0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.14 % Command : run_Leo-III %s %d 0.14/0.34 % Computer : n003.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 960 0.14/0.34 % WCLimit : 120 0.14/0.34 % DateTime : Tue Aug 9 07:19:21 EDT 2022 0.14/0.34 % CPUTime : 1.01/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 5.38/2.26 % [INFO] Parsing done (1285ms). 5.38/2.28 % [INFO] Running in sequential loop mode. 5.95/2.63 % [INFO] eprover registered as external prover. 5.95/2.63 % [INFO] cvc4 registered as external prover. 5.95/2.64 % [INFO] Scanning for conjecture ... 9.16/3.48 % [INFO] Found a conjecture and 10277 axioms. Running axiom selection ... 13.04/4.97 % [INFO] Axiom selection finished. Selected 1776 axioms (removed 8501 axioms). 15.39/5.71 % [INFO] Problem is higher-order (TPTP THF). 15.51/5.75 % [INFO] Type checking passed. 15.51/5.75 % [CONFIG] Using configuration: timeout(120) with strategy. Searching for refutation ... 84.86/25.58 % External prover 'e' found a proof! 84.86/25.59 % [INFO] Killing All external provers ... 84.86/25.59 % Time passed: 25116ms (effective reasoning time: 23300ms) 84.86/25.59 % Solved by strategy 84.86/25.61 % Axioms used in derivation (1776): fact_8657_split__div, fact_8547_list__induct3, fact_2592_not__min__Null__member, fact_1056_lambda__one, fact_3199_list__assn__aux__ineq__len, fact_2822_diff__0__eq__0, fact_8661_less__eq__div__iff__mult__less__eq, fact_8863_fact__less__mono__nat, fact_639_combine__options__cases, fact_2083_zero__eq__add__iff__both__eq__0, fact_1606_order__le__neq__trans, fact_7812_power__commutes, fact_1326_order__less__asym_H, fact_7885_power__0, fact_9470_mod__eq__dvd__iff__nat, fact_2803_add__diff__cancel__right, fact_3045_add__le__imp__le__diff, fact_10082_diff__Suc, 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fact_224_Suc__less__SucD, fact_7810_power__commutes, fact_10151_assn__basic__inequalities_I5_J, fact_141_ab__semigroup__mult__class_Omult_Ocommute, fact_802_vebt__maxt_Osimps_I2_J, fact_1306_dual__order_Ostrict__implies__not__eq, fact_2213_verit__sum__simplify, fact_8631_div__less, fact_8007_self__le__power, fact_2199_comm__monoid__add__class_Oadd__0, fact_2324_le__add2, fact_4027_triangle__Suc, fact_223_less__trans__Suc, fact_3786_prod_Oempty_H, fact_3099_diff__add__0, fact_1740_norm__assertion__simps_I1_J, fact_8688_mod__less, fact_2172_add_Oassoc, fact_10047_Suc__0__or__eq, fact_8435_length__append__singleton, fact_10176_zeros, fact_9056_binomial__less__binomial__Suc, fact_8732_div__less__mono, fact_2333_add__mult__distrib, fact_2393_add__mono__thms__linordered__field_I3_J, fact_7875_power__Suc, fact_5118_split__rule, fact_8549_list__induct3, fact_1807_htt__htD, fact_8632_div__eq__dividend__iff, fact_1045_comm__monoid__mult__class_Omult__1, fact_3013_diff__add__inverse2, 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fact_1769_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J, fact_8860_tl__upt, fact_8171_empty__replicate, fact_2471_zero__less__two, fact_9994_xor__nat__rec, fact_601_not__None__eq, fact_4645_semiring__char__0__class_Oof__nat__neq__0, fact_8123_sum_Oempty, fact_3103_less__diff__iff, fact_8225_list__assn__aux__simps_I1_J, fact_220_not__less__less__Suc__eq, fact_187_nat__0__less__mult__iff, fact_1744_norm__pre__pure__rule2, fact_1761_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I2_J, fact_1066_linordered__nonzero__semiring__class_Ozero__le__one, fact_2338_VEBT__internal_OminNull_Osimps_I3_J, fact_188_linorder__neqE__nat, fact_8738_div__mod__decomp, fact_4072_cons__pre__rule, fact_1724_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J, fact_7764_of__nat__le__of__nat__power__cancel__iff, 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fact_8046_power__minus__mult, fact_164_not0__implies__Suc, fact_3177_nat__less__add__iff2, fact_8644_times__div__less__eq__dividend, fact_4059_ent__star__mono, fact_695_option_Osize_I3_J, fact_8936_assn__aci_I3_J, fact_1578_order__le__less, fact_8649_div__less__dividend, fact_1797_norm__pre__pure__iff__htt_H, fact_484_Suc__le__eq, fact_419_le__square, fact_1451_vebt__mint_Osimps_I1_J, fact_2483_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J, fact_716_VEBT__internal_Ooption__shift_Osimps_I2_J, fact_1316_order__less__asym, fact_1085_nat__geq__1__eq__neqz, fact_7819_power__mult__distrib, fact_241_not__gr0, fact_4708_list__assn_Osimps_I2_J, fact_1798_norm__pre__pure__iff__htt_H, fact_9030_self__le__ge2__pow, fact_8995_tdeletemimi_H, fact_178_Suc__mono, fact_10139_nat__mult__min__left, fact_166_nat__mult__eq__cancel__disj, fact_8970_pow__sum, fact_3779_sum_Oempty_H, fact_32_mult__cancel__right, fact_27_mult__cancel__left, fact_345_VEBT__internal_OT__vebt__buildupi_Osimps_I2_J, fact_9076_nat__div__eq__Suc__0__iff, fact_862_VEBT__internal_Ooption__shift_Ocases, fact_9843_and__nat__numerals_I2_J, fact_5069_sup__bot_Oeq__neutr__iff, fact_368_Suc__le__mono, fact_1912_pinf_I6_J, fact_7803_of__nat__zero__less__power__iff, fact_3285_slice__complete, fact_1475_antisym__conv1, fact_2656_Skolem__list__nth, fact_8877_Suc__times__binomial__eq, fact_5116_ent__disjI1__direct, fact_4073_cons__pre__rule, fact_5140_if__rule__split, fact_3789_prod_Oempty_H, fact_2425_mlex__fst__decrI, fact_5084_merge__pure__or, fact_642_vebt__succ_Osimps_I2_J, fact_9476_power__dvd__imp__le, fact_10136_min__Suc__gt_I2_J, fact_8874_zero__less__binomial__iff, fact_10045_or__nat__numerals_I3_J, fact_397_nat__induct__at__least, fact_1796_norm__pre__pure__iff__htt_H, fact_238_gr__implies__not0, fact_2490_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J, fact_4807_pochhammer__0, fact_1943_minf_I4_J, fact_8558_list__induct4, fact_2868_Nat_Odiff__diff__right, fact_8638_div__le__dividend, fact_10114_bit__push__bit__iff__int, fact_8847_map__decr__upt, fact_4074_fi__rule, fact_8220_list__assn__aux__simps_I2_J, fact_2851_diff__add__zero, fact_7975_power__Suc__le__self, fact_7725_drop__Suc__Cons, fact_8867_upt__filter__extend, fact_1589_linorder__not__le, fact_1751_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J, fact_8533_list__induct2, fact_2870_Nat_Oadd__diff__assoc, fact_4569_length__nth__simps_I4_J, fact_1701_bot_Onot__eq__extremum, fact_1062_zero__less__one__class_Ozero__le__one, fact_9471_dvd__fact, fact_376_lesseq__shift, fact_8441_replicate__Suc__conv__snoc, fact_8879_choose__mult__lemma, fact_4722_of__nat__gt__0, fact_8710_nat__mod__lem, fact_3355_prod__decode__aux_Osimps, fact_9840_and__nat__numerals_I1_J, fact_7995_power__eq__iff__eq__base, fact_4542_of__nat__less__iff, fact_8292_take__append, fact_1742_norm__pre__pure__rule2, fact_4578_length__nth__simps_I3_J, fact_2319_trans__less__add1, fact_8888_binomial__fact__lemma, fact_5137_if__rule__split, fact_9010_Suc__1, fact_173_option_Osize_I4_J, fact_8739_modulo__nat__def, fact_43_frame__rule, fact_2164_group__cancel_Oadd1, fact_7882_power__Suc2, fact_7889_power__add, fact_8704_nat__mod__eq, fact_10182_shiftl__Suc__0, fact_3095_diff__less__Suc, fact_7831_power__mult, fact_407_bot__nat__0_Oextremum__uniqueI, fact_1082_less__1__mult, fact_7761_of__nat__power__less__of__nat__cancel__iff, fact_9053_nat__power__less__diff, fact_2523_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims, fact_2341_add__decreasing, fact_2075_add__cancel__right__left, fact_2500_VEBT__internal_Ooption__shift_Opelims, fact_9468_bezout__add__strong__nat, fact_2452_add__pos__nonneg, fact_7815_power__commutes, fact_401_le__Suc__eq, fact_4676_impossible__Cons, fact_1892_vebt__maxt_Opelims, fact_5123_norm__assertion__simps_I5_J, fact_8219_list__assn__aux__simps_I2_J, fact_8988_delt__out__of__range, fact_8535_list__induct2, fact_2596_valid__member__both__member__options, fact_2361_add__nonpos__nonpos, fact_2041_minNullmin, fact_1795_norm__pre__pure__iff__htt_H, fact_4431_nth__rule, fact_4__C5_C, fact_4795_length__Cons, fact_337_forall__finite_I3_J, fact_9013_not__mod2__eq__Suc__0__eq__0, fact_8872_binomial__Suc__Suc, fact_374_nat__mult__le__cancel__disj, fact_4885_pochhammer__product, fact_2625_VEBT_Osize_I3_J, fact_10049_or__nat__rec, fact_234_Suc__lessE, fact_3009_diffs0__imp__equal, fact_8999_pred__max, fact_7967_drop__Cons_H, fact_4056_fr__rot, fact_1414_bounded__Max__nat, fact_4590_of__nat__le__0__iff, fact_370_bot__nat__0_Oextremum, fact_8559_list__induct4, fact_4158_assnle, fact_8633_div__mult__self__is__m, fact_8916_norm__assertion__simps_I10_J, fact_10149_merge__true__star, fact_485_dec__induct, fact_2418_less__imp__add__positive, fact_398_full__nat__induct, fact_282_zero__less__mult__pos, fact_9888_take__bit__nat__eq__self__iff, fact_8997_mi__ma__2__deg, fact_9449_dvd__antisym, fact_3096_diff__less, fact_227_Nat_OAll__less__Suc, fact_9876_take__bit__of__Suc__0, fact_18_mult__zero__right, fact_4726_of__nat__diff, fact_4770_nth__non__equal__first__eq, fact_4766_list_Osize__gen_I2_J, fact_461_mult__left__mono, fact_1757_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I1_J, fact_1249_ord__eq__less__trans, fact_1074_zero__less__one, fact_7833_drop__eq__ConsD, fact_2562_length__induct, fact_8658_dividend__less__div__times, fact_4060_ent__frame__fwd, fact_424_ordered__comm__semiring__class_Ocomm__mult__left__mono, fact_7950_zero__power, fact_1820_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I4_J, fact_10118_concat__bit__0, fact_2586_add__scale__eq__noteq, fact_1401_order__less__imp__not__eq2, fact_9865_less__eq__mask, fact_1788_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I5_J, fact_3205_list__assn__aux__ineq__len, fact_8641_Euclidean__Division_Odiv__eq__0__iff, fact_8857_upt__Suc, fact_2240_le__iff__add, fact_1239_less__imp__neq, fact_9042_binomial__maximum, fact_3097_Suc__diff__le, fact_1988_pinf_I1_J, fact_1331_order__less__trans, fact_4764_list_Osize__gen_I2_J, fact_222_less__Suc__induct, fact_2291_comm__semiring__class_Odistrib, fact_1768_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I2_J, fact_1182_linorder__linear, fact_8893_times__binomial__minus1__eq, fact_2741_insersimp_H, fact_6600_nth__take__lemma, fact_9397_insertsimp, fact_1416_VEBT__internal_Onaive__member_Osimps_I1_J, fact_47_frame__rule__left, fact_4058_fr__rot__rhs, fact_7894_power__add, fact_7873_power__Suc, fact_9065_ex__power__ivl1, fact_4845_pochhammer__0__left, fact_4797_length__Cons, fact_7869_left__right__inverse__power, fact_1099_order__class_Oorder__eq__iff, fact_10174_wf__set__bits__int_Ocases, fact_2493_member__bound__height_H, fact_9891_take__bit__nat__less__self__iff, fact_8980_valid__insert__both__member__options__pres, fact_8660_td__gal, fact_7729_length__drop, fact_1730_option_Osize__gen_I1_J, fact_8899_of__nat__id, fact_5121_split__rule, fact_9054_power__minus__is__div, fact_9460_dvd__diffD1, fact_2168_group__cancel_Oadd2, fact_8840_upt__conv__Cons__Cons, fact_1566_order_Ostrict__implies__order, fact_9844_and__Suc__0__eq, fact_2225_add__mono__thms__linordered__semiring_I1_J, fact_8617_div__geq, fact_631_split__option__all, fact_157_old_Onat_Oexhaust, fact_1888_hoare__triple__refines, fact_4601_horner__sum__simps_I2_J, fact_8831_upt__conv__Nil, fact_7814_power__commutes, fact_8881_zero__less__binomial, fact_7739_power__strict__increasing__iff, fact_4615_nth__Cons__pos, fact_9025_pos2, fact_693_vebt__succ_Osimps_I5_J, fact_4635_of__nat__0__le__iff, fact_813_vebt__pred_Osimps_I5_J, fact_4743_TBOUND__of__list, fact_163_Zero__not__Suc, fact_4796_length__Cons, fact_629_split__option__ex, fact_2053_minNrulli__ruleT, fact_80_divisors__zero, fact_8510_list__rest__coinc, fact_7876_power__Suc, fact_362_le__zero__eq, fact_375_mult__le__cancel2, fact_5054_sup__bot__right, fact_4587_foldl__length, fact_8901_hd__upt, fact_847_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases, fact_415_nat__less__le, fact_3354_prod__decode__aux_Oelims, fact_634_combine__options__cases, fact_824_VEBT__internal_Omembermima_Osimps_I3_J, fact_2821_diff__self__eq__0, fact_8049_power__minus__mult, fact_4064_cons__rule, fact_9450_dvd__diff__nat, fact_3201_list__assn__aux__ineq__len, fact_10161_norm__assertion__simps_I12_J, fact_1741_assn__one__left, fact_10150_assn__basic__inequalities_I1_J, fact_9050_nat__bit__induct, fact_1824_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J, fact_3288_slice__len, fact_812_vebt__maxt_Osimps_I3_J, fact_2626_insert_H__bound__height, fact_44_frame__rule, fact_2481_VEBT__internal_OminNull_Oelims_I1_J, fact_195_nat__neq__iff, fact_618_option_Odistinct_I1_J, fact_1754_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J, fact_3261_length__replicate, fact_403_le__SucI, fact_226_Suc__less__eq2, fact_3143_nat__diff__split, fact_3106_Nat_Odiff__add__assoc, fact_8663_le__div__geq, fact_2858_le__add__diff__inverse2, fact_602_not__None__eq, fact_9043_binomial__antimono, fact_155_old_Onat_Odistinct_I1_J, fact_2411_add__is__1, fact_8258_nth__append__first, fact_4573_nth__Cons__0, fact_2043_min__Null__member, fact_8734_nat__mod__eq__lemma, fact_8534_list__induct2, fact_9663_zero__natural_Orsp, fact_2823_diff__diff__left, fact_975_false__rule, fact_150_n__not__Suc__n, fact_2910_cancel__ab__semigroup__add__class_Odiff__right__commute, fact_977_pure__false, fact_2259_add__mono__thms__linordered__field_I1_J, fact_4803_pochhammer__code, fact_1452_vebt__maxt_Osimps_I1_J, fact_4669_Suc__length__conv, fact_1048_nat__mult__1, fact_1153_Orderings_Oorder__eq__iff, fact_1301_order_Ostrict__implies__not__eq, fact_489_less__Suc__eq__le, fact_382_eq__imp__le, fact_174_Leaf__0__not, fact_4849_pochhammer__rec, fact_215_VEBT_Odistinct_I1_J, fact_5685_mult__commute__abs, fact_2534_vebt__delete_Osimps_I2_J, fact_522_mult__strict__mono_H, fact_4247_snga__same__false, fact_7910_power__le__one, fact_90_lambda__zero, fact_1819_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I4_J, fact_9949_xor__nat__numerals_I2_J, fact_2235_less__eqE, fact_10048_or__Suc__0__eq, fact_1502_order_Oorder__iff__strict, fact_356_maxt__member, fact_1281_linorder__less__wlog, fact_9011_div2__Suc__Suc, fact_4076_fi__rule, fact_9008_add__2__eq__Suc, fact_3232_slice__nth, fact_2650_list__eq__iff__nth__eq, fact_5689_mult__commute__abs, fact_1821_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I3_J, fact_231_less__SucI, fact_5109_star__or__dist1, fact_2518_dele__member__cont__corr, fact_167_list__decode_Ocases, fact_2775_nth__enumerate__eq, fact_3023_eq__diff__iff, fact_8974_semiring__norm_I85_J, fact_3102_diff__less__mono, fact_3322_map__replicate__const, fact_10099_drop__bit__of__Suc__0, fact_9165_numeral__3__eq__3, fact_7922_power__less__power__Suc, fact_8526_len__greater__imp__nonempty, fact_1078_not__one__less__zero, fact_4861_pochhammer__rec_H, fact_2107_Nat_Oadd__0__right, fact_7979_power__Suc__less__one, fact_8939_norm__assertion__simps_I14_J, fact_6291_take__all, fact_8522_length__nth__simps_I1_J, fact_8356_same__length__different, fact_2547_Ex__list__of__length, fact_2139_add__less__same__cancel2, fact_183_zero__less__Suc, fact_2448_add__strict__increasing, fact_2105_add__Suc__right, fact_974_false__rule, fact_202_lift__Suc__mono__less, fact_4565_nth__Cons__Suc, fact_2833_length__map, fact_1296_dual__order_Ostrict__trans, fact_9867_Suc__mask__eq__exp, fact_8968_semiring__norm_I87_J, fact_9444_odd__Suc__div__two, fact_3356_diff__diff__less, fact_9477_dvd__minus__add, fact_1469_nless__le, fact_1039_mult_Ocomm__neutral, fact_1548_dual__order_Ostrict__trans1, fact_158_nat__induct, fact_7798_power__decreasing__iff, fact_501_mult__le__less__imp__less, fact_8592_list__encode_Ocases, fact_7818_power__mult__distrib, fact_3098_diff__Suc__eq__diff__pred, fact_293_mult__pos__pos, fact_9915_less__Suc__numeral, fact_4595_of__nat__Suc, fact_416_mult__le__mono2, fact_8735_mod__eq__nat2E, fact_175_VEBT_Oinject_I2_J, fact_97_option_Oinject, fact_9457_nat__dvd__not__less, fact_2559_length__induct, fact_8296_drop__append, fact_3_deg__SUcn__Node, fact_1907_verit__comp__simplify1_I3_J, fact_2554_neq__if__length__neq, fact_10140_nat__mult__min__right, help_If_2_1_If_001t__Assertions__Oassn_T, fact_1669_linorder__le__less__linear, fact_5079_sup__bot_Oneutr__eq__iff, fact_9177_mod__exhaust__less__4, fact_8659_dividend__less__times__div, fact_8976_two__powr__height__bound__deg, fact_2577_vebt__delete_Osimps_I4_J, fact_4856_pochhammer__Suc, fact_2018_minf_I6_J, fact_3058_le__add__diff, fact_8025_Cons__nth__drop__Suc, fact_10143_min__Suc1, fact_2243_add__le__imp__le__left, fact_9051_two__pow__div__gt__le, fact_9913_Suc__eq__numeral, fact_8552_list__induct4, fact_9991_xor__nat__unfold, fact_8897_binomial__addition__formula, fact_9447_even__diff__nat, fact_9014_add__self__mod__2, fact_1811_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J, fact_2204_add_Ocomm__neutral, fact_278_zero__less__mult__pos2, fact_10201_card__num0, fact_8066_drop__last__conv, fact_435_mult__nonpos__nonneg, fact_651_ord__eq__le__eq__trans, fact_9842_and__nat__numerals_I4_J, fact_9922_numeral__eq__Suc 84.86/25.61 % No. of inferences in proof: 3556 84.86/25.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 25116 ms resp. 23300 ms w/o parsing 87.71/26.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 87.71/26.54 thf(produc5542196010084753463at_nat_type, type, produc5542196010084753463at_nat: $tType). 87.71/26.54 thf(produc5491161045314408544at_nat_type, type, produc5491161045314408544at_nat: $tType). 87.71/26.54 thf(produc1193250871479095198on_num_type, type, produc1193250871479095198on_num: $tType). 87.71/26.54 thf(produc8306885398267862888on_nat_type, type, produc8306885398267862888on_nat: $tType). 87.71/26.54 thf(produc6121120109295599847at_nat_type, type, produc6121120109295599847at_nat: $tType). 87.71/26.54 thf(produc3368934014287244435at_num_type, type, produc3368934014287244435at_num: $tType). 87.71/26.54 thf(produc4471711990508489141at_nat_type, type, produc4471711990508489141at_nat: $tType). 87.71/26.54 thf(produc7036089656553540234on_num_type, type, produc7036089656553540234on_num: $tType). 87.71/26.54 thf(produc2233624965454879586on_nat_type, type, produc2233624965454879586on_nat: $tType). 87.71/26.54 thf(list_l9025237890452396851T_VEBT_type, type, list_l9025237890452396851T_VEBT: $tType). 87.71/26.54 thf(list_l7743825696156707879nteger_type, type, list_l7743825696156707879nteger: $tType). 87.71/26.54 thf(set_se4344029326803248219nteger_type, type, set_se4344029326803248219nteger: $tType). 87.71/26.54 thf(list_P785718909624839377_VEBTi_type, type, list_P785718909624839377_VEBTi: $tType). 87.71/26.54 thf(set_Pr2227491710730465451_VEBTi_type, type, set_Pr2227491710730465451_VEBTi: $tType). 87.71/26.54 thf(list_P735349106241217576_VEBTi_type, type, list_P735349106241217576_VEBTi: $tType). 87.71/26.54 thf(list_P5988454224134618948T_VEBT_type, type, list_P5988454224134618948T_VEBT: $tType). 87.71/26.54 thf(list_l1703466484006042159T_real_type, type, list_l1703466484006042159T_real: $tType). 87.71/26.54 thf(list_l9159265763861337117T_VEBT_type, type, list_l9159265763861337117T_VEBT: $tType). 87.71/26.54 thf(option2651255830984564193nteger_type, type, option2651255830984564193nteger: $tType). 87.71/26.54 thf(list_l6108278773223375443BT_nat_type, type, list_l6108278773223375443BT_nat: $tType). 87.71/26.54 thf(list_l5683937569929755769T_VEBT_type, type, list_l5683937569929755769T_VEBT: $tType). 87.71/26.54 thf(list_P7413028617227757229T_VEBT_type, type, list_P7413028617227757229T_VEBT: $tType). 87.71/26.54 thf(set_Pr6192946355708809607T_VEBT_type, type, set_Pr6192946355708809607T_VEBT: $tType). 87.71/26.54 thf(list_P5578671422887162913nteger_type, type, list_P5578671422887162913nteger: $tType). 87.71/26.54 thf(set_se3932177096832370463BT_nat_type, type, set_se3932177096832370463BT_nat: $tType). 87.71/26.54 thf(set_Pr4811707699266497531nteger_type, type, set_Pr4811707699266497531nteger: $tType). 87.71/26.54 thf(produc3447558737645232053on_num_type, type, produc3447558737645232053on_num: $tType). 87.71/26.54 thf(produc4953844613479565601on_nat_type, type, produc4953844613479565601on_nat: $tType). 87.71/26.54 thf(list_l9063449193509804439VEBT_o_type, type, list_l9063449193509804439VEBT_o: $tType). 87.71/26.54 thf(produc2963631642982155120at_num_type, type, produc2963631642982155120at_num: $tType). 87.71/26.54 thf(produc7248412053542808358at_nat_type, type, produc7248412053542808358at_nat: $tType). 87.71/26.54 thf(set_Co5460287733524608044eger_o_type, type, set_Co5460287733524608044eger_o: $tType). 87.71/26.54 thf(produc3777764054643897931_VEBTi_type, type, produc3777764054643897931_VEBTi: $tType). 87.71/26.54 thf(list_P8536626330812492744i_real_type, type, list_P8536626330812492744i_real: $tType). 87.71/26.54 thf(list_l6203399509495894981l_real_type, type, list_l6203399509495894981l_real: $tType). 87.71/26.54 thf(option8994051521412888707BT_nat_type, type, option8994051521412888707BT_nat: $tType). 87.71/26.54 thf(set_op4508134149509766951at_nat_type, type, set_op4508134149509766951at_nat: $tType). 87.71/26.54 thf(list_P659468882601404396Ti_nat_type, type, list_P659468882601404396Ti_nat: $tType). 87.71/26.54 thf(list_P2320588648998582380_VEBTi_type, type, list_P2320588648998582380_VEBTi: $tType). 87.71/26.54 thf(list_l8174616293485168361al_nat_type, type, list_l8174616293485168361al_nat: $tType). 87.71/26.54 thf(list_l5372182575664697961t_real_type, type, list_l5372182575664697961t_real: $tType). 87.71/26.54 thf(produc3625547720036274456_VEBTi_type, type, produc3625547720036274456_VEBTi: $tType). 87.71/26.54 thf(produc2810682830582626868T_VEBT_type, type, produc2810682830582626868T_VEBT: $tType). 87.71/26.54 thf(list_P2623026923184700063T_real_type, type, list_P2623026923184700063T_real: $tType). 87.71/26.54 thf(list_P877281246627933069T_VEBT_type, type, list_P877281246627933069T_VEBT: $tType). 87.71/26.54 thf(produc1828647624359046049st_nat_type, type, produc1828647624359046049st_nat: $tType). 87.71/26.54 thf(produc1186641810826059865st_int_type, type, produc1186641810826059865st_int: $tType). 87.71/26.54 thf(list_l235423976042982103at_num_type, type, list_l235423976042982103at_num: $tType). 87.71/26.54 thf(list_l3264859301627795341at_nat_type, type, list_l3264859301627795341at_nat: $tType). 87.71/26.54 thf(list_l1670014477004246597nt_int_type, type, list_l1670014477004246597nt_int: $tType). 87.71/26.54 thf(set_Pr7765410600122031685T_real_type, type, set_Pr7765410600122031685T_real: $tType). 87.71/26.54 thf(set_Pr6019664923565264691T_VEBT_type, type, set_Pr6019664923565264691T_VEBT: $tType). 87.71/26.54 thf(list_P7037539587688870467BT_nat_type, type, list_P7037539587688870467BT_nat: $tType). 87.71/26.54 thf(list_P4547456442757143711BT_int_type, type, list_P4547456442757143711BT_int: $tType). 87.71/26.54 thf(list_P5647936690300460905T_VEBT_type, type, list_P5647936690300460905T_VEBT: $tType). 87.71/26.54 thf(produc8243902056947475879T_VEBT_type, type, produc8243902056947475879T_VEBT: $tType). 87.71/26.54 thf(set_Pr7556676689462069481BT_nat_type, type, set_Pr7556676689462069481BT_nat: $tType). 87.71/26.54 thf(set_Pr5066593544530342725BT_int_type, type, set_Pr5066593544530342725BT_int: $tType). 87.71/26.54 thf(set_Pr6167073792073659919T_VEBT_type, type, set_Pr6167073792073659919T_VEBT: $tType). 87.71/26.54 thf(set_se4826145725398303499at_num_type, type, set_se4826145725398303499at_num: $tType). 87.71/26.54 thf(set_se7855581050983116737at_nat_type, type, set_se7855581050983116737at_nat: $tType). 87.71/26.54 thf(set_se6260736226359567993nt_int_type, type, set_se6260736226359567993nt_int: $tType). 87.71/26.54 thf(set_Pr5085853215250843933omplex_type, type, set_Pr5085853215250843933omplex: $tType). 87.71/26.54 thf(produc8923325533196201883nteger_type, type, produc8923325533196201883nteger: $tType). 87.71/26.54 thf(heap_T5317711798761887292on_nat_type, type, heap_T5317711798761887292on_nat: $tType). 87.71/26.54 thf(heap_T8822477325091257596_VEBTi_type, type, heap_T8822477325091257596_VEBTi: $tType). 87.71/26.54 thf(heap_T4980287057938770641_VEBTi_type, type, heap_T4980287057938770641_VEBTi: $tType). 87.71/26.54 thf(list_P8833571063612306856EBTi_o_type, type, list_P8833571063612306856EBTi_o: $tType). 87.71/26.54 thf(list_l1901818099074704257real_o_type, type, list_l1901818099074704257real_o: $tType). 87.71/26.54 thf(list_l7842697462554894813_nat_o_type, type, list_l7842697462554894813_nat_o: $tType). 87.71/26.54 thf(list_P3126845725202233233VEBT_o_type, type, list_P3126845725202233233VEBT_o: $tType). 87.71/26.54 thf(list_P7495141550334521929T_VEBT_type, type, list_P7495141550334521929T_VEBT: $tType). 87.71/26.54 thf(set_VEBT_VEBT_nat_o_type, type, set_VEBT_VEBT_nat_o: $tType). 87.71/26.54 thf(set_Pr3175402225741728619VEBT_o_type, type, set_Pr3175402225741728619VEBT_o: $tType). 87.71/26.54 thf(set_Pr7543698050874017315T_VEBT_type, type, set_Pr7543698050874017315T_VEBT: $tType). 87.71/26.54 thf(produc6680258955013199682i_real_type, type, produc6680258955013199682i_real: $tType). 87.71/26.54 thf(option642762832853965969at_num_type, type, option642762832853965969at_num: $tType). 87.71/26.54 thf(option4927543243414619207at_nat_type, type, option4927543243414619207at_nat: $tType). 87.71/26.54 thf(option4624381673175914239nt_int_type, type, option4624381673175914239nt_int: $tType). 87.71/26.54 thf(list_P8689742595348180415l_real_type, type, list_P8689742595348180415l_real: $tType). 87.71/26.54 thf(set_Pr6218003697084177305l_real_type, type, set_Pr6218003697084177305l_real: $tType). 87.71/26.54 thf(produc3881548065746020326Ti_nat_type, type, produc3881548065746020326Ti_nat: $tType). 87.71/26.54 thf(produc214224863196444774_VEBTi_type, type, produc214224863196444774_VEBTi: $tType). 87.71/26.54 thf(list_P6834414599653733731al_nat_type, type, list_P6834414599653733731al_nat: $tType). 87.71/26.54 thf(list_P4344331454722006975al_int_type, type, list_P4344331454722006975al_int: $tType). 87.71/26.54 thf(list_P3644420460460130531t_real_type, type, list_P3644420460460130531t_real: $tType). 87.71/26.54 thf(produc5170161368751668367T_real_type, type, produc5170161368751668367T_real: $tType). 87.71/26.54 thf(produc3757001726724277373T_VEBT_type, type, produc3757001726724277373T_VEBT: $tType). 87.71/26.54 thf(set_Pr3510011417693777981al_nat_type, type, set_Pr3510011417693777981al_nat: $tType). 87.71/26.54 thf(set_Pr1019928272762051225al_int_type, type, set_Pr1019928272762051225al_int: $tType). 87.71/26.54 thf(set_Pr320017278500174781t_real_type, type, set_Pr320017278500174781t_real: $tType). 87.71/26.54 thf(list_P1726324292696863441at_num_type, type, list_P1726324292696863441at_num: $tType). 87.71/26.54 thf(list_P6011104703257516679at_nat_type, type, list_P6011104703257516679at_nat: $tType). 87.71/26.54 thf(list_P3521021558325789923at_int_type, type, list_P3521021558325789923at_int: $tType). 87.71/26.54 thf(list_P8198026277950538467nt_nat_type, type, list_P8198026277950538467nt_nat: $tType). 87.71/26.54 thf(list_P5707943133018811711nt_int_type, type, list_P5707943133018811711nt_int: $tType). 87.71/26.54 thf(produc9072475918466114483BT_nat_type, type, produc9072475918466114483BT_nat: $tType). 87.71/26.54 thf(produc4894624898956917775BT_int_type, type, produc4894624898956917775BT_int: $tType). 87.71/26.54 thf(produc8025551001238799321T_VEBT_type, type, produc8025551001238799321T_VEBT: $tType). 87.71/26.54 thf(set_Pr6200539531224447659at_num_type, type, set_Pr6200539531224447659at_num: $tType). 87.71/26.54 thf(set_Pr1261947904930325089at_nat_type, type, set_Pr1261947904930325089at_nat: $tType). 87.71/26.54 thf(set_Pr958786334691620121nt_int_type, type, set_Pr958786334691620121nt_int: $tType). 87.71/26.54 thf(produc4411394909380815293omplex_type, type, produc4411394909380815293omplex: $tType). 87.71/26.54 thf(heap_T2636463487746394924on_nat_type, type, heap_T2636463487746394924on_nat: $tType). 87.71/26.54 thf(set_option_VEBT_VEBT_type, type, set_option_VEBT_VEBT: $tType). 87.71/26.54 thf(heap_T8145700208782473153_VEBTi_type, type, heap_T8145700208782473153_VEBTi: $tType). 87.71/26.54 thf(set_option_set_nat_type, type, set_option_set_nat: $tType). 87.71/26.54 thf(produc5014006835512566296EBTi_o_type, type, produc5014006835512566296EBTi_o: $tType). 87.71/26.54 thf(list_P3595434254542482545real_o_type, type, list_P3595434254542482545real_o: $tType). 87.71/26.54 thf(list_P5232166724548748803o_real_type, type, list_P5232166724548748803o_real: $tType). 87.71/26.54 thf(list_list_list_nat_type, type, list_list_list_nat: $tType). 87.71/26.54 thf(list_list_list_int_type, type, list_list_list_int: $tType). 87.71/26.54 thf(heap_T3836121109492952855ay_nat_type, type, heap_T3836121109492952855ay_nat: $tType). 87.71/26.54 thf(heap_T1346037964561226099ay_int_type, type, heap_T1346037964561226099ay_int: $tType). 87.71/26.54 thf(list_list_VEBT_VEBT_type, type, list_list_VEBT_VEBT: $tType). 87.71/26.54 thf(heap_T290393402774840812st_nat_type, type, heap_T290393402774840812st_nat: $tType). 87.71/26.54 thf(set_Pr4936984352647145239real_o_type, type, set_Pr4936984352647145239real_o: $tType). 87.71/26.54 thf(set_Pr6573716822653411497o_real_type, type, set_Pr6573716822653411497o_real: $tType). 87.71/26.54 thf(list_P7333126701944960589_nat_o_type, type, list_P7333126701944960589_nat_o: $tType). 87.71/26.54 thf(list_P5087981734274514673_int_o_type, type, list_P5087981734274514673_int_o: $tType). 87.71/26.54 thf(list_P6285523579766656935_o_nat_type, type, list_P6285523579766656935_o_nat: $tType). 87.71/26.54 thf(list_P3795440434834930179_o_int_type, type, list_P3795440434834930179_o_int: $tType). 87.71/26.54 thf(set_list_VEBT_VEBT_type, type, set_list_VEBT_VEBT: $tType). 87.71/26.54 thf(set_nat_num_o_type, type, set_nat_num_o: $tType). 87.71/26.54 thf(set_nat_nat_o_type, type, set_nat_nat_o: $tType). 87.71/26.54 thf(set_int_int_o_type, type, set_int_int_o: $tType). 87.71/26.54 thf(produc334124729049499915VEBT_o_type, type, produc334124729049499915VEBT_o: $tType). 87.71/26.54 thf(produc2504756804600209347T_VEBT_type, type, produc2504756804600209347T_VEBT: $tType). 87.71/26.54 thf(set_set_list_nat_type, type, set_set_list_nat: $tType). 87.71/26.54 thf(set_Pr3149072824959771635_nat_o_type, type, set_Pr3149072824959771635_nat_o: $tType). 87.71/26.54 thf(set_li6976499617229504675nteger_type, type, set_li6976499617229504675nteger: $tType). 87.71/26.54 thf(set_set_VEBT_VEBT_type, type, set_set_VEBT_VEBT: $tType). 87.71/26.54 thf(set_set_set_nat_type, type, set_set_set_nat: $tType). 87.71/26.54 thf(set_set_Code_integer_type, type, set_set_Code_integer: $tType). 87.71/26.54 thf(produc2422161461964618553l_real_type, type, produc2422161461964618553l_real: $tType). 87.71/26.54 thf(set_VEBT_VEBT_o_type, type, set_VEBT_VEBT_o: $tType). 87.71/26.54 thf(set_set_nat_o_type, type, set_set_nat_o: $tType). 87.71/26.54 thf(produc3741383161447143261al_nat_type, type, produc3741383161447143261al_nat: $tType). 87.71/26.54 thf(produc8786904178792722361al_int_type, type, produc8786904178792722361al_int: $tType). 87.71/26.54 thf(produc7716430852924023517t_real_type, type, produc7716430852924023517t_real: $tType). 87.71/26.54 thf(heap_T5660665574680485309rray_o_type, type, heap_T5660665574680485309rray_o: $tType). 87.71/26.54 thf(heap_e7401611519738050253t_unit_type, type, heap_e7401611519738050253t_unit: $tType). 87.71/26.54 thf(heap_T844314716496656296list_o_type, type, heap_T844314716496656296list_o: $tType). 87.71/26.54 thf(product_prod_nat_num_type, type, product_prod_nat_num: $tType). 87.71/26.54 thf(product_prod_nat_nat_type, type, product_prod_nat_nat: $tType). 87.71/26.54 thf(product_prod_nat_int_type, type, product_prod_nat_int: $tType). 87.71/26.54 thf(product_prod_int_int_type, type, product_prod_int_int: $tType). 87.71/26.54 thf(list_P4002435161011370285od_o_o_type, type, list_P4002435161011370285od_o_o: $tType). 87.71/26.54 thf(set_list_complex_type, type, set_list_complex: $tType). 87.71/26.54 thf(option_VEBT_VEBTi_type, type, option_VEBT_VEBTi: $tType). 87.71/26.54 thf(set_Product_prod_o_o_type, type, set_Product_prod_o_o: $tType). 87.71/26.54 thf(array_option_nat_type, type, array_option_nat: $tType). 87.71/26.54 thf(set_set_complex_type, type, set_set_complex: $tType). 87.71/26.54 thf(set_option_real_type, type, set_option_real: $tType). 87.71/26.54 thf(list_option_nat_type, type, list_option_nat: $tType). 87.71/26.54 thf(option_VEBT_VEBT_type, type, option_VEBT_VEBT: $tType). 87.71/26.54 thf(array_VEBT_VEBTi_type, type, array_VEBT_VEBTi: $tType). 87.71/26.54 thf(set_option_num_type, type, set_option_num: $tType). 87.71/26.54 thf(set_option_nat_type, type, set_option_nat: $tType). 87.71/26.54 thf(set_option_int_type, type, set_option_int: $tType). 87.71/26.54 thf(option_set_nat_type, type, option_set_nat: $tType). 87.71/26.54 thf(option_set_int_type, type, option_set_int: $tType). 87.71/26.54 thf(option_Code_integer_type, type, option_Code_integer: $tType). 87.71/26.54 thf(list_VEBT_VEBTi_type, type, list_VEBT_VEBTi: $tType). 87.71/26.54 thf(list_list_real_type, type, list_list_real: $tType). 87.71/26.54 thf(set_VEBT_VEBTi_type, type, set_VEBT_VEBTi: $tType). 87.71/26.54 thf(set_list_real_type, type, set_list_real: $tType). 87.71/26.54 thf(product_prod_real_o_type, type, product_prod_real_o: $tType). 87.71/26.54 thf(product_prod_o_real_type, type, product_prod_o_real: $tType). 87.71/26.54 thf(list_set_real_type, type, list_set_real: $tType). 87.71/26.54 thf(list_list_nat_type, type, list_list_nat: $tType). 87.71/26.54 thf(list_list_int_type, type, list_list_int: $tType). 87.71/26.54 thf(list_VEBT_VEBT_type, type, list_VEBT_VEBT: $tType). 87.71/26.54 thf(heap_Time_Heap_nat_type, type, heap_Time_Heap_nat: $tType). 87.71/26.54 thf(heap_Time_Heap_int_type, type, heap_Time_Heap_int: $tType). 87.71/26.54 thf(set_set_real_type, type, set_set_real: $tType). 87.71/26.54 thf(set_list_nat_type, type, set_list_nat: $tType). 87.71/26.54 thf(set_list_int_type, type, set_list_int: $tType). 87.71/26.54 thf(product_prod_nat_o_type, type, product_prod_nat_o: $tType). 87.71/26.54 thf(product_prod_o_nat_type, type, product_prod_o_nat: $tType). 87.71/26.54 thf(list_set_nat_type, type, list_set_nat: $tType). 87.71/26.54 thf(list_set_int_type, type, list_set_int: $tType). 87.71/26.54 thf(list_Code_integer_type, type, list_Code_integer: $tType). 87.71/26.54 thf(set_VEBT_VEBT_type, type, set_VEBT_VEBT: $tType). 87.71/26.54 thf(set_set_nat_type, type, set_set_nat: $tType). 87.71/26.54 thf(set_set_int_type, type, set_set_int: $tType). 87.71/26.54 thf(set_Code_integer_type, type, set_Code_integer: $tType). 87.71/26.54 thf(set_real_o_type, type, set_real_o: $tType). 87.71/26.54 thf(option_assn_type, type, option_assn: $tType). 87.71/26.54 thf(set_option_o_type, type, set_option_o: $tType). 87.71/26.54 thf(set_Numeral_num0_type, type, set_Numeral_num0: $tType). 87.71/26.54 thf(set_Extended_enat_type, type, set_Extended_enat: $tType). 87.71/26.54 thf(set_nat_o_type, type, set_nat_o: $tType). 87.71/26.54 thf(set_int_o_type, type, set_int_o: $tType). 87.71/26.54 thf(list_list_o_type, type, list_list_o: $tType). 87.71/26.54 thf(itself_Numeral_num0_type, type, itself_Numeral_num0: $tType). 87.71/26.54 thf(list_complex_type, type, list_complex: $tType). 87.71/26.54 thf(list_assn_type, type, list_assn: $tType). 87.71/26.54 thf(heap_Time_Heap_o_type, type, heap_Time_Heap_o: $tType). 87.71/26.54 thf(set_list_o_type, type, set_list_o: $tType). 87.71/26.54 thf(product_prod_o_o_type, type, product_prod_o_o: $tType). 87.71/26.54 thf(list_set_o_type, type, list_set_o: $tType). 87.71/26.54 thf(set_complex_type, type, set_complex: $tType). 87.71/26.54 thf(option_real_type, type, option_real: $tType). 87.71/26.54 thf(set_literal_type, type, set_literal: $tType). 87.71/26.54 thf(set_set_o_type, type, set_set_o: $tType). 87.71/26.54 thf(option_rat_type, type, option_rat: $tType). 87.71/26.54 thf(option_num_type, type, option_num: $tType). 87.71/26.54 thf(option_nat_type, type, option_nat: $tType). 87.71/26.54 thf(option_int_type, type, option_int: $tType). 87.71/26.54 thf(vEBT_VEBTi_type, type, vEBT_VEBTi: $tType). 87.71/26.54 thf(list_real_type, type, list_real: $tType). 87.71/26.54 thf(array_nat_type, type, array_nat: $tType). 87.71/26.54 thf(array_int_type, type, array_int: $tType). 87.71/26.54 thf(set_real_type, type, set_real: $tType). 87.71/26.54 thf(list_rat_type, type, list_rat: $tType). 87.71/26.54 thf(list_num_type, type, list_num: $tType). 87.71/26.54 thf(list_nat_type, type, list_nat: $tType). 87.71/26.54 thf(list_int_type, type, list_int: $tType). 87.71/26.54 thf(vEBT_VEBT_type, type, vEBT_VEBT: $tType). 87.71/26.54 thf(set_rat_type, type, set_rat: $tType). 87.71/26.54 thf(set_num_type, type, set_num: $tType). 87.71/26.54 thf(set_nat_type, type, set_nat: $tType). 87.71/26.54 thf(set_int_type, type, set_int: $tType). 87.71/26.54 thf(code_integer_type, type, code_integer: $tType). 87.71/26.54 thf(option_o_type, type, option_o: $tType). 87.71/26.54 thf(extended_enat_type, type, extended_enat: $tType). 87.71/26.54 thf(array_o_type, type, array_o: $tType). 87.71/26.54 thf(list_o_type, type, list_o: $tType). 87.71/26.54 thf(complex_type, type, complex: $tType). 87.71/26.54 thf(assn_type, type, assn: $tType). 87.71/26.54 thf(set_o_type, type, set_o: $tType). 87.71/26.54 thf(uint32_type, type, uint32: $tType). 87.71/26.54 thf(real_type, type, real: $tType). 87.71/26.54 thf(rat_type, type, rat: $tType). 87.71/26.54 thf(num_type, type, num: $tType). 87.71/26.54 thf(nat_type, type, nat: $tType). 87.71/26.54 thf(int_type, type, int: $tType). 87.71/26.54 thf(array_8141364883501958055_VEBTi_type, type, array_8141364883501958055_VEBTi: (array_VEBT_VEBTi > heap_T4980287057938770641_VEBTi)). 87.71/26.54 thf(array_len_int_type, type, array_len_int: (array_int > heap_Time_Heap_nat)). 87.71/26.54 thf(array_len_nat_type, type, array_len_nat: (array_nat > heap_Time_Heap_nat)). 87.71/26.54 thf(array_nth_nat_type, type, array_nth_nat: (array_nat > (nat > heap_Time_Heap_nat))). 87.71/26.54 thf(array_nth_option_nat_type, type, array_nth_option_nat: (array_option_nat > (nat > heap_T2636463487746394924on_nat))). 87.71/26.54 thf(array_of_list_o_type, type, array_of_list_o: (list_o > heap_T5660665574680485309rray_o)). 87.71/26.54 thf(array_of_list_int_type, type, array_of_list_int: (list_int > heap_T1346037964561226099ay_int)). 87.71/26.54 thf(array_of_list_nat_type, type, array_of_list_nat: (list_nat > heap_T3836121109492952855ay_nat)). 87.71/26.54 thf(entails_type, type, entails: (assn > (assn > $o))). 87.71/26.54 thf(pure_assn_type, type, pure_assn: ($o > assn)). 87.71/26.54 thf(snga_assn_int_type, type, snga_assn_int: (array_int > (list_int > assn))). 87.71/26.54 thf(snga_assn_nat_type, type, snga_assn_nat: (array_nat > (list_nat > assn))). 87.71/26.54 thf(snga_assn_option_nat_type, type, snga_assn_option_nat: (array_option_nat > (list_option_nat > assn))). 87.71/26.54 thf(snga_assn_VEBT_VEBTi_type, type, snga_assn_VEBT_VEBTi: (array_VEBT_VEBTi > (list_VEBT_VEBTi > assn))). 87.71/26.54 thf(binomial_type, type, binomial: (nat > (nat > nat))). 87.71/26.54 thf(bit_wf_set_bits_int_type, type, bit_wf_set_bits_int: ((nat > $o) > $o)). 87.71/26.54 thf(bit_concat_bit_type, type, bit_concat_bit: (nat > (int > (int > int)))). 87.71/26.54 thf(bit_se727722235901077358nd_nat_type, type, bit_se727722235901077358nd_nat: (nat > (nat > nat))). 87.71/26.54 thf(bit_se8568078237143864401it_int_type, type, bit_se8568078237143864401it_int: (nat > (int > int))). 87.71/26.54 thf(bit_se8570568707652914677it_nat_type, type, bit_se8570568707652914677it_nat: (nat > (nat > nat))). 87.71/26.54 thf(bit_se2002935070580805687sk_nat_type, type, bit_se2002935070580805687sk_nat: (nat > nat)). 87.71/26.54 thf(bit_se1412395901928357646or_nat_type, type, bit_se1412395901928357646or_nat: (nat > (nat > nat))). 87.71/26.54 thf(bit_se545348938243370406it_int_type, type, bit_se545348938243370406it_int: (nat > (int > int))). 87.71/26.54 thf(bit_se547839408752420682it_nat_type, type, bit_se547839408752420682it_nat: (nat > (nat > nat))). 87.71/26.54 thf(bit_se2925701944663578781it_nat_type, type, bit_se2925701944663578781it_nat: (nat > (nat > nat))). 87.71/26.54 thf(bit_se6528837805403552850or_nat_type, type, bit_se6528837805403552850or_nat: (nat > (nat > nat))). 87.71/26.54 thf(bit_se1146084159140164899it_int_type, type, bit_se1146084159140164899it_int: (int > (nat > $o))). 87.71/26.54 thf(bit_se1148574629649215175it_nat_type, type, bit_se1148574629649215175it_nat: (nat > (nat > $o))). 87.71/26.54 thf(bit_Sh3965577149348748681tl_nat_type, type, bit_Sh3965577149348748681tl_nat: (nat > (nat > nat))). 87.71/26.54 thf(bit_Sh2154871086232339855tr_nat_type, type, bit_Sh2154871086232339855tr_nat: (nat > (nat > nat))). 87.71/26.54 thf(unique6322359934112328802ux_nat_type, type, unique6322359934112328802ux_nat: (product_prod_nat_nat > $o)). 87.71/26.54 thf(comm_s4663373288045622133er_nat_type, type, comm_s4663373288045622133er_nat: (nat > (nat > nat))). 87.71/26.54 thf(semiri1408675320244567234ct_nat_type, type, semiri1408675320244567234ct_nat: (nat > nat)). 87.71/26.54 thf(finite6454714172617411596l_num0_type, type, finite6454714172617411596l_num0: (set_Numeral_num0 > nat)). 87.71/26.54 thf(finite_card_literal_type, type, finite_card_literal: (set_literal > nat)). 87.71/26.54 thf(comp_nat_nat_nat_type, type, comp_nat_nat_nat: ((nat > nat) > ((nat > nat) > (nat > nat)))). 87.71/26.54 thf(fun_up1740315431458976348at_nat_type, type, fun_up1740315431458976348at_nat: ((int > option4927543243414619207at_nat) > (int > (option4927543243414619207at_nat > (int > option4927543243414619207at_nat))))). 87.71/26.54 thf(fun_up2252230070437638584at_nat_type, type, fun_up2252230070437638584at_nat: ((nat > option4927543243414619207at_nat) > (nat > (option4927543243414619207at_nat > (nat > option4927543243414619207at_nat))))). 87.71/26.54 thf(minus_minus_nat_type, type, minus_minus_nat: (nat > (nat > nat))). 87.71/26.54 thf(one_one_assn_type, type, one_one_assn: assn). 87.71/26.54 thf(one_one_nat_type, type, one_one_nat: nat). 87.71/26.54 thf(plus_plus_nat_type, type, plus_plus_nat: (nat > (nat > nat))). 87.71/26.54 thf(times_times_assn_type, type, times_times_assn: (assn > (assn > assn))). 87.71/26.54 thf(times_times_complex_type, type, times_times_complex: (complex > (complex > complex))). 87.71/26.54 thf(times_times_int_type, type, times_times_int: (int > (int > int))). 87.71/26.54 thf(times_times_nat_type, type, times_times_nat: (nat > (nat > nat))). 87.71/26.54 thf(times_times_real_type, type, times_times_real: (real > (real > real))). 87.71/26.54 thf(zero_zero_nat_type, type, zero_zero_nat: nat). 87.71/26.54 thf(groups8507830703676809646_o_nat_type, type, groups8507830703676809646_o_nat: (($o > nat) > (set_o > nat))). 87.71/26.54 thf(groups4556407284786078405_o_nat_type, type, groups4556407284786078405_o_nat: (($o > nat) > (set_o > nat))). 87.71/26.54 thf(groups12625163056032370o_assn_type, type, groups12625163056032370o_assn: (($o > assn) > (set_o > assn))). 87.71/26.54 thf(groups5323242076211637530_o_nat_type, type, groups5323242076211637530_o_nat: (($o > nat) > (set_o > nat))). 87.71/26.54 thf(groups8487721886752058969nt_nat_type, type, groups8487721886752058969nt_nat: ((int > nat) > (nat > (list_int > nat)))). 87.71/26.54 thf(groups7488368174851004413at_nat_type, type, groups7488368174851004413at_nat: ((nat > nat) > (nat > (list_nat > nat)))). 87.71/26.54 thf(hoare_hoare_triple_o_type, type, hoare_hoare_triple_o: (assn > (heap_Time_Heap_o > (($o > assn) > $o)))). 87.71/26.54 thf(hoare_3904069481286416050_VEBTi_type, type, hoare_3904069481286416050_VEBTi: (assn > (heap_T4980287057938770641_VEBTi > ((list_VEBT_VEBTi > assn) > $o)))). 87.71/26.54 thf(hoare_3067605981109127869le_nat_type, type, hoare_3067605981109127869le_nat: (assn > (heap_Time_Heap_nat > ((nat > assn) > $o)))). 87.71/26.54 thf(hoare_7629718768684598413on_nat_type, type, hoare_7629718768684598413on_nat: (assn > (heap_T2636463487746394924on_nat > ((option_nat > assn) > $o)))). 87.71/26.54 thf(hoare_1429296392585015714_VEBTi_type, type, hoare_1429296392585015714_VEBTi: (assn > (heap_T8145700208782473153_VEBTi > ((vEBT_VEBTi > assn) > $o)))). 87.71/26.54 thf(if_assn_type, type, if_assn: ($o > (assn > (assn > assn)))). 87.71/26.54 thf(if_Heap_Time_Heap_o_type, type, if_Heap_Time_Heap_o: ($o > (heap_Time_Heap_o > (heap_Time_Heap_o > heap_Time_Heap_o)))). 87.71/26.54 thf(if_Hea2662716070787841314ap_nat_type, type, if_Hea2662716070787841314ap_nat: ($o > (heap_Time_Heap_nat > (heap_Time_Heap_nat > heap_Time_Heap_nat)))). 87.71/26.54 thf(if_Hea5867803462524415986on_nat_type, type, if_Hea5867803462524415986on_nat: ($o > (heap_T2636463487746394924on_nat > (heap_T2636463487746394924on_nat > heap_T2636463487746394924on_nat)))). 87.71/26.54 thf(if_Hea8453224502484754311_VEBTi_type, type, if_Hea8453224502484754311_VEBTi: ($o > (heap_T8145700208782473153_VEBTi > (heap_T8145700208782473153_VEBTi > heap_T8145700208782473153_VEBTi)))). 87.71/26.54 thf(if_nat_type, type, if_nat: ($o > (nat > (nat > nat)))). 87.71/26.54 thf(if_Pro6206227464963214023at_nat_type, type, if_Pro6206227464963214023at_nat: ($o > (product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)))). 87.71/26.54 thf(inf_inf_assn_type, type, inf_inf_assn: (assn > (assn > assn))). 87.71/26.54 thf(sup_sup_assn_type, type, sup_sup_assn: (assn > (assn > assn))). 87.71/26.54 thf(append_nat_type, type, append_nat: (list_nat > (list_nat > list_nat))). 87.71/26.54 thf(concat_list_int_type, type, concat_list_int: (list_list_list_int > list_list_int)). 87.71/26.54 thf(drop_int_type, type, drop_int: (nat > (list_int > list_int))). 87.71/26.54 thf(drop_nat_type, type, drop_nat: (nat > (list_nat > list_nat))). 87.71/26.54 thf(enumerate_nat_type, type, enumerate_nat: (nat > (list_nat > list_P6011104703257516679at_nat))). 87.71/26.54 thf(filter_nat_type, type, filter_nat: ((nat > $o) > (list_nat > list_nat))). 87.71/26.54 thf(foldl_assn_assn_type, type, foldl_assn_assn: ((assn > (assn > assn)) > (assn > (list_assn > assn)))). 87.71/26.54 thf(foldl_nat_o_type, type, foldl_nat_o: ((nat > ($o > nat)) > (nat > (list_o > nat)))). 87.71/26.54 thf(foldl_nat_int_type, type, foldl_nat_int: ((nat > (int > nat)) > (nat > (list_int > nat)))). 87.71/26.54 thf(foldl_nat_nat_type, type, foldl_nat_nat: ((nat > (nat > nat)) > (nat > (list_nat > nat)))). 87.71/26.54 thf(foldl_nat_real_type, type, foldl_nat_real: ((nat > (real > nat)) > (nat > (list_real > nat)))). 87.71/26.54 thf(foldr_o_nat_type, type, foldr_o_nat: (($o > (nat > nat)) > (list_o > (nat > nat)))). 87.71/26.54 thf(foldr_int_nat_type, type, foldr_int_nat: ((int > (nat > nat)) > (list_int > (nat > nat)))). 87.71/26.54 thf(foldr_real_nat_type, type, foldr_real_nat: ((real > (nat > nat)) > (list_real > (nat > nat)))). 87.71/26.54 thf(last_int_type, type, last_int: (list_int > int)). 87.71/26.54 thf(last_nat_type, type, last_nat: (list_nat > nat)). 87.71/26.54 thf(linord737317855127579385nt_nat_type, type, linord737317855127579385nt_nat: ((int > nat) > (int > (list_int > list_int)))). 87.71/26.54 thf(cons_o_type, type, cons_o: ($o > (list_o > list_o))). 87.71/26.54 thf(cons_int_type, type, cons_int: (int > (list_int > list_int))). 87.71/26.54 thf(cons_nat_type, type, cons_nat: (nat > (list_nat > list_nat))). 87.71/26.54 thf(cons_P6512896166579812791at_nat_type, type, cons_P6512896166579812791at_nat: (product_prod_nat_nat > (list_P6011104703257516679at_nat > list_P6011104703257516679at_nat))). 87.71/26.54 thf(cons_real_type, type, cons_real: (real > (list_real > list_real))). 87.71/26.54 thf(cons_VEBT_VEBT_type, type, cons_VEBT_VEBT: (vEBT_VEBT > (list_VEBT_VEBT > list_VEBT_VEBT))). 87.71/26.54 thf(nil_o_type, type, nil_o: list_o). 87.71/26.54 thf(nil_int_type, type, nil_int: list_int). 87.71/26.54 thf(nil_nat_type, type, nil_nat: list_nat). 87.71/26.54 thf(nil_real_type, type, nil_real: list_real). 87.71/26.54 thf(hd_nat_type, type, hd_nat: (list_nat > nat)). 87.71/26.54 thf(map_int_o_type, type, map_int_o: ((int > $o) > (list_int > list_o))). 87.71/26.54 thf(map_int_list_int_type, type, map_int_list_int: ((int > list_int) > (list_int > list_list_int))). 87.71/26.54 thf(map_li8902190837986183758st_int_type, type, map_li8902190837986183758st_int: ((list_int > list_list_int) > (list_list_int > list_list_list_int))). 87.71/26.54 thf(map_nat_nat_type, type, map_nat_nat: ((nat > nat) > (list_nat > list_nat))). 87.71/26.54 thf(size_list_int_type, type, size_list_int: ((int > nat) > (list_int > nat))). 87.71/26.54 thf(size_list_nat_type, type, size_list_nat: ((nat > nat) > (list_nat > nat))). 87.71/26.54 thf(size_list_VEBT_VEBT_type, type, size_list_VEBT_VEBT: ((vEBT_VEBT > nat) > (list_VEBT_VEBT > nat))). 87.71/26.54 thf(tl_nat_type, type, tl_nat: (list_nat > list_nat)). 87.71/26.54 thf(n_lists_int_type, type, n_lists_int: (nat > (list_int > list_list_int))). 87.71/26.54 thf(nth_int_type, type, nth_int: (list_int > (nat > int))). 87.71/26.54 thf(nth_nat_type, type, nth_nat: (list_nat > (nat > nat))). 87.71/26.54 thf(nth_option_nat_type, type, nth_option_nat: (list_option_nat > (nat > option_nat))). 87.71/26.54 thf(nth_Pr7617993195940197384at_nat_type, type, nth_Pr7617993195940197384at_nat: (list_P6011104703257516679at_nat > (nat > product_prod_nat_nat))). 87.71/26.54 thf(replicate_int_type, type, replicate_int: (nat > (int > list_int))). 87.71/26.54 thf(replicate_nat_type, type, replicate_nat: (nat > (nat > list_nat))). 87.71/26.54 thf(take_nat_type, type, take_nat: (nat > (list_nat > list_nat))). 87.71/26.54 thf(upt_type, type, upt: (nat > (nat > list_nat))). 87.71/26.54 thf(map_up4628693354496902621at_nat_type, type, map_up4628693354496902621at_nat: ((int > option4927543243414619207at_nat) > (list_int > (list_P6011104703257516679at_nat > (int > option4927543243414619207at_nat))))). 87.71/26.54 thf(map_up1590851270032768825at_nat_type, type, map_up1590851270032768825at_nat: ((nat > option4927543243414619207at_nat) > (list_nat > (list_P6011104703257516679at_nat > (nat > option4927543243414619207at_nat))))). 87.71/26.54 thf(restri2754309951621987225at_nat_type, type, restri2754309951621987225at_nat: (($o > option4927543243414619207at_nat) > (set_o > ($o > option4927543243414619207at_nat)))). 87.71/26.54 thf(slice_o_type, type, slice_o: (nat > (nat > (list_o > list_o)))). 87.71/26.54 thf(slice_int_type, type, slice_int: (nat > (nat > (list_int > list_int)))). 87.71/26.54 thf(slice_nat_type, type, slice_nat: (nat > (nat > (list_nat > list_nat)))). 87.71/26.54 thf(slice_real_type, type, slice_real: (nat > (nat > (list_real > list_real)))). 