sandbox/benchmark/theBenchmark.p',fact_373_power__mult)). 159.61/70.66 thf(27135,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)],[5703])). 159.61/70.66 thf(686,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/sandbox/benchmark/theBenchmark.p',fact_2325_divide__strict__left__mono)). 159.61/70.66 thf(10443,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)],[686])). 159.61/70.66 thf(5134,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat,G:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => ((ord_less_eq_nat @ B @ G) => ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ G) = none_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_geqmaxNone)). 159.61/70.66 thf(25016,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat,G:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => ((ord_less_eq_nat @ B @ G) => ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ G) = none_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5134])). 159.61/70.66 thf(1225,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/sandbox/benchmark/theBenchmark.p',fact_3894_even__plus__one__iff)). 159.61/70.66 thf(12208,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)],[1225])). 159.61/70.66 thf(7786,axiom,((! [A:num,B:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6009_or__numerals_I3_J)). 159.61/70.66 thf(35144,plain,((! [A:num,B:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7786])). 159.61/70.66 thf(4045,axiom,((~ (ord_less_real @ pi @ zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6702_pi__not__less__zero)). 159.61/70.66 thf(21241,plain,((~ (ord_less_real @ pi @ zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4045])). 159.61/70.66 thf(1081,axiom,((ord_less_real @ zero_zero_real @ one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2129_zero__less__one)). 159.61/70.66 thf(11722,plain,((ord_less_real @ zero_zero_real @ one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081])). 159.61/70.66 thf(2201,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/sandbox/benchmark/theBenchmark.p',fact_3880_even__add)). 159.61/70.66 thf(15356,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)],[2201])). 159.61/70.66 thf(7667,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/sandbox/benchmark/theBenchmark.p',fact_3479_cong__exp__iff__simps_I4_J)). 159.61/70.66 thf(34751,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)],[7667])). 159.61/70.66 thf(8201,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/sandbox/benchmark/theBenchmark.p',fact_3832_dvd__add__times__triv__right__iff)). 159.61/70.66 thf(36475,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)],[8201])). 159.61/70.66 thf(5334,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1558_neq0__conv)). 159.61/70.66 thf(25763,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5334])). 159.61/70.66 thf(2007,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/sandbox/benchmark/theBenchmark.p',fact_6485_machin__Euler)). 159.61/70.66 thf(14738,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)],[2007])). 159.61/70.66 thf(5699,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) <= (ord_less_eq_nat @ one_one_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_power__increasing)). 159.61/70.66 thf(27123,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)) | ~ (ord_less_eq_nat @ one_one_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5699])). 159.61/70.66 thf(6316,axiom,((! [A:nat]: ((((comm_s3181272606743183617d_enat @ zero_z5237406670263579293d_enat @ A) = one_on7984719198319812577d_enat) <= (A = zero_zero_nat)) & ((A != zero_zero_nat) => ((comm_s3181272606743183617d_enat @ zero_z5237406670263579293d_enat @ A) = zero_z5237406670263579293d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8242_pochhammer__0__left)). 159.61/70.66 thf(29539,plain,((! [A:nat]: ((((comm_s3181272606743183617d_enat @ zero_z5237406670263579293d_enat @ A) = one_on7984719198319812577d_enat) | ~ (A = zero_zero_nat)) & ((~ (A = zero_zero_nat)) => ((comm_s3181272606743183617d_enat @ zero_z5237406670263579293d_enat @ A) = zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6316])). 159.61/70.66 thf(4002,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/sandbox/benchmark/theBenchmark.p',fact_6975_sin__cos__squared__add3)). 159.61/70.66 thf(21117,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)],[4002])). 159.61/70.66 thf(7759,axiom,((! [A:nat]: (((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A) => ((plus_plus_nat @ A @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3559_bits__stable__imp__add__self)). 159.61/70.66 thf(35072,plain,((! [A:nat]: (((divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = A) => ((plus_plus_nat @ A @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7759])). 159.61/70.66 thf(3170,axiom,(((^ [A:extended_enat]: (A)) = (times_7803423173614009249d_enat @ one_on7984719198319812577d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1412_lambda__one)). 159.61/70.66 thf(18450,plain,(((^ [A:extended_enat]: (A)) = (times_7803423173614009249d_enat @ one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3170])). 159.61/70.66 thf(5816,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3822_dvd__times__right__cancel__iff)). 159.61/70.66 thf(27686,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5816])). 159.61/70.66 thf(3018,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/sandbox/benchmark/theBenchmark.p',fact_8367_gbinomial__partial__row__sum)). 159.61/70.66 thf(17956,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)],[3018])). 159.61/70.66 thf(5592,axiom,((! [A:(nat > $o),B:$o]: ((A @ (zero_n2687167440665602831ol_nat @ B)) = (((A @ zero_zero_nat) <= (~ (B))) & ((A @ one_one_nat) <= (B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4407_split__of__bool)). 159.61/70.66 thf(26734,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)],[5592])). 159.61/70.66 thf(4688,axiom,((! [A:set_nat,B:nat]: ((finite_finite_nat @ A) <= (! [C:nat]: ((member_nat @ C @ A) => (ord_less_nat @ C @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3633_bounded__nat__set__is__finite)). 159.61/70.66 thf(23463,plain,((! [A:set_nat,B:nat]: ((finite_finite_nat @ A) | ~ (! [C:nat]: ((member_nat @ C @ A) => (ord_less_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4688])). 159.61/70.66 thf(6174,axiom,((! [A:num]: ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bitM @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5920_odd__numeral__BitM)). 159.61/70.66 thf(29005,plain,((! [A:num]: ~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (numeral_numeral_int @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6174])). 159.61/70.66 thf(1162,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/sandbox/benchmark/theBenchmark.p',fact_4170_unit__div__mult__swap)). 159.61/70.66 thf(11975,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)],[1162])). 159.61/70.66 thf(2020,axiom,((! [A:nat]: ((bit_se1745604003318907178nteger @ A @ one_one_Code_integer) = (zero_n356916108424825756nteger @ (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4841_take__bit__of__1)). 159.61/70.66 thf(14779,plain,((! [A:nat]: ((bit_se1745604003318907178nteger @ A @ one_one_Code_integer) = (zero_n356916108424825756nteger @ (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2020])). 159.61/70.66 thf(1507,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_add__left__cancel)). 159.61/70.66 thf(13165,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)],[1507])). 159.61/70.66 thf(3449,axiom,((! [A:int,B:int]: (((plus_plus_int @ B @ (minus_minus_int @ A @ B)) = A) <= (~ (ord_less_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1354_linordered__semidom__class_Oadd__diff__inverse)). 159.61/70.66 thf(19339,plain,((! [A:int,B:int]: (((plus_plus_int @ B @ (minus_minus_int @ A @ B)) = A) | (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3449])). 159.61/70.66 thf(6877,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1466_deg__not__0)). 159.61/70.66 thf(31786,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)],[6877])). 159.61/70.66 thf(3321,axiom,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1433_linordered__field__no__lb)). 159.61/70.66 thf(18936,plain,((! [A:real]: ? [B:real]: (ord_less_real @ B @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3321])). 159.61/70.66 thf(7862,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/sandbox/benchmark/theBenchmark.p',fact_2203_nat__mult__eq__cancel1)). 159.61/70.66 thf(35378,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)],[7862])). 159.61/70.66 thf(3207,axiom,((! [A:nat,B:nat,C:nat]: ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B) @ (semiri4939895301339042750nteger @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6613_of__nat__le__of__nat__power__cancel__iff)). 159.61/70.66 thf(18566,plain,((! [A:nat,B:nat,C:nat]: ((ord_le3102999989581377725nteger @ (power_8256067586552552935nteger @ (semiri4939895301339042750nteger @ A) @ B) @ (semiri4939895301339042750nteger @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3207])). 159.61/70.66 thf(3936,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/sandbox/benchmark/theBenchmark.p',fact_6609_of__nat__power__less__of__nat__cancel__iff)). 159.61/70.66 thf(20913,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)],[3936])). 159.61/70.66 thf(6579,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/sandbox/benchmark/theBenchmark.p',fact_892_power2__diff)). 159.61/70.66 thf(30522,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)],[6579])). 159.61/70.66 thf(6013,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((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 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1778_power__mono__iff)). 159.61/70.66 thf(28481,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((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 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6013])). 159.61/70.66 thf(1896,axiom,((! [A:real]: ((ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1594_double__add__less__zero__iff__single__add__less__zero)). 159.61/70.66 thf(14375,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)],[1896])). 159.61/70.66 thf(1249,axiom,((! [A:int,B:nat]: ((~ (bit_se1146084159140164899it_int @ A @ B)) => ((bit_ri631733984087533419it_int @ B @ A) = (bit_se2923211474154528505it_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6399_signed__take__bit__eq__if__positive)). 159.61/70.66 thf(12292,plain,((! [A:int,B:nat]: ((~ (bit_se1146084159140164899it_int @ A @ B)) => ((bit_ri631733984087533419it_int @ B @ A) = (bit_se2923211474154528505it_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249])). 159.61/70.66 thf(4034,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/sandbox/benchmark/theBenchmark.p',fact_1364_eq__add__iff2)). 159.61/70.66 thf(21209,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)],[4034])). 159.61/70.66 thf(736,axiom,((exp_real = (^ [A:real]: (plus_plus_real @ one_one_real @ (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (suc @ B))) @ (power_power_real @ A @ (suc @ B))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9296_exp__first__term)). 159.61/70.66 thf(10631,plain,(((exp_real) = (^ [A:real]: (plus_plus_real @ one_one_real @ (suminf_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ (suc @ B))) @ (power_power_real @ A @ (suc @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[736])). 159.61/70.66 thf(5358,axiom,((! [A:complex,B:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ A) @ B) = (uminus1482373934393186551omplex @ (times_times_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4633_mult__minus__left)). 159.61/70.66 thf(25913,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)],[5358])). 159.61/70.66 thf(3213,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/sandbox/benchmark/theBenchmark.p',fact_8160_pochhammer__double)). 159.61/70.66 thf(18583,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)],[3213])). 159.61/70.66 thf(4917,axiom,((! [A:nat]: ((((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat) <= (A != zero_zero_nat)) & ((A = zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ A) = one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1812_power__0__left)). 159.61/70.66 thf(24246,plain,((! [A:nat]: ((((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat) | (A = zero_zero_nat)) & ((A = zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ A) = one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4917])). 159.61/70.66 thf(2968,axiom,((! [A:(nat > real)]: ((((ord_less_real @ zero_zero_real @ (suminf_real @ A)) = (? [B:nat]: (ord_less_real @ zero_zero_real @ (A @ B)))) <= (! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B)))) <= (summable_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7081_suminf__pos__iff)). 159.61/70.66 thf(17808,plain,((! [A:(nat > real)]: (((ord_less_real @ zero_zero_real @ (suminf_real @ (A))) = (? [B:nat]: (ord_less_real @ zero_zero_real @ (A @ B)))) | ~ (! [B:nat]: (ord_less_eq_real @ zero_zero_real @ (A @ B))) | ~ (summable_real @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2968])). 159.61/70.66 thf(1907,axiom,((! [A:set_nat,B:set_nat]: ((A = B) => (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2974_equalityD1)). 159.61/70.66 thf(14411,plain,((! [A:set_nat,B:set_nat]: ((A = B) => (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1907])). 159.61/70.66 thf(1762,axiom,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = zero_zero_complex) = ((B = zero_zero_complex) | (A = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1556_divide__eq__0__iff)). 159.61/70.66 thf(13941,plain,((! [A:complex,B:complex]: (((divide1717551699836669952omplex @ A @ B) = zero_zero_complex) = ((B = zero_zero_complex) | (A = zero_zero_complex))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762])). 159.61/70.66 thf(3278,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_nat @ (nat2 @ B) @ (nat2 @ A)) = (ord_less_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9432_nat__mono__iff)). 159.61/70.66 thf(18804,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_nat @ (nat2 @ B) @ (nat2 @ A)) = (ord_less_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3278])). 159.61/70.66 thf(4602,axiom,((! [A:int,B:int]: ((times_times_int @ (uminus_uminus_int @ A) @ B) = (uminus_uminus_int @ (times_times_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4632_mult__minus__left)). 159.61/70.66 thf(23152,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)],[4602])). 159.61/70.66 thf(7240,axiom,((! [A:nat,B:int,C:int]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4235_power__mono__odd)). 159.61/70.66 thf(33288,plain,((! [A:nat,B:int,C:int]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((ord_less_eq_int @ B @ C) => (ord_less_eq_int @ (power_power_int @ B @ A) @ (power_power_int @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7240])). 159.61/70.66 thf(7410,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/sandbox/benchmark/theBenchmark.p',fact_9106_choose__rising__sum_I2_J)). 159.61/70.66 thf(33858,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)],[7410])). 159.61/70.66 thf(3099,axiom,((! [A:nat,B:int]: ((bit_se8570568707652914677it_nat @ A @ (nat2 @ B)) = (nat2 @ (bit_se8568078237143864401it_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9740_drop__bit__nat__eq)). 159.61/70.66 thf(18221,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)],[3099])). 159.61/70.66 thf(3056,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/sandbox/benchmark/theBenchmark.p',fact_6415_signed__take__bit__eq__concat__bit)). 159.61/70.66 thf(18074,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)],[3056])). 159.61/70.66 thf(1736,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_eq_real @ B @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2237_mult__less__cancel__right)). 159.61/70.66 thf(13862,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_eq_real @ B @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1736])). 159.61/70.66 thf(7741,axiom,((! [A:num,B:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6021_and__numerals_I6_J)). 159.61/70.66 thf(35021,plain,((! [A:num,B:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit0 @ B))) = (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7741])). 159.61/70.66 thf(4627,axiom,((! [A:real,B:real]: (((B != zero_zero_real) => ((times_times_real @ A @ B) != zero_zero_real)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1860_no__zero__divisors)). 159.61/70.66 thf(23247,plain,((! [A:real,B:real]: (((~ (B = zero_zero_real)) => (~ ((times_times_real @ A @ B) = zero_zero_real))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4627])). 159.61/70.66 thf(818,axiom,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ B) @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ C)) <= (ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6923_norm__add__leD)). 159.61/70.66 thf(10892,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ B) @ (plus_plus_real @ (real_V7735802525324610683m_real @ A) @ C)) | ~ (ord_less_eq_real @ (real_V7735802525324610683m_real @ (plus_plus_real @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[818])). 159.61/70.66 thf(3249,axiom,((! [A:real]: ((((divide_divide_real @ A @ A) = one_one_real) <= (A != zero_zero_real)) & ((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1668_divide__self__if)). 159.61/70.66 thf(18699,plain,((! [A:real]: ((((divide_divide_real @ A @ A) = one_one_real) | (A = zero_zero_real)) & ((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3249])). 159.61/70.66 thf(5209,axiom,((! [A:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one)) @ A) = (uminus1482373934393186551omplex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5203_mult__1s__ring__1_I1_J)). 159.61/70.66 thf(25301,plain,((! [A:complex]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ one)) @ A) = (uminus1482373934393186551omplex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5209])). 159.61/70.66 thf(7270,axiom,((! [A:nat,B:vEBT_VEBT,C:(vEBT_VEBT > $o)]: ((! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ A @ B))) => (C @ D))) = ((C @ B) | (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4355_Ball__set__replicate)). 159.61/70.66 thf(33379,plain,((! [A:nat,B:vEBT_VEBT,C:(vEBT_VEBT > $o)]: ((! [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ A @ B))) => (C @ D))) = ((C @ B) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7270])). 159.61/70.66 thf(4963,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/sandbox/benchmark/theBenchmark.p',fact_7540_sum_OatLeastAtMost__rev)). 159.61/70.66 thf(24440,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)],[4963])). 159.61/70.66 thf(6314,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => (((divide_divide_nat @ B @ A) = zero_zero_nat) = (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4046_dvd__div__eq__0__iff)). 159.61/70.66 thf(29533,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => (((divide_divide_nat @ B @ A) = zero_zero_nat) = (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6314])). 159.61/70.66 thf(3225,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/sandbox/benchmark/theBenchmark.p',fact_9496_real__root__divide)). 159.61/70.66 thf(18623,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)],[3225])). 159.61/70.66 thf(5194,axiom,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1533_div__by__0)). 159.61/70.66 thf(25231,plain,((! [A:nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5194])). 159.61/70.66 thf(78,axiom,((! [A:complex]: ((im @ (exp_complex @ A)) = (times_times_real @ (exp_real @ (re @ A)) @ (sin_real @ (im @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9666_Im__exp)). 159.61/70.66 thf(8489,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)],[78])). 159.61/70.66 thf(6942,axiom,((! [A:nat]: (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3714_finite__Collect__less__nat)). 159.61/70.66 thf(32017,plain,((! [A:nat]: (finite_finite_nat @ (collect_nat @ (^ [B:nat]: (ord_less_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6942])). 159.61/70.66 thf(6613,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/sandbox/benchmark/theBenchmark.p',fact_6349_bit__minus__numeral__Bit1__Suc__iff)). 159.61/70.66 thf(30646,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)],[6613])). 159.61/70.66 thf(3932,axiom,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (ring_1_of_int_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5898_of__int__nonneg)). 159.61/70.66 thf(20897,plain,((! [A:int]: ((ord_less_eq_int @ zero_zero_int @ A) => (ord_less_eq_int @ zero_zero_int @ (ring_1_of_int_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3932])). 159.61/70.67 thf(5088,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))) | ((bit_se1146084159140164899it_int @ B @ D) & (ord_less_nat @ D @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6414_bit__concat__bit__iff)). 159.61/70.67 thf(24873,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))) | ((bit_se1146084159140164899it_int @ B @ D) & (ord_less_nat @ D @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5088])). 159.61/70.67 thf(2694,axiom,((! [A:num,B:num]: ~ (ord_le3102999989581377725nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5027_not__numeral__le__neg__numeral)). 159.61/70.67 thf(16943,plain,((! [A:num,B:num]: ~ (ord_le3102999989581377725nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2694])). 159.61/70.67 thf(6165,axiom,((! [A:nat,B:int,C:int]: ((ord_less_nat @ zero_zero_nat @ A) => (((((power_power_int @ B @ A) = (power_power_int @ C @ A)) = (B = C)) <= (ord_less_eq_int @ zero_zero_int @ C)) <= (ord_less_eq_int @ zero_zero_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1933_power__eq__iff__eq__base)). 159.61/70.67 thf(28973,plain,((! [A:nat,B:int,C:int]: ((ord_less_nat @ zero_zero_nat @ A) => ((((power_power_int @ B @ A) = (power_power_int @ C @ A)) = (B = C)) | ~ (ord_less_eq_int @ zero_zero_int @ C) | ~ (ord_less_eq_int @ zero_zero_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6165])). 159.61/70.67 thf(1484,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/sandbox/benchmark/theBenchmark.p',fact_7816_arcsin__lt__bounded)). 159.61/70.67 thf(13096,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)],[1484])). 159.61/70.67 thf(2675,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le2932123472753598470d_enat @ C @ A) <= (ord_le72135733267957522d_enat @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4503_minf_I6_J)). 159.61/70.67 thf(16874,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le2932123472753598470d_enat @ C @ A) | ~ (ord_le72135733267957522d_enat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2675])). 159.61/70.67 thf(5427,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/sandbox/benchmark/theBenchmark.p',fact_7826_gauss__sum)). 159.61/70.67 thf(26184,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)],[5427])). 159.61/70.67 thf(6277,axiom,((! [A:int,B:int,C:int]: ((A != zero_zero_int) => (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = (B = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1857_mult__left__cancel)). 159.61/70.67 thf(29399,plain,((! [A:int,B:int,C:int]: ((~ (A = zero_zero_int)) => (((times_times_int @ A @ B) = (times_times_int @ A @ C)) = (B = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6277])). 159.61/70.67 thf(3947,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/sandbox/benchmark/theBenchmark.p',fact_307_power__less__power__Suc)). 159.61/70.67 thf(20952,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)],[3947])). 159.61/70.67 thf(4145,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/sandbox/benchmark/theBenchmark.p',fact_5136_ln__ge__zero)). 159.61/70.67 thf(21549,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)],[4145])). 159.61/70.67 thf(4600,axiom,((! [A:nat,B:vEBT_VEBT,C:(vEBT_VEBT > $o)]: ((? [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ A @ B))) & (C @ D))) = ((C @ B) & (A != zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4358_Bex__set__replicate)). 159.61/70.67 thf(23146,plain,((! [A:nat,B:vEBT_VEBT,C:(vEBT_VEBT > $o)]: ((? [D:vEBT_VEBT]: ((member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ (replicate_VEBT_VEBT @ A @ B))) & (C @ D))) = ((C @ B) & ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4600])). 159.61/70.67 thf(6073,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/sandbox/benchmark/theBenchmark.p',fact_6217_or__not__num__neg_Osimps_I6_J)). 159.61/70.67 thf(28667,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)],[6073])). 159.61/70.67 thf(1865,axiom,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ A @ (suc @ B)) = (bit_se1146084159140164899it_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6419_bit__Suc)). 159.61/70.67 thf(14278,plain,((! [A:int,B:nat]: ((bit_se1146084159140164899it_int @ A @ (suc @ B)) = (bit_se1146084159140164899it_int @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1865])). 159.61/70.67 thf(3665,axiom,((! [A:(nat > real),B:set_nat]: (((groups129246275422532515t_real @ A @ B) != one_one_real) => (~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = one_one_real))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8468_prod_Onot__neutral__contains__not__neutral)). 159.61/70.67 thf(20022,plain,((! [A:(nat > real),B:set_nat]: ((~ ((groups129246275422532515t_real @ (A) @ B) = one_one_real)) => (~ (! [C:nat]: ((member_nat @ C @ B) => ((A @ C) = one_one_real))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3665])). 159.61/70.67 thf(39,axiom,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1545_bits__div__by__0)). 159.61/70.67 thf(8368,plain,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger) = zero_z3403309356797280102nteger))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 159.61/70.67 thf(223,axiom,((! [A:complex]: (((im @ A) = zero_zero_real) => ((ord_less_eq_real @ (re @ A) @ zero_zero_real) => ((csqrt @ A) = (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sqrt @ (abs_abs_real @ (re @ A)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9651_csqrt__of__real__nonpos)). 159.61/70.67 thf(8933,plain,((! [A:complex]: (((im @ A) = zero_zero_real) => ((ord_less_eq_real @ (re @ A) @ zero_zero_real) => ((csqrt @ A) = (times_times_complex @ imaginary_unit @ (real_V4546457046886955230omplex @ (sqrt @ (abs_abs_real @ (re @ A)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 159.61/70.67 thf(1683,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/sandbox/benchmark/theBenchmark.p',fact_5851_of__int__le__numeral__power__cancel__iff)). 159.61/70.67 thf(13701,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)],[1683])). 159.61/70.67 thf(4624,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/sandbox/benchmark/theBenchmark.p',fact_5859_of__int__eq__neg__numeral__power__cancel__iff)). 159.61/70.67 thf(23237,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)],[4624])). 159.61/70.67 thf(613,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => (~ ((A != zero_zero_int) => (! [C:int]: (B != (times_times_int @ A @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4138_unit__dvdE)). 159.61/70.67 thf(10205,plain,((! [A:int,B:int]: ((dvd_dvd_int @ A @ one_one_int) => (~ ((~ (A = zero_zero_int)) => (! [C:int]: ~ (B = (times_times_int @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[613])). 159.61/70.67 thf(1320,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9026_less__imp__inverse__less__neg)). 159.61/70.67 thf(12515,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320])). 159.61/70.67 thf(3993,axiom,((! [A:real,B:real,C:real,D:real,E:real]: ((((D != E) & (B = C)) => ((plus_plus_real @ B @ (times_times_real @ A @ D)) != (plus_plus_real @ C @ (times_times_real @ A @ E)))) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4558_add__scale__eq__noteq)). 159.61/70.67 thf(21085,plain,((! [A:real,B:real,C:real,D:real,E:real]: (((~ (D = E) & (B = C)) => (~ ((plus_plus_real @ B @ (times_times_real @ A @ D)) = (plus_plus_real @ C @ (times_times_real @ A @ E))))) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3993])). 159.61/70.67 thf(2901,axiom,((! [A:real,B:real]: (((divide_divide_real @ (uminus_uminus_real @ B) @ A) = (uminus_uminus_real @ (divide_divide_real @ B @ A))) <= (dvd_dvd_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5120_dvd__neg__div)). 159.61/70.67 thf(17597,plain,((! [A:real,B:real]: (((divide_divide_real @ (uminus_uminus_real @ B) @ A) = (uminus_uminus_real @ (divide_divide_real @ B @ A))) | ~ (dvd_dvd_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2901])). 159.61/70.67 thf(2275,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ (modulo_modulo_int @ B @ A) @ zero_zero_int) <= (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3658_neg__mod__sign)). 159.61/70.67 thf(15585,plain,((! [A:int,B:int]: ((ord_less_eq_int @ (modulo_modulo_int @ B @ A) @ zero_zero_int) | ~ (ord_less_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2275])). 159.61/70.67 thf(2003,axiom,((! [A:extended_enat,B:(nat > extended_enat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le2932123472753598470d_enat @ (B @ E) @ (B @ F)))) => (ord_le72135733267957522d_enat @ A @ (B @ D)))) <= (ord_le72135733267957522d_enat @ A @ (B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3237_order__less__le__subst1)). 159.61/70.67 thf(14723,plain,((! [A:extended_enat,B:(nat > extended_enat),C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_le2932123472753598470d_enat @ (B @ E) @ (B @ F)))) => (ord_le72135733267957522d_enat @ A @ (B @ D)))) | ~ (ord_le72135733267957522d_enat @ A @ (B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2003])). 159.61/70.67 thf(7406,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1974_mult__nonneg__nonneg)). 159.61/70.67 thf(33848,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7406])). 159.61/70.67 thf(5459,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/sandbox/benchmark/theBenchmark.p',fact_5648_power2__le__iff__abs__le)). 159.61/70.67 thf(26305,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)],[5459])). 159.61/70.67 thf(3981,axiom,((divide1717551699836669952omplex = (^ [A:complex,B:complex]: (divide1717551699836669952omplex @ (times_times_complex @ A @ (cnj @ B)) @ (real_V4546457046886955230omplex @ (power_power_real @ (real_V1022390504157884413omplex @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9703_complex__div__cnj)). 159.61/70.67 thf(21053,plain,(((divide1717551699836669952omplex) = (^ [A:complex,B:complex]: (divide1717551699836669952omplex @ (times_times_complex @ A @ (cnj @ B)) @ (real_V4546457046886955230omplex @ (power_power_real @ (real_V1022390504157884413omplex @ B) @ (numeral_numeral_nat @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3981])). 159.61/70.67 thf(6456,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1256_right__diff__distrib_H)). 159.61/70.67 thf(30078,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ A @ (minus_minus_complex @ B @ C)) = (minus_minus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6456])). 159.61/70.67 thf(118,axiom,((! [A:complex]: ((plus_plus_complex @ (cosh_complex @ A) @ (sinh_complex @ A)) = (exp_complex @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9319_cosh__plus__sinh)). 159.61/70.67 thf(8616,plain,((! [A:complex]: ((plus_plus_complex @ (cosh_complex @ A) @ (sinh_complex @ A)) = (exp_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[118])). 159.61/70.67 thf(6074,axiom,((! [A:nat]: (((bit_se2002935070580805687sk_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5975_mask__eq__0__iff)). 159.61/70.67 thf(28670,plain,((! [A:nat]: (((bit_se2002935070580805687sk_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6074])). 159.61/70.67 thf(8042,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) = (nth_VEBT_VEBT @ B @ C)) <= (A != C)) & (((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ D) @ C) = D) <= (A = C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_nth__list__update)). 159.61/70.67 thf(35958,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) = (nth_VEBT_VEBT @ B @ C)) | (A = C)) & (((nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ B @ A @ D) @ C) = D) | ~ (A = C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8042])). 159.61/70.67 thf(4280,axiom,(((real_V1022390504157884413omplex @ one_one_complex) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6894_norm__one)). 159.61/70.67 thf(21981,plain,(((real_V1022390504157884413omplex @ one_one_complex) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4280])). 159.61/70.67 thf(3300,axiom,((! [A:complex,B:complex]: (((exp_complex @ (plus_plus_complex @ A @ B)) = (times_times_complex @ (exp_complex @ A) @ (exp_complex @ B))) <= ((times_times_complex @ A @ B) = (times_times_complex @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6077_exp__add__commuting)). 159.61/70.67 thf(18872,plain,((! [A:complex,B:complex]: (((exp_complex @ (plus_plus_complex @ A @ B)) = (times_times_complex @ (exp_complex @ A) @ (exp_complex @ B))) | ~ ((times_times_complex @ A @ B) = (times_times_complex @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3300])). 159.61/70.67 thf(1668,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/sandbox/benchmark/theBenchmark.p',fact_818_add__diff__add)). 159.61/70.67 thf(13652,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)],[1668])). 159.61/70.67 thf(3911,axiom,((powr_real = (^ [A:real,B:real]: (if_real @ (A = zero_zero_real) @ zero_zero_real @ (exp_real @ (times_times_real @ B @ (ln_ln_real @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7282_powr__def)). 159.61/70.67 thf(20838,plain,(((powr_real) = (^ [A:real,B:real]: (if_real @ (A = zero_zero_real) @ zero_zero_real @ (exp_real @ (times_times_real @ B @ (ln_ln_real @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3911])). 159.61/70.67 thf(3921,axiom,((! [A:int]: ((bit_se1146084159140164899it_int @ A @ zero_zero_nat) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6351_bit__0)). 159.61/70.67 thf(20865,plain,((! [A:int]: ((bit_se1146084159140164899it_int @ A @ zero_zero_nat) = (~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3921])). 159.61/70.67 thf(905,axiom,((! [A:num]: ((divide6298287555418463151nteger @ (numera6620942414471956472nteger @ (bit0 @ A)) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (numera6620942414471956472nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_numeral__Bit0__div__2)). 159.61/70.67 thf(11155,plain,((! [A:num]: ((divide6298287555418463151nteger @ (numera6620942414471956472nteger @ (bit0 @ A)) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (numera6620942414471956472nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[905])). 159.61/70.67 thf(674,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => ((nat2 @ (plus_plus_int @ A @ B)) = (plus_plus_nat @ (nat2 @ A) @ (nat2 @ B)))) <= (ord_less_eq_int @ zero_zero_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9447_nat__add__distrib)). 159.61/70.67 thf(10408,plain,((! [A:int,B:int]: (((ord_less_eq_int @ zero_zero_int @ B) => ((nat2 @ (plus_plus_int @ A @ B)) = (plus_plus_nat @ (nat2 @ A) @ (nat2 @ B)))) | ~ (ord_less_eq_int @ zero_zero_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[674])). 159.61/70.67 thf(4846,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int) <= (ord_less_eq_int @ B @ zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1973_mult__nonneg__nonpos)). 159.61/70.67 thf(24019,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((ord_less_eq_int @ (times_times_int @ A @ B) @ zero_zero_int) | ~ (ord_less_eq_int @ B @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4846])). 159.61/70.67 thf(4881,axiom,((! [A:set_nat]: (ord_less_eq_nat @ (groups3542108847815614940at_nat @ (^ [B:nat]: (B)) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ (finite_card_nat @ A))) @ (groups3542108847815614940at_nat @ (^ [B:nat]: (B)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9720_card__sum__le__nat__sum)). 159.61/70.67 thf(24127,plain,((! [A:set_nat]: (ord_less_eq_nat @ (groups3542108847815614940at_nat @ (^ [B:nat]: (B)) @ (set_or4665077453230672383an_nat @ zero_zero_nat @ (finite_card_nat @ A))) @ (groups3542108847815614940at_nat @ (^ [B:nat]: (B)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4881])). 159.61/70.67 thf(6545,axiom,((! [A:num]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5699_add__neg__numeral__special_I5_J)). 159.61/70.67 thf(30413,plain,((! [A:num]: ((plus_plus_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6545])). 159.61/70.67 thf(5042,axiom,((! [A:num]: ((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ (inc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5698_add__neg__numeral__special_I5_J)). 159.61/70.67 thf(24692,plain,((! [A:num]: ((plus_plus_int @ (uminus_uminus_int @ one_one_int) @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (uminus_uminus_int @ (numeral_numeral_int @ (inc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5042])). 159.61/70.67 thf(4336,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/sandbox/benchmark/theBenchmark.p',fact_6825_zadd__int__left)). 159.61/70.67 thf(22147,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)],[4336])). 159.61/70.67 thf(3950,axiom,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ A @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_int @ (A @ zero_zero_nat) @ (groups3539618377306564664at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8749_sum_OatMost__Suc__shift)). 159.61/70.67 thf(20962,plain,((! [A:(nat > int),B:nat]: ((groups3539618377306564664at_int @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_int @ (A @ zero_zero_nat) @ (groups3539618377306564664at_int @ (^ [C:nat]: (A @ (suc @ C))) @ (set_ord_atMost_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3950])). 159.61/70.67 thf(7348,axiom,((! [A:nat,B:code_integer]: (((B = one_one_Code_integer) | (ord_less_nat @ zero_zero_nat @ A)) => (dvd_dvd_Code_integer @ B @ (power_8256067586552552935nteger @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4214_dvd__power)). 159.61/70.67 thf(33661,plain,((! [A:nat,B:code_integer]: (((B = one_one_Code_integer) | (ord_less_nat @ zero_zero_nat @ A)) => (dvd_dvd_Code_integer @ B @ (power_8256067586552552935nteger @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7348])). 159.61/70.67 thf(7575,axiom,((! [A:$o]: ((semiri1316708129612266289at_nat @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n2687167440665602831ol_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6573_of__nat__of__bool)). 159.61/70.67 thf(34476,plain,((! [A:$o]: ((semiri1316708129612266289at_nat @ (zero_n2687167440665602831ol_nat @ A)) = (zero_n2687167440665602831ol_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7575])). 159.61/70.67 thf(5500,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (times_times_nat @ A @ B) @ A) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3400_mod__mult__self1__is__0)). 159.61/70.67 thf(26458,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)],[5500])). 159.61/70.67 thf(1383,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: (((ord_less_eq_set_nat @ A @ C) <= (B = C)) <= (ord_less_eq_set_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2738_ord__le__eq__trans)). 159.61/70.67 thf(12766,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ C) | ~ (B = C) | ~ (ord_less_eq_set_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383])). 159.61/70.67 thf(3489,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/sandbox/benchmark/theBenchmark.p',fact_8545_power__sum)). 159.61/70.67 thf(19457,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)],[3489])). 159.61/70.67 thf(4216,axiom,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4715_div__minus1__right)). 159.61/70.67 thf(21778,plain,((! [A:code_integer]: ((divide6298287555418463151nteger @ A @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4216])). 159.61/70.67 thf(6557,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((nat2 @ (times_times_int @ A @ B)) = (times_times_nat @ (nat2 @ A) @ (nat2 @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9448_nat__mult__distrib)). 159.61/70.67 thf(30450,plain,((! [A:int,B:int]: ((ord_less_eq_int @ zero_zero_int @ A) => ((nat2 @ (times_times_int @ A @ B)) = (times_times_nat @ (nat2 @ A) @ (nat2 @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6557])). 159.61/70.67 thf(6712,axiom,((! [A:num,B:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ (pred_numeral @ A) @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5742_take__bit__numeral__bit1)). 159.61/70.67 thf(31123,plain,((! [A:num,B:num]: ((bit_se2923211474154528505it_int @ (numeral_numeral_nat @ A) @ (numeral_numeral_int @ (bit1 @ B))) = (plus_plus_int @ (times_times_int @ (bit_se2923211474154528505it_int @ (pred_numeral @ A) @ (numeral_numeral_int @ B)) @ (numeral_numeral_int @ (bit0 @ one))) @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6712])). 159.61/70.67 thf(6188,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ one_one_nat) => (ord_less_eq_nat @ (power_power_nat @ A @ B) @ one_one_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2335_power__le__one)). 159.61/70.67 thf(29056,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ one_one_nat) => (ord_less_eq_nat @ (power_power_nat @ A @ B) @ one_one_nat)) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6188])). 159.61/70.67 thf(4975,axiom,((! [A:code_integer,B:code_integer]: ((times_3573771949741848930nteger @ (uminus1351360451143612070nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (times_3573771949741848930nteger @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4630_minus__mult__minus)). 159.61/70.67 thf(24474,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)],[4975])). 159.61/70.67 thf(1952,axiom,((! [A:int,B:complex]: ((times_times_complex @ (invers8013647133539491842omplex @ (ring_17405671764205052669omplex @ A)) @ B) = (times_times_complex @ B @ (invers8013647133539491842omplex @ (ring_17405671764205052669omplex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9057_mult__inverse__of__int__commute)). 159.61/70.67 thf(14546,plain,((! [A:int,B:complex]: ((times_times_complex @ (invers8013647133539491842omplex @ (ring_17405671764205052669omplex @ A)) @ B) = (times_times_complex @ B @ (invers8013647133539491842omplex @ (ring_17405671764205052669omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1952])). 159.61/70.67 thf(583,axiom,((! [A:complex,B:complex]: ((ord_less_real @ zero_zero_real @ (im @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_real @ zero_zero_real @ (im @ (times_times_complex @ A @ (cnj @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9694_Im__complex__div__gt__0)). 159.61/70.67 thf(10105,plain,((! [A:complex,B:complex]: ((ord_less_real @ zero_zero_real @ (im @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_real @ zero_zero_real @ (im @ (times_times_complex @ A @ (cnj @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[583])). 159.61/70.67 thf(6994,axiom,((! [A:num]: (one_one_Code_integer != (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5093_one__neq__neg__numeral)). 159.61/70.67 thf(32338,plain,((! [A:num]: ~ (one_one_Code_integer = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6994])). 159.61/70.67 thf(6499,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/sandbox/benchmark/theBenchmark.p',fact_5525_abs__triangle__ineq2__sym)). 159.61/70.67 thf(30244,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)],[6499])). 159.61/70.67 thf(5466,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (times_times_nat @ B @ (semiri1316708129612266289at_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6651_mult__of__nat__commute)). 159.61/70.67 thf(26327,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)],[5466])). 159.61/70.67 thf(2778,axiom,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ (modulo_modulo_int @ B @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3649_Euclidean__Division_Opos__mod__bound)). 159.61/70.67 thf(17201,plain,((! [A:int,B:int]: ((ord_less_int @ zero_zero_int @ A) => (ord_less_int @ (modulo_modulo_int @ B @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2778])). 159.61/70.67 thf(4297,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/sandbox/benchmark/theBenchmark.p',fact_4530_pinf_I9_J)). 159.61/70.67 thf(22037,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4297])). 159.61/70.67 thf(6637,axiom,((! [A:num]: ((plus_plus_real @ (numeral_numeral_real @ A) @ one_one_real) = (numeral_numeral_real @ (plus_plus_num @ A @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_numeral__plus__one)). 159.61/70.67 thf(30735,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)],[6637])). 159.61/70.67 thf(7083,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((((! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)) <= (! [D:nat]: ((B = (suc @ D)) => (C @ D)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_strict__inc__induct)). 159.61/70.67 thf(32669,plain,((! [A:nat,B:nat,C:(nat > $o)]: (((! [D:nat]: ((ord_less_nat @ D @ B) => ((C @ (suc @ D)) => (C @ D)))) => (C @ A)) | ~ (! [D:nat]: ((B = (suc @ D)) => (C @ D))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7083])). 159.61/70.67 thf(50,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (tanh_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5429_tanh__real__pos__iff)). 159.61/70.67 thf(8400,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (tanh_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 159.61/70.67 thf(2259,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/sandbox/benchmark/theBenchmark.p',fact_1355_less__diff__eq)). 159.61/70.67 thf(15540,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)],[2259])). 159.61/70.67 thf(793,axiom,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = one_one_real) = ((B = A) & (B != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1667_divide__eq__eq__1)). 159.61/70.67 thf(10809,plain,((! [A:real,B:real]: (((divide_divide_real @ A @ B) = one_one_real) = ((B = A) & ~ (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[793])). 159.61/70.67 thf(3787,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/sandbox/benchmark/theBenchmark.p',fact_2161_divide__neg__pos)). 159.61/70.67 thf(20429,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)],[3787])). 159.61/70.67 thf(6458,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_Suc__less__SucD)). 159.61/70.67 thf(30084,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)],[6458])). 159.61/70.67 thf(1213,axiom,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ C) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6924_norm__add__leD)). 159.61/70.67 thf(12177,plain,((! [A:complex,B:complex,C:real]: ((ord_less_eq_real @ (real_V1022390504157884413omplex @ (plus_plus_complex @ A @ B)) @ C) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ B) @ (plus_plus_real @ (real_V1022390504157884413omplex @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213])). 159.61/70.67 thf(5944,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/sandbox/benchmark/theBenchmark.p',fact_806_left__diff__distrib__numeral)). 159.61/70.67 thf(28264,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)],[5944])). 159.61/70.67 thf(1596,axiom,((! [A:real]: ((ord_less_eq_real @ (inverse_inverse_real @ A) @ one_one_real) = ((ord_less_eq_real @ one_one_real @ A) | (ord_less_eq_real @ A @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9067_inverse__le__1__iff)). 159.61/70.67 thf(13432,plain,((! [A:real]: ((ord_less_eq_real @ (inverse_inverse_real @ A) @ one_one_real) = ((ord_less_eq_real @ one_one_real @ A) | (ord_less_eq_real @ A @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596])). 159.61/70.67 thf(1757,axiom,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ B @ C) => (~ (ord_le72135733267957522d_enat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4447_pinf_I5_J)). 159.61/70.67 thf(13926,plain,((! [A:extended_enat]: ? [B:extended_enat]: ! [C:extended_enat]: ((ord_le72135733267957522d_enat @ B @ C) => (~ (ord_le72135733267957522d_enat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757])). 159.61/70.67 thf(4178,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/sandbox/benchmark/theBenchmark.p',fact_1356_less__diff__eq)). 159.61/70.67 thf(21653,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)],[4178])). 159.61/70.67 thf(5130,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/sandbox/benchmark/theBenchmark.p',fact_7406_sum__distrib__left)). 159.61/70.67 thf(25004,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)],[5130])). 159.61/70.67 thf(3738,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/sandbox/benchmark/theBenchmark.p',fact_6811_sin__2pi__minus)). 159.61/70.67 thf(20275,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)],[3738])). 159.61/70.67 thf(6252,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ B @ A) <= (~ (ord_less_eq_int @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2645_linorder__le__cases)). 159.61/70.67 thf(29259,plain,((! [A:int,B:int]: ((ord_less_eq_int @ B @ A) | (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6252])). 159.61/70.67 thf(834,axiom,((! [A:real,B:complex,C:complex,D:complex]: ((A != zero_zero_real) => ((B = (plus_plus_complex @ (real_V2046097035970521341omplex @ A @ C) @ D)) = ((minus_minus_complex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ A) @ B) @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ A) @ D)) = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9252_real__vector__eq__affinity)). 159.61/70.67 thf(10941,plain,((! [A:real,B:complex,C:complex,D:complex]: ((~ (A = zero_zero_real)) => ((B = (plus_plus_complex @ (real_V2046097035970521341omplex @ A @ C) @ D)) = ((minus_minus_complex @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ A) @ B) @ (real_V2046097035970521341omplex @ (inverse_inverse_real @ A) @ D)) = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[834])). 159.61/70.67 thf(3838,axiom,((! [A:(nat > real),B:real]: ((summable_real @ A) => (summable_real @ (^ [C:nat]: (times_times_real @ B @ (A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7030_summable__mult)). 159.61/70.67 thf(20608,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)],[3838])). 159.61/70.67 thf(2085,axiom,((! [A:real,B:real]: ((A != B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2765_less__imp__neq)). 159.61/70.67 thf(14967,plain,((! [A:real,B:real]: (~ (A = B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2085])). 159.61/70.67 thf(3485,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one))) => ((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)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6797_ln__series)). 159.61/70.67 thf(19445,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one))) => ((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)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3485])). 159.61/70.67 thf(7731,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ (binomial @ C @ B) @ (binomial @ C @ A)))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9130_binomial__strict__antimono)). 159.61/70.67 thf(34979,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ (binomial @ C @ B) @ (binomial @ C @ A)))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7731])). 159.61/70.67 thf(4857,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/sandbox/benchmark/theBenchmark.p',fact_4157_unit__eq__div1)). 159.61/70.67 thf(24051,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)],[4857])). 159.61/70.67 thf(6350,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (ord_less_eq_nat @ B @ zero_zero_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1972_mult__nonneg__nonpos)). 159.61/70.67 thf(29642,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_eq_nat @ B @ zero_zero_nat) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6350])). 159.61/70.67 thf(2585,axiom,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D)) <= ((C = D) & (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_add__mono__thms__linordered__semiring_I4_J)). 159.61/70.67 thf(16558,plain,((! [A:int,B:int,C:int,D:int]: (((plus_plus_int @ A @ C) = (plus_plus_int @ B @ D)) | ~ ((C = D) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2585])). 159.61/70.67 thf(755,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/sandbox/benchmark/theBenchmark.p',fact_8511_prod__ge__1)). 159.61/70.67 thf(10691,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)],[755])). 159.61/70.67 thf(1655,axiom,((! [A:real]: (((exp_real @ (ln_ln_real @ A)) = A) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6000_exp__ln)). 159.61/70.67 thf(13614,plain,((! [A:real]: (((exp_real @ (ln_ln_real @ A)) = A) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655])). 159.61/70.67 thf(1878,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)) & ((A = zero_zero_real) => ((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1653_mult__divide__mult__cancel__left__if)). 159.61/70.67 thf(14315,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)) & ((A = zero_zero_real) => ((divide_divide_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1878])). 159.61/70.67 thf(3231,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => (((ord_less_real @ (arccos @ A) @ (arccos @ B)) = (ord_less_real @ B @ A)) <= (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7707_arccos__less__mono)). 159.61/70.67 thf(18643,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ one_one_real) => (((ord_less_real @ (arccos @ A) @ (arccos @ B)) = (ord_less_real @ B @ A)) | ~ (ord_less_eq_real @ (abs_abs_real @ B) @ one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3231])). 159.61/70.67 thf(76,axiom,((! [A:real]: (sums_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))) @ (exp_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9283_exp__converges)). 159.61/70.67 thf(8484,plain,((! [A:real]: (sums_real @ (^ [B:nat]: (real_V1485227260804924795R_real @ (inverse_inverse_real @ (semiri2265585572941072030t_real @ B)) @ (power_power_real @ A @ B))) @ (exp_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 159.61/70.67 thf(1123,axiom,((bit_se9216721137139052372nteger = (^ [A:code_integer,B:nat]: (((bit_se9216721137139052372nteger @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (minus_minus_nat @ B @ one_one_nat)) <= (B != zero_zero_nat)) & ((B = zero_zero_nat) => (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6466_bit__rec)). 159.61/70.67 thf(11854,plain,(((bit_se9216721137139052372nteger) = (^ [A:code_integer,B:nat]: (((bit_se9216721137139052372nteger @ (divide6298287555418463151nteger @ A @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (minus_minus_nat @ B @ one_one_nat)) | (B = zero_zero_nat)) & ((B = zero_zero_nat) => (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123])). 159.61/70.67 thf(972,axiom,(((zero_n2684676970156552555ol_int @ ($true)) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4324_of__bool__eq_I2_J)). 159.61/70.67 thf(11362,plain,(((zero_n2684676970156552555ol_int @ ($true)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[972])). 159.61/70.67 thf(7258,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6008_or__numerals_I3_J)). 159.61/70.67 thf(33345,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (numeral_numeral_int @ (bit0 @ B))) = (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (bit_se1409905431419307370or_int @ (numeral_numeral_int @ A) @ (numeral_numeral_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7258])). 159.61/70.67 thf(8150,axiom,((! [A:nat,B:nat]: ? [C:nat]: ! [D:nat]: ((ord_less_nat @ C @ D) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B)) = (dvd_dvd_nat @ A @ (plus_plus_nat @ D @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4529_pinf_I9_J)). 159.61/70.67 thf(36318,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8150])). 159.61/70.67 thf(6381,axiom,(((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (bit0 @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4847_add__neg__numeral__special_I9_J)). 159.61/70.67 thf(29759,plain,(((plus_p5714425477246183910nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6381])). 159.61/70.67 thf(7447,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/sandbox/benchmark/theBenchmark.p',fact_1815_power__0__left)). 159.61/70.67 thf(33978,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)],[7447])). 159.61/70.67 thf(7368,axiom,((! [A:nat,B:nat,C:(nat > int),D:int]: ((((ord_less_eq_int @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F))))) <= ((C @ B) = D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2651_ord__le__eq__subst)). 159.61/70.67 thf(33725,plain,((! [A:nat,B:nat,C:(nat > int),D:int]: ((ord_less_eq_int @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ E @ F) => (ord_less_eq_int @ (C @ E) @ (C @ F)))) | ~ ((C @ B) = D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7368])). 159.61/70.67 thf(1963,axiom,((! [A:int]: ((ord_less_int @ A @ zero_zero_int) => ((abs_abs_int @ A) = (uminus_uminus_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5574_abs__of__neg)). 159.61/70.67 thf(14578,plain,((! [A:int]: ((ord_less_int @ A @ zero_zero_int) => ((abs_abs_int @ A) = (uminus_uminus_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1963])). 159.61/70.67 thf(7899,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/sandbox/benchmark/theBenchmark.p',fact_3562_div__exp__mod__exp__eq)). 159.61/70.67 thf(35505,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)],[7899])). 159.61/70.67 thf(1400,axiom,((real_V2046097035970521341omplex = (^ [A:real]: (times_times_complex @ (real_V4546457046886955230omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9219_scaleR__conv__of__real)). 159.61/70.67 thf(12820,plain,(((real_V2046097035970521341omplex) = (^ [A:real]: (times_times_complex @ (real_V4546457046886955230omplex @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400])). 159.61/70.67 thf(4984,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_one__reorient)). 159.61/70.67 thf(24500,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4984])). 159.61/70.67 thf(5795,axiom,(((semiri1406184849735516958ct_int @ zero_zero_nat) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8046_fact__0)). 159.61/70.67 thf(27516,plain,(((semiri1406184849735516958ct_int @ zero_zero_nat) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5795])). 159.61/70.67 thf(5125,axiom,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (abs_abs_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5516_abs__ge__zero)). 159.61/70.67 thf(24987,plain,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (abs_abs_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5125])). 159.61/70.67 thf(4388,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => ((dvd_dvd_int @ B @ one_one_int) => ((divide_divide_int @ A @ (times_times_int @ A @ B)) = (divide_divide_int @ one_one_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4197_is__unit__div__mult__cancel__left)). 159.61/70.67 thf(22308,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => ((dvd_dvd_int @ B @ one_one_int) => ((divide_divide_int @ A @ (times_times_int @ A @ B)) = (divide_divide_int @ one_one_int @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4388])). 159.61/70.67 thf(5329,axiom,((! [A:real,B:real]: ((A = (times_times_real @ A @ B)) = ((B = one_one_real) | (A = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1624_mult__cancel__left1)). 159.61/70.67 thf(25744,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)],[5329])). 159.61/70.67 thf(3408,axiom,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3702_verit__sum__simplify)). 159.61/70.67 thf(19212,plain,((! [A:int]: ((plus_plus_int @ A @ zero_zero_int) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3408])). 159.61/70.67 thf(7117,axiom,((ord_less_eq_real @ zero_zero_real @ zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1829_le__numeral__extra_I3_J)). 159.61/70.67 thf(32825,plain,((ord_less_eq_real @ zero_zero_real @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7117])). 159.61/70.67 thf(2063,axiom,((! [A:(nat > real)]: ((ord_less_eq_real @ (abs_abs_real @ (suminf_real @ A)) @ (suminf_real @ (^ [B:nat]: (abs_abs_real @ (A @ B))))) <= (summable_real @ (^ [B:nat]: (abs_abs_real @ (A @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7080_summable__rabs)). 159.61/70.67 thf(14903,plain,((! [A:(nat > real)]: ((ord_less_eq_real @ (abs_abs_real @ (suminf_real @ (A))) @ (suminf_real @ (^ [B:nat]: (abs_abs_real @ (A @ B))))) | ~ (summable_real @ (^ [B:nat]: (abs_abs_real @ (A @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2063])). 159.61/70.67 thf(1635,axiom,((! [A:nat,B:(nat > real),C:real,D:nat]: ((! [E:nat]: ((ord_less_eq_real @ (B @ E) @ C) <= (ord_less_nat @ E @ A))) => ((ord_less_eq_real @ (groups6591440286371151544t_real @ B @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ C)) <= (ord_less_eq_real @ zero_zero_real @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8008_real__sum__nat__ivl__bounded2)). 159.61/70.67 thf(13556,plain,((! [A:nat,B:(nat > real),C:real,D:nat]: ((! [E:nat]: ((ord_less_eq_real @ (B @ E) @ C) | ~ (ord_less_nat @ E @ A))) => ((ord_less_eq_real @ (groups6591440286371151544t_real @ (B) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ D))) @ (times_times_real @ (semiri5074537144036343181t_real @ A) @ C)) | ~ (ord_less_eq_real @ zero_zero_real @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635])). 159.61/70.67 thf(7038,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/sandbox/benchmark/theBenchmark.p',fact_6293_or__Suc__0__eq)). 159.61/70.67 thf(32478,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)],[7038])). 159.61/70.67 thf(6020,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (uminus_uminus_int @ (numeral_numeral_int @ (bit0 @ A)))) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6023_and__minus__numerals_I1_J)). 159.61/70.67 thf(28502,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)],[6020])). 159.61/70.67 thf(7878,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/sandbox/benchmark/theBenchmark.p',fact_9132_central__binomial__odd)). 159.61/70.67 thf(35434,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)],[7878])). 159.61/70.67 thf(1139,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3028_leI)). 159.61/70.67 thf(11903,plain,((! [A:real,B:real]: ((~ (ord_less_real @ A @ B)) => (ord_less_eq_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139])). 159.61/70.67 thf(6031,axiom,((! [A:real,B:num]: ((archim6058952711729229775r_real @ (minus_minus_real @ A @ (numeral_numeral_real @ B))) = (minus_minus_int @ (archim6058952711729229775r_real @ A) @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8194_floor__diff__numeral)). 159.61/70.67 thf(28538,plain,((! [A:real,B:num]: ((archim6058952711729229775r_real @ (minus_minus_real @ A @ (numeral_numeral_real @ B))) = (minus_minus_int @ (archim6058952711729229775r_real @ A) @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6031])). 159.61/70.67 thf(292,axiom,((! [A:complex,B:complex]: ((ord_less_real @ zero_zero_real @ (re @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_real @ zero_zero_real @ (re @ (times_times_complex @ A @ (cnj @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9690_Re__complex__div__gt__0)). 159.61/70.67 thf(9134,plain,((! [A:complex,B:complex]: ((ord_less_real @ zero_zero_real @ (re @ (divide1717551699836669952omplex @ A @ B))) = (ord_less_real @ zero_zero_real @ (re @ (times_times_complex @ A @ (cnj @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[292])). 159.61/70.67 thf(1341,axiom,((! [A:complex,B:complex,C:complex,D:complex]: ((dvd_dvd_complex @ A @ B) => ((dvd_dvd_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ D)) <= (dvd_dvd_complex @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3965_mult__dvd__mono)). 159.61/70.67 thf(12583,plain,((! [A:complex,B:complex,C:complex,D:complex]: ((dvd_dvd_complex @ A @ B) => ((dvd_dvd_complex @ (times_times_complex @ A @ C) @ (times_times_complex @ B @ D)) | ~ (dvd_dvd_complex @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341])). 159.61/70.67 thf(2124,axiom,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int) <= (ord_less_int @ B @ zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2120_add__neg__neg)). 159.61/70.67 thf(15091,plain,((! [A:int,B:int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_int @ (plus_plus_int @ A @ B) @ zero_zero_int) | ~ (ord_less_int @ B @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2124])). 159.61/70.67 thf(7089,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/sandbox/benchmark/theBenchmark.p',fact_3423_Suc__mod__mult__self4)). 159.61/70.67 thf(32701,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)],[7089])). 159.61/70.67 thf(7671,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/sandbox/benchmark/theBenchmark.p',fact_4289_even__even__mod__4__iff)). 159.61/70.67 thf(34764,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)],[7671])). 159.61/70.67 thf(5349,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((((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)) <= ((A = B) | (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_insert__simp__mima)). 159.61/70.67 thf(25846,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((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) | ~ ((A = B) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5349])). 159.61/70.67 thf(4306,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ B @ A)) = (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3799_dvd__add__triv__right__iff)). 159.61/70.67 thf(22062,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)],[4306])). 159.61/70.67 thf(1475,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/sandbox/benchmark/theBenchmark.p',fact_6412_log__base__change)). 159.61/70.67 thf(13068,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)],[1475])). 159.61/70.67 thf(3722,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/sandbox/benchmark/theBenchmark.p',fact_5914_real__of__int__div__aux)). 159.61/70.67 thf(20222,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)],[3722])). 159.61/70.67 thf(3144,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/sandbox/benchmark/theBenchmark.p',fact_5845_of__int__less__of__int__power__cancel__iff)). 159.61/70.67 thf(18369,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)],[3144])). 159.61/70.67 thf(4079,axiom,((! [A:real,B:real]: ((sqrt @ (divide_divide_real @ A @ B)) = (divide_divide_real @ (sqrt @ A) @ (sqrt @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6369_real__sqrt__divide)). 159.61/70.67 thf(21344,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)],[4079])). 159.61/70.67 thf(1463,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/sandbox/benchmark/theBenchmark.p',fact_7412_sum_Odistrib)). 159.61/70.67 thf(13028,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)],[1463])). 159.61/70.67 thf(5891,axiom,((! [A:real,B:real,C:nat]: (((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ C))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1940_power__strict__mono)). 159.61/70.67 thf(28021,plain,((! [A:real,B:real,C:nat]: (((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ C))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5891])). 159.61/70.67 thf(2257,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/sandbox/benchmark/theBenchmark.p',fact_7197_cos__zero__lemma)). 159.61/70.67 thf(15533,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)],[2257])). 159.61/70.67 thf(8113,axiom,((! [A:set_list_o]: ((finite_finite_list_o @ A) => (? [B:nat]: ! [C:list_o]: ((ord_less_nat @ (size_size_list_o @ C) @ B) <= (member_list_o @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3742_finite__maxlen)). 159.61/70.67 thf(36186,plain,((! [A:set_list_o]: ((finite_finite_list_o @ A) => (? [B:nat]: ! [C:list_o]: ((ord_less_nat @ (size_size_list_o @ C) @ B) | ~ (member_list_o @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8113])). 159.61/70.67 thf(3041,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4453_pinf_I7_J)). 159.61/70.67 thf(18025,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3041])). 159.61/70.67 thf(2146,axiom,((! [A:nat,B:nat]: ((bit_se2923211474154528505it_int @ A @ (semiri1314217659103216013at_int @ B)) = (semiri1314217659103216013at_int @ (bit_se2925701944663578781it_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6713_take__bit__of__nat)). 159.61/70.67 thf(15177,plain,((! [A:nat,B:nat]: ((bit_se2923211474154528505it_int @ A @ (semiri1314217659103216013at_int @ B)) = (semiri1314217659103216013at_int @ (bit_se2925701944663578781it_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2146])). 159.61/70.67 thf(4191,axiom,((! [A:complex,B:complex]: ((uminus1482373934393186551omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1482373934393186551omplex @ B) @ (uminus1482373934393186551omplex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4962_add_Oinverse__distrib__swap)). 159.61/70.67 thf(21690,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)],[4191])). 159.61/70.67 thf(7867,axiom,((! [A:$o]: ((divide_divide_nat @ (zero_n2687167440665602831ol_nat @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4372_of__bool__half__eq__0)). 159.61/70.67 thf(35392,plain,((! [A:$o]: ((divide_divide_nat @ (zero_n2687167440665602831ol_nat @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7867])). 159.61/70.67 thf(5808,axiom,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => ((accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ A) => (((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ ($false) @ ($false)))) <= (A = (vEBT_Leaf @ ($false) @ ($false)))) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9758_VEBT__internal_OminNull_Opelims_I2_J)). 159.61/70.67 thf(27604,plain,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => ((accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ A) => ((~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Leaf @ ($false) @ ($false))) | ~ (A = (vEBT_Leaf @ ($false) @ ($false)))) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D)) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5808])). 159.61/70.67 thf(4023,axiom,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ pi) => ((arccos @ (cos_real @ A)) = (abs_abs_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7715_arccos__cos__eq__abs)). 159.61/70.67 thf(21177,plain,((! [A:real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ pi) => ((arccos @ (cos_real @ A)) = (abs_abs_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4023])). 159.61/70.67 thf(3084,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/sandbox/benchmark/theBenchmark.p',fact_2369_divide__diff__eq__iff)). 159.61/70.67 thf(18157,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)],[3084])). 159.61/70.67 thf(219,axiom,((! [A:nat]: ((sin_coeff @ (suc @ A)) = (divide_divide_real @ (cos_coeff @ A) @ (semiri5074537144036343181t_real @ (suc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8155_sin__coeff__Suc)). 159.61/70.67 thf(8921,plain,((! [A:nat]: ((sin_coeff @ (suc @ A)) = (divide_divide_real @ (cos_coeff @ A) @ (semiri5074537144036343181t_real @ (suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[219])). 159.61/70.67 thf(7582,axiom,((! [A:nat,B:nat]: (((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_le__SucE)). 159.61/70.67 thf(34500,plain,((! [A:nat,B:nat]: (((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B))) | ~ (ord_less_eq_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7582])). 159.61/70.67 thf(2536,axiom,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (numeral_numeral_int @ (bit1 @ A))) = (numeral_numeral_int @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5988_or__numerals_I2_J)). 159.61/70.67 thf(16407,plain,((! [A:num]: ((bit_se1409905431419307370or_int @ one_one_int @ (numeral_numeral_int @ (bit1 @ A))) = (numeral_numeral_int @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2536])). 159.61/70.67 thf(4701,axiom,((! [A:(produc6271795597528267376eger_o > $o),B:produc6271795597528267376eger_o]: ((A @ B) <= (! [C:code_integer,D:$o]: (A @ (produc6677183202524767010eger_o @ C @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3677_prod__cases)). 159.61/70.67 thf(23506,plain,((! [A:(produc6271795597528267376eger_o > $o),B:produc6271795597528267376eger_o]: ((A @ B) | ~ (! [C:code_integer,D:$o]: (A @ (produc6677183202524767010eger_o @ C @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4701])). 159.61/70.67 thf(6725,axiom,((! [A:num,B:num]: ((~ (ord_less_num @ A @ B)) = (~ (ord_less_eq_num @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3036_nless__le)). 159.61/70.67 thf(31184,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)],[6725])). 159.61/70.67 thf(1713,axiom,((! [A:real,B:nat]: ((exp_real @ (times_times_real @ A @ (semiri5074537144036343181t_real @ B))) = (power_power_real @ (exp_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6731_exp__of__nat2__mult)). 159.61/70.67 thf(13787,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)],[1713])). 159.61/70.67 thf(6644,axiom,(((sqrt @ zero_zero_real) = zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6310_real__sqrt__zero)). 159.61/70.67 thf(30767,plain,(((sqrt @ zero_zero_real) = zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6644])). 159.61/70.67 thf(7801,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/sandbox/benchmark/theBenchmark.p',fact_506_left__add__mult__distrib)). 159.61/70.67 thf(35187,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)],[7801])). 159.61/70.67 thf(246,axiom,((! [A:int,B:int]: ((ord_less_eq_int @ A @ B) => ((ord_max_int @ B @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3302_max__absorb1)). 159.61/70.67 thf(9002,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)],[246])). 159.61/70.67 thf(2166,axiom,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ D) => (ord_less_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1223_diff__strict__mono)). 159.61/70.67 thf(15236,plain,((! [A:int,B:int,C:int,D:int]: ((ord_less_int @ A @ B) => ((ord_less_int @ C @ D) => (ord_less_int @ (minus_minus_int @ A @ D) @ (minus_minus_int @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2166])). 159.61/70.67 thf(3406,axiom,((! [A:real,B:real]: ((? [C:real]: ((ord_less_eq_real @ C @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) & (B = (sin_real @ C)) & (A = (cos_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/sandbox/benchmark/theBenchmark.p',fact_7201_sincos__total__2pi__le)). 159.61/70.67 thf(19200,plain,((! [A:real,B:real]: (? [C:real]: ((ord_less_eq_real @ C @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) & (B = (sin_real @ C)) & (A = (cos_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)],[3406])). 159.61/70.67 thf(6497,axiom,((! [A:num]: (one != (bit1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5388_semiring__norm_I84_J)). 159.61/70.67 thf(30237,plain,((! [A:num]: ~ (one = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6497])). 159.61/70.67 thf(4958,axiom,((! [A:(nat > $o),B:nat,C:nat,D:nat]: (((ord_less_nat @ B @ C) => ((ord_less_nat @ D @ C) => ((! [E:nat]: ((ord_less_nat @ E @ C) => ((A @ (modulo_modulo_nat @ (suc @ E) @ C)) <= (A @ E)))) => (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3486_mod__induct)). 159.61/70.67 thf(24376,plain,((! [A:(nat > $o),B:nat,C:nat,D:nat]: (((ord_less_nat @ B @ C) => ((ord_less_nat @ D @ C) => ((! [E:nat]: ((ord_less_nat @ E @ C) => ((A @ (modulo_modulo_nat @ (suc @ E) @ C)) | ~ (A @ E)))) => (A @ D)))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4958])). 159.61/70.67 thf(5827,axiom,((! [A:nat,B:nat]: ((bit_se727722235901077358nd_nat @ A @ (bit_se727722235901077358nd_nat @ A @ B)) = (bit_se727722235901077358nd_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5936_and_Oleft__idem)). 159.61/70.67 thf(27719,plain,((! [A:nat,B:nat]: ((bit_se727722235901077358nd_nat @ A @ (bit_se727722235901077358nd_nat @ A @ B)) = (bit_se727722235901077358nd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5827])). 159.61/70.67 thf(7565,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/sandbox/benchmark/theBenchmark.p',fact_9426_nat__le__numeral__power__cancel__iff)). 159.61/70.67 thf(34384,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)],[7565])). 159.61/70.67 thf(2574,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (((plus_plus_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int)))) <= (ord_less_eq_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2019_add__nonpos__eq__0__iff)). 159.61/70.67 thf(16526,plain,((! [A:int,B:int]: (((ord_less_eq_int @ B @ zero_zero_int) => (((plus_plus_int @ A @ B) = zero_zero_int) = ((B = zero_zero_int) & (A = zero_zero_int)))) | ~ (ord_less_eq_int @ A @ zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2574])). 159.61/70.67 thf(4561,axiom,((! [A:nat]: (((groups2073611262835488442omplex @ (^ [B:nat]: (times_times_complex @ (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (semiri8010041392384452111omplex @ B)) @ (semiri8010041392384452111omplex @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_complex) <= (A != one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9165_choose__alternating__linear__sum)). 159.61/70.67 thf(23000,plain,((! [A:nat]: (((groups2073611262835488442omplex @ (^ [B:nat]: (times_times_complex @ (times_times_complex @ (power_power_complex @ (uminus1482373934393186551omplex @ one_one_complex) @ B) @ (semiri8010041392384452111omplex @ B)) @ (semiri8010041392384452111omplex @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_zero_complex) | (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4561])). 159.61/70.67 thf(6938,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (binomial @ B @ A) @ (power_power_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9053_binomial__le__pow)). 159.61/70.67 thf(31997,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (binomial @ B @ A) @ (power_power_nat @ B @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6938])). 159.61/70.67 thf(7398,axiom,((! [A:num,B:real]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (numeral_numeral_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8187_numeral__le__floor)). 159.61/70.67 thf(33826,plain,((! [A:num,B:real]: ((ord_less_eq_int @ (numeral_numeral_int @ A) @ (archim6058952711729229775r_real @ B)) = (ord_less_eq_real @ (numeral_numeral_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7398])). 159.61/70.67 thf(1268,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/sandbox/benchmark/theBenchmark.p',fact_7535_sum__power__add)). 159.61/70.67 thf(12352,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)],[1268])). 159.61/70.67 thf(509,axiom,(((semiri4939895301339042750nteger @ zero_zero_nat) = zero_z3403309356797280102nteger)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6500_of__nat__0)). 159.61/70.67 thf(9874,plain,(((semiri4939895301339042750nteger @ zero_zero_nat) = zero_z3403309356797280102nteger)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])). 159.61/70.67 thf(1316,axiom,((! [A:real,B:real,C:real]: (((log @ (powr_real @ A @ B) @ C) = (divide_divide_real @ (log @ A @ C) @ B)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7253_log__base__powr)). 159.61/70.67 thf(12503,plain,((! [A:real,B:real,C:real]: (((log @ (powr_real @ A @ B) @ C) = (divide_divide_real @ (log @ A @ C) @ B)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316])). 159.61/70.67 thf(4778,axiom,((! [A:num]: ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bitM @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5918_odd__numeral__BitM)). 159.61/70.67 thf(23765,plain,((! [A:num]: ~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4778])). 159.61/70.67 thf(5377,axiom,((divide_divide_nat = (^ [A:nat,B:nat]: (if_nat @ ((ord_less_nat @ A @ B) | (B = zero_zero_nat)) @ zero_zero_nat @ (suc @ (divide_divide_nat @ (minus_minus_nat @ A @ B) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2478_div__if)). 159.61/70.67 thf(25981,plain,(((divide_divide_nat) = (^ [A:nat,B:nat]: (if_nat @ ((ord_less_nat @ A @ B) | (B = zero_zero_nat)) @ zero_zero_nat @ (suc @ (divide_divide_nat @ (minus_minus_nat @ A @ B) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5377])). 159.61/70.67 thf(3652,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((divide_divide_real @ (abs_abs_real @ B) @ A) = (abs_abs_real @ (divide_divide_real @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5569_abs__div__pos)). 159.61/70.67 thf(19979,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((divide_divide_real @ (abs_abs_real @ B) @ A) = (abs_abs_real @ (divide_divide_real @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3652])). 159.61/70.67 thf(2251,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/sandbox/benchmark/theBenchmark.p',fact_5830_of__int__1__less__iff)). 159.61/70.67 thf(15512,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)],[2251])). 159.61/70.67 thf(3569,axiom,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B)) = (modulo364778990260209775nteger @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3539_minus__div__mult__eq__mod)). 159.61/70.67 thf(19718,plain,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (times_3573771949741848930nteger @ (divide6298287555418463151nteger @ A @ B) @ B)) = (modulo364778990260209775nteger @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3569])). 159.61/70.67 thf(2684,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/sandbox/benchmark/theBenchmark.p',fact_8254_gbinomial__mult__1)). 159.61/70.67 thf(16901,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)],[2684])). 159.61/70.67 thf(4120,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (real_V7735802525324610683m_real @ (inverse_inverse_real @ B)) @ (inverse_inverse_real @ A)) <= (ord_less_real @ zero_zero_real @ A)) <= (ord_less_eq_real @ A @ (real_V7735802525324610683m_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9020_norm__inverse__le__norm)). 159.61/70.67 thf(21468,plain,((! [A:real,B:real]: ((ord_less_eq_real @ (real_V7735802525324610683m_real @ (inverse_inverse_real @ B)) @ (inverse_inverse_real @ A)) | ~ (ord_less_real @ zero_zero_real @ A) | ~ (ord_less_eq_real @ A @ (real_V7735802525324610683m_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4120])). 159.61/70.67 thf(5381,axiom,(((! [A:vEBT_VEBT]: ((~ (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B))) <= (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList)))) <= (mi = ma))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40__C5_C)). 159.61/70.67 thf(25992,plain,((! [A:vEBT_VEBT]: (~ (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B)) | ~ (member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList))) | ~ (mi = ma))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5381])). 159.61/70.67 thf(4497,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/sandbox/benchmark/theBenchmark.p',fact_381_power__add)). 159.61/70.67 thf(22716,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)],[4497])). 159.61/70.67 thf(3316,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/sandbox/benchmark/theBenchmark.p',fact_1377_square__diff__one__factored)). 159.61/70.67 thf(18919,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)],[3316])). 159.61/70.67 thf(2796,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/sandbox/benchmark/theBenchmark.p',fact_8451_prod_OatMost__Suc)). 159.61/70.67 thf(17252,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)],[2796])). 159.61/70.67 thf(6730,axiom,((! [A:num,B:num]: (((numeral_numeral_real @ A) = (numeral_numeral_real @ B)) = (A = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_numeral__eq__iff)). 159.61/70.67 thf(31199,plain,((! [A:num,B:num]: (((numeral_numeral_real @ A) = (numeral_numeral_real @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6730])). 159.61/70.67 thf(4949,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_succ @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = none_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1389_vebt__succ_Osimps_I3_J)). 159.61/70.67 thf(24343,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_succ @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4949])). 159.61/70.67 thf(5601,axiom,((! [A:nat,B:nat]: ((~ ((! [C:nat]: (B != (times_times_nat @ A @ C))) <= (A != zero_zero_nat))) <= (dvd_dvd_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4137_unit__dvdE)). 159.61/70.67 thf(26781,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ~ (B = (times_times_nat @ A @ C)) | (A = zero_zero_nat)) | ~ (dvd_dvd_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5601])). 159.61/70.67 thf(4640,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/sandbox/benchmark/theBenchmark.p',fact_6886_norm__mult__numeral2)). 159.61/70.67 thf(23289,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)],[4640])). 159.61/70.67 thf(6230,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)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1993_mult__nonpos__nonpos)). 159.61/70.67 thf(29183,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)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6230])). 159.61/70.67 thf(5873,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/sandbox/benchmark/theBenchmark.p',fact_4792_semiring__norm_I170_J)). 159.61/70.67 thf(27951,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)],[5873])). 159.61/70.67 thf(1780,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_eq_real @ (times_times_real @ C @ A) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2433_neg__divide__le__eq)). 159.61/70.67 thf(14001,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ C) = (ord_less_eq_real @ (times_times_real @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1780])). 159.61/70.67 thf(4038,axiom,((! [A:(nat > real),B:set_nat]: ((summable_real @ A) => (((! [C:nat]: ((ord_less_eq_real @ zero_zero_real @ (A @ C)) <= (member_nat @ C @ (uminus5710092332889474511et_nat @ B)))) => (ord_less_eq_real @ (groups6591440286371151544t_real @ A @ B) @ (suminf_real @ A))) <= (finite_finite_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7722_sum__le__suminf)). 159.61/70.67 thf(21221,plain,((! [A:(nat > real),B:set_nat]: ((summable_real @ (A)) => (((! [C:nat]: ((ord_less_eq_real @ zero_zero_real @ (A @ C)) | ~ (member_nat @ C @ (uminus5710092332889474511et_nat @ B)))) => (ord_less_eq_real @ (groups6591440286371151544t_real @ (A) @ B) @ (suminf_real @ (A)))) | ~ (finite_finite_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4038])). 159.61/70.67 thf(3742,axiom,((! [A:nat,B:nat,C:nat]: (((power_power_complex @ (semiri8010041392384452111omplex @ A) @ B) = (semiri8010041392384452111omplex @ C)) = ((power_power_nat @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6564_of__nat__eq__of__nat__power__cancel__iff)). 159.61/70.67 thf(20292,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)],[3742])). 159.61/70.67 thf(5535,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/sandbox/benchmark/theBenchmark.p',fact_6636_numeral__power__le__of__nat__cancel__iff)). 159.61/70.67 thf(26558,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)],[5535])). 159.61/70.67 thf(2510,axiom,((abs_abs_int = (^ [A:int]: (if_int @ (ord_less_int @ A @ zero_zero_int) @ (uminus_uminus_int @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5577_abs__if)). 159.61/70.67 thf(16331,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)],[2510])). 159.61/70.67 thf(7163,axiom,((! [A:set_nat,B:(nat > nat)]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (groups708209901874060359at_nat @ B @ A)) = (? [C:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (B @ C)) & (member_nat @ C @ A)))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8783_even__prod__iff)). 159.61/70.67 thf(32980,plain,((! [A:set_nat,B:(nat > nat)]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (groups708209901874060359at_nat @ (B) @ A)) = (? [C:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (B @ C)) & (member_nat @ C @ A)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7163])). 159.61/70.67 thf(2306,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) => ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2250_mult__left__less__imp__less)). 159.61/70.67 thf(15673,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) => ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2306])). 159.61/70.67 thf(6588,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => ((modulo_modulo_nat @ A @ B) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3494_unique__euclidean__semiring__numeral__class_Omod__less)). 159.61/70.67 thf(30553,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => ((modulo_modulo_nat @ A @ B) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6588])). 159.61/70.67 thf(923,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/sandbox/benchmark/theBenchmark.p',fact_8346_pochhammer__minus)). 159.61/70.67 thf(11209,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)],[923])). 159.61/70.67 thf(7276,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2225_mult__le__less__imp__less)). 159.61/70.67 thf(33397,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C @ D) => ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7276])). 159.61/70.67 thf(8198,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:vEBT_VEBT,J:vEBT_VEBT,K:list_VEBT_VEBT]: (((A != C) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => (((vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = E) => ((((((K = (list_u1324408373059187874T_VEBT @ H @ E @ G)) => (((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ H @ J) @ B) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (if_nat @ ((vEBT_vebt_maxt @ I) = none_nat) @ A @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ I))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ (the_nat @ (vEBT_vebt_maxt @ I))))))) @ C))) @ D @ K @ I)) <= (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)))) <= (I = (vEBT_vebt_delete @ J @ E))) <= (vEBT_VEBT_minNull @ G)) <= (G = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ E) @ F))) <= ((vEBT_VEBT_low @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F))))) <= ((ord_less_nat @ A @ B) & (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1398_del__x__not__mi__new__node__nil)). 159.61/70.67 thf(36464,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat,F:nat,G:vEBT_VEBT,H:list_VEBT_VEBT,I:vEBT_VEBT,J:vEBT_VEBT,K:list_VEBT_VEBT]: (((~ (A = C)) => ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D) => (((vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = E) => (((K = (list_u1324408373059187874T_VEBT @ H @ E @ G)) => (((vEBT_vebt_delete @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ C)) @ D @ H @ J) @ B) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ (if_nat @ (B = C) @ (if_nat @ ((vEBT_vebt_maxt @ I) = none_nat) @ A @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ I))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ K @ (the_nat @ (vEBT_vebt_maxt @ I))))))) @ C))) @ D @ K @ I)) | ~ (ord_less_nat @ (vEBT_VEBT_high @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ H)))) | ~ (I = (vEBT_vebt_delete @ J @ E)) | ~ (vEBT_VEBT_minNull @ G) | ~ (G = (vEBT_vebt_delete @ (nth_VEBT_VEBT @ H @ E) @ F)) | ~ ((vEBT_VEBT_low @ B @ (divide_divide_nat @ D @ (numeral_numeral_nat @ (bit0 @ one)))) = F))))) | ~ ((ord_less_nat @ A @ B) & (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8198])). 159.61/70.67 thf(7669,axiom,((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4206_odd__one)). 159.61/70.67 thf(34759,plain,((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7669])). 159.61/70.67 thf(1836,axiom,((! [A:complex,B:complex,C:complex]: ((divide1717551699836669952omplex @ A @ (divide1717551699836669952omplex @ B @ C)) = (divide1717551699836669952omplex @ (times_times_complex @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1384_divide__divide__eq__right)). 159.61/70.67 thf(14191,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)],[1836])). 159.61/70.67 thf(8039,axiom,((vEBT_VEBT_high = (^ [A:nat,B:nat]: (divide_divide_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_high__def)). 159.61/70.67 thf(35951,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)],[8039])). 159.61/70.67 thf(313,axiom,((ord_less_eq_int = (^ [A:int,B:int]: (B = (ord_max_int @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_max_Oorder__iff)). 159.61/70.67 thf(9215,plain,(((ord_less_eq_int) = (^ [A:int,B:int]: (B = (ord_max_int @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 159.61/70.67 thf(5658,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]: (((C @ D) & (A @ D)) = ((C @ (minus_minus_int @ D @ (times_times_int @ E @ B))) & (A @ (minus_minus_int @ D @ (times_times_int @ E @ B)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4518_inf__period_I1_J)). 