87.71/26.54 thf(suc_type, type, suc: (nat > nat)). 87.71/26.54 thf(case_nat_nat_type, type, case_nat_nat: (nat > ((nat > nat) > (nat > nat)))). 87.71/26.54 thf(semiri1316708129612266289at_nat_type, type, semiri1316708129612266289at_nat: (nat > nat)). 87.71/26.54 thf(semiri8422978514062236437ux_nat_type, type, semiri8422978514062236437ux_nat: ((nat > nat) > (nat > (nat > nat)))). 87.71/26.54 thf(size_size_list_o_type, type, size_size_list_o: (list_o > nat)). 87.71/26.54 thf(size_size_list_int_type, type, size_size_list_int: (list_int > nat)). 87.71/26.54 thf(size_s533118279054570080st_int_type, type, size_s533118279054570080st_int: (list_list_int > nat)). 87.71/26.54 thf(size_size_list_nat_type, type, size_size_list_nat: (list_nat > nat)). 87.71/26.54 thf(size_s6086282163384603972on_nat_type, type, size_s6086282163384603972on_nat: (list_option_nat > nat)). 87.71/26.54 thf(size_size_list_real_type, type, size_size_list_real: (list_real > nat)). 87.71/26.54 thf(size_size_option_nat_type, type, size_size_option_nat: (option_nat > nat)). 87.71/26.54 thf(size_size_option_num_type, type, size_size_option_num: (option_num > nat)). 87.71/26.54 thf(size_s170228958280169651at_nat_type, type, size_s170228958280169651at_nat: (option4927543243414619207at_nat > nat)). 87.71/26.54 thf(size_size_VEBT_VEBT_type, type, size_size_VEBT_VEBT: (vEBT_VEBT > nat)). 87.71/26.54 thf(nat_prod_decode_aux_type, type, nat_prod_decode_aux: (nat > (nat > product_prod_nat_nat))). 87.71/26.54 thf(nat_triangle_type, type, nat_triangle: (nat > nat)). 87.71/26.54 thf(bit0_type, type, bit0: (num > num)). 87.71/26.54 thf(bit1_type, type, bit1: (num > num)). 87.71/26.54 thf(one_type, type, one: num). 87.71/26.54 thf(numeral_numeral_nat_type, type, numeral_numeral_nat: (num > nat)). 87.71/26.54 thf(pred_numeral_type, type, pred_numeral: (num > nat)). 87.71/26.54 thf(none_nat_type, type, none_nat: option_nat). 87.71/26.54 thf(none_num_type, type, none_num: option_num). 87.71/26.54 thf(none_P5556105721700978146at_nat_type, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat). 87.71/26.54 thf(some_nat_type, type, some_nat: (nat > option_nat)). 87.71/26.54 thf(some_num_type, type, some_num: (num > option_num)). 87.71/26.54 thf(some_P7363390416028606310at_nat_type, type, some_P7363390416028606310at_nat: (product_prod_nat_nat > option4927543243414619207at_nat)). 87.71/26.54 thf(size_option_nat_type, type, size_option_nat: ((nat > nat) > (option_nat > nat))). 87.71/26.54 thf(size_option_num_type, type, size_option_num: ((num > nat) > (option_num > nat))). 87.71/26.54 thf(size_o8335143837870341156at_nat_type, type, size_o8335143837870341156at_nat: ((product_prod_nat_nat > nat) > (option4927543243414619207at_nat > nat))). 87.71/26.54 thf(bot_bot_assn_type, type, bot_bot_assn: assn). 87.71/26.54 thf(bot_bot_nat_type, type, bot_bot_nat: nat). 87.71/26.54 thf(bot_bot_set_o_type, type, bot_bot_set_o: set_o). 87.71/26.54 thf(ord_less_nat_type, type, ord_less_nat: (nat > (nat > $o))). 87.71/26.54 thf(ord_less_eq_nat_type, type, ord_less_eq_nat: (nat > (nat > $o))). 87.71/26.54 thf(ord_min_nat_type, type, ord_min_nat: (nat > (nat > nat))). 87.71/26.54 thf(top_top_assn_type, type, top_top_assn: assn). 87.71/26.54 thf(top_to3689904424835650196l_num0_type, type, top_to3689904424835650196l_num0: set_Numeral_num0). 87.71/26.54 thf(top_top_set_literal_type, type, top_top_set_literal: set_literal). 87.71/26.54 thf(power_power_assn_type, type, power_power_assn: (assn > (nat > assn))). 87.71/26.54 thf(power_power_complex_type, type, power_power_complex: (complex > (nat > complex))). 87.71/26.54 thf(power_power_int_type, type, power_power_int: (int > (nat > int))). 87.71/26.54 thf(power_power_nat_type, type, power_power_nat: (nat > (nat > nat))). 87.71/26.54 thf(power_power_real_type, type, power_power_real: (real > (nat > real))). 87.71/26.54 thf(produc3994169339658061776at_nat_type, type, produc3994169339658061776at_nat: ((product_prod_nat_nat > (product_prod_nat_nat > $o)) > (produc6121120109295599847at_nat > produc5491161045314408544at_nat))). 87.71/26.54 thf(produc2899441246263362727at_nat_type, type, produc2899441246263362727at_nat: ((product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)) > (produc6121120109295599847at_nat > produc5542196010084753463at_nat))). 87.71/26.54 thf(product_Pair_nat_nat_type, type, product_Pair_nat_nat: (nat > (nat > product_prod_nat_nat))). 87.71/26.54 thf(produc488173922507101015at_nat_type, type, produc488173922507101015at_nat: (option4927543243414619207at_nat > (option4927543243414619207at_nat > produc6121120109295599847at_nat))). 87.71/26.54 thf(produc738532404422230701BT_nat_type, type, produc738532404422230701BT_nat: (vEBT_VEBT > (nat > produc9072475918466114483BT_nat))). 87.71/26.54 thf(refine7594492741263601813on_nat_type, type, refine7594492741263601813on_nat: (heap_T2636463487746394924on_nat > (heap_T2636463487746394924on_nat > $o))). 87.71/26.54 thf(divide_divide_nat_type, type, divide_divide_nat: (nat > (nat > nat))). 87.71/26.54 thf(dvd_dvd_nat_type, type, dvd_dvd_nat: (nat > (nat > $o))). 87.71/26.54 thf(modulo_modulo_nat_type, type, modulo_modulo_nat: (nat > (nat > nat))). 87.71/26.54 thf(zero_n2687167440665602831ol_nat_type, type, zero_n2687167440665602831ol_nat: ($o > nat)). 87.71/26.54 thf(set_fo2584398358068434914at_nat_type, type, set_fo2584398358068434914at_nat: ((nat > (nat > nat)) > (nat > (nat > (nat > nat))))). 87.71/26.54 thf(time_TBOUND_o_type, type, time_TBOUND_o: (heap_Time_Heap_o > (nat > $o))). 87.71/26.54 thf(time_TBOUND_array_o_type, type, time_TBOUND_array_o: (heap_T5660665574680485309rray_o > (nat > $o))). 87.71/26.54 thf(time_T8667231999468956601ay_int_type, type, time_T8667231999468956601ay_int: (heap_T1346037964561226099ay_int > (nat > $o))). 87.71/26.54 thf(time_T3621710982123377501ay_nat_type, type, time_T3621710982123377501ay_nat: (heap_T3836121109492952855ay_nat > (nat > $o))). 87.71/26.54 thf(time_htt_o_type, type, time_htt_o: (assn > (heap_Time_Heap_o > (($o > assn) > (nat > $o))))). 87.71/26.54 thf(time_htt_nat_type, type, time_htt_nat: (assn > (heap_Time_Heap_nat > ((nat > assn) > (nat > $o))))). 87.71/26.54 thf(time_htt_option_nat_type, type, time_htt_option_nat: (assn > (heap_T2636463487746394924on_nat > ((option_nat > assn) > (nat > $o))))). 87.71/26.54 thf(time_htt_VEBT_VEBTi_type, type, time_htt_VEBT_VEBTi: (assn > (heap_T8145700208782473153_VEBTi > ((vEBT_VEBTi > assn) > (nat > $o))))). 87.71/26.54 thf(time_time_array_o_type, type, time_time_array_o: (heap_T5660665574680485309rray_o > (heap_e7401611519738050253t_unit > nat))). 87.71/26.54 thf(time_time_array_int_type, type, time_time_array_int: (heap_T1346037964561226099ay_int > (heap_e7401611519738050253t_unit > nat))). 87.71/26.54 thf(time_time_array_nat_type, type, time_time_array_nat: (heap_T3836121109492952855ay_nat > (heap_e7401611519738050253t_unit > nat))). 87.71/26.54 thf(type_l4264026598287037464l_num0_type, type, type_l4264026598287037464l_num0: (itself_Numeral_num0 > nat)). 87.71/26.54 thf(vEBT_T_i_n_s_e_r_t_type, type, vEBT_T_i_n_s_e_r_t: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_T_i_n_s_e_r_t2_type, type, vEBT_T_i_n_s_e_r_t2: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_T_m_a_x_t_type, type, vEBT_T_m_a_x_t: (vEBT_VEBT > nat)). 87.71/26.54 thf(vEBT_T_m_a_x_t_rel_type, type, vEBT_T_m_a_x_t_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 87.71/26.54 thf(vEBT_T_m_e_m_b_e_r_type, type, vEBT_T_m_e_m_b_e_r: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_T_m_e_m_b_e_r2_type, type, vEBT_T_m_e_m_b_e_r2: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_T_m_i_n_N_u_l_l_type, type, vEBT_T_m_i_n_N_u_l_l: (vEBT_VEBT > nat)). 87.71/26.54 thf(vEBT_T_m_i_n_t_type, type, vEBT_T_m_i_n_t: (vEBT_VEBT > nat)). 87.71/26.54 thf(vEBT_T_m_i_n_t_rel_type, type, vEBT_T_m_i_n_t_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 87.71/26.54 thf(vEBT_T_p_r_e_d_type, type, vEBT_T_p_r_e_d: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_T_p_r_e_d2_type, type, vEBT_T_p_r_e_d2: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_T_s_u_c_c_type, type, vEBT_T_s_u_c_c: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_T_s_u_c_c2_type, type, vEBT_T_s_u_c_c2: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_V441764108873111860ildupi_type, type, vEBT_V441764108873111860ildupi: (nat > nat)). 87.71/26.54 thf(vEBT_VEBT_minNulli_type, type, vEBT_VEBT_minNulli: (vEBT_VEBTi > heap_Time_Heap_o)). 87.71/26.54 thf(vEBT_V3964819847710782039nserti_type, type, vEBT_V3964819847710782039nserti: (vEBT_VEBT > (vEBT_VEBTi > (nat > heap_T8145700208782473153_VEBTi)))). 87.71/26.54 thf(vEBT_V854960066525838166emberi_type, type, vEBT_V854960066525838166emberi: (vEBT_VEBT > (vEBT_VEBTi > (nat > heap_Time_Heap_o)))). 87.71/26.54 thf(vEBT_vebt_assn_raw_type, type, vEBT_vebt_assn_raw: (vEBT_VEBT > (vEBT_VEBTi > assn))). 87.71/26.54 thf(vEBT_vebt_maxti_type, type, vEBT_vebt_maxti: (vEBT_VEBTi > heap_T2636463487746394924on_nat)). 87.71/26.54 thf(vEBT_vebt_minti_type, type, vEBT_vebt_minti: (vEBT_VEBTi > heap_T2636463487746394924on_nat)). 87.71/26.54 thf(vEBT_Leaf_type, type, vEBT_Leaf: ($o > ($o > vEBT_VEBT))). 87.71/26.54 thf(vEBT_Node_type, type, vEBT_Node: (option4927543243414619207at_nat > (nat > (list_VEBT_VEBT > (vEBT_VEBT > vEBT_VEBT))))). 87.71/26.54 thf(vEBT_size_VEBT_type, type, vEBT_size_VEBT: (vEBT_VEBT > nat)). 87.71/26.54 thf(vEBT_V8194947554948674370ptions_type, type, vEBT_V8194947554948674370ptions: (vEBT_VEBT > (nat > $o))). 87.71/26.54 thf(vEBT_VEBT_membermima_type, type, vEBT_VEBT_membermima: (vEBT_VEBT > (nat > $o))). 87.71/26.54 thf(vEBT_V5719532721284313246member_type, type, vEBT_V5719532721284313246member: (vEBT_VEBT > (nat > $o))). 87.71/26.54 thf(vEBT_invar_vebt_type, type, vEBT_invar_vebt: (vEBT_VEBT > (nat > $o))). 87.71/26.54 thf(vEBT_T_d_e_l_e_t_e_type, type, vEBT_T_d_e_l_e_t_e: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_V1232361888498592333_e_t_e_type, type, vEBT_V1232361888498592333_e_t_e: (vEBT_VEBT > (nat > nat))). 87.71/26.54 thf(vEBT_vebt_delete_type, type, vEBT_vebt_delete: (vEBT_VEBT > (nat > vEBT_VEBT))). 87.71/26.54 thf(vEBT_VEBT_height_type, type, vEBT_VEBT_height: (vEBT_VEBT > nat)). 87.71/26.54 thf(vEBT_vebt_insert_type, type, vEBT_vebt_insert: (vEBT_VEBT > (nat > vEBT_VEBT))). 87.71/26.54 thf(vEBT_L4782520652837395649_o_int_type, type, vEBT_L4782520652837395649_o_int: (($o > (int > assn)) > (list_o > (list_int > assn)))). 87.71/26.54 thf(vEBT_L4785011123346445925_o_nat_type, type, vEBT_L4785011123346445925_o_nat: (($o > (nat > assn)) > (list_o > (list_nat > assn)))). 87.71/26.54 thf(vEBT_L4725278957065240257o_real_type, type, vEBT_L4725278957065240257o_real: (($o > (real > assn)) > (list_o > (list_real > assn)))). 87.71/26.54 thf(vEBT_L77084186935402305nt_nat_type, type, vEBT_L77084186935402305nt_nat: ((int > (nat > assn)) > (list_int > (list_nat > assn)))). 87.71/26.54 thf(vEBT_L7887682484454631235_nat_o_type, type, vEBT_L7887682484454631235_nat_o: ((nat > ($o > assn)) > (list_nat > (list_o > assn)))). 87.71/26.54 thf(vEBT_L8298612041380073281at_int_type, type, vEBT_L8298612041380073281at_int: ((nat > (int > assn)) > (list_nat > (list_int > assn)))). 87.71/26.54 thf(vEBT_L6102073776069194049t_real_type, type, vEBT_L6102073776069194049t_real: ((nat > (real > assn)) > (list_nat > (list_real > assn)))). 87.71/26.54 thf(vEBT_L6234343332106409831real_o_type, type, vEBT_L6234343332106409831real_o: ((real > ($o > assn)) > (list_real > (list_o > assn)))). 87.71/26.54 thf(vEBT_L1443519841834266653al_int_type, type, vEBT_L1443519841834266653al_int: ((real > (int > assn)) > (list_real > (list_int > assn)))). 87.71/26.54 thf(vEBT_L1446010312343316929al_nat_type, type, vEBT_L1446010312343316929al_nat: ((real > (nat > assn)) > (list_real > (list_nat > assn)))). 87.71/26.54 thf(vEBT_L6296928887356842470_VEBTi_type, type, vEBT_L6296928887356842470_VEBTi: ((vEBT_VEBT > (vEBT_VEBTi > assn)) > (list_VEBT_VEBT > (list_VEBT_VEBTi > assn)))). 87.71/26.54 thf(vEBT_VEBT_minNull_type, type, vEBT_VEBT_minNull: (vEBT_VEBT > $o)). 87.71/26.54 thf(vEBT_V6963167321098673237ll_rel_type, type, vEBT_V6963167321098673237ll_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 87.71/26.54 thf(vEBT_vebt_member_type, type, vEBT_vebt_member: (vEBT_VEBT > (nat > $o))). 87.71/26.54 thf(vEBT_VEBT_lesseq_type, type, vEBT_VEBT_lesseq: (option_nat > (option_nat > $o))). 87.71/26.54 thf(vEBT_V1502963449132264192at_nat_type, type, vEBT_V1502963449132264192at_nat: ((product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)) > (option4927543243414619207at_nat > (option4927543243414619207at_nat > option4927543243414619207at_nat)))). 87.71/26.54 thf(vEBT_V7235779383477046023at_nat_type, type, vEBT_V7235779383477046023at_nat: (produc5542196010084753463at_nat > (produc5542196010084753463at_nat > $o))). 87.71/26.54 thf(vEBT_vebt_maxt_type, type, vEBT_vebt_maxt: (vEBT_VEBT > option_nat)). 87.71/26.54 thf(vEBT_vebt_maxt_rel_type, type, vEBT_vebt_maxt_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 87.71/26.54 thf(vEBT_vebt_mint_type, type, vEBT_vebt_mint: (vEBT_VEBT > option_nat)). 87.71/26.54 thf(vEBT_vebt_mint_rel_type, type, vEBT_vebt_mint_rel: (vEBT_VEBT > (vEBT_VEBT > $o))). 87.71/26.54 thf(vEBT_vebt_pred_type, type, vEBT_vebt_pred: (vEBT_VEBT > (nat > option_nat))). 87.71/26.54 thf(vEBT_VEBT_vebt_succi_type, type, vEBT_VEBT_vebt_succi: (vEBT_VEBT > (vEBT_VEBTi > (nat > heap_T2636463487746394924on_nat)))). 87.71/26.54 thf(vEBT_vebt_succ_type, type, vEBT_vebt_succ: (vEBT_VEBT > (nat > option_nat))). 87.71/26.54 thf(accp_P3267385326087170368at_nat_type, type, accp_P3267385326087170368at_nat: ((produc5542196010084753463at_nat > (produc5542196010084753463at_nat > $o)) > (produc5542196010084753463at_nat > $o))). 87.71/26.54 thf(accp_VEBT_VEBT_type, type, accp_VEBT_VEBT: ((vEBT_VEBT > (vEBT_VEBT > $o)) > (vEBT_VEBT > $o))). 87.71/26.54 thf(na_type, type, na: nat). 87.71/26.54 thf(tia_type, type, tia: vEBT_VEBTi). 87.71/26.54 thf(v_type, type, v: product_prod_nat_nat). 87.71/26.54 thf(vg_type, type, vg: list_VEBT_VEBT). 87.71/26.54 thf(vh_type, type, vh: vEBT_VEBT). 87.71/26.54 thf(vi_type, type, vi: nat). 87.71/26.54 thf(643,axiom,(((('!') @ option_nat) = (^ [A:(option_nat > $o)]: ((A @ none_nat) & ! [B:nat]: (A @ (some_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_split__option__all)). 87.71/26.54 thf(4447,plain,(((('!') @ option_nat) = (^ [A:(option_nat > $o)]: ((A @ none_nat) & ! [B:nat]: (A @ (some_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[643])). 87.71/26.54 thf(510,axiom,((! [A:$o,B:$o,C:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_Leaf @ A @ B) @ C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_VEBT__internal_Omembermima_Osimps_I1_J)). 87.71/26.54 thf(3944,plain,((! [A:$o,B:$o,C:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_Leaf @ A @ B) @ C))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[510])). 87.71/26.54 thf(939,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ zero_zero_nat)) => (? [C:nat]: ((A @ (suc @ C)) & ! [D:nat]: ((~ (A @ D)) <= (ord_less_eq_nat @ D @ C)) & (ord_less_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_ex__least__nat__less)). 87.71/26.54 thf(5593,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ zero_zero_nat)) => (? [C:nat]: ((A @ (suc @ C)) & ! [D:nat]: (~ (A @ D) | ~ (ord_less_eq_nat @ D @ C)) & (ord_less_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[939])). 87.71/26.54 thf(1234,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C)))))) => (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_infinite__descent0)). 87.71/26.54 thf(6712,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) => ((~ (A @ C)) => (? [D:nat]: (~ (A @ D) & (ord_less_nat @ D @ C)))))) => (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234])). 87.71/26.54 thf(515,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (modulo_modulo_nat @ B @ C)) = (((C != zero_zero_nat) => (! [D:nat,E:nat]: ((ord_less_nat @ E @ C) => ((A @ E) <= (B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)))))) & ((C = zero_zero_nat) => (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8741_split__mod)). 87.71/26.54 thf(3969,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (modulo_modulo_nat @ B @ C)) = (((~ (C = zero_zero_nat)) => (! [D:nat,E:nat]: ((ord_less_nat @ E @ C) => ((A @ E) | ~ (B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)))))) & ((C = zero_zero_nat) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[515])). 87.71/26.54 thf(1048,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ A @ (times_times_assn @ B @ C)) => (entails @ A @ (times_times_assn @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4058_fr__rot__rhs)). 87.71/26.54 thf(5999,plain,((! [A:assn,B:assn,C:assn]: ((entails @ A @ (times_times_assn @ B @ C)) => (entails @ A @ (times_times_assn @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048])). 87.71/26.54 thf(1308,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2324_le__add2)). 87.71/26.54 thf(6986,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308])). 87.71/26.54 thf(817,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_less__eq__nat_Osimps_I1_J)). 87.71/26.54 thf(5131,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[817])). 87.71/26.54 thf(1710,axiom,((! [A:assn,B:$o,C:assn]: ((inf_inf_assn @ (times_times_assn @ A @ (pure_assn @ B)) @ C) = (times_times_assn @ (inf_inf_assn @ A @ C) @ (pure_assn @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8907_and__extract__pure__left__ctx__iff)). 87.71/26.54 thf(8536,plain,((! [A:assn,B:$o,C:assn]: ((inf_inf_assn @ (times_times_assn @ A @ (pure_assn @ B)) @ C) = (times_times_assn @ (inf_inf_assn @ A @ C) @ (pure_assn @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1710])). 87.71/26.54 thf(107,axiom,((! [A:nat]: (((A = zero_zero_nat) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = one_one_nat)) & ((A != zero_zero_nat) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4845_pochhammer__0__left)). 87.71/26.54 thf(2199,plain,((! [A:nat]: (((A = zero_zero_nat) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = one_one_nat)) & ((~ (A = zero_zero_nat)) => ((comm_s4663373288045622133er_nat @ zero_zero_nat @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[107])). 87.71/26.54 thf(1573,axiom,((! [A:complex,B:nat,C:nat]: ((power_power_complex @ A @ (times_times_nat @ B @ C)) = (power_power_complex @ (power_power_complex @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7830_power__mult)). 87.71/26.54 thf(8062,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)],[1573])). 87.71/26.54 thf(201,axiom,((! [A:nat,B:nat]: (((bit_se2925701944663578781it_nat @ A @ B) = B) = (ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9888_take__bit__nat__eq__self__iff)). 87.71/26.54 thf(2630,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)],[201])). 87.71/26.54 thf(500,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((ord_less_nat @ zero_zero_nat @ E) => ((A @ D @ E) <= (A @ E @ (modulo_modulo_nat @ D @ E))))) => (A @ B @ C)) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8712_gcd__nat__induct)). 87.71/26.54 thf(3873,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((ord_less_nat @ zero_zero_nat @ E) => ((A @ D @ E) | ~ (A @ E @ (modulo_modulo_nat @ D @ E))))) => (A @ B @ C)) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[500])). 87.71/26.54 thf(580,axiom,((! [A:nat,B:nat,C:list_nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((nth_nat @ (cons_nat @ B @ C) @ A) = (nth_nat @ C @ (minus_minus_nat @ A @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4615_nth__Cons__pos)). 87.71/26.54 thf(4201,plain,((! [A:nat,B:nat,C:list_nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((nth_nat @ (cons_nat @ B @ C) @ A) = (nth_nat @ C @ (minus_minus_nat @ A @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[580])). 87.71/26.54 thf(1409,axiom,((! [A:nat,B:$o,C:$o]: (((A != zero_zero_nat) => ((((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ ($true))) <= (A = one_one_nat)) & (((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 @ ($true) @ C)) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2579_vebt__insert_Osimps_I1_J)). 87.71/26.54 thf(7373,plain,((! [A:nat,B:$o,C:$o]: (((~ (A = zero_zero_nat)) => ((((vEBT_vebt_insert @ (vEBT_Leaf @ B @ C) @ A) = (vEBT_Leaf @ B @ ($true))) | ~ (A = one_one_nat)) & (((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 @ ($true) @ C)) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409])). 87.71/26.54 thf(1140,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (minus_minus_nat @ A @ (modulo_modulo_nat @ A @ B)) @ B) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8716_nat__minus__mod)). 87.71/26.54 thf(6387,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (minus_minus_nat @ A @ (modulo_modulo_nat @ A @ B)) @ B) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140])). 87.71/26.54 thf(815,axiom,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1784_less__numeral__extra_I4_J)). 87.71/26.54 thf(5116,plain,((~ (ord_less_nat @ one_one_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[815])). 87.71/26.54 thf(1306,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1788_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I5_J)). 87.71/26.54 thf(6979,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306])). 87.71/26.54 thf(197,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ A) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (binomial @ C @ B) @ (binomial @ C @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9043_binomial__antimono)). 87.71/26.54 thf(2612,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))) @ A) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (binomial @ C @ B) @ (binomial @ C @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[197])). 87.71/26.54 thf(226,axiom,((! [A:nat,B:list_nat,C:nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((nth_Pr7617993195940197384at_nat @ (enumerate_nat @ C @ B) @ A) = (product_Pair_nat_nat @ (plus_plus_nat @ C @ A) @ (nth_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2775_nth__enumerate__eq)). 87.71/26.54 thf(2744,plain,((! [A:nat,B:list_nat,C:nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((nth_Pr7617993195940197384at_nat @ (enumerate_nat @ C @ B) @ A) = (product_Pair_nat_nat @ (plus_plus_nat @ C @ A) @ (nth_nat @ B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[226])). 87.71/26.54 thf(1222,axiom,((! [A:nat,B:nat,C:nat]: ((((dvd_dvd_nat @ A @ C) <= (ord_less_eq_nat @ C @ B)) <= (dvd_dvd_nat @ A @ B)) <= (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9460_dvd__diffD1)). 87.71/26.54 thf(6669,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ C) | ~ (ord_less_eq_nat @ C @ B) | ~ (dvd_dvd_nat @ A @ B) | ~ (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222])). 87.71/26.54 thf(1130,axiom,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:nat,E:assn,F:(nat > assn),G:nat]: ((((! [H:nat]: (entails @ (C @ H) @ (F @ H))) => ((ord_less_eq_nat @ D @ G) => (time_htt_nat @ E @ B @ F @ G))) <= (entails @ E @ A)) <= (time_htt_nat @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4081_htt__cons__rule)). 87.71/26.54 thf(6355,plain,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:nat,E:assn,F:(nat > assn),G:nat]: (((! [H:nat]: (entails @ (C @ H) @ (F @ H))) => ((ord_less_eq_nat @ D @ G) => (time_htt_nat @ E @ B @ (F) @ G))) | ~ (entails @ E @ A) | ~ (time_htt_nat @ A @ B @ (C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130])). 87.71/26.54 thf(1532,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ A) = (ord_less_eq_nat @ B @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2113_add__le__same__cancel1)). 87.71/26.54 thf(7890,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)],[1532])). 87.71/26.54 thf(527,axiom,((! [A:option4927543243414619207at_nat,B:product_prod_nat_nat]: ((A = (some_P7363390416028606310at_nat @ B)) => (A != none_P5556105721700978146at_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_option_OdiscI)). 87.71/26.54 thf(4005,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)],[527])). 87.71/26.54 thf(1457,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_less__not__refl3)). 87.71/26.54 thf(7569,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1457])). 87.71/26.54 thf(1641,axiom,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8630_div__by__Suc__0)). 87.71/26.54 thf(8288,plain,((! [A:nat]: ((divide_divide_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1641])). 87.71/26.54 thf(850,axiom,((! [A:nat,B:nat,C:nat]: (((A != zero_zero_nat) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8591_nat__mult__div__cancel__disj)). 87.71/26.54 thf(5260,plain,((! [A:nat,B:nat,C:nat]: (((~ (A = zero_zero_nat)) => ((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (divide_divide_nat @ B @ C))) & (((divide_divide_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = zero_zero_nat) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[850])). 87.71/26.54 thf(1731,axiom,(((vEBT_V441764108873111860ildupi @ zero_zero_nat) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_VEBT__internal_OT__vebt__buildupi_Osimps_I1_J)). 87.71/26.54 thf(8663,plain,(((vEBT_V441764108873111860ildupi @ zero_zero_nat) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1731])). 87.71/26.54 thf(1305,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1211_order__antisym__conv)). 87.71/26.54 thf(6976,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)],[1305])). 87.71/26.54 thf(451,axiom,((! [A:list_int,B:list_int,C:int]: ((ord_less_eq_nat @ (size_size_list_int @ A) @ (size_size_list_int @ B)) => (A != (cons_int @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4678_impossible__Cons)). 87.71/26.54 thf(3661,plain,((! [A:list_int,B:list_int,C:int]: ((ord_less_eq_nat @ (size_size_list_int @ A) @ (size_size_list_int @ B)) => (~ (A = (cons_int @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[451])). 87.71/26.54 thf(541,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((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))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9477_dvd__minus__add)). 87.71/26.54 thf(4062,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((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))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[541])). 87.71/26.54 thf(452,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/sandbox2/benchmark/theBenchmark.p',fact_9470_mod__eq__dvd__iff__nat)). 87.71/26.54 thf(3666,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)],[452])). 87.71/26.54 thf(722,axiom,((! [A:list_int,B:list_int]: (((size_size_list_int @ A) != (size_size_list_int @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_size__neq__size__imp__neq)). 87.71/26.54 thf(4729,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)],[722])). 87.71/26.54 thf(330,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ (bit1 @ (bit0 @ one))))))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9401_insert__bound__height)). 87.71/26.54 thf(3167,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ (bit1 @ (bit0 @ one))))))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[330])). 87.71/26.54 thf(1589,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_Zero__neq__Suc)). 87.71/26.54 thf(8114,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1589])). 87.71/26.54 thf(259,axiom,((! [A:complex,B:nat]: ((times_times_complex @ (power_power_complex @ A @ B) @ A) = (times_times_complex @ A @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7815_power__commutes)). 87.71/26.54 thf(2876,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)],[259])). 87.71/26.54 thf(869,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => ((A != B) => (? [G:nat]: ((ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ F @ (divide_divide_nat @ F @ (numeral_numeral_nat @ (bit0 @ one)))))) & ((some_nat @ G) = (vEBT_vebt_mint @ E))) & (ord_less_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8967_mintlistlength)). 87.71/26.54 thf(5320,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => ((~ (A = B)) => (? [G:nat]: ((ord_less_nat @ G @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ F @ (divide_divide_nat @ F @ (numeral_numeral_nat @ (bit0 @ one)))))) & ((some_nat @ G) = (vEBT_vebt_mint @ E))) & (ord_less_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[869])). 87.71/26.54 thf(1111,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (minus_minus_nat @ C @ B)) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3045_add__le__imp__le__diff)). 87.71/26.54 thf(6283,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)],[1111])). 87.71/26.54 thf(601,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_T_m_a_x_t @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2601_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I3_J)). 87.71/26.54 thf(4290,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_T_m_a_x_t @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[601])). 87.71/26.54 thf(1655,axiom,((! [A:int,B:int]: ((bit_concat_bit @ zero_zero_nat @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10118_concat__bit__0)). 87.71/26.54 thf(8338,plain,((! [A:int,B:int]: ((bit_concat_bit @ zero_zero_nat @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1655])). 87.71/26.54 thf(462,axiom,((! [A:nat,B:nat,C:nat]: (((comm_s4663373288045622133er_nat @ C @ B) = (times_times_nat @ (comm_s4663373288045622133er_nat @ C @ A) @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ C @ (semiri1316708129612266289at_nat @ A)) @ (minus_minus_nat @ B @ A)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4885_pochhammer__product)). 87.71/26.54 thf(3698,plain,((! [A:nat,B:nat,C:nat]: (((comm_s4663373288045622133er_nat @ C @ B) = (times_times_nat @ (comm_s4663373288045622133er_nat @ C @ A) @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ C @ (semiri1316708129612266289at_nat @ A)) @ (minus_minus_nat @ B @ A)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[462])). 87.71/26.54 thf(518,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ (divide_divide_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8642_Suc__div__le__mono)). 87.71/26.54 thf(3979,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)],[518])). 87.71/26.54 thf(884,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: (((! [D:nat]: (C @ D @ (suc @ D))) => ((C @ A @ B) <= (! [D:nat,E:nat,F:nat]: (((((C @ E @ F) => (C @ D @ F)) <= (C @ D @ E)) <= (ord_less_nat @ E @ F)) <= (ord_less_nat @ D @ E))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_less__Suc__induct)). 87.71/26.54 thf(5390,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: (((! [D:nat]: (C @ D @ (suc @ D))) => ((C @ A @ B) | ~ (! [D:nat,E:nat,F:nat]: (((C @ E @ F) => (C @ D @ F)) | ~ (C @ D @ E) | ~ (ord_less_nat @ E @ F) | ~ (ord_less_nat @ D @ E))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[884])). 87.71/26.54 thf(1112,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_T_s_u_c_c @ (vEBT_Leaf @ A @ B) @ (suc @ C)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1818_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I2_J)). 87.71/26.54 thf(6285,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_T_s_u_c_c @ (vEBT_Leaf @ A @ B) @ (suc @ C)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112])). 87.71/26.54 thf(160,axiom,((! [A:list_real,B:list_real,C:real]: ((ord_less_eq_nat @ (size_size_list_real @ A) @ (size_size_list_real @ B)) => (A != (cons_real @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4675_impossible__Cons)). 87.71/26.54 thf(2463,plain,((! [A:list_real,B:list_real,C:real]: ((ord_less_eq_nat @ (size_size_list_real @ A) @ (size_size_list_real @ B)) => (~ (A = (cons_real @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[160])). 87.71/26.54 thf(23,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10046_or__nat__numerals_I1_J)). 87.71/26.54 thf(1840,plain,((! [A:num]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[23])). 87.71/26.54 thf(745,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1244_order_Oasym)). 87.71/26.54 thf(4852,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[745])). 87.71/26.54 thf(956,axiom,((! [A:assn,B:assn,C:($o > assn),D:($o > assn),E:heap_Time_Heap_o]: (((! [F:$o]: (entails @ (C @ F) @ (D @ F))) => ((hoare_hoare_triple_o @ B @ E @ C) => (hoare_hoare_triple_o @ A @ E @ D))) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4062_cons__rule)). 87.71/26.54 thf(5654,plain,((! [A:assn,B:assn,C:($o > assn),D:($o > assn),E:heap_Time_Heap_o]: (((! [F:$o]: (entails @ (C @ F) @ (D @ F))) => ((hoare_hoare_triple_o @ B @ E @ (C)) => (hoare_hoare_triple_o @ A @ E @ (D)))) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[956])). 87.71/26.54 thf(964,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1326_order__less__asym_H)). 87.71/26.54 thf(5676,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[964])). 87.71/26.54 thf(1120,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (~ (ord_less_eq_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1912_pinf_I6_J)). 87.71/26.54 thf(6317,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)],[1120])). 87.71/26.54 thf(1556,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((suc @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2871_Suc__pred)). 87.71/26.54 thf(7990,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((suc @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1556])). 87.71/26.54 thf(431,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_less__not__refl)). 87.71/26.54 thf(3566,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[431])). 87.71/26.54 thf(793,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2318_add__less__mono1)). 87.71/26.54 thf(5028,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)],[793])). 87.71/26.54 thf(1192,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat))) => ((((((~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G)))) <= (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ zero_zero_nat) @ D @ E) @ F)))) <= (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ zero_zero_nat @ D @ E) @ F)))) <= (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E)))) <= (! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ (suc @ D)))))) <= (! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ zero_zero_nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_947_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Ocases)). 87.71/26.54 thf(6566,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))) | ~ (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ zero_zero_nat) @ D @ E) @ F))) | ~ (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ zero_zero_nat @ D @ E) @ F))) | ~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))) | ~ (! [B:$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)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192])). 87.71/26.54 thf(1300,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((~ (! [D:nat]: ((A @ D) => (~ (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D))))))) <= (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1414_bounded__Max__nat)). 87.71/26.54 thf(6954,plain,((! [A:(nat > $o),B:nat,C:nat]: (~ (! [D:nat]: ((A @ D) => (~ (! [E:nat]: ((A @ E) => (ord_less_eq_nat @ E @ D)))))) | ~ (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300])). 87.71/26.54 thf(1414,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2334_add__mult__distrib2)). 87.71/26.54 thf(7396,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1414])). 87.71/26.54 thf(768,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2327_le__Suc__ex)). 87.71/26.54 thf(4931,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (? [C:nat]: (B = (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[768])). 87.71/26.54 thf(1679,axiom,((! [A:list_o]: ((foldl_nat_o @ (^ [B:nat,C:$o]: (suc @ B)) @ zero_zero_nat @ A) = (size_size_list_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4585_foldl__length)). 87.71/26.54 thf(8417,plain,((! [A:list_o]: ((foldl_nat_o @ (^ [B:nat,C:$o]: (suc @ B)) @ zero_zero_nat @ A) = (size_size_list_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1679])). 87.71/26.54 thf(174,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (bit_se2002935070580805687sk_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9862_mask__nat__positive__iff)). 87.71/26.54 thf(2512,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (bit_se2002935070580805687sk_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[174])). 87.71/26.54 thf(545,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2460_add__nonneg__pos)). 87.71/26.54 thf(4075,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[545])). 87.71/26.54 thf(490,axiom,((! [A:assn]: (entails @ bot_bot_assn @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4069_ent__false)). 87.71/26.54 thf(3813,plain,((! [A:assn]: (entails @ bot_bot_assn @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[490])). 87.71/26.54 thf(1102,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8646_div__mult__le)). 87.71/26.54 thf(6219,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102])). 87.71/26.54 thf(193,axiom,((! [A:vEBT_VEBT]: ((~ (vEBT_VEBT_minNull @ A)) => ((accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ A) => ((! [B:$o]: ((A = (vEBT_Leaf @ ($true) @ B)) => (~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ ($true) @ B))))) => ((~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E)) => (~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (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 @ ($true)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2617_VEBT__internal_OminNull_Opelims_I3_J)). 87.71/26.54 thf(2590,plain,((! [A:vEBT_VEBT]: ((~ (vEBT_VEBT_minNull @ A)) => ((accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ A) => ((! [B:$o]: ((A = (vEBT_Leaf @ ($true) @ B)) => (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Leaf @ ($true) @ B))))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E)) => (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (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)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[193])). 87.71/26.54 thf(1378,axiom,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1039_mult_Ocomm__neutral)). 87.71/26.54 thf(7253,plain,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378])). 87.71/26.54 thf(839,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1948_minf_I3_J)). 87.71/26.54 thf(5224,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[839])). 87.71/26.54 thf(612,axiom,((! [A:nat,B:nat]: (((upt @ A @ B) = (cons_nat @ A @ (upt @ (suc @ A) @ B))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8846_upt__conv__Cons)). 87.71/26.54 thf(4326,plain,((! [A:nat,B:nat]: (((upt @ A @ B) = (cons_nat @ A @ (upt @ (suc @ A) @ B))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[612])). 87.71/26.54 thf(1570,axiom,((! [A:nat,B:nat,C:(nat > $o)]: (((! [D:nat]: ((C @ D) <= (B = (suc @ D)))) => ((C @ A) <= (! [D:nat]: (((C @ D) <= (C @ (suc @ D))) <= (ord_less_nat @ D @ B))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_strict__inc__induct)). 87.71/26.54 thf(8045,plain,((! [A:nat,B:nat,C:(nat > $o)]: (((! [D:nat]: ((C @ D) | ~ (B = (suc @ D)))) => ((C @ A) | ~ (! [D:nat]: ((C @ D) | ~ (C @ (suc @ D)) | ~ (ord_less_nat @ D @ B))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1570])). 87.71/26.54 thf(1167,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ one_one_nat @ C) => (ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7956_power__increasing)). 87.71/26.54 thf(6480,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ one_one_nat @ C) => (ord_less_eq_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167])). 87.71/26.54 thf(672,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ one_one_nat @ (power_power_nat @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7930_power__gt1)). 87.71/26.54 thf(4532,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ one_one_nat @ (power_power_nat @ A @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[672])). 87.71/26.54 thf(1065,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2413_less__imp__Suc__add)). 87.71/26.54 thf(6057,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)],[1065])). 87.71/26.54 thf(336,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ B) <= (ord_less_nat @ A @ (divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9051_two__pow__div__gt__le)). 87.71/26.54 thf(3185,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ B) | ~ (ord_less_nat @ A @ (divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[336])). 87.71/26.54 thf(1562,axiom,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1062_zero__less__one__class_Ozero__le__one)). 87.71/26.54 thf(8005,plain,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1562])). 87.71/26.54 thf(1195,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/sandbox2/benchmark/theBenchmark.p',fact_10142_min__diff)). 87.71/26.54 thf(6576,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)],[1195])). 87.71/26.54 thf(307,axiom,((! [A:nat,B:list_o]: ((B != nil_o) <= (ord_less_nat @ A @ (size_size_list_o @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8527_len__greater__imp__nonempty)). 87.71/26.54 thf(3072,plain,((! [A:nat,B:list_o]: (~ (B = nil_o) | ~ (ord_less_nat @ A @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[307])). 87.71/26.54 thf(109,axiom,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => ((((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ ($false) @ ($false)))) <= (A = (vEBT_Leaf @ ($false) @ ($false)))) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D)))))) <= (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2618_VEBT__internal_OminNull_Opelims_I2_J)). 87.71/26.54 thf(2210,plain,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => (((~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Leaf @ ($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)))))) | ~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[109])). 87.71/26.54 thf(821,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1508_order_Ostrict__iff__order)). 87.71/26.54 thf(5141,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[821])). 87.71/26.54 thf(1297,axiom,((! [A:list_nat,B:heap_e7401611519738050253t_unit]: ((time_time_array_nat @ (array_of_list_nat @ A) @ B) = (plus_plus_nat @ (size_size_list_nat @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4785_time__array__of__list)). 87.71/26.54 thf(6944,plain,((! [A:list_nat,B:heap_e7401611519738050253t_unit]: ((time_time_array_nat @ (array_of_list_nat @ A) @ B) = (plus_plus_nat @ (size_size_list_nat @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297])). 87.71/26.54 thf(1443,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/sandbox2/benchmark/theBenchmark.p',fact_10137_min__Suc__numeral)). 87.71/26.54 thf(7517,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)],[1443])). 87.71/26.54 thf(662,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1048_nat__mult__1)). 87.71/26.54 thf(4500,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[662])). 87.71/26.54 thf(1752,axiom,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ A @ (times_times_assn @ B @ C)) = (times_times_assn @ B @ (times_times_assn @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_star__aci_I3_J)). 87.71/26.54 thf(8723,plain,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ A @ (times_times_assn @ B @ C)) = (times_times_assn @ B @ (times_times_assn @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1752])). 87.71/26.54 thf(1418,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/sandbox2/benchmark/theBenchmark.p',fact_443_mult__nonneg__nonneg)). 87.71/26.54 thf(7409,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)],[1418])). 87.71/26.54 thf(973,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2868_Nat_Odiff__diff__right)). 87.71/26.54 thf(5718,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)],[973])). 87.71/26.54 thf(113,axiom,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (semiri1316708129612266289at_nat @ (comm_s4663373288045622133er_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4811_pochhammer__of__nat)). 87.71/26.54 thf(2231,plain,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (semiri1316708129612266289at_nat @ (comm_s4663373288045622133er_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[113])). 87.71/26.54 thf(495,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_vebt_mint @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = (some_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_811_vebt__mint_Osimps_I3_J)). 87.71/26.54 thf(3858,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)],[495])). 87.71/26.54 thf(953,axiom,((! [A:nat,B:nat]: (((times_times_nat @ (power_power_nat @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_nat @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8046_power__minus__mult)). 87.71/26.54 thf(5644,plain,((! [A:nat,B:nat]: (((times_times_nat @ (power_power_nat @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_nat @ B @ A)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[953])). 87.71/26.54 thf(269,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ (suc @ A))) = (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9443_even__Suc__Suc__iff)). 87.71/26.54 thf(2908,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)],[269])). 87.71/26.54 thf(75,axiom,((! [A:nat,B:list_nat,C:nat]: ((nth_nat @ (cons_nat @ A @ B) @ (suc @ C)) = (nth_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4569_length__nth__simps_I4_J)). 87.71/26.54 thf(2062,plain,((! [A:nat,B:list_nat,C:nat]: ((nth_nat @ (cons_nat @ A @ B) @ (suc @ C)) = (nth_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[75])). 87.71/26.54 thf(425,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => ((entails @ A @ (inf_inf_assn @ B @ C)) <= (entails @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8914_ent__conjI)). 87.71/26.54 thf(3549,plain,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => ((entails @ A @ (inf_inf_assn @ B @ C)) | ~ (entails @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[425])). 87.71/26.54 thf(412,axiom,((! [A:real,B:real,C:nat]: (((times_times_real @ A @ B) = (times_times_real @ B @ A)) => ((times_times_real @ (power_power_real @ A @ C) @ B) = (times_times_real @ B @ (power_power_real @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7822_power__commuting__commutes)). 87.71/26.54 thf(3509,plain,((! [A:real,B:real,C:nat]: (((times_times_real @ A @ B) = (times_times_real @ B @ A)) => ((times_times_real @ (power_power_real @ A @ C) @ B) = (times_times_real @ B @ (power_power_real @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[412])). 87.71/26.54 thf(1206,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_Suc__leI)). 87.71/26.54 thf(6619,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)],[1206])). 87.71/26.54 thf(1262,axiom,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1232_gt__ex)). 87.71/26.54 thf(6813,plain,((! [A:nat]: ? [B:nat]: (ord_less_nat @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262])). 87.71/26.54 thf(630,axiom,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:assn]: (((hoare_hoare_triple_o @ (sup_sup_assn @ A @ D) @ B @ C) <= (hoare_hoare_triple_o @ D @ B @ C)) <= (hoare_hoare_triple_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5119_split__rule)). 87.71/26.54 thf(4391,plain,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:assn]: ((hoare_hoare_triple_o @ (sup_sup_assn @ A @ D) @ B @ (C)) | ~ (hoare_hoare_triple_o @ D @ B @ (C)) | ~ (hoare_hoare_triple_o @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[630])). 87.71/26.54 thf(1738,axiom,((! [A:assn,B:$o,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn),E:nat]: ((time_htt_VEBT_VEBTi @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ D @ E) = ((time_htt_VEBT_VEBTi @ A @ C @ D @ E) <= (B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1792_norm__pre__pure__iff__htt)). 87.71/26.54 thf(8682,plain,((! [A:assn,B:$o,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn),E:nat]: ((time_htt_VEBT_VEBTi @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ (D) @ E) = ((time_htt_VEBT_VEBTi @ A @ C @ (D) @ E) | ~ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1738])). 87.71/26.54 thf(713,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/sandbox2/benchmark/theBenchmark.p',fact_322_n__less__m__mult__n)). 87.71/26.54 thf(4697,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)],[713])). 87.71/26.54 thf(1590,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_V5719532721284313246member @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_VEBT__internal_Onaive__member_Osimps_I2_J)). 87.71/26.54 thf(8118,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)],[1590])). 87.71/26.54 thf(946,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (power_power_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8866_fact__div__fact__le__pow)). 87.71/26.54 thf(5625,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))) @ (power_power_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[946])). 87.71/26.54 thf(1014,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_less__eq__Suc__le)). 87.71/26.54 thf(5878,plain,(((ord_less_nat) = (^ [A:nat]: (ord_less_eq_nat @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014])). 87.71/26.54 thf(1257,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1301_order_Ostrict__implies__not__eq)). 87.71/26.54 thf(6798,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257])). 87.71/26.54 thf(73,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:$o]: (((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ C @ ($true)))) <= (~ (B))) <= (A = (vEBT_Leaf @ C @ ($true))))) => ((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => ((B) => (~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))) => (~ (! [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F))) <= (~ (B))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F))))))) <= (! [C:$o]: ((A = (vEBT_Leaf @ ($true) @ C)) => ((~ (B)) => (~ (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ (vEBT_Leaf @ ($true) @ C)))))))) <= (accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2583_VEBT__internal_OminNull_Opelims_I1_J)). 