159.61/70.67 thf(26975,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]: (((C @ D) & (A @ D)) = ((C @ (minus_minus_int @ D @ (times_times_int @ E @ B))) & (A @ (minus_minus_int @ D @ (times_times_int @ E @ B)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5658])). 159.61/70.67 thf(1996,axiom,((minus_minus_complex = (^ [A:complex,B:complex]: (plus_plus_complex @ A @ (uminus1482373934393186551omplex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5108_ab__group__add__class_Oab__diff__conv__add__uminus)). 159.61/70.67 thf(14704,plain,(((minus_minus_complex) = (^ [A:complex,B:complex]: (plus_plus_complex @ A @ (uminus1482373934393186551omplex @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1996])). 159.61/70.67 thf(5716,axiom,((! [A:num,B:nat]: (((numeral_numeral_nat @ A) = (suc @ B)) = ((pred_numeral @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5682_eq__numeral__Suc)). 159.61/70.67 thf(27173,plain,((! [A:num,B:nat]: (((numeral_numeral_nat @ A) = (suc @ B)) = ((pred_numeral @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5716])). 159.61/70.67 thf(621,axiom,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2963_subset__refl)). 159.61/70.67 thf(10237,plain,((! [A:set_nat]: (ord_less_eq_set_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[621])). 159.61/70.67 thf(2989,axiom,((ord_le72135733267957522d_enat = (^ [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) & (B != A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3111_dual__order_Ostrict__iff__order)). 159.61/70.67 thf(17868,plain,(((ord_le72135733267957522d_enat) = (^ [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ B) & ~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2989])). 159.61/70.67 thf(2525,axiom,((! [A:nat,B:nat,C:int]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ C) @ (bit_se2923211474154528505it_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5019_take__bit__tightened__less__eq__int)). 159.61/70.67 thf(16378,plain,((! [A:nat,B:nat,C:int]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_int @ (bit_se2923211474154528505it_int @ A @ C) @ (bit_se2923211474154528505it_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2525])). 159.61/70.67 thf(4842,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 @ 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/sandbox/benchmark/theBenchmark.p',fact_1978_split__mult__neg__le)). 159.61/70.67 thf(24007,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 @ 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)],[4842])). 159.61/70.67 thf(6334,axiom,((bit_se727722235901077358nd_nat = (^ [A:nat,B:nat]: (bit_se727722235901077358nd_nat @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6046_and_Ocommute)). 159.61/70.67 thf(29592,plain,(((bit_se727722235901077358nd_nat) = (^ [A:nat,B:nat]: (bit_se727722235901077358nd_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6334])). 159.61/70.67 thf(7388,axiom,((! [A:num]: (ord_less_eq_int @ zero_zero_int @ (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1958_zero__le__numeral)). 159.61/70.67 thf(33794,plain,((! [A:num]: (ord_less_eq_int @ zero_zero_int @ (numeral_numeral_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7388])). 159.61/70.67 thf(7064,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_max_nat @ A @ B) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_max_Oabsorb__iff2)). 159.61/70.67 thf(32592,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_max_nat @ A @ B) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7064])). 159.61/70.67 thf(1065,axiom,((! [A:complex]: ((real_V2046097035970521341omplex @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_complex @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9248_scaleR__2)). 159.61/70.67 thf(11668,plain,((! [A:complex]: ((real_V2046097035970521341omplex @ (numeral_numeral_real @ (bit0 @ one)) @ A) = (plus_plus_complex @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065])). 159.61/70.67 thf(4610,axiom,((! [A:int]: (ord_less_eq_int @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3666_verit__comp__simplify1_I2_J)). 159.61/70.67 thf(23188,plain,((! [A:int]: (ord_less_eq_int @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4610])). 159.61/70.67 thf(7687,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/sandbox/benchmark/theBenchmark.p',fact_7_high__inv)). 159.61/70.67 thf(34816,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)],[7687])). 159.61/70.67 thf(3441,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/sandbox/benchmark/theBenchmark.p',fact_7766_sin__arccos__nonzero)). 159.61/70.67 thf(19313,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)],[3441])). 159.61/70.67 thf(4507,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2798_dual__order_Oasym)). 159.61/70.67 thf(22751,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (ord_less_num @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4507])). 159.61/70.67 thf(2639,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat,D:extended_enat]: (((((ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ A @ C) @ (times_7803423173614009249d_enat @ B @ D)) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C)) <= (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B)) <= (ord_le2932123472753598470d_enat @ C @ D)) <= (ord_le2932123472753598470d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2004_mult__mono)). 159.61/70.67 thf(16756,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat,D:extended_enat]: ((ord_le2932123472753598470d_enat @ (times_7803423173614009249d_enat @ A @ C) @ (times_7803423173614009249d_enat @ B @ D)) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ C) | ~ (ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ B) | ~ (ord_le2932123472753598470d_enat @ C @ D) | ~ (ord_le2932123472753598470d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2639])). 159.61/70.67 thf(7610,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) => ((ord_less_nat @ zero_zero_nat @ A) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2082_zero__less__mult__pos2)). 159.61/70.67 thf(34586,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_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)],[7610])). 159.61/70.67 thf(4712,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 @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1208_diff__mono)). 159.61/70.67 thf(23538,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 @ (minus_minus_real @ A @ D) @ (minus_minus_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4712])). 159.61/70.67 thf(485,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)) = (ord_less_real @ C @ (real_V1485227260804924795R_real @ A @ B))) <= (ord_less_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9260_neg__less__divideR__eq)). 159.61/70.67 thf(9795,plain,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ (real_V1485227260804924795R_real @ (inverse_inverse_real @ A) @ C)) = (ord_less_real @ C @ (real_V1485227260804924795R_real @ A @ B))) | ~ (ord_less_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[485])). 159.61/70.67 thf(2325,axiom,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ C) => (dvd_dvd_real @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3956_dvd__mult__left)). 159.61/70.67 thf(15726,plain,((! [A:real,B:real,C:real]: ((dvd_dvd_real @ (times_times_real @ A @ B) @ C) => (dvd_dvd_real @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2325])). 159.61/70.67 thf(374,axiom,((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ zero_z3403309356797280102nteger)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4187_even__zero)). 159.61/70.67 thf(9414,plain,((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ zero_z3403309356797280102nteger)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])). 159.61/70.67 thf(2159,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/sandbox/benchmark/theBenchmark.p',fact_5750_of__int__code__if)). 159.61/70.67 thf(15213,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)],[2159])). 159.61/70.67 thf(4923,axiom,((! [A:nat,B:nat,C:nat]: ((ord_min_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ C @ B)) = (minus_minus_nat @ (ord_min_nat @ A @ C) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10173_min__diff)). 159.61/70.67 thf(24268,plain,((! [A:nat,B:nat,C:nat]: ((ord_min_nat @ (minus_minus_nat @ A @ B) @ (minus_minus_nat @ C @ B)) = (minus_minus_nat @ (ord_min_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4923])). 159.61/70.67 thf(1099,axiom,((! [A:int,B:int,C:int,D: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))) <= (A != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4149_dvd__div__div__eq__mult)). 159.61/70.67 thf(11779,plain,((! [A:int,B:int,C:int,D: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))) | (A = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099])). 159.61/70.67 thf(5215,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_Suc__lessD)). 159.61/70.67 thf(25318,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5215])). 159.61/70.67 thf(2957,axiom,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ A @ (divide6298287555418463151nteger @ B @ A)) @ (modulo364778990260209775nteger @ B @ A)) = B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3506_mult__div__mod__eq)). 159.61/70.67 thf(17778,plain,((! [A:code_integer,B:code_integer]: ((plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ A @ (divide6298287555418463151nteger @ B @ A)) @ (modulo364778990260209775nteger @ B @ A)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2957])). 159.61/70.67 thf(1741,axiom,((~ (ord_less_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5159_less__minus__one__simps_I3_J)). 159.61/70.67 thf(13877,plain,((~ (ord_less_real @ zero_zero_real @ (uminus_uminus_real @ one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741])). 159.61/70.67 thf(2609,axiom,((! [A:(complex > (complex > $o)),B:set_nat,C:(nat > complex),D:(nat > complex)]: ((A @ zero_zero_complex @ zero_zero_complex) => ((((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups2073611262835488442omplex @ C @ B) @ (groups2073611262835488442omplex @ D @ B))) <= (finite_finite_nat @ 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)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7485_sum_Orelated)). 159.61/70.67 thf(16642,plain,((! [A:(complex > (complex > $o)),B:set_nat,C:(nat > complex),D:(nat > complex)]: ((A @ zero_zero_complex @ zero_zero_complex) => (((! [E:nat]: ((member_nat @ E @ B) => (A @ (C @ E) @ (D @ E)))) => (A @ (groups2073611262835488442omplex @ (C) @ B) @ (groups2073611262835488442omplex @ (D) @ B))) | ~ (finite_finite_nat @ 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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2609])). 159.61/70.67 thf(4605,axiom,((! [A:set_nat,B:(nat > 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))) & (((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (B @ C) @ (power_power_real @ zero_zero_real @ C))) @ A) = zero_zero_real) <= (~ ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7365_sum__zero__power)). 159.61/70.67 thf(23165,plain,((! [A:set_nat,B:(nat > 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))) & (((groups6591440286371151544t_real @ (^ [C:nat]: (times_times_real @ (B @ C) @ (power_power_real @ zero_zero_real @ C))) @ A) = zero_zero_real) | ((member_nat @ zero_zero_nat @ A) & (finite_finite_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4605])). 159.61/70.67 thf(1517,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)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2140_divide__nonpos__nonneg)). 159.61/70.67 thf(13194,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)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517])). 159.61/70.67 thf(3175,axiom,((! [A:real,B:real,C:real]: (((ord_less_real @ B @ (divide_divide_real @ C @ A)) <= (ord_less_real @ (times_times_real @ B @ A) @ C)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2326_mult__imp__less__div__pos)). 159.61/70.67 thf(18467,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ B @ (divide_divide_real @ C @ A)) | ~ (ord_less_real @ (times_times_real @ B @ A) @ C) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3175])). 159.61/70.67 thf(3658,axiom,((! [A:(nat > (nat > $o)),B:(product_prod_nat_nat > $o)]: (((produc6081775807080527818_nat_o @ A) = B) <= (! [C:nat,D:nat]: ((A @ C @ D) = (B @ (product_Pair_nat_nat @ C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5002_cond__case__prod__eta)). 159.61/70.67 thf(20002,plain,((! [A:(nat > (nat > $o)),B:(product_prod_nat_nat > $o)]: (((produc6081775807080527818_nat_o @ A) = (B)) | ~ (! [C:nat,D:nat]: ((A @ C @ D) = (B @ (product_Pair_nat_nat @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3658])). 159.61/70.67 thf(2037,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4941_verit__negate__coefficient_I2_J)). 159.61/70.67 thf(14828,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)],[2037])). 159.61/70.67 thf(862,axiom,((! [A:num,B:num]: ((ord_less_real @ (numeral_numeral_real @ A) @ (numeral_numeral_real @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_numeral__less__iff)). 159.61/70.67 thf(11028,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)],[862])). 159.61/70.67 thf(6400,axiom,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ A))) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6002_and__numerals_I1_J)). 159.61/70.67 thf(29851,plain,((! [A:num]: ((bit_se725231765392027082nd_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ A))) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6400])). 159.61/70.67 thf(5918,axiom,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((((ord_less_nat @ (C @ A) @ D) <= (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) <= (ord_less_eq_nat @ E @ F)))) <= (ord_less_nat @ (C @ B) @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3230_order__le__less__subst2)). 159.61/70.67 thf(28122,plain,((! [A:nat,B:nat,C:(nat > nat),D:nat]: ((ord_less_nat @ (C @ A) @ D) | ~ (! [E:nat,F:nat]: ((ord_less_eq_nat @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_nat @ E @ F))) | ~ (ord_less_nat @ (C @ B) @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5918])). 159.61/70.67 thf(4646,axiom,((! [A:real,B:real]: (((times_times_real @ A @ B) != zero_zero_real) => ((A != zero_zero_real) & (B != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1870_mult__not__zero)). 159.61/70.67 thf(23307,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)],[4646])). 159.61/70.67 thf(511,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/sandbox/benchmark/theBenchmark.p',fact_9612_or__not__numerals_I5_J)). 159.61/70.67 thf(9883,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)],[511])). 159.61/70.67 thf(4874,axiom,((! [A:nat,B:nat]: (((ord_max_nat @ A @ B) = B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_max_Oabsorb4)). 159.61/70.67 thf(24102,plain,((! [A:nat,B:nat]: (((ord_max_nat @ A @ B) = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4874])). 159.61/70.67 thf(5545,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/sandbox/benchmark/theBenchmark.p',fact_6881_pi__series)). 159.61/70.67 thf(26590,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)],[5545])). 159.61/70.67 thf(4110,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/sandbox/benchmark/theBenchmark.p',fact_8253_gbinomial__ge__n__over__k__pow__k)). 159.61/70.67 thf(21436,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)],[4110])). 159.61/70.67 thf(885,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/sandbox/benchmark/theBenchmark.p',fact_2979_subset__eq)). 159.61/70.67 thf(11099,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)],[885])). 159.61/70.67 thf(4944,axiom,((! [A:complex]: ((one_one_complex = A) = (A = one_one_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153_one__reorient)). 159.61/70.67 thf(24329,plain,((! [A:complex]: ((one_one_complex = A) = (A = one_one_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4944])). 159.61/70.67 thf(3259,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/sandbox/benchmark/theBenchmark.p',fact_7667_sum_OatLeast__Suc__atMost)). 159.61/70.67 thf(18740,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)],[3259])). 159.61/70.67 thf(494,axiom,((! [A:code_integer,B:nat]: ((comm_s8582702949713902594nteger @ A @ (suc @ B)) = (times_3573771949741848930nteger @ (plus_p5714425477246183910nteger @ A @ (semiri4939895301339042750nteger @ B)) @ (comm_s8582702949713902594nteger @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8277_pochhammer__rec_H)). 159.61/70.67 thf(9827,plain,((! [A:code_integer,B:nat]: ((comm_s8582702949713902594nteger @ A @ (suc @ B)) = (times_3573771949741848930nteger @ (plus_p5714425477246183910nteger @ A @ (semiri4939895301339042750nteger @ B)) @ (comm_s8582702949713902594nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[494])). 159.61/70.67 thf(3374,axiom,((! [A:nat]: ((set_ord_lessThan_nat @ (suc @ A)) = (set_ord_atMost_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8526_lessThan__Suc__atMost)). 159.61/70.67 thf(19096,plain,((! [A:nat]: ((set_ord_lessThan_nat @ (suc @ A)) = (set_ord_atMost_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3374])). 159.61/70.67 thf(3304,axiom,((! [A:real,B:real]: (((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)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6401_sqrt__add__le__add__sqrt)). 159.61/70.67 thf(18882,plain,((! [A:real,B:real]: ((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) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3304])). 159.61/70.67 thf(2917,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_eq_real @ (cosh_real @ A) @ (cosh_real @ B)) = (ord_less_eq_real @ A @ B)) <= (ord_less_eq_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9335_cosh__real__nonneg__le__iff)). 159.61/70.67 thf(17648,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => (((ord_less_eq_real @ (cosh_real @ A) @ (cosh_real @ B)) = (ord_less_eq_real @ A @ B)) | ~ (ord_less_eq_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2917])). 159.61/70.67 thf(4366,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) => ((ord_le72135733267957522d_enat @ B @ zero_z5237406670263579293d_enat) => (ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ zero_z5237406670263579293d_enat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2267_add__nonpos__neg)). 159.61/70.67 thf(22235,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le2932123472753598470d_enat @ A @ zero_z5237406670263579293d_enat) => ((ord_le72135733267957522d_enat @ B @ zero_z5237406670263579293d_enat) => (ord_le72135733267957522d_enat @ (plus_p3455044024723400733d_enat @ A @ B) @ zero_z5237406670263579293d_enat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4366])). 159.61/70.67 thf(7815,axiom,(((finite_card_char @ top_top_set_char) = (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ (bit0 @ one))))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9823_card__UNIV__char)). 159.61/70.67 thf(35228,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)],[7815])). 159.61/70.67 thf(2429,axiom,((! [A:real]: (((times_times_real @ (inverse_inverse_real @ A) @ A) = one_one_real) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9005_left__inverse)). 159.61/70.67 thf(16073,plain,((! [A:real]: (((times_times_real @ (inverse_inverse_real @ A) @ A) = one_one_real) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2429])). 159.61/70.67 thf(7319,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6011_or__numerals_I1_J)). 159.61/70.67 thf(33565,plain,((! [A:num]: ((bit_se1412395901928357646or_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7319])). 159.61/70.67 thf(2001,axiom,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ A) <= (ord_less_real @ C @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4478_minf_I5_J)). 159.61/70.67 thf(14717,plain,((! [A:real]: ? [B:real]: ! [C:real]: ((ord_less_real @ C @ A) | ~ (ord_less_real @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2001])). 159.61/70.67 thf(2099,axiom,((! [A:int]: ((bit_se2923211474154528505it_int @ zero_zero_nat @ A) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4721_take__bit__0)). 159.61/70.67 thf(15012,plain,((! [A:int]: ((bit_se2923211474154528505it_int @ zero_zero_nat @ A) = zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2099])). 159.61/70.67 thf(1531,axiom,((! [A:real,B:real]: ((~ (ord_less_real @ B @ A)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3021_leD)). 159.61/70.67 thf(13235,plain,((! [A:real,B:real]: (~ (ord_less_real @ B @ A) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531])). 159.61/70.67 thf(7299,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((! [D:nat,E:nat]: ((A @ D @ E) => (A @ D @ (plus_plus_nat @ 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/sandbox/benchmark/theBenchmark.p',fact_4266_Euclid__induct)). 159.61/70.67 thf(33479,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((A @ D @ E) => (A @ D @ (plus_plus_nat @ 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)],[7299])). 159.61/70.67 thf(372,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/sandbox/benchmark/theBenchmark.p',fact_3321_set__bit__negative__int__iff)). 159.61/70.67 thf(9409,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)],[372])). 159.61/70.67 thf(7656,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/sandbox/benchmark/theBenchmark.p',fact_7789_sum_Oin__pairs)). 159.61/70.67 thf(34719,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)],[7656])). 159.61/70.67 thf(3457,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/sandbox/benchmark/theBenchmark.p',fact_6304_arctan__half)). 159.61/70.67 thf(19360,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)],[3457])). 159.61/70.67 thf(6594,axiom,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1253_comm__monoid__mult__class_Omult__1)). 159.61/70.67 thf(30585,plain,((! [A:real]: ((times_times_real @ one_one_real @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6594])). 159.61/70.67 thf(1110,axiom,(((('?') @ extended_enat) = (^ [A:(extended_enat > $o)]: ? [B:extended_enat]: (! [C:extended_enat]: ((ord_le72135733267957522d_enat @ C @ B) => (~ (A @ C))) & (A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2806_exists__least__iff)). 159.61/70.67 thf(11818,plain,(((('?') @ extended_enat) = (^ [A:(extended_enat > $o)]: ? [B:extended_enat]: (! [C:extended_enat]: ((ord_le72135733267957522d_enat @ C @ B) => (~ (A @ C))) & (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110])). 159.61/70.67 thf(7124,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/sandbox/benchmark/theBenchmark.p',fact_303_four__x__squared)). 159.61/70.67 thf(32845,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)],[7124])). 159.61/70.67 thf(6724,axiom,((! [A:nat,B:code_integer]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (power_8256067586552552935nteger @ B @ A))) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ B @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5290_uminus__power__if)). 159.61/70.67 thf(31177,plain,((! [A:nat,B:code_integer]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (power_8256067586552552935nteger @ B @ A))) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (power_8256067586552552935nteger @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6724])). 159.61/70.67 thf(4998,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)) | ((ord_less_eq_real @ zero_zero_real @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3886_zero__le__power__eq__numeral)). 159.61/70.67 thf(24552,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)) | ((ord_less_eq_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)],[4998])). 159.61/70.67 thf(7333,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ B)) = (((A != zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ((ord_less_real @ zero_zero_real @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4264_zero__less__power__eq)). 159.61/70.67 thf(33611,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ B)) = ((~ (A = zero_zero_real) & (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ((ord_less_real @ zero_zero_real @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7333])). 159.61/70.67 thf(6867,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/sandbox/benchmark/theBenchmark.p',fact_5236_take__bit__minus__small__eq)). 159.61/70.67 thf(31754,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)],[6867])). 159.61/70.67 thf(6771,axiom,((! [A:nat,B:nat,C:(nat > extended_enat),D:(nat > extended_enat)]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ A) => ((groups7961826882256487087d_enat @ (^ [E:nat]: (if_Extended_enat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_Extended_enat @ (E = B) @ one_on7984719198319812577d_enat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups7961826882256487087d_enat @ (^ [E:nat]: (if_Extended_enat @ (ord_less_nat @ E @ B) @ (C @ E) @ (D @ E))) @ (set_ord_atMost_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8633_prod_Ozero__middle)). 159.61/70.67 thf(31356,plain,((! [A:nat,B:nat,C:(nat > extended_enat),D:(nat > extended_enat)]: ((ord_less_eq_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ A) => ((groups7961826882256487087d_enat @ (^ [E:nat]: (if_Extended_enat @ (ord_less_nat @ E @ B) @ (C @ E) @ (if_Extended_enat @ (E = B) @ one_on7984719198319812577d_enat @ (D @ (minus_minus_nat @ E @ (suc @ zero_zero_nat)))))) @ (set_ord_atMost_nat @ A)) = (groups7961826882256487087d_enat @ (^ [E:nat]: (if_Extended_enat @ (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)],[6771])). 159.61/70.67 thf(2341,axiom,(((real_V1022390504157884413omplex @ imaginary_unit) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9314_norm__ii)). 159.61/70.67 thf(15773,plain,(((real_V1022390504157884413omplex @ imaginary_unit) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2341])). 159.61/70.67 thf(4680,axiom,((! [A:nat]: ((binomial @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8998_binomial__n__0)). 159.61/70.67 thf(23431,plain,((! [A:nat]: ((binomial @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4680])). 159.61/70.67 thf(4674,axiom,((! [A:option_nat]: ((A != none_nat) => (~ (! [B:nat]: (A != (some_nat @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_option_Oexhaust)). 159.61/70.67 thf(23414,plain,((! [A:option_nat]: ((~ (A = none_nat)) => (~ (! [B:nat]: ~ (A = (some_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4674])). 159.61/70.67 thf(363,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/sandbox/benchmark/theBenchmark.p',fact_9673_inverse__complex_Osimps_I1_J)). 159.61/70.67 thf(9382,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)],[363])). 159.61/70.67 thf(4841,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/sandbox/benchmark/theBenchmark.p',fact_4877_diff__numeral__special_I4_J)). 159.61/70.67 thf(24004,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)],[4841])). 159.61/70.67 thf(935,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (powr_real @ A @ B)) = (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7212_powr__gt__zero)). 159.61/70.67 thf(11246,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (powr_real @ A @ B)) = (~ (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[935])). 159.61/70.67 thf(7157,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => ((B != zero_zero_int) => ((times_times_int @ A @ B) != zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1862_no__zero__divisors)). 159.61/70.67 thf(32961,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int)) => ((~ (B = zero_zero_int)) => (~ ((times_times_int @ A @ B) = zero_zero_int)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7157])). 159.61/70.67 thf(1135,axiom,((! [A:real]: ((uminus_uminus_real @ (sin_real @ A)) = (cos_real @ (plus_plus_real @ A @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7799_minus__sin__cos__eq)). 159.61/70.67 thf(11890,plain,((! [A:real]: ((uminus_uminus_real @ (sin_real @ A)) = (cos_real @ (plus_plus_real @ A @ (divide_divide_real @ (real_V1803761363581548252l_real @ pi) @ (numeral_numeral_real @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135])). 159.61/70.67 thf(7555,axiom,((! [A:option4927543243414619207at_nat]: ((A != none_P5556105721700978146at_nat) = (? [B:product_prod_nat_nat]: (A = (some_P7363390416028606310at_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_not__None__eq)). 159.61/70.67 thf(34357,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)],[7555])). 159.61/70.67 thf(977,axiom,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3667_verit__comp__simplify1_I1_J)). 159.61/70.67 thf(11377,plain,((! [A:extended_enat]: ~ (ord_le72135733267957522d_enat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[977])). 159.61/70.67 thf(1578,axiom,((! [A:real,B:real]: ((uminus_uminus_real @ (divide_divide_real @ A @ B)) = (divide_divide_real @ A @ (uminus_uminus_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4987_minus__divide__right)). 159.61/70.67 thf(13377,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)],[1578])). 159.61/70.67 thf(8030,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (((C = zero_zero_nat) => (A @ zero_zero_nat)) & ((C != zero_zero_nat) => (! [D:nat,E:nat]: ((ord_less_nat @ E @ C) => ((B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)) => (A @ D))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2485_split__div)). 159.61/70.67 thf(35919,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (((C = zero_zero_nat) => (A @ zero_zero_nat)) & ((~ (C = zero_zero_nat)) => (! [D:nat,E:nat]: ((ord_less_nat @ E @ C) => ((B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)) => (A @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8030])). 159.61/70.67 thf(3841,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/sandbox/benchmark/theBenchmark.p',fact_3475_cong__exp__iff__simps_I9_J)). 159.61/70.67 thf(20616,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)],[3841])). 159.61/70.67 thf(5386,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((A = zero_zero_real) <= (! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_eq_real @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ A) @ B)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6758_real__archimedian__rdiv__eq__0)). 159.61/70.67 thf(26007,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => ((A = zero_zero_real) | ~ (! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_eq_real @ (times_times_real @ (semiri5074537144036343181t_real @ C) @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5386])). 159.61/70.67 thf(6229,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/sandbox/benchmark/theBenchmark.p',fact_9137_binomial__fact)). 159.61/70.67 thf(29180,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)],[6229])). 159.61/70.67 thf(4040,axiom,((bit_se1412395901928357646or_nat = (^ [A:nat,B:nat]: (nat2 @ (bit_se1409905431419307370or_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9441_or__nat__def)). 159.61/70.67 thf(21228,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)],[4040])). 159.61/70.67 thf(5120,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1475_le__zero__eq)). 159.61/70.67 thf(24972,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5120])). 159.61/70.67 thf(3506,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A)) <= (ord_less_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9024_less__imp__inverse__less)). 159.61/70.67 thf(19509,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (inverse_inverse_real @ B) @ (inverse_inverse_real @ A)) | ~ (ord_less_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3506])). 159.61/70.67 thf(6135,axiom,((! [A:int,B:int]: (((A != zero_zero_int) & (B != zero_zero_int)) <= ((times_times_int @ A @ B) != zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1872_mult__not__zero)). 159.61/70.67 thf(28866,plain,((! [A:int,B:int]: ((~ (A = zero_zero_int) & ~ (B = zero_zero_int)) | ((times_times_int @ A @ B) = zero_zero_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6135])). 159.61/70.67 thf(6801,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/sandbox/benchmark/theBenchmark.p',fact_4273_even__mask__div__iff)). 159.61/70.67 thf(31447,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)],[6801])). 159.61/70.67 thf(3269,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/sandbox/benchmark/theBenchmark.p',fact_3006_neg__zdiv__mult__2)). 159.61/70.67 thf(18776,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)],[3269])). 159.61/70.67 thf(6900,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/sandbox/benchmark/theBenchmark.p',fact_2217_vebt__insert_Osimps_I2_J)). 159.61/70.67 thf(31857,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)],[6900])). 159.61/70.67 thf(6318,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/sandbox/benchmark/theBenchmark.p',fact_8473_prod__power__distrib)). 159.61/70.67 thf(29550,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)],[6318])). 159.61/70.67 thf(4021,axiom,((! [A:int]: ((bit_se725231765392027082nd_int @ one_one_int @ A) = (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6108_one__and__eq)). 159.61/70.67 thf(21172,plain,((! [A:int]: ((bit_se725231765392027082nd_int @ one_one_int @ A) = (modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4021])). 159.61/70.67 thf(5325,axiom,((! [A:extended_enat]: ((one_on7984719198319812577d_enat = A) = (A = one_on7984719198319812577d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1152_one__reorient)). 159.61/70.67 thf(25731,plain,((! [A:extended_enat]: ((one_on7984719198319812577d_enat = A) = (A = one_on7984719198319812577d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5325])). 159.61/70.67 thf(7048,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/sandbox/benchmark/theBenchmark.p',fact_804_left__diff__distrib__numeral)). 159.61/70.67 thf(32513,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)],[7048])). 159.61/70.67 thf(6099,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/sandbox/benchmark/theBenchmark.p',fact_807_right__diff__distrib__numeral)). 159.61/70.67 thf(28746,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)],[6099])). 159.61/70.67 thf(7149,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/sandbox/benchmark/theBenchmark.p',fact_4977_minus__diff__minus)). 159.61/70.67 thf(32937,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)],[7149])). 159.61/70.67 thf(3319,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/sandbox/benchmark/theBenchmark.p',fact_4734_dbl__simps_I1_J)). 159.61/70.67 thf(18929,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)],[3319])). 159.61/70.67 thf(5457,axiom,((! [A:nat,B:nat,C:(nat > real)]: (((~ (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)) = zero_zero_real)) & ((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/sandbox/benchmark/theBenchmark.p',fact_7776_sum__natinterval__diff)). 159.61/70.67 thf(26295,plain,((! [A:nat,B:nat,C:(nat > real)]: (((~ (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)) = zero_zero_real)) & ((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)],[5457])). 159.61/70.67 thf(3858,axiom,((! [A:real]: ((ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ (archim6058952711729229775r_real @ A) @ one_one_int))) & (ord_less_eq_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8303_floor__correct)). 159.61/70.67 thf(20671,plain,((! [A:real]: ((ord_less_real @ A @ (ring_1_of_int_real @ (plus_plus_int @ (archim6058952711729229775r_real @ A) @ one_one_int))) & (ord_less_eq_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ A)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3858])). 159.61/70.67 thf(4313,axiom,((! [A:(nat > real),B:real]: ((! [C:real]: (summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ C @ D))))) => (summable_real @ (^ [C:nat]: (times_times_real @ (diffs_real @ A @ C) @ (power_power_real @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8116_termdiff__converges__all)). 159.61/70.67 thf(22079,plain,((! [A:(nat > real),B:real]: ((! [C:real]: (summable_real @ (^ [D:nat]: (times_times_real @ (A @ D) @ (power_power_real @ C @ D))))) => (summable_real @ (^ [C:nat]: (times_times_real @ (diffs_real @ A @ C) @ (power_power_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4313])). 159.61/70.67 thf(4409,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/sandbox/benchmark/theBenchmark.p',fact_7092_sin__diff)). 159.61/70.67 thf(22373,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)],[4409])). 159.61/70.67 thf(2848,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/sandbox/benchmark/theBenchmark.p',fact_5781_of__int__add)). 159.61/70.67 thf(17409,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)],[2848])). 159.61/70.67 thf(5784,axiom,((! [A:complex,B:complex,C:num]: ((A = (divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)))) = ((((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex) => (A = zero_zero_complex)) & (((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) != zero_zero_complex) => ((times_times_complex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4829_eq__divide__eq__numeral1_I2_J)). 159.61/70.67 thf(27484,plain,((! [A:complex,B:complex,C:num]: ((A = (divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)))) = ((((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex) => (A = zero_zero_complex)) & ((~ ((uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C)) = zero_zero_complex)) => ((times_times_complex @ A @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ C))) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5784])). 159.61/70.67 thf(5928,axiom,((! [A:real,B:nat,C:real]: (((power_power_real @ A @ B) = (power_power_real @ C @ B)) => (((ord_less_eq_real @ zero_zero_real @ C) => ((A = C) <= (ord_less_nat @ zero_zero_nat @ B))) <= (ord_less_eq_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1928_power__eq__imp__eq__base)). 159.61/70.67 thf(28154,plain,((! [A:real,B:nat,C:real]: (((power_power_real @ A @ B) = (power_power_real @ C @ B)) => (((ord_less_eq_real @ zero_zero_real @ C) => ((A = C) | ~ (ord_less_nat @ zero_zero_nat @ B))) | ~ (ord_less_eq_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5928])). 159.61/70.67 thf(4123,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/sandbox/benchmark/theBenchmark.p',fact_5824_of__int__numeral__less__iff)). 159.61/70.67 thf(21475,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)],[4123])). 159.61/70.67 thf(1773,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3668_verit__comp__simplify1_I1_J)). 159.61/70.67 thf(13977,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773])). 159.61/70.67 thf(139,axiom,((! [A:real,B:real]: ((((ord_less_real @ (tan_real @ A) @ (tan_real @ B)) <= (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))))) <= (ord_less_real @ A @ B)) <= (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7286_tan__monotone)). 159.61/70.67 thf(8675,plain,((! [A:real,B:real]: ((ord_less_real @ (tan_real @ A) @ (tan_real @ B)) | ~ (ord_less_real @ B @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_real @ A @ B) | ~ (ord_less_real @ (uminus_uminus_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 159.61/70.67 thf(145,axiom,((! [A:nat,B:nat]: (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ (semiri3624122377584611663nteger @ A) @ (semiri3624122377584611663nteger @ B)) @ (semiri3624122377584611663nteger @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8082_fact__fact__dvd__fact)). 159.61/70.67 thf(8692,plain,((! [A:nat,B:nat]: (dvd_dvd_Code_integer @ (times_3573771949741848930nteger @ (semiri3624122377584611663nteger @ A) @ (semiri3624122377584611663nteger @ B)) @ (semiri3624122377584611663nteger @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 159.61/70.67 thf(3794,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/sandbox/benchmark/theBenchmark.p',fact_7955_suminf__le__const)). 159.61/70.67 thf(20461,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)],[3794])). 159.61/70.67 thf(6640,axiom,((! [A:$o,B:$o]: ((zero_n2687167440665602831ol_nat @ ((A) & (B))) = (times_times_nat @ (zero_n2687167440665602831ol_nat @ A) @ (zero_n2687167440665602831ol_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4387_of__bool__conj)). 159.61/70.67 thf(30745,plain,((! [A:$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)],[6640])). 159.61/70.67 thf(412,axiom,((! [A:real,B:complex]: ((re @ (real_V2046097035970521341omplex @ A @ B)) = (times_times_real @ A @ (re @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9635_scaleR__complex_Osimps_I1_J)). 159.61/70.67 thf(9547,plain,((! [A:real,B:complex]: ((re @ (real_V2046097035970521341omplex @ A @ B)) = (times_times_real @ A @ (re @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])). 159.61/70.67 thf(7645,axiom,((! [A:nat]: ((groups3542108847815614940at_nat @ (binomial @ A) @ (set_ord_atMost_nat @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9141_choose__row__sum)). 159.61/70.67 thf(34689,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)],[7645])). 159.61/70.67 thf(2081,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/sandbox/benchmark/theBenchmark.p',fact_1381_times__divide__eq__right)). 159.61/70.67 thf(14956,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)],[2081])). 159.61/70.67 thf(7206,axiom,((! [A:real,B:real]: ((times_times_real @ A @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (times_times_real @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4623_mult__minus__right)). 159.61/70.67 thf(33160,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)],[7206])). 159.61/70.67 thf(6629,axiom,((! [A:real,B:nat]: (((power_power_real @ A @ B) != zero_zero_real) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1893_power__not__zero)). 159.61/70.67 thf(30700,plain,((! [A:real,B:nat]: (~ ((power_power_real @ A @ B) = zero_zero_real) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6629])). 159.61/70.67 thf(842,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ one)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_divide__numeral__1)). 159.61/70.67 thf(10966,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ (numera6690914467698888265omplex @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[842])). 159.61/70.67 thf(3493,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/sandbox/benchmark/theBenchmark.p',fact_5874_of__int__less__neg__numeral__power__cancel__iff)). 159.61/70.67 thf(19469,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)],[3493])). 159.61/70.67 thf(5712,axiom,((! [A:set_nat,B:nat]: (((~ (? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ B)))) <= (finite_finite_nat @ A)) <= (~ (? [C:nat]: (vEBT_is_pred_in_set @ A @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3600_pred__none__empty)). 159.61/70.67 thf(27163,plain,((! [A:set_nat,B:nat]: (~ (? [C:nat]: ((member_nat @ C @ A) & (ord_less_nat @ C @ B))) | ~ (finite_finite_nat @ A) | ? [C:nat]: (vEBT_is_pred_in_set @ A @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5712])). 159.61/70.67 thf(7249,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/sandbox/benchmark/theBenchmark.p',fact_5530_abs__triangle__ineq2)). 159.61/70.67 thf(33320,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)],[7249])). 159.61/70.67 thf(6462,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/sandbox/benchmark/theBenchmark.p',fact_826_diff__le__mono2)). 159.61/70.67 thf(30097,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)],[6462])). 159.61/70.67 thf(70,axiom,((! [A:complex,B:complex]: ((ord_less_real @ (re @ (divide1717551699836669952omplex @ A @ B)) @ zero_zero_real) = (ord_less_real @ (re @ (times_times_complex @ A @ (cnj @ B))) @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9691_Re__complex__div__lt__0)). 159.61/70.67 thf(8460,plain,((! [A:complex,B:complex]: ((ord_less_real @ (re @ (divide1717551699836669952omplex @ A @ B)) @ zero_zero_real) = (ord_less_real @ (re @ (times_times_complex @ A @ (cnj @ B))) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 159.61/70.67 thf(4845,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (divide_divide_nat @ A @ B)) = (divide_divide_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6696_unique__euclidean__semiring__with__nat__class_Oof__nat__div)). 159.61/70.67 thf(24016,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)],[4845])). 159.61/70.67 thf(7604,axiom,((! [A:nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1330_less__add__one)). 159.61/70.67 thf(34571,plain,((! [A:nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7604])). 159.61/70.67 thf(2827,axiom,((! [A:nat,B:nat]: ((semiri5074537144036343181t_real @ (plus_plus_nat @ A @ B)) = (plus_plus_real @ (semiri5074537144036343181t_real @ A) @ (semiri5074537144036343181t_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6528_of__nat__add)). 159.61/70.67 thf(17340,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)],[2827])). 159.61/70.67 thf(3692,axiom,((minus_8373710615458151222nteger = (^ [A:code_integer,B:code_integer]: (plus_p5714425477246183910nteger @ A @ (uminus1351360451143612070nteger @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5105_diff__conv__add__uminus)). 159.61/70.67 thf(20110,plain,(((minus_8373710615458151222nteger) = (^ [A:code_integer,B:code_integer]: (plus_p5714425477246183910nteger @ A @ (uminus1351360451143612070nteger @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3692])). 159.61/70.67 thf(1113,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/sandbox/benchmark/theBenchmark.p',fact_5821_of__int__le__numeral__iff)). 159.61/70.67 thf(11826,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)],[1113])). 159.61/70.67 thf(2775,axiom,((! [A:(nat > real),B:real]: (((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))) <= (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7127_powser__split__head_I1_J)). 159.61/70.67 thf(17192,plain,((! [A:(nat > real),B:real]: (((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))) | ~ (summable_real @ (^ [C:nat]: (times_times_real @ (A @ C) @ (power_power_real @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2775])). 159.61/70.67 thf(490,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/sandbox/benchmark/theBenchmark.p',fact_7291_tan__inverse)). 159.61/70.67 thf(9816,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)],[490])). 159.61/70.67 thf(1285,axiom,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (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/sandbox/benchmark/theBenchmark.p',fact_7817_arcsin__lbound)). 159.61/70.67 thf(12406,plain,((! [A:real]: (((ord_less_eq_real @ A @ one_one_real) => (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)],[1285])). 159.61/70.67 thf(8214,axiom,((! [A:num,B:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6025_and__numerals_I7_J)). 159.61/70.67 thf(36520,plain,((! [A:num,B:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (numeral_numeral_nat @ (bit1 @ B))) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8214])). 159.61/70.67 thf(1351,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/sandbox/benchmark/theBenchmark.p',fact_3383_mult__le__cancel__iff2)). 159.61/70.67 thf(12611,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)],[1351])). 159.61/70.67 thf(7747,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 @ D @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4544_minf_I10_J)). 159.61/70.67 thf(35035,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7747])). 159.61/70.67 thf(6127,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/sandbox/benchmark/theBenchmark.p',fact_9128_vandermonde)). 159.61/70.67 thf(28842,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)],[6127])). 159.61/70.67 thf(488,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ zero_zero_real)) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9244_scaleR__nonpos__nonneg)). 159.61/70.67 thf(9810,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ A @ B) @ zero_zero_real)) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[488])). 159.61/70.67 thf(3355,axiom,((! [A:int,B:int]: (((modulo_modulo_int @ B @ A) = zero_zero_int) <= (dvd_dvd_int @ A @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4180_unit__imp__mod__eq__0)). 159.61/70.67 thf(19036,plain,((! [A:int,B:int]: (((modulo_modulo_int @ B @ A) = zero_zero_int) | ~ (dvd_dvd_int @ A @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3355])). 159.61/70.67 thf(3566,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/sandbox/benchmark/theBenchmark.p',fact_6678_div__mult2__eq_H)). 159.61/70.67 thf(19706,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)],[3566])). 159.61/70.67 thf(2591,axiom,((ord_less_real @ (cos_real @ (numeral_numeral_real @ (bit0 @ one))) @ zero_zero_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7145_cos__two__less__zero)). 159.61/70.67 thf(16578,plain,((ord_less_real @ (cos_real @ (numeral_numeral_real @ (bit0 @ one))) @ zero_zero_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2591])). 159.61/70.67 thf(715,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/sandbox/benchmark/theBenchmark.p',fact_5877_mult__of__int__commute)). 159.61/70.67 thf(10554,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)],[715])). 159.61/70.67 thf(7121,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/sandbox/benchmark/theBenchmark.p',fact_1169_add__left__mono)). 159.61/70.67 thf(32834,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)],[7121])). 159.61/70.67 thf(6916,axiom,((! [A:num]: (ord_less_eq_real @ zero_zero_real @ (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1956_zero__le__numeral)). 159.61/70.67 thf(31916,plain,((! [A:num]: (ord_less_eq_real @ zero_zero_real @ (numeral_numeral_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6916])). 159.61/70.67 thf(5682,axiom,((! [A:num,B:num]: ((times_times_complex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A)) @ (numera6690914467698888265omplex @ B)) = (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ (times_times_num @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4810_mult__neg__numeral__simps_I2_J)). 159.61/70.67 thf(27074,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)],[5682])). 159.61/70.67 thf(1786,axiom,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1196_add__strict__mono)). 159.61/70.67 thf(14018,plain,((! [A:real,B:real,C:real,D:real]: (((ord_less_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1786])). 159.61/70.67 thf(3101,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ B @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1768_divide__le__eq__1__pos)). 159.61/70.67 thf(18227,plain,((! [A:real,B:real]: (((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ B @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3101])). 159.61/70.67 thf(2703,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_add__right__cancel)). 159.61/70.67 thf(16971,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)],[2703])). 159.61/70.67 thf(4588,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2735_order__antisym)). 159.61/70.67 thf(23097,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)],[4588])). 159.61/70.67 thf(5298,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/sandbox/benchmark/theBenchmark.p',fact_9499_real__root__mult)). 159.61/70.67 thf(25609,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)],[5298])). 159.61/70.67 thf(3160,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/sandbox/benchmark/theBenchmark.p',fact_8358_gbinomial__code)). 159.61/70.67 thf(18423,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)],[3160])). 159.61/70.67 thf(1761,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/sandbox/benchmark/theBenchmark.p',fact_1747_div__mult__self2)). 159.61/70.67 thf(13937,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)],[1761])). 159.61/70.67 thf(8210,axiom,((! [A:nat,B:nat]: ((times_times_nat @ A @ (suc @ B)) = (plus_plus_nat @ A @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_mult__Suc__right)). 159.61/70.67 thf(36510,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)],[8210])). 159.61/70.67 thf(5748,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (bit_se727722235901077358nd_nat @ A @ B)) = (bit_se727722235901077358nd_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6717_of__nat__and__eq)). 159.61/70.67 thf(27290,plain,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (bit_se727722235901077358nd_nat @ A @ B)) = (bit_se727722235901077358nd_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5748])). 159.61/70.67 thf(4485,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1975_mult__nonneg__nonneg)). 159.61/70.67 thf(22679,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (times_times_nat @ A @ B))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4485])). 159.61/70.67 thf(5851,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_eq_num @ A @ C) <= (ord_less_num @ B @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4500_pinf_I8_J)). 159.61/70.67 thf(27879,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_eq_num @ A @ C) | ~ (ord_less_num @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5851])). 159.61/70.67 thf(1204,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/sandbox/benchmark/theBenchmark.p',fact_1091_add__diff__cancel__right)). 159.61/70.67 thf(12134,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)],[1204])). 159.61/70.67 thf(6385,axiom,((! [A:real,B:nat]: (((comm_s7457072308508201937r_real @ A @ B) = zero_zero_real) = (? [C:nat]: ((ord_less_nat @ C @ B) & (A = (uminus_uminus_real @ (semiri5074537144036343181t_real @ C)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8286_pochhammer__eq__0__iff)). 159.61/70.67 thf(29768,plain,((! [A:real,B:nat]: (((comm_s7457072308508201937r_real @ A @ B) = zero_zero_real) = (? [C:nat]: ((ord_less_nat @ C @ B) & (A = (uminus_uminus_real @ (semiri5074537144036343181t_real @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6385])). 159.61/70.67 thf(7209,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/sandbox/benchmark/theBenchmark.p',fact_1108_ab__semigroup__mult__class_Omult__ac_I1_J)). 159.61/70.67 thf(33171,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)],[7209])). 159.61/70.67 thf(1155,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_add_Oleft__cancel)). 159.61/70.67 thf(11953,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)],[1155])). 159.61/70.67 thf(938,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/sandbox/benchmark/theBenchmark.p',fact_2993_in__mono)). 159.61/70.67 thf(11258,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)],[938])). 159.61/70.67 thf(1118,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/sandbox/benchmark/theBenchmark.p',fact_6932_norm__diff__triangle__less)). 159.61/70.67 thf(11839,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)],[1118])). 159.61/70.67 thf(8056,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/sandbox/benchmark/theBenchmark.p',fact_4584_crossproduct__noteq)). 159.61/70.67 thf(36011,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)],[8056])). 159.61/70.67 thf(7629,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/sandbox/benchmark/theBenchmark.p',fact_1109_ab__semigroup__mult__class_Omult__ac_I1_J)). 159.61/70.67 thf(34642,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)],[7629])). 159.61/70.67 thf(7294,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/sandbox/benchmark/theBenchmark.p',fact_1178_add__mono__thms__linordered__semiring_I2_J)). 159.61/70.67 thf(33461,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)],[7294])). 159.61/70.67 thf(454,axiom,((! [A:nat]: (((groups7501900531339628137nteger @ (^ [B:nat]: (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (semiri4939895301339042750nteger @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_z3403309356797280102nteger) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9172_choose__alternating__sum)). 159.61/70.67 thf(9679,plain,((! [A:nat]: (((groups7501900531339628137nteger @ (^ [B:nat]: (times_3573771949741848930nteger @ (power_8256067586552552935nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer) @ B) @ (semiri4939895301339042750nteger @ (binomial @ A @ B)))) @ (set_ord_atMost_nat @ A)) = zero_z3403309356797280102nteger) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])). 159.61/70.67 thf(8228,axiom,((! [A:num,B:num]: ((ord_less_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_numeral__less__iff)). 159.61/70.67 thf(36560,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)],[8228])). 159.61/70.67 thf(6014,axiom,((! [A:real]: ((ord_less_eq_int @ one_one_int @ (archim6058952711729229775r_real @ A)) = (ord_less_eq_real @ one_one_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8191_one__le__floor)). 159.61/70.67 thf(28485,plain,((! [A:real]: ((ord_less_eq_int @ one_one_int @ (archim6058952711729229775r_real @ A)) = (ord_less_eq_real @ one_one_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6014])). 159.61/70.67 thf(6757,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1254_comm__monoid__mult__class_Omult__1)). 159.61/70.67 thf(31299,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6757])). 159.61/70.67 thf(3755,axiom,((! [A:int,B:int]: ((A = B) | (ord_less_int @ B @ A) | (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2922_linorder__less__linear)). 159.61/70.67 thf(20329,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)],[3755])). 159.61/70.67 thf(475,axiom,((! [A:num,B:num,C:real]: ((real_V1485227260804924795R_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A)) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (real_V1485227260804924795R_real @ (divide_divide_real @ (numeral_numeral_real @ B) @ (numeral_numeral_real @ A)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9205_inverse__scaleR__times)). 159.61/70.67 thf(9763,plain,((! [A:num,B:num,C:real]: ((real_V1485227260804924795R_real @ (divide_divide_real @ one_one_real @ (numeral_numeral_real @ A)) @ (times_times_real @ (numeral_numeral_real @ B) @ C)) = (real_V1485227260804924795R_real @ (divide_divide_real @ (numeral_numeral_real @ B) @ (numeral_numeral_real @ A)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[475])). 159.61/70.67 thf(5128,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/sandbox/benchmark/theBenchmark.p',fact_4788_diff__numeral__simps_I3_J)). 159.61/70.67 thf(24998,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)],[5128])). 159.61/70.67 thf(6992,axiom,((! [A:option_nat,B:(option_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: (((A = none_nat) => (B @ A @ C)) => (((! [D:nat,E:product_prod_nat_nat]: (((C = (some_P7363390416028606310at_nat @ E)) => (B @ A @ C)) <= (A = (some_nat @ D)))) => (B @ A @ C)) <= ((B @ A @ C) <= (C = none_P5556105721700978146at_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_combine__options__cases)). 159.61/70.67 thf(32321,plain,((! [A:option_nat,B:(option_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: (((A = none_nat) => (B @ A @ C)) => (((! [D:nat,E:product_prod_nat_nat]: (((C = (some_P7363390416028606310at_nat @ E)) => (B @ A @ C)) | ~ (A = (some_nat @ D)))) => (B @ A @ C)) | ~ ((B @ A @ C) | ~ (C = none_P5556105721700978146at_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6992])). 159.61/70.67 thf(5635,axiom,((! [A:num]: ((bitM @ (bit0 @ A)) = (bit1 @ (bitM @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5889_semiring__norm_I27_J)). 159.61/70.67 thf(26893,plain,((! [A:num]: ((bitM @ (bit0 @ A)) = (bit1 @ (bitM @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5635])). 159.61/70.67 thf(5875,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/sandbox/benchmark/theBenchmark.p',fact_1175_add__mono__thms__linordered__semiring_I1_J)). 159.61/70.67 thf(27956,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)],[5875])). 159.61/70.67 thf(6971,axiom,((! [A:nat,B:nat,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => ((ord_less_real @ (root @ B @ C) @ (root @ A @ C)) <= (ord_less_real @ one_one_real @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9512_real__root__strict__decreasing)). 159.61/70.67 thf(32132,plain,((! [A:nat,B:nat,C:real]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ B) => ((ord_less_real @ (root @ B @ C) @ (root @ A @ C)) | ~ (ord_less_real @ one_one_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6971])). 159.61/70.67 thf(2483,axiom,((! [A:complex]: ((divide1717551699836669952omplex @ A @ zero_zero_complex) = zero_zero_complex))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1550_division__ring__divide__zero)). 159.61/70.67 thf(16239,plain,((! [A:complex]: ((divide1717551699836669952omplex @ A @ zero_zero_complex) = zero_zero_complex))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2483])). 159.61/70.67 thf(7050,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (suc @ (minus_minus_nat @ B @ A)) @ C) = (minus_minus_nat @ (suc @ B) @ (plus_plus_nat @ A @ C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_diff__Suc__diff__eq2)). 159.61/70.67 thf(32520,plain,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (suc @ (minus_minus_nat @ B @ A)) @ C) = (minus_minus_nat @ (suc @ B) @ (plus_plus_nat @ A @ C))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7050])). 159.61/70.67 thf(3863,axiom,((! [A:int,B:int]: ((divide_divide_int @ (modulo_modulo_int @ A @ B) @ B) = zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3410_bits__mod__div__trivial)). 159.61/70.67 thf(20686,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)],[3863])). 159.61/70.67 thf(1076,axiom,((! [A:nat,B:real]: ((((nat2 @ (archim6058952711729229775r_real @ B)) = A) <= (ord_less_real @ B @ (semiri5074537144036343181t_real @ (suc @ A)))) <= (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9469_floor__eq4)). 159.61/70.67 thf(11707,plain,((! [A:nat,B:real]: (((nat2 @ (archim6058952711729229775r_real @ B)) = A) | ~ (ord_less_real @ B @ (semiri5074537144036343181t_real @ (suc @ A))) | ~ (ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076])). 159.61/70.67 thf(1157,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/sandbox/benchmark/theBenchmark.p',fact_4651_mod__minus__minus)). 159.61/70.67 thf(11958,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)],[1157])). 159.61/70.67 thf(2366,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/sandbox/benchmark/theBenchmark.p',fact_2763_dense)). 159.61/70.67 thf(15845,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)],[2366])). 159.61/70.67 thf(2466,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/sandbox/benchmark/theBenchmark.p',fact_3119_dual__order_Ostrict__trans1)). 159.61/70.67 thf(16190,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)],[2466])). 159.61/70.67 thf(1096,axiom,((! [A:(nat > real),B:real,C:(nat > real),D:real]: (((sums_real @ C @ D) => (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 @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8016_sums__if)). 159.61/70.67 thf(11764,plain,((! [A:(nat > real),B:real,C:(nat > real),D:real]: (((sums_real @ (C) @ D) => (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 @ (A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096])). 159.61/70.67 thf(6785,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ zero_zero_real @ (arccos @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7685_arccos__lbound)). 159.61/70.67 thf(31403,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ zero_zero_real @ (arccos @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6785])). 159.61/70.67 thf(6710,axiom,((! [A:num,B:num]: ((times_times_complex @ (numera6690914467698888265omplex @ A) @ (numera6690914467698888265omplex @ B)) = (numera6690914467698888265omplex @ (times_times_num @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_numeral__times__numeral)). 159.61/70.67 thf(31117,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)],[6710])). 159.61/70.67 thf(4007,axiom,((bit_se1409905431419307370or_int = (^ [A:int,B:int]: (if_int @ ((B = (uminus_uminus_int @ one_one_int)) | (A = (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/sandbox/benchmark/theBenchmark.p',fact_5932_or__int__unfold)). 159.61/70.67 thf(21131,plain,(((bit_se1409905431419307370or_int) = (^ [A:int,B:int]: (if_int @ ((B = (uminus_uminus_int @ one_one_int)) | (A = (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)],[4007])). 159.61/70.67 thf(7458,axiom,((zero_zero_int != (uminus_uminus_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5069_zero__neq__neg__one)). 159.61/70.67 thf(34014,plain,((~ (zero_zero_int = (uminus_uminus_int @ one_one_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7458])). 159.61/70.67 thf(8197,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/sandbox/benchmark/theBenchmark.p',fact_4367_nth__replicate)). 159.61/70.67 thf(36460,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)],[8197])). 159.61/70.67 thf(7094,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/sandbox/benchmark/theBenchmark.p',fact_4099_div__unit__dvd__iff)). 159.61/70.67 thf(32716,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)],[7094])). 159.61/70.67 thf(6157,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ (suc @ (times_times_nat @ A @ B)) @ A) = one_one_nat) <= (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3555_Suc__times__mod__eq)). 159.61/70.67 thf(28938,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ (suc @ (times_times_nat @ A @ B)) @ A) = one_one_nat) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6157])). 159.61/70.67 thf(4565,axiom,((! [A:nat]: ((ord_less_eq_real @ (semiri5074537144036343181t_real @ A) @ zero_zero_real) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6577_of__nat__le__0__iff)). 159.61/70.67 thf(23013,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)],[4565])). 159.61/70.67 thf(4276,axiom,((! [A:int]: ((divide_divide_int @ A @ (uminus_uminus_int @ one_one_int)) = (uminus_uminus_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4714_div__minus1__right)). 159.61/70.67 thf(21971,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)],[4276])). 159.61/70.67 thf(6581,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_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_mint @ (nth_VEBT_VEBT @ D @ (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 @ 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/sandbox/benchmark/theBenchmark.p',fact_1405_pred__less__length__list)). 159.61/70.67 thf(30527,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_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_mint @ (nth_VEBT_VEBT @ D @ (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 @ 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)],[6581])). 159.61/70.67 thf(1535,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/sandbox/benchmark/theBenchmark.p',fact_8348_gbinomial__sum__up__index)). 159.61/70.67 thf(13247,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)],[1535])). 159.61/70.67 thf(7035,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/sandbox/benchmark/theBenchmark.p',fact_8972_choose__even__sum)). 159.61/70.67 thf(32461,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)],[7035])). 159.61/70.67 thf(1872,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/sandbox/benchmark/theBenchmark.p',fact_4968_is__num__normalize_I8_J)). 159.61/70.67 thf(14298,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)],[1872])). 159.61/70.67 thf(5191,axiom,((! [A:num,B:num]: ((A != B) <= (ord_less_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2925_order__less__imp__not__eq)). 159.61/70.67 thf(25218,plain,((! [A:num,B:num]: (~ (A = B) | ~ (ord_less_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5191])). 159.61/70.67 thf(971,axiom,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2078_mult__less__cancel__left__pos)). 159.61/70.67 thf(11358,plain,((! [A:int,B:int,C:int]: ((ord_less_int @ zero_zero_int @ A) => ((ord_less_int @ (times_times_int @ A @ B) @ (times_times_int @ A @ C)) = (ord_less_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[971])). 159.61/70.67 thf(3830,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/sandbox/benchmark/theBenchmark.p',fact_8213_pochhammer__pos)). 159.61/70.67 thf(20563,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)],[3830])). 159.61/70.67 thf(1728,axiom,((! [A:(nat > real),B:nat]: ((summable_real @ (^ [C:nat]: (A @ (plus_plus_nat @ C @ B)))) = (summable_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6962_summable__iff__shift)). 159.61/70.67 thf(13837,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)],[1728])). 159.61/70.67 thf(1184,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/sandbox/benchmark/theBenchmark.p',fact_8205_floor__minus__divide__eq__div__numeral)). 159.61/70.67 thf(12042,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)],[1184])). 159.61/70.67 thf(8175,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B)) @ (power_power_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2445_power__Suc__less)). 159.61/70.67 thf(36394,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B)) @ (power_power_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8175])). 159.61/70.67 thf(4058,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/sandbox/benchmark/theBenchmark.p',fact_3692_mod__pos__neg__trivial)). 159.61/70.67 thf(21277,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)],[4058])). 159.61/70.67 thf(4220,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (ord_less_int @ (semiri1314217659103216013at_int @ A) @ (semiri1314217659103216013at_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6821_nat__int__comparison_I2_J)). 159.61/70.67 thf(21804,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)],[4220])). 159.61/70.67 thf(2604,axiom,((! [A:real]: (((ln_ln_real @ (sqrt @ A)) = (divide_divide_real @ (ln_ln_real @ A) @ (numeral_numeral_real @ (bit0 @ one)))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6462_ln__sqrt)). 159.61/70.67 thf(16627,plain,((! [A:real]: (((ln_ln_real @ (sqrt @ A)) = (divide_divide_real @ (ln_ln_real @ A) @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2604])). 159.61/70.67 thf(7304,axiom,(((semiri1406184849735516958ct_int @ (suc @ zero_zero_nat)) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8057_fact__Suc__0)). 159.61/70.67 thf(33501,plain,(((semiri1406184849735516958ct_int @ (suc @ zero_zero_nat)) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7304])). 159.61/70.67 thf(5100,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/sandbox/benchmark/theBenchmark.p',fact_5284_power2__eq__1__iff)). 159.61/70.67 thf(24912,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)],[5100])). 159.61/70.67 thf(6003,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/sandbox/benchmark/theBenchmark.p',fact_9485_real__root__eq__1__iff)). 159.61/70.67 thf(28452,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)],[6003])). 159.61/70.67 thf(6093,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_diff__le__self)). 159.61/70.67 thf(28729,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6093])). 159.61/70.67 thf(5557,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ (suc @ B)) = (A = B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_not__less__less__Suc__eq)). 159.61/70.67 thf(26622,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)],[5557])). 159.61/70.67 thf(5914,axiom,((! [A:num]: ((bitM @ (bit1 @ A)) = (bit1 @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5888_semiring__norm_I28_J)). 159.61/70.67 thf(28110,plain,((! [A:num]: ((bitM @ (bit1 @ A)) = (bit1 @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5914])). 159.61/70.67 thf(4354,axiom,(((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7001_cos__two__pi)). 159.61/70.67 thf(22203,plain,(((cos_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4354])). 159.61/70.67 thf(6919,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/sandbox/benchmark/theBenchmark.p',fact_4900_neg__one__odd__power)). 159.61/70.67 thf(31925,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)],[6919])). 159.61/70.67 thf(5755,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)))) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2240_mult__strict__mono_H)). 159.61/70.67 thf(27311,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)))) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5755])). 159.61/70.67 thf(2361,axiom,((! [A:real]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ one_one_int) = (ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8201_floor__le__one)). 159.61/70.67 thf(15833,plain,((! [A:real]: ((ord_less_eq_int @ (archim6058952711729229775r_real @ A) @ one_one_int) = (ord_less_real @ A @ (numeral_numeral_real @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2361])). 159.61/70.67 thf(6874,axiom,((! [A:real,B:real,C:real]: ((((times_times_real @ A @ B) = (times_times_real @ A @ C)) = (B = C)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1855_mult__left__cancel)). 159.61/70.67 thf(31776,plain,((! [A:real,B:real,C:real]: ((((times_times_real @ A @ B) = (times_times_real @ A @ C)) = (B = C)) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6874])). 159.61/70.67 thf(1334,axiom,((! [A:set_nat,B:(nat > extended_enat),C:(nat > $o)]: (((groups7961826882256487087d_enat @ B @ (collect_nat @ (^ [D:nat]: ((C @ D) & (member_nat @ D @ A))))) = (groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (C @ D) @ (B @ D) @ one_on7984719198319812577d_enat)) @ A)) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8530_prod_Ointer__filter)). 159.61/70.67 thf(12560,plain,((! [A:set_nat,B:(nat > extended_enat),C:(nat > $o)]: (((groups7961826882256487087d_enat @ (B) @ (collect_nat @ (^ [D:nat]: ((C @ D) & (member_nat @ D @ A))))) = (groups7961826882256487087d_enat @ (^ [D:nat]: (if_Extended_enat @ (C @ D) @ (B @ D) @ one_on7984719198319812577d_enat)) @ A)) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334])). 159.61/70.67 thf(7640,axiom,((! [A:vEBT_VEBT]: ((member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList)) => (! [B:nat]: (vEBT_invar_vebt @ (vEBT_vebt_delete @ A @ B) @ na) & (vEBT_invar_vebt @ A @ na))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36__C5_OIH_C_I1_J)). 159.61/70.67 thf(34674,plain,((! [A:vEBT_VEBT]: ((member_VEBT_VEBT @ A @ (set_VEBT_VEBT2 @ treeList)) => (! [B:nat]: (vEBT_invar_vebt @ (vEBT_vebt_delete @ A @ B) @ na) & (vEBT_invar_vebt @ A @ na))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7640])). 159.61/70.67 thf(2520,axiom,((! [A:code_integer,B:code_integer]: (((divide6298287555418463151nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (divide6298287555418463151nteger @ B @ A))) <= (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5123_dvd__neg__div)). 159.61/70.67 thf(16363,plain,((! [A:code_integer,B:code_integer]: (((divide6298287555418463151nteger @ (uminus1351360451143612070nteger @ B) @ A) = (uminus1351360451143612070nteger @ (divide6298287555418463151nteger @ B @ A))) | ~ (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2520])). 159.61/70.67 thf(2770,axiom,((semiri4449623510593786356d_enat = (comm_s3181272606743183617d_enat @ one_on7984719198319812577d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8219_pochhammer__fact)). 159.61/70.67 thf(17177,plain,(((semiri4449623510593786356d_enat) = (comm_s3181272606743183617d_enat @ one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2770])). 159.61/70.67 thf(2228,axiom,((! [A:real,B:real]: ((minus_minus_real @ A @ (uminus_uminus_real @ B)) = (plus_plus_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4706_diff__minus__eq__add)). 159.61/70.67 thf(15444,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)],[2228])). 159.61/70.67 thf(5541,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9113_choose__reduce__nat)). 159.61/70.67 thf(26578,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5541])). 159.61/70.67 thf(4043,axiom,((sgn_sgn_real = (^ [A:real]: (divide_divide_real @ A @ (abs_abs_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9503_real__sgn__eq)). 159.61/70.67 thf(21236,plain,(((sgn_sgn_real) = (^ [A:real]: (divide_divide_real @ A @ (abs_abs_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4043])). 159.61/70.67 thf(6798,axiom,(((^ [A:int]: (zero_zero_int)) = (times_times_int @ zero_zero_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1938_lambda__zero)). 159.61/70.67 thf(31439,plain,(((^ [A:int]: (zero_zero_int)) = (times_times_int @ zero_zero_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6798])). 159.61/70.67 thf(382,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ (real_V1485227260804924795R_real @ B @ C) @ (real_V1485227260804924795R_real @ A @ C)) <= (ord_less_eq_real @ C @ zero_zero_real)) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9223_scaleR__right__mono__neg)). 159.61/70.67 thf(9446,plain,((! [A:real,B:real,C:real]: ((ord_less_eq_real @ (real_V1485227260804924795R_real @ B @ C) @ (real_V1485227260804924795R_real @ A @ C)) | ~ (ord_less_eq_real @ C @ zero_zero_real) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])). 159.61/70.67 thf(7491,axiom,((vEBT_invar_vebt @ summary @ m)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35__C1_C)). 159.61/70.67 thf(34161,plain,((vEBT_invar_vebt @ summary @ m)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7491])). 159.61/70.67 thf(762,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/sandbox/benchmark/theBenchmark.p',fact_3828_dvd__add__times__triv__left__iff)). 159.61/70.67 thf(10713,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)],[762])). 159.61/70.67 thf(6980,axiom,((! [A:list_int,B:list_int]: ((A != B) <= ((size_size_list_int @ A) != (size_size_list_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_neq__if__length__neq)). 159.61/70.67 thf(32267,plain,((! [A:list_int,B:list_int]: (~ (A = B) | ((size_size_list_int @ A) = (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6980])). 159.61/70.67 thf(1509,axiom,((! [A:extended_enat]: ((A != zero_z5237406670263579293d_enat) => (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1838_gr__zeroI)). 159.61/70.67 thf(13171,plain,((! [A:extended_enat]: ((~ (A = zero_z5237406670263579293d_enat)) => (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1509])). 159.61/70.67 thf(3783,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/sandbox/benchmark/theBenchmark.p',fact_5232_ln__add__one__self__le__self)). 159.61/70.67 thf(20417,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)],[3783])). 159.61/70.67 thf(3541,axiom,((! [A:num,B:num,C:(num > real),D:real]: (((ord_less_real @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D))) <= (ord_less_eq_num @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3223_order__le__less__subst2)). 159.61/70.67 thf(19614,plain,((! [A:num,B:num,C:(num > real),D:real]: (((ord_less_real @ (C @ B) @ D) => ((! [E:num,F:num]: ((ord_less_eq_num @ E @ F) => (ord_less_eq_real @ (C @ E) @ (C @ F)))) => (ord_less_real @ (C @ A) @ D))) | ~ (ord_less_eq_num @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3541])). 159.61/70.67 thf(5304,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = none_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2491_vebt__succ_Osimps_I4_J)). 159.61/70.67 thf(25641,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5304])). 159.61/70.67 thf(5824,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/sandbox/benchmark/theBenchmark.p',fact_76_numeral__le__iff)). 159.61/70.67 thf(27711,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)],[5824])). 159.61/70.67 thf(5109,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/sandbox/benchmark/theBenchmark.p',fact_9078_Suc__times__binomial__add)). 159.61/70.67 thf(24940,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)],[5109])). 159.61/70.67 thf(5011,axiom,((! [A:nat,B:nat]: ((set_or4665077453230672383an_nat @ A @ (suc @ B)) = (set_or1269000886237332187st_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9582_atLeastLessThanSuc__atLeastAtMost)). 159.61/70.67 thf(24590,plain,((! [A:nat,B:nat]: ((set_or4665077453230672383an_nat @ A @ (suc @ B)) = (set_or1269000886237332187st_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5011])). 159.61/70.67 thf(2074,axiom,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (times_times_complex @ B @ A) @ C) @ A)) <= (A != zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2346_add__divide__eq__iff)). 159.61/70.67 thf(14935,plain,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ B @ (divide1717551699836669952omplex @ C @ A)) = (divide1717551699836669952omplex @ (plus_plus_complex @ (times_times_complex @ B @ A) @ C) @ A)) | (A = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2074])). 159.61/70.67 thf(8057,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/sandbox/benchmark/theBenchmark.p',fact_112_distrib__left__numeral)). 159.61/70.67 thf(36014,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)],[8057])). 159.61/70.67 thf(6052,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 @ B @ A) @ zero_zero_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1967_mult__nonneg__nonpos2)). 159.61/70.67 thf(28606,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 @ B @ A) @ zero_zero_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6052])). 159.61/70.67 thf(3725,axiom,((! [A:real,B:(extended_enat > real),C:extended_enat,D:extended_enat]: ((A = (B @ C)) => ((ord_le72135733267957522d_enat @ C @ D) => ((ord_less_real @ A @ (B @ D)) <= (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2864_ord__eq__less__subst)). 159.61/70.67 thf(20231,plain,((! [A:real,B:(extended_enat > real),C:extended_enat,D:extended_enat]: ((A = (B @ C)) => ((ord_le72135733267957522d_enat @ C @ D) => ((ord_less_real @ A @ (B @ D)) | ~ (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ E @ F) => (ord_less_real @ (B @ E) @ (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3725])). 159.61/70.67 thf(2412,axiom,((! [A:complex,B:complex,C:real,D:complex,E:real]: (((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 @ B @ D)) @ E)) <= (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6936_norm__diff__triangle__le)). 159.61/70.67 thf(16002,plain,((! [A:complex,B:complex,C:real,D:complex,E:real]: ((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 @ B @ D)) @ E) | ~ (ord_less_eq_real @ (real_V1022390504157884413omplex @ (minus_minus_complex @ A @ B)) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2412])). 159.61/70.67 thf(370,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/sandbox/benchmark/theBenchmark.p',fact_7295_add__tan__eq)). 159.61/70.67 thf(9402,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)],[370])). 159.61/70.67 thf(7303,axiom,((! [A:nat,B:nat]: ((((suc @ (modulo_modulo_nat @ A @ B)) != B) => ((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))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3485_mod__Suc)). 159.61/70.67 thf(33494,plain,((! [A:nat,B:nat]: (((~ ((suc @ (modulo_modulo_nat @ A @ B)) = B)) => ((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7303])). 159.61/70.67 thf(4318,axiom,((! [A:complex,B:complex]: ((exp_complex @ (minus_minus_complex @ A @ B)) = (divide1717551699836669952omplex @ (exp_complex @ A) @ (exp_complex @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6082_exp__diff)). 159.61/70.67 thf(22094,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)],[4318])). 159.61/70.67 thf(2314,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2160_divide__pos__neg)). 159.61/70.67 thf(15694,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2314])). 159.61/70.67 thf(2635,axiom,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (modulo364778990260209775nteger @ A @ B)) = (times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3533_minus__mod__eq__mult__div)). 159.61/70.67 thf(16743,plain,((! [A:code_integer,B:code_integer]: ((minus_8373710615458151222nteger @ A @ (modulo364778990260209775nteger @ A @ B)) = (times_3573771949741848930nteger @ B @ (divide6298287555418463151nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2635])). 159.61/70.67 thf(3008,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/sandbox/benchmark/theBenchmark.p',fact_4635_minus__add__distrib)). 159.61/70.67 thf(17927,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)],[3008])). 159.61/70.67 thf(4900,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/sandbox/benchmark/theBenchmark.p',fact_9034_Suc__times__binomial__eq)). 159.61/70.67 thf(24191,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)],[4900])). 159.61/70.67 thf(7274,axiom,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) != (size_size_list_nat @ B)) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_neq__if__length__neq)). 159.61/70.67 thf(33390,plain,((! [A:list_nat,B:list_nat]: ((~ ((size_size_list_nat @ A) = (size_size_list_nat @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7274])). 159.61/70.67 thf(6667,axiom,((! [A:(nat > nat)]: (((ord_less_eq_nat @ zero_zero_nat @ (suminf_nat @ A)) <= (! [B:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ B)))) <= (summable_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7054_suminf__nonneg)). 159.61/70.67 thf(30839,plain,((! [A:(nat > nat)]: ((ord_less_eq_nat @ zero_zero_nat @ (suminf_nat @ (A))) | ~ (! [B:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ B))) | ~ (summable_nat @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6667])). 159.61/70.67 thf(1987,axiom,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (groups705719431365010083at_int @ (^ [C:nat]: (plus_plus_int @ A @ (semiri1314217659103216013at_int @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8923_pochhammer__Suc__prod__rev)). 159.61/70.67 thf(14672,plain,((! [A:int,B:nat]: ((comm_s4660882817536571857er_int @ A @ (suc @ B)) = (groups705719431365010083at_int @ (^ [C:nat]: (plus_plus_int @ A @ (semiri1314217659103216013at_int @ (minus_minus_nat @ B @ C)))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1987])). 159.61/70.67 thf(5461,axiom,((! [A:num]: ((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (plus_plus_num @ A @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4880_diff__numeral__special_I4_J)). 159.61/70.67 thf(26312,plain,((! [A:num]: ((minus_8373710615458151222nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ one_one_Code_integer) = (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ (plus_plus_num @ A @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5461])). 159.61/70.67 thf(7805,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: (((ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) <= (vEBT_invar_vebt @ A @ C)) <= (vEBT_vebt_member @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_member__bound)). 159.61/70.67 thf(35200,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) | ~ (vEBT_invar_vebt @ A @ C) | ~ (vEBT_vebt_member @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7805])). 159.61/70.67 thf(3951,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/sandbox/benchmark/theBenchmark.p',fact_7828_double__gauss__sum__from__Suc__0)). 159.61/70.67 thf(20965,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)],[3951])). 159.61/70.67 thf(1939,axiom,((! [A:set_nat,B:nat]: ((ord_less_eq_nat @ (finite_card_nat @ A) @ B) <= (ord_less_eq_set_nat @ A @ (set_or4665077453230672383an_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9719_subset__eq__atLeast0__lessThan__card)). 159.61/70.67 thf(14511,plain,((! [A:set_nat,B:nat]: ((ord_less_eq_nat @ (finite_card_nat @ A) @ B) | ~ (ord_less_eq_set_nat @ A @ (set_or4665077453230672383an_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1939])). 159.61/70.67 thf(2733,axiom,((! [A:complex,B:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_add__diff__cancel__right_H)). 159.61/70.67 thf(17062,plain,((! [A:complex,B:complex]: ((minus_minus_complex @ (plus_plus_complex @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2733])). 159.61/70.67 thf(7369,axiom,(((zero_n2687167440665602831ol_nat @ ($true)) = one_one_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4323_of__bool__eq_I2_J)). 159.61/70.67 thf(33733,plain,(((zero_n2687167440665602831ol_nat @ ($true)) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7369])). 159.61/70.67 thf(7898,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (((ord_less_eq_nat @ B @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ 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_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3577_divmod__digit__1_I1_J)). 159.61/70.67 thf(35501,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => (((ord_less_eq_nat @ B @ (modulo_modulo_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ 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_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7898])). 159.61/70.67 thf(4595,axiom,((! [A:num]: ((abs_abs_real @ (uminus_uminus_real @ (numeral_numeral_real @ A))) = (numeral_numeral_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5412_abs__neg__numeral)). 159.61/70.67 thf(23120,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)],[4595])). 159.61/70.67 thf(5444,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/sandbox/benchmark/theBenchmark.p',fact_6612_of__nat__le__of__nat__power__cancel__iff)). 159.61/70.67 thf(26249,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)],[5444])). 159.61/70.67 thf(6662,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (C != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4444_pinf_I4_J)). 159.61/70.67 thf(30822,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (~ (C = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6662])). 159.61/70.67 thf(5667,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_Suc__le__eq)). 159.61/70.67 thf(27007,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)],[5667])). 159.61/70.67 thf(4300,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (times_7803423173614009249d_enat @ A @ B)) = ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) & (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2630_enat__0__less__mult__iff)). 159.61/70.67 thf(22044,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (times_7803423173614009249d_enat @ A @ B)) = ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ A) & (ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4300])). 159.61/70.67 thf(564,axiom,((real_V2046097035970521341omplex = (^ [A:real,B:complex]: (complex2 @ (times_times_real @ A @ (re @ B)) @ (times_times_real @ A @ (im @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9661_scaleR__complex_Ocode)). 159.61/70.67 thf(10045,plain,(((real_V2046097035970521341omplex) = (^ [A:real,B:complex]: (complex2 @ (times_times_real @ A @ (re @ B)) @ (times_times_real @ A @ (im @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[564])). 159.61/70.67 thf(5053,axiom,((! [A:num]: ((ord_less_int @ (uminus_uminus_int @ (numeral_numeral_int @ A)) @ (uminus_uminus_int @ one_one_int)) = (A != one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4833_neg__numeral__less__neg__one__iff)). 159.61/70.67 thf(24750,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)],[5053])). 159.61/70.67 thf(3834,axiom,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ A @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_complex @ (groups2073611262835488442omplex @ A @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8440_sum_OatMost__Suc)). 159.61/70.67 thf(20595,plain,((! [A:(nat > complex),B:nat]: ((groups2073611262835488442omplex @ (A) @ (set_ord_atMost_nat @ (suc @ B))) = (plus_plus_complex @ (groups2073611262835488442omplex @ (A) @ (set_ord_atMost_nat @ B)) @ (A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3834])). 159.61/70.67 thf(3525,axiom,((! [A:nat]: ((groups2073611262835488442omplex @ (^ [B:nat]: (divide1717551699836669952omplex @ (gbinomial_complex @ (semiri8010041392384452111omplex @ (plus_plus_nat @ A @ B)) @ B) @ (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ B))) @ (set_ord_atMost_nat @ A)) = (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8949_gbinomial__sum__nat__pow2)). 159.61/70.67 thf(19568,plain,((! [A:nat]: ((groups2073611262835488442omplex @ (^ [B:nat]: (divide1717551699836669952omplex @ (gbinomial_complex @ (semiri8010041392384452111omplex @ (plus_plus_nat @ A @ B)) @ B) @ (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ B))) @ (set_ord_atMost_nat @ A)) = (power_power_complex @ (numera6690914467698888265omplex @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3525])). 159.61/70.67 thf(635,axiom,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ B) => ((divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ A)) = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5118_dvd__div__neg)). 159.61/70.67 thf(10287,plain,((! [A:complex,B:complex]: ((dvd_dvd_complex @ A @ B) => ((divide1717551699836669952omplex @ B @ (uminus1482373934393186551omplex @ A)) = (uminus1482373934393186551omplex @ (divide1717551699836669952omplex @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[635])). 159.61/70.67 thf(5513,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (ord_less_eq_real @ (abs_abs_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5482_abs__le__D1)). 