87.71/26.54 thf(2014,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 @ C @ ($true))) | (B) | ~ (A = (vEBT_Leaf @ C @ ($true))))) => ((! [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]: (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F)) | (B) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F))))))) | ~ (! [C:$o]: ((A = (vEBT_Leaf @ ($true) @ C)) => ((~ (B)) => (~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ (vEBT_Leaf @ ($true) @ C)))))))) | ~ (accp_VEBT_VEBT @ (vEBT_V6963167321098673237ll_rel) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[73])). 87.71/26.54 thf(993,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_le__trans)). 87.71/26.54 thf(5793,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)],[993])). 87.71/26.54 thf(829,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C)) @ B) = (modulo_modulo_nat @ (suc @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8699_Suc__mod__mult__self3)). 87.71/26.54 thf(5173,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)],[829])). 87.71/26.54 thf(717,axiom,((! [A:nat,B:nat]: ((B != zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_gr__implies__not__zero)). 87.71/26.54 thf(4711,plain,((! [A:nat,B:nat]: (~ (B = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[717])). 87.71/26.54 thf(1267,axiom,((! [A:nat]: (dvd_dvd_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9451_gcd__nat_Oextremum)). 87.71/26.54 thf(6830,plain,((! [A:nat]: (dvd_dvd_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267])). 87.71/26.54 thf(1153,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) = ((A = (suc @ B)) | (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_le__Suc__eq)). 87.71/26.54 thf(6426,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)],[1153])). 87.71/26.54 thf(1523,axiom,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9437_nat__dvd__1__iff__1)). 87.71/26.54 thf(7850,plain,((! [A:nat]: ((dvd_dvd_nat @ A @ one_one_nat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1523])). 87.71/26.54 thf(1507,axiom,((! [A:$o,B:$o]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1757_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I1_J)). 87.71/26.54 thf(7781,plain,((! [A:$o,B:$o]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1507])). 87.71/26.54 thf(968,axiom,(((('!') @ option4927543243414619207at_nat) = (^ [A:(option4927543243414619207at_nat > $o)]: (! [B:product_prod_nat_nat]: (A @ (some_P7363390416028606310at_nat @ B)) & (A @ none_P5556105721700978146at_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_split__option__all)). 87.71/26.54 thf(5691,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)],[968])). 87.71/26.54 thf(694,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ B @ A)) => ((times_times_nat @ (power_power_nat @ A @ C) @ B) = (times_times_nat @ B @ (power_power_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7824_power__commuting__commutes)). 87.71/26.54 thf(4614,plain,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ B @ A)) => ((times_times_nat @ (power_power_nat @ A @ C) @ B) = (times_times_nat @ B @ (power_power_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[694])). 87.71/26.54 thf(251,axiom,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (plus_plus_nat @ B @ C)) = (times_times_real @ (power_power_real @ A @ B) @ (power_power_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7889_power__add)). 87.71/26.54 thf(2854,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)],[251])). 87.71/26.54 thf(1716,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_nat_Odistinct_I1_J)). 87.71/26.54 thf(8563,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1716])). 87.71/26.54 thf(654,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t2 @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2740_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I4_J)). 87.71/26.54 thf(4479,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t2 @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[654])). 87.71/26.54 thf(1096,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => (ord_less_eq_nat @ one_one_nat @ (vEBT_VEBT_height @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1893_height__node)). 87.71/26.54 thf(6194,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F) => (ord_less_eq_nat @ one_one_nat @ (vEBT_VEBT_height @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096])). 87.71/26.54 thf(345,axiom,((! [A:$o,B:$o]: ((vEBT_T_m_i_n_t @ (vEBT_Leaf @ A @ B)) = (plus_plus_nat @ one_one_nat @ (if_nat @ A @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2521_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I1_J)). 87.71/26.54 thf(3217,plain,((! [A:$o,B:$o]: ((vEBT_T_m_i_n_t @ (vEBT_Leaf @ A @ B)) = (plus_plus_nat @ one_one_nat @ (if_nat @ A @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[345])). 87.71/26.54 thf(1109,axiom,((power_power_nat = (^ [A:nat,B:nat]: (if_nat @ (B = zero_zero_nat) @ one_one_nat @ (times_times_nat @ A @ (power_power_nat @ A @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8040_power__eq__if)). 87.71/26.54 thf(6278,plain,(((power_power_nat) = (^ [A:nat,B:nat]: (if_nat @ (B = zero_zero_nat) @ one_one_nat @ (times_times_nat @ A @ (power_power_nat @ A @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109])). 87.71/26.54 thf(1458,axiom,((! [A:nat,B:list_int]: ((foldl_nat_int @ (^ [C:nat,D:int]: (suc @ C)) @ A @ B) = (plus_plus_nat @ A @ (size_size_list_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4749_foldl__length__aux)). 87.71/26.54 thf(7573,plain,((! [A:nat,B:list_int]: ((foldl_nat_int @ (^ [C:nat,D:int]: (suc @ C)) @ A @ B) = (plus_plus_nat @ A @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1458])). 87.71/26.54 thf(1078,axiom,((! [A:$o,B:$o]: ((vEBT_T_p_r_e_d2 @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1816_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I1_J)). 87.71/26.54 thf(6127,plain,((! [A:$o,B:$o]: ((vEBT_T_p_r_e_d2 @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078])). 87.71/26.54 thf(333,axiom,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_mult_Oassoc)). 87.71/26.54 thf(3175,plain,((! [A:complex,B:complex,C:complex]: ((times_times_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ A @ (times_times_complex @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[333])). 87.71/26.54 thf(1071,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3024_diff__mult__distrib2)). 87.71/26.54 thf(6089,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071])). 87.71/26.54 thf(868,axiom,((! [A:nat,B:nat,C:nat]: (((~ (! [D:nat]: (A != (plus_plus_nat @ C @ (times_times_nat @ B @ D))))) <= (ord_less_eq_nat @ C @ A)) <= ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8736_mod__eq__nat1E)). 87.71/26.54 thf(5316,plain,((! [A:nat,B:nat,C:nat]: (~ (! [D:nat]: ~ (A = (plus_plus_nat @ C @ (times_times_nat @ B @ D)))) | ~ (ord_less_eq_nat @ C @ A) | ~ ((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[868])). 87.71/26.54 thf(747,axiom,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ one_one_nat) => (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_968_deg__1__Leaf)). 87.71/26.54 thf(4856,plain,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ one_one_nat) => (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[747])). 87.71/26.54 thf(1069,axiom,((! [A:nat]: ((((power_power_nat @ zero_zero_nat @ A) = one_one_nat) <= (A = zero_zero_nat)) & ((A != zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7933_power__0__left)). 87.71/26.54 thf(6078,plain,((! [A:nat]: ((((power_power_nat @ zero_zero_nat @ A) = one_one_nat) | ~ (A = zero_zero_nat)) & ((~ (A = zero_zero_nat)) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069])). 87.71/26.54 thf(827,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1128_linorder__wlog)). 87.71/26.54 thf(5163,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_eq_nat @ D @ E) => (A @ D @ E))) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[827])). 87.71/26.54 thf(1359,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4612_of__nat__0__less__iff)). 87.71/26.54 thf(7188,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)],[1359])). 87.71/26.54 thf(429,axiom,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1772_le__numeral__extra_I3_J)). 87.71/26.54 thf(3562,plain,((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[429])). 87.71/26.54 thf(468,axiom,((! [A:nat]: ((^ [B:nat]: (times_times_nat @ B @ A)) = (times_times_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5687_mult__commute__abs)). 87.71/26.54 thf(3717,plain,((! [A:nat]: ((^ [B:nat]: (times_times_nat @ B @ A)) = (times_times_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[468])). 87.71/26.54 thf(731,axiom,((! [A:num]: (none_num != (some_num @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_option_Odistinct_I1_J)). 87.71/26.54 thf(4762,plain,((! [A:num]: ~ (none_num = (some_num @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[731])). 87.71/26.54 thf(1646,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (times_times_nat @ A @ B)) = ((B = (suc @ zero_zero_nat)) & (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_one__eq__mult__iff)). 87.71/26.54 thf(8303,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)],[1646])). 87.71/26.54 thf(1509,axiom,(((('?') @ option4927543243414619207at_nat) = (^ [A:(option4927543243414619207at_nat > $o)]: ((A @ none_P5556105721700978146at_nat) | ? [B:product_prod_nat_nat]: (A @ (some_P7363390416028606310at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_split__option__ex)). 87.71/26.54 thf(7793,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)],[1509])). 87.71/26.54 thf(1650,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (hoare_7629718768684598413on_nat @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_vebt_minti @ B) @ (^ [C:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_vebt_mint @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_710_vebt__minti__h)). 87.71/26.54 thf(8320,plain,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (hoare_7629718768684598413on_nat @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_vebt_minti @ B) @ (^ [C:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_vebt_mint @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1650])). 87.71/26.54 thf(1612,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C) @ D) = (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2580_vebt__insert_Osimps_I3_J)). 87.71/26.54 thf(8182,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)],[1612])). 87.71/26.54 thf(700,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((power_power_nat @ C @ (minus_minus_nat @ B @ A)) = (divide_divide_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A))) <= (ord_less_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8665_power__sub)). 87.71/26.54 thf(4633,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (((power_power_nat @ C @ (minus_minus_nat @ B @ A)) = (divide_divide_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A))) | ~ (ord_less_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[700])). 87.71/26.54 thf(1245,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => (entails @ A @ (sup_sup_assn @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5115_ent__disjI2_H)). 87.71/26.54 thf(6764,plain,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => (entails @ A @ (sup_sup_assn @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245])). 87.71/26.54 thf(1763,axiom,((! [A:assn,B:$o,C:heap_T2636463487746394924on_nat,D:(option_nat > assn)]: ((hoare_7629718768684598413on_nat @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ D) = ((hoare_7629718768684598413on_nat @ A @ C @ D) <= (B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_norm__pre__pure__iff)). 87.71/26.54 thf(8765,plain,((! [A:assn,B:$o,C:heap_T2636463487746394924on_nat,D:(option_nat > assn)]: ((hoare_7629718768684598413on_nat @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ (D)) = ((hoare_7629718768684598413on_nat @ A @ C @ (D)) | ~ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1763])). 87.71/26.54 thf(1175,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/sandbox2/benchmark/theBenchmark.p',fact_2577_vebt__delete_Osimps_I4_J)). 87.71/26.54 thf(6505,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)],[1175])). 87.71/26.54 thf(1145,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2331_trans__le__add2)). 87.71/26.54 thf(6401,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145])). 87.71/26.54 thf(935,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_Suc__le__mono)). 87.71/26.54 thf(5565,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)],[935])). 87.71/26.54 thf(302,axiom,((! [A:list_o,B:list_real,C:(list_o > (list_real > $o))]: (((size_size_list_o @ A) = (size_size_list_real @ B)) => (((C @ A @ B) <= (! [D:$o,E:list_o,F:real,G:list_real]: (((C @ E @ G) => (C @ (cons_o @ D @ E) @ (cons_real @ F @ G))) <= ((size_size_list_o @ E) = (size_size_list_real @ G))))) <= (C @ nil_o @ nil_real))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8534_list__induct2)). 87.71/26.54 thf(3049,plain,((! [A:list_o,B:list_real,C:(list_o > (list_real > $o))]: (((size_size_list_o @ A) = (size_size_list_real @ B)) => ((C @ A @ B) | ~ (! [D:$o,E:list_o,F:real,G:list_real]: (((C @ E @ G) => (C @ (cons_o @ D @ E) @ (cons_real @ F @ G))) | ~ ((size_size_list_o @ E) = (size_size_list_real @ G)))) | ~ (C @ nil_o @ nil_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[302])). 87.71/26.54 thf(725,axiom,((! [A:$o,B:heap_Time_Heap_o,C:($o > assn)]: ((hoare_hoare_triple_o @ (pure_assn @ A) @ B @ C) <= ((hoare_hoare_triple_o @ one_one_assn @ B @ C) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1743_norm__pre__pure__rule2)). 87.71/26.54 thf(4739,plain,((! [A:$o,B:heap_Time_Heap_o,C:($o > assn)]: ((hoare_hoare_triple_o @ (pure_assn @ A) @ B @ (C)) | ~ ((hoare_hoare_triple_o @ one_one_assn @ B @ (C)) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[725])). 87.71/26.54 thf(1425,axiom,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:assn,E:assn]: (((hoare_3067605981109127869le_nat @ D @ B @ (^ [F:nat]: (times_times_assn @ (C @ F) @ E))) <= (entails @ D @ (times_times_assn @ A @ E))) <= (hoare_3067605981109127869le_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4077_fi__rule)). 87.71/26.54 thf(7431,plain,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:assn,E:assn]: ((hoare_3067605981109127869le_nat @ D @ B @ (^ [F:nat]: (times_times_assn @ (C @ F) @ E))) | ~ (entails @ D @ (times_times_assn @ A @ E)) | ~ (hoare_3067605981109127869le_nat @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1425])). 87.71/26.54 thf(292,axiom,((! [A:real,B:real,C:nat]: ((power_power_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ (power_power_real @ A @ C) @ (power_power_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7816_power__mult__distrib)). 87.71/26.54 thf(3004,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)],[292])). 87.71/26.54 thf(1107,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C))) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9450_dvd__diff__nat)). 87.71/26.54 thf(6246,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C))) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107])). 87.71/26.54 thf(377,axiom,((! [A:nat,B:list_nat]: ((nth_nat @ (cons_nat @ A @ B) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4577_length__nth__simps_I3_J)). 87.71/26.54 thf(3367,plain,((! [A:nat,B:list_nat]: ((nth_nat @ (cons_nat @ A @ B) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[377])). 87.71/26.54 thf(446,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/sandbox2/benchmark/theBenchmark.p',fact_8840_upt__conv__Cons__Cons)). 87.71/26.54 thf(3648,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)],[446])). 87.71/26.54 thf(509,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1381_order__less__not__sym)). 87.71/26.54 thf(3942,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[509])). 87.71/26.54 thf(325,axiom,((! [A:list_int,B:list_real,C:list_real,D:list_real,E:(list_int > (list_real > (list_real > (list_real > $o))))]: ((((((! [F:int,G:list_int,H:real,I:list_real,J:real,K:list_real,L:real,M:list_real]: (((((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_real @ J @ K) @ (cons_real @ L @ M)) <= (E @ G @ I @ K @ M)) <= ((size_size_list_real @ K) = (size_size_list_real @ M))) <= ((size_size_list_real @ I) = (size_size_list_real @ K))) <= ((size_size_list_int @ G) = (size_size_list_real @ I)))) => (E @ A @ B @ C @ D)) <= (E @ nil_int @ nil_real @ nil_real @ nil_real)) <= ((size_size_list_real @ C) = (size_size_list_real @ D))) <= ((size_size_list_real @ B) = (size_size_list_real @ C))) <= ((size_size_list_int @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8550_list__induct4)). 87.71/26.54 thf(3135,plain,((! [A:list_int,B:list_real,C:list_real,D:list_real,E:(list_int > (list_real > (list_real > (list_real > $o))))]: (((! [F:int,G:list_int,H:real,I:list_real,J:real,K:list_real,L:real,M:list_real]: ((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_real @ J @ K) @ (cons_real @ L @ M)) | ~ (E @ G @ I @ K @ M) | ~ ((size_size_list_real @ K) = (size_size_list_real @ M)) | ~ ((size_size_list_real @ I) = (size_size_list_real @ K)) | ~ ((size_size_list_int @ G) = (size_size_list_real @ I)))) => (E @ A @ B @ C @ D)) | ~ (E @ nil_int @ nil_real @ nil_real @ nil_real) | ~ ((size_size_list_real @ C) = (size_size_list_real @ D)) | ~ ((size_size_list_real @ B) = (size_size_list_real @ C)) | ~ ((size_size_list_int @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[325])). 87.71/26.54 thf(553,axiom,((! [A:list_o,B:nat]: ((foldr_o_nat @ (^ [C:$o]: (suc)) @ A @ B) = (plus_plus_nat @ B @ (size_size_list_o @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2733_foldr__length__aux)). 87.71/26.54 thf(4097,plain,((! [A:list_o,B:nat]: ((foldr_o_nat @ (^ [C:$o]: (suc)) @ A @ B) = (plus_plus_nat @ B @ (size_size_list_o @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[553])). 87.71/26.54 thf(756,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_bot__nat__0_Oextremum)). 87.71/26.54 thf(4884,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[756])). 87.71/26.54 thf(376,axiom,((! [A:nat,B:nat]: (ord_less_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9889_take__bit__nat__less__exp)). 87.71/26.54 thf(3365,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)],[376])). 87.71/26.54 thf(1220,axiom,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:assn]: ((hoare_3067605981109127869le_nat @ A @ B @ C) => (hoare_3067605981109127869le_nat @ (times_times_assn @ D @ A) @ B @ (^ [E:nat]: (times_times_assn @ D @ (C @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_frame__rule__left)). 87.71/26.54 thf(6665,plain,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:assn]: ((hoare_3067605981109127869le_nat @ A @ B @ (C)) => (hoare_3067605981109127869le_nat @ (times_times_assn @ D @ A) @ B @ (^ [E:nat]: (times_times_assn @ D @ (C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220])). 87.71/26.54 thf(1760,axiom,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ A @ (times_times_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_assn__times__assoc)). 87.71/26.54 thf(8747,plain,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ A @ (times_times_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1760])). 87.71/26.54 thf(1341,axiom,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_valid__0__not)). 87.71/26.54 thf(7096,plain,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341])). 87.71/26.54 thf(151,axiom,((! [A:list_o]: (((size_size_list_o @ A) = zero_zero_nat) = (A = nil_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8140_length__0__conv)). 87.71/26.54 thf(2434,plain,((! [A:list_o]: (((size_size_list_o @ A) = zero_zero_nat) = (A = nil_o)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[151])). 87.71/26.54 thf(1150,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/sandbox2/benchmark/theBenchmark.p',fact_8634_div__mult__self1__is__m)). 87.71/26.54 thf(6416,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)],[1150])). 87.71/26.54 thf(1657,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t2 @ (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2739_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I3_J)). 87.71/26.54 thf(8342,plain,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t2 @ (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1657])). 87.71/26.54 thf(970,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((modulo_modulo_nat @ (minus_minus_nat @ A @ C) @ B) = (minus_minus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8718_mod__nat__sub)). 87.71/26.54 thf(5701,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((modulo_modulo_nat @ (minus_minus_nat @ A @ C) @ B) = (minus_minus_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[970])). 87.71/26.54 thf(439,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1254_ord__less__eq__trans)). 87.71/26.54 thf(3616,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((B = C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[439])). 87.71/26.54 thf(49,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: (((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t @ A @ C) @ (numeral_numeral_nat @ (bit1 @ one))) <= (~ (? [D:nat]: (vEBT_V8194947554948674370ptions @ A @ D)))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9396_insersimp)). 87.71/26.54 thf(1919,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t @ A @ C) @ (numeral_numeral_nat @ (bit1 @ one))) | ? [D:nat]: (vEBT_V8194947554948674370ptions @ A @ D) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[49])). 87.71/26.54 thf(1619,axiom,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:(option_nat > assn)]: ((hoare_7629718768684598413on_nat @ A @ B @ C) => ((hoare_7629718768684598413on_nat @ A @ B @ D) <= (! [E:option_nat]: (entails @ (C @ E) @ (D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4065_cons__post__rule)). 87.71/26.54 thf(8210,plain,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:(option_nat > assn)]: ((hoare_7629718768684598413on_nat @ A @ B @ (C)) => ((hoare_7629718768684598413on_nat @ A @ B @ (D)) | ~ (! [E:option_nat]: (entails @ (C @ E) @ (D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1619])). 87.71/26.54 thf(1497,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3170_nz__le__conv__less)). 87.71/26.54 thf(7716,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1497])). 87.71/26.54 thf(248,axiom,((! [A:nat]: ((upt @ A @ zero_zero_nat) = nil_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8841_upt__0)). 87.71/26.54 thf(2844,plain,((! [A:nat]: ((upt @ A @ zero_zero_nat) = nil_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[248])). 87.71/26.54 thf(1259,axiom,((! [A:option4927543243414619207at_nat]: ((! [B:product_prod_nat_nat]: (A != (some_P7363390416028606310at_nat @ B))) = (A = none_P5556105721700978146at_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_not__Some__eq)). 87.71/26.54 thf(6804,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)],[1259])). 87.71/26.54 thf(435,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_maxt @ A) = B) => ((! [C:$o,D:$o]: ((~ (((D) => (B = (some_nat @ one_one_nat))) & ((((B = (some_nat @ zero_zero_nat)) <= (C)) & ((B = none_nat) <= (~ (C)))) <= (~ (D))))) <= (A = (vEBT_Leaf @ C @ D)))) => ((~ (! [C:nat,D:nat]: ((B != (some_nat @ D)) <= (? [E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))))) <= ((B != none_nat) <= (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_948_vebt__maxt_Oelims)). 87.71/26.54 thf(3577,plain,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_maxt @ A) = B) => ((! [C:$o,D:$o]: (~ (((D) => (B = (some_nat @ one_one_nat))) & ((((B = (some_nat @ zero_zero_nat)) | ~ (C)) & ((B = none_nat) | (C))) | (D))) | ~ (A = (vEBT_Leaf @ C @ D)))) => (~ (! [C:nat,D:nat]: (~ (B = (some_nat @ D)) | ~ (? [E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))))) | ~ (~ (B = none_nat) | ~ (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[435])). 87.71/26.54 thf(1286,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_nat__mult__eq__cancel1)). 87.71/26.54 thf(6894,plain,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286])). 87.71/26.55 thf(1552,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3019_diff__le__self)). 87.71/26.55 thf(7980,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1552])). 87.71/26.55 thf(89,axiom,((! [A:nat,B:nat,C:nat]: (((nth_nat @ (replicate_nat @ B @ C) @ A) = C) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3277_nth__replicate)). 87.71/26.55 thf(2146,plain,((! [A:nat,B:nat,C:nat]: (((nth_nat @ (replicate_nat @ B @ C) @ A) = C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[89])). 87.71/26.55 thf(784,axiom,((! [A:$o,B:$o]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1767_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I2_J)). 87.71/26.55 thf(4980,plain,((! [A:$o,B:$o]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[784])). 87.71/26.55 thf(536,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_mult__cancel__right)). 87.71/26.55 thf(4047,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)],[536])). 87.71/26.55 thf(1193,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_Suc__leD)). 87.71/26.55 thf(6570,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)],[1193])). 87.71/26.55 thf(1290,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8645_div__times__less__eq__dividend)). 87.71/26.55 thf(6914,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)],[1290])). 87.71/26.55 thf(1652,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1724_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J)). 87.71/26.55 thf(8325,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1652])). 87.71/26.55 thf(660,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_nat__less__le)). 87.71/26.55 thf(4496,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[660])). 87.71/26.55 thf(1720,axiom,((! [A:($o > nat)]: ((groups4556407284786078405_o_nat @ A @ bot_bot_set_o) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3779_sum_Oempty_H)). 87.71/26.55 thf(8578,plain,((! [A:($o > nat)]: ((groups4556407284786078405_o_nat @ (A) @ bot_bot_set_o) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1720])). 87.71/26.55 thf(695,axiom,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_Suc__n__not__le__n)). 87.71/26.55 thf(4618,plain,((! [A:nat]: ~ (ord_less_eq_nat @ (suc @ A) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[695])). 87.71/26.55 thf(1695,axiom,((! [A:$o,B:$o]: (((pure_assn @ A) = (pure_assn @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_pure__assn__eq__conv)). 87.71/26.55 thf(8472,plain,((! [A:$o,B:$o]: (((pure_assn @ A) = (pure_assn @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1695])). 87.71/26.55 thf(863,axiom,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ (comm_s4663373288045622133er_nat @ A @ B) @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4856_pochhammer__Suc)). 87.71/26.55 thf(5301,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)],[863])). 87.71/26.55 thf(579,axiom,((! [A:assn,B:assn]: (((sup_sup_assn @ A @ B) = bot_bot_assn) = ((A = bot_bot_assn) & (B = bot_bot_assn))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5064_sup__eq__bot__iff)). 87.71/26.55 thf(4198,plain,((! [A:assn,B:assn]: (((sup_sup_assn @ A @ B) = bot_bot_assn) = ((A = bot_bot_assn) & (B = bot_bot_assn))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[579])). 87.71/26.55 thf(98,axiom,((! [A:nat]: ((divide_divide_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9011_div2__Suc__Suc)). 87.71/26.55 thf(2173,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)],[98])). 87.71/26.55 thf(1074,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((((C @ A) <= (! [D:nat]: ((((C @ D) <= (C @ (suc @ D))) <= (ord_less_nat @ D @ B)) <= (ord_less_eq_nat @ A @ D)))) <= (C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_inc__induct)). 87.71/26.55 thf(6102,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((C @ A) | ~ (! [D:nat]: ((C @ D) | ~ (C @ (suc @ D)) | ~ (ord_less_nat @ D @ B) | ~ (ord_less_eq_nat @ A @ D))) | ~ (C @ B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074])). 87.71/26.55 thf(501,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: ((((C @ F) | (A @ F)) = ((B @ F) | (D @ F))) <= (ord_less_nat @ E @ F))) <= (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ E @ F)))) <= (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) <= (ord_less_nat @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1983_pinf_I2_J)). 87.71/26.55 thf(3878,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (? [E:nat]: ! [F:nat]: ((((C @ F) | (A @ F)) = ((B @ F) | (D @ F))) | ~ (ord_less_nat @ E @ F)) | ~ (? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ E @ F))) | ~ (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) | ~ (ord_less_nat @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[501])). 87.71/26.55 thf(459,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (semiri1316708129612266289at_nat @ B) @ C)) = (ord_less_eq_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7768_of__nat__power__le__of__nat__cancel__iff)). 87.71/26.55 thf(3688,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)],[459])). 87.71/26.55 thf(1412,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2907_diff__commute)). 87.71/26.55 thf(7390,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)],[1412])). 87.71/26.55 thf(1469,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ A @ (times_times_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ B @ (modulo_modulo_nat @ (divide_divide_nat @ A @ B) @ C)) @ (modulo_modulo_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8737_mod__mult2__eq)). 87.71/26.55 thf(7605,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)],[1469])). 87.71/26.55 thf(378,axiom,((! [A:list_nat,B:nat]: ((size_size_list_nat @ (append_nat @ A @ (cons_nat @ B @ nil_nat))) = (suc @ (size_size_list_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8435_length__append__singleton)). 87.71/26.55 thf(3370,plain,((! [A:list_nat,B:nat]: ((size_size_list_nat @ (append_nat @ A @ (cons_nat @ B @ nil_nat))) = (suc @ (size_size_list_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[378])). 87.71/26.55 thf(1545,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3106_Nat_Odiff__add__assoc)). 87.71/26.55 thf(7944,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)],[1545])). 87.71/26.55 thf(848,axiom,((! [A:nat,B:nat]: (((((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))) <= (ord_less_eq_nat @ B @ zero_zero_nat)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2369_add__nonpos__eq__0__iff)). 87.71/26.55 thf(5252,plain,((! [A:nat,B:nat]: ((((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))) | ~ (ord_less_eq_nat @ B @ zero_zero_nat) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[848])). 87.71/26.55 thf(1332,axiom,((! [A:nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2405_less__add__one)). 87.71/26.55 thf(7064,plain,((! [A:nat]: (ord_less_nat @ A @ (plus_plus_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332])). 87.71/26.55 thf(523,axiom,((! [A:($o > assn)]: ((groups12625163056032370o_assn @ A @ bot_bot_set_o) = one_one_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3786_prod_Oempty_H)). 87.71/26.55 thf(3994,plain,((! [A:($o > assn)]: ((groups12625163056032370o_assn @ (A) @ bot_bot_set_o) = one_one_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[523])). 87.71/26.55 thf(1479,axiom,((! [A:option_num]: ((A != none_num) = (? [B:num]: (A = (some_num @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_not__None__eq)). 87.71/26.55 thf(7637,plain,((! [A:option_num]: ((~ (A = none_num)) = (? [B:num]: (A = (some_num @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1479])). 87.71/26.55 thf(4,axiom,((! [A:nat,B:nat,C:list_nat]: ((ord_less_nat @ A @ B) => ((nth_nat @ (take_nat @ B @ C) @ A) = (nth_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6300_nth__take)). 87.71/26.55 thf(1782,plain,((! [A:nat,B:nat,C:list_nat]: ((ord_less_nat @ A @ B) => ((nth_nat @ (take_nat @ B @ C) @ A) = (nth_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])). 87.71/26.55 thf(1711,axiom,(((size_s170228958280169651at_nat @ none_P5556105721700978146at_nat) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_option_Osize_I3_J)). 87.71/26.55 thf(8539,plain,(((size_s170228958280169651at_nat @ none_P5556105721700978146at_nat) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1711])). 87.71/26.55 thf(352,axiom,((! [A:heap_Time_Heap_o,B:heap_Time_Heap_o]: ((if_Heap_Time_Heap_o @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Heap____Time____Monad__OHeap_I_Eo_J_T)). 87.71/26.55 thf(3249,plain,((! [A:heap_Time_Heap_o,B:heap_Time_Heap_o]: ((if_Heap_Time_Heap_o @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[352])). 87.71/26.55 thf(623,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2314_add__lessD1)). 87.71/26.55 thf(4371,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[623])). 87.71/26.55 thf(1279,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_zero__less__iff__neq__zero)). 87.71/26.55 thf(6872,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279])). 87.71/26.55 thf(413,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_p_r_e_d @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ (bit1 @ one))))))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9179_pred__bound__height)). 87.71/26.55 thf(3513,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_p_r_e_d @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit1 @ (bit1 @ one))))))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[413])). 87.71/26.55 thf(1502,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2147_less__add__same__cancel2)). 87.71/26.55 thf(7734,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)],[1502])). 87.71/26.55 thf(1595,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ (suc @ (suc @ A))))) = (! [C:nat]: ((B @ (suc @ C)) <= (ord_less_nat @ C @ (suc @ A))) & (B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_forall__finite_I3_J)). 87.71/26.55 thf(8133,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ (suc @ (suc @ A))))) = (! [C:nat]: ((B @ (suc @ C)) | ~ (ord_less_nat @ C @ (suc @ A))) & (B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1595])). 87.71/26.55 thf(909,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3177_nat__less__add__iff2)). 87.71/26.55 thf(5476,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)],[909])). 87.71/26.55 thf(1027,axiom,((! [A:nat]: ? [B:list_int]: ((size_size_list_int @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2550_Ex__list__of__length)). 87.71/26.55 thf(5921,plain,((! [A:nat]: ? [B:list_int]: ((size_size_list_int @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027])). 87.71/26.55 thf(1374,axiom,((! [A:nat]: ((! [B:nat]: (A != (plus_plus_nat @ B @ B))) => (~ (! [B:nat]: (A != (plus_plus_nat @ B @ (suc @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2042_even__odd__cases)). 87.71/26.55 thf(7240,plain,((! [A:nat]: ((! [B:nat]: ~ (A = (plus_plus_nat @ B @ B))) => (~ (! [B:nat]: ~ (A = (plus_plus_nat @ B @ (suc @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374])). 87.71/26.55 thf(53,axiom,((! [A:vEBT_VEBTi]: (time_TBOUND_o @ (vEBT_VEBT_minNulli @ A) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2023_TBOUND__minNulli)). 87.71/26.55 thf(1935,plain,((! [A:vEBT_VEBTi]: (time_TBOUND_o @ (vEBT_VEBT_minNulli @ A) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[53])). 87.71/26.55 thf(1633,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1824_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I5_J)). 87.71/26.55 thf(8256,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1633])). 87.71/26.55 thf(1022,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1206_linorder__le__cases)). 87.71/26.55 thf(5903,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)],[1022])). 87.71/26.55 thf(1606,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/sandbox2/benchmark/theBenchmark.p',fact_693_vebt__succ_Osimps_I5_J)). 87.71/26.55 thf(8165,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)],[1606])). 87.71/26.55 thf(1525,axiom,((! [A:(nat > $o)]: ((bit_wf_set_bits_int @ A) => ((! [B:nat]: ~ (! [C:nat]: ((~ (A @ C)) <= (ord_less_eq_nat @ B @ C)))) => (~ (! [B:nat]: ~ (! [C:nat]: ((ord_less_eq_nat @ B @ C) => (A @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10174_wf__set__bits__int_Ocases)). 87.71/26.55 thf(7856,plain,((! [A:(nat > $o)]: ((bit_wf_set_bits_int @ (A)) => ((! [B:nat]: ~ (! [C:nat]: (~ (A @ C) | ~ (ord_less_eq_nat @ B @ C)))) => (~ (! [B:nat]: ~ (! [C:nat]: ((ord_less_eq_nat @ B @ C) => (A @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1525])). 87.71/26.55 thf(530,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/sandbox2/benchmark/theBenchmark.p',fact_8734_nat__mod__eq__lemma)). 87.71/26.55 thf(4030,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)],[530])). 87.71/26.55 thf(778,axiom,(((^ [A:assn]: (A)) = (times_times_assn @ one_one_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1058_lambda__one)). 87.71/26.55 thf(4963,plain,(((^ [A:assn]: (A)) = (times_times_assn @ one_one_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[778])). 87.71/26.55 thf(1168,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_le__0__eq)). 87.71/26.55 thf(6483,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168])). 87.71/26.55 thf(1356,axiom,((! [A:assn,B:assn,C:heap_Time_Heap_nat,D:(nat > assn)]: ((entails @ A @ B) => ((hoare_3067605981109127869le_nat @ B @ C @ D) => (hoare_3067605981109127869le_nat @ A @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4073_cons__pre__rule)). 87.71/26.55 thf(7178,plain,((! [A:assn,B:assn,C:heap_Time_Heap_nat,D:(nat > assn)]: ((entails @ A @ B) => ((hoare_3067605981109127869le_nat @ B @ C @ (D)) => (hoare_3067605981109127869le_nat @ A @ C @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356])). 87.71/26.55 thf(649,axiom,((! [A:(list_int > $o),B:list_int]: ((! [C:list_int]: ((! [D:list_int]: ((ord_less_nat @ (size_size_list_int @ D) @ (size_size_list_int @ C)) => (A @ D))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2562_length__induct)). 87.71/26.55 thf(4467,plain,((! [A:(list_int > $o),B:list_int]: ((! [C:list_int]: ((! [D:list_int]: ((ord_less_nat @ (size_size_list_int @ D) @ (size_size_list_int @ C)) => (A @ D))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[649])). 87.71/26.55 thf(1624,axiom,((! [A:($o > nat)]: ((groups8507830703676809646_o_nat @ A @ bot_bot_set_o) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8123_sum_Oempty)). 87.71/26.55 thf(8224,plain,((! [A:($o > nat)]: ((groups8507830703676809646_o_nat @ (A) @ bot_bot_set_o) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1624])). 87.71/26.55 thf(1464,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_Suc__lessD)). 87.71/26.55 thf(7592,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1464])). 87.71/26.55 thf(1557,axiom,((! [A:nat,B:list_int]: ((size_s533118279054570080st_int @ (n_lists_int @ A @ B)) = (power_power_nat @ (size_size_list_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7984_length__n__lists)). 87.71/26.55 thf(7993,plain,((! [A:nat,B:list_int]: ((size_s533118279054570080st_int @ (n_lists_int @ A @ B)) = (power_power_nat @ (size_size_list_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1557])). 87.71/26.55 thf(791,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1669_linorder__le__less__linear)). 87.71/26.55 thf(5024,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[791])). 87.71/26.55 thf(701,axiom,((! [A:num,B:num]: (((some_num @ A) = (some_num @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_option_Oinject)). 87.71/26.55 thf(4637,plain,((! [A:num,B:num]: (((some_num @ A) = (some_num @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[701])). 87.71/26.55 thf(675,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/sandbox2/benchmark/theBenchmark.p',fact_2229_add__mono)). 87.71/26.55 thf(4539,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)],[675])). 87.71/26.55 thf(1508,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ one_one_nat) => (ord_less_eq_nat @ (power_power_nat @ A @ (suc @ B)) @ A)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7975_power__Suc__le__self)). 87.71/26.55 thf(7790,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ one_one_nat) => (ord_less_eq_nat @ (power_power_nat @ A @ (suc @ B)) @ A)) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1508])). 87.71/26.55 thf(1474,axiom,((! [A:assn,B:assn]: ((entails @ A @ B) => ((entails @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4052_ent__iffI)). 87.71/26.55 thf(7620,plain,((! [A:assn,B:assn]: ((entails @ A @ B) => ((entails @ B @ A) => (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1474])). 87.71/26.55 thf(857,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 @ C @ one_one_nat) => (ord_less_eq_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7991_power__decreasing)). 87.71/26.55 thf(5284,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 @ C @ one_one_nat) => (ord_less_eq_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[857])). 87.71/26.55 thf(1485,axiom,((! [A:vEBT_VEBT,B:nat]: (((vEBT_T_m_i_n_t @ A) = B) => (((~ ((B != one_one_nat) <= (? [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))))) <= ((B != one_one_nat) <= (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))))) <= (! [C:$o]: ((? [D:$o]: (A = (vEBT_Leaf @ C @ D))) => (B != (plus_plus_nat @ one_one_nat @ (if_nat @ C @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2516_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Oelims)). 87.71/26.55 thf(7652,plain,((! [A:vEBT_VEBT,B:nat]: (((vEBT_T_m_i_n_t @ A) = B) => (~ (~ (B = one_one_nat) | ~ (? [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))) | ~ (~ (B = one_one_nat) | ~ (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) | ~ (! [C:$o]: ((? [D:$o]: (A = (vEBT_Leaf @ C @ D))) => (~ (B = (plus_plus_nat @ one_one_nat @ (if_nat @ C @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1485])). 87.71/26.55 thf(480,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_nat__le__linear)). 87.71/26.55 thf(3776,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)],[480])). 87.71/26.55 thf(826,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (A = C))) <= ((power_power_nat @ A @ (suc @ B)) = (power_power_nat @ C @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7914_power__inject__base)). 87.71/26.55 thf(5160,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (A = C))) | ~ ((power_power_nat @ A @ (suc @ B)) = (power_power_nat @ C @ (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[826])). 87.71/26.55 thf(904,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1463_leI)). 87.71/26.55 thf(5461,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[904])). 87.71/26.55 thf(1285,axiom,((! [A:heap_T8145700208782473153_VEBTi,B:(vEBT_VEBTi > assn)]: (hoare_1429296392585015714_VEBTi @ bot_bot_assn @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_974_false__rule)). 87.71/26.55 thf(6892,plain,((! [A:heap_T8145700208782473153_VEBTi,B:(vEBT_VEBTi > assn)]: (hoare_1429296392585015714_VEBTi @ bot_bot_assn @ A @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285])). 87.71/26.55 thf(195,axiom,((! [A:$o,B:list_o]: ((size_size_list_o @ (cons_o @ A @ B)) = (suc @ (size_size_list_o @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4796_length__Cons)). 87.71/26.55 thf(2603,plain,((! [A:$o,B:list_o]: ((size_size_list_o @ (cons_o @ A @ B)) = (suc @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[195])). 87.71/26.55 thf(272,axiom,((! [A:nat,B:list_int]: ((nil_int = (drop_int @ A @ B)) = (ord_less_eq_nat @ (size_size_list_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8275_drop__eq__Nil2)). 87.71/26.55 thf(2916,plain,((! [A:nat,B:list_int]: ((nil_int = (drop_int @ A @ B)) = (ord_less_eq_nat @ (size_size_list_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[272])). 87.71/26.55 thf(1386,axiom,((power_power_assn = (^ [A:assn,B:nat]: (if_assn @ (B = zero_zero_nat) @ one_one_assn @ (times_times_assn @ A @ (power_power_assn @ A @ (minus_minus_nat @ B @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8042_power__eq__if)). 87.71/26.55 thf(7277,plain,(((power_power_assn) = (^ [A:assn,B:nat]: (if_assn @ (B = zero_zero_nat) @ one_one_assn @ (times_times_assn @ A @ (power_power_assn @ A @ (minus_minus_nat @ B @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386])). 87.71/26.55 thf(1699,axiom,(((nat_triangle @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4045_triangle__0)). 87.71/26.55 thf(8500,plain,(((nat_triangle @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1699])). 87.71/26.55 thf(619,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_delete @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = (vEBT_Leaf @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2575_vebt__delete_Osimps_I3_J)). 87.71/26.55 thf(4348,plain,((! [A:$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)],[619])). 87.71/26.55 thf(1387,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3058_le__add__diff)). 87.71/26.55 thf(7279,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387])). 87.71/26.55 thf(1540,axiom,((! [A:assn,B:assn,C:assn]: ((inf_inf_assn @ A @ (inf_inf_assn @ B @ C)) = (inf_inf_assn @ B @ (inf_inf_assn @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8936_assn__aci_I3_J)). 87.71/26.55 thf(7914,plain,((! [A:assn,B:assn,C:assn]: ((inf_inf_assn @ A @ (inf_inf_assn @ B @ C)) = (inf_inf_assn @ B @ (inf_inf_assn @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1540])). 87.71/26.55 thf(750,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/sandbox2/benchmark/theBenchmark.p',fact_2349_add__decreasing2)). 87.71/26.55 thf(4866,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)],[750])). 87.71/26.55 thf(1188,axiom,((! [A:int,B:int,C:list_int,D:nat]: ((((nth_int @ (cons_int @ A @ C) @ D) = B) = (((nth_int @ C @ (minus_minus_nat @ D @ one_one_nat)) = B) & (ord_less_nat @ zero_zero_nat @ D))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4770_nth__non__equal__first__eq)). 87.71/26.55 thf(6552,plain,((! [A:int,B:int,C:list_int,D:nat]: ((((nth_int @ (cons_int @ A @ C) @ D) = B) = (((nth_int @ C @ (minus_minus_nat @ D @ one_one_nat)) = B) & (ord_less_nat @ zero_zero_nat @ D))) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188])). 87.71/26.55 thf(7,axiom,((! [A:product_prod_nat_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ B @ C @ D)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1764_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I5_J)). 87.71/26.55 thf(1792,plain,((! [A:product_prod_nat_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ B @ C @ D)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])). 87.71/26.55 thf(1381,axiom,((! [A:vEBT_VEBT]: (((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) => (~ (! [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:$o,C:$o]: (A != (vEBT_Leaf @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_834_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Ocases)). 87.71/26.55 thf(7262,plain,((! [A:vEBT_VEBT]: (((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F))))) | ~ (! [B:$o,C:$o]: ~ (A = (vEBT_Leaf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381])). 87.71/26.55 thf(683,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2444_add__strict__increasing2)). 87.71/26.55 thf(4563,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)],[683])). 87.71/26.55 thf(1057,axiom,((! [A:option_nat]: ((! [B:nat]: (A != (some_nat @ B))) = (A = none_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_not__Some__eq)). 87.71/26.55 thf(6034,plain,((! [A:option_nat]: ((! [B:nat]: ~ (A = (some_nat @ B))) = (A = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057])). 87.71/26.55 thf(1517,axiom,((! [A:assn]: ((sup_sup_assn @ A @ bot_bot_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5122_norm__assertion__simps_I6_J)). 87.71/26.55 thf(7825,plain,((! [A:assn]: ((sup_sup_assn @ A @ bot_bot_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1517])). 87.71/26.55 thf(1491,axiom,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((A = B) <= (dvd_dvd_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9449_dvd__antisym)). 87.71/26.55 thf(7696,plain,((! [A:nat,B:nat]: ((dvd_dvd_nat @ A @ B) => ((A = B) | ~ (dvd_dvd_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1491])). 87.71/26.55 thf(776,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/sandbox2/benchmark/theBenchmark.p',fact_248_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono)). 87.71/26.55 thf(4956,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)],[776])). 87.71/26.55 thf(1421,axiom,((! [A:assn]: ((sup_sup_assn @ A @ bot_bot_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5097_sup__bot_Oright__neutral)). 87.71/26.55 thf(7418,plain,((! [A:assn]: ((sup_sup_assn @ A @ bot_bot_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1421])). 87.71/26.55 thf(1016,axiom,((! [A:nat,B:list_real]: ((foldl_nat_real @ (^ [C:nat,D:real]: (suc @ C)) @ A @ B) = (plus_plus_nat @ A @ (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4746_foldl__length__aux)). 87.71/26.55 thf(5883,plain,((! [A:nat,B:list_real]: ((foldl_nat_real @ (^ [C:nat,D:real]: (suc @ C)) @ A @ B) = (plus_plus_nat @ A @ (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016])). 87.71/26.55 thf(434,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ B @ A) => (B = A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1138_dual__order_Oantisym)). 