159.61/70.67 thf(26497,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)],[5513])). 159.61/70.67 thf(7883,axiom,((! [A:num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_one__plus__numeral)). 159.61/70.67 thf(35449,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)],[7883])). 159.61/70.67 thf(6442,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/sandbox/benchmark/theBenchmark.p',fact_232_power__mult__numeral)). 159.61/70.67 thf(30031,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)],[6442])). 159.61/70.67 thf(3155,axiom,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (? [C:real]: (((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 @ C @ B) & (ord_less_real @ zero_zero_real @ C)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8144_Maclaurin__sin__expansion3)). 159.61/70.67 thf(18406,plain,((! [A:nat,B:real]: (((ord_less_real @ zero_zero_real @ B) => (? [C:real]: (((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 @ C @ B) & (ord_less_real @ zero_zero_real @ C)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3155])). 159.61/70.67 thf(7595,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2831_order_Ostrict__implies__not__eq)). 159.61/70.67 thf(34544,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7595])). 159.61/70.67 thf(1945,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ B @ A)) = (dvd_dvd_Code_integer @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3795_dvd__add__triv__right__iff)). 159.61/70.67 thf(14528,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ B @ A)) = (dvd_dvd_Code_integer @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1945])). 159.61/70.67 thf(963,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ one_one_int) = ((dvd_dvd_int @ A @ one_one_int) & (dvd_dvd_int @ B @ one_one_int))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4053_is__unit__mult__iff)). 159.61/70.67 thf(11330,plain,((! [A:int,B:int]: ((dvd_dvd_int @ (times_times_int @ A @ B) @ one_one_int) = ((dvd_dvd_int @ A @ one_one_int) & (dvd_dvd_int @ B @ one_one_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[963])). 159.61/70.67 thf(4013,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/sandbox/benchmark/theBenchmark.p',fact_2060_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)). 159.61/70.67 thf(21148,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)],[4013])). 159.61/70.67 thf(109,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/sandbox/benchmark/theBenchmark.p',fact_3398_unset__bit__negative__int__iff)). 159.61/70.67 thf(8585,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)],[109])). 159.61/70.67 thf(4257,axiom,((! [A:real,B:real]: ((ord_less_real @ B @ (times_times_real @ (plus_plus_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ (divide_divide_real @ B @ A))) @ one_one_real) @ A)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8330_floor__divide__upper)). 159.61/70.67 thf(21913,plain,((! [A:real,B:real]: ((ord_less_real @ B @ (times_times_real @ (plus_plus_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ (divide_divide_real @ B @ A))) @ one_one_real) @ A)) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4257])). 159.61/70.67 thf(3495,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/sandbox/benchmark/theBenchmark.p',fact_1136_add_Oassoc)). 159.61/70.67 thf(19476,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)],[3495])). 159.61/70.67 thf(6585,axiom,((! [A:num,B:num]: ((dvd_dvd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (unique6322359934112328802ux_nat @ (unique5055182867167087721od_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5455_dvd__numeral__simp)). 159.61/70.67 thf(30544,plain,((! [A:num,B:num]: ((dvd_dvd_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (unique6322359934112328802ux_nat @ (unique5055182867167087721od_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6585])). 159.61/70.67 thf(2888,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/sandbox/benchmark/theBenchmark.p',fact_7269_powr__neg__one)). 159.61/70.67 thf(17548,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)],[2888])). 159.61/70.67 thf(7306,axiom,((! [A: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))))) <= ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit1 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5664_odd__mod__4__div__2)). 159.61/70.67 thf(33506,plain,((! [A: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)))) | ~ ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit1 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7306])). 159.61/70.67 thf(5048,axiom,((! [A:num,B:num,C:num,D:num]: (((product_Pair_num_num @ A @ B) = (product_Pair_num_num @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3604_old_Oprod_Oinject)). 159.61/70.67 thf(24737,plain,((! [A:num,B:num,C:num,D:num]: (((product_Pair_num_num @ A @ B) = (product_Pair_num_num @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5048])). 159.61/70.67 thf(8252,axiom,((! [A:num]: ((bit_se2002935070580805687sk_nat @ (numeral_numeral_nat @ A)) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2002935070580805687sk_nat @ (pred_numeral @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5928_mask__numeral)). 159.61/70.67 thf(36784,plain,((! [A:num]: ((bit_se2002935070580805687sk_nat @ (numeral_numeral_nat @ A)) = (plus_plus_nat @ one_one_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2002935070580805687sk_nat @ (pred_numeral @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8252])). 159.61/70.67 thf(3279,axiom,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_real @ B @ A))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8993_inverse__less__iff__less)). 159.61/70.67 thf(18808,plain,((! [A:real,B:real]: (((ord_less_real @ zero_zero_real @ B) => ((ord_less_real @ (inverse_inverse_real @ A) @ (inverse_inverse_real @ B)) = (ord_less_real @ B @ A))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3279])). 159.61/70.67 thf(5837,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1450_discrete)). 159.61/70.67 thf(27792,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)],[5837])). 159.61/70.67 thf(5083,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3079_order_Ostrict__iff__order)). 159.61/70.67 thf(24860,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5083])). 159.61/70.67 thf(2026,axiom,((! [A:real,B:real]: ((ord_less_real @ (exp_real @ A) @ (exp_real @ B)) => (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6057_exp__less__cancel)). 159.61/70.67 thf(14796,plain,((! [A:real,B:real]: ((ord_less_real @ (exp_real @ A) @ (exp_real @ B)) => (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2026])). 159.61/70.67 thf(4341,axiom,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1885_comm__monoid__add__class_Oadd__0)). 159.61/70.67 thf(22162,plain,((! [A:int]: ((plus_plus_int @ zero_zero_int @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4341])). 159.61/70.67 thf(3285,axiom,((! [A:int,B:int]: ((~ (ord_less_int @ B @ A)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3026_leD)). 159.61/70.67 thf(18826,plain,((! [A:int,B:int]: (~ (ord_less_int @ B @ A) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3285])). 159.61/70.67 thf(641,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/sandbox/benchmark/theBenchmark.p',fact_5270_ln__le__minus__one)). 159.61/70.67 thf(10304,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)],[641])). 159.61/70.67 thf(7017,axiom,((! [A:nat,B:nat]: ((bit_se2925701944663578781it_nat @ A @ (semiri1316708129612266289at_nat @ B)) = (semiri1316708129612266289at_nat @ (bit_se2925701944663578781it_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6714_take__bit__of__nat)). 159.61/70.67 thf(32406,plain,((! [A:nat,B:nat]: ((bit_se2925701944663578781it_nat @ A @ (semiri1316708129612266289at_nat @ B)) = (semiri1316708129612266289at_nat @ (bit_se2925701944663578781it_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7017])). 159.61/70.67 thf(3395,axiom,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (ord_le2932123472753598470d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3146_dual__order_Ostrict__implies__order)). 159.61/70.67 thf(19168,plain,((! [A:extended_enat,B:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => (ord_le2932123472753598470d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3395])). 159.61/70.67 thf(1150,axiom,((! [A:(nat > complex),B:nat,C:complex]: ((minus_minus_complex @ (groups2073611262835488442omplex @ A @ (set_ord_lessThan_nat @ B)) @ (times_times_complex @ (semiri8010041392384452111omplex @ B) @ C)) = (groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7967_sumr__diff__mult__const2)). 159.61/70.67 thf(11935,plain,((! [A:(nat > complex),B:nat,C:complex]: ((minus_minus_complex @ (groups2073611262835488442omplex @ (A) @ (set_ord_lessThan_nat @ B)) @ (times_times_complex @ (semiri8010041392384452111omplex @ B) @ C)) = (groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (A @ D) @ C)) @ (set_ord_lessThan_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150])). 159.61/70.67 thf(4380,axiom,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ A) = (plus_p3455044024723400733d_enat @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_mult__2)). 159.61/70.67 thf(22281,plain,((! [A:extended_enat]: ((times_7803423173614009249d_enat @ (numera1916890842035813515d_enat @ (bit0 @ one)) @ A) = (plus_p3455044024723400733d_enat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4380])). 159.61/70.67 thf(5724,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/sandbox/benchmark/theBenchmark.p',fact_1923_nat__mult__eq__cancel__disj)). 159.61/70.67 thf(27206,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)],[5724])). 159.61/70.67 thf(6162,axiom,((! [A:$o,B:$o]: (((~ (A)) => ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = none_nat)) & ((A) => ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (some_nat @ zero_zero_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1948_vebt__pred_Osimps_I2_J)). 159.61/70.67 thf(28953,plain,((! [A:$o,B:$o]: (((~ (A)) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6162])). 159.61/70.67 thf(7601,axiom,((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__C12_C)). 159.61/70.67 thf(34564,plain,((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7601])). 159.61/70.67 thf(5992,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/sandbox/benchmark/theBenchmark.p',fact_3849_unit__div__1__unit)). 159.61/70.67 thf(28412,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)],[5992])). 159.61/70.67 thf(6447,axiom,((! [A:real,B:real,C:num]: (((divide_divide_real @ A @ B) = (uminus_uminus_real @ (numeral_numeral_real @ C))) = ((((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real) <= (B = zero_zero_real)) & ((A = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B)) <= (B != zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5245_divide__eq__eq__numeral_I2_J)). 159.61/70.67 thf(30046,plain,((! [A:real,B:real,C:num]: (((divide_divide_real @ A @ B) = (uminus_uminus_real @ (numeral_numeral_real @ C))) = ((((uminus_uminus_real @ (numeral_numeral_real @ C)) = zero_zero_real) | ~ (B = zero_zero_real)) & ((A = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ C)) @ B)) | (B = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6447])). 159.61/70.67 thf(4271,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/sandbox/benchmark/theBenchmark.p',fact_6148_of__int__round__abs__le)). 159.61/70.67 thf(21956,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)],[4271])). 159.61/70.67 thf(1326,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((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)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6305_log__base__10__eq2)). 159.61/70.67 thf(12535,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ A) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326])). 159.61/70.67 thf(4303,axiom,((! [A:real,B:real,C:complex]: ((real_V2046097035970521341omplex @ A @ (real_V2046097035970521341omplex @ B @ C)) = (real_V2046097035970521341omplex @ (times_times_real @ A @ B) @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9192_scaleR__scaleR)). 159.61/70.67 thf(22054,plain,((! [A:real,B:real,C:complex]: ((real_V2046097035970521341omplex @ A @ (real_V2046097035970521341omplex @ B @ C)) = (real_V2046097035970521341omplex @ (times_times_real @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4303])). 159.61/70.67 thf(4103,axiom,((! [A:nat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (semiri4216267220026989637d_enat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6587_of__nat__0__less__iff)). 159.61/70.67 thf(21417,plain,((! [A:nat]: ((ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ (semiri4216267220026989637d_enat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4103])). 159.61/70.67 thf(5105,axiom,((! [A:(int > (int > $o)),B:int]: ((A @ (abs_abs_int @ B) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) <= (! [C:int]: ((A @ C @ (power_power_int @ C @ (numeral_numeral_nat @ (bit0 @ one)))) <= (ord_less_eq_int @ zero_zero_int @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5646_abs__sqrt__wlog)). 159.61/70.67 thf(24927,plain,((! [A:(int > (int > $o)),B:int]: ((A @ (abs_abs_int @ B) @ (power_power_int @ B @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (! [C:int]: ((A @ C @ (power_power_int @ C @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (ord_less_eq_int @ zero_zero_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5105])). 159.61/70.67 thf(4552,axiom,((! [A:nat,B:nat,C:nat]: ((member_nat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3362_atLeastAtMost__iff)). 159.61/70.67 thf(22975,plain,((! [A:nat,B:nat,C:nat]: ((member_nat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4552])). 159.61/70.67 thf(1856,axiom,((! [A:complex,B:complex,C:complex,D:complex]: (((plus_plus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ D)) = (plus_plus_complex @ (times_times_complex @ A @ D) @ (times_times_complex @ C @ B))) = ((B = D) | (A = C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4578_crossproduct__eq)). 159.61/70.67 thf(14251,plain,((! [A:complex,B:complex,C:complex,D:complex]: (((plus_plus_complex @ (times_times_complex @ A @ B) @ (times_times_complex @ C @ D)) = (plus_plus_complex @ (times_times_complex @ A @ D) @ (times_times_complex @ C @ B))) = ((B = D) | (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1856])). 159.61/70.67 thf(6379,axiom,((! [A:nat]: ((((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) != zero_zero_nat) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (~ ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) != one_one_nat)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4255_parity__cases)). 159.61/70.67 thf(29748,plain,((! [A:nat]: ((~ ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => (~ ((~ (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)],[6379])). 159.61/70.67 thf(6061,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/sandbox/benchmark/theBenchmark.p',fact_5540_abs__le__iff)). 159.61/70.67 thf(28635,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)],[6061])). 159.61/70.67 thf(6995,axiom,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (ord_less_num @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4454_pinf_I7_J)). 159.61/70.67 thf(32342,plain,((! [A:num]: ? [B:num]: ! [C:num]: ((ord_less_num @ B @ C) => (ord_less_num @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6995])). 159.61/70.67 thf(6824,axiom,((((=) @ list_int) = (^ [A:list_int,B:list_int]: (((size_size_list_int @ A) = (size_size_list_int @ B)) & ! [C:nat]: (((nth_int @ A @ C) = (nth_int @ B @ C)) <= (ord_less_nat @ C @ (size_size_list_int @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_list__eq__iff__nth__eq)). 159.61/70.67 thf(31516,plain,((((=) @ list_int) = (^ [A:list_int,B:list_int]: (((size_size_list_int @ A) = (size_size_list_int @ B)) & ! [C:nat]: (((nth_int @ A @ C) = (nth_int @ B @ C)) | ~ (ord_less_nat @ C @ (size_size_list_int @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6824])). 159.61/70.67 thf(502,axiom,((! [A:complex]: (((csqrt @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = A) <= ((((re @ A) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ (im @ A))) | (ord_less_real @ zero_zero_real @ (re @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9676_csqrt__square)). 159.61/70.67 thf(9848,plain,((! [A:complex]: (((csqrt @ (power_power_complex @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = A) | ~ ((((re @ A) = zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ (im @ A))) | (ord_less_real @ zero_zero_real @ (re @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])). 159.61/70.67 thf(6612,axiom,((! [A:nat,B:real]: (((times_times_real @ (power_power_real @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_real @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2530_power__minus__mult)). 159.61/70.67 thf(30642,plain,((! [A:nat,B:real]: (((times_times_real @ (power_power_real @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_real @ B @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6612])). 159.61/70.67 thf(3062,axiom,((! [A:real,B:nat]: (((B = zero_zero_nat) | ((real_V7735802525324610683m_real @ A) = one_one_real)) <= ((power_power_real @ A @ B) = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6945_power__eq__1__iff)). 159.61/70.67 thf(18093,plain,((! [A:real,B:nat]: ((B = zero_zero_nat) | ((real_V7735802525324610683m_real @ A) = one_one_real) | ~ ((power_power_real @ A @ B) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3062])). 159.61/70.67 thf(4480,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/sandbox/benchmark/theBenchmark.p',fact_6151_or__minus__numerals_I1_J)). 159.61/70.67 thf(22664,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)],[4480])). 159.61/70.67 thf(4532,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/sandbox/benchmark/theBenchmark.p',fact_4423_replicate__length__same)). 159.61/70.67 thf(22897,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)],[4532])). 159.61/70.67 thf(1130,axiom,((! [A:nat,B:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_vebt_buildup @ A) @ B))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2599_buildup__nothing__in__min__max)). 159.61/70.67 thf(11875,plain,((! [A:nat,B:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_vebt_buildup @ A) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130])). 159.61/70.67 thf(1646,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ (times_times_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ (divide_divide_real @ B @ A))) @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8317_floor__divide__lower)). 159.61/70.67 thf(13589,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ (times_times_real @ (ring_1_of_int_real @ (archim6058952711729229775r_real @ (divide_divide_real @ B @ A))) @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1646])). 159.61/70.67 thf(6231,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/sandbox/benchmark/theBenchmark.p',fact_6185_or__minus__numerals_I8_J)). 159.61/70.67 thf(29186,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)],[6231])). 159.61/70.67 thf(6062,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/sandbox/benchmark/theBenchmark.p',fact_5529_abs__triangle__ineq2)). 159.61/70.67 thf(28638,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)],[6062])). 159.61/70.67 thf(7044,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3151_dual__order_Ostrict__implies__order)). 159.61/70.67 thf(32498,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7044])). 159.61/70.67 thf(6795,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/sandbox/benchmark/theBenchmark.p',fact_6220_or__not__num__neg_Osimps_I5_J)). 159.61/70.67 thf(31430,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)],[6795])). 159.61/70.67 thf(500,axiom,((! [A:(nat > extended_enat),B:nat,C:nat]: ((groups7108830773950497114d_enat @ A @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo2538466533108834004d_enat @ (^ [D:nat]: (plus_p3455044024723400733d_enat @ (A @ D))) @ B @ C @ zero_z5237406670263579293d_enat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8907_sum__atLeastAtMost__code)). 159.61/70.67 thf(9842,plain,((! [A:(nat > extended_enat),B:nat,C:nat]: ((groups7108830773950497114d_enat @ (A) @ (set_or1269000886237332187st_nat @ B @ C)) = (set_fo2538466533108834004d_enat @ (^ [D:nat]: (plus_p3455044024723400733d_enat @ (A @ D))) @ B @ C @ zero_z5237406670263579293d_enat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[500])). 159.61/70.67 thf(3471,axiom,((! [A:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) @ one_one_int) = A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3915_odd__two__times__div__two__succ)). 159.61/70.67 thf(19400,plain,((! [A:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((plus_plus_int @ (times_times_int @ (numeral_numeral_int @ (bit0 @ one)) @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one)))) @ one_one_int) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3471])). 159.61/70.67 thf(205,axiom,((! [A:complex,B:complex]: ((re @ (plus_plus_complex @ A @ B)) = (plus_plus_real @ (re @ A) @ (re @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9634_plus__complex_Osimps_I1_J)). 159.61/70.67 thf(8876,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)],[205])). 159.61/70.67 thf(898,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/sandbox/benchmark/theBenchmark.p',fact_7009_sin__cos__squared__add)). 159.61/70.67 thf(11135,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)],[898])). 159.61/70.67 thf(4230,axiom,((! [A:int,B:int]: ((ord_less_eq_nat @ (nat2 @ A) @ (nat2 @ B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9428_nat__mono)). 159.61/70.67 thf(21832,plain,((! [A:int,B:int]: ((ord_less_eq_nat @ (nat2 @ A) @ (nat2 @ B)) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4230])). 159.61/70.67 thf(3386,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le72135733267957522d_enat @ C @ A) => (ord_le72135733267957522d_enat @ C @ B)) <= (ord_le2932123472753598470d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3118_dual__order_Ostrict__trans1)). 159.61/70.67 thf(19136,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le72135733267957522d_enat @ C @ A) => (ord_le72135733267957522d_enat @ C @ B)) | ~ (ord_le2932123472753598470d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3386])). 159.61/70.67 thf(218,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/sandbox/benchmark/theBenchmark.p',fact_9158_tan__cot)). 159.61/70.67 thf(8918,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)],[218])). 159.61/70.67 thf(2052,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/sandbox/benchmark/theBenchmark.p',fact_5873_of__int__less__neg__numeral__power__cancel__iff)). 159.61/70.67 thf(14873,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)],[2052])). 159.61/70.67 thf(8206,axiom,((! [A:nat,B:list_num,C:list_num]: (((nth_Pr6456567536196504476um_num @ (product_num_num @ B @ C) @ A) = (product_Pair_num_num @ (nth_num @ B @ (divide_divide_nat @ A @ (size_size_list_num @ C))) @ (nth_num @ C @ (modulo_modulo_nat @ A @ (size_size_list_num @ C))))) <= (ord_less_nat @ A @ (times_times_nat @ (size_size_list_num @ B) @ (size_size_list_num @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3587_product__nth)). 159.61/70.67 thf(36499,plain,((! [A:nat,B:list_num,C:list_num]: (((nth_Pr6456567536196504476um_num @ (product_num_num @ B @ C) @ A) = (product_Pair_num_num @ (nth_num @ B @ (divide_divide_nat @ A @ (size_size_list_num @ C))) @ (nth_num @ C @ (modulo_modulo_nat @ A @ (size_size_list_num @ C))))) | ~ (ord_less_nat @ A @ (times_times_nat @ (size_size_list_num @ B) @ (size_size_list_num @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8206])). 159.61/70.67 thf(1193,axiom,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (inverse_inverse_real @ A)) = ((ord_less_eq_real @ A @ one_one_real) & (ord_less_real @ zero_zero_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9090_one__le__inverse__iff)). 159.61/70.67 thf(12085,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (inverse_inverse_real @ A)) = ((ord_less_eq_real @ A @ one_one_real) & (ord_less_real @ zero_zero_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193])). 159.61/70.67 thf(6520,axiom,((! [A:num]: ((size_size_num @ (bit0 @ A)) = (plus_plus_nat @ (size_size_num @ A) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2380_num_Osize_I5_J)). 159.61/70.67 thf(30309,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)],[6520])). 159.61/70.67 thf(7077,axiom,((! [A:(nat > nat),B:nat]: (((! [C:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ C))) => ((ord_less_nat @ zero_zero_nat @ (A @ B)) => (ord_less_nat @ zero_zero_nat @ (suminf_nat @ A)))) <= (summable_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7085_suminf__pos2)). 159.61/70.67 thf(32637,plain,((! [A:(nat > nat),B:nat]: (((! [C:nat]: (ord_less_eq_nat @ zero_zero_nat @ (A @ C))) => ((ord_less_nat @ zero_zero_nat @ (A @ B)) => (ord_less_nat @ zero_zero_nat @ (suminf_nat @ (A))))) | ~ (summable_nat @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7077])). 159.61/70.67 thf(7053,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((ord_less_eq_nat @ (groups3542108847815614940at_nat @ B @ A) @ (groups3542108847815614940at_nat @ C @ A)) <= (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7394_sum__mono)). 159.61/70.67 thf(32530,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((ord_less_eq_nat @ (groups3542108847815614940at_nat @ (B) @ A) @ (groups3542108847815614940at_nat @ (C) @ A)) | ~ (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_nat @ (B @ D) @ (C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7053])). 159.61/70.67 thf(4056,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/sandbox/benchmark/theBenchmark.p',fact_4567_signed__take__bit__diff)). 159.61/70.67 thf(21272,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)],[4056])). 159.61/70.67 thf(4192,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/sandbox/benchmark/theBenchmark.p',fact_94_add__numeral__left)). 159.61/70.67 thf(21693,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)],[4192])). 159.61/70.67 thf(2202,axiom,((! [A:real]: ((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (inverse_inverse_real @ A) @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9029_negative__imp__inverse__negative)). 159.61/70.67 thf(15359,plain,((! [A:real]: ((ord_less_real @ A @ zero_zero_real) => (ord_less_real @ (inverse_inverse_real @ A) @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2202])). 159.61/70.67 thf(3437,axiom,((! [A:complex,B:nat,C:nat]: ((((comm_s2602460028002588243omplex @ A @ C) = zero_zero_complex) <= (ord_less_eq_nat @ B @ C)) <= ((comm_s2602460028002588243omplex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8215_pochhammer__eq__0__mono)). 159.61/70.67 thf(19298,plain,((! [A:complex,B:nat,C:nat]: (((comm_s2602460028002588243omplex @ A @ C) = zero_zero_complex) | ~ (ord_less_eq_nat @ B @ C) | ~ ((comm_s2602460028002588243omplex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3437])). 159.61/70.67 thf(2522,axiom,((! [A:nat]: ((divide6298287555418463151nteger @ one_one_Code_integer @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) = (zero_n356916108424825756nteger @ (A = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4380_one__div__2__pow__eq)). 159.61/70.67 thf(16368,plain,((! [A:nat]: ((divide6298287555418463151nteger @ one_one_Code_integer @ (power_8256067586552552935nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)) = (zero_n356916108424825756nteger @ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2522])). 159.61/70.67 thf(1147,axiom,((! [A:real,B:real]: ((one_one_real = (divide_divide_real @ A @ B)) = ((B = A) & (B != zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1666_eq__divide__eq__1)). 159.61/70.67 thf(11925,plain,((! [A:real,B:real]: ((one_one_real = (divide_divide_real @ A @ B)) = ((B = A) & ~ (B = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147])). 159.61/70.67 thf(2563,axiom,((! [A:num]: ~ (ord_le6747313008572928689nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5186_not__numeral__less__neg__one)). 159.61/70.67 thf(16490,plain,((! [A:num]: ~ (ord_le6747313008572928689nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2563])). 159.61/70.67 thf(2223,axiom,((! [A:int,B:int]: ((archim6058952711729229775r_real @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))) = (divide_divide_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8229_floor__divide__of__int__eq)). 159.61/70.67 thf(15429,plain,((! [A:int,B:int]: ((archim6058952711729229775r_real @ (divide_divide_real @ (ring_1_of_int_real @ A) @ (ring_1_of_int_real @ B))) = (divide_divide_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2223])). 159.61/70.67 thf(7413,axiom,((! [A:int]: ((^ [B:int]: (times_times_int @ B @ A)) = (times_times_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1411_mult__commute__abs)). 159.61/70.67 thf(33867,plain,((! [A:int]: ((^ [B:int]: (times_times_int @ B @ A)) = (times_times_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7413])). 159.61/70.67 thf(7700,axiom,((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ zero_zero_nat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4188_even__zero)). 159.61/70.67 thf(34855,plain,((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7700])). 159.61/70.67 thf(1172,axiom,((! [A:real,B:real,C:num]: ((A = (divide_divide_real @ B @ (numeral_numeral_real @ C))) = ((((times_times_real @ A @ (numeral_numeral_real @ C)) = B) <= ((numeral_numeral_real @ C) != zero_zero_real)) & ((A = zero_zero_real) <= ((numeral_numeral_real @ C) = zero_zero_real)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1730_eq__divide__eq__numeral1_I1_J)). 159.61/70.67 thf(12007,plain,((! [A:real,B:real,C:num]: ((A = (divide_divide_real @ B @ (numeral_numeral_real @ C))) = ((((times_times_real @ A @ (numeral_numeral_real @ C)) = B) | ((numeral_numeral_real @ C) = zero_zero_real)) & ((A = zero_zero_real) | ~ ((numeral_numeral_real @ C) = zero_zero_real)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172])). 159.61/70.67 thf(976,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/sandbox/benchmark/theBenchmark.p',fact_5195_nonzero__neg__divide__eq__eq)). 159.61/70.67 thf(11373,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)],[976])). 159.61/70.67 thf(7825,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/sandbox/benchmark/theBenchmark.p',fact_6645_even__of__nat)). 159.61/70.67 thf(35273,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)],[7825])). 159.61/70.67 thf(198,axiom,((! [A:num]: ((ord_max_int @ (numeral_numeral_int @ A) @ one_one_int) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_max__0__1_I6_J)). 159.61/70.67 thf(8857,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)],[198])). 159.61/70.67 thf(2004,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ C @ A))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2033_add__increasing2)). 159.61/70.67 thf(14727,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ C @ A))) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2004])). 159.61/70.67 thf(5426,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/sandbox/benchmark/theBenchmark.p',fact_4221_dvd__mult__cancel2)). 159.61/70.67 thf(26180,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)],[5426])). 159.61/70.67 thf(7283,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/sandbox/benchmark/theBenchmark.p',fact_4798_semiring__norm_I171_J)). 159.61/70.67 thf(33418,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)],[7283])). 159.61/70.67 thf(859,axiom,((! [A:real]: ((ord_less_int @ one_one_int @ (archim6058952711729229775r_real @ A)) = (ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8200_one__less__floor)). 159.61/70.67 thf(11021,plain,((! [A:real]: ((ord_less_int @ one_one_int @ (archim6058952711729229775r_real @ A)) = (ord_less_eq_real @ (numeral_numeral_real @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[859])). 159.61/70.67 thf(7453,axiom,((! [A:nat]: ((member_nat @ zero_zero_nat @ (nat_set_decode @ A)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4552_set__decode__0)). 159.61/70.67 thf(33999,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)],[7453])). 159.61/70.67 thf(1106,axiom,((! [A:int,B:int,C:int]: (((plus_plus_int @ A @ B) = (plus_plus_int @ C @ B)) = (A = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_add__right__cancel)). 159.61/70.67 thf(11803,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)],[1106])). 159.61/70.67 thf(944,axiom,((ord_less_eq_real @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one))) @ (numeral_numeral_real @ (bit0 @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6761_pi__half__le__two)). 159.61/70.67 thf(11276,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)],[944])). 159.61/70.67 thf(6591,axiom,((! [A:int,B:int]: ((A = B) | ~ (ord_less_eq_int @ A @ B) | ~ (ord_less_eq_int @ B @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3661_verit__la__disequality)). 159.61/70.67 thf(30576,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)],[6591])). 159.61/70.67 thf(2864,axiom,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ (uminus5710092332889474511et_nat @ A)) = (A = bot_bot_set_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5126_subset__Compl__self__eq)). 159.61/70.67 thf(17469,plain,((! [A:set_nat]: ((ord_less_eq_set_nat @ A @ (uminus5710092332889474511et_nat @ A)) = (A = bot_bot_set_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2864])). 159.61/70.67 thf(6040,axiom,((! [A:nat]: ? [B:list_nat]: ((size_size_list_nat @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_Ex__list__of__length)). 159.61/70.67 thf(28568,plain,((! [A:nat]: ? [B:list_nat]: ((size_size_list_nat @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6040])). 159.61/70.67 thf(1657,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))) = ((A = C) | (B = D))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4581_crossproduct__eq)). 159.61/70.67 thf(13620,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))) = ((A = C) | (B = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657])). 159.61/70.67 thf(8238,axiom,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ (produc738532404422230701BT_nat @ A @ B)) => (((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (((C = (vEBT_Leaf @ D @ ($false))) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ zero_zero_nat))))) <= (B = (suc @ zero_zero_nat))))) => (((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B))) <= (C = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)))) => ((! [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_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:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (((~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B))) <= (((~ ((ord_less_nat @ B @ D) | (ord_less_nat @ E @ B))) => (((C = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (if_nat @ ((((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) = E) <= (B = D)) & ((B != D) => (B = E))) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (if_nat @ (((B = D) => ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) = E)) & ((B = E) <= (B != D))) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ 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))) <= (~ ((B = D) & (B = E)))) & (((B = D) & (B = E)) => (C = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ F)) @ G @ H))))) & ((C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)) <= ((ord_less_nat @ E @ B) | (ord_less_nat @ B @ D))))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (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)) @ (suc @ zero_zero_nat) @ F @ G)) => ((C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ zero_zero_nat) @ F @ G)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ zero_zero_nat) @ F @ G) @ B))))))))) <= (! [D:$o,E:$o]: ((! [F:nat]: ((B = (suc @ (suc @ F))) => ((C = (vEBT_Leaf @ D @ E)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ (suc @ F)))))))) <= (A = (vEBT_Leaf @ D @ E)))))) <= (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (((C = (vEBT_Leaf @ ($false) @ E)) => (~ (accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ zero_zero_nat)))) <= (B = zero_zero_nat)))))) <= ((vEBT_vebt_delete @ A @ B) = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3311_vebt__delete_Opelims)). 159.61/70.67 thf(36658,plain,((! [A:vEBT_VEBT,B:nat,C:vEBT_VEBT]: (((accp_P2887432264394892906BT_nat @ (vEBT_vebt_delete_rel) @ (produc738532404422230701BT_nat @ A @ B)) => (((! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (((C = (vEBT_Leaf @ D @ ($false))) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_delete_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ zero_zero_nat))))) | ~ (B = (suc @ zero_zero_nat))))) => (((! [D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_delete_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F) @ B)) | ~ (C = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ D @ E @ F)))) => ((! [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ zero_zero_nat @ F @ G)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_delete_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:nat,F:nat,G:list_VEBT_VEBT,H:vEBT_VEBT]: (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_delete_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H) @ B)) | ~ (((~ ((ord_less_nat @ B @ D) | (ord_less_nat @ E @ B))) => (((C = (if_VEBT_VEBT @ (ord_less_nat @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (size_s6755466524823107622T_VEBT @ G)) @ (if_VEBT_VEBT @ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (if_nat @ ((((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) = E) | ~ (B = D)) & ((~ (B = D)) => (B = E))) @ (if_nat @ ((vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) = none_nat) @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (plus_plus_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (the_nat @ (vEBT_vebt_maxt @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_vebt_delete @ H @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ (if_nat @ (B = D) @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ D) @ (if_nat @ (((B = D) => ((plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) = E)) & ((B = E) | (B = D))) @ (plus_plus_nat @ (times_times_nat @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_maxt @ (nth_VEBT_VEBT @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ E))) @ (suc @ (suc @ F)) @ (list_u1324408373059187874T_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one)))) @ (vEBT_vebt_delete @ (nth_VEBT_VEBT @ G @ (vEBT_VEBT_high @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ B) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (vEBT_VEBT_low @ (if_nat @ (B = D) @ (plus_plus_nat @ (times_times_nat @ (the_nat @ (vEBT_vebt_mint @ H)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (suc @ (suc @ F)) @ (numeral_numeral_nat @ (bit0 @ one))))) @ (the_nat @ (vEBT_vebt_mint @ (nth_VEBT_VEBT @ G @ (the_nat @ (vEBT_vebt_mint @ H)))))) @ 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))) | ((B = D) & (B = E))) & (((B = D) & (B = E)) => (C = (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ F)) @ G @ H))))) & ((C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (suc @ F)) @ G @ H)) | ~ ((ord_less_nat @ E @ B) | (ord_less_nat @ B @ D)))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ (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)) @ (suc @ zero_zero_nat) @ F @ G)) => ((C = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ zero_zero_nat) @ F @ G)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_delete_rel) @ (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ E)) @ (suc @ zero_zero_nat) @ F @ G) @ B))))))))) | ~ (! [D:$o,E:$o]: (! [F:nat]: ((B = (suc @ (suc @ F))) => ((C = (vEBT_Leaf @ D @ E)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_delete_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ (suc @ (suc @ F))))))) | ~ (A = (vEBT_Leaf @ D @ E)))))) | ~ (! [D:$o,E:$o]: ((A = (vEBT_Leaf @ D @ E)) => (((C = (vEBT_Leaf @ ($false) @ E)) => (~ (accp_P2887432264394892906BT_nat @ (vEBT_vebt_delete_rel) @ (produc738532404422230701BT_nat @ (vEBT_Leaf @ D @ E) @ zero_zero_nat)))) | ~ (B = zero_zero_nat)))))) | ~ ((vEBT_vebt_delete @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8238])). 159.61/70.67 thf(7221,axiom,((! [A:nat,B:int,C:int]: ((((power_power_int @ B @ A) = C) = ((groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (if_int @ (D = zero_zero_nat) @ (uminus_uminus_int @ C) @ (if_int @ (D = A) @ one_one_int @ zero_zero_int)) @ (power_power_int @ B @ D))) @ (set_ord_atMost_nat @ A)) = zero_zero_int)) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8943_root__polyfun)). 159.61/70.67 thf(33225,plain,((! [A:nat,B:int,C:int]: ((((power_power_int @ B @ A) = C) = ((groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (if_int @ (D = zero_zero_nat) @ (uminus_uminus_int @ C) @ (if_int @ (D = A) @ one_one_int @ zero_zero_int)) @ (power_power_int @ B @ D))) @ (set_ord_atMost_nat @ A)) = zero_zero_int)) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7221])). 159.61/70.67 thf(6197,axiom,((zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1886_zero__neq__one)). 159.61/70.67 thf(29083,plain,((~ (zero_z5237406670263579293d_enat = one_on7984719198319812577d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6197])). 159.61/70.67 thf(7614,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/sandbox/benchmark/theBenchmark.p',fact_8611_prod_Oin__pairs__0)). 159.61/70.67 thf(34596,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)],[7614])). 159.61/70.67 thf(3402,axiom,((! [A:real,B:real]: ((A != B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2829_order_Ostrict__implies__not__eq)). 159.61/70.67 thf(19188,plain,((! [A:real,B:real]: (~ (A = B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3402])). 159.61/70.67 thf(3078,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ B @ C)) = (dvd_dvd_Code_integer @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3989_dvd__add__right__iff)). 159.61/70.67 thf(18139,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((dvd_dvd_Code_integer @ A @ B) => ((dvd_dvd_Code_integer @ A @ (plus_p5714425477246183910nteger @ B @ C)) = (dvd_dvd_Code_integer @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3078])). 159.61/70.67 thf(8203,axiom,(((! [A:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => (! [B:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ B @ na)) & ((vEBT_VEBT_high @ B @ na) = A)) => ((ord_less_nat @ mi @ B) & (ord_less_eq_nat @ B @ ma))) & (((vEBT_VEBT_high @ ma @ na) = A) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ ma @ na)))))) <= (mi != ma))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33__C7_C)). 159.61/70.67 thf(36482,plain,((! [A:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ m)) => (! [B:nat]: (((vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ B @ na)) & ((vEBT_VEBT_high @ B @ na) = A)) => ((ord_less_nat @ mi @ B) & (ord_less_eq_nat @ B @ ma))) & (((vEBT_VEBT_high @ ma @ na) = A) => (vEBT_V8194947554948674370ptions @ (nth_VEBT_VEBT @ treeList @ A) @ (vEBT_VEBT_low @ ma @ na))))) | (mi = ma))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8203])). 159.61/70.67 thf(7913,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/sandbox/benchmark/theBenchmark.p',fact_3565_divmod__digit__0_I1_J)). 159.61/70.67 thf(35549,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)],[7913])). 159.61/70.67 thf(1801,axiom,((! [A:set_nat,B:(nat > real),C:(nat > real)]: ((((? [D:nat]: ((member_nat @ D @ A) & (ord_less_real @ (B @ D) @ (C @ D)))) => (ord_less_real @ (groups6591440286371151544t_real @ B @ A) @ (groups6591440286371151544t_real @ C @ A))) <= (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (B @ D) @ (C @ D))))) <= (finite_finite_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7481_sum__strict__mono__ex1)). 159.61/70.67 thf(14062,plain,((! [A:set_nat,B:(nat > real),C:(nat > real)]: (((? [D:nat]: ((member_nat @ D @ A) & (ord_less_real @ (B @ D) @ (C @ D)))) => (ord_less_real @ (groups6591440286371151544t_real @ (B) @ A) @ (groups6591440286371151544t_real @ (C) @ A))) | ~ (! [D:nat]: ((member_nat @ D @ A) => (ord_less_eq_real @ (B @ D) @ (C @ D)))) | ~ (finite_finite_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1801])). 159.61/70.67 thf(5137,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/sandbox/benchmark/theBenchmark.p',fact_3897_odd__Suc__minus__one)). 159.61/70.67 thf(25026,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)],[5137])). 159.61/70.67 thf(3542,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/sandbox/benchmark/theBenchmark.p',fact_6605_of__nat__less__of__nat__power__cancel__iff)). 159.61/70.67 thf(19618,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)],[3542])). 159.61/70.67 thf(2336,axiom,((! [A:int,B:int]: ((B != A) <= (ord_less_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2932_order__less__imp__not__eq2)). 159.61/70.67 thf(15758,plain,((! [A:int,B:int]: (~ (B = A) | ~ (ord_less_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2336])). 159.61/70.67 thf(7917,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2093_mult__pos__pos)). 159.61/70.67 thf(35561,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7917])). 159.61/70.67 thf(5943,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_power__increasing__iff)). 159.61/70.67 thf(28260,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_eq_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)],[5943])). 159.61/70.67 thf(2456,axiom,((! [A:int]: ((ord_less_int @ A @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4684_less__neg__neg)). 159.61/70.67 thf(16157,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)],[2456])). 159.61/70.67 thf(7105,axiom,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT]: (((A = (replicate_VEBT_VEBT @ B @ C)) <= (! [D:vEBT_VEBT]: ((D = C) <= (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A))))) <= ((size_s6755466524823107622T_VEBT @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4419_replicate__eqI)). 159.61/70.67 thf(32748,plain,((! [A:list_VEBT_VEBT,B:nat,C:vEBT_VEBT]: ((A = (replicate_VEBT_VEBT @ B @ C)) | ~ (! [D:vEBT_VEBT]: ((D = C) | ~ (member_VEBT_VEBT @ D @ (set_VEBT_VEBT2 @ A)))) | ~ ((size_s6755466524823107622T_VEBT @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7105])). 159.61/70.67 thf(508,axiom,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ C) => ((minus_minus_set_nat @ B @ (minus_minus_set_nat @ C @ A)) = A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2995_double__diff)). 159.61/70.67 thf(9870,plain,((! [A:set_nat,B:set_nat,C:set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ C) => ((minus_minus_set_nat @ B @ (minus_minus_set_nat @ C @ A)) = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])). 159.61/70.67 thf(303,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/sandbox/benchmark/theBenchmark.p',fact_8908_sum__atLeastAtMost__code)). 159.61/70.67 thf(9188,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)],[303])). 159.61/70.67 thf(3021,axiom,((! [A:extended_enat,B:nat]: ((comm_s3181272606743183617d_enat @ A @ (suc @ B)) = (times_7803423173614009249d_enat @ A @ (comm_s3181272606743183617d_enat @ (plus_p3455044024723400733d_enat @ A @ one_on7984719198319812577d_enat) @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8263_pochhammer__rec)). 159.61/70.67 thf(17965,plain,((! [A:extended_enat,B:nat]: ((comm_s3181272606743183617d_enat @ A @ (suc @ B)) = (times_7803423173614009249d_enat @ A @ (comm_s3181272606743183617d_enat @ (plus_p3455044024723400733d_enat @ A @ one_on7984719198319812577d_enat) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3021])). 159.61/70.67 thf(5069,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/sandbox/benchmark/theBenchmark.p',fact_5676_signed__take__bit__numeral__bit1)). 159.61/70.67 thf(24810,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)],[5069])). 159.61/70.67 thf(4994,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/sandbox/benchmark/theBenchmark.p',fact_1850_mult__right__cancel)). 159.61/70.67 thf(24527,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)],[4994])). 159.61/70.67 thf(1166,axiom,(((neg_nu8295874005876285629c_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5799_dbl__inc__simps_I4_J)). 159.61/70.67 thf(11992,plain,(((neg_nu8295874005876285629c_real @ (uminus_uminus_real @ one_one_real)) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166])). 159.61/70.67 thf(3852,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/sandbox/benchmark/theBenchmark.p',fact_1289_add__diff__eq)). 159.61/70.67 thf(20654,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)],[3852])). 159.61/70.67 thf(1068,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/sandbox/benchmark/theBenchmark.p',fact_7873_lessThan__subset__iff)). 159.61/70.67 thf(11675,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)],[1068])). 159.61/70.67 thf(4700,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/sandbox/benchmark/theBenchmark.p',fact_5633_abs__square__eq__1)). 159.61/70.67 thf(23503,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)],[4700])). 159.61/70.67 thf(7728,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_group__cancel_Oadd1)). 159.61/70.67 thf(34968,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ D) = (plus_plus_nat @ B @ (plus_plus_nat @ C @ D))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7728])). 159.61/70.67 thf(6572,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((suc @ (minus_minus_nat @ B @ (suc @ A))) = (minus_minus_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_Suc__diff__Suc)). 159.61/70.67 thf(30497,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((suc @ (minus_minus_nat @ B @ (suc @ A))) = (minus_minus_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6572])). 159.61/70.67 thf(7196,axiom,((! [A:nat]: ((set_ord_atMost_nat @ (suc @ A)) = (insert_nat @ (suc @ A) @ (set_ord_atMost_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8527_atMost__Suc)). 159.61/70.67 thf(33130,plain,((! [A:nat]: ((set_ord_atMost_nat @ (suc @ A)) = (insert_nat @ (suc @ A) @ (set_ord_atMost_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7196])). 159.61/70.67 thf(5544,axiom,((! [A:nat,B:num,C:nat]: (((semiri4216267220026989637d_enat @ A) = (power_8040749407984259932d_enat @ (numera1916890842035813515d_enat @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6598_real__of__nat__eq__numeral__power__cancel__iff)). 159.61/70.67 thf(26587,plain,((! [A:nat,B:num,C:nat]: (((semiri4216267220026989637d_enat @ A) = (power_8040749407984259932d_enat @ (numera1916890842035813515d_enat @ B) @ C)) = (A = (power_power_nat @ (numeral_numeral_nat @ B) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5544])). 159.61/70.67 thf(6493,axiom,((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2322_zero__less__two)). 159.61/70.67 thf(30222,plain,((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6493])). 159.61/70.67 thf(8218,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/sandbox/benchmark/theBenchmark.p',fact_4553_set__decode__Suc)). 159.61/70.67 thf(36531,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)],[8218])). 159.61/70.67 thf(4348,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/sandbox/benchmark/theBenchmark.p',fact_295_power__one__over)). 159.61/70.67 thf(22183,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)],[4348])). 159.61/70.67 thf(831,axiom,((! [A:nat,B:nat]: ((finite_card_nat @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_nat @ (suc @ B) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9712_card__atLeastAtMost)). 159.61/70.67 thf(10931,plain,((! [A:nat,B:nat]: ((finite_card_nat @ (set_or1269000886237332187st_nat @ A @ B)) = (minus_minus_nat @ (suc @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[831])). 159.61/70.67 thf(7853,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ one_one_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_power__gt1__lemma)). 159.61/70.67 thf(35351,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ one_one_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7853])). 159.61/70.67 thf(2047,axiom,((! [A:$o]: ((ord_less_int @ (zero_n2684676970156552555ol_int @ A) @ one_one_int) = (~ (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4346_of__bool__less__one__iff)). 159.61/70.67 thf(14858,plain,((! [A:$o]: ((ord_less_int @ (zero_n2684676970156552555ol_int @ A) @ one_one_int) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2047])). 159.61/70.67 thf(3235,axiom,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ A @ (plus_plus_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1270_diff__diff__eq)). 159.61/70.67 thf(18655,plain,((! [A:complex,B:complex,C:complex]: ((minus_minus_complex @ (minus_minus_complex @ A @ B) @ C) = (minus_minus_complex @ A @ (plus_plus_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3235])). 159.61/70.67 thf(3798,axiom,((! [A:complex]: ((times_times_complex @ (exp_complex @ A) @ A) = (times_times_complex @ A @ (exp_complex @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6058_exp__times__arg__commute)). 159.61/70.67 thf(20471,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)],[3798])). 159.61/70.67 thf(5553,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/sandbox/benchmark/theBenchmark.p',fact_5127_real__minus__mult__self__le)). 159.61/70.67 thf(26612,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)],[5553])). 159.61/70.67 thf(1756,axiom,((! [A:(nat > int),B:int,C:nat]: (((groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (A @ D) @ (power_power_int @ B @ D))) @ (set_ord_atMost_nat @ C)) = zero_zero_int) => (~ (! [D:(nat > int)]: ~ (! [E:int]: ((groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (A @ F) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ C)) = (times_times_int @ (minus_minus_int @ E @ B) @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (D @ F) @ (power_power_int @ E @ F))) @ (set_ord_lessThan_nat @ C)))))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8883_polyfun__linear__factor__root)). 159.61/70.67 thf(13922,plain,((! [A:(nat > int),B:int,C:nat]: (((groups3539618377306564664at_int @ (^ [D:nat]: (times_times_int @ (A @ D) @ (power_power_int @ B @ D))) @ (set_ord_atMost_nat @ C)) = zero_zero_int) => (~ (! [D:(nat > int)]: ~ (! [E:int]: ((groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (A @ F) @ (power_power_int @ E @ F))) @ (set_ord_atMost_nat @ C)) = (times_times_int @ (minus_minus_int @ E @ B) @ (groups3539618377306564664at_int @ (^ [F:nat]: (times_times_int @ (D @ F) @ (power_power_int @ E @ F))) @ (set_ord_lessThan_nat @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756])). 159.61/70.67 thf(8117,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1600_less__add__same__cancel1)). 159.61/70.67 thf(36196,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)],[8117])). 159.61/70.67 thf(4668,axiom,((! [A:real]: (ord_less_eq_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2508_zero__le__power2)). 159.61/70.67 thf(23395,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)],[4668])). 159.61/70.67 thf(2190,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/sandbox/benchmark/theBenchmark.p',fact_1589_add__le__same__cancel1)). 159.61/70.67 thf(15310,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)],[2190])). 159.61/70.67 thf(1459,axiom,(((plus_plus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4738_add__neg__numeral__special_I7_J)). 159.61/70.67 thf(13016,plain,(((plus_plus_int @ one_one_int @ (uminus_uminus_int @ one_one_int)) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459])). 159.61/70.67 thf(1428,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ C @ A) => (ord_less_real @ C @ B)) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3126_dual__order_Ostrict__trans2)). 159.61/70.67 thf(12908,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ C @ A) => (ord_less_real @ C @ B)) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428])). 159.61/70.67 thf(2908,axiom,((! [A:extended_enat,B:extended_enat,C:(extended_enat > extended_enat),D:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ (C @ B) @ D) => ((ord_le72135733267957522d_enat @ (C @ A) @ D) <= (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)) <= (ord_le72135733267957522d_enat @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2898_order__less__subst2)). 159.61/70.67 thf(17616,plain,((! [A:extended_enat,B:extended_enat,C:(extended_enat > extended_enat),D:extended_enat]: ((ord_le72135733267957522d_enat @ A @ B) => ((ord_le72135733267957522d_enat @ (C @ B) @ D) => ((ord_le72135733267957522d_enat @ (C @ A) @ D) | ~ (! [E:extended_enat,F:extended_enat]: ((ord_le72135733267957522d_enat @ (C @ E) @ (C @ F)) | ~ (ord_le72135733267957522d_enat @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2908])). 159.61/70.67 thf(90,axiom,((! [A:real]: ((minus_minus_real @ (power_power_real @ (cosh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (sinh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9346_hyperbolic__pythagoras)). 159.61/70.67 thf(8525,plain,((! [A:real]: ((minus_minus_real @ (power_power_real @ (cosh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_real @ (sinh_real @ A) @ (numeral_numeral_nat @ (bit0 @ one)))) = one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 159.61/70.67 thf(699,axiom,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2929_order__less__imp__not__eq2)). 159.61/70.67 thf(10492,plain,((! [A:real,B:real]: ((ord_less_real @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[699])). 159.61/70.67 thf(5315,axiom,((! [A:nat,B:nat]: ((ord_max_nat @ (suc @ A) @ (suc @ B)) = (suc @ (ord_max_nat @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_max__Suc__Suc)). 159.61/70.67 thf(25699,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)],[5315])). 159.61/70.67 thf(1876,axiom,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_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/sandbox/benchmark/theBenchmark.p',fact_2156_zero__less__divide__iff)). 159.61/70.67 thf(14310,plain,((! [A:real,B:real]: ((ord_less_real @ zero_zero_real @ (divide_divide_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)],[1876])). 159.61/70.67 thf(1721,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/sandbox/benchmark/theBenchmark.p',fact_1288_add__diff__eq)). 159.61/70.67 thf(13817,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)],[1721])). 159.61/70.67 thf(7324,axiom,((! [A:nat]: ~ (ord_less_eq_int @ zero_zero_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ (suc @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6851_not__zle__0__negative)). 159.61/70.67 thf(33582,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)],[7324])). 159.61/70.67 thf(5037,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/sandbox/benchmark/theBenchmark.p',fact_3450_mod__mult__eq)). 159.61/70.67 thf(24677,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)],[5037])). 159.61/70.67 thf(948,axiom,((! [A:real,B:complex,C:complex]: ((real_V2046097035970521341omplex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (real_V2046097035970521341omplex @ A @ B) @ (real_V2046097035970521341omplex @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9213_scaleR__right__distrib)). 159.61/70.67 thf(11286,plain,((! [A:real,B:complex,C:complex]: ((real_V2046097035970521341omplex @ A @ (plus_plus_complex @ B @ C)) = (plus_plus_complex @ (real_V2046097035970521341omplex @ A @ B) @ (real_V2046097035970521341omplex @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[948])). 159.61/70.67 thf(4367,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/sandbox/benchmark/theBenchmark.p',fact_8328_pochhammer__absorb__comp)). 159.61/70.67 thf(22238,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)],[4367])). 159.61/70.67 thf(1946,axiom,((! [A:real]: (((ord_less_real @ zero_zero_real @ (cot_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/sandbox/benchmark/theBenchmark.p',fact_9404_cot__gt__zero)). 159.61/70.67 thf(14531,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (cot_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)],[1946])). 159.61/70.67 thf(880,axiom,((! [A:complex,B:complex]: (sums_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (if_complex @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ (times_times_complex @ (real_V2046097035970521341omplex @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C)) @ (power_power_complex @ A @ D)) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_complex)) @ (set_ord_atMost_nat @ C))) @ (cos_complex @ (plus_plus_complex @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9179_sums__cos__x__plus__y)). 159.61/70.67 thf(11086,plain,((! [A:complex,B:complex]: (sums_complex @ (^ [C:nat]: (groups2073611262835488442omplex @ (^ [D:nat]: (if_complex @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ (times_times_complex @ (real_V2046097035970521341omplex @ (divide_divide_real @ (ring_1_of_int_real @ (times_times_int @ (power_power_int @ (uminus_uminus_int @ one_one_int) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) @ (semiri1314217659103216013at_int @ (binomial @ C @ D)))) @ (semiri2265585572941072030t_real @ C)) @ (power_power_complex @ A @ D)) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D))) @ zero_zero_complex)) @ (set_ord_atMost_nat @ C))) @ (cos_complex @ (plus_plus_complex @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[880])). 159.61/70.67 thf(2445,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/sandbox/benchmark/theBenchmark.p',fact_7788_sum_Oin__pairs)). 159.61/70.67 thf(16125,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)],[2445])). 159.61/70.67 thf(225,axiom,((bit_se1745604003318907178nteger = (^ [A:nat,B:code_integer]: (if_Code_integer @ (A = zero_zero_nat) @ zero_z3403309356797280102nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (bit_se1745604003318907178nteger @ (minus_minus_nat @ A @ one_one_nat) @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))) @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4598_take__bit__rec)). 159.61/70.67 thf(8940,plain,(((bit_se1745604003318907178nteger) = (^ [A:nat,B:code_integer]: (if_Code_integer @ (A = zero_zero_nat) @ zero_z3403309356797280102nteger @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (bit_se1745604003318907178nteger @ (minus_minus_nat @ A @ one_one_nat) @ (divide6298287555418463151nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))) @ (numera6620942414471956472nteger @ (bit0 @ one))) @ (modulo364778990260209775nteger @ B @ (numera6620942414471956472nteger @ (bit0 @ one)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[225])). 159.61/70.67 thf(691,axiom,((! [A:int,B:int,C:int]: ((bit_se725231765392027082nd_int @ A @ (bit_se725231765392027082nd_int @ B @ C)) = (bit_se725231765392027082nd_int @ B @ (bit_se725231765392027082nd_int @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6041_and_Oleft__commute)). 159.61/70.67 thf(10460,plain,((! [A:int,B:int,C:int]: ((bit_se725231765392027082nd_int @ A @ (bit_se725231765392027082nd_int @ B @ C)) = (bit_se725231765392027082nd_int @ B @ (bit_se725231765392027082nd_int @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[691])). 159.61/70.67 thf(4937,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3100_order_Ostrict__iff__not)). 159.61/70.67 thf(24310,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)],[4937])). 159.61/70.67 thf(6176,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/sandbox/benchmark/theBenchmark.p',fact_240_power__add__numeral2)). 159.61/70.67 thf(29011,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)],[6176])). 159.61/70.67 thf(8190,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/sandbox/benchmark/theBenchmark.p',fact_2578_set__bit__0)). 159.61/70.67 thf(36439,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)],[8190])). 159.61/70.67 thf(2460,axiom,((! [A:real]: ~ (ord_less_real @ A @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2802_dual__order_Oirrefl)). 159.61/70.67 thf(16171,plain,((! [A:real]: ~ (ord_less_real @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2460])). 159.61/70.67 thf(7446,axiom,((! [A:num]: (one != (bit1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5502_verit__eq__simplify_I12_J)). 159.61/70.67 thf(33974,plain,((! [A:num]: ~ (one = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7446])). 159.61/70.67 thf(2748,axiom,((! [A:real]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ one_one_int) = (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6980_ceiling__less__one)). 159.61/70.67 thf(17108,plain,((! [A:real]: ((ord_less_int @ (archim7802044766580827645g_real @ A) @ one_one_int) = (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2748])). 159.61/70.67 thf(2921,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/sandbox/benchmark/theBenchmark.p',fact_4118_le__imp__power__dvd)). 159.61/70.67 thf(17661,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)],[2921])). 159.61/70.67 thf(5364,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/sandbox/benchmark/theBenchmark.p',fact_1300_max__add__distrib__right)). 159.61/70.67 thf(25930,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)],[5364])). 159.61/70.67 thf(5354,axiom,((! [A:num]: ((bit_or_not_num_neg @ one @ (bit1 @ A)) = (bit1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6219_or__not__num__neg_Osimps_I3_J)). 159.61/70.67 thf(25867,plain,((! [A:num]: ((bit_or_not_num_neg @ one @ (bit1 @ A)) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5354])). 159.61/70.67 thf(984,axiom,((! [A:int,B:int]: ((dvd_dvd_int @ A @ (plus_plus_int @ A @ B)) = (dvd_dvd_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3794_dvd__add__triv__left__iff)). 159.61/70.67 thf(11397,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)],[984])). 159.61/70.67 thf(4503,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ A @ C) <= ((vEBT_vebt_maxt @ A) = (some_nat @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_maxt__member)). 159.61/70.67 thf(22734,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ A @ C) | ~ ((vEBT_vebt_maxt @ A) = (some_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4503])). 159.61/70.67 thf(3038,axiom,((! [A:$o]: ((ord_le6747313008572928689nteger @ (zero_n356916108424825756nteger @ A) @ one_one_Code_integer) = (~ (A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4347_of__bool__less__one__iff)). 159.61/70.67 thf(18014,plain,((! [A:$o]: ((ord_le6747313008572928689nteger @ (zero_n356916108424825756nteger @ A) @ one_one_Code_integer) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3038])). 159.61/70.67 thf(2714,axiom,((! [A:real,B:num]: ((archim7802044766580827645g_real @ (plus_plus_real @ A @ (numeral_numeral_real @ B))) = (plus_plus_int @ (archim7802044766580827645g_real @ A) @ (numeral_numeral_int @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6985_ceiling__add__numeral)). 159.61/70.67 thf(17007,plain,((! [A:real,B:num]: ((archim7802044766580827645g_real @ (plus_plus_real @ A @ (numeral_numeral_real @ B))) = (plus_plus_int @ (archim7802044766580827645g_real @ A) @ (numeral_numeral_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2714])). 159.61/70.67 thf(704,axiom,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (arccos @ A) @ pi))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7708_arccos__ubound)). 159.61/70.67 thf(10522,plain,((! [A:real]: ((ord_less_eq_real @ (uminus_uminus_real @ one_one_real) @ A) => ((ord_less_eq_real @ A @ one_one_real) => (ord_less_eq_real @ (arccos @ A) @ pi))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[704])). 159.61/70.67 thf(7822,axiom,((! [A:num]: ((A != one) => ((~ (! [B:num]: (A != (bit1 @ B)))) <= (! [B:num]: (A != (bit0 @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5549_num_Oexhaust)). 159.61/70.67 thf(35264,plain,((! [A:num]: ((~ (A = one)) => (~ (! [B:num]: ~ (A = (bit1 @ B))) | ~ (! [B:num]: ~ (A = (bit0 @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7822])). 159.61/70.67 thf(2142,axiom,((! [A:num]: ((neg_nu8557863876264182079omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu6511756317524482435omplex @ (numera6690914467698888265omplex @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5755_dbl__inc__simps_I1_J)). 159.61/70.67 thf(15164,plain,((! [A:num]: ((neg_nu8557863876264182079omplex @ (uminus1482373934393186551omplex @ (numera6690914467698888265omplex @ A))) = (uminus1482373934393186551omplex @ (neg_nu6511756317524482435omplex @ (numera6690914467698888265omplex @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2142])). 159.61/70.67 thf(369,axiom,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ C @ A) @ (real_V1485227260804924795R_real @ C @ B))) <= (ord_less_eq_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9229_scaleR__left__mono)). 159.61/70.67 thf(9399,plain,((! [A:real,B:real,C:real]: (((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (real_V1485227260804924795R_real @ C @ A) @ (real_V1485227260804924795R_real @ C @ B))) | ~ (ord_less_eq_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])). 159.61/70.67 thf(7408,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/sandbox/benchmark/theBenchmark.p',fact_5820_of__int__le__numeral__iff)). 159.61/70.67 thf(33853,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)],[7408])). 159.61/70.67 thf(5165,axiom,((! [A:real]: ((times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ A)) = (times_times_real @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5391_abs__mult__self__eq)). 159.61/70.67 thf(25135,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)],[5165])). 159.61/70.67 thf(832,axiom,((! [A:real]: (((ring_1_of_int_real @ (archim7802044766580827645g_real @ A)) = A) = (? [B:int]: (A = (ring_1_of_int_real @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6961_of__int__ceiling__cancel)). 159.61/70.67 thf(10934,plain,((! [A:real]: (((ring_1_of_int_real @ (archim7802044766580827645g_real @ A)) = A) = (? [B:int]: (A = (ring_1_of_int_real @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[832])). 159.61/70.67 thf(6001,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/sandbox/benchmark/theBenchmark.p',fact_3852_unit__div__1__div__1)). 159.61/70.67 thf(28447,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)],[6001])). 159.61/70.67 thf(3634,axiom,((! [A:extended_enat,B:extended_enat,C:extended_enat]: (((ord_le72135733267957522d_enat @ A @ C) <= (ord_le72135733267957522d_enat @ B @ C)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2813_order_Ostrict__trans)). 159.61/70.67 thf(19923,plain,((! [A:extended_enat,B:extended_enat,C:extended_enat]: ((ord_le72135733267957522d_enat @ A @ C) | ~ (ord_le72135733267957522d_enat @ B @ C) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3634])). 159.61/70.67 thf(1550,axiom,((! [A:(nat > complex),B:(nat > real)]: ((? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (A @ D)) @ (B @ D)))) => ((summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C)))) <= (summable_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7078_summable__norm__comparison__test)). 159.61/70.67 thf(13289,plain,((! [A:(nat > complex),B:(nat > real)]: ((? [C:nat]: ! [D:nat]: ((ord_less_eq_nat @ C @ D) => (ord_less_eq_real @ (real_V1022390504157884413omplex @ (A @ D)) @ (B @ D)))) => ((summable_real @ (^ [C:nat]: (real_V1022390504157884413omplex @ (A @ C)))) | ~ (summable_real @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550])). 159.61/70.67 thf(624,axiom,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_add__left__cancel)). 159.61/70.67 thf(10245,plain,((! [A:complex,B:complex,C:complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[624])). 159.61/70.67 thf(6800,axiom,((! [A:num,B:code_integer]: ((times_3573771949741848930nteger @ (numera6620942414471956472nteger @ A) @ (uminus1351360451143612070nteger @ B)) = (times_3573771949741848930nteger @ B @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5075_numeral__times__minus__swap)). 159.61/70.67 thf(31444,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)],[6800])). 159.61/70.67 thf(2048,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/sandbox/benchmark/theBenchmark.p',fact_6448_bit__int__def)). 159.61/70.67 thf(14863,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)],[2048])). 159.61/70.67 thf(5376,axiom,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((bit_se1148574629649215175it_nat @ A @ B) = ((B = zero_zero_nat) | (bit_se1148574629649215175it_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6454_odd__bit__iff__bit__pred)). 159.61/70.67 thf(25977,plain,((! [A:nat,B:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((bit_se1148574629649215175it_nat @ A @ B) = ((B = zero_zero_nat) | (bit_se1148574629649215175it_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5376])). 159.61/70.67 thf(5479,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ A) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6183_Suc__0__and__eq)). 159.61/70.67 thf(26375,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)],[5479])). 159.61/70.67 thf(7027,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/sandbox/benchmark/theBenchmark.p',fact_4761_minus__one__mult__self)). 159.61/70.67 thf(32438,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)],[7027])). 159.61/70.67 thf(6270,axiom,((! [A:num]: ((plus_plus_num @ (bit0 @ A) @ one) = (bit1 @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5441_semiring__norm_I5_J)). 159.61/70.67 thf(29379,plain,((! [A:num]: ((plus_plus_num @ (bit0 @ A) @ one) = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6270])). 159.61/70.67 thf(2581,axiom,(((semiri1314217659103216013at_int @ zero_zero_nat) = zero_zero_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6497_of__nat__0)). 159.61/70.67 thf(16546,plain,(((semiri1314217659103216013at_int @ zero_zero_nat) = zero_zero_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2581])). 159.61/70.67 thf(6389,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/sandbox/benchmark/theBenchmark.p',fact_5835_numeral__power__eq__of__int__cancel__iff)). 159.61/70.67 thf(29800,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)],[6389])). 159.61/70.67 thf(1423,axiom,((! [A:real,B:real,C:real,D:real]: (((A != B) & (C != D)) = ((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/sandbox/benchmark/theBenchmark.p',fact_4583_crossproduct__noteq)). 159.61/70.67 thf(12887,plain,((! [A:real,B:real,C:real,D:real]: ((~ (A = B) & ~ (C = D)) = (~ ((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)],[1423])). 159.61/70.67 thf(6075,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/sandbox/benchmark/theBenchmark.p',fact_2569_VEBT__internal_OminNull_Osimps_I5_J)). 159.61/70.67 thf(28673,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)],[6075])). 159.61/70.67 thf(7693,axiom,((! [A:nat,B:nat]: (((? [C:nat]: ((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)) @ B)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_ex__power__ivl2)). 159.61/70.67 thf(34833,plain,((! [A:nat,B:nat]: (? [C:nat]: ((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)) @ B) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7693])). 159.61/70.67 thf(4427,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B))) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2029_add__nonneg__nonneg)). 159.61/70.67 thf(22436,plain,((! [A:real,B:real]: (((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_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)],[4427])). 159.61/70.67 thf(5788,axiom,((! [A:num]: ((divide6298287555418463151nteger @ (numera6620942414471956472nteger @ (bit1 @ A)) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (numera6620942414471956472nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5617_numeral__Bit1__div__2)). 159.61/70.67 thf(27495,plain,((! [A:num]: ((divide6298287555418463151nteger @ (numera6620942414471956472nteger @ (bit1 @ A)) @ (numera6620942414471956472nteger @ (bit0 @ one))) = (numera6620942414471956472nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5788])). 159.61/70.67 thf(3119,axiom,((! [A:code_integer]: ((~ (! [B:code_integer]: (A != (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) @ one_one_Code_integer)))) <= (~ (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4248_oddE)). 159.61/70.67 thf(18285,plain,((! [A:code_integer]: (~ (! [B:code_integer]: ~ (A = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B) @ one_one_Code_integer))) | (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3119])). 159.61/70.67 thf(3685,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) <= (ord_less_real @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3178_order__less__imp__le)). 159.61/70.67 thf(20086,plain,((! [A:real,B:real]: ((ord_less_eq_real @ A @ B) | ~ (ord_less_real @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3685])). 159.61/70.67 thf(4378,axiom,((! [A:real]: (((ord_less_real @ zero_zero_real @ A) => (ord_less_eq_real @ one_one_real @ A)) <= (ord_less_eq_real @ zero_zero_real @ (ln_ln_real @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5231_ln__ge__zero__imp__ge__one)). 159.61/70.67 thf(22276,plain,((! [A:real]: (((ord_less_real @ zero_zero_real @ A) => (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)],[4378])). 159.61/70.67 thf(2753,axiom,((! [A:int,B:int]: ((A != zero_zero_int) => ((divide_divide_int @ (times_times_int @ A @ B) @ A) = B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1633_nonzero__mult__div__cancel__left)). 159.61/70.67 thf(17123,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)],[2753])). 159.61/70.67 thf(1055,axiom,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((divide_divide_int @ C @ (times_times_int @ B @ A)) = (divide_divide_int @ (divide_divide_int @ C @ B) @ A)) <= (dvd_dvd_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4164_div__mult__unit2)). 159.61/70.67 thf(11631,plain,((! [A:int,B:int,C:int]: ((dvd_dvd_int @ A @ one_one_int) => (((divide_divide_int @ C @ (times_times_int @ B @ A)) = (divide_divide_int @ (divide_divide_int @ C @ B) @ A)) | ~ (dvd_dvd_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055])). 159.61/70.67 thf(1306,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/sandbox/benchmark/theBenchmark.p',fact_2629_zdiv__zmult2__eq)). 159.61/70.67 thf(12471,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)],[1306])). 159.61/70.67 thf(6451,axiom,((! [A:num]: ((plus_plus_int @ one_one_int @ (numeral_numeral_int @ A)) = (numeral_numeral_int @ (plus_plus_num @ one @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_one__plus__numeral)). 159.61/70.67 thf(30063,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)],[6451])). 159.61/70.67 thf(1842,axiom,((! [A:real,B:real,C:real]: ((A = (divide_divide_real @ B @ C)) = (((A = zero_zero_real) <= (C = zero_zero_real)) & ((C != zero_zero_real) => ((times_times_real @ A @ C) = B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2174_eq__divide__eq)). 159.61/70.67 thf(14210,plain,((! [A:real,B:real,C:real]: ((A = (divide_divide_real @ B @ C)) = (((A = zero_zero_real) | ~ (C = zero_zero_real)) & ((~ (C = zero_zero_real)) => ((times_times_real @ A @ C) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1842])). 159.61/70.67 thf(1712,axiom,((! [A:extended_enat,B:extended_enat]: ((~ (ord_le72135733267957522d_enat @ B @ A)) <= (ord_le72135733267957522d_enat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2853_order__less__asym_H)). 159.61/70.67 thf(13785,plain,((! [A:extended_enat,B:extended_enat]: (~ (ord_le72135733267957522d_enat @ B @ A) | ~ (ord_le72135733267957522d_enat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712])). 159.61/70.67 thf(2470,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/sandbox/benchmark/theBenchmark.p',fact_3820_dvd__times__left__cancel__iff)). 159.61/70.67 thf(16203,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)],[2470])). 159.61/70.67 thf(779,axiom,((~ (dvd_dvd_int @ zero_zero_int @ one_one_int))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4045_not__is__unit__0)). 159.61/70.67 thf(10763,plain,((~ (dvd_dvd_int @ zero_zero_int @ one_one_int))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[779])). 159.61/70.67 thf(3367,axiom,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1148_ab__semigroup__add__class_Oadd__ac_I1_J)). 159.61/70.67 thf(19072,plain,((! [A:complex,B:complex,C:complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3367])). 159.61/70.67 thf(1613,axiom,((ring_18347121197199848620nteger = (^ [A:int]: (if_Code_integer @ (A = zero_zero_int) @ zero_z3403309356797280102nteger @ (if_Code_integer @ (ord_less_int @ A @ zero_zero_int) @ (uminus1351360451143612070nteger @ (ring_18347121197199848620nteger @ (uminus_uminus_int @ A))) @ (if_Code_integer @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (ring_18347121197199848620nteger @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (ring_18347121197199848620nteger @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_Code_integer))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5752_of__int__code__if)). 159.61/70.67 thf(13493,plain,(((ring_18347121197199848620nteger) = (^ [A:int]: (if_Code_integer @ (A = zero_zero_int) @ zero_z3403309356797280102nteger @ (if_Code_integer @ (ord_less_int @ A @ zero_zero_int) @ (uminus1351360451143612070nteger @ (ring_18347121197199848620nteger @ (uminus_uminus_int @ A))) @ (if_Code_integer @ ((modulo_modulo_int @ A @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int) @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (ring_18347121197199848620nteger @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (ring_18347121197199848620nteger @ (divide_divide_int @ A @ (numeral_numeral_int @ (bit0 @ one))))) @ one_one_Code_integer))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1613])). 159.61/70.67 thf(3580,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/sandbox/benchmark/theBenchmark.p',fact_5849_numeral__power__le__of__int__cancel__iff)). 159.61/70.67 thf(19750,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)],[3580])). 159.61/70.67 thf(342,axiom,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_ri6519982836138164636nteger @ A @ B)) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4570_even__signed__take__bit__iff)). 159.61/70.67 thf(9310,plain,((! [A:nat,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (bit_ri6519982836138164636nteger @ A @ B)) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 159.61/70.67 thf(7345,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/sandbox/benchmark/theBenchmark.p',fact_231_power__mult__numeral)). 159.61/70.67 thf(33652,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)],[7345])). 159.61/70.67 thf(7586,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ A @ (set_or1269000886237332187st_nat @ (suc @ B) @ (suc @ C))) = (groups3542108847815614940at_nat @ (^ [D:nat]: (A @ (suc @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7452_sum_Oshift__bounds__cl__Suc__ivl)). 159.61/70.67 thf(34512,plain,((! [A:(nat > nat),B:nat,C:nat]: ((groups3542108847815614940at_nat @ (A) @ (set_or1269000886237332187st_nat @ (suc @ B) @ (suc @ C))) = (groups3542108847815614940at_nat @ (^ [D:nat]: (A @ (suc @ D))) @ (set_or1269000886237332187st_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7586])). 159.61/70.67 thf(3584,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/sandbox/benchmark/theBenchmark.p',fact_2314_not__sum__squares__lt__zero)). 159.61/70.67 thf(19760,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)],[3584])). 159.61/70.67 thf(821,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/sandbox/benchmark/theBenchmark.p',fact_7077_polar__Ex)). 159.61/70.67 thf(10900,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)],[821])). 159.61/70.67 thf(4405,axiom,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => ((ord_less_real @ (cosh_real @ A) @ (cosh_real @ B)) = (ord_less_real @ B @ A))) <= (ord_less_eq_real @ A @ zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9340_cosh__real__nonpos__less__iff)). 159.61/70.67 thf(22362,plain,((! [A:real,B:real]: (((ord_less_eq_real @ B @ zero_zero_real) => ((ord_less_real @ (cosh_real @ A) @ (cosh_real @ B)) = (ord_less_real @ B @ A))) | ~ (ord_less_eq_real @ A @ zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4405])). 159.61/70.67 thf(8077,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/sandbox/benchmark/theBenchmark.p',fact_3522_cancel__div__mod__rules_I1_J)). 159.61/70.67 thf(36079,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)],[8077])). 159.61/70.67 thf(2103,axiom,((! [A:real,B:int]: ((ord_less_eq_real @ zero_zero_real @ A) => (((A != zero_zero_real) | (ord_less_int @ zero_zero_int @ B)) => ((powr_real @ A @ (ring_1_of_int_real @ B)) = (power_int_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10157_powr__real__of__int_H)). 159.61/70.67 thf(15024,plain,((! [A:real,B:int]: ((ord_less_eq_real @ zero_zero_real @ A) => ((~ (A = zero_zero_real) | (ord_less_int @ zero_zero_int @ B)) => ((powr_real @ A @ (ring_1_of_int_real @ B)) = (power_int_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2103])). 159.61/70.67 thf(5374,axiom,((! [A:real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1493_mult__zero__right)). 159.61/70.67 thf(25966,plain,((! [A:real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5374])). 159.61/70.67 thf(4025,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/sandbox/benchmark/theBenchmark.p',fact_8231_gbinomial__pochhammer)). 159.61/70.67 thf(21184,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)],[4025])). 159.61/70.67 thf(7226,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((! [B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ B @ C) @ D))) => (((! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ D) @ E @ F) @ G))) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ B) @ C @ D) @ E))))) <= (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ zero_zero_nat @ D @ E) @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2213_VEBT__internal_Omembermima_Ocases)). 159.61/70.67 thf(33239,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$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)],[7226])). 159.61/70.67 thf(7569,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/sandbox/benchmark/theBenchmark.p',fact_6486_exp__ge__one__minus__x__over__n__power__n)). 159.61/70.67 thf(34459,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)],[7569])). 159.61/70.67 thf(7170,axiom,((! [A:real,B:num]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ B))) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_real @ zero_zero_real @ A)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (A != zero_zero_real)) | ((numeral_numeral_nat @ B) = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3899_zero__less__power__eq__numeral)). 159.61/70.67 thf(33024,plain,((! [A:real,B:num]: ((ord_less_real @ zero_zero_real @ (power_power_real @ A @ (numeral_numeral_nat @ B))) = ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & (ord_less_real @ zero_zero_real @ A)) | ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (numeral_numeral_nat @ B)) & ~ (A = zero_zero_real)) | ((numeral_numeral_nat @ B) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7170])). 159.61/70.67 thf(3166,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/sandbox/benchmark/theBenchmark.p',fact_5930_tanh__real__altdef)). 159.61/70.67 thf(18440,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)],[3166])). 159.61/70.67 thf(5600,axiom,((! [A:nat,B:nat]: ((((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 @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9790_num__of__nat__plus__distrib)). 159.61/70.67 thf(26777,plain,((! [A:nat,B:nat]: (((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 @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5600])). 159.61/70.67 thf(5727,axiom,((! [A:complex]: ((times_times_complex @ A @ (numera6690914467698888265omplex @ one)) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_mult__numeral__1__right)). 159.61/70.67 thf(27219,plain,((! [A:complex]: ((times_times_complex @ A @ (numera6690914467698888265omplex @ one)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5727])). 159.61/70.67 thf(7969,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4485_minf_I7_J)). 159.61/70.67 thf(35722,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)],[7969])). 159.61/70.67 thf(7247,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/sandbox/benchmark/theBenchmark.p',fact_2531_power__minus__mult)). 159.61/70.67 thf(33313,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)],[7247])). 159.61/70.67 thf(2738,axiom,((! [A:real]: (((ord_less_eq_real @ (arccos @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_eq_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7815_arccos__le__pi2)). 159.61/70.67 thf(17076,plain,((! [A:real]: ((ord_less_eq_real @ (arccos @ A) @ (divide_divide_real @ pi @ (numeral_numeral_real @ (bit0 @ one)))) | ~ (ord_less_eq_real @ A @ one_one_real) | ~ (ord_less_eq_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2738])). 159.61/70.67 thf(4124,axiom,((! [A:real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1549_division__ring__divide__zero)). 159.61/70.67 thf(21478,plain,((! [A:real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4124])). 159.61/70.67 thf(6010,axiom,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_power__one__right)). 159.61/70.67 thf(28472,plain,((! [A:int]: ((power_power_int @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6010])). 159.61/70.67 thf(1619,axiom,((neg_nu5851722552734809277nc_int = (^ [A:int]: (plus_plus_int @ (plus_plus_int @ A @ A) @ one_one_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5913_dbl__inc__def)). 159.61/70.67 thf(13510,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)],[1619])). 159.61/70.67 thf(1261,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/sandbox/benchmark/theBenchmark.p',fact_6479_take__bit__Suc__from__most)). 159.61/70.67 thf(12331,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)],[1261])). 159.61/70.67 thf(1791,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/sandbox/benchmark/theBenchmark.p',fact_4919_take__bit__mult)). 159.61/70.67 thf(14033,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)],[1791])). 159.61/70.67 thf(933,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/sandbox/benchmark/theBenchmark.p',fact_2312_power__less__imp__less__base)). 159.61/70.67 thf(11241,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)],[933])). 159.61/70.67 thf(6999,axiom,((! [A:real,B:real,C:real]: (((times_times_real @ A @ B) = (times_times_real @ A @ C)) = ((B = C) | (A = zero_zero_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1483_mult__cancel__left)). 159.61/70.67 thf(32353,plain,((! [A:real,B:real,C:real]: (((times_times_real @ A @ B) = (times_times_real @ A @ C)) = ((B = C) | (A = zero_zero_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6999])). 159.61/70.67 thf(3925,axiom,((! [A:real,B:real,C:real]: ((powr_real @ A @ (minus_minus_real @ B @ C)) = (divide_divide_real @ (powr_real @ A @ B) @ (powr_real @ A @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7259_powr__diff)). 159.61/70.67 thf(20878,plain,((! [A:real,B:real,C:real]: ((powr_real @ A @ (minus_minus_real @ B @ C)) = (divide_divide_real @ (powr_real @ A @ B) @ (powr_real @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3925])). 159.61/70.67 thf(8242,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/sandbox/benchmark/theBenchmark.p',fact_709_add__mult__distrib2)). 159.61/70.67 thf(36752,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)],[8242])). 159.61/70.67 thf(3590,axiom,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (minus_8373710615458151222nteger @ A @ B)) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ A @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3895_even__diff)). 159.61/70.67 thf(19779,plain,((! [A:code_integer,B:code_integer]: ((dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (minus_8373710615458151222nteger @ A @ B)) = (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (plus_p5714425477246183910nteger @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3590])). 159.61/70.67 thf(2131,axiom,(((neg_nu6075765906172075777c_real @ zero_zero_real) = (uminus_uminus_real @ one_one_real))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5693_dbl__dec__simps_I2_J)). 159.61/70.67 thf(15134,plain,(((neg_nu6075765906172075777c_real @ zero_zero_real) = (uminus_uminus_real @ one_one_real))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2131])). 159.61/70.67 thf(6181,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8078_fact__gt__zero)). 