87.71/26.55 thf(3574,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)],[434])). 87.71/26.55 thf(1775,axiom,((! [A:assn,B:nat]: ((power_power_assn @ A @ (suc @ B)) = (times_times_assn @ (power_power_assn @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7881_power__Suc2)). 87.71/26.55 thf(8806,plain,((! [A:assn,B:nat]: ((power_power_assn @ A @ (suc @ B)) = (times_times_assn @ (power_power_assn @ A @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1775])). 87.71/26.55 thf(305,axiom,((! [A:nat,B:(nat > (nat > $o))]: ((~ (! [C:list_nat]: ((~ (! [D:nat]: ((B @ (nth_nat @ C @ D) @ D) <= (ord_less_nat @ D @ A)))) <= ((size_size_list_nat @ C) = A)))) <= (! [C:nat]: ((? [D:nat]: (B @ D @ C)) <= (ord_less_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2668_obtain__list__from__elements)). 87.71/26.55 thf(3061,plain,((! [A:nat,B:(nat > (nat > $o))]: (~ (! [C:list_nat]: (~ (! [D:nat]: ((B @ (nth_nat @ C @ D) @ D) | ~ (ord_less_nat @ D @ A))) | ~ ((size_size_list_nat @ C) = A))) | ~ (! [C:nat]: (? [D:nat]: (B @ D @ C) | ~ (ord_less_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[305])). 87.71/26.55 thf(1152,axiom,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ (comm_s4663373288045622133er_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4861_pochhammer__rec_H)). 87.71/26.55 thf(6423,plain,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ (comm_s4663373288045622133er_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152])). 87.71/26.55 thf(214,axiom,((! [A:list_nat]: ((ord_less_nat @ zero_zero_nat @ (size_size_list_nat @ A)) = (A != nil_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8252_length__greater__0__conv)). 87.71/26.55 thf(2708,plain,((! [A:list_nat]: ((ord_less_nat @ zero_zero_nat @ (size_size_list_nat @ A)) = (~ (A = nil_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[214])). 87.71/26.55 thf(493,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ A) => (((~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((B = (some_nat @ D)) => (~ (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))))) <= (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => ((B = none_nat) => (~ (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))))))) <= (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((((((C) => (B = (some_nat @ zero_zero_nat))) & ((~ (C)) => (B = none_nat))) <= (~ (D))) & ((D) => (B = (some_nat @ one_one_nat)))) => (~ (accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ (vEBT_Leaf @ C @ D)))))))) <= ((vEBT_vebt_maxt @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1892_vebt__maxt_Opelims)). 87.71/26.55 thf(3821,plain,((! [A:vEBT_VEBT,B:option_nat]: (((accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ A) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((B = (some_nat @ D)) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))) | ~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => ((B = none_nat) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))) | ~ (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((((((C) => (B = (some_nat @ zero_zero_nat))) & ((~ (C)) => (B = none_nat))) | (D)) & ((D) => (B = (some_nat @ one_one_nat)))) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_maxt_rel) @ (vEBT_Leaf @ C @ D)))))))) | ~ ((vEBT_vebt_maxt @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[493])). 87.71/26.55 thf(705,axiom,((! [A:$o]: (((pure_assn @ A) = bot_bot_assn) = (~ (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_976_pure__assn__eq__false__iff)). 87.71/26.55 thf(4654,plain,((! [A:$o]: (((pure_assn @ A) = bot_bot_assn) = (~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[705])). 87.71/26.55 thf(30,axiom,((! [A:vEBT_VEBT]: (ord_less_eq_nat @ (vEBT_T_m_i_n_t @ A) @ (numeral_numeral_nat @ (bit1 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9170_mint__bound)). 87.71/26.55 thf(1860,plain,((! [A:vEBT_VEBT]: (ord_less_eq_nat @ (vEBT_T_m_i_n_t @ A) @ (numeral_numeral_nat @ (bit1 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[30])). 87.71/26.55 thf(615,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/sandbox2/benchmark/theBenchmark.p',fact_7867_left__right__inverse__power)). 87.71/26.55 thf(4334,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)],[615])). 87.71/26.55 thf(321,axiom,((! [A:list_int]: (((drop_int @ (minus_minus_nat @ (size_size_list_int @ A) @ (suc @ zero_zero_nat)) @ A) = (cons_int @ (last_int @ A) @ nil_int)) <= (A != nil_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8067_drop__last__conv)). 87.71/26.55 thf(3125,plain,((! [A:list_int]: (((drop_int @ (minus_minus_nat @ (size_size_list_int @ A) @ (suc @ zero_zero_nat)) @ A) = (cons_int @ (last_int @ A) @ nil_int)) | (A = nil_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[321])). 87.71/26.55 thf(823,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((~ (ord_less_nat @ C @ A)) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1968_pinf_I5_J)). 87.71/26.55 thf(5150,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (ord_less_nat @ C @ A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[823])). 87.71/26.55 thf(1225,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t2 @ A @ C) @ one_one_nat) <= (~ (? [D:nat]: (vEBT_V8194947554948674370ptions @ A @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2741_insersimp_H)). 87.71/26.55 thf(6676,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t2 @ A @ C) @ one_one_nat) | ? [D:nat]: (vEBT_V8194947554948674370ptions @ A @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225])). 87.71/26.55 thf(1119,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2325_add__leD1)). 87.71/26.55 thf(6315,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119])). 87.71/26.55 thf(596,axiom,((! [A:vEBT_VEBT,B:nat]: ((~ (vEBT_vebt_member @ A @ B)) <= (vEBT_VEBT_minNull @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2043_min__Null__member)). 87.71/26.55 thf(4275,plain,((! [A:vEBT_VEBT,B:nat]: (~ (vEBT_vebt_member @ A @ B) | ~ (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[596])). 87.71/26.55 thf(475,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/sandbox2/benchmark/theBenchmark.p',fact_3149_nat__le__add__iff1)). 87.71/26.55 thf(3749,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)],[475])). 87.71/26.55 thf(185,axiom,((! [A:(int > nat),B:nat]: ((groups8487721886752058969nt_nat @ A @ B @ nil_int) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8195_horner__sum__simps_I1_J)). 87.71/26.55 thf(2562,plain,((! [A:(int > nat),B:nat]: ((groups8487721886752058969nt_nat @ (A) @ B @ nil_int) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[185])). 87.71/26.55 thf(68,axiom,((! [A:nat,B:nat,C:(nat > $o),D:nat]: (((C @ (nth_nat @ (replicate_nat @ B @ D) @ A)) <= (C @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3235_intind)). 87.71/26.55 thf(1992,plain,((! [A:nat,B:nat,C:(nat > $o),D:nat]: ((C @ (nth_nat @ (replicate_nat @ B @ D) @ A)) | ~ (C @ D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[68])). 87.71/26.55 thf(1313,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))) => ((! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ zero_zero_nat) @ C @ D) @ E))) => ((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ B)) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_872_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Ocases)). 87.71/26.55 thf(7000,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))) => ((! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ zero_zero_nat) @ C @ D) @ E))) => ((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ B)) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313])). 87.71/26.55 thf(685,axiom,((! [A:$o,B:$o]: ((((((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = none_nat) <= (~ (B))) & ((B) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ zero_zero_nat)))) <= (~ (A))) & ((A) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1452_vebt__maxt_Osimps_I1_J)). 87.71/26.55 thf(4568,plain,((! [A:$o,B:$o]: ((((((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = none_nat) | (B)) & ((B) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ zero_zero_nat)))) | (A)) & ((A) => ((vEBT_vebt_maxt @ (vEBT_Leaf @ B @ A)) = (some_nat @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[685])). 87.71/26.55 thf(732,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((power_power_nat @ A @ B) != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7806_semiring__1__no__zero__divisors__class_Opower__not__zero)). 87.71/26.55 thf(4766,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)],[732])). 87.71/26.55 thf(1099,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/sandbox2/benchmark/theBenchmark.p',fact_3150_nat__eq__add__iff2)). 87.71/26.55 thf(6208,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)],[1099])). 87.71/26.55 thf(494,axiom,((! [A:(nat > nat),B:nat]: ((size_option_nat @ A @ (some_nat @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2488_option_Osize__gen_I2_J)). 87.71/26.55 thf(3855,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)],[494])). 87.71/26.55 thf(1591,axiom,((! [A:nat]: ((bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10007_bit__Suc__0__iff)). 87.71/26.55 thf(8121,plain,((! [A:nat]: ((bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1591])). 87.71/26.55 thf(1638,axiom,((! [A:$o,B:heap_T2636463487746394924on_nat,C:(option_nat > assn)]: (((hoare_7629718768684598413on_nat @ one_one_assn @ B @ C) <= (A)) => (hoare_7629718768684598413on_nat @ (pure_assn @ A) @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1742_norm__pre__pure__rule2)). 87.71/26.55 thf(8278,plain,((! [A:$o,B:heap_T2636463487746394924on_nat,C:(option_nat > assn)]: (((hoare_7629718768684598413on_nat @ one_one_assn @ B @ (C)) | ~ (A)) => (hoare_7629718768684598413on_nat @ (pure_assn @ A) @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1638])). 87.71/26.55 thf(1174,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2819_Suc__diff__diff)). 87.71/26.55 thf(6502,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ (suc @ A) @ B) @ (suc @ C)) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174])). 87.71/26.55 thf(576,axiom,((! [A:nat,B:list_nat]: ((size_size_list_nat @ (cons_nat @ A @ B)) = (plus_plus_nat @ (size_size_list_nat @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4752_list_Osize_I4_J)). 87.71/26.55 thf(4179,plain,((! [A:nat,B:list_nat]: ((size_size_list_nat @ (cons_nat @ A @ B)) = (plus_plus_nat @ (size_size_list_nat @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[576])). 87.71/26.55 thf(1196,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ (minus_minus_nat @ A @ B) @ B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8720_mod__geq)). 87.71/26.55 thf(6579,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ (minus_minus_nat @ A @ B) @ B)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196])). 87.71/26.55 thf(910,axiom,((! [A:$o,B:$o]: ((vEBT_T_s_u_c_c @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = (plus_plus_nat @ one_one_nat @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2483_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I1_J)). 87.71/26.55 thf(5480,plain,((! [A:$o,B:$o]: ((vEBT_T_s_u_c_c @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = (plus_plus_nat @ one_one_nat @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[910])). 87.71/26.55 thf(402,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((ord_less_eq_nat @ (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ A @ C @ D) @ E) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit0 @ one))))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9131_tdeletemimi)). 87.71/26.55 thf(3470,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((ord_less_eq_nat @ (vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ A @ C @ D) @ E) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit0 @ one))))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[402])). 87.71/26.55 thf(449,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1153_Orderings_Oorder__eq__iff)). 87.71/26.55 thf(3657,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)],[449])). 87.71/26.55 thf(981,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2182_ab__semigroup__add__class_Oadd_Ocommute)). 87.71/26.55 thf(5746,plain,(((plus_plus_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[981])). 87.71/26.55 thf(287,axiom,((! [A:list_nat,B:nat]: (((size_size_list_nat @ A) = (suc @ B)) = (? [C:list_nat,D:nat]: ((A = (append_nat @ C @ (cons_nat @ D @ nil_nat))) & ((size_size_list_nat @ C) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8427_length__Suc__rev__conv)). 87.71/26.55 thf(2989,plain,((! [A:list_nat,B:nat]: (((size_size_list_nat @ A) = (suc @ B)) = (? [C:list_nat,D:nat]: ((A = (append_nat @ C @ (cons_nat @ D @ nil_nat))) & ((size_size_list_nat @ C) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[287])). 87.71/26.55 thf(1696,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ D @ C) => (A @ D))) => (A @ (suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_nat__compl__induct_H)). 87.71/26.55 thf(8483,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((! [D:nat]: ((ord_less_eq_nat @ D @ C) => (A @ D))) => (A @ (suc @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1696])). 87.71/26.55 thf(666,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (times_times_nat @ B @ C)) = (times_times_nat @ B @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_ab__semigroup__mult__class_Omult_Oleft__commute)). 87.71/26.55 thf(4514,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)],[666])). 87.71/26.55 thf(485,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_mult_Oassoc)). 87.71/26.55 thf(3788,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)],[485])). 87.71/26.55 thf(50,axiom,((! [A:nat,B:list_nat,C:list_nat]: ((ord_less_eq_nat @ A @ (size_size_list_nat @ B)) => ((ord_less_eq_nat @ A @ (size_size_list_nat @ C)) => ((! [D:nat]: (((nth_nat @ B @ D) = (nth_nat @ C @ D)) <= (ord_less_nat @ D @ A))) => ((take_nat @ A @ B) = (take_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6600_nth__take__lemma)). 87.71/26.55 thf(1922,plain,((! [A:nat,B:list_nat,C:list_nat]: ((ord_less_eq_nat @ A @ (size_size_list_nat @ B)) => ((ord_less_eq_nat @ A @ (size_size_list_nat @ C)) => ((! [D:nat]: (((nth_nat @ B @ D) = (nth_nat @ C @ D)) | ~ (ord_less_nat @ D @ A))) => ((take_nat @ A @ B) = (take_nat @ A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[50])). 87.71/26.55 thf(1526,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ (minus_minus_nat @ B @ C))) = ((ord_less_nat @ A @ C) & (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3356_diff__diff__less)). 87.71/26.55 thf(7862,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ (minus_minus_nat @ B @ C))) = ((ord_less_nat @ A @ C) & (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1526])). 87.71/26.55 thf(41,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10044_or__nat__numerals_I2_J)). 87.71/26.55 thf(1892,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)],[41])). 87.71/26.55 thf(849,axiom,((! [A:nat,B:nat]: ((B != zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_gr__implies__not0)). 87.71/26.55 thf(5256,plain,((! [A:nat,B:nat]: (~ (B = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[849])). 87.71/26.55 thf(252,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (bit_se2925701944663578781it_nat @ A @ C) @ (bit_se2925701944663578781it_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9882_take__bit__tightened__less__eq__nat)). 87.71/26.55 thf(2857,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)],[252])). 87.71/26.55 thf(1011,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ B) => (((~ (ord_less_nat @ (plus_plus_nat @ A @ C) @ B)) => ((modulo_modulo_nat @ (plus_plus_nat @ A @ C) @ B) = (minus_minus_nat @ (plus_plus_nat @ A @ C) @ B))) & ((ord_less_nat @ (plus_plus_nat @ A @ C) @ B) => ((modulo_modulo_nat @ (plus_plus_nat @ A @ C) @ B) = (plus_plus_nat @ A @ C))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8733_mod__nat__add)). 87.71/26.55 thf(5866,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ B) => (((~ (ord_less_nat @ (plus_plus_nat @ A @ C) @ B)) => ((modulo_modulo_nat @ (plus_plus_nat @ A @ C) @ B) = (minus_minus_nat @ (plus_plus_nat @ A @ C) @ B))) & ((ord_less_nat @ (plus_plus_nat @ A @ C) @ B) => ((modulo_modulo_nat @ (plus_plus_nat @ A @ C) @ B) = (plus_plus_nat @ A @ C))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011])). 87.71/26.55 thf(1672,axiom,((! [A:product_prod_nat_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (vEBT_VEBT_minNull @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2428_VEBT__internal_OminNull_Osimps_I5_J)). 87.71/26.55 thf(8389,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)],[1672])). 87.71/26.55 thf(1162,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => ((! [D:nat]: (A @ D @ zero_zero_nat)) => ((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ D @ (plus_plus_nat @ D @ E)) <= (A @ D @ E)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2639_Euclid__induct)). 87.71/26.55 thf(6455,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((! [D:nat,E:nat]: ((A @ D @ E) = (A @ E @ D))) => ((! [D:nat]: (A @ D @ zero_zero_nat)) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ D @ (plus_plus_nat @ D @ E)) | ~ (A @ D @ E)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162])). 87.71/26.55 thf(1288,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2168_group__cancel_Oadd2)). 87.71/26.55 thf(6905,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ D @ A) = (plus_plus_nat @ B @ (plus_plus_nat @ D @ C))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288])). 87.71/26.55 thf(1348,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1755_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I3_J)). 87.71/26.55 thf(7124,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348])). 87.71/26.55 thf(1364,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBTi,C:nat]: (hoare_1429296392585015714_VEBTi @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_V3964819847710782039nserti @ A @ B @ C) @ (vEBT_vebt_assn_raw @ (vEBT_vebt_insert @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2524_vebt__inserti_H__rf__abstr)). 87.71/26.55 thf(7209,plain,((! [A:vEBT_VEBT,B:vEBT_VEBTi,C:nat]: (hoare_1429296392585015714_VEBTi @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_V3964819847710782039nserti @ A @ B @ C) @ (vEBT_vebt_assn_raw @ (vEBT_vebt_insert @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364])). 87.71/26.55 thf(1513,axiom,((! [A:$o]: (bit_wf_set_bits_int @ (^ [B:nat]: (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10178_wf__set__bits__int__const)). 87.71/26.55 thf(7803,plain,((! [A:$o]: (bit_wf_set_bits_int @ (^ [B:nat]: (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1513])). 87.71/26.55 thf(1083,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_le0)). 87.71/26.55 thf(6149,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083])). 87.71/26.55 thf(767,axiom,((! [A:(int > nat),B:int,C:list_int]: ((size_list_int @ A @ (cons_int @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (A @ B) @ (size_list_int @ A @ C)) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4765_list_Osize__gen_I2_J)). 87.71/26.55 thf(4928,plain,((! [A:(int > nat),B:int,C:list_int]: ((size_list_int @ (A) @ (cons_int @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (A @ B) @ (size_list_int @ (A) @ C)) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[767])). 87.71/26.55 thf(885,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (((ord_less_eq_nat @ zero_zero_nat @ A) & (ord_less_eq_nat @ B @ zero_zero_nat)) | ((ord_less_eq_nat @ zero_zero_nat @ B) & (ord_less_eq_nat @ A @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_split__mult__neg__le)). 87.71/26.55 thf(5397,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (((ord_less_eq_nat @ zero_zero_nat @ A) & (ord_less_eq_nat @ B @ zero_zero_nat)) | ((ord_less_eq_nat @ zero_zero_nat @ B) & (ord_less_eq_nat @ A @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[885])). 87.71/26.55 thf(945,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/sandbox2/benchmark/theBenchmark.p',fact_821_vebt__succ_Osimps_I3_J)). 87.71/26.55 thf(5622,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)],[945])). 87.71/26.55 thf(1251,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((~ (ord_less_nat @ A @ C)) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1933_minf_I7_J)). 87.71/26.55 thf(6781,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (ord_less_nat @ A @ C) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251])). 87.71/26.55 thf(1665,axiom,((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ na)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__C5_C)). 87.71/26.55 thf(8367,plain,((vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ na)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1665])). 87.71/26.55 thf(1326,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_eq_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_Suc__le__lessD)). 87.71/26.55 thf(7047,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)],[1326])). 87.71/26.55 thf(622,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8631_div__less)). 87.71/26.55 thf(4368,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[622])). 87.71/26.55 thf(1670,axiom,((! [A:(nat > $o)]: ((bit_wf_set_bits_int @ (^ [B:nat]: (A @ (suc @ B)))) = (bit_wf_set_bits_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10172_wf__set__bits__int__Suc)). 87.71/26.55 thf(8384,plain,((! [A:(nat > $o)]: ((bit_wf_set_bits_int @ (^ [B:nat]: (A @ (suc @ B)))) = (bit_wf_set_bits_int @ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1670])). 87.71/26.55 thf(177,axiom,((! [A:nat,B:num]: ((ord_less_eq_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (ord_less_eq_nat @ A @ (pred_numeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9916_le__Suc__numeral)). 87.71/26.55 thf(2520,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)],[177])). 87.71/26.55 thf(1745,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_nat_Oinject)). 87.71/26.55 thf(8703,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1745])). 87.71/26.55 thf(465,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ C) @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3011_less__imp__diff__less)). 87.71/26.55 thf(3708,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ C) @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[465])). 87.71/26.55 thf(125,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) <= (A @ C))) => ((! [C:nat]: ((A @ C) => (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) => (A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9050_nat__bit__induct)). 87.71/26.55 thf(2301,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((! [C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) | ~ (A @ C))) => ((! [C:nat]: ((A @ C) => (A @ (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))))) => (A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[125])). 87.71/26.55 thf(15,axiom,((! [A:num]: ((bit1 @ A) != one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9129_semiring__norm_I86_J)). 87.71/26.55 thf(1815,plain,((! [A:num]: ~ ((bit1 @ A) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[15])). 87.71/26.55 thf(647,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_neq0__conv)). 87.71/26.55 thf(4460,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[647])). 87.71/26.55 thf(1568,axiom,((! [A:list_nat,B:list_nat]: ((A != B) <= ((size_size_list_nat @ A) != (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2553_neq__if__length__neq)). 87.71/26.55 thf(8037,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)],[1568])). 87.71/26.55 thf(36,axiom,((! [A:heap_Time_Heap_o,B:nat,C:nat]: ((time_TBOUND_o @ A @ B) => ((time_TBOUND_o @ A @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1862_TBOUND__mono)). 87.71/26.55 thf(1875,plain,((! [A:heap_Time_Heap_o,B:nat,C:nat]: ((time_TBOUND_o @ A @ B) => ((time_TBOUND_o @ A @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[36])). 87.71/26.55 thf(1757,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ zero_zero_nat) @ C @ D) @ E) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1725_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I6_J)). 87.71/26.55 thf(8738,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ zero_zero_nat) @ C @ D) @ E) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1757])). 87.71/26.55 thf(790,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat))) => ((((((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))))) <= (! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E)))) <= (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E)))) <= (! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ (suc @ D)))))) <= (! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ zero_zero_nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_870_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Ocases)). 87.71/26.55 thf(5020,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat))) => (((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))))) | ~ (! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E))) | ~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))) | ~ (! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ (suc @ D))))) | ~ (! [B:$o,C:$o]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ zero_zero_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[790])). 87.71/26.55 thf(436,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2329_add__le__mono1)). 87.71/26.55 thf(3602,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)],[436])). 87.71/26.55 thf(1138,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7943_power__less__imp__less__exp)). 87.71/26.55 thf(6382,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138])). 87.71/26.55 thf(355,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_mult_Oassoc)). 87.71/26.55 thf(3258,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)],[355])). 87.71/26.55 thf(959,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ bot_bot_nat) = (A = bot_bot_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1686_bot_Oextremum__unique)). 87.71/26.55 thf(5663,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ bot_bot_nat) = (A = bot_bot_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[959])). 87.71/26.55 thf(1105,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((A = B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ A @ E) @ C) @ (plus_plus_nat @ (times_times_nat @ B @ E) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2424_mlex__snd__decrI)). 87.71/26.55 thf(6227,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((A = B) => ((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ A @ E) @ C) @ (plus_plus_nat @ (times_times_nat @ B @ E) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105])). 87.71/26.55 thf(156,axiom,((! [A:nat,B:list_real]: ((ord_less_nat @ A @ (size_size_list_real @ B)) => (B != nil_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8526_len__greater__imp__nonempty)). 87.71/26.55 thf(2451,plain,((! [A:nat,B:list_real]: ((ord_less_nat @ A @ (size_size_list_real @ B)) => (~ (B = nil_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[156])). 87.71/26.55 thf(1182,axiom,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:assn]: ((hoare_hoare_triple_o @ (times_times_assn @ D @ A) @ B @ (^ [E:$o]: (times_times_assn @ D @ (C @ E)))) <= (hoare_hoare_triple_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_frame__rule__left)). 87.71/26.55 thf(6534,plain,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:assn]: ((hoare_hoare_triple_o @ (times_times_assn @ D @ A) @ B @ (^ [E:$o]: (times_times_assn @ D @ (C @ E)))) | ~ (hoare_hoare_triple_o @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182])). 87.71/26.55 thf(373,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8861_fact__mono__nat)). 87.71/26.55 thf(3357,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)],[373])). 87.71/26.55 thf(819,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2117_add__le__same__cancel2)). 87.71/26.55 thf(5135,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)],[819])). 87.71/26.55 thf(557,axiom,((! [A:nat,B:nat,C:nat]: ((divide_divide_nat @ A @ (times_times_nat @ B @ C)) = (divide_divide_nat @ (divide_divide_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8640_div__mult2__eq)). 87.71/26.55 thf(4115,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)],[557])). 87.71/26.55 thf(235,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9480_odd__pos)). 87.71/26.55 thf(2777,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)],[235])). 87.71/26.55 thf(1677,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)) = ((A = E) & (B = F) & (C = G) & (D = H))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_VEBT_Oinject_I1_J)). 87.71/26.55 thf(8411,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)) = ((A = E) & (B = F) & (C = G) & (D = H))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1677])). 87.71/26.55 thf(100,axiom,((times_times_int = (^ [A:int,B:int]: (times_times_int @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_ab__semigroup__mult__class_Omult_Ocommute)). 87.71/26.55 thf(2178,plain,(((times_times_int) = (^ [A:int,B:int]: (times_times_int @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[100])). 87.71/26.55 thf(966,axiom,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((((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) & (dvd_dvd_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9464_bezout1__nat)). 87.71/26.55 thf(5682,plain,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((((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) & (dvd_dvd_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[966])). 87.71/26.55 thf(991,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (((modulo_modulo_nat @ A @ C) = zero_zero_nat) => ((ord_less_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) <= ((modulo_modulo_nat @ B @ C) = zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8732_div__less__mono)). 87.71/26.55 thf(5787,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (((modulo_modulo_nat @ A @ C) = zero_zero_nat) => ((ord_less_nat @ (divide_divide_nat @ A @ C) @ (divide_divide_nat @ B @ C)) | ~ ((modulo_modulo_nat @ B @ C) = zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[991])). 87.71/26.55 thf(1038,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1316_order__less__asym)). 87.71/26.55 thf(5957,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038])). 87.71/26.55 thf(581,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4635_of__nat__0__le__iff)). 87.71/26.55 thf(4205,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ (semiri1316708129612266289at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[581])). 87.71/26.55 thf(115,axiom,((! [A:complex,B:nat,C:nat]: ((power_power_complex @ A @ (plus_plus_nat @ B @ C)) = (times_times_complex @ (power_power_complex @ A @ B) @ (power_power_complex @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7894_power__add)). 87.71/26.55 thf(2237,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)],[115])). 87.71/26.55 thf(1438,axiom,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4528_of__nat__eq__0__iff)). 87.71/26.55 thf(7492,plain,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1438])). 87.71/26.55 thf(1350,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]: (((B @ A @ C) <= (C = (some_P7363390416028606310at_nat @ E))) <= (A = (some_nat @ D)))) => (B @ A @ C)) <= ((C = none_P5556105721700978146at_nat) => (B @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_combine__options__cases)). 87.71/26.55 thf(7144,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]: ((B @ A @ C) | ~ (C = (some_P7363390416028606310at_nat @ E)) | ~ (A = (some_nat @ D)))) => (B @ A @ C)) | ~ ((C = none_P5556105721700978146at_nat) => (B @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350])). 87.71/26.55 thf(613,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_divisors__zero)). 87.71/26.55 thf(4329,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)],[613])). 87.71/26.55 thf(514,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/sandbox2/benchmark/theBenchmark.p',fact_8639_div__le__mono)). 87.71/26.55 thf(3966,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)],[514])). 87.71/26.55 thf(129,axiom,((! [A:nat]: (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9028_n__less__equal__power__2)). 87.71/26.55 thf(2324,plain,((! [A:nat]: (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[129])). 87.71/26.55 thf(1566,axiom,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9467_nat__mult__dvd__cancel1)). 87.71/26.55 thf(8029,plain,((! [A:nat,B:nat,C:nat]: (((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1566])). 87.71/26.55 thf(687,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (A = B) | (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1391_linorder__less__linear)). 87.71/26.55 thf(4583,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)],[687])). 87.71/26.55 thf(760,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((times_times_nat @ (binomial @ C @ B) @ (binomial @ B @ A)) = (times_times_nat @ (binomial @ C @ A) @ (binomial @ (minus_minus_nat @ C @ A) @ (minus_minus_nat @ B @ A))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8884_choose__mult)). 87.71/26.55 thf(4903,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => ((times_times_nat @ (binomial @ C @ B) @ (binomial @ B @ A)) = (times_times_nat @ (binomial @ C @ A) @ (binomial @ (minus_minus_nat @ C @ A) @ (minus_minus_nat @ B @ A))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[760])). 87.71/26.55 thf(806,axiom,((! [A:$o,B:$o]: ((vEBT_T_p_r_e_d @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (plus_plus_nat @ one_one_nat @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2490_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I2_J)). 87.71/26.55 thf(5084,plain,((! [A:$o,B:$o]: ((vEBT_T_p_r_e_d @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (plus_plus_nat @ one_one_nat @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[806])). 87.71/26.55 thf(1455,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4649_of__nat__less__imp__less)). 87.71/26.55 thf(7564,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) | ~ (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1455])). 87.71/26.55 thf(544,axiom,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:($o > assn)]: ((hoare_hoare_triple_o @ A @ B @ C) => ((hoare_hoare_triple_o @ A @ B @ D) <= (! [E:$o]: (entails @ (C @ E) @ (D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4066_cons__post__rule)). 87.71/26.55 thf(4072,plain,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:($o > assn)]: ((hoare_hoare_triple_o @ A @ B @ (C)) => ((hoare_hoare_triple_o @ A @ B @ (D)) | ~ (! [E:$o]: (entails @ (C @ E) @ (D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[544])). 87.71/26.55 thf(1391,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1331_order__less__trans)). 87.71/26.55 thf(7290,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391])). 87.71/26.55 thf(1355,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ (suc @ B)) = (A = B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_not__less__less__Suc__eq)). 87.71/26.55 thf(7175,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)],[1355])). 87.71/26.55 thf(788,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3059_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2)). 87.71/26.55 thf(5013,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)],[788])). 87.71/26.55 thf(46,axiom,((set_fo2584398358068434914at_nat = (^ [A:(nat > (nat > nat)),B:nat,C:nat,D:nat]: (if_nat @ (ord_less_nat @ C @ B) @ D @ (set_fo2584398358068434914at_nat @ A @ (plus_plus_nat @ B @ one_one_nat) @ C @ (A @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2738_fold__atLeastAtMost__nat_Osimps)). 87.71/26.55 thf(1911,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)],[46])). 87.71/26.55 thf(365,axiom,((! [A:nat,B:(int > (nat > $o))]: ((~ (! [C:list_int]: ((~ (! [D:nat]: ((B @ (nth_int @ C @ D) @ D) <= (ord_less_nat @ D @ A)))) <= ((size_size_list_int @ C) = A)))) <= (! [C:nat]: ((? [D:int]: (B @ D @ C)) <= (ord_less_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2669_obtain__list__from__elements)). 87.71/26.55 thf(3295,plain,((! [A:nat,B:(int > (nat > $o))]: (~ (! [C:list_int]: (~ (! [D:nat]: ((B @ (nth_int @ C @ D) @ D) | ~ (ord_less_nat @ D @ A))) | ~ ((size_size_list_int @ C) = A))) | ~ (! [C:nat]: (? [D:int]: (B @ D @ C) | ~ (ord_less_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[365])). 87.71/26.55 thf(237,axiom,((! [A:list_nat]: ((map_nat_nat @ (^ [B:nat]: (B)) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2906_list_Omap__ident)). 87.71/26.55 thf(2782,plain,((! [A:list_nat]: ((map_nat_nat @ (^ [B:nat]: (B)) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[237])). 87.71/26.55 thf(1376,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ (times_times_nat @ B @ A) @ B) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1215_mult__left__le)). 87.71/26.55 thf(7247,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376])). 87.71/26.55 thf(1219,axiom,((! [A:nat,B:nat,C:(nat > $o)]: (((! [D:nat]: ((~ (C @ D)) <= ((ord_less_eq_nat @ A @ D) & (ord_less_nat @ D @ B)))) => ((filter_nat @ C @ (upt @ zero_zero_nat @ A)) = (filter_nat @ C @ (upt @ zero_zero_nat @ B)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8867_upt__filter__extend)). 87.71/26.55 thf(6657,plain,((! [A:nat,B:nat,C:(nat > $o)]: (((! [D:nat]: (~ (C @ D) | ~ ((ord_less_eq_nat @ A @ D) & (ord_less_nat @ D @ B)))) => ((filter_nat @ (C) @ (upt @ zero_zero_nat @ A)) = (filter_nat @ (C) @ (upt @ zero_zero_nat @ B)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219])). 87.71/26.55 thf(453,axiom,((! [A:assn,B:assn,C:assn,D:assn]: ((entails @ A @ B) => ((entails @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ D)) <= (entails @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4059_ent__star__mono)). 87.71/26.55 thf(3670,plain,((! [A:assn,B:assn,C:assn,D:assn]: ((entails @ A @ B) => ((entails @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ D)) | ~ (entails @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[453])). 87.71/26.55 thf(723,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (suc @ (minus_minus_nat @ B @ A)) @ C) = (minus_minus_nat @ (suc @ B) @ (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2872_diff__Suc__diff__eq2)). 87.71/26.55 thf(4733,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (suc @ (minus_minus_nat @ B @ A)) @ C) = (minus_minus_nat @ (suc @ B) @ (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[723])). 87.71/26.55 thf(872,axiom,((! [A:nat,B:nat]: ((((binomial @ A @ B) = (plus_plus_nat @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ (minus_minus_nat @ B @ one_one_nat)) @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ B))) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8892_choose__reduce__nat)). 87.71/26.55 thf(5333,plain,((! [A:nat,B:nat]: (((binomial @ A @ B) = (plus_plus_nat @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ (minus_minus_nat @ B @ one_one_nat)) @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ B))) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[872])). 87.71/26.55 thf(1008,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) = ((B = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7709_nat__zero__less__power__iff)). 87.71/26.55 thf(5856,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B)) = ((B = zero_zero_nat) | (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008])). 87.71/26.55 thf(403,axiom,((! [A:nat]: (((upt @ zero_zero_nat @ A) = nil_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8830_upt__0__eq__Nil__conv)). 87.71/26.55 thf(3473,plain,((! [A:nat]: (((upt @ zero_zero_nat @ A) = nil_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[403])). 87.71/26.55 thf(463,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (power_power_nat @ A @ (suc @ B)) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7979_power__Suc__less__one)). 87.71/26.55 thf(3702,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (power_power_nat @ A @ (suc @ B)) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[463])). 87.71/26.55 thf(1505,axiom,((! [A:(int > $o),B:list_int]: ((size_size_list_o @ (map_int_o @ A @ B)) = (size_size_list_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2833_length__map)). 87.71/26.55 thf(7775,plain,((! [A:(int > $o),B:list_int]: ((size_size_list_o @ (map_int_o @ (A) @ B)) = (size_size_list_int @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1505])). 87.71/26.55 thf(1769,axiom,((! [A:assn]: ((times_times_assn @ top_top_assn @ (times_times_assn @ top_top_assn @ A)) = (times_times_assn @ top_top_assn @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10159_merge__true__star__ctx)). 87.71/26.55 thf(8791,plain,((! [A:assn]: ((times_times_assn @ top_top_assn @ (times_times_assn @ top_top_assn @ A)) = (times_times_assn @ top_top_assn @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1769])). 87.71/26.55 thf(933,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/sandbox2/benchmark/theBenchmark.p',fact_2259_add__mono__thms__linordered__field_I1_J)). 87.71/26.55 thf(5558,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)],[933])). 87.71/26.55 thf(1034,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_eq_nat @ B @ C) <= (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_nat__mult__le__cancel__disj)). 87.71/26.55 thf(5946,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)],[1034])). 87.71/26.55 thf(395,axiom,((times_times_complex = (^ [A:complex,B:complex]: (times_times_complex @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_ab__semigroup__mult__class_Omult_Ocommute)). 87.71/26.55 thf(3438,plain,(((times_times_complex) = (^ [A:complex,B:complex]: (times_times_complex @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[395])). 87.71/26.55 thf(1544,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ D @ D)) => ((A @ B @ C) <= (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))) <= (! [D:nat,E:nat]: ((A @ D @ E) <= (ord_less_nat @ D @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1281_linorder__less__wlog)). 87.71/26.55 thf(7926,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat]: (A @ D @ D)) => ((A @ B @ C) | ~ (! [D:nat,E:nat]: ((A @ E @ D) => (A @ D @ E))))) | ~ (! [D:nat,E:nat]: ((A @ D @ E) | ~ (ord_less_nat @ D @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1544])). 87.71/26.55 thf(537,axiom,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:assn]: ((hoare_1429296392585015714_VEBTi @ A @ B @ C) => (hoare_1429296392585015714_VEBTi @ (times_times_assn @ A @ D) @ B @ (^ [E:vEBT_VEBTi]: (times_times_assn @ (C @ E) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_frame__rule)). 87.71/26.55 thf(4050,plain,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:assn]: ((hoare_1429296392585015714_VEBTi @ A @ B @ (C)) => (hoare_1429296392585015714_VEBTi @ (times_times_assn @ A @ D) @ B @ (^ [E:vEBT_VEBTi]: (times_times_assn @ (C @ E) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[537])). 87.71/26.55 thf(734,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat)))) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2365_add__nonneg__eq__0__iff)). 87.71/26.55 thf(4815,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat)))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[734])). 87.71/26.55 thf(1090,axiom,((! [A:assn]: ((times_times_assn @ A @ bot_bot_assn) = bot_bot_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_970_star__false__right)). 87.71/26.55 thf(6176,plain,((! [A:assn]: ((times_times_assn @ A @ bot_bot_assn) = bot_bot_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090])). 87.71/26.55 thf(1574,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_less__or__eq__imp__le)). 87.71/26.55 thf(8065,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)],[1574])). 87.71/26.55 thf(19,axiom,((! [A:nat,B:num]: ((modulo_modulo_nat @ (suc @ (suc @ (suc @ A))) @ (numeral_numeral_nat @ B)) = (modulo_modulo_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9162_Suc__mod__eq__add3__mod__numeral)). 87.71/26.55 thf(1828,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)],[19])). 87.71/26.55 thf(440,axiom,((! [A:($o > option4927543243414619207at_nat)]: ((restri2754309951621987225at_nat @ A @ bot_bot_set_o) = (^ [B:$o]: (none_P5556105721700978146at_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5795_restrict__map__to__empty)). 87.71/26.55 thf(3621,plain,((! [A:($o > option4927543243414619207at_nat)]: ((restri2754309951621987225at_nat @ A @ bot_bot_set_o) = (^ [B:$o]: (none_P5556105721700978146at_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[440])). 87.71/26.55 thf(1301,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1124_order__trans)). 87.71/26.55 thf(6964,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301])). 87.71/26.55 thf(997,axiom,((! [A:nat]: ? [B:list_o]: ((size_size_list_o @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2548_Ex__list__of__length)). 87.71/26.55 thf(5804,plain,((! [A:nat]: ? [B:list_o]: ((size_size_list_o @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[997])). 87.71/26.55 thf(825,axiom,((! [A:list_nat,B:list_o,C:(nat > ($o > assn))]: (((vEBT_L7887682484454631235_nat_o @ C @ A @ B) = bot_bot_assn) <= ((size_size_list_nat @ A) != (size_size_list_o @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3206_list__assn__aux__ineq__len)). 87.71/26.55 thf(5156,plain,((! [A:list_nat,B:list_o,C:(nat > ($o > assn))]: (((vEBT_L7887682484454631235_nat_o @ (C) @ A @ B) = bot_bot_assn) | ((size_size_list_nat @ A) = (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[825])). 87.71/26.55 thf(1707,axiom,((! [A:nat,B:nat]: ((A = B) <= ((suc @ A) = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_Suc__inject)). 87.71/26.55 thf(8526,plain,((! [A:nat,B:nat]: ((A = B) | ~ ((suc @ A) = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1707])). 87.71/26.55 thf(432,axiom,((suc = (^ [A:nat]: (plus_plus_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2421_Suc__eq__plus1)). 87.71/26.55 thf(3569,plain,(((suc) = (^ [A:nat]: (plus_plus_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[432])). 87.71/26.55 thf(1190,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ (divide_divide_nat @ B @ A) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8658_dividend__less__div__times)). 87.71/26.55 thf(6559,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ B @ (plus_plus_nat @ A @ (times_times_nat @ (divide_divide_nat @ B @ A) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190])). 87.71/26.55 thf(681,axiom,((! [A:assn,B:$o]: ((inf_inf_assn @ A @ (pure_assn @ B)) = (times_times_assn @ (inf_inf_assn @ one_one_assn @ A) @ (pure_assn @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8910_and__extract__pure__right__iff)). 87.71/26.55 thf(4556,plain,((! [A:assn,B:$o]: ((inf_inf_assn @ A @ (pure_assn @ B)) = (times_times_assn @ (inf_inf_assn @ one_one_assn @ A) @ (pure_assn @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[681])). 87.71/26.55 thf(79,axiom,((! [A:heap_T8145700208782473153_VEBTi,B:heap_T8145700208782473153_VEBTi]: ((if_Hea8453224502484754311_VEBTi @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__VEBT____BuildupMemImp__OVEBTi_J_T)). 87.71/26.55 thf(2073,plain,((! [A:heap_T8145700208782473153_VEBTi,B:heap_T8145700208782473153_VEBTi]: ((if_Hea8453224502484754311_VEBTi @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[79])). 87.71/26.55 thf(571,axiom,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:assn,E:assn]: ((hoare_hoare_triple_o @ A @ B @ C) => ((hoare_hoare_triple_o @ D @ B @ (^ [F:$o]: (times_times_assn @ (C @ F) @ E))) <= (entails @ D @ (times_times_assn @ A @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4075_fi__rule)). 87.71/26.55 thf(4162,plain,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:assn,E:assn]: ((hoare_hoare_triple_o @ A @ B @ (C)) => ((hoare_hoare_triple_o @ D @ B @ (^ [F:$o]: (times_times_assn @ (C @ F) @ E))) | ~ (entails @ D @ (times_times_assn @ A @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[571])). 87.71/26.55 thf(1535,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2357_add__nonneg__nonneg)). 87.71/26.55 thf(7899,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1535])). 87.71/26.55 thf(1191,axiom,((! [A:list_o,B:list_int,C:($o > (int > assn))]: (((size_size_list_o @ A) != (size_size_list_int @ B)) => ((vEBT_L4782520652837395649_o_int @ C @ A @ B) = bot_bot_assn)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3204_list__assn__aux__ineq__len)). 87.71/26.55 thf(6562,plain,((! [A:list_o,B:list_int,C:($o > (int > assn))]: ((~ ((size_size_list_o @ A) = (size_size_list_int @ B))) => ((vEBT_L4782520652837395649_o_int @ (C) @ A @ B) = bot_bot_assn)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191])). 87.71/26.55 thf(901,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_eq__imp__le)). 87.71/26.55 thf(5448,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[901])). 87.71/26.55 thf(1242,axiom,((! [A:nat,B:list_nat]: (((suc @ A) = (size_size_list_nat @ B)) = (? [C:nat,D:list_nat]: ((B = (cons_nat @ C @ D)) & ((size_size_list_nat @ D) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4669_Suc__length__conv)). 87.71/26.55 thf(6755,plain,((! [A:nat,B:list_nat]: (((suc @ A) = (size_size_list_nat @ B)) = (? [C:nat,D:list_nat]: ((B = (cons_nat @ C @ D)) & ((size_size_list_nat @ D) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242])). 87.71/26.55 thf(828,axiom,((! [A:list_real,B:list_nat,C:(real > (nat > assn))]: (((vEBT_L1446010312343316929al_nat @ C @ A @ B) = bot_bot_assn) <= ((size_size_list_real @ A) != (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3199_list__assn__aux__ineq__len)). 