159.61/70.67 thf(29026,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6181])). 159.61/70.67 thf(5241,axiom,(((abs_abs_int @ one_one_int) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5488_abs__one)). 159.61/70.67 thf(25408,plain,(((abs_abs_int @ one_one_int) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5241])). 159.61/70.67 thf(7871,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/sandbox/benchmark/theBenchmark.p',fact_3418_mod__mult__self2)). 159.61/70.67 thf(35406,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)],[7871])). 159.61/70.67 thf(364,axiom,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ A @ (uminus1351360451143612070nteger @ A)) = (ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4669_less__eq__neg__nonpos)). 159.61/70.67 thf(9385,plain,((! [A:code_integer]: ((ord_le3102999989581377725nteger @ A @ (uminus1351360451143612070nteger @ A)) = (ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[364])). 159.61/70.67 thf(1151,axiom,((! [A:real,B:nat]: ((real_V7735802525324610683m_real @ (power_power_real @ A @ B)) = (power_power_real @ (real_V7735802525324610683m_real @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6905_norm__power)). 159.61/70.67 thf(11938,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)],[1151])). 159.61/70.67 thf(5705,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/sandbox/benchmark/theBenchmark.p',fact_4803_semiring__norm_I172_J)). 159.61/70.67 thf(27141,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)],[5705])). 159.61/70.67 thf(4648,axiom,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (B != A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2835_dual__order_Ostrict__implies__not__eq)). 159.61/70.67 thf(23317,plain,((! [A:num,B:num]: ((ord_less_num @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4648])). 159.61/70.67 thf(3680,axiom,((! [A:nat,B:real]: ((times_times_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ A)) @ B) = (times_times_real @ B @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9054_mult__inverse__of__nat__commute)). 159.61/70.67 thf(20071,plain,((! [A:nat,B:real]: ((times_times_real @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ A)) @ B) = (times_times_real @ B @ (inverse_inverse_real @ (semiri5074537144036343181t_real @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3680])). 159.61/70.67 thf(1093,axiom,((! [A:int,B:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4204_odd__even__add)). 159.61/70.67 thf(11754,plain,((! [A:int,B:int]: ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ A)) => ((~ (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ B)) => (dvd_dvd_int @ (numeral_numeral_int @ (bit0 @ one)) @ (plus_plus_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093])). 159.61/70.67 thf(5668,axiom,((! [A:num]: ((unique5055182867167087721od_nat @ one @ (bit1 @ A)) = (product_Pair_nat_nat @ zero_zero_nat @ (numeral_numeral_nat @ one))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5467_divmod__algorithm__code_I4_J)). 159.61/70.67 thf(27010,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)],[5668])). 159.61/70.67 thf(733,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/sandbox/benchmark/theBenchmark.p',fact_1157_add__le__imp__le__right)). 159.61/70.67 thf(10618,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)],[733])). 159.61/70.67 thf(1815,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/sandbox/benchmark/theBenchmark.p',fact_1586_add__le__same__cancel2)). 159.61/70.67 thf(14112,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)],[1815])). 159.61/70.67 thf(8143,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_less__add__Suc2)). 159.61/70.67 thf(36292,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8143])). 159.61/70.67 thf(2660,axiom,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((powr_real @ (inverse_inverse_real @ A) @ B) = (inverse_inverse_real @ (powr_real @ A @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9084_inverse__powr)). 159.61/70.67 thf(16827,plain,((! [A:real,B:real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((powr_real @ (inverse_inverse_real @ A) @ B) = (inverse_inverse_real @ (powr_real @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2660])). 159.61/70.67 thf(5680,axiom,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_eq_int @ C @ B) => ((ord_less_eq_int @ zero_zero_int @ D) => ((ord_less_eq_int @ zero_zero_int @ E) => ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ D @ A) @ (times_times_int @ E @ C)) @ B) <= ((plus_plus_int @ D @ E) = one_one_int))))) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2440_convex__bound__le)). 159.61/70.67 thf(27068,plain,((! [A:int,B:int,C:int,D:int,E:int]: (((ord_less_eq_int @ C @ B) => ((ord_less_eq_int @ zero_zero_int @ D) => ((ord_less_eq_int @ zero_zero_int @ E) => ((ord_less_eq_int @ (plus_plus_int @ (times_times_int @ D @ A) @ (times_times_int @ E @ C)) @ B) | ~ ((plus_plus_int @ D @ E) = one_one_int))))) | ~ (ord_less_eq_int @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5680])). 159.61/70.67 thf(338,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/sandbox/benchmark/theBenchmark.p',fact_9656_times__complex_Osimps_I2_J)). 159.61/70.67 thf(9297,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)],[338])). 159.61/70.67 thf(5437,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/sandbox/benchmark/theBenchmark.p',fact_8635_prod_Ozero__middle)). 159.61/70.67 thf(26225,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)],[5437])). 159.61/70.67 thf(5982,axiom,((semiri2265585572941072030t_real = (^ [A:nat]: (semiri5074537144036343181t_real @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8765_fact__prod)). 159.61/70.67 thf(28385,plain,(((semiri2265585572941072030t_real) = (^ [A:nat]: (semiri5074537144036343181t_real @ (groups708209901874060359at_nat @ (^ [B:nat]: (B)) @ (set_or1269000886237332187st_nat @ one_one_nat @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5982])). 159.61/70.67 thf(998,axiom,((vEBT_VEBT_valid = vEBT_invar_vebt)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9621_valid__eq)). 159.61/70.67 thf(11444,plain,(((vEBT_VEBT_valid) = (vEBT_invar_vebt))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[998])). 159.61/70.67 thf(5,axiom,((! [A:real]: ((ord_less_real @ zero_zero_real @ (sinh_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9309_sinh__real__pos__iff)). 159.61/70.67 thf(8264,plain,((! [A:real]: ((ord_less_real @ zero_zero_real @ (sinh_real @ A)) = (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 159.61/70.67 thf(868,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/sandbox/benchmark/theBenchmark.p',fact_2577_set__bit__0)). 159.61/70.67 thf(11048,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)],[868])). 159.61/70.67 thf(6056,axiom,((! [A:nat,B:(nat > real),C:real,D:real]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_real @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (B @ E) @ (power_power_real @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (B @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_real @ (minus_minus_real @ C @ D) @ (groups6591440286371151544t_real @ (^ [E:nat]: (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (times_times_real @ (B @ (plus_plus_nat @ (plus_plus_nat @ E @ F) @ one_one_nat)) @ (power_power_real @ D @ F)) @ (power_power_real @ C @ E))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ E)))) @ (set_ord_lessThan_nat @ A))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8955_polyfun__diff__alt)). 159.61/70.67 thf(28620,plain,((! [A:nat,B:(nat > real),C:real,D:real]: ((ord_less_eq_nat @ one_one_nat @ A) => ((minus_minus_real @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (B @ E) @ (power_power_real @ C @ E))) @ (set_ord_atMost_nat @ A)) @ (groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (B @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ A))) = (times_times_real @ (minus_minus_real @ C @ D) @ (groups6591440286371151544t_real @ (^ [E:nat]: (groups6591440286371151544t_real @ (^ [F:nat]: (times_times_real @ (times_times_real @ (B @ (plus_plus_nat @ (plus_plus_nat @ E @ F) @ one_one_nat)) @ (power_power_real @ D @ F)) @ (power_power_real @ C @ E))) @ (set_ord_lessThan_nat @ (minus_minus_nat @ A @ E)))) @ (set_ord_lessThan_nat @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6056])). 159.61/70.67 thf(113,axiom,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ A) = (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4682_neg__less__pos)). 159.61/70.67 thf(8596,plain,((! [A:code_integer]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ A) @ A) = (ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 159.61/70.67 thf(2723,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/sandbox/benchmark/theBenchmark.p',fact_8326_pochhammer__absorb__comp)). 159.61/70.67 thf(17035,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)],[2723])). 159.61/70.67 thf(5946,axiom,((! [A:num]: ((ord_max_nat @ zero_zero_nat @ (numeral_numeral_nat @ A)) = (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1700_max__0__1_I3_J)). 159.61/70.67 thf(28269,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)],[5946])). 159.61/70.67 thf(4630,axiom,((! [A:real]: ((times_times_real @ (uminus_uminus_real @ one_one_real) @ A) = (uminus_uminus_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4698_mult__minus1)). 159.61/70.67 thf(23257,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)],[4630])). 159.61/70.67 thf(4088,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/sandbox/benchmark/theBenchmark.p',fact_7657_sum_OatLeast0__atMost__Suc)). 159.61/70.67 thf(21372,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)],[4088])). 159.61/70.67 thf(435,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/sandbox/benchmark/theBenchmark.p',fact_9650_csqrt__minus)). 159.61/70.67 thf(9611,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)],[435])). 159.61/70.67 thf(2290,axiom,((! [A:list_nat,B:set_nat]: (((finite_finite_nat @ B) => ((groups3542108847815614940at_nat @ (count_list_nat @ A) @ B) = (size_size_list_nat @ A))) <= (ord_less_eq_set_nat @ (set_nat2 @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9412_sum__count__set)). 159.61/70.67 thf(15629,plain,((! [A:list_nat,B:set_nat]: (((finite_finite_nat @ B) => ((groups3542108847815614940at_nat @ (count_list_nat @ A) @ B) = (size_size_list_nat @ A))) | ~ (ord_less_eq_set_nat @ (set_nat2 @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2290])). 159.61/70.67 thf(5745,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C))) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1904_diff__induct)). 159.61/70.67 thf(27279,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) => ((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5745])). 159.61/70.67 thf(7060,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/sandbox/benchmark/theBenchmark.p',fact_2513_exp__add__not__zero__imp__right)). 159.61/70.67 thf(32562,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)],[7060])). 159.61/70.67 thf(753,axiom,((! [A:int]: ((ord_less_int @ (plus_plus_int @ A @ A) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1595_double__add__less__zero__iff__single__add__less__zero)). 159.61/70.67 thf(10686,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)],[753])). 159.61/70.67 thf(1920,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/sandbox/benchmark/theBenchmark.p',fact_5769_of__int__less__iff)). 159.61/70.67 thf(14450,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)],[1920])). 159.61/70.67 thf(8082,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 @ ((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)) & ~ ((F = B) | (F = A))) @ (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/sandbox/benchmark/theBenchmark.p',fact_1445_vebt__insert_Osimps_I5_J)). 159.61/70.67 thf(36094,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 @ ((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)) & ~ ((F = B) | (F = A))) @ (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)],[8082])). 159.61/70.67 thf(8052,axiom,(((power_power_real @ one_one_real @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_one__power2)). 159.61/70.67 thf(35997,plain,(((power_power_real @ one_one_real @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_real)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8052])). 159.61/70.67 thf(773,axiom,((! [A:real]: ((A != zero_zero_real) => ((times_times_real @ (inverse_inverse_real @ A) @ A) = one_one_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9074_field__class_Ofield__inverse)). 159.61/70.67 thf(10745,plain,((! [A:real]: ((~ (A = zero_zero_real)) => ((times_times_real @ (inverse_inverse_real @ A) @ A) = one_one_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[773])). 159.61/70.67 thf(6460,axiom,((! [A:nat,B:nat,C:nat]: ((! [D:nat]: (~ (bit_se1148574629649215175it_nat @ A @ D) | ~ (bit_se1148574629649215175it_nat @ B @ D))) => ((bit_se1148574629649215175it_nat @ (plus_plus_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ A @ C) | (bit_se1148574629649215175it_nat @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6364_bit__disjunctive__add__iff)). 159.61/70.67 thf(30088,plain,((! [A:nat,B:nat,C:nat]: ((! [D:nat]: (~ (bit_se1148574629649215175it_nat @ A @ D) | ~ (bit_se1148574629649215175it_nat @ B @ D))) => ((bit_se1148574629649215175it_nat @ (plus_plus_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ A @ C) | (bit_se1148574629649215175it_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6460])). 159.61/70.67 thf(5995,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/sandbox/benchmark/theBenchmark.p',fact_4923_minus__le__iff)). 159.61/70.67 thf(28420,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)],[5995])). 159.61/70.67 thf(5454,axiom,((! [A:int,B:int,C:(int > num),D:num]: ((ord_less_eq_int @ A @ B) => (((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) <= (! [E:int,F:int]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) <= (ord_less_eq_int @ E @ F)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2652_ord__le__eq__subst)). 159.61/70.67 thf(26280,plain,((! [A:int,B:int,C:(int > num),D:num]: ((ord_less_eq_int @ A @ B) => (((C @ B) = D) => ((ord_less_eq_num @ (C @ A) @ D) | ~ (! [E:int,F:int]: ((ord_less_eq_num @ (C @ E) @ (C @ F)) | ~ (ord_less_eq_int @ E @ F)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5454])). 159.61/70.67 thf(5344,axiom,((! [A:complex]: ((power_power_complex @ A @ (numeral_numeral_nat @ (bit1 @ one))) = (times_times_complex @ (times_times_complex @ A @ A) @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5623_power3__eq__cube)). 159.61/70.67 thf(25831,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)],[5344])). 159.61/70.67 thf(6622,axiom,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (C @ D) @ (C @ (minus_minus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (minus_minus_complex @ (C @ B) @ (C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7777_sum__telescope_H_H)). 159.61/70.67 thf(30681,plain,((! [A:nat,B:nat,C:(nat > complex)]: ((ord_less_eq_nat @ A @ B) => ((groups2073611262835488442omplex @ (^ [D:nat]: (minus_minus_complex @ (C @ D) @ (C @ (minus_minus_nat @ D @ one_one_nat)))) @ (set_or1269000886237332187st_nat @ (suc @ A) @ B)) = (minus_minus_complex @ (C @ B) @ (C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6622])). 159.61/70.67 thf(43,axiom,((~ (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5154_le__minus__one__simps_I3_J)). 159.61/70.67 thf(8380,plain,((~ (ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ (uminus1351360451143612070nteger @ one_one_Code_integer)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 159.61/70.67 thf(3193,axiom,((! [A:complex,B:complex,C:nat]: ((power_power_complex @ (plus_plus_complex @ A @ B) @ C) = (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ (binomial @ C @ D)) @ (power_power_complex @ A @ D)) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9146_binomial__ring)). 159.61/70.67 thf(18523,plain,((! [A:complex,B:complex,C:nat]: ((power_power_complex @ (plus_plus_complex @ A @ B) @ C) = (groups2073611262835488442omplex @ (^ [D:nat]: (times_times_complex @ (times_times_complex @ (semiri8010041392384452111omplex @ (binomial @ C @ D)) @ (power_power_complex @ A @ D)) @ (power_power_complex @ B @ (minus_minus_nat @ C @ D)))) @ (set_ord_atMost_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3193])). 159.61/70.67 thf(4554,axiom,((! [A:nat]: ((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ (suc @ A)) = zero_z5237406670263579293d_enat))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1676_power__0__Suc)). 159.61/70.67 thf(22981,plain,((! [A:nat]: ((power_8040749407984259932d_enat @ zero_z5237406670263579293d_enat @ (suc @ A)) = zero_z5237406670263579293d_enat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4554])). 159.61/70.67 thf(336,axiom,((! [A:code_integer,B:code_integer,C:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A) => ((modulo364778990260209775nteger @ B @ (times_3573771949741848930nteger @ C @ A)) = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ C @ (modulo364778990260209775nteger @ (divide6298287555418463151nteger @ B @ C) @ A)) @ (modulo364778990260209775nteger @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3552_unique__euclidean__semiring__numeral__class_Omod__mult2__eq)). 159.61/70.67 thf(9286,plain,((! [A:code_integer,B:code_integer,C:code_integer]: ((ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A) => ((modulo364778990260209775nteger @ B @ (times_3573771949741848930nteger @ C @ A)) = (plus_p5714425477246183910nteger @ (times_3573771949741848930nteger @ C @ (modulo364778990260209775nteger @ (divide6298287555418463151nteger @ B @ C) @ A)) @ (modulo364778990260209775nteger @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 159.61/70.67 thf(2351,axiom,((! [A:num]: (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bit0 @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4151_even__numeral)). 159.61/70.67 thf(15801,plain,((! [A:num]: (dvd_dvd_Code_integer @ (numera6620942414471956472nteger @ (bit0 @ one)) @ (numera6620942414471956472nteger @ (bit0 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2351])). 159.61/70.67 thf(2615,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_real @ C @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2079_mult__less__cancel__left__neg)). 159.61/70.67 thf(16681,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (ord_less_real @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2615])). 159.61/70.67 thf(2178,axiom,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (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) @ (numeral_numeral_int @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6026_or__numerals_I4_J)). 159.61/70.67 thf(15273,plain,((! [A:num,B:num]: ((bit_se1409905431419307370or_int @ (numeral_numeral_int @ (bit0 @ A)) @ (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) @ (numeral_numeral_int @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2178])). 159.61/70.67 thf(2384,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/sandbox/benchmark/theBenchmark.p',fact_7941_sum_Onat__diff__reindex)). 159.61/70.67 thf(15906,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)],[2384])). 159.61/70.67 thf(2211,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/sandbox/benchmark/theBenchmark.p',fact_7252_divide__powr__uminus)). 159.61/70.67 thf(15386,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)],[2211])). 159.61/70.67 thf(4036,axiom,((! [A:real]: (((ord_less_eq_real @ one_one_real @ (inverse_inverse_real @ A)) <= (ord_less_eq_real @ A @ one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9088_one__le__inverse)). 159.61/70.67 thf(21216,plain,((! [A:real]: ((ord_less_eq_real @ one_one_real @ (inverse_inverse_real @ A)) | ~ (ord_less_eq_real @ A @ one_one_real) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4036])). 159.61/70.67 thf(5019,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/sandbox/benchmark/theBenchmark.p',fact_1964_zero__le__mult__iff)). 159.61/70.67 thf(24622,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)],[5019])). 159.61/70.67 thf(5858,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se547839408752420682it_nat @ A @ B) @ C) = ((ord_less_eq_nat @ A @ C) & (bit_se1148574629649215175it_nat @ B @ (minus_minus_nat @ C @ A)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9561_bit__push__bit__iff__nat)). 159.61/70.67 thf(27899,plain,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se547839408752420682it_nat @ A @ B) @ C) = ((ord_less_eq_nat @ A @ C) & (bit_se1148574629649215175it_nat @ B @ (minus_minus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5858])). 159.61/70.67 thf(6763,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/sandbox/benchmark/theBenchmark.p',fact_5558_abs__eq__iff_H)). 159.61/70.67 thf(31320,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)],[6763])). 159.61/70.67 thf(1992,axiom,(((archim7802044766580827645g_real @ one_one_real) = one_one_int)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6966_ceiling__one)). 159.61/70.67 thf(14691,plain,(((archim7802044766580827645g_real @ one_one_real) = one_one_int)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1992])). 159.61/70.67 thf(2518,axiom,(((neg_nu7009210354673126013omplex @ zero_zero_complex) = zero_zero_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3807_dbl__simps_I2_J)). 159.61/70.67 thf(16358,plain,(((neg_nu7009210354673126013omplex @ zero_zero_complex) = zero_zero_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2518])). 159.61/70.67 thf(4506,axiom,((! [A:(nat > real),B:nat,C:real]: ((! [D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (A @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ B)) = C)) = (((A @ zero_zero_nat) = C) & ! [D:nat]: (((A @ D) = zero_zero_real) <= (member_nat @ D @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8925_polyfun__eq__const)). 159.61/70.67 thf(22748,plain,((! [A:(nat > real),B:nat,C:real]: ((! [D:real]: ((groups6591440286371151544t_real @ (^ [E:nat]: (times_times_real @ (A @ E) @ (power_power_real @ D @ E))) @ (set_ord_atMost_nat @ B)) = C)) = (((A @ zero_zero_nat) = C) & ! [D:nat]: (((A @ D) = zero_zero_real) | ~ (member_nat @ D @ (set_or1269000886237332187st_nat @ one_one_nat @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4506])). 159.61/70.67 thf(1020,axiom,((! [A:nat,B:code_integer]: ((times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ B) = (times_3573771949741848930nteger @ B @ (semiri4939895301339042750nteger @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6653_mult__of__nat__commute)). 159.61/70.67 thf(11511,plain,((! [A:nat,B:code_integer]: ((times_3573771949741848930nteger @ (semiri4939895301339042750nteger @ A) @ B) = (times_3573771949741848930nteger @ B @ (semiri4939895301339042750nteger @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020])). 159.61/70.67 thf(3897,axiom,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (times_times_complex @ (comm_s2602460028002588243omplex @ A @ B) @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8271_pochhammer__Suc)). 159.61/70.67 thf(20795,plain,((! [A:complex,B:nat]: ((comm_s2602460028002588243omplex @ A @ (suc @ B)) = (times_times_complex @ (comm_s2602460028002588243omplex @ A @ B) @ (plus_plus_complex @ A @ (semiri8010041392384452111omplex @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3897])). 159.61/70.67 thf(6886,axiom,((! [A:num]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (A != one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4834_neg__numeral__less__neg__one__iff)). 159.61/70.67 thf(31812,plain,((! [A:num]: ((ord_le6747313008572928689nteger @ (uminus1351360451143612070nteger @ (numera6620942414471956472nteger @ A)) @ (uminus1351360451143612070nteger @ one_one_Code_integer)) = (~ (A = one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6886])). 159.61/70.67 thf(6271,axiom,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (groups708209901874060359at_nat @ (^ [C:nat]: (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8880_pochhammer__Suc__prod)). 159.61/70.67 thf(29382,plain,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (groups708209901874060359at_nat @ (^ [C:nat]: (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ C))) @ (set_or1269000886237332187st_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6271])). 159.61/70.67 thf(5618,axiom,(((('!') @ option4927543243414619207at_nat) = (^ [A:(option4927543243414619207at_nat > $o)]: ((A @ none_P5556105721700978146at_nat) & ! [B:product_prod_nat_nat]: (A @ (some_P7363390416028606310at_nat @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_split__option__all)). 159.61/70.67 thf(26840,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)],[5618])). 159.61/70.67 thf(6490,axiom,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o)]: ((! [C:vEBT_VEBT]: ((B @ C) <= (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A)))) = (! [C:nat]: ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)) => (B @ (nth_VEBT_VEBT @ A @ C))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_all__set__conv__all__nth)). 159.61/70.67 thf(30212,plain,((! [A:list_VEBT_VEBT,B:(vEBT_VEBT > $o)]: ((! [C:vEBT_VEBT]: ((B @ C) | ~ (member_VEBT_VEBT @ C @ (set_VEBT_VEBT2 @ A)))) = (! [C:nat]: ((ord_less_nat @ C @ (size_s6755466524823107622T_VEBT @ A)) => (B @ (nth_VEBT_VEBT @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6490])). 159.61/70.67 thf(2882,axiom,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = B) = ((plus_plus_complex @ A @ B) = zero_zero_complex)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5044_neg__eq__iff__add__eq__0)). 159.61/70.67 thf(17520,plain,((! [A:complex,B:complex]: (((uminus1482373934393186551omplex @ A) = B) = ((plus_plus_complex @ A @ B) = zero_zero_complex)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2882])). 159.61/70.67 thf(1799,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/sandbox/benchmark/theBenchmark.p',fact_4718_minus__mod__self1)). 159.61/70.67 thf(14055,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)],[1799])). 159.61/70.67 thf(1557,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/sandbox/benchmark/theBenchmark.p',fact_1375_less__add__iff1)). 159.61/70.67 thf(13311,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)],[1557])). 159.61/70.67 thf(1301,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/sandbox/benchmark/theBenchmark.p',fact_4568_subset__decode__imp__le)). 159.61/70.67 thf(12456,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)],[1301])). 159.61/70.67 thf(4780,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/sandbox/benchmark/theBenchmark.p',fact_5351_signed__take__bit__Suc__minus__bit1)). 159.61/70.67 thf(23770,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)],[4780])). 159.61/70.67 thf(5496,axiom,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ (abs_abs_real @ A) @ B)) = ((A != zero_zero_real) | (B = zero_zero_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5448_zero__less__power__abs__iff)). 159.61/70.67 thf(26430,plain,((! [A:real,B:nat]: ((ord_less_real @ zero_zero_real @ (power_power_real @ (abs_abs_real @ A) @ B)) = (~ (A = zero_zero_real) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5496])). 159.61/70.67 thf(6091,axiom,((! [A:nat,B:nat,C:(nat > int)]: (((times_times_int @ (groups705719431365010083at_int @ C @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (times_times_int @ (C @ A) @ (groups705719431365010083at_int @ (^ [D:nat]: (C @ (suc @ D))) @ (set_or1269000886237332187st_nat @ A @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8747_prod_OSuc__reindex__ivl)). 159.61/70.67 thf(28722,plain,((! [A:nat,B:nat,C:(nat > int)]: (((times_times_int @ (groups705719431365010083at_int @ (C) @ (set_or1269000886237332187st_nat @ A @ B)) @ (C @ (suc @ B))) = (times_times_int @ (C @ A) @ (groups705719431365010083at_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)],[6091])). 159.61/70.67 thf(7195,axiom,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: ((((groups3542108847815614940at_nat @ B @ A) = (groups3542108847815614940at_nat @ C @ A)) <= (! [D:nat]: (((B @ (suc @ D)) = (C @ (suc @ D))) <= (member_nat @ (suc @ D) @ A)))) <= (~ (member_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7448_sum__cong__Suc)). 159.61/70.67 thf(33124,plain,((! [A:set_nat,B:(nat > nat),C:(nat > nat)]: (((groups3542108847815614940at_nat @ (B) @ A) = (groups3542108847815614940at_nat @ (C) @ A)) | ~ (! [D:nat]: (((B @ (suc @ D)) = (C @ (suc @ D))) | ~ (member_nat @ (suc @ D) @ A))) | (member_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7195])). 159.61/70.67 thf(7612,axiom,((! [A:num]: (((numeral_numeral_nat @ A) = one_one_nat) = (A = one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_numeral__eq__one__iff)). 159.61/70.67 thf(34591,plain,((! [A:num]: (((numeral_numeral_nat @ A) = one_one_nat) = (A = one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7612])). 159.61/70.67 thf(1812,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/sandbox/benchmark/theBenchmark.p',fact_4781_semiring__norm_I168_J)). 159.61/70.67 thf(14102,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)],[1812])). 159.61/70.67 thf(1609,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_real @ zero_zero_real @ C)) => (((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real) <= (~ (ord_less_real @ C @ zero_zero_real))) & ((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_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5307_le__divide__eq__numeral_I2_J)). 159.61/70.67 thf(13478,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_real @ zero_zero_real @ C)) => (((ord_less_eq_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ zero_zero_real) | (ord_less_real @ C @ zero_zero_real)) & ((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_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ A)) @ C) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609])). 159.61/70.67 thf(4886,axiom,((! [A:nat,B:nat,C:real]: ((((ord_less_real @ (power_power_real @ C @ B) @ (power_power_real @ C @ A)) <= (ord_less_real @ C @ one_one_real)) <= (ord_less_real @ zero_zero_real @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2454_power__strict__decreasing)). 159.61/70.67 thf(24140,plain,((! [A:nat,B:nat,C:real]: ((ord_less_real @ (power_power_real @ C @ B) @ (power_power_real @ C @ A)) | ~ (ord_less_real @ C @ one_one_real) | ~ (ord_less_real @ zero_zero_real @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4886])). 159.61/70.67 thf(93,axiom,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ (real_V1485227260804924795R_real @ B @ C)) = (plus_plus_real @ C @ (real_V1485227260804924795R_real @ B @ A))) = ((C = A) | (B = one_one_real))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9193_scaleR__eq__iff)). 159.61/70.67 thf(8538,plain,((! [A:real,B:real,C:real]: (((plus_plus_real @ A @ (real_V1485227260804924795R_real @ B @ C)) = (plus_plus_real @ C @ (real_V1485227260804924795R_real @ B @ A))) = ((C = A) | (B = one_one_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 159.61/70.67 thf(5647,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_add__diff__cancel__right_H)). 159.61/70.67 thf(26925,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5647])). 159.61/70.67 thf(3142,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/sandbox/benchmark/theBenchmark.p',fact_4969_is__num__normalize_I8_J)). 159.61/70.67 thf(18362,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)],[3142])). 159.61/70.67 thf(6192,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/sandbox/benchmark/theBenchmark.p',fact_4664_neg__0__le__iff__le)). 159.61/70.67 thf(29068,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)],[6192])). 159.61/70.67 thf(3552,axiom,((! [A:real,B:real,C:real,D:real]: (((((divide_divide_real @ C @ A) = (divide_divide_real @ D @ B)) = ((times_times_real @ C @ B) = (times_times_real @ D @ A))) <= (B != zero_zero_real)) <= (A != zero_zero_real)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2178_frac__eq__eq)). 159.61/70.67 thf(19645,plain,((! [A:real,B:real,C:real,D:real]: ((((divide_divide_real @ C @ A) = (divide_divide_real @ D @ B)) = ((times_times_real @ C @ B) = (times_times_real @ D @ A))) | (B = zero_zero_real) | (A = zero_zero_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3552])). 159.61/70.67 thf(7230,axiom,((! [A:complex,B:complex]: (((times_times_complex @ A @ B) = B) = ((A = one_one_complex) | (B = zero_zero_complex))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1614_mult__cancel__right2)). 159.61/70.67 thf(33256,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)],[7230])). 159.61/70.67 thf(3764,axiom,((! [A:real]: ((((ln_ln_real @ A) = zero_zero_real) = (A = one_one_real)) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4725_ln__eq__zero__iff)). 159.61/70.67 thf(20357,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)],[3764])). 159.61/70.67 thf(7214,axiom,((! [A:num]: ((ord_le2932123472753598470d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat) = (ord_less_eq_num @ A @ one)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_numeral__le__one__iff)). 159.61/70.67 thf(33203,plain,((! [A:num]: ((ord_le2932123472753598470d_enat @ (numera1916890842035813515d_enat @ A) @ one_on7984719198319812577d_enat) = (ord_less_eq_num @ A @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7214])). 159.61/70.67 thf(6112,axiom,((! [A:nat,B:nat]: ((binomial @ (suc @ A) @ (suc @ B)) = (plus_plus_nat @ (binomial @ A @ B) @ (binomial @ A @ (suc @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8997_binomial__Suc__Suc)). 159.61/70.67 thf(28791,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)],[6112])). 159.61/70.67 thf(8026,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/sandbox/benchmark/theBenchmark.p',fact_11_bit__concat__def)). 159.61/70.67 thf(35896,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)],[8026])). 159.61/70.67 thf(232,axiom,((! [A:int,B:real]: ((sin_real @ (times_times_real @ (ring_1_of_int_real @ A) @ (real_V1803761363581548252l_real @ B))) = (real_V1803761363581548252l_real @ (sin_real @ (times_times_real @ (ring_1_of_int_real @ A) @ B)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7769_sin__int__times__real)). 159.61/70.67 thf(8961,plain,((! [A:int,B:real]: ((sin_real @ (times_times_real @ (ring_1_of_int_real @ A) @ (real_V1803761363581548252l_real @ B))) = (real_V1803761363581548252l_real @ (sin_real @ (times_times_real @ (ring_1_of_int_real @ A) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 159.61/70.67 thf(5604,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4496_pinf_I6_J)). 159.61/70.67 thf(26794,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)],[5604])). 159.61/70.67 thf(137,axiom,((! [A:set_nat,B:(nat > complex),C:nat]: ((finite_finite_nat @ A) => ((groups6464643781859351333omplex @ B @ (insert_nat @ C @ A)) = (times_times_complex @ (B @ C) @ (groups6464643781859351333omplex @ B @ (minus_minus_set_nat @ A @ (insert_nat @ C @ bot_bot_set_nat)))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8799_prod_Oinsert__remove)). 159.61/70.67 thf(8670,plain,((! [A:set_nat,B:(nat > complex),C:nat]: ((finite_finite_nat @ A) => ((groups6464643781859351333omplex @ (B) @ (insert_nat @ C @ A)) = (times_times_complex @ (B @ C) @ (groups6464643781859351333omplex @ (B) @ (minus_minus_set_nat @ A @ (insert_nat @ C @ bot_bot_set_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 159.61/70.67 thf(3431,axiom,((! [A:real]: (((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))) <= (ord_less_real @ zero_zero_real @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5347_tanh__ln__real)). 159.61/70.67 thf(19281,plain,((! [A:real]: (((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))) | ~ (ord_less_real @ zero_zero_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3431])). 159.61/70.67 thf(6077,axiom,((! [A:int,B:int]: (((ord_less_eq_int @ B @ A) => (A = B)) <= (ord_less_eq_int @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2703_antisym)). 159.61/70.67 thf(28680,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)],[6077])). 159.61/70.67 thf(5739,axiom,((! [A:(nat > int),B:nat,C:nat]: (((ord_less_eq_int @ (A @ B) @ (A @ C)) <= (ord_less_eq_nat @ B @ C)) <= (! [D:nat]: (ord_less_eq_int @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_lift__Suc__mono__le)). 159.61/70.67 thf(27262,plain,((! [A:(nat > int),B:nat,C:nat]: ((ord_less_eq_int @ (A @ B) @ (A @ C)) | ~ (ord_less_eq_nat @ B @ C) | ~ (! [D:nat]: (ord_less_eq_int @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5739])). 159.61/70.67 thf(5414,axiom,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1999_zero__le__square)). 159.61/70.67 thf(26106,plain,((! [A:int]: (ord_less_eq_int @ zero_zero_int @ (times_times_int @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5414])). 159.61/70.67 thf(5524,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/sandbox/benchmark/theBenchmark.p',fact_6638_numeral__power__le__of__nat__cancel__iff)). 159.61/70.67 thf(26529,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)],[5524])). 159.61/70.67 thf(1697,axiom,(((cos_complex @ zero_zero_complex) = one_one_complex)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6963_cos__zero)). 159.61/70.67 thf(13743,plain,(((cos_complex @ zero_zero_complex) = one_one_complex)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697])). 159.61/70.67 thf(3276,axiom,((! [A:complex,B:complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1041_diff__add__cancel)). 159.61/70.67 thf(18798,plain,((! [A:complex,B:complex]: ((plus_plus_complex @ (minus_minus_complex @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3276])). 159.61/70.67 thf(3420,axiom,((! [A:num]: ~ (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5145_not__zero__less__neg__numeral)). 159.61/70.67 thf(19247,plain,((! [A:num]: ~ (ord_less_int @ zero_zero_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3420])). 159.61/70.67 thf(6247,axiom,(((('?') @ option4927543243414619207at_nat) = (^ [A:(option4927543243414619207at_nat > $o)]: (? [B:product_prod_nat_nat]: (A @ (some_P7363390416028606310at_nat @ B)) | (A @ none_P5556105721700978146at_nat))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_split__option__ex)). 159.61/70.67 thf(29235,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)],[6247])). 159.61/70.67 thf(4470,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2002935070580805687sk_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6122_semiring__bit__operations__class_Oeven__mask__iff)). 159.61/70.67 thf(22624,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se2002935070580805687sk_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4470])). 159.61/70.67 thf(1821,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/sandbox/benchmark/theBenchmark.p',fact_7004_cos__npi)). 159.61/70.67 thf(14129,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)],[1821])). 159.61/70.67 thf(7073,axiom,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((power_power_real @ (root @ A @ B) @ A) = B) <= (ord_less_real @ zero_zero_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9520_real__root__pow__pos)). 159.61/70.67 thf(32624,plain,((! [A:nat,B:real]: ((ord_less_nat @ zero_zero_nat @ A) => (((power_power_real @ (root @ A @ B) @ A) = B) | ~ (ord_less_real @ zero_zero_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7073])). 159.61/70.67 thf(6948,axiom,((! [A:num]: ((abs_abs_int @ (uminus_uminus_int @ (numeral_numeral_int @ A))) = (numeral_numeral_int @ A)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5413_abs__neg__numeral)). 159.61/70.67 thf(32039,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)],[6948])). 159.61/70.67 thf(580,axiom,((! [A:nat,B:nat]: (((comm_s4660882817536571857er_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ B) = zero_zero_int) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8279_pochhammer__of__nat__eq__0__lemma)). 159.61/70.67 thf(10096,plain,((! [A:nat,B:nat]: (((comm_s4660882817536571857er_int @ (uminus_uminus_int @ (semiri1314217659103216013at_int @ A)) @ B) = zero_zero_int) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[580])). 159.61/70.67 thf(1473,axiom,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_real @ C @ B)) & ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ B @ C)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2245_mult__less__cancel__left)). 159.61/70.67 thf(13061,plain,((! [A:real,B:real,C:real]: ((ord_less_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)) = (((ord_less_eq_real @ A @ zero_zero_real) => (ord_less_real @ C @ B)) & ((ord_less_eq_real @ zero_zero_real @ A) => (ord_less_real @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1473])). 159.61/70.67 thf(3027,axiom,((! [A:int,B:nat]: ((ring_17405671764205052669omplex @ (power_power_int @ A @ B)) = (power_power_complex @ (ring_17405671764205052669omplex @ A) @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5791_of__int__power)). 159.61/70.67 thf(17982,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)],[3027])). 159.61/70.67 thf(6351,axiom,((! [A:nat,B:nat]: ((map_nat_nat @ (^ [C:nat]: (minus_minus_nat @ C @ (suc @ zero_zero_nat))) @ (upt @ (suc @ A) @ (suc @ B))) = (upt @ A @ B)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10141_map__decr__upt)). 159.61/70.67 thf(29645,plain,((! [A:nat,B:nat]: ((map_nat_nat @ (^ [C:nat]: (minus_minus_nat @ C @ (suc @ zero_zero_nat))) @ (upt @ (suc @ A) @ (suc @ B))) = (upt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6351])). 159.61/70.67 thf(6339,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_add__mono)). 159.61/70.67 thf(29607,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6339])). 159.61/70.67 thf(3629,axiom,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ (times_times_complex @ B @ A) @ C)) = (dvd_dvd_complex @ A @ C)))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3825_dvd__add__times__triv__left__iff)). 159.61/70.67 thf(19908,plain,((! [A:complex,B:complex,C:complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ (times_times_complex @ B @ A) @ C)) = (dvd_dvd_complex @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3629])). 159.61/70.67 thf(4749,axiom,((! [A:num,B:num]: ~ (ord_less_eq_real @ (numeral_numeral_real @ A) @ (uminus_uminus_real @ (numeral_numeral_real @ B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5026_not__numeral__le__neg__numeral)). 159.61/70.67 thf(23646,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)],[4749])). 159.61/70.67 thf(3635,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/sandbox/benchmark/theBenchmark.p',fact_3560_bits__stable__imp__add__self)). 159.61/70.67 thf(19926,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)],[3635])). 159.61/70.67 thf(4161,axiom,((! [A:int,B:int,C:int]: ((bit_se725231765392027082nd_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = (bit_se1409905431419307370or_int @ (bit_se725231765392027082nd_int @ A @ C) @ (bit_se725231765392027082nd_int @ B @ C))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6038_bit_Oconj__disj__distrib2)). 159.61/70.67 thf(21602,plain,((! [A:int,B:int,C:int]: ((bit_se725231765392027082nd_int @ (bit_se1409905431419307370or_int @ A @ B) @ C) = (bit_se1409905431419307370or_int @ (bit_se725231765392027082nd_int @ A @ C) @ (bit_se725231765392027082nd_int @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4161])). 159.61/70.67 thf(4966,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_diff__add__inverse2)). 159.61/70.67 thf(24449,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4966])). 159.61/70.67 thf(3736,axiom,((ord_less_eq_real = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3154_order__le__less)). 159.61/70.67 thf(20269,plain,(((ord_less_eq_real) = (^ [A:real,B:real]: ((ord_less_real @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3736])). 159.61/70.67 thf(36810,plain,(($false)),inference(cvc4,[status(thm)],[13950,23162,18180,31885,33394,31720,14977,11866,12928,21605,13650,25521,24338,15767,34178,26820,9982,14852,21729,15806,13266,9131,34665,10917,15643,26413,29473,29163,27510,23428,16340,17959,13024,35325,17505,10609,14038,29879,24963,14782,10647,19672,25098,28526,17803,25705,19364,24265,34748,17043,26016,35193,13162,22966,31818,12055,21175,20432,35813,25071,30266,10259,29824,24978,36066,9273,12490,13859,33707,13740,9786,27283,14367,16013,19326,9886,10785,25943,12564,19772,17950,17072,24804,19726,34716,24659,13690,25916,25489,25491,13854,15009,8288,15418,11192,16676,14606,14801,8663,16962,20014,32927,11186,26625,22328,30140,10452,32507,12526,33118,16576,12570,15752,29071,21908,21595,35679,26085,25531,12975,28409,14574,11517,33575,24459,27151,24477,17510,8514,26048,14890,10520,14404,14463,11235,21050,9833,24966,8976,11313,17226,22998,34761,25622,22893,15558,18442,32058,8283,8507,10134,18906,35400,24028,16808,20559,20464,29462,9731,32045,28324,30758,14220,26775,35894,19990,22133,34484,28097,9685,10812,30866,12731,27529,29267,15055,21012,35965,9076,35795,8843,35061,20640,34645,29520,33658,12934,19148,26842,10753,26461,10081,34844,31389,19350,22521,20516,29929,20332,24108,18629,9676,25214,27601,32066,36340,22012,34797,33954,8646,20527,35649,19649,14709,25580,32643,16103,30003,8415,11620,9965,26810,16797,15413,34220,31408,20124,11394,21326,10987,11385,21136,12468,17734,34533,23640,35029,19451,14932,8755,9091,24981,8828,20765,27779,19611,11527,22047,12507,11659,12462,15380,22257,27708,17774,15526,16248,18985,12549,29723,34320,24644,27840,17656,32918,35877,12500,10844,16898,17326,21386,32356,26549,10387,28146,27359,15019,22930,8855,22118,12458,15361,18857,24585,21521,15450,16135,9020,24087,15980,22915,26169,31545,28701,12949,24759,32351,29676,21353,34260,27126,24076,23951,10299,28977,31904,33219,14895,32427,13834,21375,21645,13244,15859,9573,27679,16708,28932,12094,30991,35574,22759,15190,27170,12334,14468,10446,28045,26218,11635,20798,10234,36478,10431,22738,13712,21114,19142,36360,25685,18995,14235,21662,16228,14625,11043,18981,32950,30158,14748,31004,20922,11880,14880,9251,23219,13177,19406,25769,20258,9590,16184,15267,30895,15671,25304,12040,19994,17278,16765,23240,18193,24173,11571,9604,21585,29435,12376,34071,30603,15770,18233,11277,24037,18459,35461,20354,22417,11409,18365,28205,17641,33870,30318,10912,9324,18549,35928,34565,18972,18706,33751,20320,10331,26642,15816,29103,9120,20835,32631,36426,23230,29214,19438,28008,10711,8463,31780,24949,14662,10262,32959,28499,15827,13525,13035,29888,13672,16105,10705,29844,9918,23810,36451,27596,20484,21072,19274,32091,16940,28281,23406,23374,32558,21961,13283,12774,17424,13707,11122,26076,9337,25140,10837,21844,10314,17104,25425,26890,9469,29763,8271,9059,17495,32881,20626,32257,15568,12911,9191,12221,18114,29223,35110,15185,17046,21939,14241,28042,14538,13586,32319,12896,29525,30606,12789,25921,28057,11556,28305,15504,35745,17715,8563,10294,33601,28531,24666,10805,34662,29363,28734,15780,30516,25494,29441,10463,18837,27881,35542,25591,10694,32723,21834,22508,13212,35862,36275,31421,20566,20081,30841,13687,36551,24373,27195,15239,27696,35806,14765,34188,33764,35674,20830,26598,18951,27138,20345,30375,21899,20598,20198,29717,27492,14441,34911,16196,18356,24654,30070,23342,19883,30283,24188,23268,36749,12193,18592,17820,18265,30194,13187,25204,28288,9644,25147,23745,24946,33843,20145,35217,18878,29952,21047,23460,32683,36351,34531,20469,9212,9526,11112,8335,36633,28423,31148,19423,34240,11848,34934,25766,16336,13219,16777,18316,27789,27683,11072,12852,35602,19873,35553,9978,26333,26770,13317,29403,23992,32366,16413,25253,23665,20117,26950,18210,13623,13675,26004,21192,18667,33106,26257,21839,22175,15651,10772,25196,33283,20088,22214,15263,26089,24437,10093,32069,17988,19236,22434,28737,13747,14905,15158,29059,16572,27391,36336,10358,26542,29339,26717,35134,17594,8981,29946,15632,17343,20524,8622,20507,8879,16688,31288,22347,14665,8747,18897,9261,11303,12097,27948,20312,20352,10864,8519,30531,20611,19374,28922,9813,18161,23251,35938,19636,25328,27259,11075,16817,8298,18614,22076,8342,29604,30799,33409,24323,32458,31271,22987,30230,15755,34916,12522,31151,21454,26483,25380,25734,35222,21383,15762,31369,15885,31729,30814,12725,13655,13115,21999,24220,21156,31892,23929,28398,19986,14959,34992,19159,10827,36115,32334,33818,35890,17246,8385,31171,20063,35659,9509,26670,10594,23821,33697,15051,35338,10170,11994,20066,36418,16762,30782,9961,28018,17577,18684,27505,35688,25727,8881,33266,14689,16965,24290,20761,15848,30385,32930,31835,28646,14301,13145,19323,35345,24430,28987,10991,15207,21096,10737,17390,13174,22300,30269,28514,19932,28366,20722,33036,29668,29371,11786,17285,11816,33431,21781,36137,23547,24166,14354,8752,31875,16630,18595,20885,9540,32363,20011,26108,33337,36771,8303,25444,31573,19975,36386,10351,14292,11684,26488,19123,26979,17924,18674,34709,15683,17243,16752,10662,21398,8911,22165,21517,11449,18425,23061,16668,18661,31220,35012,20034,36796,32101,33511,26547,34784,34494,10336,22223,33722,14168,13628,20556,35437,24581,24686,17492,31761,15823,21824,27244,17290,26674,34039,32565,36226,30446,33912,27098,35713,10923,28302,18384,13874,18090,13965,24178,9845,33421,18563,12916,19575,12141,28231,10022,16849,26833,11542,21948,19553,34303,34653,34467,13970,10599,35175,17710,20752,27230,21422,33177,30785,35767,18793,16623,15723,18463,11568,21896,31239,24755,30972,33367,29324,17081,8816,22704,24163,8578,18321,18040,11613,25150,12763,29108,9735,28001,19012,31872,28054,33631,26361,26024,18304,9027,12303,9379,12757,19732,9096,10078,18992,32533,9994,28879,12646,32898,31821,19069,22115,20107,31436,11588,33167,20818,26057,12960,28862,11024,18955,11863,28818,18938,26040,12257,33922,14488,29557,17053,29708,35108,16268,35730,25035,30241,25457,30286,9971,13751,16530,12388,9465,18252,15688,16469,17100,16398,31882,36505,25374,20643,20409,23500,21203,18120,29086,9396,28659,31907,19387,8678,22476,22370,27592,8330,22474,8699,31684,23479,30779,29199,8504,33796,17111,29140,17697,30343,9657,11912,32430,24683,30162,11481,35314,23030,19209,31293,34880,13800,27298,14871,11831,14245,27323,21921,28541,13611,26318,11151,28714,20239,26240,17475,34292,26520,35249,28821,16636,25348,36319,19836,24934,23532,27344,25126,20078,20441,29884,29997,10633,21021,10248,30534,10584,36055,31716,14213,24060,28627,20679,30315,27624,8583,28697,33294,12879,27212,13258,18437,33608,28691,22412,12843,18866,12254,30350,29044,20894,32791,18754,21004,22493,13191,32742,11426,9300,9056,24922,25367,36569,16552,28160,17415,13658,15922,20191,32895,32651,16420,21916,21017,14552,15353,12475,25307,28830,31539,14474,30984,36251,12197,14701,22353,13360,23243,33815,30456,17610,35044,15033,16251,12943,19145,25117,8967,35452,25074,28726,29031,18671,19763,18801,33568,11203,15990,21794,22621,25054,36097,32516,27362,34506,10997,15229,13429,19342,10751,18750,28794,17824,24433,12286,23587,22121,17857,20245,9988,9084,26827,16287,25861,29155,14351,35130,8357,31372,10251,24316,32369,27725,11431,8806,24839,30258,18155,26866,21684,11289,34360,11299,33715,11010,20017,22710,33876,14088,30630,23123,28694,28602,24013,17017,15648,9128,33832,27192,14173,34965,35424,26934,36300,19895,16067,11966,30579,11944,20881,10142,16325,31487,16890,13151,21861,21755,24469,21880,10221,13241,26538,32548,29388,28138,26552,34057,15171,31711,35987,22536,10719,26172,31561,34328,29636,8785,30506,35584,24194,21631,23006,8834,18353,27487,16480,13820,11458,31542,26406,28942,9360,16146,17481,19472,31815,36363,35682,17270,27920,21407,11200,8522,27060,15663,31896,12993,17613,36073,24842,21281,12394,29264,14515,24680,20858,22229,21430,36322,24558,16789,9909,10010,28213,24224,16712,14923,18030,17371,17149,12589,30667,31453,31879,10606,24857,28882,8374,19155,12606,35816,31302,36781,23988,15706,10174,22254,24823,15787,11051,9938,19621,24237,15441,11416,30013,13275,23713,12003,27092,23551,35039,23140,30997,28815,25644,33930,12713,22955,35525,23941,19226,18688,24327,18236,11760,33270,23864,34805,14830,8257,28089,35778,28005,22585,9420,25615,34780,8849,17154,19795,15182,33322,35727,9629,13704,26991,20445,16740,19052,11183,22827,13826,32863,13754,15819,11641,8278,20074,18143,11232,34705,14331,15911,31981,28298,18380,24095,24740,17894,34837,26073,12837,28897,20719,8590,26606,10534,23781,11463,17097,18190,35611,26474,26321,14024,23945,23108,9480,30802,21491,24045,31340,36002,11264,16300,14455,31832,31385,32710,10516,18292,33206,13226,19905,21447,17049,10110,8310,27102,11564,14616,17517,8819,26425,31738,15742,16495,17562,15900,24890,14773,19414,12137,33549,34252,33761,22902,22488,34869,20027,30321,24262,23803,27964,22627,18846,32848,36156,24490,14564,12229,31770,18492,17962,33174,25022,25717,34172,9529,11741,25612,26705,19937,11132,34538,31193,10650,13393,25599,16223,22659,20647,32940,22498,8543,26190,9240,15161,8674,30134,18215,35429,24871,8632,8703,22425,13123,18511,14949,15462,20822,10570,10665,36315,30289,10945,18964,36008,23026,32052,17603,19956,34939,13102,13506,10702,29123,16315,24561,35623,26160,13044,26343,15167,33993,30920,11716,29576,32129,15193,15073,34490,22150,30166,36368,17620,13350,23475,25467,20592,25336,26403,29470,8352,26767,8558,30503,15199,9475,21588,17136,20790,30859,26061,21128,29756,31928,13715,21075,28591,12517,18043,29095,9712,21852,20755,33655,9266,20716,18479,28334,13895,21249,17723,10025,28779,34274,11533,13474,15954,19840,10527,31773,13575,19578,25555,23768,26502,35478,31971,23611,32977,17667,19892,10309,17652,22784,11163,25989,29585,35865,33353,15878,24599,9204,30049,26649,8394,14533,9304,35364,33604,21582,26629,36129,10729,27923,24943,8956,9593,36743,25858,34045,33385,26100,25345,12347,10419,29958,36114,35225,22608,16141,10818,12018,33468,10641,9283,29517,11441,16151,34306,22767,28654,19643,29875,17354,28599,36383,18571,36312,26571,12281,11656,15716,20373,19250,22442,13987,36180,11344,33700,33055,33719,12023,29980,16929,27615,35024,14697,21829,32891,26254,21953,23115,34277,9330,22178,21029,34883,18681,30253,33898,24137,32202,22127,24663,19020,17171,17635,18273,36146,29990,31860,28651,24509,24975,13382,12828,29891,9071,26916,13647,19514,27179,13538,30994,28885,33803,17899,36046,33246,16448,31016,19485,15515,30312,21599,33986,29648,12593,35809,14584,17747,25153,34232,33539,14132,8802,8860,22112,31552,35991,35564,27295,22887,32923,11154,16608,11577,34084,21633,14267,15468,19495,27843,24596,9837,35596,19598,34961,24695,26919,24001,34607,8321,20304,17090,31279,9860,30378,13013,15150,20978,17994,24032,17398,30081,34793,13414,11748,18126,17485,27233,36294,33571,16293,32831,27365,29612,21656,27147,11083,10972,32912,33485,8642,21614,18301,35115,9415,24390,14066,16946,17498,11793,31968,12276,30977,15678,11446,10378,9388,8759,17862,11971,32568,24546,22325,16431,14238,31689,21303,18324,33091,24648,35770,24514,19845,26358,12379,14232,10734,34323,9319,12236,20091,31936,24954,15856,13533,33810,29477,17078,36041,23860,11036,15893,23301,22838,18560,27714,34677,35970,11523,11168,18037,35831,17210,27087,17835,22713,31549,15618,16131,26799,12998,30863,36034,8438,20317,34245,22420,14284,33881,10799,19675,15710,23964,26998,11478,21069,12638,36526,25603,28033,19591,30615,18123,22217,25948,35731,11325,18065,20104,19546,20934,34020,35759,9616,23280,16544,14987,29923,27119,13865,28141,16885,16841,32401,35570,13305,15784,34733,12430,19585,8454,20619,33404,19608,18737,30154,8575,11119,27537,23643,31939,9255,21774,36554,24284,9928,10833,34548,10551,31490,32030,20368,27019,30891,22065,10538,31366,12777,9452,24055,8406,17349,28995,15799,18604,35981,20530,11104,11806,9140,16725,17702,28490,29703,31347,26237,21290,26887,32360,11413,28804,24496,33334,11723,23814,30000,18260,10405,35589,24160,34617,15343,13072,15691,30491,18392,25339,8347,23223,17322,23226,20826,29926,14733,8686,32288,23700,9914,11885,18869,13420,24854,35051,24169,26724,12411,9341,16562,16028,11490,14622,10390,26574,26346,18329,28285,23524,35125,19085,23788,13600,35083,21200,20401,30885,32511,14798,15986,29695,23451,11728,20809,36124,29865,35834,26166,12860,11783,35738,32727,17933,19678,25587,34469,10422,25435,26737,25010,15350,26396,20605,25702,24277,35850,22038,25185,34284,11596,15041,19033,34982,8443,21848,11367,34052,25666,18888,25933,24201,18814,16433,22466,24369,36415,20775,16858,25007,21665,36287,32055,15591,19411,35289,22685,23628,25741,10256,11195,14900,23492,12306,13155,8992,21816,18146,24573,32759,24881,18148,35533,10113,19310,14160,33297,26243,18607,9896,35190,16565,20736,19729,15958,30902,26824,18412,16109,17811,24762,14196,9822,8924,13683,35221,24302,28435,24480,26037,14911,27865,22314,33823,9048,22992,34930,19639,10779,14569,20299,9703,18344,14558,9472,16428,22896,23304,31249,29365,21009,9556,14184,9997,31698,25834,29682,18022,20998,33412,29226,26187,20533,9720,23332,23581,13286,27063,13352,19877,30761,14730,22232,30371,23175,26788,8486,14162,21983,23688,18445,18520,25183,18909,28308,8999,22909,29489,20602,23617,9682,23607,24603,17555,11897,33933,23033,24702,31450,23111,12586,8655,17523,13814,34281,31456,29137,22406,27617,11255,16076,30466,25079,15345,21078,10742,10954,8927,10875,20725,17257,28772,20348,31410,18212,28824,29499,18312,18941,36242,9968,36445,30712,36541,13038,19502,16091,34317,14712,10139,14785,26703,35748,35522,8382,11170,16044,28340,18774,18177,33146,29169,32739,29256,18852,12200,26678,23881,34336,18658,18664,11820,25738,15364,8418,36092,14295,22722,23967,10197,27265,15697,25986,13104,33972,18915,28267,35761,21133,8959,30685,26509,26658,9209,8397,13051,11687,26330,35781,13049,33840,13956,11456,22496,20889,33014,16333,11069,34862,32254,36163,30263,13426,28807,19507,12705,30292,23757,21444,23155,19329,10831,23995,31007,26851,35949,36357,20749,16516,31743,31360,23594,8481,23731,16297,21098,12205,35094,31918,28208,12127,26092,17363,20326,26710,14693,28130,18112,14808,24493,26923,29105,8668,9043,19218,25505,21320,11499,23295,30652,31794,22386,29160,27945,34204,32971,21438,13644,33559,25156,22097,8712,22699,30324,10345,17526,33691,11292,26941,26645,17980,12100,16697,13547,15082,21801,33059,17844,21507,13448,16487,28187,34249,19595,35579,27165,15486,22136,12437,11147,30619,21925,11520,10099,34481,11751,12385,21402,36310,35184,11339,15574,15610,28740,23703,20684,8783,13423,15488,13126,17936,28615,28685,24197,18332,8778,16861,9522,35719,33400,36289,11238,18200,16729,16210,32943,19914,33459,32707,22667,31296,11388,19842,17146,23935,15843,16633,19305,26906,13301,22524,31564,27054,13850,14357,31405,19099,14323,10975,19571,26202,23081,23970,26302,26393,19534,9412,31749,28210,25569,26582,34877,12510,22682,20931,19813,33163,14943,18600,21806,22635,13892,35162,21238,25081,34781,28458,8888,25594,20989,19744,33503,17303,13572,10858,11719,33104,16386,36412,19967,24234,23649,22260,35734,16215,11223,12190,31208,18784,14222,28505,30199,26477,25954,18589,16465,12576,34048,12970,27332,19231,23143,27926,17567,28743,21579,34745,17838,36159,10657,19006,17683,26000,21293,20188,30624,23562,18068,11471,10612,25123,18767,33735,33901,30965,8724,19290,23748,12591,28980,15097,36406,31378,13829,8550,27022,15061,25812,12846,24748,23514,20689,26261,25095,11003,33424,10102,11106,30788,35311,24157,16597,12715,30776,10394,28414,13078,10084,20550,22082,24244,30847,35047,30044,15719,21030,23932,22346,13401,21893,30443,11908,24281,21958,11212,36027,35487,28583,32372,29949,29618,19396,33808,14921,13583,16307,10278,12037,20972,34830,13250,18372,17902,33940,12058,17945,17467,22029,9455,18764,36247,32441,8683,23454,15471,31157,10721,13551,33231,13778,34340,27869,18415,35956,21628,22278,22035,15174,16801,28895,21206,21979,14401,19390,15129,8832,29385,14804,10756,30246,35206,26614,20047,9217,25838,28102,29018,24350,14541,18340,23841,14217,23358,16371,8371,18535,36088,23776,17623,19139,29128,29261,15253,10490,36765,24111,31314,26378,23577,12340,33263,26315,14248,17887,19058,21591,12279,34959,14926,14363,34308,21700,22015,8942,13810,22284,14477,17870,16790,31323,15383,25649,29633,14430,22471,15103,28643,24312,12822,9277,16123,10369,27082,17659,17385,35685,15665,21611,20220,10116,24253,13763,36565,25293,16440,29509,29701,24576,8852,25844,11249,33595,9758,19454,36370,29686,14681,21855,31164,16556,27489,36188,10765,29480,12692,34634,29806,33744,23282,11629,16497,20758,28784,19886,17005,17726,28350,27621,23568,13530,12025,35203,17406,31713,33018,33233,26902,22186,31011,18268,32119,19539,17908,32399,35375,18183,18557,29173,27704,21470,10794,34858,21890,14338,17114,29502,32904,26229,22741,21732,32967,35639,35528,34577,8964,28935,21066,12849,35354,17891,28291,17889,27241,36333,16793,28704,16274,8847,22159,34076,12930,25562,31681,10035,23604,23190,27277,25416,15638,13237,16981,15546,23854,22393,20745,11284,15279,18481,20637,10615,17296,10907,30494,13681,35820,36516,9080,35472,13411,23024,13515,11602,29237,28493,23018,33099,14100,12478,17032,11101,16569,31493,10926,18108,34461,25402,16360,20504,18989,20851,17346,28395,27182,8403,13269,27722,16019,28024,28134,29626,26234,14395,17770,30131,21608,36297,35856,14135,21905,18816,15142,27967,15947,9095,8314,11961,35458,29205,21110,34272,16893,20309,29615,21511,33746,10131,30483,20481,10716,20052,20264,21123,18569,15702,15915,27341,12760,12414,13463,8530,35279,23254,29092,8694,12866,36284,9493,12863,28876,19786,26742,35871,15373,8446,13362,22428,26864,28752,32555,32042,23195,36152,20861,15739,12728,29711,10748,34754,8545,17306,27589,16472,25480,19652,36421,12493,12538,17174,27080,16588,26389,12404,10887,13347,27958,12792,25512,13222,22528,17232,15616,17274,35307,34722,16949,15211,26222,15481,15456,9073,19918,21063,20787,9355,27095,21498,16519,26595,26791,20513,22085,33342,22322,36755,11056,20985,16968,12382,20360,31433,10791,14941,32756,15606,28586,29665,9945,24063,9245,18586,10281,8339,11096,9889,34008,27209,22769,9773,12546,30832,18718,15896,27314,25441,16163,17213,18677,28812,32455,17010,27837,17412,28038,20148,23049,35716,20387,21673,11007,36548,35015,35443,10566,35888,24771,10644,8435,14398,20538,18351,33989,30975,8931,22241,33310,32788,8984,8619,28382,33348,29794,31217,19302,14505,36787,29376,22319,18860,21275,24786,23518,8451,34194,9576,36402,20553,17985,36380,14348,16144,21577,32404,35281,36020,24670,26499,14855,23837,18828,14381,11128,22209,19556,10434,23094,24862,26732,11845,28827,13099,17065,20570,21771,22969,23355,14990,32409,11400,21687,36279,12796,22154,33200,29003,8429,15459,15201,9376,11189,33544,8567,29453,13344,22919,8572,10882,13458,35147,15313,34826,14520,33046,35475,16055,16031,14120,16242,13468,19566,30076,10760,13084,11467,22124,29563,21026,14908,13899,16504,16673,24614,11019,23055,12211,19287,10203,11923,26043,36389,9530,30118,34258,11088,25165,25697,9566,30185,28920,20855,22533,23511,16805,19277,13782,26139,25143,13928,13790,22145,9117,14893,22181,29994,29081,14914,20739,22191,14437,17939,35798,17503,12151,13635,15054,14841,20248,33259,35097,20771,16847,10708,34557,15410,33448,11860,15249,21727,30796,25413,22336,30888,25192,32279,12179,18653,24346,33961,20633,25829,33782,18386,35334,36437,19075,23418,18885,12967,10185,17883,10120,24241,30086,22288,16436,23625,11364,9667,13308,21813,22343,35511,17478,30403,14313,22511,25936,22963,32775,34789,22100,21739,14752,10015,15944,16786,17942,34659,13495,15793,11625,11403,27518,11496,11869,21267,33925,14598,35539,35317,10381,35079,11757,8743,17133,10342,16700,24931,19758,33476,14052,26969,17912,24957,28913,16958,25101,36052,8258,23740,21514,27356,22409,25876,28596,36205,12885,32064,33686,34374,32037,22952,34457,23635,10620,31000,10671,15495,9609,20742,11229,36746,11243,33094,24578,27016,35655,16583,29838,18540,16715,15803,22072,26274,29028,34708,20069,27874,25120,12803,8275,13512,21389,34135,27999,34354,27396,14882,9100,12091,29679,23556,24989,24293,23043,29714,16844,31275,17165,17118,33712,15270,19588,18289,12454,33777,20261,21572,32122,15728,11797,13184,28757,22460,21306,14719,11026,32387,16451,18978,30210,36169,10239,29630,36348,30688,25566,26796,18650,28105,27521,20271,21742,35642,19195,31950,9429,15421,15830,8952,32778,32597,12622,32527,10487,16773,24176,22618,11116,26535,21463,13387,18137,35724,12314,33435,21001,12045,20129,15001,19997,24079,28095,15510,34786,27937,15247,22778,26210,30698,9200,25470,25794,30487,22673,13081,24366,15555,31509,34268,23657,8599,32736,12418,17318,19790,23571,26870,17450,21006,31397,29917,12408,15151,32628,31474,21559,21841,17360,35153,23103,20940,17229,21284,18076,8891,23046,29220,17720,12481,28848,15369,18421,13366,32051,30595,10560,23857,28027,18396,30519,13805,15972,19393,21944,36024,32451,14655,23818,35756,16690,28275,19911,20335,22641,17582,21543,36140,15602,14740,23199,15322,27954,16837,12532,31229,22690,32907,22201,27329,33888,27305,8410,9893,25038,21162,30525,27980,34525,10603,16083,16112,12870,33039,29114,20434,23352,23361,33137,31418,21246,24783,9201,32002,19711,25797,10158,26419,14929,22781,18476,24651,28450,19562,35055,35270,9932,36469,18347,16722,29594,13868,21243,34702,19049,21368,10455,20666,24084,24273,22168,10148,19889,33861,13718,9112,9053,35698,18027,32282,14271,10306,32381,10122,29561,9017,26392,35285,26883,15285,20681,23496,10047,10879,11347,35666,16932,35793,16051,23574,21902,17546,15232,36183,30805,12946,26142,20542,17678,31788,27786,22922,27905,22450,16237,14794,8775,20391,25951,8995,29573,8425,12310,15478,19398,32344,14965,29064,11300,34923,21546,10588,35455,24780,9607,28888,25688,35302,17267,24899,8307,29270,20097,9598,11261,10550,11610,29117,18975,12800,21826,17675,25646,18452,18581,33042,25313,10075,13693,19262,16410,24893,13490,12641,31246,11093,30202,32019,18276,33846,30627,11274,25169,18998,30204,21270,27319,30347,12831,9942,11000,20669,20510,10894,24593,28564,21976,9068,31350,12005,31695,16328,19498,25720,24525,31724,16445,14424,13758,10212,16996,23397,23559,13522,24466,28763,11031,14918,27730,33671,13398,8971,21986,19354,9534,8796,18640,26064,31791,14657,26079,23521,10802,11216,15290,15039,29253,28903,23182,28390,25714,33407,15538,20840,10366,31025,10597,30869,36806,20629,10815,30663,21055,16080,27859,21659,32412,27057,30275,17293,11197,25188,31253,14821,24743,11856,18508,13554,24498,18012,25583,21317,18049,10338,13232,19332,12783,25393,21883,32768,31112,24985,11997,18626,15101,27249,8512,8989,29493,26691,25239,23716,28544,15499,34994,30006,34369,36529,14590,9689,35348,14008,9436,16548,30988,20476,35390,14157,9176,35515,21485,36793,10524,21989,10689,16220,19198,27268,33851,23591,21395,33356,24320,24217,9716,33488,26022,16405,8422,35299,25276,9008,34378,15624,34185,8871,33291,23037,10069,22540,32444,31863,21759,17767,15307,16048,15136,27383,23058,35230,33836,18100,36397,23631,29726,20290,13772,34840,12329,28092,25983,26640,31846,23384,26986,17784,20037,28900,12938,14092,30207,18757,9171,34332,26592,15552,31827,22358,22590,22514,11777,10951,26096,13137,11559,8945,11065,17335,15215,8609,34131,25320,11328,14886,23948,13879,16296,33109,28521,32495,16990,25509,9925,12361,10090,12913,20120,36353,17367,20793,18389,22332,30557,19871,27349,25419,8824,36173,23878,22731,28387,30656,17382,9137,31236,26662,35331,31583,20422,21197,14433,19775,25438,32094,29590,27862,30296,32126,28547,19245,31501,13326,29662,19511,17514,9562,31333,35898,26806,9985,26518,14848,12318,22109,23425,14085,10983,22390,22208,23467,27388,29601,17235,25160,12596,35464,21023,27025,28144,22650,21678,31211,31393,18472,33154,23785,11165,33491,27896,17182,19380,21473,31931,12609,21159,13444,17454,16265,16464,9484,17338,22032,28508,9237,25383,10683,18196,32500,23693,12295,9040,9726,32233,18080,22479,25515,22001,20812,31196,11506,17848,14816,27917,16483,11692,18403,13264,17806,27368,29766,22059,16395,20060,29456,35847,18255,11747,30621,9352,26655,8903,13603,17282,24336,11710,13041,16100,14762,14388,23985,19809,35775,22396,15147,16593,31692,27301,14946,29240,29316,27001,32714,28331,13544,20207,13201,22453,27914,15976,11138,31424,16188,15675,22960,9502,28731,12233,18787,35142,25085,26471,19963,19740,12813,14254,25388,18455,20419,30695,9709,33375,33027,25669,22995,34295,13135,29579,29939,19941,25207,34850,29166,35215,24363,33865,36256,13466,9122,21142,33884,30016,20466,8906,25477,35268,16737,18709,14281,17851,20217,25201,10043,18428,23386,14373,13947,12683,15226,16311,25229,12290,10993,36636,33920,23271,12654,8771,9853,22220,9635,10321,21568,34942,30772,30916,34300,13336,18819,15660,28640,27929,17795,30809,26082,19861,12052,8718,17991,28633,17880,33286,18577,34919,27185,34601,21724,24925,30143,20384,9650,18242,35825,8874,26339,14776,16876,9974,29149,12513,25919,11561,16343,33552,23276,13031,22296,20185,27599,25864,10890,20899,31506,18376,29321,16612,34698,22787,21954,13296,21877,14072,20657,28665,29689,8495,31285,34872,20394,21218,15681,21465,16750,36076,26545,30741,20009,35518,12028,13710,15180,22831,28947,15070,31958,25464,14974,27128,10425,12441,32901,26486,16935,22753,13471,21647,23783,10194,8909,28278,18529,20315,11434,32933,24089,12951,33969,12688,9062,24583,14466,20278,34823,32888,27286,14097,35994,35576,21428,11333,26729,21151,14760,36177,15909,28838,34243,29396,20549,23354,26880,32589,18795,18096,27902,35168,34672,31515,11836,34973,18245,32648,12986,36456,10547,33769,27531,19858,13075,12835,14994,8900,17800,19817,10200,15030,12170,10334,11905,17700,8470,10963,11941,30826,31941,12301,27109,22790,9543,35750,17854,32680,29547,33428,11226,35645,26555,32524,16855,9025,29089,29212,9706,9114,14572,26726,23827,33737,35481,30416,28873,36132,26059,17573,28657,24813,31947,29193,18418,12541,19949,8894,13569,16154,18494,28190,20411,36273,17605,11124,35708,16199,12184,31214,13745,16400,16532,30390,35840,12840,32276,14544,19215,29655,13563,8697,17737,11851,10242,29368,31233,13281,31477,36126,25029,16278,14971,22912,19659,30151,28749,23100,29570,30127,30448,28440,8332,35868,10557,14021,19296,26163,33621,28347,32432,15079,35613,8740,26604,29014,14326,33856,30608,22890,34011,32135,31558,17705,25315,25177,25870,21703,9585,24567,19015,13847,25557,33588,12787,12322,19782,21035,26019,30728,18944,24151,17130,19170,36409,35984,11714,29706,21233,35295,36373,14044,12964,21974,13132,28716,34381,34127,34166,35531,22772,11483,18812,18863,17669,10284,23565,29428,18497,25525,20705,30303,21735,13197,13358,12242,8318,14619,13908,22491,14508,23509,30819,19176,24340,15641,17905,14743,31332,17818,25283,13054,35383,9935,26512,33236,17686,11671,28194,14258,24745,24296,17041,26102,19269,13319,29443,33049,19042,29046,30480,31580,20501,14384,17865,29597,9587,35669,14074,13953,17744,29148,21622,9125,15765,36330,34936,13217,35336,34350,29515,23421,24119,25754,26772,25194,13730,29822,21309,25410,20005,10948,17162,25255,22972,18484,11060,14010,26967,21186,21045,16779,26277,12566,13503,19345,21997,18218,27733,28800,19234,14517,26532,24700,13093,32856,32594,31483,14275,19479,11502,17789,30183,13380,17458,35136,10348,26697,20019,30836,8624,10051,11662,11423,19376,25854,21460,32915,35368,12451,8492,34640,11370,21169,25061,8745,18822,8300,30215,20995,10215,21859,18086,9776,18616,11678,16065,25326,17628,19466,19973,15594,32418,24022,12423,15936,8344,25378,28319,32837,23719,17918,9496,14082,26857,21768,24833,14461,29049,21154,14587,26609,33152,20975,21886,34218,15244,25751,27077,20872,13638,15036,18003,34265,31746,21014,34560,9290,14549,33710,31964,28553,26324,34799,14307,23773,32088,20426,15733,23794,12825,16782,12167,21257,32698,16246,14360,32199,11618,18135,27794,11900,30387,27090,17204,24848,36492,34614,20041,16174,19352,17786,17287,30358,14835,34314,10361,14027,18399,12979,13606,10416,33268,34625,21287,21381,31114,10176,9089,28368,9258,9307,34503,35764,15708,18431,19930,33101,29336,15205,27380,23751,18487,36429,24656,21551,25294,9248,15941,16500,10056,34767,35237,9670,25574,14502,26684,22103,9835,20141,9390,18309,24817,30406,17860,18695,31767,22244,34154,13417,36502,31205,34060,22719,17401,13995,17332,28379,12445,19698,23314,19121,9243,11451,23939,35027,16542,14290,36238,35065,20228,34620,9344,12082,36049,15530,36405,16000,12806,29098,27144,28707,33328,13609,9422,16088,16735,24260,33509,21527,34169,30633,15367,34711,29530,16883,15492,21493,10151,13871,33641,15700,15406,19829,31307,33592,26911,31190,10317,10429,18849,36228,20266,10910,22905,36270,23867,9349,31555,35630,12651,12990,35999,31466,34286,14878,32974,26505,16454,8715,11508,24919,35587,20774,33382,33279,24484,11932,27594,25518,8799,35836,21950,36776,10066,15853,15316,18103,15507,24452,33996,18551,29486,26292,24043,17971,24753,13064,10677,33547,25020,31126,12034,12619,23805,11878,20801,20398,22932,22195,9322,25618,8868,20833,23206,16732,14788,10898,13253,26352,26568,15983,36507,28438,11735,23831,30412,17179,24951,17418,29842,18966,19520,35106,16938,33300,25048,9185,11829,27887,13794,30660,19385,27374,34731,28511,35953,12182,29559,34588,10037,25298,24800,24129,22661,34599,34814,25138,11268,23335,21667,26267,28892,14471,17841,26436,9570,30596,11554,36231,36085,13749,33773,12337,16600,28909,9723,29319,20204,30164,14322,22350,9146,17461,10019,21699,15778,21642,10296,29496,29582,29527,34874,16864,26896,25132,34650,36534,23584,29651,32435,13210,9789,15453,12894,30040,34472,26146,16231,20179,33895,15713,21810,22088,30692,26070,25841,27690,22439,35427,15654,18150,35676,9491,16177,12780,14555,30732,14581,11979,21746,21540,14865,11306,26468,24307,13018,22273,15577,24993,32920,35412,23040,13204,33370,12882,15810,19335,27132,35123,20479,35180,16381,24887,29587,20875,29373,32285,23389,10265,34005,34985,19523,35372,16263,36345,30306,35359,26252,12248,33006,33927,9206,18790,36202,17637,19898,29447,23324,32947,9857,16984,22041,34346,14458,35804,30072,15465,15880,20112,13499,19421,10957,11947,24503,19362,28312,15626,16535,18006,21837,10397,16015,15389,15438,22106,22446,35018,22212,25432,23623,30055,15259,34223,32492,29761,21084,13592,24639,33792,20295,10179,12712,13857,35059,13323,28928,20371,26383,23403,19271,15543,8661,11419,11893,13980,9830,11205,9642,8517,10628,32781,10005,31282,32071,35323,30925,30588,33614,20522,19064,27050,13272,32022,19357,15015,14706,24318,12973,26944,29189,31498,15297,23589,9263,26848,16425,22693,25400,15745,8750,20458,8355,13766,34946,11964,18270,17914,21635,16819,31416,35598,9487,27293,32291,19185,19103,30816,11158,22074,24026,33211,26174,9553,28612,10136,21488,9280,21869,27271,16999,24520,26861,18912,35694,35091,28400,34990,19934,17396,23620,22818,19025,34647,16069,17248,29857,18057,22006,20342,25501,28688,34842,18780,13518,22305,12496,27834,25578,10412,16128,33873,9905,30137,22263,35117,12000,17579,33628,33133,34736,34078,19747,23541,11767,33115,19753,15993,17974,18131,15668,28983,24271,30871,34610,8652,12810,36100,13535,27225,14824,30764,12079,19853,34679,16952,15966,19737,35033,8281,27176,35546,9030,28030,26422,16834,15094,20728,23638,34225,35789,33089,32704,12274,12573,8413,11551,28648,30829,16703,9327,16366,28116,23448,15528,36769,35701,21341,33829,33364,20992,26619,22725,27157,34770,25450,10402,12680,11310,11643,20968,15960,21565,34541,24531,23185,35086,11173,33756,28463,35885,24488,8440,16670,33221,16005,16904,26928,11220,23632,25486,21296,27013,32099,21254,21392,33766,22612,23377,36234,31480,27117,28035,18712,15188,13578,14329,12336,15475,9619,9143,15635,17444,24625,16706,30469,24132,29658,14525,16538,34158,26480,9478,21718,13944,14370,16887,31470,23834,8588,10301,25032,30874,30704,33645,31567,20805,35967,20201,26837,27246,26200,14207,17223,28496,34922,32634,20924,15588,33275,14768,16493,14876,14453,18071,30361,35626,24915,20323,25280,29482,31809,36199,33011,19602,8821,24332,28711,16770,9899,14115,34289,35853,22067,17708,10544,12465,20815,10782,32617,12358,19257,21420,13339,13666,15933,12556,15432,19125,24154,33551,23926,19734,26601,32640,20731,23202,24456,32720,27377,27203,13112,36174,24299,30769,18993,11380,21365,20660,24611,23734,19179,28052,28163,27335,33317,35276,34692,14660,9916,9197,19448,17313,23062,36448,10979,14287,20176,8541,34686,32794,33451,17921,23801,32375,20132,34042,11607,17102,10108,9698,21166,20403,35171,9106,31512,15583,15868,18637,34023,29217,11605,32957,27114,10063,13598,34155,31028,19426,22518,20536,20154,9011,31400,19880,19680,14639,24257,25694,35244,11342,28311,13884,35491,29871,26271,35112,24122,24203,14675,26636,36762,10031,18505,19631,14194,27702,11141,9921,34954,12224,34211,32313,13330,8291,31851,15340,13214,33891,16181,16217,12890,21230,14898,33634,26931,36366,35753,8763,27004,31291,23759,29698,13727,16510,36017,17896,13737,28860,35127,14628,11493,17300,19409,10499,14049,20907,29797,34390,14427,35860,8457,9582,17430,20734,25597,29523,20828,17664,10226,13840,24905,29896,8689,18715,11887,35320,21918,27526,16094,30592,14535,9958,28528,24937,23292,22026,25365,34190,13662,25104,27890,23851,26899,32685,17625,11161,14983,33021,12922,35772,31014,26651,27065,24143,32602,32878,33470,23975,36167,9595,33253,35608,13278,29854,22984,16253,11316,22414,19080,12326,20692,35555,33112,18358,25181,19641,30434,11665,17038,10824,19293,30191,15657,17781,15400,27498,12708,21425,23434,18891,13168,19542,28593,19316,28561,28475,14126,19018,12021,34724,17070,12941,9086,28845,25995,20338,25803,15276,9673,23600,14813,12288,19695,11062,34802,14012,32390,33121,24767,18698,34151,29078,21103,10191,9334,12723,21639,10354,33947,36543,23413,20650,9695,30714,12048,20843,33702,34573,30255,10223,8979,17977,14827,10867,27072,12599,13641,8936,22251,26914,15447,18000,12627,24674,17487,15004,10920,17472,18434,14265,11077,33243,32613,35594,15918,19806,30223,10449,28084,21405,21711,28099,15301,33157,30100,8949,23883,15006,8789,10384,14406,19150,17826,19367,12239,32489,35508,29145,29393,30677,15797,25560,9639,12107,22002,12434,20302,21350,31154,11689,29610,17376,26540,11579,33909,8657,27235,35582,23321,22676,24806,29771,33445,28026,31804,34807,24642,27513,28466,21616,19849,16097,23087,12854,26668,19182,20936,13541,10788,9232,21442,13292,21301,14810,9783,13117,21263,15058,8885,27933,34141,35843,15415,16457,26491,8863,22638,32826,11391,28676,22483,25528,23016,34237,11872,15571,16917,23328,17764,10471,22292,28166,17151,29803,34064,12817,18554,35212,26953,16831,31571,16166,9317,31413,35080,27085,24774,28343,27716,30393,10653,22949,30233,26989,34375,23954,28183,17156,25800,23052,28406,15871,11738,15021,28916,24304,35567,34262,16521,22266,24629,22091,29973,16389,28336,23381,8593,33556,10797,9022,26972,19429,35403,22825,14304,17393,20983,17208,24066,13450,10290,14201,17217,11045,25454,17564,25815,31495,28851,14609,12487,8569,25946,22587,17551,23260,26523,16759,33617,20406,23754,22142,23106,31900,20545,24460,28011,11461,21195,27908,32482,27962,35948,17953,32762,20702,14635,10001,27105,23136,11575,13967,30791,12088,10476,36327,35173,13181,34464,15549,34201,35828,24777,23149,34926,19089,24228,26427,29120,36652,19221,28624,17968,24706,29229,29450,8707,23875,11694,17060,24866,31740,20306,24896,14998,23485,16621,26707,14336,13698,8466,19793,36030,21696,17144,14485,11808,28403,30573,12103,23273,34739,32621,19118,13108,12174,17276,25129,29177,12271,28966,34162,14444,33666,25461,12648,15043,36758,19460,30188,10059,27727,22431,9037,18947,32033,21251,32725,23683,13121,34343,19954,16974,18957,10581,34145,12954,35283,18490,19284,23228,35068,31441,27338,11989,24035,30123,32745,24207,11956,25001,32953,31317,26739,22376,19320,10371,13508,21818,17055,24869,29941,13435,29202,13882,16079,35156,10667,11726,16579,33455,24357,13261,22670,25372,12873,21501,24909,26694,9766,9005,17105,35925,19838,18009,17717,13916,25482,16870,19531,9499,11126,13990,34215,8350,21039,33638,21941,21126,34866,22644,8364,8295,9948,19067,17013,17187,27830,8813,15603,20779,23808,18835,9270,17002,34509,13843,29133,28777,16345,17536,13229,33649,28589,20714,14215,17689,19436,34909,33677,21090,25287,23791,28294,26232,11428,27502,36245,33229,26309,24960,14036,18771,19944,10915,15645,10218,29432,24876,29623,35916,34628,19441,33904,13912,33598,12187,18537,17255,9462,11823,13769,23737,22355,31381,18054,23440,25092,17356,29860,30454,8498,30431,23553,27274,36221,21333,30541,35042,28108,10328,33387,9991,10439,25076,13369,25758,11842,32730,21058,31726,31460,15396,13140,18526,8377,28371,13677,21706,30600,21708,28524,26207,16416,29061,26177,23409,12720,17877,26095,12364,24969,22312,25422,28126,23597,9065,34147,19724,34714,10162,25405,28760,20044,25057,19628,33951,17822,15288,23544,28376,32608,13089,21041,31986,28374,29152,20115,21721,13823,20438,20613,13617,9050,23472,17240,17600,15519,31227,23998,17948,27222,11915,24511,8625,20379,17586,22205,9182,13384,18903,13560,11295,15598,23824,26355,19106,21225,9518,16384,10466,26904,10724,17632,27893,36193,29425,13931,26386,9550,28315,22486,20225,32546,10144,10861,34856,33820,21356,17832,16678,24471,32965,19983,23009,8845,9358,13149,27481,15256,24689,11674,12202,8509,18128,16374,30793,30636,21496,16695,36058,12995,34311,36779,32236,16234,28488,11622,14962,16478,33705,20868,8528,18318,14513,35100,28557,23690,21650,11109,15883,28944,8327,8840,11180,36513,36144,22157,8391,30278,11081,34528,18307,16987,25747,15969,9313,33561,23798,23285,8644,36557,23979,23084,12529,33958,33359,14832,14498,13403,21432,24844,20919,25290,29506,15613,26264,19492,10012,9911,11637,8757,14226,9963,14179,17730,12580,33097,25234,15888,19115,22131,14567,10846,12983,9220,10739,17388,15836,19348,36063,33339,22302,31735,27317,22764,32464,29332,33936,26688,23209,35931,21457,14421,15085,19061,24646,20489,16811,33140,31242,14005,25273,34497,21347,16895,21872,15304,14378,32061,17057,9194,9109,9891,15557,33373,36472,11354,10129,18720,36061,36110,25013,12416,16318,13461,26845,24633,33748,36208,15241,19952,32610,34197,19046,21414,17570,22821,22171,8448,35695,27167,28683,29919,30066,20916,18295,12630,11835,20863,36423,27238,31531,12262,12771,17308,29008,31311,17997,17215,16475,10531,28058,24765,11486,16354,18547,21260,34387,16692,8547,19920,30674,32449,9863,27982,19549,28719,24057,31807,29909,15154,15839,14755,19665,30550,20699,15925,29023,17027,26450,23193,19656,13299,13724,19001,28321,15890,29818,9363,13481,22501,25969,19929,34575,15580,19055,28357,31921,21676,28857,30725,35973,33033,12014,23742,24555,15196,21504,15790,14868,15736,21537,29671,35880,19833,10028,14631,17262,8602,29474,25310,30437,34002,20030,31888,18574,18692,9632,33694,32271,25606,31353,11351,22247,14668,27911,25723,35497,9622,28854,10841,9406,28950,35177,24443,35036,36142,25927,28456,19164,23437,35120,10884,13374,14838,35328,23424,16085,34988,33325,16138,12856,15483,31764,34017,35196,10436,19031,20519,15841,28014,29936,17489,13831,18747,30094,21681,27612,32765,35309,19820,12402,21821,33785,26877,14123,36538,22050,34568,23488,34727,9654,32542,11280,8565,34298,29438,14118,29020,16852,30477,34828,10769,30845,13342,30250,28416,33213,14482,17750,15319,13595,28478,33938,35663,10674,15731,24231,10680,30218,13994,18969,30922,32384,34742,16618,9601,23920,13256,11017,21362,33879,29987,8431,9902,17067,15283,11921,31518,21850,9770,16443,35139,14791,29391,8681,26561,19517,29209,8360,30582,29459,18926,19192,8830,13160,34594,24211,31866,20888,14447,34683,31159,13396,15131,13057,31839,33181,15294,35484,30509,34087,13566,10496,8973,32273,21359,14058,32097,19633,17352,9046,31022,29196,31704,21968,15347,13934,13756,36082,32414,16418,34175,10727,29639,22226,12343,31824,26380,23178,22018,17421,32416,34182,14678,24523,23686,23035,14479,28469,24135,28906,28272,29536,35822,8987,33578,21315,13797,35103,20082,15501,35616,24570,21212,28119,10364,10873,17501,35558,34055,16352,34366,22469,35801,18894,33780,17127,24105,35075,22728,9876,17259,26616,36376,9760,13087,35537,21749,20251,11530,31223,19624,15377,18281,30500,21910,26803,35209,28113,19756,9780,14182,20214,11789,35077,27693,9438,28782,15223,31162,28352,29720,24073,16814,10821,32397,21180,26416,8260,28151,18061,23614,19876,29553,9417,28787,20782,34579,9819,14257,12925,12633,31844,22647,10008,13021,31375,15749,13974,35690,16914,11681,27154,15997,28257,31984,21524,17760,26720,29968,17508,25711,29955,12130,17120,24446,24092,31989,32481,14344,12484,34551,17743,30261,15903,10541,33689,26514,27347,13632,36191,31687,29983,10905,10188,18900,13178,28925,28574,14015,21411,12226,30034,32645,17220,26368,32865,16925,22070,24618,9866,16685,35431,34656,25638,8666,14108,12355,8579,27856,19111,36442,28998,30460,11383,23469,20849,31849,31796,10578,22458,19482,15144,17088,16956,9647,20242,22697,13549,17237,19463,19243,20135,19798,10479,33906,16603,36135,34515,20487,19593,28662,29692,12957,18727,15964,19028,32048,20846,8337,17930,18611,31783,20942,16320,29568,12544,24517,10072,31732,35620,33331,28609,31535,26349,25691,12157,12010,25051,30148,20182,19801,17316,11732,10697,35741,20050,9014,34669,15685,36518,18117,21120,25924,34695,35397,24010,29075,18249,20959,9234,29913,36267,26526,32884,11514,13959,36106,30649,18840,8474,18298,12786,9802,18724,11319,21061,21936,31174,30037,30721,34138,24360,9102,27699,25939,33029,23972,22775,26908,8766,31187,27884,13919,13333,20785,13902,12552,25386,23265,31933,11039,26584,33625,30299,17427,18224,27508,16009,18598,15067,33585,31751,13485,14069,18034,15436,20195,9482,11585,23529,33361,17464,15088,22423,35922,12370,22366,27326,35652,17020,28460,17698,10969,14041,35704,35032,12061,13129,25956,11800,12685,35361,18875,19581,10659,35874,23392,19128,19009,30689,18932,16213,24147,10325,30400,35382,27985,17672,26632,32379,25089,25998,32733,34536,33415,8606,21330,19173,26885,21140,18843,12245,18019,10428,24463,23746,19077,14204,9459,17311,21562,25237,16867,13625,24901,35441,32474,8634,24287,25708,26013,25475,14980,22398,22926,35159,21081,10182,8897,19260,22687,31120,28328,19692,17434,29001,13721,21032,8781,33052,17185,9824,24048,33542,33789,10870,32264,17195,30547,23778,10254,20365,9449,20663,15561,21875,13733,24506,23886,13581,17797,22317,30473,12268,11013,13998,20414,27110,9692,25342,25210,18501,11091,16746,11145,35298,20282,9179,20382,26873,14415,14770,34255,33674,17792,30180,20150,35233,29232,36391,11918,31202,24851,28433,30409,19240,20094,15404,16322,25163,26565,22990,23003,14560,11599,18518,35446,10563,8865,20210,13887,29052,34207,10937,14596,33351,27783,31837,14845,36563,9718,18083,21145,14715,12900,19559,30464,17608,18744,34976,19023,26288,32394,19224,10040,17740,27852,21618,33149,34604,30639,34081,29868,18634,31961,22531,33669,31018,9701,18960,35672,16149,21964,18447,24115,18051,17814,26433,9569,31576,19403,32829,29932,18881,28017,8837,24549,8388,14187,28571,29143,34214,29126,25369,19823,22009,9393,20910,31110,19489,30381,21298,32347,31700,9792,29848,28630,8649,35150,8638,17198,14418,23216,26817,25910,22615,25397,34636,35388,23527,30899,31168,35409,14592,23298,16403,24820,29511,34362,9223,26681,20255,21481,35240,26701,23982,32446,15139,15950,26813,11405,26465,9537,32852,20768,29808,33943,28149,34631,11454,32984,28549,27160,31463,16193,15875,9955,29158,34583,31999,22139,14165,24214,34372,12448,8793,35934,21093,12194,17159,19278,16993,30354,22756,32841,20474,25390,19371,33834,9173,12031,14047,9559,15621,20498,20891,33812,10087,30877,10960,19092,36655,12427,25198,32694,17329,12601,36523,18532,11982,26204,13143,9799,19590,9660,18647,26336,35356,30738,19537,35710,30426,19669,30428,36218,14261,8721,28755,14435,31944,20927,16225,23923,8267,19721,31800,34811,19766,19605,11653,11322,23729,16303,28797,36069,28393,36496,20622,21574,11537,21100,22198,31503,36121,17015,18106,22707,13389,31869,24836,17528,12298,19901,15775,27371,18263,21189,31758,19109,22462,12125,13669,23020,19769,24697,9839,26664,15218,26830,27386,31363,8710,18922,16038,36037,19505,35165,12367,20054,25472,23697,36648,16271,11744,25323,30485,34026,15425,26494,18470,14105,25222,36646,15813,17829,14229,29674,29111,19970,16041,12391,20955,21378,20495,26045,22978,14176,18206,34847,36454,12153,25513,9346,36118,35292,21312,28577,34325,28970,14952,21670,30440,16393,8324,18855,22369,19826,34073,13775,35494,34487,19040,33303,17265,15064,24070,9034,15565,14030,13453,34820,32909,20676,24564,31427,16639,22057,20138,18231,16289,30418,12702,32004,32316,12615,23710,23535,33992,23481,33216,30272,22455,25571,14386,33465,9229,21323,19526,11271,24884,35341,36432,24039,19709,14170,11928,17024,34554,34124,21932,14939,13890,28534,22761,33143,36282,17140,13207,22958,27307,9579,18203,16207,12374,24099,26067,12876,36103,15076,35901,16507,8769,24082,18278,29565,28157,28833,36546,26982,16160,13905,10312,19266,20492,35605,17693,24636,30052,13314,19432,23339,27135,10443,25016,12208,35144,21241,11722,15356,34751,36475,25763,14738,27123,29539,21117,35072,18450,27686,17956,26734,23463,29005,11975,14779,13165,19339,31786,18936,35378,18566,20913,30522,28481,14375,12292,21209,10631,25913,18583,24246,17808,14411,13941,18804,23152,33288,33858,18221,18074,13862,35021,23247,10892,18699,25301,33379,24440,29533,18623,25231,8489,32017,30646,20897,24873,16943,28973,13096,16874,26184,29399,20952,21549,23146,28667,14278,20022,8368,8933,13701,23237,10205,12515,21085,17597,15585,14723,33848,26305,21053,30078,8616,28670,35958,21981,18872,13652,20838,20865,11155,10408,24019,24127,30413,24692,22147,20962,33661,34476,26458,12766,19457,21778,30450,31123,29056,24474,14546,10105,32338,30244,26327,17201,22037,30735,32669,8400,15540,10809,20429,30084,12177,28264,13432,13926,21653,25004,20275,29259,10941,20608,14967,19445,34979,24051,29642,16558,10691,13614,14315,18643,8484,11854,11362,33345,36318,29759,33978,33725,14578,35505,12820,24500,27516,24987,22308,25744,19212,32825,14903,13556,32478,28502,35434,11903,28538,9134,12583,15091,32701,34764,25846,22062,13068,20222,18369,21344,13028,28021,15533,36186,18025,15177,21690,35392,27604,21177,18157,8921,34500,16407,23506,31184,13787,30767,35187,9002,15236,19200,30237,24376,27719,34384,16526,23000,31997,33826,12352,9874,12503,23765,25981,19979,15512,19718,16901,21468,25992,22716,18919,17252,31199,24343,26781,23289,29183,27951,14001,21221,20292,26558,16331,32980,15673,30553,11209,33397,36464,34759,14191,35951,9215,26975,14704,27173,10237,17868,16378,24007,29592,33794,32592,11668,23188,34816,19313,22751,16756,34586,23538,9795,15726,9414,15213,24268,11779,25318,17778,13877,16642,23165,13194,18467,20002,14828,11028,29851,28122,23307,9883,24102,26590,21436,11099,24329,18740,9827,19096,18882,17648,22235,35228,16073,33565,14717,15012,13235,33479,9409,34719,19360,30585,11818,32845,31177,24552,33611,31754,31356,15773,23431,23414,9382,24004,11246,32961,11890,34357,11377,13377,35919,20616,26007,29180,21228,24972,19509,28866,31447,18776,31857,29550,21172,25731,32513,28746,32937,18929,26295,20671,22079,22373,17409,27484,28154,21475,13977,8675,8692,20461,30745,9547,34689,14956,33160,30700,10966,19469,27163,33320,30097,8460,24016,34571,17340,20110,11826,17192,9816,12406,36520,12611,35035,28842,9810,19036,19706,16578,10554,32834,31916,27074,14018,18227,16971,23097,25609,18423,13937,36510,27290,22679,27879,12134,29768,33171,11953,11258,11839,36011,34642,33461,9679,36560,28485,31299,20329,9763,24998,32321,26893,27956,32132,16239,32520,20686,11707,11958,15845,16190,11764,31403,31117,21131,34014,36460,32716,28938,23013,21971,30527,13247,32461,14298,25218,11358,20563,13837,12042,36394,21277,21804,16627,33501,24912,28452,28729,26622,28110,22203,31925,27311,15833,31776,12560,34674,16363,17177,15444,26578,21236,31439,9446,34161,10713,32267,13171,20417,19614,25641,27711,24940,24590,14935,36014,28606,20231,16002,9402,33494,22094,15694,16743,17927,24191,33390,30839,14672,26312,35200,20965,14511,17062,33733,35501,23120,26249,30822,27007,22044,10045,24750,20595,19568,10287,26497,35449,30031,18406,34544,14528,11330,21148,8585,21913,19476,30544,17548,33506,24737,36784,18808,27792,24860,14796,22162,18826,10304,32406,19168,11935,22281,27206,28953,34564,28412,30046,21956,12535,22054,21417,24927,22975,14251,29748,28635,32342,31516,9848,30642,18093,22664,22897,11875,13589,29186,28638,32498,31430,9842,19400,8876,11135,21832,19136,8918,14873,36499,12085,30309,32637,32530,21272,21693,15359,19298,16368,11925,16490,15429,33867,34855,12007,11373,35273,8857,14727,26180,33418,11021,33999,11803,11276,30576,17469,28568,13620,36658,33225,29083,34596,19188,18139,36482,35549,14062,25026,19618,15758,35561,28260,16157,32748,9870,9188,17965,24810,24527,11992,20654,11675,23503,34968,30497,33130,26587,30222,36531,22183,10931,35351,14858,18655,20471,26612,13922,36196,23395,15310,13016,12908,17616,8525,10492,25699,14310,13817,33582,24677,11286,22238,14531,11086,16125,8940,10460,24310,29011,36439,16171,33974,17108,17661,25930,25867,11397,22734,18014,17007,10522,35264,15164,9399,33853,25135,10934,28447,19923,13289,10245,31444,14863,25977,26375,32438,29379,16546,29800,12887,28673,34833,22436,27495,18285,20086,22276,17123,11631,12471,30063,14210,13785,16203,10763,19072,13493,19750,9310,33652,34512,19760,10900,22362,36079,15024,25966,21184,33239,34459,33024,18440,26777,27219,35722,33313,17076,21478,28472,13510,12331,14033,11241,32353,20878,36752,19779,15134,29026,25408,35406,9385,11938,27141,23317,20071,11754,27010,10618,14112,36292,16827,27068,9297,26225,28385,11444,8264,11048,28620,8596,17035,28269,23257,21372,9611,15629,27279,32562,10686,14450,36094,35997,10745,30088,28420,26280,25831,30681,8380,18523,22981,9286,15801,16681,15273,15906,15386,21216,24622,27899,31320,14691,16358,22748,11511,20795,31812,29382,26840,30212,17520,14055,13311,12456,23770,26430,28722,33124,34591,14102,13478,24140,8538,26925,18362,29068,19645,33256,20357,33203,28791,35896,8961,26794,8670,19281,28680,27262,26106,26529,13743,18798,19247,29235,22624,14129,32624,32039,10096,13061,17982,29645,29607,19908,23646,19926,21602,24449,20269])). 159.61/70.67 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p 159.61/70.67 % [INFO] Killing All external provers ... 159.64/70.71 EOF