87.71/26.55 thf(5169,plain,((! [A:list_real,B:list_nat,C:(real > (nat > assn))]: (((vEBT_L1446010312343316929al_nat @ (C) @ A @ B) = bot_bot_assn) | ((size_size_list_real @ A) = (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[828])). 87.71/26.55 thf(911,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ B) => (~ (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2013_minf_I8_J)). 87.71/26.55 thf(5489,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)],[911])). 87.71/26.55 thf(346,axiom,((! [A:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (suc @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9008_add__2__eq__Suc)). 87.71/26.55 thf(3226,plain,((! [A:nat]: ((plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) = (suc @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[346])). 87.71/26.55 thf(1685,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1786_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J)). 87.71/26.55 thf(8443,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1685])). 87.71/26.55 thf(1205,axiom,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4027_triangle__Suc)). 87.71/26.55 thf(6616,plain,((! [A:nat]: ((nat_triangle @ (suc @ A)) = (plus_plus_nat @ (nat_triangle @ A) @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205])). 87.71/26.55 thf(1403,axiom,((! [A:nat]: ((one_one_nat = (semiri1316708129612266289at_nat @ A)) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4558_of__nat__1__eq__iff)). 87.71/26.55 thf(7354,plain,((! [A:nat]: ((one_one_nat = (semiri1316708129612266289at_nat @ A)) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403])). 87.71/26.55 thf(384,axiom,((! [A:assn,B:assn]: ((if_assn @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Assertions__Oassn_T)). 87.71/26.55 thf(3389,plain,((! [A:assn,B:assn]: ((if_assn @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[384])). 87.71/26.55 thf(1494,axiom,((! [A:assn]: ((inf_inf_assn @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8938_norm__assertion__simps_I31_J)). 87.71/26.55 thf(7707,plain,((! [A:assn]: ((inf_inf_assn @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1494])). 87.71/26.55 thf(24,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: (((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t @ A @ C) @ (numeral_numeral_nat @ (bit1 @ one))) <= (vEBT_VEBT_minNull @ A)) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9397_insertsimp)). 87.71/26.55 thf(1843,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t @ A @ C) @ (numeral_numeral_nat @ (bit1 @ one))) | ~ (vEBT_VEBT_minNull @ A) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[24])). 87.71/26.55 thf(1200,axiom,((! [A:$o,B:$o]: ((sup_sup_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((A) | (B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5084_merge__pure__or)). 87.71/26.55 thf(6591,plain,((! [A:$o,B:$o]: ((sup_sup_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((A) | (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200])). 87.71/26.55 thf(719,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9391_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I2_J)). 87.71/26.55 thf(4718,plain,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[719])). 87.71/26.55 thf(1683,axiom,((! [A:nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ A) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7707_power__Suc__0)). 87.71/26.55 thf(8438,plain,((! [A:nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ A) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1683])). 87.71/26.55 thf(152,axiom,((! [A:nat,B:nat,C:nat]: ((comm_s4663373288045622133er_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (comm_s4663373288045622133er_nat @ A @ B) @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4866_pochhammer__product_H)). 87.71/26.55 thf(2437,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)],[152])). 87.71/26.55 thf(51,axiom,((! [A:num,B:num]: ((bit1 @ A) != (bit0 @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9127_semiring__norm_I89_J)). 87.71/26.55 thf(1928,plain,((! [A:num,B:num]: ~ ((bit1 @ A) = (bit0 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[51])). 87.71/26.55 thf(1161,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3018_le__diff__iff_H)). 87.71/26.55 thf(6451,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ B @ C)) = (ord_less_eq_nat @ C @ A)) | ~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161])). 87.71/26.55 thf(1560,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) => ((ord_less_nat @ B @ C) <= (ord_less_eq_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_mult__left__less__imp__less)). 87.71/26.55 thf(8001,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) => ((ord_less_nat @ B @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1560])). 87.71/26.55 thf(531,axiom,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1008_less__one)). 87.71/26.55 thf(4033,plain,((! [A:nat]: ((ord_less_nat @ A @ one_one_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[531])). 87.71/26.55 thf(473,axiom,((! [A:$o,B:heap_Time_Heap_nat,C:(nat > assn)]: (((hoare_3067605981109127869le_nat @ one_one_assn @ B @ C) <= (A)) => (hoare_3067605981109127869le_nat @ (pure_assn @ A) @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1745_norm__pre__pure__rule2)). 87.71/26.55 thf(3739,plain,((! [A:$o,B:heap_Time_Heap_nat,C:(nat > assn)]: (((hoare_3067605981109127869le_nat @ one_one_assn @ B @ (C)) | ~ (A)) => (hoare_3067605981109127869le_nat @ (pure_assn @ A) @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[473])). 87.71/26.55 thf(808,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1099_order__class_Oorder__eq__iff)). 87.71/26.55 thf(5096,plain,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[808])). 87.71/26.55 thf(104,axiom,((! [A:list_nat,B:nat]: (((size_size_list_nat @ A) = (suc @ B)) = (? [C:nat,D:list_nat]: (((size_size_list_nat @ D) = B) & (A = (append_nat @ D @ (cons_nat @ C @ nil_nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8431_length__Suc__conv__rev)). 87.71/26.55 thf(2190,plain,((! [A:list_nat,B:nat]: (((size_size_list_nat @ A) = (suc @ B)) = (? [C:nat,D:list_nat]: (((size_size_list_nat @ D) = B) & (A = (append_nat @ D @ (cons_nat @ C @ nil_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[104])). 87.71/26.55 thf(881,axiom,((! [A:$o,B:$o]: ((vEBT_T_p_r_e_d @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1817_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I1_J)). 87.71/26.55 thf(5375,plain,((! [A:$o,B:$o]: ((vEBT_T_p_r_e_d @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[881])). 87.71/26.55 thf(882,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (suc @ B)) = (minus_minus_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3098_diff__Suc__eq__diff__pred)). 87.71/26.55 thf(5384,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)],[882])). 87.71/26.55 thf(810,axiom,((! [A:assn]: ((sup_sup_assn @ bot_bot_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5074_sup__bot_Oleft__neutral)). 87.71/26.55 thf(5101,plain,((! [A:assn]: ((sup_sup_assn @ bot_bot_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[810])). 87.71/26.55 thf(1314,axiom,((! [A:nat,B:nat]: ((binomial @ (suc @ A) @ (suc @ B)) = (plus_plus_nat @ (binomial @ A @ B) @ (binomial @ A @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8872_binomial__Suc__Suc)). 87.71/26.55 thf(7004,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)],[1314])). 87.71/26.55 thf(458,axiom,((! [A:nat,B:list_nat]: ((ord_less_eq_nat @ (suc @ A) @ (size_size_list_nat @ B)) = (? [C:nat,D:list_nat]: ((B = (cons_nat @ C @ D)) & (ord_less_eq_nat @ A @ (size_size_list_nat @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4729_Suc__le__length__iff)). 87.71/26.55 thf(3685,plain,((! [A:nat,B:list_nat]: ((ord_less_eq_nat @ (suc @ A) @ (size_size_list_nat @ B)) = (? [C:nat,D:list_nat]: ((B = (cons_nat @ C @ D)) & (ord_less_eq_nat @ A @ (size_size_list_nat @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[458])). 87.71/26.55 thf(1647,axiom,((! [A:nat]: ((dvd_dvd_nat @ A @ (suc @ zero_zero_nat)) = (A = (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9439_dvd__1__iff__1)). 87.71/26.55 thf(8306,plain,((! [A:nat]: ((dvd_dvd_nat @ A @ (suc @ zero_zero_nat)) = (A = (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1647])). 87.71/26.55 thf(954,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3099_diff__add__0)). 87.71/26.55 thf(5648,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)],[954])). 87.71/26.55 thf(39,axiom,((! [A:num,B:num]: (((bit1 @ A) = (bit1 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9125_semiring__norm_I90_J)). 87.71/26.55 thf(1886,plain,((! [A:num,B:num]: (((bit1 @ A) = (bit1 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[39])). 87.71/26.55 thf(1676,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) <= (A = (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_nat_OdiscI)). 87.71/26.55 thf(8406,plain,((! [A:nat,B:nat]: (~ (A = zero_zero_nat) | ~ (A = (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1676])). 87.71/26.55 thf(1298,axiom,((! [A:nat,B:nat]: (((semiri1316708129612266289at_nat @ A) = (semiri1316708129612266289at_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4517_of__nat__eq__iff)). 87.71/26.55 thf(6947,plain,((! [A:nat,B:nat]: (((semiri1316708129612266289at_nat @ A) = (semiri1316708129612266289at_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298])). 87.71/26.55 thf(488,axiom,((! [A:list_VEBT_VEBT,B:vEBT_VEBT,C:nat]: ~ (vEBT_VEBT_membermima @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ A @ B) @ C))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_814_VEBT__internal_Omembermima_Osimps_I2_J)). 87.71/26.55 thf(3808,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)],[488])). 87.71/26.55 thf(178,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/sandbox2/benchmark/theBenchmark.p',fact_148_ab__semigroup__mult__class_Omult_Oleft__commute)). 87.71/26.55 thf(2523,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)],[178])). 87.71/26.55 thf(299,axiom,(((size_size_list_o @ nil_o) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8523_length__nth__simps_I1_J)). 87.71/26.55 thf(3036,plain,(((size_size_list_o @ nil_o) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[299])). 87.71/26.55 thf(621,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) <= (ord_less_nat @ D @ E))) => (ord_less_eq_nat @ (plus_plus_nat @ (A @ B) @ C) @ (A @ (plus_plus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2422_mono__nat__linear__lb)). 87.71/26.55 thf(4364,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat,E:nat]: ((ord_less_nat @ (A @ D) @ (A @ E)) | ~ (ord_less_nat @ D @ E))) => (ord_less_eq_nat @ (plus_plus_nat @ (A @ B) @ C) @ (A @ (plus_plus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[621])). 87.71/26.55 thf(1103,axiom,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:nat,E:assn,F:(vEBT_VEBTi > assn),G:nat]: ((((! [H:vEBT_VEBTi]: (entails @ (C @ H) @ (F @ H))) => ((ord_less_eq_nat @ D @ G) => (time_htt_VEBT_VEBTi @ E @ B @ F @ G))) <= (entails @ E @ A)) <= (time_htt_VEBT_VEBTi @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4079_htt__cons__rule)). 87.71/26.55 thf(6221,plain,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:nat,E:assn,F:(vEBT_VEBTi > assn),G:nat]: (((! [H:vEBT_VEBTi]: (entails @ (C @ H) @ (F @ H))) => ((ord_less_eq_nat @ D @ G) => (time_htt_VEBT_VEBTi @ E @ B @ (F) @ G))) | ~ (entails @ E @ A) | ~ (time_htt_VEBT_VEBTi @ A @ B @ (C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103])). 87.71/26.55 thf(861,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3065_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse)). 87.71/26.55 thf(5296,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[861])). 87.71/26.55 thf(327,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/sandbox2/benchmark/theBenchmark.p',fact_2596_valid__member__both__member__options)). 87.71/26.55 thf(3157,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)],[327])). 87.71/26.55 thf(1482,axiom,(((semiri1316708129612266289at_nat @ zero_zero_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4538_semiring__1__class_Oof__nat__0)). 87.71/26.55 thf(7645,plain,(((semiri1316708129612266289at_nat @ zero_zero_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1482])). 87.71/26.55 thf(875,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_800_vebt__pred_Osimps_I4_J)). 87.71/26.55 thf(5343,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)],[875])). 87.71/26.55 thf(846,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) => ((semiri1408675320244567234ct_nat @ (minus_minus_nat @ (suc @ B) @ A)) = (times_times_nat @ (minus_minus_nat @ (suc @ B) @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8865_fact__diff__Suc)). 87.71/26.55 thf(5246,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) => ((semiri1408675320244567234ct_nat @ (minus_minus_nat @ (suc @ B) @ A)) = (times_times_nat @ (minus_minus_nat @ (suc @ B) @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[846])). 87.71/26.55 thf(607,axiom,((! [A:$o,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ (pure_assn @ A) @ B @ C) = ((hoare_1429296392585015714_VEBTi @ one_one_assn @ B @ C) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1737_norm__pre__pure__iff__sng)). 87.71/26.55 thf(4307,plain,((! [A:$o,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ (pure_assn @ A) @ B @ (C)) = ((hoare_1429296392585015714_VEBTi @ one_one_assn @ B @ (C)) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[607])). 87.71/26.55 thf(1020,axiom,((! [A:nat,B:nat,C:nat]: (((modulo_modulo_nat @ A @ B) = (modulo_modulo_nat @ C @ B)) = (? [D:nat,E:nat]: ((plus_plus_nat @ A @ (times_times_nat @ B @ D)) = (plus_plus_nat @ C @ (times_times_nat @ B @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8724_nat__mod__eq__iff)). 87.71/26.55 thf(5897,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)],[1020])). 87.71/26.55 thf(1248,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/sandbox2/benchmark/theBenchmark.p',fact_2452_add__pos__nonneg)). 87.71/26.55 thf(6772,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)],[1248])). 87.71/26.55 thf(737,axiom,((! [A:nat]: ((ord_less_eq_nat @ one_one_nat @ A) = (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1085_nat__geq__1__eq__neqz)). 87.71/26.55 thf(4825,plain,((! [A:nat]: ((ord_less_eq_nat @ one_one_nat @ A) = (~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[737])). 87.71/26.55 thf(1276,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 @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_mult__mono_H)). 87.71/26.55 thf(6863,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 @ zero_zero_nat @ A) => ((ord_less_eq_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)],[1276])). 87.71/26.55 thf(1741,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2411_add__is__1)). 87.71/26.55 thf(8691,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = (suc @ zero_zero_nat)) = (((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))) | ((B = zero_zero_nat) & (A = (suc @ zero_zero_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1741])). 87.71/26.55 thf(477,axiom,((! [A:vEBT_VEBT]: (((! [B:$o]: (A != (vEBT_Leaf @ ($true) @ B))) => ((~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E)))) <= (! [B:$o]: (A != (vEBT_Leaf @ B @ ($true)))))) <= (~ (vEBT_VEBT_minNull @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2476_VEBT__internal_OminNull_Oelims_I3_J)). 87.71/26.55 thf(3756,plain,((! [A:vEBT_VEBT]: (((! [B:$o]: ~ (A = (vEBT_Leaf @ ($true) @ B))) => (~ (! [B:product_prod_nat_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ C @ D @ E))) | ~ (! [B:$o]: ~ (A = (vEBT_Leaf @ B @ ($true)))))) | (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[477])). 87.71/26.55 thf(1054,axiom,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2821_diff__self__eq__0)). 87.71/26.55 thf(6021,plain,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054])). 87.71/26.55 thf(242,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/sandbox2/benchmark/theBenchmark.p',fact_9481_dvd__power__iff__le)). 87.71/26.55 thf(2799,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)],[242])). 87.71/26.55 thf(204,axiom,((! [A:list_nat]: ((A != nil_nat) => (~ (! [B:nat,C:list_nat]: (A != (cons_nat @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8592_list__encode_Ocases)). 87.71/26.55 thf(2639,plain,((! [A:list_nat]: ((~ (A = nil_nat)) => (~ (! [B:nat,C:list_nat]: ~ (A = (cons_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[204])). 87.71/26.55 thf(626,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2238_add__right__mono)). 87.71/26.55 thf(4379,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)],[626])). 87.71/26.55 thf(428,axiom,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ A @ B @ C) => ((hoare_1429296392585015714_VEBTi @ A @ B @ D) <= (! [E:vEBT_VEBTi]: (entails @ (C @ E) @ (D @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4067_cons__post__rule)). 87.71/26.55 thf(3559,plain,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ A @ B @ (C)) => ((hoare_1429296392585015714_VEBTi @ A @ B @ (D)) | ~ (! [E:vEBT_VEBTi]: (entails @ (C @ E) @ (D @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[428])). 87.71/26.55 thf(343,axiom,((! [A:nat,B:nat]: ((replicate_nat @ (suc @ A) @ B) = (cons_nat @ B @ (replicate_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4696_replicate__Suc)). 87.71/26.55 thf(3211,plain,((! [A:nat,B:nat]: ((replicate_nat @ (suc @ A) @ B) = (cons_nat @ B @ (replicate_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[343])). 87.71/26.55 thf(144,axiom,((! [A:list_real,B:list_real,C:(list_real > (list_real > $o))]: (((C @ nil_real @ nil_real) => ((C @ A @ B) <= (! [D:real,E:list_real,F:real,G:list_real]: (((size_size_list_real @ E) = (size_size_list_real @ G)) => ((C @ E @ G) => (C @ (cons_real @ D @ E) @ (cons_real @ F @ G))))))) <= ((size_size_list_real @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8530_list__induct2)). 87.71/26.55 thf(2392,plain,((! [A:list_real,B:list_real,C:(list_real > (list_real > $o))]: (((C @ nil_real @ nil_real) => ((C @ A @ B) | ~ (! [D:real,E:list_real,F:real,G:list_real]: (((size_size_list_real @ E) = (size_size_list_real @ G)) => ((C @ E @ G) => (C @ (cons_real @ D @ E) @ (cons_real @ F @ G))))))) | ~ ((size_size_list_real @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[144])). 87.71/26.55 thf(1567,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:$o,F:$o]: ((vEBT_Node @ A @ B @ C @ D) != (vEBT_Leaf @ E @ F)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_VEBT_Odistinct_I1_J)). 87.71/26.55 thf(8033,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:$o,F:$o]: ~ ((vEBT_Node @ A @ B @ C @ D) = (vEBT_Leaf @ E @ F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1567])). 87.71/26.55 thf(217,axiom,((! [A:nat,B:list_nat]: ((((last_nat @ (take_nat @ A @ B)) = (nth_nat @ B @ (minus_minus_nat @ A @ one_one_nat))) <= (A != zero_zero_nat)) <= (ord_less_eq_nat @ A @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6670_last__take__nth__conv)). 87.71/26.55 thf(2718,plain,((! [A:nat,B:list_nat]: (((last_nat @ (take_nat @ A @ B)) = (nth_nat @ B @ (minus_minus_nat @ A @ one_one_nat))) | (A = zero_zero_nat) | ~ (ord_less_eq_nat @ A @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[217])). 87.71/26.55 thf(1275,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4545_of__nat__le__iff)). 87.71/26.55 thf(6860,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)],[1275])). 87.71/26.55 thf(651,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_965_order__refl)). 87.71/26.55 thf(4475,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[651])). 87.71/26.55 thf(262,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => ((last_nat @ (replicate_nat @ A @ B)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6692_last__replicate)). 87.71/26.55 thf(2884,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => ((last_nat @ (replicate_nat @ A @ B)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[262])). 87.71/26.55 thf(1529,axiom,((! [A:nat]: ((A != zero_zero_nat) = (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_bot__nat__0_Onot__eq__extremum)). 87.71/26.55 thf(7882,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1529])). 87.71/26.55 thf(1371,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2799_add__diff__cancel__right_H)). 87.71/26.55 thf(7230,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371])). 87.71/26.55 thf(347,axiom,((! [A:int,B:list_int,C:nat]: ((nth_int @ (cons_int @ A @ B) @ (suc @ C)) = (nth_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4566_nth__Cons__Suc)). 87.71/26.55 thf(3229,plain,((! [A:int,B:list_int,C:nat]: ((nth_int @ (cons_int @ A @ B) @ (suc @ C)) = (nth_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[347])). 87.71/26.55 thf(1445,axiom,((! [A:nat,B:nat]: ((size_size_list_nat @ (upt @ A @ B)) = (minus_minus_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8832_length__upt)). 87.71/26.55 thf(7533,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)],[1445])). 87.71/26.55 thf(1321,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_eq_nat @ B @ C) <= (ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8003_power__le__imp__le__exp)). 87.71/26.55 thf(7022,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)],[1321])). 87.71/26.55 thf(1578,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1825_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I4_J)). 87.71/26.55 thf(8078,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1578])). 87.71/26.55 thf(789,axiom,((! [A:option_num]: ((! [B:num]: (A != (some_num @ B))) = (A = none_num)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_not__Some__eq)). 87.71/26.55 thf(5017,plain,((! [A:option_num]: ((! [B:num]: ~ (A = (some_num @ B))) = (A = none_num)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[789])). 87.71/26.55 thf(1199,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ B) = (plus_plus_nat @ B @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2423_mult__Suc)). 87.71/26.55 thf(6588,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)],[1199])). 87.71/26.55 thf(1383,axiom,((times_times_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_ab__semigroup__mult__class_Omult_Ocommute)). 87.71/26.55 thf(7269,plain,(((times_times_nat) = (^ [A:nat,B:nat]: (times_times_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383])). 87.71/26.55 thf(1481,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Suc__le__D)). 87.71/26.55 thf(7642,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) => (? [C:nat]: (B = (suc @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1481])). 87.71/26.55 thf(1116,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1502_order_Oorder__iff__strict)). 87.71/26.55 thf(6307,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116])). 87.71/26.55 thf(1098,axiom,((! [A:nat,B:nat,C:list_nat]: (((A = zero_zero_nat) => ((nth_nat @ (cons_nat @ B @ C) @ A) = B)) & ((A != zero_zero_nat) => ((nth_nat @ (cons_nat @ B @ C) @ A) = (nth_nat @ C @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4756_nth__Cons_H)). 87.71/26.55 thf(6200,plain,((! [A:nat,B:nat,C:list_nat]: (((A = zero_zero_nat) => ((nth_nat @ (cons_nat @ B @ C) @ A) = B)) & ((~ (A = zero_zero_nat)) => ((nth_nat @ (cons_nat @ B @ C) @ A) = (nth_nat @ C @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098])). 87.71/26.55 thf(1706,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ (suc @ A)))) = ((B @ zero_zero_nat) & ! [C:nat]: ((B @ (suc @ C)) <= (ord_less_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_All__less__Suc2)). 87.71/26.55 thf(8523,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ (suc @ A)))) = ((B @ zero_zero_nat) & ! [C:nat]: ((B @ (suc @ C)) | ~ (ord_less_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1706])). 87.71/26.55 thf(394,axiom,((! [A:nat,B:list_nat,C:nat,D:list_nat]: (((drop_nat @ (suc @ A) @ B) = D) <= ((drop_nat @ A @ B) = (cons_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7833_drop__eq__ConsD)). 87.71/26.55 thf(3435,plain,((! [A:nat,B:list_nat,C:nat,D:list_nat]: (((drop_nat @ (suc @ A) @ B) = D) | ~ ((drop_nat @ A @ B) = (cons_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[394])). 87.71/26.55 thf(1548,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ (suc @ B) @ (suc @ A))) = (times_times_nat @ (suc @ B) @ (binomial @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8876_Suc__times__binomial)). 87.71/26.55 thf(7952,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)],[1548])). 87.71/26.55 thf(714,axiom,((! [A:option_num,B:num]: ((A != none_num) <= (A = (some_num @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_option_OdiscI)). 87.71/26.55 thf(4700,plain,((! [A:option_num,B:num]: (~ (A = none_num) | ~ (A = (some_num @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[714])). 87.71/26.55 thf(279,axiom,((! [A:nat,B:nat]: (((? [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)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9065_ex__power__ivl1)). 87.71/26.55 thf(2954,plain,((! [A:nat,B:nat]: (? [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) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[279])). 87.71/26.55 thf(1398,axiom,((! [A:nat,B:list_nat]: ((size_size_list_nat @ (cons_nat @ A @ B)) = (suc @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4797_length__Cons)). 87.71/26.55 thf(7321,plain,((! [A:nat,B:list_nat]: ((size_size_list_nat @ (cons_nat @ A @ B)) = (suc @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398])). 87.71/26.55 thf(1702,axiom,(((finite6454714172617411596l_num0 @ top_to3689904424835650196l_num0) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10201_card__num0)). 87.71/26.55 thf(8508,plain,(((finite6454714172617411596l_num0 @ top_to3689904424835650196l_num0) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1702])). 87.71/26.55 thf(72,axiom,((! [A:list_nat]: (((drop_nat @ (minus_minus_nat @ (size_size_list_nat @ A) @ (suc @ zero_zero_nat)) @ A) = (cons_nat @ (last_nat @ A) @ nil_nat)) <= (A != nil_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8066_drop__last__conv)). 87.71/26.55 thf(2011,plain,((! [A:list_nat]: (((drop_nat @ (minus_minus_nat @ (size_size_list_nat @ A) @ (suc @ zero_zero_nat)) @ A) = (cons_nat @ (last_nat @ A) @ nil_nat)) | (A = nil_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[72])). 87.71/26.55 thf(397,axiom,((! [A:nat,B:nat,C:int]: (((nth_int @ (replicate_int @ B @ C) @ A) = C) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3279_nth__replicate)). 87.71/26.55 thf(3450,plain,((! [A:nat,B:nat,C:int]: (((nth_int @ (replicate_int @ B @ C) @ A) = C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[397])). 87.71/26.55 thf(410,axiom,((! [A:num,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (ord_less_eq_nat @ (pred_numeral @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9917_le__numeral__Suc)). 87.71/26.55 thf(3503,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)],[410])). 87.71/26.55 thf(1013,axiom,((! [A:assn,B:assn,C:assn,D:assn]: ((entails @ A @ (times_times_assn @ B @ top_top_assn)) => ((entails @ C @ (times_times_assn @ D @ top_top_assn)) => (entails @ (times_times_assn @ (times_times_assn @ A @ C) @ top_top_assn) @ (times_times_assn @ (times_times_assn @ B @ D) @ top_top_assn)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10155_ent__star__mono__true)). 87.71/26.55 thf(5875,plain,((! [A:assn,B:assn,C:assn,D:assn]: ((entails @ A @ (times_times_assn @ B @ top_top_assn)) => ((entails @ C @ (times_times_assn @ D @ top_top_assn)) => (entails @ (times_times_assn @ (times_times_assn @ A @ C) @ top_top_assn) @ (times_times_assn @ (times_times_assn @ B @ D) @ top_top_assn)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013])). 87.71/26.55 thf(585,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ B @ (suc @ A))) = (times_times_nat @ B @ (binomial @ (minus_minus_nat @ B @ one_one_nat) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8887_binomial__absorption)). 87.71/26.55 thf(4216,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)],[585])). 87.71/26.55 thf(611,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ (suc @ A) @ B) @ (times_times_nat @ (suc @ A) @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_Suc__mult__le__cancel1)). 87.71/26.55 thf(4323,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)],[611])). 87.71/26.55 thf(1730,axiom,((! [A:$o,B:assn,C:heap_Time_Heap_o,D:($o > assn),E:nat]: ((time_htt_o @ (times_times_assn @ (pure_assn @ A) @ B) @ C @ D @ E) = ((time_htt_o @ B @ C @ D @ E) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1797_norm__pre__pure__iff__htt_H)). 87.71/26.55 thf(8655,plain,((! [A:$o,B:assn,C:heap_Time_Heap_o,D:($o > assn),E:nat]: ((time_htt_o @ (times_times_assn @ (pure_assn @ A) @ B) @ C @ (D) @ E) = ((time_htt_o @ B @ C @ (D) @ E) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1730])). 87.71/26.55 thf(366,axiom,((! [A:complex]: ((^ [B:complex]: (times_times_complex @ B @ A)) = (times_times_complex @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5690_mult__commute__abs)). 87.71/26.55 thf(3303,plain,((! [A:complex]: ((^ [B:complex]: (times_times_complex @ B @ A)) = (times_times_complex @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[366])). 87.71/26.55 thf(689,axiom,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: (((A = none_P5556105721700978146at_nat) => (B @ A @ C)) => (((B @ A @ C) <= (C = none_P5556105721700978146at_nat)) => ((B @ A @ C) <= (! [D:product_prod_nat_nat,E:product_prod_nat_nat]: (((B @ A @ C) <= (C = (some_P7363390416028606310at_nat @ E))) <= (A = (some_P7363390416028606310at_nat @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_combine__options__cases)). 87.71/26.55 thf(4589,plain,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: (((A = none_P5556105721700978146at_nat) => (B @ A @ C)) => (((B @ A @ C) | ~ (C = none_P5556105721700978146at_nat)) => ((B @ A @ C) | ~ (! [D:product_prod_nat_nat,E:product_prod_nat_nat]: ((B @ A @ C) | ~ (C = (some_P7363390416028606310at_nat @ E)) | ~ (A = (some_P7363390416028606310at_nat @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[689])). 87.71/26.55 thf(635,axiom,((! [A:option_nat,B:(option_nat > (option_num > $o)),C:option_num]: (((B @ A @ C) <= (A = none_nat)) => (((C = none_num) => (B @ A @ C)) => ((B @ A @ C) <= (! [D:nat,E:num]: ((A = (some_nat @ D)) => ((B @ A @ C) <= (C = (some_num @ E)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_combine__options__cases)). 87.71/26.55 thf(4407,plain,((! [A:option_nat,B:(option_nat > (option_num > $o)),C:option_num]: (((B @ A @ C) | ~ (A = none_nat)) => (((C = none_num) => (B @ A @ C)) => ((B @ A @ C) | ~ (! [D:nat,E:num]: ((A = (some_nat @ D)) => ((B @ A @ C) | ~ (C = (some_num @ E)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[635])). 87.71/26.55 thf(983,axiom,((! [A:assn,B:assn,C:assn,D:assn,E:assn]: (((entails @ C @ (times_times_assn @ A @ D)) => ((entails @ (times_times_assn @ B @ D) @ E) => (entails @ C @ E))) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4060_ent__frame__fwd)). 87.71/26.55 thf(5751,plain,((! [A:assn,B:assn,C:assn,D:assn,E:assn]: (((entails @ C @ (times_times_assn @ A @ D)) => ((entails @ (times_times_assn @ B @ D) @ E) => (entails @ C @ E))) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[983])). 87.71/26.55 thf(1052,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (ord_less_nat @ B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_mult__pos__neg)). 87.71/26.55 thf(6015,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_nat @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052])). 87.71/26.55 thf(1413,axiom,((top_top_assn != one_one_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10150_assn__basic__inequalities_I1_J)). 87.71/26.55 thf(7393,plain,((~ (top_top_assn = one_one_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413])). 87.71/26.55 thf(469,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ (plus_plus_nat @ A @ C)) <= (ord_less_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2382_pos__add__strict)). 87.71/26.55 thf(3720,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ B @ (plus_plus_nat @ A @ C)) | ~ (ord_less_nat @ B @ C) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[469])). 87.71/26.55 thf(889,axiom,((! [A:(list_o > $o),B:list_o]: ((A @ B) <= (! [C:list_o]: ((A @ C) <= (! [D:list_o]: ((A @ D) <= (ord_less_nat @ (size_size_list_o @ D) @ (size_size_list_o @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2560_length__induct)). 87.71/26.55 thf(5411,plain,((! [A:(list_o > $o),B:list_o]: ((A @ B) | ~ (! [C:list_o]: ((A @ C) | ~ (! [D:list_o]: ((A @ D) | ~ (ord_less_nat @ (size_size_list_o @ D) @ (size_size_list_o @ C))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[889])). 87.71/26.55 thf(520,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/sandbox2/benchmark/theBenchmark.p',fact_574_mint__member)). 87.71/26.55 thf(3984,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)],[520])). 87.71/26.55 thf(1451,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_eq_nat @ A @ C) => (~ (B @ C)))) => (bit_wf_set_bits_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10176_zeros)). 87.71/26.55 thf(7550,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_eq_nat @ A @ C) => (~ (B @ C)))) => (bit_wf_set_bits_int @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1451])). 87.71/26.55 thf(1061,axiom,((! [A:(int > nat),B:nat,C:int,D:list_int]: ((groups8487721886752058969nt_nat @ A @ B @ (cons_int @ C @ D)) = (plus_plus_nat @ (A @ C) @ (times_times_nat @ B @ (groups8487721886752058969nt_nat @ A @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4601_horner__sum__simps_I2_J)). 87.71/26.55 thf(6047,plain,((! [A:(int > nat),B:nat,C:int,D:list_int]: ((groups8487721886752058969nt_nat @ (A) @ B @ (cons_int @ C @ D)) = (plus_plus_nat @ (A @ C) @ (times_times_nat @ B @ (groups8487721886752058969nt_nat @ (A) @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061])). 87.71/26.55 thf(1228,axiom,(((plus_plus_nat @ one_one_nat) = suc)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2420_plus__1__eq__Suc)). 87.71/26.55 thf(6684,plain,(((plus_plus_nat @ one_one_nat) = (suc))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228])). 87.71/26.55 thf(95,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ B)) = (times_times_real @ A @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7871_power__Suc)). 87.71/26.55 thf(2164,plain,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ B)) = (times_times_real @ A @ (power_power_real @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[95])). 87.71/26.55 thf(897,axiom,((! [A:heap_Time_Heap_o,B:($o > assn)]: (hoare_hoare_triple_o @ bot_bot_assn @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_973_false__rule)). 87.71/26.55 thf(5438,plain,((! [A:heap_Time_Heap_o,B:($o > assn)]: (hoare_hoare_triple_o @ bot_bot_assn @ A @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[897])). 87.71/26.55 thf(1080,axiom,((! [A:nat,B:nat]: ((((divide_divide_nat @ B @ A) = (suc @ (divide_divide_nat @ (minus_minus_nat @ B @ A) @ A))) <= (~ (ord_less_nat @ B @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8617_div__geq)). 87.71/26.55 thf(6139,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ B @ A) = (suc @ (divide_divide_nat @ (minus_minus_nat @ B @ A) @ A))) | (ord_less_nat @ B @ A) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080])). 87.71/26.55 thf(1040,axiom,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1178_order__eq__refl)). 87.71/26.55 thf(5968,plain,((! [A:nat,B:nat]: ((A = B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040])). 87.71/26.55 thf(1530,axiom,((! [A:assn]: (entails @ A @ (times_times_assn @ A @ top_top_assn)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10156_ent__refl__true)). 87.71/26.55 thf(7885,plain,((! [A:assn]: (entails @ A @ (times_times_assn @ A @ top_top_assn)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1530])). 87.71/26.55 thf(803,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) => ((~ (ord_less_nat @ A @ B)) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_less__SucE)). 87.71/26.55 thf(5070,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)],[803])). 87.71/26.55 thf(859,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ (suc @ B) @ A) = (suc @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3097_Suc__diff__le)). 87.71/26.55 thf(5291,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ (suc @ B) @ A) = (suc @ (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[859])). 87.71/26.55 thf(1320,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t2 @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2736_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I2_J)). 87.71/26.55 thf(7019,plain,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t2 @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320])). 87.71/26.55 thf(934,axiom,((! [A:assn,B:assn,C:assn]: ((inf_inf_assn @ (inf_inf_assn @ A @ B) @ C) = (inf_inf_assn @ A @ (inf_inf_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8939_norm__assertion__simps_I14_J)). 87.71/26.55 thf(5562,plain,((! [A:assn,B:assn,C:assn]: ((inf_inf_assn @ (inf_inf_assn @ A @ B) @ C) = (inf_inf_assn @ A @ (inf_inf_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[934])). 87.71/26.55 thf(1404,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_less__irrefl__nat)). 87.71/26.55 thf(7357,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404])). 87.71/26.55 thf(1631,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t @ (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9392_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I3_J)). 87.71/26.55 thf(8250,plain,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t @ (vEBT_Node @ A @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1631])). 87.71/26.55 thf(554,axiom,((! [A:nat]: ((binomial @ (suc @ A) @ A) = (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8868_binomial__Suc__n)). 87.71/26.55 thf(4100,plain,((! [A:nat]: ((binomial @ (suc @ A) @ A) = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[554])). 87.71/26.55 thf(170,axiom,((! [A:list_nat,B:list_nat]: ((((size_size_list_nat @ A) = (size_size_list_nat @ B)) => (? [C:list_nat,D:nat,E:list_nat,F:nat,G:list_nat]: ((D != F) & (B = (append_nat @ C @ (append_nat @ (cons_nat @ F @ nil_nat) @ G))) & (A = (append_nat @ C @ (append_nat @ (cons_nat @ D @ nil_nat) @ E)))))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8356_same__length__different)). 87.71/26.55 thf(2496,plain,((! [A:list_nat,B:list_nat]: ((((size_size_list_nat @ A) = (size_size_list_nat @ B)) => (? [C:list_nat,D:nat,E:list_nat,F:nat,G:list_nat]: (~ (D = F) & (B = (append_nat @ C @ (append_nat @ (cons_nat @ F @ nil_nat) @ G))) & (A = (append_nat @ C @ (append_nat @ (cons_nat @ D @ nil_nat) @ E)))))) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[170])). 87.71/26.55 thf(540,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1114_order__antisym)). 87.71/26.55 thf(4059,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)],[540])). 87.71/26.55 thf(33,axiom,(((take_nat @ zero_zero_nat) = (^ [A:list_nat]: (nil_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8158_take0)). 87.71/26.55 thf(1868,plain,(((take_nat @ zero_zero_nat) = (^ [A:list_nat]: (nil_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[33])). 87.71/26.55 thf(1733,axiom,((! [A:nat]: (((~ (! [B:nat]: (A != (suc @ (suc @ B))))) <= (A != (suc @ zero_zero_nat))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_VEBT__internal_OT_092_060_094sub_062b_092_060_094sub_062u_092_060_094sub_062i_092_060_094sub_062l_092_060_094sub_062d_092_060_094sub_062u_092_060_094sub_062p_Ocases)). 87.71/26.55 thf(8668,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)],[1733])). 87.71/26.55 thf(1559,axiom,((times_times_nat = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ zero_zero_nat @ (plus_plus_nat @ B @ (times_times_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3175_mult__eq__if)). 87.71/26.55 thf(7999,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)],[1559])). 87.71/26.55 thf(70,axiom,((! [A:list_o,B:list_int,C:(list_o > (list_int > $o))]: (((size_size_list_o @ A) = (size_size_list_int @ B)) => ((C @ nil_o @ nil_int) => ((C @ A @ B) <= (! [D:$o,E:list_o,F:int,G:list_int]: (((C @ E @ G) => (C @ (cons_o @ D @ E) @ (cons_int @ F @ G))) <= ((size_size_list_o @ E) = (size_size_list_int @ G))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8537_list__induct2)). 87.71/26.55 thf(2000,plain,((! [A:list_o,B:list_int,C:(list_o > (list_int > $o))]: (((size_size_list_o @ A) = (size_size_list_int @ B)) => ((C @ nil_o @ nil_int) => ((C @ A @ B) | ~ (! [D:$o,E:list_o,F:int,G:list_int]: (((C @ E @ G) => (C @ (cons_o @ D @ E) @ (cons_int @ F @ G))) | ~ ((size_size_list_o @ E) = (size_size_list_int @ G))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[70])). 87.71/26.55 thf(1164,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2110_nat__add__left__cancel__le)). 87.71/26.55 thf(6464,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)],[1164])). 87.71/26.55 thf(766,axiom,((! [A:nat,B:nat]: ((one_one_nat = (times_times_nat @ A @ B)) = ((A = one_one_nat) & (B = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_991_nat__1__eq__mult__iff)). 87.71/26.55 thf(4925,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)],[766])). 87.71/26.55 thf(1072,axiom,((! [A:nat,B:int,C:list_int]: ((((drop_int @ A @ (cons_int @ B @ C)) = (drop_int @ (minus_minus_nat @ A @ one_one_nat) @ C)) <= (A != zero_zero_nat)) & (((drop_int @ A @ (cons_int @ B @ C)) = (cons_int @ B @ C)) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7968_drop__Cons_H)). 87.71/26.55 thf(6092,plain,((! [A:nat,B:int,C:list_int]: ((((drop_int @ A @ (cons_int @ B @ C)) = (drop_int @ (minus_minus_nat @ A @ one_one_nat) @ C)) | (A = zero_zero_nat)) & (((drop_int @ A @ (cons_int @ B @ C)) = (cons_int @ B @ C)) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072])). 87.71/26.55 thf(1748,axiom,((! [A:assn,B:$o,C:assn]: ((entails @ (times_times_assn @ A @ (pure_assn @ B)) @ C) = ((B) => (entails @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4046_ent__pure__pre__iff)). 87.71/26.55 thf(8712,plain,((! [A:assn,B:$o,C:assn]: ((entails @ (times_times_assn @ A @ (pure_assn @ B)) @ C) = ((B) => (entails @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1748])). 87.71/26.55 thf(472,axiom,((! [A:nat,B:assn]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_assn @ (power_power_assn @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_assn @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8048_power__minus__mult)). 87.71/26.55 thf(3735,plain,((! [A:nat,B:assn]: ((ord_less_nat @ zero_zero_nat @ A) => ((times_times_assn @ (power_power_assn @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_assn @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[472])). 87.71/26.55 thf(145,axiom,(((map_nat_nat @ (^ [A:nat]: (A))) = (^ [A:list_nat]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2777_map__ident)). 87.71/26.55 thf(2409,plain,(((map_nat_nat @ (^ [A:nat]: (A))) = (^ [A:list_nat]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[145])). 87.71/26.55 thf(1212,axiom,((! [A:assn]: ((times_times_assn @ bot_bot_assn @ A) = bot_bot_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_971_star__false__left)). 87.71/26.55 thf(6635,plain,((! [A:assn]: ((times_times_assn @ bot_bot_assn @ A) = bot_bot_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212])). 87.71/26.55 thf(119,axiom,((! [A:nat,B:list_nat,C:list_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((nth_nat @ (append_nat @ B @ C) @ A) = (nth_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8258_nth__append__first)). 87.71/26.55 thf(2249,plain,((! [A:nat,B:list_nat,C:list_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((nth_nat @ (append_nat @ B @ C) @ A) = (nth_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[119])). 87.71/26.55 thf(1495,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2099_add__less__cancel__left)). 87.71/26.55 thf(7710,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)],[1495])). 87.71/26.55 thf(1424,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7855_zero__less__power)). 87.71/26.55 thf(7428,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (power_power_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1424])). 87.71/26.55 thf(481,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2323_le__add1)). 87.71/26.55 thf(3778,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[481])). 87.71/26.55 thf(1704,axiom,((! [A:$o,B:assn,C:heap_Time_Heap_nat,D:(nat > assn)]: (((hoare_3067605981109127869le_nat @ B @ C @ D) <= (A)) => (hoare_3067605981109127869le_nat @ (times_times_assn @ B @ (pure_assn @ A)) @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_norm__pre__pure__rule1)). 87.71/26.55 thf(8513,plain,((! [A:$o,B:assn,C:heap_Time_Heap_nat,D:(nat > assn)]: (((hoare_3067605981109127869le_nat @ B @ C @ (D)) | ~ (A)) => (hoare_3067605981109127869le_nat @ (times_times_assn @ B @ (pure_assn @ A)) @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1704])). 87.71/26.55 thf(835,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_vebt_maxt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = (some_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_812_vebt__maxt_Osimps_I3_J)). 87.71/26.55 thf(5206,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)],[835])). 87.71/26.55 thf(1501,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1978_pinf_I3_J)). 87.71/26.55 thf(7730,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1501])). 87.71/26.55 thf(356,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = (suc @ zero_zero_nat)) = ((ord_less_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9076_nat__div__eq__Suc__0__iff)). 87.71/26.55 thf(3261,plain,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = (suc @ zero_zero_nat)) = ((ord_less_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) & (ord_less_eq_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[356])). 87.71/26.55 thf(1127,axiom,((! [A:(list_real > $o),B:list_real]: ((! [C:list_real]: ((! [D:list_real]: ((A @ D) <= (ord_less_nat @ (size_size_list_real @ D) @ (size_size_list_real @ C)))) => (A @ C))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2559_length__induct)). 87.71/26.55 thf(6343,plain,((! [A:(list_real > $o),B:list_real]: ((! [C:list_real]: ((! [D:list_real]: ((A @ D) | ~ (ord_less_nat @ (size_size_list_real @ D) @ (size_size_list_real @ C)))) => (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127])). 87.71/26.55 thf(194,axiom,((binomial = (^ [A:nat,B:nat]: (if_nat @ (ord_less_nat @ A @ B) @ zero_zero_nat @ (if_nat @ (ord_less_nat @ A @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ (binomial @ A @ (minus_minus_nat @ A @ B)) @ (divide_divide_nat @ (set_fo2584398358068434914at_nat @ times_times_nat @ (plus_plus_nat @ (minus_minus_nat @ A @ B) @ one_one_nat) @ A @ one_one_nat) @ (semiri1408675320244567234ct_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9104_binomial__code)). 87.71/26.55 thf(2601,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)],[194])). 87.71/26.55 thf(1767,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_vebt__member_Osimps_I4_J)). 87.71/26.55 thf(8778,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)],[1767])). 87.71/26.55 thf(1076,axiom,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7885_power__0)). 87.71/26.55 thf(6122,plain,((! [A:nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076])). 87.71/26.55 thf(948,axiom,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBTi,C:array_VEBT_VEBTi,D:vEBT_VEBT,E:vEBT_VEBTi]: (entails @ (times_times_assn @ (vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ A @ B) @ (times_times_assn @ (snga_assn_VEBT_VEBTi @ C @ B) @ (vEBT_vebt_assn_raw @ D @ E))) @ (times_times_assn @ (times_times_assn @ (vEBT_vebt_assn_raw @ D @ E) @ (snga_assn_VEBT_VEBTi @ C @ B)) @ (vEBT_L6296928887356842470_VEBTi @ vEBT_vebt_assn_raw @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4158_assnle)). 87.71/26.55 thf(5630,plain,((! [A:list_VEBT_VEBT,B:list_VEBT_VEBTi,C:array_VEBT_VEBTi,D:vEBT_VEBT,E:vEBT_VEBTi]: (entails @ (times_times_assn @ (vEBT_L6296928887356842470_VEBTi @ (vEBT_vebt_assn_raw) @ A @ B) @ (times_times_assn @ (snga_assn_VEBT_VEBTi @ C @ B) @ (vEBT_vebt_assn_raw @ D @ E))) @ (times_times_assn @ (times_times_assn @ (vEBT_vebt_assn_raw @ D @ E) @ (snga_assn_VEBT_VEBTi @ C @ B)) @ (vEBT_L6296928887356842470_VEBTi @ (vEBT_vebt_assn_raw) @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[948])). 87.71/26.55 thf(466,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2139_add__less__same__cancel2)). 87.71/26.55 thf(3711,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)],[466])). 87.71/26.55 thf(222,axiom,((! [A:complex,B:complex,C:nat]: ((power_power_complex @ (times_times_complex @ A @ B) @ C) = (times_times_complex @ (power_power_complex @ A @ C) @ (power_power_complex @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7821_power__mult__distrib)). 87.71/26.55 thf(2733,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)],[222])). 87.71/26.55 thf(1607,axiom,((! [A:num]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10009_not__bit__Suc__0__numeral)). 87.71/26.55 thf(8168,plain,((! [A:num]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1607])). 87.71/26.55 thf(1493,axiom,((! [A:nat,B:nat]: (((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)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8893_times__binomial__minus1__eq)). 87.71/26.55 thf(7703,plain,((! [A:nat,B:nat]: (((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)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1493])). 87.71/26.55 thf(516,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ A @ C) => ((vEBT_V5719532721284313246member @ A @ C) | (vEBT_VEBT_membermima @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_member__valid__both__member__options)). 87.71/26.55 thf(3972,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ A @ C) => ((vEBT_V5719532721284313246member @ A @ C) | (vEBT_VEBT_membermima @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[516])). 87.71/26.55 thf(754,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_le__antisym)). 87.71/26.55 thf(4878,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)],[754])). 87.71/26.55 thf(1180,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2271_add__strict__right__mono)). 87.71/26.55 thf(6528,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)],[1180])). 87.71/26.55 thf(785,axiom,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => ((C @ B) <= (! [D:nat]: ((ord_less_eq_nat @ A @ D) => (((C @ D) => (C @ (suc @ D))) <= (ord_less_nat @ D @ B)))))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_dec__induct)). 87.71/26.55 thf(4989,plain,((! [A:nat,B:nat,C:(nat > $o)]: (((C @ A) => ((C @ B) | ~ (! [D:nat]: ((ord_less_eq_nat @ A @ D) => (((C @ D) => (C @ (suc @ D))) | ~ (ord_less_nat @ D @ B)))))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[785])). 87.71/26.55 thf(798,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1973_pinf_I4_J)). 87.71/26.55 thf(5044,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[798])). 87.71/26.55 thf(903,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/sandbox2/benchmark/theBenchmark.p',fact_9971_int__bit__bound)). 87.71/26.55 thf(5455,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)],[903])). 87.71/26.55 thf(1001,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ one_one_nat @ B) => (ord_less_nat @ one_one_nat @ (times_times_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1082_less__1__mult)). 87.71/26.55 thf(5815,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)],[1001])). 87.71/26.55 thf(878,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_960_dual__order_Orefl)). 87.71/26.55 thf(5366,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[878])). 87.71/26.55 thf(306,axiom,((! [A:nat]: ((bit_se1412395901928357646or_nat @ (suc @ zero_zero_nat) @ A) = (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10047_Suc__0__or__eq)). 87.71/26.55 thf(3069,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)],[306])). 87.71/26.55 thf(1713,axiom,(((size_size_option_num @ none_num) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_option_Osize_I3_J)). 87.71/26.55 thf(8550,plain,(((size_size_option_num @ none_num) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1713])). 87.71/26.55 thf(1339,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_bot__nat__0_Oextremum__uniqueI)). 87.71/26.55 thf(7084,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339])). 87.71/26.55 thf(907,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (! [D:nat]: ((A @ D) <= (B = (plus_plus_nat @ C @ D))) & ((ord_less_nat @ B @ C) => (A @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3143_nat__diff__split)). 87.71/26.55 thf(5470,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (! [D:nat]: ((A @ D) | ~ (B = (plus_plus_nat @ C @ D))) & ((ord_less_nat @ B @ C) => (A @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[907])). 87.71/26.55 thf(1480,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2225_add__mono__thms__linordered__semiring_I1_J)). 87.71/26.55 thf(7640,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ A @ B) & (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1480])). 87.71/26.55 thf(644,axiom,((! [A:list_o,B:heap_e7401611519738050253t_unit]: ((time_time_array_o @ (array_of_list_o @ A) @ B) = (plus_plus_nat @ (size_size_list_o @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4784_time__array__of__list)). 87.71/26.55 thf(4449,plain,((! [A:list_o,B:heap_e7401611519738050253t_unit]: ((time_time_array_o @ (array_of_list_o @ A) @ B) = (plus_plus_nat @ (size_size_list_o @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[644])). 87.71/26.55 thf(1579,axiom,((! [A:nat]: ((size_size_option_nat @ (some_nat @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_option_Osize_I4_J)). 87.71/26.55 thf(8081,plain,((! [A:nat]: ((size_size_option_nat @ (some_nat @ A)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1579])). 87.71/26.55 thf(659,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/sandbox2/benchmark/theBenchmark.p',fact_2373_add__neg__neg)). 87.71/26.55 thf(4493,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)],[659])). 87.71/26.55 thf(984,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_T_p_r_e_d2 @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1815_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I3_J)). 87.71/26.55 thf(5754,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_T_p_r_e_d2 @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[984])). 87.71/26.55 thf(599,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2143_less__add__same__cancel1)). 87.71/26.55 thf(4284,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)],[599])). 87.71/26.55 thf(90,axiom,((! [A:nat,B:nat]: (((upt @ A @ B) = nil_nat) = ((ord_less_eq_nat @ B @ A) | (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8835_upt__eq__Nil__conv)). 87.71/26.55 thf(2150,plain,((! [A:nat,B:nat]: (((upt @ A @ B) = nil_nat) = ((ord_less_eq_nat @ B @ A) | (B = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[90])). 87.71/26.55 thf(1172,axiom,((! [A:nat,B:nat]: ((((suc @ A) != B) => (ord_less_nat @ (suc @ A) @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_Suc__lessI)). 87.71/26.55 thf(6496,plain,((! [A:nat,B:nat]: (((~ ((suc @ A) = B)) => (ord_less_nat @ (suc @ A) @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172])). 87.71/26.55 thf(917,axiom,((! [A:real,B:nat,C:nat]: ((power_power_real @ A @ (times_times_nat @ B @ C)) = (power_power_real @ (power_power_real @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7829_power__mult)). 87.71/26.55 thf(5507,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)],[917])). 87.71/26.55 thf(147,axiom,((! [A:nat,B:nat]: ((((upt @ A @ (suc @ B)) = (append_nat @ (upt @ A @ B) @ (cons_nat @ B @ nil_nat))) <= (ord_less_eq_nat @ A @ B)) & ((~ (ord_less_eq_nat @ A @ B)) => ((upt @ A @ (suc @ B)) = nil_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8857_upt__Suc)). 87.71/26.55 thf(2414,plain,((! [A:nat,B:nat]: ((((upt @ A @ (suc @ B)) = (append_nat @ (upt @ A @ B) @ (cons_nat @ B @ nil_nat))) | ~ (ord_less_eq_nat @ A @ B)) & ((~ (ord_less_eq_nat @ A @ B)) => ((upt @ A @ (suc @ B)) = nil_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[147])). 87.71/26.55 thf(740,axiom,((divide_divide_nat = (^ [A:nat,B:nat]: (if_nat @ ((B = zero_zero_nat) | (ord_less_nat @ A @ B)) @ zero_zero_nat @ (suc @ (divide_divide_nat @ (minus_minus_nat @ A @ B) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8655_div__if)). 87.71/26.55 thf(4836,plain,(((divide_divide_nat) = (^ [A:nat,B:nat]: (if_nat @ ((B = zero_zero_nat) | (ord_less_nat @ A @ B)) @ zero_zero_nat @ (suc @ (divide_divide_nat @ (minus_minus_nat @ A @ B) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[740])). 87.71/26.55 thf(706,axiom,((! [A:option_nat,B:(option_nat > (option_nat > $o)),C:option_nat]: ((((! [D:nat,E:nat]: ((A = (some_nat @ D)) => ((B @ A @ C) <= (C = (some_nat @ E))))) => (B @ A @ C)) <= ((C = none_nat) => (B @ A @ C))) <= ((B @ A @ C) <= (A = none_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_combine__options__cases)). 87.71/26.55 thf(4661,plain,((! [A:option_nat,B:(option_nat > (option_nat > $o)),C:option_nat]: (((! [D:nat,E:nat]: ((A = (some_nat @ D)) => ((B @ A @ C) | ~ (C = (some_nat @ E))))) => (B @ A @ C)) | ~ ((C = none_nat) => (B @ A @ C)) | ~ ((B @ A @ C) | ~ (A = none_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[706])). 87.71/26.55 thf(1106,axiom,((! [A:nat,B:nat,C:(nat > (nat > $o))]: (((((C @ A @ B) <= (! [D:nat]: (C @ D @ (suc @ D)))) <= (! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F))))) <= (! [D:nat]: (C @ D @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_transitive__stepwise__le)). 87.71/26.55 thf(6232,plain,((! [A:nat,B:nat,C:(nat > (nat > $o))]: ((C @ A @ B) | ~ (! [D:nat]: (C @ D @ (suc @ D))) | ~ (! [D:nat,E:nat,F:nat]: ((C @ D @ E) => ((C @ E @ F) => (C @ D @ F)))) | ~ (! [D:nat]: (C @ D @ D)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106])). 87.71/26.55 thf(1375,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/sandbox2/benchmark/theBenchmark.p',fact_8722_le__mod__geq)). 87.71/26.55 thf(7244,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)],[1375])). 87.71/26.55 thf(457,axiom,((! [A:(nat > nat),B:nat,C:nat,D:list_nat]: ((groups7488368174851004413at_nat @ A @ B @ (cons_nat @ C @ D)) = (plus_plus_nat @ (A @ C) @ (times_times_nat @ B @ (groups7488368174851004413at_nat @ A @ B @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4600_horner__sum__simps_I2_J)). 87.71/26.55 thf(3682,plain,((! [A:(nat > nat),B:nat,C:nat,D:list_nat]: ((groups7488368174851004413at_nat @ (A) @ B @ (cons_nat @ C @ D)) = (plus_plus_nat @ (A @ C) @ (times_times_nat @ B @ (groups7488368174851004413at_nat @ (A) @ B @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[457])). 87.71/26.55 thf(1028,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2267_add__strict__left__mono)). 87.71/26.55 thf(5924,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028])). 87.71/26.55 thf(362,axiom,((! [A:nat]: ((comm_s4663373288045622133er_nat @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4807_pochhammer__0)). 87.71/26.55 thf(3286,plain,((! [A:nat]: ((comm_s4663373288045622133er_nat @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[362])). 87.71/26.55 thf(1197,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 @ C @ A) @ (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_mult__less__mono2)). 87.71/26.55 thf(6582,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 @ C @ A) @ (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197])). 87.71/26.55 thf(38,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9947_xor__nat__numerals_I4_J)). 87.71/26.55 thf(1883,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)],[38])). 87.71/26.55 thf(280,axiom,((vEBT_V8194947554948674370ptions = (^ [A:vEBT_VEBT,B:nat]: ((vEBT_VEBT_membermima @ A @ B) | (vEBT_V5719532721284313246member @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2597_both__member__options__def)). 87.71/26.55 thf(2958,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)],[280])). 87.71/26.55 thf(258,axiom,((! [A:nat,B:list_real]: (((suc @ A) = (size_size_list_real @ B)) = (? [C:real,D:list_real]: (((size_size_list_real @ D) = A) & (B = (cons_real @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4667_Suc__length__conv)). 87.71/26.55 thf(2873,plain,((! [A:nat,B:list_real]: (((suc @ A) = (size_size_list_real @ B)) = (? [C:real,D:list_real]: (((size_size_list_real @ D) = A) & (B = (cons_real @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[258])). 87.71/26.55 thf(1155,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/sandbox2/benchmark/theBenchmark.p',fact_3060_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc)). 87.71/26.55 thf(6432,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)],[1155])). 87.71/26.55 thf(744,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2317_not__add__less2)). 87.71/26.55 thf(4849,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[744])). 87.71/26.55 thf(569,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2811_add__diff__cancel__left)). 87.71/26.55 thf(4155,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)],[569])). 87.71/26.55 thf(427,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ C) => ((ord_less_nat @ C @ (times_times_nat @ A @ (suc @ B))) => ((divide_divide_nat @ C @ A) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8656_div__nat__eqI)). 87.71/26.55 thf(3556,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ C) => ((ord_less_nat @ C @ (times_times_nat @ A @ (suc @ B))) => ((divide_divide_nat @ C @ A) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[427])). 87.71/26.55 thf(1189,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => (entails @ (inf_inf_assn @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8913_ent__conjE1)). 87.71/26.55 thf(6556,plain,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => (entails @ (inf_inf_assn @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189])). 87.71/26.55 thf(628,axiom,((plus_plus_nat = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ B @ (suc @ (plus_plus_nat @ (minus_minus_nat @ A @ one_one_nat) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3173_add__eq__if)). 87.71/26.55 thf(4385,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)],[628])). 87.71/26.55 thf(680,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ B @ C) @ D) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ D)) @ (suc @ (suc @ A)) @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2578_vebt__insert_Osimps_I4_J)). 87.71/26.55 thf(4553,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)],[680])). 87.71/26.55 thf(1081,axiom,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:nat]: ((hoare_3067605981109127869le_nat @ A @ B @ C) <= (time_htt_nat @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1809_htt__htD)). 87.71/26.55 thf(6143,plain,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:nat]: ((hoare_3067605981109127869le_nat @ A @ B @ (C)) | ~ (time_htt_nat @ A @ B @ (C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081])). 87.71/26.55 thf(874,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_le__eq__less__or__eq)). 87.71/26.55 thf(5341,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[874])). 87.71/26.55 thf(1496,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => (entails @ A @ (sup_sup_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5114_ent__disjI1_H)). 87.71/26.55 thf(7713,plain,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => (entails @ A @ (sup_sup_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1496])). 87.71/26.55 thf(1066,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1458_leD)). 87.71/26.55 thf(6060,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066])). 87.71/26.55 thf(504,axiom,((! [A:assn]: ((sup_sup_assn @ A @ top_top_assn) = top_top_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10161_norm__assertion__simps_I12_J)). 87.71/26.55 thf(3926,plain,((! [A:assn]: ((sup_sup_assn @ A @ top_top_assn) = top_top_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[504])). 87.71/26.55 thf(83,axiom,((! [A:int,B:list_int]: ((nth_int @ (cons_int @ A @ B) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4578_length__nth__simps_I3_J)). 87.71/26.55 thf(2112,plain,((! [A:int,B:list_int]: ((nth_int @ (cons_int @ A @ B) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[83])). 87.71/26.55 thf(1596,axiom,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_old_Onat_Oinject)). 87.71/26.55 thf(8136,plain,((! [A:nat,B:nat]: (((suc @ A) = (suc @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1596])). 87.71/26.55 thf(1397,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_T_i_n_s_e_r_t @ (vEBT_Leaf @ A @ B) @ C) = (plus_plus_nat @ one_one_nat @ (if_nat @ (C = zero_zero_nat) @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9393_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I1_J)). 87.71/26.55 thf(7308,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_T_i_n_s_e_r_t @ (vEBT_Leaf @ A @ B) @ C) = (plus_plus_nat @ one_one_nat @ (if_nat @ (C = zero_zero_nat) @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397])). 87.71/26.55 thf(1373,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1520_order_Ostrict__trans2)). 87.71/26.55 thf(7237,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373])). 87.71/26.55 thf(1216,axiom,((! [A:nat,B:nat]: ((((divide_divide_nat @ A @ B) = A) = (B = one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8632_div__eq__dividend__iff)). 87.71/26.55 thf(6646,plain,((! [A:nat,B:nat]: ((((divide_divide_nat @ A @ B) = A) = (B = one_one_nat)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216])). 87.71/26.55 thf(22,axiom,((! [A:nat,B:list_nat]: (((take_nat @ A @ B) = B) = (ord_less_eq_nat @ (size_size_list_nat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6295_take__all__iff)). 87.71/26.55 thf(1837,plain,((! [A:nat,B:list_nat]: (((take_nat @ A @ B) = B) = (ord_less_eq_nat @ (size_size_list_nat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[22])). 87.71/26.55 thf(1033,axiom,((! [A:$o,B:$o]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1758_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I1_J)). 87.71/26.55 thf(5937,plain,((! [A:$o,B:$o]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033])). 87.71/26.55 thf(1734,axiom,((! [A:assn,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn)]: (((hoare_7629718768684598413on_nat @ A @ C @ D) <= (hoare_7629718768684598413on_nat @ B @ C @ D)) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4070_cons__pre__rule)). 87.71/26.55 thf(8672,plain,((! [A:assn,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn)]: ((hoare_7629718768684598413on_nat @ A @ C @ (D)) | ~ (hoare_7629718768684598413on_nat @ B @ C @ (D)) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1734])). 87.71/26.55 thf(692,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2955_diff__diff__eq)). 87.71/26.55 thf(4608,plain,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[692])). 87.71/26.55 thf(1459,axiom,((! [A:vEBT_VEBT]: ((~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ B @ C @ D @ E)))) <= (! [B:$o,C:$o]: (A != (vEBT_Leaf @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1833_VEBT__internal_Oheight_Ocases)). 87.71/26.55 thf(7576,plain,((! [A:vEBT_VEBT]: (~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ B @ C @ D @ E))) | ~ (! [B:$o,C:$o]: ~ (A = (vEBT_Leaf @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1459])). 87.71/26.55 thf(1565,axiom,((! [A:list_nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (size_size_list_nat @ A)) = (A != nil_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8329_length__ge__1__conv)). 87.71/26.55 thf(8026,plain,((! [A:list_nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (size_size_list_nat @ A)) = (~ (A = nil_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1565])). 87.71/26.55 thf(1744,axiom,((! [A:int]: ((power_power_int @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7723_power__Suc0__right)). 87.71/26.55 thf(8700,plain,((! [A:int]: ((power_power_int @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1744])). 87.71/26.55 thf(538,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) @ (plus_plus_nat @ A @ C)) @ (binomial @ (plus_plus_nat @ A @ C) @ C)) = (times_times_nat @ (binomial @ (plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) @ C) @ (binomial @ (plus_plus_nat @ A @ B) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8879_choose__mult__lemma)). 87.71/26.55 thf(4053,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)],[538])). 87.71/26.55 thf(164,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/sandbox2/benchmark/theBenchmark.p',fact_7827_power__commuting__commutes)). 87.71/26.55 thf(2477,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)],[164])). 87.71/26.55 thf(312,axiom,((! [A:list_real,B:list_nat,C:list_o,D:(list_real > (list_nat > (list_o > $o)))]: ((((size_size_list_nat @ B) = (size_size_list_o @ C)) => (((! [E:real,F:list_real,G:nat,H:list_nat,I:$o,J:list_o]: ((((size_size_list_nat @ H) = (size_size_list_o @ J)) => ((D @ (cons_real @ E @ F) @ (cons_nat @ G @ H) @ (cons_o @ I @ J)) <= (D @ F @ H @ J))) <= ((size_size_list_real @ F) = (size_size_list_nat @ H)))) => (D @ A @ B @ C)) <= (D @ nil_real @ nil_nat @ nil_o))) <= ((size_size_list_real @ A) = (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8549_list__induct3)). 87.71/26.55 thf(3090,plain,((! [A:list_real,B:list_nat,C:list_o,D:(list_real > (list_nat > (list_o > $o)))]: ((((size_size_list_nat @ B) = (size_size_list_o @ C)) => (((! [E:real,F:list_real,G:nat,H:list_nat,I:$o,J:list_o]: ((((size_size_list_nat @ H) = (size_size_list_o @ J)) => ((D @ (cons_real @ E @ F) @ (cons_nat @ G @ H) @ (cons_o @ I @ J)) | ~ (D @ F @ H @ J))) | ~ ((size_size_list_real @ F) = (size_size_list_nat @ H)))) => (D @ A @ B @ C)) | ~ (D @ nil_real @ nil_nat @ nil_o))) | ~ ((size_size_list_real @ A) = (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[312])). 87.71/26.55 thf(1729,axiom,((! [A:(nat > (nat > $o)),B:nat,C:nat]: ((((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C)) <= (! [D:nat]: (A @ zero_zero_nat @ (suc @ D)))) <= (! [D:nat]: (A @ D @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_diff__induct)). 87.71/26.55 thf(8651,plain,((! [A:(nat > (nat > $o)),B:nat,C:nat]: (((! [D:nat,E:nat]: ((A @ D @ E) => (A @ (suc @ D) @ (suc @ E)))) => (A @ B @ C)) | ~ (! [D:nat]: (A @ zero_zero_nat @ (suc @ D))) | ~ (! [D:nat]: (A @ D @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1729])). 87.71/26.55 thf(1273,axiom,((! [A:$o,B:assn,C:heap_Time_Heap_nat,D:(nat > assn),E:heap_Time_Heap_nat,F:(nat > assn),G:(nat > assn)]: ((((~ (A)) => (hoare_3067605981109127869le_nat @ B @ E @ F)) => ((hoare_3067605981109127869le_nat @ B @ (if_Hea2662716070787841314ap_nat @ A @ C @ E) @ G) <= (! [H:nat]: (entails @ (sup_sup_assn @ (times_times_assn @ (D @ H) @ (pure_assn @ A)) @ (times_times_assn @ (F @ H) @ (pure_assn @ (~ (A))))) @ (G @ H))))) <= ((hoare_3067605981109127869le_nat @ B @ C @ D) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5140_if__rule__split)). 87.71/26.55 thf(6848,plain,((! [A:$o,B:assn,C:heap_Time_Heap_nat,D:(nat > assn),E:heap_Time_Heap_nat,F:(nat > assn),G:(nat > assn)]: ((((~ (A)) => (hoare_3067605981109127869le_nat @ B @ E @ (F))) => ((hoare_3067605981109127869le_nat @ B @ (if_Hea2662716070787841314ap_nat @ A @ C @ E) @ (G)) | ~ (! [H:nat]: (entails @ (sup_sup_assn @ (times_times_assn @ (D @ H) @ (pure_assn @ A)) @ (times_times_assn @ (F @ H) @ (pure_assn @ (~ (A))))) @ (G @ H))))) | ~ ((hoare_3067605981109127869le_nat @ B @ C @ (D)) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273])). 87.71/26.55 thf(186,axiom,((bit_se6528837805403552850or_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) != (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se6528837805403552850or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9994_xor__nat__rec)). 87.71/26.55 thf(2565,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)],[186])). 87.71/26.55 thf(1599,axiom,((! [A:(nat > option4927543243414619207at_nat),B:nat,C:list_nat,D:product_prod_nat_nat,E:list_P6011104703257516679at_nat]: ((map_up1590851270032768825at_nat @ A @ (cons_nat @ B @ C) @ (cons_P6512896166579812791at_nat @ D @ E)) = (map_up1590851270032768825at_nat @ (fun_up2252230070437638584at_nat @ A @ B @ (some_P7363390416028606310at_nat @ D)) @ C @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6338_map__upds__Cons)). 87.71/26.55 thf(8145,plain,((! [A:(nat > option4927543243414619207at_nat),B:nat,C:list_nat,D:product_prod_nat_nat,E:list_P6011104703257516679at_nat]: ((map_up1590851270032768825at_nat @ A @ (cons_nat @ B @ C) @ (cons_P6512896166579812791at_nat @ D @ E)) = (map_up1590851270032768825at_nat @ (fun_up2252230070437638584at_nat @ A @ B @ (some_P7363390416028606310at_nat @ D)) @ C @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1599])). 87.71/26.55 thf(1536,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1917_pinf_I8_J)). 87.71/26.55 thf(7902,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)],[1536])). 87.71/26.55 thf(926,axiom,((! [A:nat]: ((ord_less_nat @ A @ (bit_se2002935070580805687sk_nat @ A)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9866_less__mask)). 87.71/26.55 thf(5534,plain,((! [A:nat]: ((ord_less_nat @ A @ (bit_se2002935070580805687sk_nat @ A)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[926])). 87.71/26.55 thf(77,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (comm_s4663373288045622133er_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4839_pochhammer__nonneg)). 87.71/26.55 thf(2068,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ (comm_s4663373288045622133er_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[77])). 87.71/26.55 thf(16,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((take_nat @ B @ (upt @ A @ C)) = (upt @ A @ (plus_plus_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8829_take__upt)). 87.71/26.55 thf(1819,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((take_nat @ B @ (upt @ A @ C)) = (upt @ A @ (plus_plus_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[16])). 87.71/26.55 thf(931,axiom,((! [A:list_o,B:list_o]: (((size_size_list_o @ A) != (size_size_list_o @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_size__neq__size__imp__neq)). 87.71/26.55 thf(5551,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)],[931])). 87.71/26.55 thf(423,axiom,((inf_inf_assn = (^ [A:assn,B:assn]: (inf_inf_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8937_assn__aci_I1_J)). 87.71/26.55 thf(3546,plain,(((inf_inf_assn) = (^ [A:assn,B:assn]: (inf_inf_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[423])). 87.71/26.55 thf(797,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)) => ((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) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8988_delt__out__of__range)). 87.71/26.55 thf(5038,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)) => ((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) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[797])). 87.71/26.55 thf(726,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1907_verit__comp__simplify1_I3_J)). 87.71/26.55 thf(4746,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[726])). 87.71/26.55 thf(419,axiom,((! [A:assn]: ((one_one_assn = A) = (A = one_one_assn)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1009_one__reorient)). 87.71/26.55 thf(3535,plain,((! [A:assn]: ((one_one_assn = A) = (A = one_one_assn)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[419])). 87.71/26.55 thf(814,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_s_u_c_c2 @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2492_succ_H__bound__height)). 87.71/26.55 thf(5113,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_s_u_c_c2 @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[814])). 87.71/26.55 thf(1142,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_980_mult__1)). 87.71/26.55 thf(6392,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142])). 87.71/26.55 thf(183,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/sandbox2/benchmark/theBenchmark.p',fact_8972_member__bound)). 87.71/26.55 thf(2547,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)],[183])). 87.71/26.55 thf(479,axiom,((! [A:option_num,B:(option_num > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: ((((B @ A @ C) <= (C = none_P5556105721700978146at_nat)) => ((B @ A @ C) <= (! [D:num,E:product_prod_nat_nat]: (((B @ A @ C) <= (C = (some_P7363390416028606310at_nat @ E))) <= (A = (some_num @ D)))))) <= ((A = none_num) => (B @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_combine__options__cases)). 87.71/26.55 thf(3763,plain,((! [A:option_num,B:(option_num > (option4927543243414619207at_nat > $o)),C:option4927543243414619207at_nat]: ((((B @ A @ C) | ~ (C = none_P5556105721700978146at_nat)) => ((B @ A @ C) | ~ (! [D:num,E:product_prod_nat_nat]: ((B @ A @ C) | ~ (C = (some_P7363390416028606310at_nat @ E)) | ~ (A = (some_num @ D)))))) | ~ ((A = none_num) => (B @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[479])). 87.71/26.55 thf(169,axiom,((! [A:nat,B:nat,C:list_nat,D:nat]: ((ord_less_nat @ A @ B) => ((((nth_nat @ (slice_nat @ A @ B @ C) @ D) = (nth_nat @ C @ (plus_plus_nat @ A @ D))) <= (ord_less_nat @ D @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ B @ (size_size_list_nat @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3232_slice__nth)). 87.71/26.55 thf(2492,plain,((! [A:nat,B:nat,C:list_nat,D:nat]: ((ord_less_nat @ A @ B) => (((nth_nat @ (slice_nat @ A @ B @ C) @ D) = (nth_nat @ C @ (plus_plus_nat @ A @ D))) | ~ (ord_less_nat @ D @ (minus_minus_nat @ B @ A)) | ~ (ord_less_eq_nat @ B @ (size_size_list_nat @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[169])). 87.71/26.55 thf(1524,axiom,((! [A:assn]: ((sup_sup_assn @ A @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5431_norm__assertion__simps_I32_J)). 87.71/26.55 thf(7853,plain,((! [A:assn]: ((sup_sup_assn @ A @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1524])). 87.71/26.55 thf(225,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (plus_plus_nat @ A @ B)) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8970_pow__sum)). 87.71/26.55 thf(2741,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)],[225])). 87.71/26.55 thf(976,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/sandbox2/benchmark/theBenchmark.p',fact_2377_add__pos__pos)). 87.71/26.55 thf(5729,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)],[976])). 87.71/26.55 thf(1640,axiom,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn)]: ((hoare_7629718768684598413on_nat @ A @ B @ C) <= (hoare_7629718768684598413on_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_is__hoare__triple)). 87.71/26.55 thf(8287,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1640])). 87.71/26.55 thf(112,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ (power_power_int @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7880_power__Suc2)). 87.71/26.55 thf(2228,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)],[112])). 87.71/26.55 thf(708,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => ((entails @ B @ C) => (entails @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4054_ent__trans)). 87.71/26.55 thf(4680,plain,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => ((entails @ B @ C) => (entails @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[708])). 87.71/26.55 thf(1675,axiom,((! [A:nat,B:list_int]: ((n_lists_int @ (suc @ A) @ B) = (concat_list_int @ (map_li8902190837986183758st_int @ (^ [C:list_int]: (map_int_list_int @ (^ [D:int]: (cons_int @ D @ C)) @ B)) @ (n_lists_int @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4759_n__lists_Osimps_I2_J)). 87.71/26.55 thf(8403,plain,((! [A:nat,B:list_int]: ((n_lists_int @ (suc @ A) @ B) = (concat_list_int @ (map_li8902190837986183758st_int @ (^ [C:list_int]: (map_int_list_int @ (^ [D:int]: (cons_int @ D @ C)) @ B)) @ (n_lists_int @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1675])). 87.71/26.55 thf(871,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ bot_bot_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1696_bot_Oextremum__strict)). 87.71/26.55 thf(5330,plain,((! [A:nat]: ~ (ord_less_nat @ A @ bot_bot_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[871])). 87.71/26.55 thf(1662,axiom,((! [A:nat]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10008_not__bit__Suc__0__Suc)). 87.71/26.55 thf(8358,plain,((! [A:nat]: ~ (bit_se1148574629649215175it_nat @ (suc @ zero_zero_nat) @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1662])). 87.71/26.55 thf(1576,axiom,((times_times_assn = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_star__aci_I2_J)). 87.71/26.55 thf(8073,plain,(((times_times_assn) = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1576])). 87.71/26.55 thf(1284,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/sandbox2/benchmark/theBenchmark.p',fact_8753_Suc__times__mod__eq)). 87.71/26.55 thf(6888,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)],[1284])). 87.71/26.55 thf(1233,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2824_diff__diff__cancel)). 87.71/26.55 thf(6709,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ B @ (minus_minus_nat @ B @ A)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233])). 87.71/26.55 thf(1470,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ A @ B) <= (A != B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1606_order__le__neq__trans)). 87.71/26.55 thf(7608,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)],[1470])). 87.71/26.55 thf(1149,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2070_add__cancel__left__right)). 87.71/26.55 thf(6413,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149])). 87.71/26.55 thf(852,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2199_comm__monoid__add__class_Oadd__0)). 87.71/26.55 thf(5270,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[852])). 87.71/26.55 thf(1541,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ (divide_divide_nat @ C @ A)) = (ord_less_eq_nat @ (times_times_nat @ B @ A) @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8661_less__eq__div__iff__mult__less__eq)). 87.71/26.55 thf(7917,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)],[1541])). 87.71/26.55 thf(995,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (((ord_less_nat @ C @ one_one_nat) => (ord_less_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A))) <= (ord_less_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7987_power__strict__decreasing)). 87.71/26.55 thf(5798,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (((ord_less_nat @ C @ one_one_nat) => (ord_less_nat @ (power_power_nat @ C @ B) @ (power_power_nat @ C @ A))) | ~ (ord_less_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[995])). 87.71/26.55 thf(212,axiom,((! [A:heap_T2636463487746394924on_nat,B:heap_T2636463487746394924on_nat]: ((if_Hea5867803462524415986on_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Option__Ooption_It__Nat__Onat_J_J_T)). 87.71/26.55 thf(2692,plain,((! [A:heap_T2636463487746394924on_nat,B:heap_T2636463487746394924on_nat]: ((if_Hea5867803462524415986on_nat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[212])). 87.71/26.55 thf(350,axiom,((! [A:nat,B:nat]: ((if_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Nat__Onat_T)). 87.71/26.55 thf(3237,plain,((! [A:nat,B:nat]: ((if_nat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[350])). 87.71/26.55 thf(1101,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ C @ D) & (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2221_add__mono__thms__linordered__semiring_I2_J)). 87.71/26.55 thf(6215,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ C @ D) & (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101])). 87.71/26.55 thf(1235,axiom,(((('!') @ option_num) = (^ [A:(option_num > $o)]: (! [B:num]: (A @ (some_num @ B)) & (A @ none_num))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_split__option__all)). 87.71/26.55 thf(6728,plain,(((('!') @ option_num) = (^ [A:(option_num > $o)]: (! [B:num]: (A @ (some_num @ B)) & (A @ none_num))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235])). 87.71/26.55 thf(1644,axiom,((! [A:list_real]: ((foldl_nat_real @ (^ [B:nat,C:real]: (suc @ B)) @ zero_zero_nat @ A) = (size_size_list_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4584_foldl__length)). 87.71/26.55 thf(8297,plain,((! [A:list_real]: ((foldl_nat_real @ (^ [B:nat,C:real]: (suc @ B)) @ zero_zero_nat @ A) = (size_size_list_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1644])). 87.71/26.55 thf(867,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t2 @ A @ C) @ one_one_nat) <= (vEBT_VEBT_minNull @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2742_insertsimp_H)). 87.71/26.55 thf(5313,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t2 @ A @ C) @ one_one_nat) | ~ (vEBT_VEBT_minNull @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[867])). 87.71/26.55 thf(1400,axiom,(((('?') @ option_nat) = (^ [A:(option_nat > $o)]: (? [B:nat]: (A @ (some_nat @ B)) | (A @ none_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_split__option__ex)). 87.71/26.55 thf(7346,plain,(((('?') @ option_nat) = (^ [A:(option_nat > $o)]: (? [B:nat]: (A @ (some_nat @ B)) | (A @ none_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400])). 87.71/26.55 thf(833,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: (((C @ D) => (C @ (suc @ D))) <= (ord_less_eq_nat @ A @ D))) => (C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_nat__induct__at__least)). 87.71/26.55 thf(5189,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_eq_nat @ A @ B) => ((C @ A) => ((! [D:nat]: (((C @ D) => (C @ (suc @ D))) | ~ (ord_less_eq_nat @ A @ D))) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[833])). 87.71/26.55 thf(1742,axiom,((! [A:assn,B:list_assn]: ((times_times_assn @ A @ (foldl_assn_assn @ times_times_assn @ one_one_assn @ B)) = (foldl_assn_assn @ times_times_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4704_foldl__absorb1)). 87.71/26.55 thf(8694,plain,((! [A:assn,B:list_assn]: ((times_times_assn @ A @ (foldl_assn_assn @ (times_times_assn) @ one_one_assn @ B)) = (foldl_assn_assn @ (times_times_assn) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1742])). 87.71/26.55 thf(401,axiom,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8968_semiring__norm_I87_J)). 87.71/26.55 thf(3467,plain,((! [A:num,B:num]: (((bit0 @ A) = (bit0 @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[401])). 87.71/26.55 thf(1708,axiom,((! [A:(nat > $o)]: ((! [B:nat]: ((A @ B) <= (ord_less_nat @ B @ (suc @ zero_zero_nat)))) = (A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_forall__finite_I2_J)). 87.71/26.55 thf(8530,plain,((! [A:(nat > $o)]: ((! [B:nat]: ((A @ B) | ~ (ord_less_nat @ B @ (suc @ zero_zero_nat)))) = (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1708])). 87.71/26.55 thf(1686,axiom,((! [A:nat,B:list_option_nat,C:array_option_nat]: ((hoare_7629718768684598413on_nat @ (snga_assn_option_nat @ C @ B) @ (array_nth_option_nat @ C @ A) @ (^ [D:option_nat]: (times_times_assn @ (snga_assn_option_nat @ C @ B) @ (pure_assn @ (D = (nth_option_nat @ B @ A)))))) <= (ord_less_nat @ A @ (size_s6086282163384603972on_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4428_nth__rule)). 87.71/26.55 thf(8446,plain,((! [A:nat,B:list_option_nat,C:array_option_nat]: ((hoare_7629718768684598413on_nat @ (snga_assn_option_nat @ C @ B) @ (array_nth_option_nat @ C @ A) @ (^ [D:option_nat]: (times_times_assn @ (snga_assn_option_nat @ C @ B) @ (pure_assn @ (D = (nth_option_nat @ B @ A)))))) | ~ (ord_less_nat @ A @ (size_s6086282163384603972on_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1686])). 87.71/26.55 thf(972,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ one_one_nat) => ((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ C @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7776_power__strict__decreasing__iff)). 87.71/26.55 thf(5714,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ one_one_nat) => ((ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_nat @ C @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[972])). 87.71/26.55 thf(941,axiom,((! [A:assn,B:assn,C:nat]: (((times_times_assn @ (power_power_assn @ A @ C) @ (power_power_assn @ B @ C)) = one_one_assn) <= ((times_times_assn @ A @ B) = one_one_assn)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7869_left__right__inverse__power)). 87.71/26.55 thf(5609,plain,((! [A:assn,B:assn,C:nat]: (((times_times_assn @ (power_power_assn @ A @ C) @ (power_power_assn @ B @ C)) = one_one_assn) | ~ ((times_times_assn @ A @ B) = one_one_assn)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[941])). 87.71/26.55 thf(84,axiom,((! [A:list_int,B:list_real,C:list_real,D:list_int,E:(list_int > (list_real > (list_real > (list_int > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => ((((size_size_list_real @ C) = (size_size_list_int @ D)) => (((! [F:int,G:list_int,H:real,I:list_real,J:real,K:list_real,L:int,M:list_int]: ((((size_size_list_real @ I) = (size_size_list_real @ K)) => (((size_size_list_real @ K) = (size_size_list_int @ M)) => ((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_real @ J @ K) @ (cons_int @ L @ M)) <= (E @ G @ I @ K @ M)))) <= ((size_size_list_int @ G) = (size_size_list_real @ I)))) => (E @ A @ B @ C @ D)) <= (E @ nil_int @ nil_real @ nil_real @ nil_int))) <= ((size_size_list_real @ B) = (size_size_list_real @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8553_list__induct4)). 87.71/26.55 thf(2115,plain,((! [A:list_int,B:list_real,C:list_real,D:list_int,E:(list_int > (list_real > (list_real > (list_int > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => ((((size_size_list_real @ C) = (size_size_list_int @ D)) => (((! [F:int,G:list_int,H:real,I:list_real,J:real,K:list_real,L:int,M:list_int]: ((((size_size_list_real @ I) = (size_size_list_real @ K)) => (((size_size_list_real @ K) = (size_size_list_int @ M)) => ((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_real @ J @ K) @ (cons_int @ L @ M)) | ~ (E @ G @ I @ K @ M)))) | ~ ((size_size_list_int @ G) = (size_size_list_real @ I)))) => (E @ A @ B @ C @ D)) | ~ (E @ nil_int @ nil_real @ nil_real @ nil_int))) | ~ ((size_size_list_real @ B) = (size_size_list_real @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[84])). 87.71/26.55 thf(1422,axiom,((! [A:int,B:list_int,C:nat,D:int]: (((cons_int @ A @ B) = (replicate_int @ C @ D)) = ((B = (replicate_int @ (minus_minus_nat @ C @ one_one_nat) @ A)) & (ord_less_nat @ zero_zero_nat @ C) & (A = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4779_Cons__replicate__eq)). 87.71/26.55 thf(7421,plain,((! [A:int,B:list_int,C:nat,D:int]: (((cons_int @ A @ B) = (replicate_int @ C @ D)) = ((B = (replicate_int @ (minus_minus_nat @ C @ one_one_nat) @ A)) & (ord_less_nat @ zero_zero_nat @ C) & (A = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1422])). 87.71/26.55 thf(838,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((dvd_dvd_nat @ C @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ (modulo_modulo_nat @ A @ C)) @ (minus_minus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9479_diff__mod__le)). 87.71/26.55 thf(5221,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((dvd_dvd_nat @ C @ B) => (ord_less_eq_nat @ (minus_minus_nat @ A @ (modulo_modulo_nat @ A @ C)) @ (minus_minus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[838])). 87.71/26.55 thf(175,axiom,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: ((if_Pro6206227464963214023at_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T)). 87.71/26.55 thf(2515,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)],[175])). 87.71/26.55 thf(27,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ A @ (suc @ zero_zero_nat)) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9844_and__Suc__0__eq)). 87.71/26.55 thf(1851,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)],[27])). 87.71/26.55 thf(809,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1514_order_Ostrict__trans1)). 87.71/26.55 thf(5098,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[809])). 87.71/26.55 thf(1736,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/sandbox2/benchmark/theBenchmark.p',fact_647_vebt__succ_Osimps_I4_J)). 87.71/26.55 thf(8677,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)],[1736])). 87.71/26.55 thf(320,axiom,((! [A:list_nat,B:nat,C:list_nat]: ((nth_nat @ (append_nat @ A @ (append_nat @ (cons_nat @ B @ nil_nat) @ C)) @ (size_size_list_nat @ A)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8088_concat__inth)). 87.71/26.55 thf(3122,plain,((! [A:list_nat,B:nat,C:list_nat]: ((nth_nat @ (append_nat @ A @ (append_nat @ (cons_nat @ B @ nil_nat) @ C)) @ (size_size_list_nat @ A)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[320])). 87.71/26.55 thf(843,axiom,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:assn]: ((hoare_3067605981109127869le_nat @ (times_times_assn @ A @ D) @ B @ (^ [E:nat]: (times_times_assn @ (C @ E) @ D))) <= (hoare_3067605981109127869le_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_frame__rule)). 87.71/26.55 thf(5238,plain,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:assn]: ((hoare_3067605981109127869le_nat @ (times_times_assn @ A @ D) @ B @ (^ [E:nat]: (times_times_assn @ (C @ E) @ D))) | ~ (hoare_3067605981109127869le_nat @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[843])). 87.71/26.55 thf(1125,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((A @ C) <= (! [D:nat]: ((A @ D) <= (ord_less_nat @ D @ C))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_nat__less__induct)). 87.71/26.55 thf(6335,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)],[1125])). 87.71/26.55 thf(963,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (times_times_nat @ B @ C)) = (power_power_int @ (power_power_int @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7831_power__mult)). 87.71/26.55 thf(5673,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)],[963])). 87.71/26.55 thf(782,axiom,((! [A:assn]: ((sup_sup_assn @ A @ bot_bot_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5054_sup__bot__right)). 87.71/26.55 thf(4974,plain,((! [A:assn]: ((sup_sup_assn @ A @ bot_bot_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[782])). 87.71/26.55 thf(11,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ (suc @ (suc @ (suc @ A))) @ B) = (divide_divide_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9172_Suc__div__eq__add3__div)). 87.71/26.55 thf(1804,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)],[11])). 87.71/26.55 thf(1136,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2047_add__left__cancel)). 87.71/26.55 thf(6375,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)],[1136])). 87.71/26.55 thf(1475,axiom,((! [A:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4590_of__nat__le__0__iff)). 87.71/26.55 thf(7623,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)],[1475])). 87.71/26.55 thf(1166,axiom,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:assn,E:assn]: (((hoare_1429296392585015714_VEBTi @ D @ B @ (^ [F:vEBT_VEBTi]: (times_times_assn @ (C @ F) @ E))) <= (entails @ D @ (times_times_assn @ A @ E))) <= (hoare_1429296392585015714_VEBTi @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4076_fi__rule)). 87.71/26.55 thf(6477,plain,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:assn,E:assn]: ((hoare_1429296392585015714_VEBTi @ D @ B @ (^ [F:vEBT_VEBTi]: (times_times_assn @ (C @ F) @ E))) | ~ (entails @ D @ (times_times_assn @ A @ E)) | ~ (hoare_1429296392585015714_VEBTi @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166])). 87.71/26.55 thf(1678,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/sandbox2/benchmark/theBenchmark.p',fact_2526_vebt__delete_Osimps_I5_J)). 87.71/26.55 thf(8414,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)],[1678])). 87.71/26.55 thf(950,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3013_diff__add__inverse2)). 87.71/26.55 thf(5635,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[950])). 87.71/26.55 thf(381,axiom,((! [A:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ A) => (ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9049_div__2__gt__zero)). 87.71/26.55 thf(3381,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)],[381])). 87.71/26.55 thf(1569,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)) <= (ord_less_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7784_power__increasing__iff)). 87.71/26.55 thf(8041,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)) | ~ (ord_less_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1569])). 87.71/26.55 thf(712,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ C) = (plus_plus_nat @ B @ D)) <= ((A = B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2160_add__mono__thms__linordered__semiring_I4_J)). 87.71/26.55 thf(4693,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)],[712])). 87.71/26.55 thf(894,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ A) = (ord_less_nat @ B @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2135_add__less__same__cancel1)). 87.71/26.55 thf(5428,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)],[894])). 87.71/26.55 thf(1764,axiom,((! [A:nat]: ((A != zero_zero_nat) => (~ (! [B:nat]: (A != (suc @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_list__decode_Ocases)). 87.71/26.55 thf(8768,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (~ (! [B:nat]: ~ (A = (suc @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1764])). 87.71/26.55 thf(415,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ C))) => ((ord_less_eq_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) <= (ord_less_eq_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9055_nat__le__power__trans)). 87.71/26.55 thf(3518,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ C))) => ((ord_less_eq_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ (ord_less_eq_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[415])). 87.71/26.55 thf(513,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3015_diff__cancel2)). 87.71/26.55 thf(3963,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)],[513])). 87.71/26.55 thf(37,axiom,((! [A:$o]: ((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Leaf @ A @ ($true))) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1751_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I3_J)). 87.71/26.55 thf(1878,plain,((! [A:$o]: ((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Leaf @ A @ ($true))) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[37])). 87.71/26.55 thf(383,axiom,((! [A:nat,B:int]: ((size_size_list_int @ (replicate_int @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3262_length__replicate)). 87.71/26.55 thf(3386,plain,((! [A:nat,B:int]: ((size_size_list_int @ (replicate_int @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[383])). 87.71/26.55 thf(219,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ A @ B) @ (binomial @ A @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9042_binomial__maximum)). 87.71/26.55 thf(2726,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)],[219])). 87.71/26.55 thf(1026,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1406_order__less__imp__not__less)). 87.71/26.55 thf(5919,plain,((! [A:nat,B:nat]: (~ (ord_less_nat @ B @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026])). 87.71/26.55 thf(1043,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_less__zeroE)). 87.71/26.55 thf(5978,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043])). 87.71/26.55 thf(1296,axiom,((! [A:option_nat]: ((A != none_nat) = (? [B:nat]: (A = (some_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_not__None__eq)). 87.71/26.55 thf(6941,plain,((! [A:option_nat]: ((~ (A = none_nat)) = (? [B:nat]: (A = (some_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296])). 87.71/26.55 thf(552,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((B != A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1542_dual__order_Ostrict__iff__order)). 87.71/26.55 thf(4095,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (B = A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[552])). 87.71/26.55 thf(319,axiom,((! [A:int,B:list_int,C:nat]: ((nth_int @ (cons_int @ A @ B) @ (suc @ C)) = (nth_int @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4570_length__nth__simps_I4_J)). 87.71/26.55 thf(3119,plain,((! [A:int,B:list_int,C:nat]: ((nth_int @ (cons_int @ A @ B) @ (suc @ C)) = (nth_int @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[319])). 87.71/26.55 thf(474,axiom,((! [A:nat]: ? [B:list_nat]: ((size_size_list_nat @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2549_Ex__list__of__length)). 87.71/26.55 thf(3746,plain,((! [A:nat]: ? [B:list_nat]: ((size_size_list_nat @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[474])). 87.71/26.55 thf(1208,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1819_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I4_J)). 87.71/26.55 thf(6624,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208])). 87.71/26.55 thf(1717,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_822_vebt__pred_Osimps_I6_J)). 87.71/26.55 thf(8567,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)],[1717])). 87.71/26.55 thf(1362,axiom,((! [A:assn,B:assn]: (entails @ A @ (sup_sup_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5117_ent__disjI2__direct)). 87.71/26.55 thf(7204,plain,((! [A:assn,B:assn]: (entails @ A @ (sup_sup_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362])). 87.71/26.55 thf(1368,axiom,((! [A:assn,B:nat,C:nat]: ((power_power_assn @ A @ (plus_plus_nat @ B @ C)) = (times_times_assn @ (power_power_assn @ A @ B) @ (power_power_assn @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7893_power__add)). 87.71/26.55 thf(7222,plain,((! [A:assn,B:nat,C:nat]: ((power_power_assn @ A @ (plus_plus_nat @ B @ C)) = (times_times_assn @ (power_power_assn @ A @ B) @ (power_power_assn @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368])). 87.71/26.55 thf(1432,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_nat__mult__less__cancel1)). 87.71/26.55 thf(7468,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (ord_less_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1432])). 87.71/26.55 thf(1515,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2401_add__less__le__mono)). 87.71/26.55 thf(7809,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1515])). 87.71/26.55 thf(396,axiom,((! [A:list_real,B:list_o,C:list_nat,D:(list_real > (list_o > (list_nat > $o)))]: (((size_size_list_real @ A) = (size_size_list_o @ B)) => (((size_size_list_o @ B) = (size_size_list_nat @ C)) => ((D @ nil_real @ nil_o @ nil_nat) => ((! [E:real,F:list_real,G:$o,H:list_o,I:nat,J:list_nat]: ((((D @ (cons_real @ E @ F) @ (cons_o @ G @ H) @ (cons_nat @ I @ J)) <= (D @ F @ H @ J)) <= ((size_size_list_o @ H) = (size_size_list_nat @ J))) <= ((size_size_list_real @ F) = (size_size_list_o @ H)))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8546_list__induct3)). 87.71/26.55 thf(3440,plain,((! [A:list_real,B:list_o,C:list_nat,D:(list_real > (list_o > (list_nat > $o)))]: (((size_size_list_real @ A) = (size_size_list_o @ B)) => (((size_size_list_o @ B) = (size_size_list_nat @ C)) => ((D @ nil_real @ nil_o @ nil_nat) => ((! [E:real,F:list_real,G:$o,H:list_o,I:nat,J:list_nat]: ((D @ (cons_real @ E @ F) @ (cons_o @ G @ H) @ (cons_nat @ I @ J)) | ~ (D @ F @ H @ J) | ~ ((size_size_list_o @ H) = (size_size_list_nat @ J)) | ~ ((size_size_list_real @ F) = (size_size_list_o @ H)))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[396])). 87.71/26.55 thf(586,axiom,((! [A:assn]: ((inf_inf_assn @ A @ top_top_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10153_norm__assertion__simps_I4_J)). 87.71/26.55 thf(4219,plain,((! [A:assn]: ((inf_inf_assn @ A @ top_top_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[586])). 87.71/26.55 thf(914,axiom,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4722_of__nat__gt__0)). 87.71/26.55 thf(5497,plain,((! [A:nat]: ((~ ((semiri1316708129612266289at_nat @ A) = zero_zero_nat)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[914])). 87.71/26.55 thf(291,axiom,((! [A:nat]: ((ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = ((A = (suc @ zero_zero_nat)) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9034_less__2__cases__iff)). 87.71/26.55 thf(3001,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)],[291])). 87.71/26.55 thf(1036,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) <= (~ (ord_less_nat @ A @ B))) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1311_linorder__neqE)). 87.71/26.55 thf(5951,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B) | (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036])). 87.71/26.55 thf(605,axiom,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2781_cancel__comm__monoid__add__class_Odiff__cancel)). 87.71/26.55 thf(4301,plain,((! [A:nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[605])). 87.71/26.55 thf(794,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ (times_times_nat @ A @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_le__cube)). 87.71/26.55 thf(5031,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)],[794])). 87.71/26.55 thf(812,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_vebt_maxt @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_802_vebt__maxt_Osimps_I2_J)). 87.71/26.55 thf(5107,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)],[812])). 87.71/26.55 thf(720,axiom,((! [A:option_nat,B:nat]: ((A != none_nat) <= (A = (some_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_option_OdiscI)). 87.71/26.55 thf(4721,plain,((! [A:option_nat,B:nat]: (~ (A = none_nat) | ~ (A = (some_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[720])). 87.71/26.55 thf(256,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: (((ord_less_eq_nat @ (vEBT_T_d_e_l_e_t_e @ A @ C) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit0 @ one))))) <= (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ A @ C))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9134_minNull__delete__time__bound)). 87.71/26.55 thf(2868,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_d_e_l_e_t_e @ A @ C) @ (numeral_numeral_nat @ (bit1 @ (bit0 @ (bit0 @ one))))) | ~ (vEBT_VEBT_minNull @ (vEBT_vebt_delete @ A @ C)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[256])). 87.71/26.55 thf(1115,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (~ (? [D:nat]: (~ (A @ D) & (B = (plus_plus_nat @ C @ D))) | (~ (A @ zero_zero_nat) & (ord_less_nat @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3144_nat__diff__split__asm)). 87.71/26.55 thf(6304,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) = (~ (? [D:nat]: (~ (A @ D) & (B = (plus_plus_nat @ C @ D))) | (~ (A @ zero_zero_nat) & (ord_less_nat @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115])). 87.71/26.55 thf(703,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_mult__le__mono1)). 87.71/26.55 thf(4648,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[703])). 87.71/26.55 thf(136,axiom,((! [A:nat,B:int]: ((nil_int = (replicate_int @ A @ B)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8171_empty__replicate)). 87.71/26.55 thf(2349,plain,((! [A:nat,B:int]: ((nil_int = (replicate_int @ A @ B)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[136])). 87.71/26.55 thf(1143,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/sandbox2/benchmark/theBenchmark.p',fact_7851_zero__le__power)). 87.71/26.55 thf(6395,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)],[1143])). 87.71/26.55 thf(1514,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1624_order__less__le__trans)). 87.71/26.55 thf(7806,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)],[1514])). 87.71/26.55 thf(1392,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_T_m_i_n_t @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2522_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I3_J)). 87.71/26.55 thf(7293,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((vEBT_T_m_i_n_t @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392])). 87.71/26.55 thf(1068,axiom,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option_num > $o)),C:option_num]: ((((B @ A @ C) <= (! [D:product_prod_nat_nat,E:num]: (((C = (some_num @ E)) => (B @ A @ C)) <= (A = (some_P7363390416028606310at_nat @ D))))) <= ((C = none_num) => (B @ A @ C))) <= ((B @ A @ C) <= (A = none_P5556105721700978146at_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_combine__options__cases)). 87.71/26.55 thf(6065,plain,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option_num > $o)),C:option_num]: ((B @ A @ C) | ~ (! [D:product_prod_nat_nat,E:num]: (((C = (some_num @ E)) => (B @ A @ C)) | ~ (A = (some_P7363390416028606310at_nat @ D)))) | ~ ((C = none_num) => (B @ A @ C)) | ~ ((B @ A @ C) | ~ (A = none_P5556105721700978146at_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068])). 87.71/26.55 thf(159,axiom,((! [A:nat,B:list_nat,C:nat]: ((nth_nat @ (cons_nat @ A @ B) @ (suc @ C)) = (nth_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4565_nth__Cons__Suc)). 87.71/26.55 thf(2460,plain,((! [A:nat,B:list_nat,C:nat]: ((nth_nat @ (cons_nat @ A @ B) @ (suc @ C)) = (nth_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[159])). 87.71/26.55 thf(1610,axiom,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: (((some_P7363390416028606310at_nat @ A) = (some_P7363390416028606310at_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_option_Oinject)). 87.71/26.55 thf(8176,plain,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: (((some_P7363390416028606310at_nat @ A) = (some_P7363390416028606310at_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1610])). 87.71/26.55 thf(1586,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_813_vebt__pred_Osimps_I5_J)). 87.71/26.55 thf(8105,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1586])). 87.71/26.55 thf(805,axiom,((! [A:$o,B:$o]: ((vEBT_T_p_r_e_d2 @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1822_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I2_J)). 87.71/26.55 thf(5075,plain,((! [A:$o,B:$o]: ((vEBT_T_p_r_e_d2 @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[805])). 87.71/26.55 thf(1302,axiom,((! [A:assn]: ((inf_inf_assn @ top_top_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10154_norm__assertion__simps_I3_J)). 87.71/26.55 thf(6967,plain,((! [A:assn]: ((inf_inf_assn @ top_top_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302])). 87.71/26.55 thf(1002,axiom,((! [A:list_real,B:list_real]: ((A != B) <= ((size_size_list_real @ A) != (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_size__neq__size__imp__neq)). 87.71/26.55 thf(5818,plain,((! [A:list_real,B:list_real]: (~ (A = B) | ((size_size_list_real @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002])). 87.71/26.55 thf(503,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/sandbox2/benchmark/theBenchmark.p',fact_3108_Nat_Ole__imp__diff__is__add)). 87.71/26.55 thf(3922,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)],[503])). 87.71/26.55 thf(390,axiom,((! [A:list_int,B:list_real,C:list_o,D:list_o,E:(list_int > (list_real > (list_o > (list_o > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => (((size_size_list_real @ B) = (size_size_list_o @ C)) => ((((E @ A @ B @ C @ D) <= (! [F:int,G:list_int,H:real,I:list_real,J:$o,K:list_o,L:$o,M:list_o]: (((size_size_list_int @ G) = (size_size_list_real @ I)) => (((size_size_list_real @ I) = (size_size_list_o @ K)) => (((size_size_list_o @ K) = (size_size_list_o @ M)) => ((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_o @ J @ K) @ (cons_o @ L @ M)) <= (E @ G @ I @ K @ M))))))) <= (E @ nil_int @ nil_real @ nil_o @ nil_o)) <= ((size_size_list_o @ C) = (size_size_list_o @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8555_list__induct4)). 87.71/26.55 thf(3407,plain,((! [A:list_int,B:list_real,C:list_o,D:list_o,E:(list_int > (list_real > (list_o > (list_o > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => (((size_size_list_real @ B) = (size_size_list_o @ C)) => ((E @ A @ B @ C @ D) | ~ (! [F:int,G:list_int,H:real,I:list_real,J:$o,K:list_o,L:$o,M:list_o]: (((size_size_list_int @ G) = (size_size_list_real @ I)) => (((size_size_list_real @ I) = (size_size_list_o @ K)) => (((size_size_list_o @ K) = (size_size_list_o @ M)) => ((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_o @ J @ K) @ (cons_o @ L @ M)) | ~ (E @ G @ I @ K @ M)))))) | ~ (E @ nil_int @ nil_real @ nil_o @ nil_o) | ~ ((size_size_list_o @ C) = (size_size_list_o @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[390])). 87.71/26.55 thf(971,axiom,((! [A:$o,B:assn,C:heap_Time_Heap_o,D:($o > assn),E:heap_Time_Heap_o,F:($o > assn),G:($o > assn)]: (((hoare_hoare_triple_o @ B @ C @ D) <= (A)) => (((hoare_hoare_triple_o @ B @ (if_Heap_Time_Heap_o @ A @ C @ E) @ G) <= (! [H:$o]: (entails @ (sup_sup_assn @ (times_times_assn @ (D @ H) @ (pure_assn @ A)) @ (times_times_assn @ (F @ H) @ (pure_assn @ (~ (A))))) @ (G @ H)))) <= ((hoare_hoare_triple_o @ B @ E @ F) <= (~ (A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5138_if__rule__split)). 87.71/26.55 thf(5705,plain,((! [A:$o,B:assn,C:heap_Time_Heap_o,D:($o > assn),E:heap_Time_Heap_o,F:($o > assn),G:($o > assn)]: (((hoare_hoare_triple_o @ B @ C @ (D)) | ~ (A)) => ((hoare_hoare_triple_o @ B @ (if_Heap_Time_Heap_o @ A @ C @ E) @ (G)) | ~ (! [H:$o]: (entails @ (sup_sup_assn @ (times_times_assn @ (D @ H) @ (pure_assn @ A)) @ (times_times_assn @ (F @ H) @ (pure_assn @ (~ (A))))) @ (G @ H))) | ~ ((hoare_hoare_triple_o @ B @ E @ (F)) | (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[971])). 87.71/26.55 thf(955,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_mult__zero__right)). 87.71/26.55 thf(5651,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[955])). 87.71/26.55 thf(342,axiom,((! [A:$o]: ((A = ($false)) | (A = ($true))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T)). 87.71/26.55 thf(3210,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[342])). 87.71/26.55 thf(992,axiom,((! [A:heap_Time_Heap_nat,B:(nat > assn)]: (hoare_3067605981109127869le_nat @ bot_bot_assn @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_975_false__rule)). 87.71/26.55 thf(5791,plain,((! [A:heap_Time_Heap_nat,B:(nat > assn)]: (hoare_3067605981109127869le_nat @ bot_bot_assn @ A @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[992])). 87.71/26.55 thf(467,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((modulo_modulo_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8688_mod__less)). 87.71/26.55 thf(3714,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((modulo_modulo_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[467])). 87.71/26.55 thf(608,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ A @ B)) => (ord_less_nat @ B @ A)) <= (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_linorder__neqE__nat)). 87.71/26.55 thf(4315,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)],[608])). 87.71/26.55 thf(294,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/sandbox2/benchmark/theBenchmark.p',fact_2663_nth__equalityI)). 87.71/26.55 thf(3010,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)],[294])). 87.71/26.55 thf(157,axiom,((modulo_modulo_nat = (^ [A:nat,B:nat]: (if_nat @ (ord_less_nat @ A @ B) @ A @ (modulo_modulo_nat @ (minus_minus_nat @ A @ B) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8719_mod__if)). 87.71/26.55 thf(2455,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)],[157])). 87.71/26.55 thf(677,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/sandbox2/benchmark/theBenchmark.p',fact_230_Ex__less__Suc)). 87.71/26.55 thf(4545,plain,((! [A:nat,B:(nat > $o)]: ((? [C:nat]: ((ord_less_nat @ C @ (suc @ A)) & (B @ C))) = (? [C:nat]: ((B @ C) & (ord_less_nat @ C @ A)) | (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[677])). 87.71/26.55 thf(873,axiom,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => ((A != (vEBT_Leaf @ ($false) @ ($false))) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2477_VEBT__internal_OminNull_Oelims_I2_J)). 87.71/26.55 thf(5337,plain,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) => ((~ (A = (vEBT_Leaf @ ($false) @ ($false)))) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[873])). 87.71/26.55 thf(106,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/sandbox2/benchmark/theBenchmark.p',fact_9444_odd__Suc__div__two)). 87.71/26.55 thf(2196,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)],[106])). 87.71/26.55 thf(116,axiom,((! [A:list_nat,B:list_nat]: ((size_size_list_nat @ (append_nat @ A @ B)) = (plus_plus_nat @ (size_size_list_nat @ A) @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8155_length__append)). 87.71/26.55 thf(2240,plain,((! [A:list_nat,B:list_nat]: ((size_size_list_nat @ (append_nat @ A @ B)) = (plus_plus_nat @ (size_size_list_nat @ A) @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[116])). 87.71/26.55 thf(1571,axiom,((! [A:nat,B:nat]: (ord_less_nat @ (minus_minus_nat @ A @ B) @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3095_diff__less__Suc)). 87.71/26.55 thf(8053,plain,((! [A:nat,B:nat]: (ord_less_nat @ (minus_minus_nat @ A @ B) @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1571])). 87.71/26.55 thf(1087,axiom,((! [A:(int > nat),B:int,C:int,D:list_int]: ((((linord737317855127579385nt_nat @ A @ B @ (cons_int @ C @ D)) = (cons_int @ B @ (cons_int @ C @ D))) <= (ord_less_eq_nat @ (A @ B) @ (A @ C))) & ((~ (ord_less_eq_nat @ (A @ B) @ (A @ C))) => ((linord737317855127579385nt_nat @ A @ B @ (cons_int @ C @ D)) = (cons_int @ C @ (linord737317855127579385nt_nat @ A @ B @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5663_insort__key_Osimps_I2_J)). 87.71/26.55 thf(6164,plain,((! [A:(int > nat),B:int,C:int,D:list_int]: ((((linord737317855127579385nt_nat @ (A) @ B @ (cons_int @ C @ D)) = (cons_int @ B @ (cons_int @ C @ D))) | ~ (ord_less_eq_nat @ (A @ B) @ (A @ C))) & ((~ (ord_less_eq_nat @ (A @ B) @ (A @ C))) => ((linord737317855127579385nt_nat @ (A) @ B @ (cons_int @ C @ D)) = (cons_int @ C @ (linord737317855127579385nt_nat @ (A) @ B @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087])). 87.71/26.55 thf(1637,axiom,((! [A:int]: ((bit_se8568078237143864401it_int @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10102_drop__bit__int__code_I1_J)). 87.71/26.55 thf(8275,plain,((! [A:int]: ((bit_se8568078237143864401it_int @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1637])). 87.71/26.55 thf(1210,axiom,((! [A:nat,B:nat]: ((B = zero_zero_nat) <= ((plus_plus_nat @ A @ B) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2313_add__eq__self__zero)). 87.71/26.55 thf(6630,plain,((! [A:nat,B:nat]: ((B = zero_zero_nat) | ~ ((plus_plus_nat @ A @ B) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210])). 87.71/26.55 thf(54,axiom,((! [A:num,B:num]: ((bit0 @ A) != (bit1 @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9128_semiring__norm_I88_J)). 87.71/26.55 thf(1937,plain,((! [A:num,B:num]: ~ ((bit0 @ A) = (bit1 @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[54])). 87.71/26.55 thf(1031,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8705_mod__less__eq__dividend)). 87.71/26.55 thf(5932,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031])). 87.71/26.55 thf(470,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2243_add__le__imp__le__left)). 87.71/26.55 thf(3723,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)],[470])). 87.71/26.55 thf(444,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ A) <= (ord_less_nat @ zero_zero_nat @ B)) <= (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_zero__less__mult__pos2)). 87.71/26.55 thf(3643,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[444])). 87.71/26.55 thf(642,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_eq_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2125_le__add__same__cancel2)). 87.71/26.55 thf(4444,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)],[642])). 87.71/26.55 thf(1023,axiom,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8875_binomial__eq__0)). 87.71/26.55 thf(5905,plain,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023])). 87.71/26.55 thf(40,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9843_and__nat__numerals_I2_J)). 87.71/26.55 thf(1889,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)],[40])). 87.71/26.55 thf(284,axiom,((! [A:num,B:nat]: (((numeral_numeral_nat @ A) = (suc @ B)) = ((pred_numeral @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9912_eq__numeral__Suc)). 87.71/26.55 thf(2978,plain,((! [A:num,B:nat]: (((numeral_numeral_nat @ A) = (suc @ B)) = ((pred_numeral @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[284])). 87.71/26.55 thf(696,axiom,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_mult__0__right)). 87.71/26.55 thf(4621,plain,((! [A:nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[696])). 87.71/26.55 thf(883,axiom,((! [A:nat,B:nat]: (((ord_min_nat @ B @ (suc @ A)) = (suc @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10136_min__Suc__gt_I2_J)). 87.71/26.55 thf(5387,plain,((! [A:nat,B:nat]: (((ord_min_nat @ B @ (suc @ A)) = (suc @ A)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[883])). 87.71/26.55 thf(1604,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((size_size_VEBT_VEBT @ (vEBT_Node @ A @ B @ C @ D)) = (plus_plus_nat @ (plus_plus_nat @ (size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ C) @ (size_size_VEBT_VEBT @ D)) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2625_VEBT_Osize_I3_J)). 87.71/26.55 thf(8159,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((size_size_VEBT_VEBT @ (vEBT_Node @ A @ B @ C @ D)) = (plus_plus_nat @ (plus_plus_nat @ (size_list_VEBT_VEBT @ (size_size_VEBT_VEBT) @ C) @ (size_size_VEBT_VEBT @ D)) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1604])). 87.71/26.55 thf(421,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ C @ B)) = ((B = zero_zero_nat) | (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_mult__cancel2)). 87.71/26.55 thf(3541,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)],[421])). 87.71/26.55 thf(117,axiom,((! [A:nat,B:(nat > (nat > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:nat]: (B @ C @ D)))) = (? [C:list_nat]: (((size_size_list_nat @ C) = A) & ! [D:nat]: ((B @ D @ (nth_nat @ C @ D)) <= (ord_less_nat @ D @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2656_Skolem__list__nth)). 87.71/26.55 thf(2243,plain,((! [A:nat,B:(nat > (nat > $o))]: ((! [C:nat]: ((ord_less_nat @ C @ A) => (? [D:nat]: (B @ C @ D)))) = (? [C:list_nat]: (((size_size_list_nat @ C) = A) & ! [D:nat]: ((B @ D @ (nth_nat @ C @ D)) | ~ (ord_less_nat @ D @ A))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[117])). 87.71/26.55 thf(1334,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_eq_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2393_add__mono__thms__linordered__field_I3_J)). 87.71/26.55 thf(7069,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)],[1334])). 87.71/26.55 thf(1439,axiom,((! [A:nat,B:nat]: ((zero_zero_nat = (plus_plus_nat @ A @ B)) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2083_zero__eq__add__iff__both__eq__0)). 87.71/26.55 thf(7495,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)],[1439])). 87.71/26.55 thf(769,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2233_add__left__mono)). 87.71/26.55 thf(4934,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[769])). 87.71/26.55 thf(1615,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = (suc @ zero_zero_nat)) = ((A = (suc @ zero_zero_nat)) & (B = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_mult__eq__1__iff)). 87.71/26.55 thf(8191,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)],[1615])). 87.71/26.55 thf(1682,axiom,((! [A:$o,B:$o]: ((times_times_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((B) & (A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_merge__pure__star)). 87.71/26.55 thf(8425,plain,((! [A:$o,B:$o]: ((times_times_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((B) & (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1682])). 87.71/26.55 thf(568,axiom,((! [A:nat,B:nat]: (((A = zero_zero_nat) | (B = one_one_nat)) <= (A = (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1086_mult__eq__self__implies__10)). 87.71/26.55 thf(4152,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)],[568])). 87.71/26.55 thf(1093,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ zero_zero_nat @ B)) <= (dvd_dvd_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9465_dvd__imp__le)). 87.71/26.55 thf(6186,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ zero_zero_nat @ B) | ~ (dvd_dvd_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093])). 87.71/26.55 thf(310,axiom,((! [A:real]: ((^ [B:real]: (times_times_real @ B @ A)) = (times_times_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5685_mult__commute__abs)). 87.71/26.55 thf(3083,plain,((! [A:real]: ((^ [B:real]: (times_times_real @ B @ A)) = (times_times_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[310])). 87.71/26.55 thf(620,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_mult__less__cancel2)). 87.71/26.55 thf(4361,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) & (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[620])). 87.71/26.55 thf(18,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9842_and__nat__numerals_I4_J)). 87.71/26.55 thf(1825,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)],[18])). 87.71/26.55 thf(171,axiom,((! [A:nat,B:list_nat]: ((size_size_list_nat @ (drop_nat @ A @ B)) = (minus_minus_nat @ (size_size_list_nat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7729_length__drop)). 87.71/26.55 thf(2504,plain,((! [A:nat,B:list_nat]: ((size_size_list_nat @ (drop_nat @ A @ B)) = (minus_minus_nat @ (size_size_list_nat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[171])). 87.71/26.55 thf(1725,axiom,((! [A:$o,B:$o]: ((inf_inf_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((A) & (B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8905_merge__pure__and)). 87.71/26.55 thf(8599,plain,((! [A:$o,B:$o]: ((inf_inf_assn @ (pure_assn @ A) @ (pure_assn @ B)) = (pure_assn @ ((A) & (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1725])). 87.71/26.55 thf(853,axiom,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:nat]: ((hoare_1429296392585015714_VEBTi @ A @ B @ C) <= (time_htt_VEBT_VEBTi @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1808_htt__htD)). 87.71/26.55 thf(5273,plain,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:nat]: ((hoare_1429296392585015714_VEBTi @ A @ B @ (C)) | ~ (time_htt_VEBT_VEBTi @ A @ B @ (C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[853])). 87.71/26.55 thf(743,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_vebt_member @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_803_vebt__member_Osimps_I2_J)). 87.71/26.55 thf(4846,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)],[743])). 87.71/26.55 thf(1690,axiom,((! [A:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),B:product_prod_nat_nat,C:product_prod_nat_nat]: ((vEBT_V1502963449132264192at_nat @ A @ (some_P7363390416028606310at_nat @ B) @ (some_P7363390416028606310at_nat @ C)) = (some_P7363390416028606310at_nat @ (A @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_825_VEBT__internal_Ooption__shift_Osimps_I3_J)). 87.71/26.55 thf(8458,plain,((! [A:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),B:product_prod_nat_nat,C:product_prod_nat_nat]: ((vEBT_V1502963449132264192at_nat @ (A) @ (some_P7363390416028606310at_nat @ B) @ (some_P7363390416028606310at_nat @ C)) = (some_P7363390416028606310at_nat @ (A @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1690])). 87.71/26.55 thf(1546,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3101_add__diff__inverse__nat)). 87.71/26.55 thf(7948,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)],[1546])). 87.71/26.55 thf(407,axiom,((! [A:list_real,B:nat]: (((size_size_list_real @ A) = (suc @ B)) = (? [C:real,D:list_real]: ((A = (cons_real @ C @ D)) & ((size_size_list_real @ D) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4671_length__Suc__conv)). 87.71/26.55 thf(3486,plain,((! [A:list_real,B:nat]: (((size_size_list_real @ A) = (suc @ B)) = (? [C:real,D:list_real]: ((A = (cons_real @ C @ D)) & ((size_size_list_real @ D) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[407])). 87.71/26.55 thf(448,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ A @ D) @ C) @ (times_times_nat @ B @ D)) <= (ord_less_nat @ C @ D)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2426_mlex__bound)). 87.71/26.55 thf(3654,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ A @ D) @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_nat @ C @ D) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[448])). 87.71/26.55 thf(1449,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_not__less__eq)). 87.71/26.55 thf(7544,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_nat @ B @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1449])). 87.71/26.55 thf(1660,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => ((~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ C) @ D @ E) @ F)))) <= (! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_869_VEBT__internal_Onaive__member_Ocases)). 87.71/26.55 thf(8351,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => (~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ (suc @ C) @ D @ E) @ F))) | ~ (! [B:option4927543243414619207at_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ zero_zero_nat @ C @ D) @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1660])). 87.71/26.55 thf(484,axiom,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn)]: ((hoare_hoare_triple_o @ A @ B @ C) <= (hoare_hoare_triple_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_is__hoare__triple)). 87.71/26.55 thf(3787,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[484])). 87.71/26.55 thf(167,axiom,((! [A:list_o]: ((slice_o @ zero_zero_nat @ (size_size_list_o @ A) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3283_slice__complete)). 87.71/26.55 thf(2487,plain,((! [A:list_o]: ((slice_o @ zero_zero_nat @ (size_size_list_o @ A) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[167])). 87.71/26.55 thf(1318,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ (suc @ B)) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8713_mod__Suc__le__divisor)). 87.71/26.55 thf(7014,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (modulo_modulo_nat @ A @ (suc @ B)) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318])). 87.71/26.55 thf(304,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (ord_less_nat @ (binomial @ B @ A) @ (binomial @ B @ (suc @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9056_binomial__less__binomial__Suc)). 87.71/26.55 thf(3059,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) => (ord_less_nat @ (binomial @ B @ A) @ (binomial @ B @ (suc @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[304])). 87.71/26.55 thf(1124,axiom,((! [A:vEBT_VEBT]: ((! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A != (vEBT_Node @ B @ C @ D @ E))) => (~ (! [B:$o,C:$o]: (A != (vEBT_Leaf @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_VEBT_Oexhaust)). 87.71/26.55 thf(6331,plain,((! [A:vEBT_VEBT]: ((! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ~ (A = (vEBT_Node @ B @ C @ D @ E))) => (~ (! [B:$o,C:$o]: ~ (A = (vEBT_Leaf @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124])). 87.71/26.55 thf(91,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/sandbox2/benchmark/theBenchmark.p',fact_9485_odd__mod__4__div__2)). 87.71/26.55 thf(2153,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)],[91])). 87.71/26.55 thf(20,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9948_xor__nat__numerals_I3_J)). 87.71/26.55 thf(1831,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)],[20])). 87.71/26.55 thf(842,axiom,((! [A:nat,B:int,C:list_int]: (((nth_int @ (cons_int @ B @ C) @ A) = (nth_int @ C @ (minus_minus_nat @ A @ one_one_nat))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4616_nth__Cons__pos)). 87.71/26.55 thf(5234,plain,((! [A:nat,B:int,C:list_int]: (((nth_int @ (cons_int @ B @ C) @ A) = (nth_int @ C @ (minus_minus_nat @ A @ one_one_nat))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[842])). 87.71/26.55 thf(1021,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((~ (ord_less_nat @ A @ B)) = (A = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1481_antisym__conv2)). 87.71/26.55 thf(5900,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)],[1021])). 87.71/26.55 thf(1643,axiom,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ A @ (times_times_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_mult_Oassoc)). 87.71/26.55 thf(8294,plain,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ A @ (times_times_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1643])). 87.71/26.55 thf(655,axiom,((! [A:list_nat,B:nat]: (((size_size_list_nat @ A) = (suc @ B)) = (? [C:nat,D:list_nat]: (((size_size_list_nat @ D) = B) & (A = (cons_nat @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4673_length__Suc__conv)). 87.71/26.55 thf(4482,plain,((! [A:list_nat,B:nat]: (((size_size_list_nat @ A) = (suc @ B)) = (? [C:nat,D:list_nat]: (((size_size_list_nat @ D) = B) & (A = (cons_nat @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[655])). 87.71/26.55 thf(52,axiom,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:nat]: (((time_htt_o @ A @ B @ C @ D) <= (time_TBOUND_o @ B @ D)) <= (hoare_hoare_triple_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1865_httI__TBOUND)). 87.71/26.55 thf(1932,plain,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:nat]: ((time_htt_o @ A @ B @ (C) @ D) | ~ (time_TBOUND_o @ B @ D) | ~ (hoare_hoare_triple_o @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[52])). 87.71/26.55 thf(1466,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) <= (ord_less_nat @ B @ zero_zero_nat)) <= (ord_less_eq_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2456_add__nonpos__neg)). 87.71/26.55 thf(7597,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_nat @ B @ zero_zero_nat) | ~ (ord_less_eq_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1466])). 87.71/26.55 thf(1755,axiom,((! [A:(product_prod_nat_nat > nat),B:product_prod_nat_nat]: ((size_o8335143837870341156at_nat @ A @ (some_P7363390416028606310at_nat @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2487_option_Osize__gen_I2_J)). 87.71/26.55 thf(8732,plain,((! [A:(product_prod_nat_nat > nat),B:product_prod_nat_nat]: ((size_o8335143837870341156at_nat @ (A) @ (some_P7363390416028606310at_nat @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1755])). 87.71/26.55 thf(57,axiom,((! [A:$o]: ((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Leaf @ ($true) @ A)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1752_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I2_J)). 87.71/26.55 thf(1947,plain,((! [A:$o]: ((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Leaf @ ($true) @ A)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[57])). 87.71/26.55 thf(559,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => ((ord_less_nat @ one_one_nat @ A) => (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9476_power__dvd__imp__le)). 87.71/26.55 thf(4120,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) => ((ord_less_nat @ one_one_nat @ A) => (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[559])). 87.71/26.55 thf(1323,axiom,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:nat,E:assn,F:($o > assn),G:nat]: (((entails @ E @ A) => ((! [H:$o]: (entails @ (C @ H) @ (F @ H))) => ((time_htt_o @ E @ B @ F @ G) <= (ord_less_eq_nat @ D @ G)))) <= (time_htt_o @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4080_htt__cons__rule)). 87.71/26.55 thf(7027,plain,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:nat,E:assn,F:($o > assn),G:nat]: (((entails @ E @ A) => ((! [H:$o]: (entails @ (C @ H) @ (F @ H))) => ((time_htt_o @ E @ B @ (F) @ G) | ~ (ord_less_eq_nat @ D @ G)))) | ~ (time_htt_o @ A @ B @ (C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323])). 87.71/26.55 thf(1472,axiom,((! [A:(vEBT_VEBT > nat),B:vEBT_VEBT,C:list_VEBT_VEBT]: ((size_list_VEBT_VEBT @ A @ (cons_VEBT_VEBT @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (A @ B) @ (size_list_VEBT_VEBT @ A @ C)) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4766_list_Osize__gen_I2_J)). 87.71/26.55 thf(7614,plain,((! [A:(vEBT_VEBT > nat),B:vEBT_VEBT,C:list_VEBT_VEBT]: ((size_list_VEBT_VEBT @ (A) @ (cons_VEBT_VEBT @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (A @ B) @ (size_list_VEBT_VEBT @ (A) @ C)) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1472])). 87.71/26.55 thf(318,axiom,((! [A:nat,B:nat,C:nat]: (((upt @ A @ (plus_plus_nat @ B @ C)) = (append_nat @ (upt @ A @ B) @ (upt @ B @ (plus_plus_nat @ B @ C)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8850_upt__add__eq__append)). 87.71/26.55 thf(3115,plain,((! [A:nat,B:nat,C:nat]: (((upt @ A @ (plus_plus_nat @ B @ C)) = (append_nat @ (upt @ A @ B) @ (upt @ B @ (plus_plus_nat @ B @ C)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[318])). 87.71/26.55 thf(478,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (power_power_nat @ A @ B)) <= (ord_less_eq_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7963_nat__one__le__power)). 87.71/26.55 thf(3760,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (power_power_nat @ A @ B)) | ~ (ord_less_eq_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[478])). 87.71/26.55 thf(1689,axiom,((! [A:vEBT_VEBT,B:nat]: ((? [C:option4927543243414619207at_nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ C @ (suc @ (suc @ B)) @ D @ E))) <= (vEBT_invar_vebt @ A @ (suc @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_deg__SUcn__Node)). 87.71/26.55 thf(8455,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)],[1689])). 87.71/26.55 thf(1766,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1810_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I5_J)). 87.71/26.55 thf(8775,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1766])). 87.71/26.55 thf(1582,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1811_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I6_J)). 87.71/26.55 thf(8090,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1582])). 87.71/26.55 thf(996,axiom,((! [A:assn,B:assn]: (((sup_sup_assn @ A @ B) = bot_bot_assn) = ((A = bot_bot_assn) & (B = bot_bot_assn))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5069_sup__bot_Oeq__neutr__iff)). 87.71/26.55 thf(5801,plain,((! [A:assn,B:assn]: (((sup_sup_assn @ A @ B) = bot_bot_assn) = ((A = bot_bot_assn) & (B = bot_bot_assn))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[996])). 87.71/26.55 thf(775,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2306_combine__common__factor)). 87.71/26.55 thf(4953,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)],[775])). 87.71/26.55 thf(792,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (time_htt_o @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_VEBT_minNulli @ B) @ (^ [C:$o]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_VEBT_minNull @ A))))) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2053_minNrulli__ruleT)). 87.71/26.55 thf(5026,plain,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (time_htt_o @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_VEBT_minNulli @ B) @ (^ [C:$o]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_VEBT_minNull @ A))))) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[792])). 87.71/26.55 thf(543,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => (((ord_less_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 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_mult__strict__mono_H)). 87.71/26.55 thf(4069,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C @ D) => ((ord_less_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 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[543])). 87.71/26.55 thf(549,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2080_add__cancel__right__right)). 87.71/26.55 thf(4086,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[549])). 87.71/26.55 thf(1104,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1119_order_Otrans)). 87.71/26.55 thf(6224,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104])). 87.71/26.55 thf(1309,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_m_e_m_b_e_r2 @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2493_member__bound__height_H)). 87.71/26.55 thf(6988,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_m_e_m_b_e_r2 @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309])). 87.71/26.55 thf(230,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/sandbox2/benchmark/theBenchmark.p',fact_2595_both__member__options__equiv__member)). 87.71/26.55 thf(2756,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)],[230])). 87.71/26.55 thf(866,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_less__trans__Suc)). 87.71/26.55 thf(5310,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (suc @ A) @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[866])). 87.71/26.55 thf(1727,axiom,((! [A:list_nat]: ((foldl_nat_nat @ (^ [B:nat,C:nat]: (suc @ B)) @ zero_zero_nat @ A) = (size_size_list_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4586_foldl__length)). 87.71/26.55 thf(8614,plain,((! [A:list_nat]: ((foldl_nat_nat @ (^ [B:nat,C:nat]: (suc @ B)) @ zero_zero_nat @ A) = (size_size_list_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1727])). 87.71/26.55 thf(547,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (power_power_nat @ A @ B)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7962_power__gt__expt)). 87.71/26.55 thf(4081,plain,((! [A:nat,B:nat]: ((ord_less_nat @ B @ (power_power_nat @ A @ B)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[547])). 87.71/26.55 thf(332,axiom,(((size_size_list_int @ nil_int) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8525_length__nth__simps_I1_J)). 87.71/26.55 thf(3173,plain,(((size_size_list_int @ nil_int) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[332])). 87.71/26.55 thf(890,axiom,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3010_minus__nat_Odiff__0)). 87.71/26.55 thf(5415,plain,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[890])). 87.71/26.55 thf(896,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ (times_times_nat @ C @ A)) = (ord_less_nat @ (divide_divide_nat @ B @ A) @ C)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8650_td__gal__lt)). 87.71/26.55 thf(5434,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ (times_times_nat @ C @ A)) = (ord_less_nat @ (divide_divide_nat @ B @ A) @ C)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[896])). 87.71/26.55 thf(1137,axiom,((! [A:produc9072475918466114483BT_nat]: (((! [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))))) <= (! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_890_VEBT__internal_Omembermima_Ocases)). 87.71/26.55 thf(6378,plain,((! [A:produc9072475918466114483BT_nat]: (((! [B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ B @ C) @ D))) => (((! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ D) @ E @ F) @ G))) => (~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ B) @ C @ D) @ E))))) | ~ (! [B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ zero_zero_nat @ D @ E) @ F))))) | ~ (! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137])). 87.71/26.55 thf(153,axiom,((! [A:nat,B:list_nat]: ((nth_nat @ (cons_nat @ A @ B) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4573_nth__Cons__0)). 87.71/26.55 thf(2440,plain,((! [A:nat,B:list_nat]: ((nth_nat @ (cons_nat @ A @ B) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[153])). 87.71/26.55 thf(42,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit1 @ A))) = (numeral_numeral_nat @ (bit0 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9949_xor__nat__numerals_I2_J)). 87.71/26.55 thf(1895,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)],[42])). 87.71/26.55 thf(1336,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1037_mult_Ocomm__neutral)). 87.71/26.55 thf(7074,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336])). 87.71/26.55 thf(326,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ one_one_nat) => ((A @ B) <= (! [C:nat]: ((A @ (plus_plus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) <= (A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9035_nat__induct2)). 87.71/26.55 thf(3147,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ one_one_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ (plus_plus_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))) | ~ (A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[326])). 87.71/26.55 thf(398,axiom,((! [A:nat,B:list_nat,C:list_nat]: ((drop_nat @ A @ (append_nat @ B @ C)) = (append_nat @ (drop_nat @ A @ B) @ (drop_nat @ (minus_minus_nat @ A @ (size_size_list_nat @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8296_drop__append)). 87.71/26.55 thf(3454,plain,((! [A:nat,B:list_nat,C:list_nat]: ((drop_nat @ A @ (append_nat @ B @ C)) = (append_nat @ (drop_nat @ A @ B) @ (drop_nat @ (minus_minus_nat @ A @ (size_size_list_nat @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[398])). 87.71/26.55 thf(1088,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (binomial @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8874_zero__less__binomial__iff)). 87.71/26.55 thf(6171,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)],[1088])). 87.71/26.55 thf(404,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) <= ((vEBT_vebt_succ @ A @ C) = (some_nat @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8978_helpyd)). 87.71/26.55 thf(3476,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ ((vEBT_vebt_succ @ A @ C) = (some_nat @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[404])). 87.71/26.55 thf(1593,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (suc @ B)) = (case_nat_nat @ zero_zero_nat @ (^ [C:nat]: (C)) @ (minus_minus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10082_diff__Suc)). 87.71/26.55 thf(8127,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)],[1593])). 87.71/26.55 thf(673,axiom,((semiri1316708129612266289at_nat = (^ [A:nat]: (A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8899_of__nat__id)). 87.71/26.55 thf(4535,plain,(((semiri1316708129612266289at_nat) = (^ [A:nat]: (A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[673])). 87.71/26.55 thf(1609,axiom,((one_one_nat = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1084_One__nat__def)). 87.71/26.55 thf(8174,plain,((one_one_nat = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1609])). 87.71/26.55 thf(1771,axiom,((! [A:list_real]: ((foldr_real_nat @ (^ [B:real]: (suc)) @ A @ zero_zero_nat) = (size_size_list_real @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2642_foldr__length)). 87.71/26.55 thf(8796,plain,((! [A:list_real]: ((foldr_real_nat @ (^ [B:real]: (suc)) @ A @ zero_zero_nat) = (size_size_list_real @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1771])). 87.71/26.55 thf(29,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = (numeral_numeral_nat @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9394_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J)). 87.71/26.55 thf(1857,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = (numeral_numeral_nat @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[29])). 87.71/26.55 thf(239,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ (power_power_nat @ A @ B)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9030_self__le__ge2__pow)). 87.71/26.55 thf(2788,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ (power_power_nat @ A @ B)) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[239])). 87.71/26.55 thf(929,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/sandbox2/benchmark/theBenchmark.p',fact_7739_power__strict__increasing__iff)). 87.71/26.55 thf(5544,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)],[929])). 87.71/26.55 thf(430,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ B) <= (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1143_dual__order_Otrans)). 87.71/26.55 thf(3563,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[430])). 87.71/26.55 thf(1630,axiom,((! [A:assn,B:assn,C:$o]: ((inf_inf_assn @ A @ (times_times_assn @ B @ (pure_assn @ C))) = (times_times_assn @ (inf_inf_assn @ A @ B) @ (pure_assn @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8906_and__extract__pure__right__ctx__iff)). 87.71/26.55 thf(8247,plain,((! [A:assn,B:assn,C:$o]: ((inf_inf_assn @ A @ (times_times_assn @ B @ (pure_assn @ C))) = (times_times_assn @ (inf_inf_assn @ A @ B) @ (pure_assn @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1630])). 87.71/26.55 thf(1,conjecture,((hoare_7629718768684598413on_nat @ (vEBT_vebt_assn_raw @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ tia) @ (vEBT_VEBT_vebt_succi @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ tia @ vi) @ (^ [A:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ tia) @ (pure_assn @ (A = (vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ vi))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)). 87.71/26.55 thf(2,negated_conjecture,((~ (hoare_7629718768684598413on_nat @ (vEBT_vebt_assn_raw @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ tia) @ (vEBT_VEBT_vebt_succi @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ tia @ vi) @ (^ [A:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ tia) @ (pure_assn @ (A = (vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ vi)))))))),inference(neg_conjecture,[status(cth)],[1])). 87.71/26.55 thf(1779,plain,((~ (hoare_7629718768684598413on_nat @ (vEBT_vebt_assn_raw @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ tia) @ (vEBT_VEBT_vebt_succi @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ tia @ vi) @ (^ [A:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ tia) @ (pure_assn @ (A = (vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ v) @ (suc @ zero_zero_nat) @ vg @ vh) @ vi)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 87.71/26.55 thf(441,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_bot__nat__0_Oextremum__unique)). 87.71/26.55 thf(3624,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[441])). 87.71/26.55 thf(1328,axiom,((! [A:vEBT_VEBT]: (((vEBT_vebt_mint @ A) = none_nat) <= (vEBT_VEBT_minNull @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2041_minNullmin)). 87.71/26.55 thf(7052,plain,((! [A:vEBT_VEBT]: (((vEBT_vebt_mint @ A) = none_nat) | ~ (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328])). 87.71/26.55 thf(1169,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2319_trans__less__add1)). 87.71/26.55 thf(6486,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169])). 87.71/26.55 thf(1663,axiom,((! [A:complex]: ((power_power_complex @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7722_power__Suc0__right)). 87.71/26.55 thf(8361,plain,((! [A:complex]: ((power_power_complex @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1663])). 87.71/26.55 thf(1681,axiom,((! [A:nat]: ((power_power_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7716_power__0__Suc)). 87.71/26.55 thf(8422,plain,((! [A:nat]: ((power_power_nat @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1681])). 87.71/26.55 thf(1488,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) => (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_less__antisym)). 87.71/26.55 thf(7687,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) => ((ord_less_nat @ A @ (suc @ B)) => (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1488])). 87.71/26.55 thf(937,axiom,((! [A:option_num,B:(option_num > (option_nat > $o)),C:option_nat]: (((B @ A @ C) <= (A = none_num)) => (((B @ A @ C) <= (! [D:num,E:nat]: (((B @ A @ C) <= (C = (some_nat @ E))) <= (A = (some_num @ D))))) <= ((B @ A @ C) <= (C = none_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_combine__options__cases)). 87.71/26.55 thf(5571,plain,((! [A:option_num,B:(option_num > (option_nat > $o)),C:option_nat]: (((B @ A @ C) | ~ (A = none_num)) => ((B @ A @ C) | ~ (! [D:num,E:nat]: ((B @ A @ C) | ~ (C = (some_nat @ E)) | ~ (A = (some_num @ D)))) | ~ ((B @ A @ C) | ~ (C = none_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[937])). 87.71/26.55 thf(367,axiom,((! [A:nat,B:nat]: ((map_nat_nat @ suc @ (upt @ A @ B)) = (upt @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8838_map__Suc__upt)). 87.71/26.55 thf(3306,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)],[367])). 87.71/26.55 thf(25,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = (numeral_numeral_nat @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9398_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J)). 87.71/26.55 thf(1846,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = (numeral_numeral_nat @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[25])). 87.71/26.55 thf(80,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/sandbox2/benchmark/theBenchmark.p',fact_9447_even__diff__nat)). 87.71/26.55 thf(2076,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)],[80])). 87.71/26.55 thf(227,axiom,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ B)) = (times_times_complex @ A @ (power_power_complex @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7876_power__Suc)). 87.71/26.55 thf(2748,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)],[227])). 87.71/26.55 thf(282,axiom,((! [A:list_int,B:list_real,C:list_nat,D:list_real,E:(list_int > (list_real > (list_nat > (list_real > $o))))]: ((((size_size_list_real @ B) = (size_size_list_nat @ C)) => (((size_size_list_nat @ C) = (size_size_list_real @ D)) => (((E @ A @ B @ C @ D) <= (! [F:int,G:list_int,H:real,I:list_real,J:nat,K:list_nat,L:real,M:list_real]: ((((size_size_list_real @ I) = (size_size_list_nat @ K)) => (((size_size_list_nat @ K) = (size_size_list_real @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_nat @ J @ K) @ (cons_real @ L @ M))))) <= ((size_size_list_int @ G) = (size_size_list_real @ I))))) <= (E @ nil_int @ nil_real @ nil_nat @ nil_real)))) <= ((size_size_list_int @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8558_list__induct4)). 87.71/26.55 thf(2963,plain,((! [A:list_int,B:list_real,C:list_nat,D:list_real,E:(list_int > (list_real > (list_nat > (list_real > $o))))]: ((((size_size_list_real @ B) = (size_size_list_nat @ C)) => (((size_size_list_nat @ C) = (size_size_list_real @ D)) => ((E @ A @ B @ C @ D) | ~ (! [F:int,G:list_int,H:real,I:list_real,J:nat,K:list_nat,L:real,M:list_real]: ((((size_size_list_real @ I) = (size_size_list_nat @ K)) => (((size_size_list_nat @ K) = (size_size_list_real @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_nat @ J @ K) @ (cons_real @ L @ M))))) | ~ ((size_size_list_int @ G) = (size_size_list_real @ I)))) | ~ (E @ nil_int @ nil_real @ nil_nat @ nil_real)))) | ~ ((size_size_list_int @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[282])). 87.71/26.55 thf(369,axiom,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ A @ B) @ A) = (times_times_int @ A @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7813_power__commutes)). 87.71/26.55 thf(3321,plain,((! [A:int,B:nat]: ((times_times_int @ (power_power_int @ A @ B) @ A) = (times_times_int @ A @ (power_power_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[369])). 87.71/26.55 thf(836,axiom,((! [A:$o,B:$o]: ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_804_vebt__pred_Osimps_I1_J)). 87.71/26.55 thf(5209,plain,((! [A:$o,B:$o]: ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[836])). 87.71/26.55 thf(1030,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1572_dual__order_Ostrict__implies__order)). 87.71/26.55 thf(5930,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030])). 87.71/26.55 thf(338,axiom,(((pure_assn @ ($false)) = bot_bot_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_977_pure__false)). 87.71/26.55 thf(3190,plain,(((pure_assn @ ($false)) = bot_bot_assn)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[338])). 87.71/26.55 thf(1435,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ one_one_nat @ C) => (ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7939_power__strict__increasing)). 87.71/26.55 thf(7476,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ one_one_nat @ C) => (ord_less_nat @ (power_power_nat @ C @ A) @ (power_power_nat @ C @ B))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1435])). 87.71/26.55 thf(1307,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((A @ C) <= (! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_full__nat__induct)). 87.71/26.55 thf(6982,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((A @ C) | ~ (! [D:nat]: ((ord_less_eq_nat @ (suc @ D) @ C) => (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307])). 87.71/26.55 thf(1203,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (plus_plus_nat @ B @ C)) = (times_times_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7891_power__add)). 87.71/26.55 thf(6610,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)],[1203])). 87.71/26.55 thf(1668,axiom,((! [A:nat]: ((ord_min_nat @ A @ zero_zero_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10134_min__0R)). 87.71/26.55 thf(8378,plain,((! [A:nat]: ((ord_min_nat @ A @ zero_zero_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1668])). 87.71/26.55 thf(532,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7757_of__nat__less__of__nat__power__cancel__iff)). 87.71/26.55 thf(4036,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)],[532])). 87.71/26.55 thf(392,axiom,((! [A:list_real,B:list_real,C:list_o,D:(list_real > (list_real > (list_o > $o)))]: ((((D @ nil_real @ nil_real @ nil_o) => ((! [E:real,F:list_real,G:real,H:list_real,I:$o,J:list_o]: (((size_size_list_real @ F) = (size_size_list_real @ H)) => (((D @ F @ H @ J) => (D @ (cons_real @ E @ F) @ (cons_real @ G @ H) @ (cons_o @ I @ J))) <= ((size_size_list_real @ H) = (size_size_list_o @ J))))) => (D @ A @ B @ C))) <= ((size_size_list_real @ B) = (size_size_list_o @ C))) <= ((size_size_list_real @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8541_list__induct3)). 87.71/26.55 thf(3422,plain,((! [A:list_real,B:list_real,C:list_o,D:(list_real > (list_real > (list_o > $o)))]: (((D @ nil_real @ nil_real @ nil_o) => ((! [E:real,F:list_real,G:real,H:list_real,I:$o,J:list_o]: (((size_size_list_real @ F) = (size_size_list_real @ H)) => (((D @ F @ H @ J) => (D @ (cons_real @ E @ F) @ (cons_real @ G @ H) @ (cons_o @ I @ J))) | ~ ((size_size_list_real @ H) = (size_size_list_o @ J))))) => (D @ A @ B @ C))) | ~ ((size_size_list_real @ B) = (size_size_list_o @ C)) | ~ ((size_size_list_real @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[392])). 87.71/26.55 thf(920,axiom,((! [A:nat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((vEBT_V441764108873111860ildupi @ (suc @ (suc @ A))) = (suc @ (suc @ (suc @ (plus_plus_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))))))) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((vEBT_V441764108873111860ildupi @ (suc @ (suc @ A))) = (suc @ (suc @ (suc @ (plus_plus_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (times_times_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9487_VEBT__internal_OT__vebt__buildupi_Osimps_I3_J)). 87.71/26.55 thf(5513,plain,((! [A:nat]: (((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((vEBT_V441764108873111860ildupi @ (suc @ (suc @ A))) = (suc @ (suc @ (suc @ (plus_plus_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))))))))) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((vEBT_V441764108873111860ildupi @ (suc @ (suc @ A))) = (suc @ (suc @ (suc @ (plus_plus_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (times_times_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[920])). 87.71/26.55 thf(289,axiom,((! [A:(nat > (int > assn)),B:list_nat]: ((vEBT_L8298612041380073281at_int @ A @ B @ nil_int) = (pure_assn @ (B = nil_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8220_list__assn__aux__simps_I2_J)). 87.71/26.55 thf(2995,plain,((! [A:(nat > (int > assn)),B:list_nat]: ((vEBT_L8298612041380073281at_int @ (A) @ B @ nil_int) = (pure_assn @ (B = nil_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[289])). 87.71/26.55 thf(847,axiom,((! [A:nat,B:int,C:int,D:nat]: ((bit_se1146084159140164899it_int @ (bit_concat_bit @ A @ B @ C) @ D) = (((bit_se1146084159140164899it_int @ B @ D) & (ord_less_nat @ D @ A)) | ((bit_se1146084159140164899it_int @ C @ (minus_minus_nat @ D @ A)) & (ord_less_eq_nat @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10123_bit__concat__bit__iff)). 87.71/26.55 thf(5249,plain,((! [A:nat,B:int,C:int,D:nat]: ((bit_se1146084159140164899it_int @ (bit_concat_bit @ A @ B @ C) @ D) = (((bit_se1146084159140164899it_int @ B @ D) & (ord_less_nat @ D @ A)) | ((bit_se1146084159140164899it_int @ C @ (minus_minus_nat @ D @ A)) & (ord_less_eq_nat @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[847])). 87.71/26.55 thf(1278,axiom,((! [A:nat]: ((bit_se2925701944663578781it_nat @ A @ (suc @ zero_zero_nat)) = (zero_n2687167440665602831ol_nat @ (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9876_take__bit__of__Suc__0)). 87.71/26.55 thf(6869,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)],[1278])). 87.71/26.55 thf(1299,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => ((B = one_one_nat) => (? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_969_deg__1__Leafy)). 87.71/26.55 thf(6950,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => ((B = one_one_nat) => (? [C:$o,D:$o]: (A = (vEBT_Leaf @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299])). 87.71/26.55 thf(1012,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (power_power_nat @ (semiri1316708129612266289at_nat @ A) @ B) @ (semiri1316708129612266289at_nat @ C)) = (ord_less_eq_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7764_of__nat__le__of__nat__power__cancel__iff)). 87.71/26.55 thf(5872,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)],[1012])). 87.71/26.55 thf(455,axiom,((! [A:assn]: ((sup_sup_assn @ A @ bot_bot_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4965_boolean__algebra_Odisj__zero__right)). 87.71/26.55 thf(3675,plain,((! [A:assn]: ((sup_sup_assn @ A @ bot_bot_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[455])). 87.71/26.55 thf(149,axiom,((! [A:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ A @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9014_add__self__mod__2)). 87.71/26.55 thf(2423,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)],[149])). 87.71/26.55 thf(180,axiom,((! [A:list_real,B:list_nat,C:list_real,D:(list_real > (list_nat > (list_real > $o)))]: ((((D @ nil_real @ nil_nat @ nil_real) => ((D @ A @ B @ C) <= (! [E:real,F:list_real,G:nat,H:list_nat,I:real,J:list_real]: ((((size_size_list_nat @ H) = (size_size_list_real @ J)) => ((D @ F @ H @ J) => (D @ (cons_real @ E @ F) @ (cons_nat @ G @ H) @ (cons_real @ I @ J)))) <= ((size_size_list_real @ F) = (size_size_list_nat @ H)))))) <= ((size_size_list_nat @ B) = (size_size_list_real @ C))) <= ((size_size_list_real @ A) = (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8548_list__induct3)). 87.71/26.55 thf(2529,plain,((! [A:list_real,B:list_nat,C:list_real,D:(list_real > (list_nat > (list_real > $o)))]: (((D @ nil_real @ nil_nat @ nil_real) => ((D @ A @ B @ C) | ~ (! [E:real,F:list_real,G:nat,H:list_nat,I:real,J:list_real]: ((((size_size_list_nat @ H) = (size_size_list_real @ J)) => ((D @ F @ H @ J) => (D @ (cons_real @ E @ F) @ (cons_nat @ G @ H) @ (cons_real @ I @ J)))) | ~ ((size_size_list_real @ F) = (size_size_list_nat @ H)))))) | ~ ((size_size_list_nat @ B) = (size_size_list_real @ C)) | ~ ((size_size_list_real @ A) = (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[180])). 87.71/26.55 thf(1429,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1270_dual__order_Oasym)). 87.71/26.55 thf(7444,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1429])). 87.71/26.55 thf(1627,axiom,((! [A:list_o]: ((foldr_o_nat @ (^ [B:$o]: (suc)) @ A @ zero_zero_nat) = (size_size_list_o @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2643_foldr__length)). 87.71/26.55 thf(8234,plain,((! [A:list_o]: ((foldr_o_nat @ (^ [B:$o]: (suc)) @ A @ zero_zero_nat) = (size_size_list_o @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1627])). 87.71/26.55 thf(679,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/sandbox2/benchmark/theBenchmark.p',fact_8659_dividend__less__times__div)). 87.71/26.55 thf(4550,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)],[679])). 87.71/26.55 thf(1293,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ (suc @ (plus_plus_nat @ A @ B)) @ (suc @ A))) = (times_times_nat @ (suc @ B) @ (binomial @ (suc @ (plus_plus_nat @ A @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8882_Suc__times__binomial__add)). 87.71/26.55 thf(6922,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)],[1293])). 87.71/26.55 thf(974,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2108_nat__add__left__cancel__less)). 87.71/26.55 thf(5722,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)],[974])). 87.71/26.55 thf(60,axiom,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (suc @ (numeral_numeral_nat @ (bit0 @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9164_eval__nat__numeral_I3_J)). 87.71/26.55 thf(1959,plain,((! [A:num]: ((numeral_numeral_nat @ (bit1 @ A)) = (suc @ (numeral_numeral_nat @ (bit0 @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[60])). 87.71/26.55 thf(191,axiom,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (vEBT_VEBT_height @ A)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8976_two__powr__height__bound__deg)). 87.71/26.55 thf(2585,plain,((! [A:vEBT_VEBT,B:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (vEBT_VEBT_height @ A)) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[191])). 87.71/26.55 thf(1231,axiom,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ B) & (((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ A @ E) @ C)) | ((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C))) & (dvd_dvd_nat @ C @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9463_bezout__add__nat)). 87.71/26.55 thf(6699,plain,((! [A:nat,B:nat]: ? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ B) & (((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ A @ E) @ C)) | ((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C))) & (dvd_dvd_nat @ C @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231])). 87.71/26.55 thf(855,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1560_dual__order_Ostrict__iff__not)). 87.71/26.55 thf(5278,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)],[855])). 87.71/26.55 thf(1369,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_nat__mult__eq__cancel__disj)). 87.71/26.55 thf(7225,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)],[1369])). 87.71/26.55 thf(1255,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4656_of__nat__mono)). 87.71/26.55 thf(6792,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)],[1255])). 87.71/26.55 thf(799,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1566_order_Ostrict__implies__order)). 87.71/26.55 thf(5048,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[799])). 87.71/26.55 thf(502,axiom,((! [A:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),B:option4927543243414619207at_nat,C:option4927543243414619207at_nat,D:option4927543243414619207at_nat]: (((vEBT_V1502963449132264192at_nat @ A @ B @ C) = D) => (((B = none_P5556105721700978146at_nat) => (D != none_P5556105721700978146at_nat)) => (((? [E:product_prod_nat_nat]: (B = (some_P7363390416028606310at_nat @ E))) => ((C = none_P5556105721700978146at_nat) => (D != none_P5556105721700978146at_nat))) => (~ (! [E:product_prod_nat_nat]: ((B = (some_P7363390416028606310at_nat @ E)) => (! [F:product_prod_nat_nat]: ((D != (some_P7363390416028606310at_nat @ (A @ E @ F))) <= (C = (some_P7363390416028606310at_nat @ F)))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_719_VEBT__internal_Ooption__shift_Oelims)). 87.71/26.55 thf(3888,plain,((! [A:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),B:option4927543243414619207at_nat,C:option4927543243414619207at_nat,D:option4927543243414619207at_nat]: (((vEBT_V1502963449132264192at_nat @ (A) @ B @ C) = D) => (((B = none_P5556105721700978146at_nat) => (~ (D = none_P5556105721700978146at_nat))) => (((? [E:product_prod_nat_nat]: (B = (some_P7363390416028606310at_nat @ E))) => ((C = none_P5556105721700978146at_nat) => (~ (D = none_P5556105721700978146at_nat)))) => (~ (! [E:product_prod_nat_nat]: ((B = (some_P7363390416028606310at_nat @ E)) => (! [F:product_prod_nat_nat]: (~ (D = (some_P7363390416028606310at_nat @ (A @ E @ F))) | ~ (C = (some_P7363390416028606310at_nat @ F)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[502])). 87.71/26.55 thf(663,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/sandbox2/benchmark/theBenchmark.p',fact_2263_add__strict__mono)). 87.71/26.55 thf(4503,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)],[663])). 87.71/26.55 thf(1539,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/sandbox2/benchmark/theBenchmark.p',fact_9478_mod__nat__eqI)). 87.71/26.55 thf(7910,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)],[1539])). 87.71/26.55 thf(886,axiom,((! [A:list_real,B:list_int,C:(real > (int > assn))]: (((vEBT_L1443519841834266653al_int @ C @ A @ B) = bot_bot_assn) <= ((size_size_list_real @ A) != (size_size_list_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3200_list__assn__aux__ineq__len)). 87.71/26.55 thf(5400,plain,((! [A:list_real,B:list_int,C:(real > (int > assn))]: (((vEBT_L1443519841834266653al_int @ (C) @ A @ B) = bot_bot_assn) | ((size_size_list_real @ A) = (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[886])). 87.71/26.55 thf(844,axiom,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_zero__le)). 87.71/26.55 thf(5241,plain,((! [A:nat]: (ord_less_eq_nat @ zero_zero_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[844])). 87.71/26.55 thf(1352,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)))) & ((~ (ord_less_eq_nat @ B @ A)) => (C = (nat_prod_decode_aux @ (suc @ A) @ (minus_minus_nat @ B @ (suc @ A)))))) <= ((nat_prod_decode_aux @ A @ B) = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3354_prod__decode__aux_Oelims)). 87.71/26.55 thf(7160,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)))) & ((~ (ord_less_eq_nat @ B @ A)) => (C = (nat_prod_decode_aux @ (suc @ A) @ (minus_minus_nat @ B @ (suc @ A)))))) | ~ ((nat_prod_decode_aux @ A @ B) = C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352])). 87.71/26.55 thf(1554,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_le__square)). 87.71/26.55 thf(7985,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (times_times_nat @ A @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1554])). 87.71/26.55 thf(960,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (time_htt_option_nat @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_vebt_maxti @ B) @ (^ [C:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_vebt_maxt @ A))))) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1706_vebt__maxti__hT)). 87.71/26.55 thf(5666,plain,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (time_htt_option_nat @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_vebt_maxti @ B) @ (^ [C:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_vebt_maxt @ A))))) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[960])). 87.71/26.55 thf(870,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_nat @ (vEBT_V1232361888498592333_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ A @ C @ D) @ E) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8995_tdeletemimi_H)). 87.71/26.55 thf(5327,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_nat @ (vEBT_V1232361888498592333_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ B)) @ A @ C @ D) @ E) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[870])). 87.71/26.55 thf(1651,axiom,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ A @ (times_times_assn @ B @ C)) = (times_times_assn @ B @ (times_times_assn @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_ab__semigroup__mult__class_Omult_Oleft__commute)). 87.71/26.55 thf(8322,plain,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ A @ (times_times_assn @ B @ C)) = (times_times_assn @ B @ (times_times_assn @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1651])). 87.71/26.55 thf(764,axiom,((! [A:real,B:list_real]: ((size_size_list_real @ (cons_real @ A @ B)) = (plus_plus_nat @ (size_size_list_real @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4750_list_Osize_I4_J)). 87.71/26.55 thf(4919,plain,((! [A:real,B:list_real]: ((size_size_list_real @ (cons_real @ A @ B)) = (plus_plus_nat @ (size_size_list_real @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[764])). 87.71/26.55 thf(323,axiom,((! [A:nat]: (ord_less_nat @ (bit_se2002935070580805687sk_nat @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9868_mask__nat__less__exp)). 87.71/26.55 thf(3130,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)],[323])). 87.71/26.55 thf(210,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ B) = (ord_less_eq_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9891_take__bit__nat__less__self__iff)). 87.71/26.55 thf(2677,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)],[210])). 87.71/26.55 thf(99,axiom,((bit_se727722235901077358nd_nat = (^ [A:nat,B:nat]: (if_nat @ ((A = zero_zero_nat) | (B = zero_zero_nat)) @ zero_zero_nat @ (plus_plus_nat @ (times_times_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9846_and__nat__unfold)). 87.71/26.55 thf(2176,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)],[99])). 87.71/26.55 thf(716,axiom,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_982_mult__1)). 87.71/26.55 thf(4708,plain,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[716])). 87.71/26.55 thf(752,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_not__less0)). 87.71/26.55 thf(4872,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[752])). 87.71/26.55 thf(267,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ A @ (semiri1408675320244567234ct_nat @ B))) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9471_dvd__fact)). 87.71/26.55 thf(2904,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) => (dvd_dvd_nat @ A @ (semiri1408675320244567234ct_nat @ B))) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[267])). 87.71/26.55 thf(1584,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1731_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I5_J)). 87.71/26.55 thf(8095,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1584])). 87.71/26.55 thf(820,axiom,((! [A:nat]: ((minus_minus_nat @ (suc @ A) @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2865_diff__Suc__1)). 87.71/26.55 thf(5138,plain,((! [A:nat]: ((minus_minus_nat @ (suc @ A) @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[820])). 87.71/26.55 thf(120,axiom,((! [A:vEBT_VEBT,B:nat]: (((vEBT_T_m_i_n_N_u_l_l @ A) = B) => ((((B != one_one_nat) <= (? [C:$o]: (A = (vEBT_Leaf @ ($true) @ C)))) => (((~ ((B != one_one_nat) <= (? [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F))))) <= ((B != one_one_nat) <= (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))))) <= ((? [C:$o]: (A = (vEBT_Leaf @ C @ ($true)))) => (B != one_one_nat)))) <= ((A = (vEBT_Leaf @ ($false) @ ($false))) => (B != one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1727_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Oelims)). 87.71/26.55 thf(2253,plain,((! [A:vEBT_VEBT,B:nat]: (((vEBT_T_m_i_n_N_u_l_l @ A) = B) => (((~ (B = one_one_nat) | ~ (? [C:$o]: (A = (vEBT_Leaf @ ($true) @ C)))) => (~ (~ (B = one_one_nat) | ~ (? [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F)))) | ~ (~ (B = one_one_nat) | ~ (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) | ~ ((? [C:$o]: (A = (vEBT_Leaf @ C @ ($true)))) => (~ (B = one_one_nat))))) | ~ ((A = (vEBT_Leaf @ ($false) @ ($false))) => (~ (B = one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[120])). 87.71/26.55 thf(499,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2247_add__le__imp__le__right)). 87.71/26.55 thf(3871,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[499])). 87.71/26.55 thf(188,axiom,((! [A:$o,B:$o]: ((vEBT_T_m_a_x_t @ (vEBT_Leaf @ A @ B)) = (plus_plus_nat @ one_one_nat @ (if_nat @ B @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2599_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I1_J)). 87.71/26.55 thf(2570,plain,((! [A:$o,B:$o]: ((vEBT_T_m_a_x_t @ (vEBT_Leaf @ A @ B)) = (plus_plus_nat @ one_one_nat @ (if_nat @ B @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[188])). 87.71/26.55 thf(277,axiom,((! [A:list_real]: ((slice_real @ zero_zero_nat @ (size_size_list_real @ A) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3282_slice__complete)). 87.71/26.55 thf(2941,plain,((! [A:list_real]: ((slice_real @ zero_zero_nat @ (size_size_list_real @ A) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[277])). 87.71/26.55 thf(1049,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1759_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I4_J)). 87.71/26.55 thf(6001,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049])). 87.71/26.55 thf(363,axiom,((! [A:nat,B:(nat > (int > $o))]: ((! [C:nat]: ((? [D:int]: (B @ C @ D)) <= (ord_less_nat @ C @ A))) = (? [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/sandbox2/benchmark/theBenchmark.p',fact_2657_Skolem__list__nth)). 87.71/26.55 thf(3289,plain,((! [A:nat,B:(nat > (int > $o))]: ((! [C:nat]: (? [D:int]: (B @ C @ D) | ~ (ord_less_nat @ C @ A))) = (? [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)],[363])). 87.71/26.55 thf(1186,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2448_add__strict__increasing)). 87.71/26.55 thf(6546,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ C) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186])). 87.71/26.55 thf(923,axiom,((! [A:list_int]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (size_size_list_int @ A)) = (A != nil_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8330_length__ge__1__conv)). 87.71/26.55 thf(5525,plain,((! [A:list_int]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (size_size_list_int @ A)) = (~ (A = nil_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[923])). 87.71/26.55 thf(1750,axiom,((! [A:produc5491161045314408544at_nat]: ((! [B:(product_prod_nat_nat > (product_prod_nat_nat > $o)),C:option4927543243414619207at_nat]: (A != (produc3994169339658061776at_nat @ B @ (produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ C)))) => ((! [B:(product_prod_nat_nat > (product_prod_nat_nat > $o)),C:product_prod_nat_nat]: (A != (produc3994169339658061776at_nat @ B @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ C) @ none_P5556105721700978146at_nat)))) => (~ (! [B:(product_prod_nat_nat > (product_prod_nat_nat > $o)),C:product_prod_nat_nat,D:product_prod_nat_nat]: (A != (produc3994169339658061776at_nat @ B @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ C) @ (some_P7363390416028606310at_nat @ D)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_865_VEBT__internal_Ooption__comp__shift_Ocases)). 87.71/26.55 thf(8718,plain,((! [A:produc5491161045314408544at_nat]: ((! [B:(product_prod_nat_nat > (product_prod_nat_nat > $o)),C:option4927543243414619207at_nat]: ~ (A = (produc3994169339658061776at_nat @ (B) @ (produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ C)))) => ((! [B:(product_prod_nat_nat > (product_prod_nat_nat > $o)),C:product_prod_nat_nat]: ~ (A = (produc3994169339658061776at_nat @ (B) @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ C) @ none_P5556105721700978146at_nat)))) => (~ (! [B:(product_prod_nat_nat > (product_prod_nat_nat > $o)),C:product_prod_nat_nat,D:product_prod_nat_nat]: ~ (A = (produc3994169339658061776at_nat @ (B) @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ C) @ (some_P7363390416028606310at_nat @ D)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1750])). 87.71/26.55 thf(594,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_VEBT_minNull @ (vEBT_vebt_delete @ A @ C)) => (ord_less_eq_nat @ (vEBT_V1232361888498592333_e_t_e @ A @ C) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2503_minNull__delete__time__bound_H)). 87.71/26.55 thf(4269,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_VEBT_minNull @ (vEBT_vebt_delete @ A @ C)) => (ord_less_eq_nat @ (vEBT_V1232361888498592333_e_t_e @ A @ C) @ one_one_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[594])). 87.71/26.55 thf(1346,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ B)) @ A @ E @ F) @ C) = (some_nat @ B)) <= (ord_less_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8999_pred__max)). 87.71/26.55 thf(7118,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (((vEBT_vebt_pred @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ D @ B)) @ A @ E @ F) @ C) = (some_nat @ B)) | ~ (ord_less_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346])). 87.71/26.55 thf(1171,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1401_order__less__imp__not__eq2)). 87.71/26.55 thf(6492,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171])). 87.71/26.55 thf(1063,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_less__Suc__eq)). 87.71/26.55 thf(6052,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)],[1063])). 87.71/26.55 thf(1390,axiom,((! [A:nat]: ((A = bot_bot_nat) <= (ord_less_eq_nat @ A @ bot_bot_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1691_bot_Oextremum__uniqueI)). 87.71/26.55 thf(7287,plain,((! [A:nat]: ((A = bot_bot_nat) | ~ (ord_less_eq_nat @ A @ bot_bot_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390])). 87.71/26.55 thf(354,axiom,((! [A:heap_Time_Heap_o,B:heap_Time_Heap_o]: ((if_Heap_Time_Heap_o @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Heap____Time____Monad__OHeap_I_Eo_J_T)). 87.71/26.55 thf(3255,plain,((! [A:heap_Time_Heap_o,B:heap_Time_Heap_o]: ((if_Heap_Time_Heap_o @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[354])). 87.71/26.55 thf(1118,axiom,((! [A:list_o]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (size_size_list_o @ A)) = (A != nil_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8328_length__ge__1__conv)). 87.71/26.55 thf(6312,plain,((! [A:list_o]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (size_size_list_o @ A)) = (~ (A = nil_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118])). 87.71/26.55 thf(285,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9445_even__Suc__div__two)). 87.71/26.55 thf(2981,plain,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[285])). 87.71/26.55 thf(560,axiom,((! [A:list_nat,B:list_real,C:(nat > (real > assn))]: (((vEBT_L6102073776069194049t_real @ C @ A @ B) = bot_bot_assn) <= ((size_size_list_nat @ A) != (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3205_list__assn__aux__ineq__len)). 87.71/26.55 thf(4122,plain,((! [A:list_nat,B:list_real,C:(nat > (real > assn))]: (((vEBT_L6102073776069194049t_real @ (C) @ A @ B) = bot_bot_assn) | ((size_size_list_nat @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[560])). 87.71/26.55 thf(1592,axiom,((! [A:product_prod_nat_nat]: ((size_s170228958280169651at_nat @ (some_P7363390416028606310at_nat @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_option_Osize_I4_J)). 87.71/26.55 thf(8124,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)],[1592])). 87.71/26.55 thf(1743,axiom,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:assn]: ((hoare_7629718768684598413on_nat @ A @ B @ C) => (hoare_7629718768684598413on_nat @ (times_times_assn @ A @ D) @ B @ (^ [E:option_nat]: (times_times_assn @ (C @ E) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_frame__rule)). 87.71/26.55 thf(8697,plain,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:assn]: ((hoare_7629718768684598413on_nat @ A @ B @ (C)) => (hoare_7629718768684598413on_nat @ (times_times_assn @ A @ D) @ B @ (^ [E:option_nat]: (times_times_assn @ (C @ E) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1743])). 87.71/26.55 thf(1433,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (suc @ A) @ (binomial @ A @ B)) = (times_times_nat @ (binomial @ (suc @ A) @ (suc @ B)) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8877_Suc__times__binomial__eq)). 87.71/26.55 thf(7472,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)],[1433])). 87.71/26.55 thf(213,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_T_m_e_m_b_e_r @ (vEBT_Leaf @ A @ B) @ C) = (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (C = zero_zero_nat) @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9400_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J)). 87.71/26.55 thf(2695,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_T_m_e_m_b_e_r @ (vEBT_Leaf @ A @ B) @ C) = (plus_plus_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (if_nat @ (C = zero_zero_nat) @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[213])). 87.71/26.55 thf(1232,axiom,((! [A:nat,B:nat,C:list_nat,D:nat]: ((A != B) => (((nth_nat @ (cons_nat @ A @ C) @ D) = B) = (((nth_nat @ C @ (minus_minus_nat @ D @ one_one_nat)) = B) & (ord_less_nat @ zero_zero_nat @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4769_nth__non__equal__first__eq)). 87.71/26.55 thf(6705,plain,((! [A:nat,B:nat,C:list_nat,D:nat]: ((~ (A = B)) => (((nth_nat @ (cons_nat @ A @ C) @ D) = B) = (((nth_nat @ C @ (minus_minus_nat @ D @ one_one_nat)) = B) & (ord_less_nat @ zero_zero_nat @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232])). 87.71/26.55 thf(772,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ (suc @ A) @ B) = (times_times_nat @ (suc @ A) @ C)) = (B = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_Suc__mult__cancel1)). 87.71/26.55 thf(4943,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)],[772])). 87.71/26.55 thf(1471,axiom,((! [A:assn]: ((power_power_assn @ A @ zero_zero_nat) = one_one_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7883_power__0)). 87.71/26.55 thf(7611,plain,((! [A:assn]: ((power_power_assn @ A @ zero_zero_nat) = one_one_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1471])). 87.71/26.55 thf(525,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_Suc__mono)). 87.71/26.55 thf(4000,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)],[525])). 87.71/26.55 thf(337,axiom,((! [A:real,B:list_real]: ((size_size_list_real @ (cons_real @ A @ B)) = (suc @ (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4795_length__Cons)). 87.71/26.55 thf(3187,plain,((! [A:real,B:list_real]: ((size_size_list_real @ (cons_real @ A @ B)) = (suc @ (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[337])). 87.71/26.55 thf(48,axiom,((! [A:nat]: ((suc @ (suc @ (suc @ A))) = (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9166_Suc3__eq__add__3)). 87.71/26.55 thf(1916,plain,((! [A:nat]: ((suc @ (suc @ (suc @ A))) = (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[48])). 87.71/26.55 thf(1634,axiom,((! [A:(nat > $o),B:nat]: (((A @ B) <= (! [C:nat]: ((A @ (suc @ C)) <= (A @ C)))) <= (A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_nat__induct)). 87.71/26.55 thf(8259,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((A @ (suc @ C)) | ~ (A @ C))) | ~ (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1634])). 87.71/26.55 thf(349,axiom,((! [A:nat]: (((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (minus_minus_nat @ A @ one_one_nat)) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9448_odd__two__times__div__two__nat)). 87.71/26.55 thf(3234,plain,((! [A:nat]: (((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = (minus_minus_nat @ A @ one_one_nat)) | (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[349])). 87.71/26.55 thf(1291,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/sandbox2/benchmark/theBenchmark.p',fact_9474_dvd__mult__cancel1)). 87.71/26.55 thf(6916,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)],[1291])). 87.71/26.55 thf(276,axiom,((! [A:nat,B:nat,C:nat]: (((nth_nat @ (upt @ A @ C) @ B) = (plus_plus_nat @ A @ B)) <= (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8836_nth__upt)). 87.71/26.55 thf(2938,plain,((! [A:nat,B:nat,C:nat]: (((nth_nat @ (upt @ A @ C) @ B) = (plus_plus_nat @ A @ B)) | ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[276])). 87.71/26.55 thf(1177,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2997_left__diff__distrib_H)). 87.71/26.55 thf(6510,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)],[1177])). 87.71/26.55 thf(489,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ C @ A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2018_minf_I6_J)). 87.71/26.55 thf(3811,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)],[489])). 87.71/26.55 thf(240,axiom,((! [A:nat,B:nat]: ((suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) != (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9026_Suc__double__not__eq__double)). 87.71/26.55 thf(2791,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)],[240])). 87.71/26.55 thf(351,axiom,((! [A:$o,B:$o]: ((vEBT_vebt_delete @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = (vEBT_Leaf @ ($false) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2576_vebt__delete_Osimps_I1_J)). 87.71/26.55 thf(3240,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)],[351])). 87.71/26.55 thf(438,axiom,((! [A:nat,B:int,C:list_int]: ((((nth_int @ (cons_int @ B @ C) @ A) = (nth_int @ C @ (minus_minus_nat @ A @ one_one_nat))) <= (A != zero_zero_nat)) & (((nth_int @ (cons_int @ B @ C) @ A) = B) <= (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4757_nth__Cons_H)). 87.71/26.55 thf(3609,plain,((! [A:nat,B:int,C:list_int]: ((((nth_int @ (cons_int @ B @ C) @ A) = (nth_int @ C @ (minus_minus_nat @ A @ one_one_nat))) | (A = zero_zero_nat)) & (((nth_int @ (cons_int @ B @ C) @ A) = B) | ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[438])). 87.71/26.55 thf(1372,axiom,((! [A:nat,B:nat]: (((product_Pair_nat_nat @ (divide_divide_nat @ B @ A) @ (modulo_modulo_nat @ B @ A)) = (if_Pro6206227464963214023at_nat @ (ord_less_eq_nat @ A @ (minus_minus_nat @ B @ (times_times_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ A))) @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ one_one_nat) @ (minus_minus_nat @ (minus_minus_nat @ B @ (times_times_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ A)) @ A)) @ (product_Pair_nat_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ (minus_minus_nat @ B @ (times_times_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ A))))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9122_div__half__nat)). 87.71/26.55 thf(7233,plain,((! [A:nat,B:nat]: (((product_Pair_nat_nat @ (divide_divide_nat @ B @ A) @ (modulo_modulo_nat @ B @ A)) = (if_Pro6206227464963214023at_nat @ (ord_less_eq_nat @ A @ (minus_minus_nat @ B @ (times_times_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ A))) @ (product_Pair_nat_nat @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ one_one_nat) @ (minus_minus_nat @ (minus_minus_nat @ B @ (times_times_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ A)) @ A)) @ (product_Pair_nat_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ (minus_minus_nat @ B @ (times_times_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))) @ A)) @ A))))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372])). 87.71/26.55 thf(1006,axiom,((! [A:nat,B:nat,C:list_nat]: ((((drop_nat @ A @ (cons_nat @ B @ C)) = (cons_nat @ B @ C)) <= (A = zero_zero_nat)) & ((A != zero_zero_nat) => ((drop_nat @ A @ (cons_nat @ B @ C)) = (drop_nat @ (minus_minus_nat @ A @ one_one_nat) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7967_drop__Cons_H)). 87.71/26.55 thf(5844,plain,((! [A:nat,B:nat,C:list_nat]: ((((drop_nat @ A @ (cons_nat @ B @ C)) = (cons_nat @ B @ C)) | ~ (A = zero_zero_nat)) & ((~ (A = zero_zero_nat)) => ((drop_nat @ A @ (cons_nat @ B @ C)) = (drop_nat @ (minus_minus_nat @ A @ one_one_nat) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006])). 87.71/26.55 thf(1778,axiom,((! [A:assn,B:assn,C:nat]: (((times_times_assn @ A @ B) = (times_times_assn @ B @ A)) => ((times_times_assn @ (power_power_assn @ A @ C) @ B) = (times_times_assn @ B @ (power_power_assn @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7826_power__commuting__commutes)). 87.71/26.55 thf(8814,plain,((! [A:assn,B:assn,C:nat]: (((times_times_assn @ A @ B) = (times_times_assn @ B @ A)) => ((times_times_assn @ (power_power_assn @ A @ C) @ B) = (times_times_assn @ B @ (power_power_assn @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1778])). 87.71/26.55 thf(311,axiom,((! [A:nat,B:list_nat,C:nat,D:nat]: (((ord_less_nat @ C @ (size_size_list_nat @ B)) => (((nth_nat @ (append_nat @ (take_nat @ C @ B) @ (append_nat @ (cons_nat @ D @ nil_nat) @ (drop_nat @ (plus_plus_nat @ C @ one_one_nat) @ B))) @ A) = (nth_nat @ B @ A)) <= (A != C))) <= (ord_less_nat @ A @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8113_nth__repl)). 87.71/26.55 thf(3086,plain,((! [A:nat,B:list_nat,C:nat,D:nat]: (((ord_less_nat @ C @ (size_size_list_nat @ B)) => (((nth_nat @ (append_nat @ (take_nat @ C @ B) @ (append_nat @ (cons_nat @ D @ nil_nat) @ (drop_nat @ (plus_plus_nat @ C @ one_one_nat) @ B))) @ A) = (nth_nat @ B @ A)) | (A = C))) | ~ (ord_less_nat @ A @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[311])). 87.71/26.55 thf(1597,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_old_Onat_Odistinct_I1_J)). 87.71/26.55 thf(8139,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1597])). 87.71/26.55 thf(1428,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) = ((modulo_modulo_nat @ B @ A) = B)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8710_nat__mod__lem)). 87.71/26.55 thf(7440,plain,((! [A:nat,B:nat]: (((ord_less_nat @ B @ A) = ((modulo_modulo_nat @ B @ A) = B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1428])). 87.71/26.55 thf(309,axiom,(((pred_numeral @ one) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9911_pred__numeral__simps_I1_J)). 87.71/26.55 thf(3081,plain,(((pred_numeral @ one) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[309])). 87.71/26.55 thf(361,axiom,((! [A:nat,B:nat]: (((upt @ A @ (suc @ B)) = (append_nat @ (upt @ A @ B) @ (cons_nat @ B @ nil_nat))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8856_upt__Suc__append)). 87.71/26.55 thf(3283,plain,((! [A:nat,B:nat]: (((upt @ A @ (suc @ B)) = (append_nat @ (upt @ A @ B) @ (cons_nat @ B @ nil_nat))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[361])). 87.71/26.55 thf(947,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d2 @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1820_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I4_J)). 87.71/26.55 thf(5627,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d2 @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[947])). 87.71/26.55 thf(1776,axiom,((! [A:(nat > nat)]: ((size_option_nat @ A @ none_nat) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1728_option_Osize__gen_I1_J)). 87.71/26.55 thf(8809,plain,((! [A:(nat > nat)]: ((size_option_nat @ (A) @ none_nat) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1776])). 87.71/26.55 thf(691,axiom,((! [A:(nat > (int > assn)),B:nat,C:list_nat,D:int,E:list_int]: ((vEBT_L8298612041380073281at_int @ A @ (cons_nat @ B @ C) @ (cons_int @ D @ E)) = (times_times_assn @ (A @ B @ D) @ (vEBT_L8298612041380073281at_int @ A @ C @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4712_list__assn__simps_I2_J)). 87.71/26.55 thf(4605,plain,((! [A:(nat > (int > assn)),B:nat,C:list_nat,D:int,E:list_int]: ((vEBT_L8298612041380073281at_int @ (A) @ (cons_nat @ B @ C) @ (cons_int @ D @ E)) = (times_times_assn @ (A @ B @ D) @ (vEBT_L8298612041380073281at_int @ (A) @ C @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[691])). 87.71/26.55 thf(800,axiom,((! [A:option_num]: ((A != none_num) => (~ (! [B:num]: (A != (some_num @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_option_Oexhaust)). 87.71/26.55 thf(5050,plain,((! [A:option_num]: ((~ (A = none_num)) => (~ (! [B:num]: ~ (A = (some_num @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[800])). 87.71/26.55 thf(244,axiom,((! [A:list_nat,B:list_nat,C:list_nat,D:list_nat]: ((((append_nat @ A @ C) = (append_nat @ B @ D)) = ((C = D) & (A = B))) <= (((size_size_list_nat @ C) = (size_size_list_nat @ D)) | ((size_size_list_nat @ A) = (size_size_list_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8096_append__eq__append__conv)). 87.71/26.55 thf(2806,plain,((! [A:list_nat,B:list_nat,C:list_nat,D:list_nat]: ((((append_nat @ A @ C) = (append_nat @ B @ D)) = ((C = D) & (A = B))) | ~ (((size_size_list_nat @ C) = (size_size_list_nat @ D)) | ((size_size_list_nat @ A) = (size_size_list_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[244])). 87.71/26.55 thf(1045,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ one_one_nat @ A) => ((suc @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat)))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3174_Suc__n__minus__m__eq)). 87.71/26.55 thf(5984,plain,((! [A:nat,B:nat]: (((ord_less_nat @ one_one_nat @ A) => ((suc @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat)))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045])). 87.71/26.55 thf(1287,axiom,((! [A:num,B:num]: ((((upt @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (cons_nat @ (numeral_numeral_nat @ A) @ (upt @ (suc @ (numeral_numeral_nat @ A)) @ (numeral_numeral_nat @ B)))) <= (ord_less_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))) & (((upt @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = nil_nat) <= (~ (ord_less_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8959_upt__rec__numeral)). 87.71/26.55 thf(6898,plain,((! [A:num,B:num]: ((((upt @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = (cons_nat @ (numeral_numeral_nat @ A) @ (upt @ (suc @ (numeral_numeral_nat @ A)) @ (numeral_numeral_nat @ B)))) | ~ (ord_less_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B))) & (((upt @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)) = nil_nat) | (ord_less_nat @ (numeral_numeral_nat @ A) @ (numeral_numeral_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287])). 87.71/26.55 thf(8,axiom,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = one_one_nat) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit1 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit0 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9177_mod__exhaust__less__4)). 87.71/26.55 thf(1795,plain,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = one_one_nat) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit1 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (numeral_numeral_nat @ (bit0 @ one))) | ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[8])). 87.71/26.55 thf(1721,axiom,((! [A:$o,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn),E:nat]: ((time_htt_option_nat @ (times_times_assn @ (pure_assn @ A) @ B) @ C @ D @ E) = ((A) => (time_htt_option_nat @ B @ C @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1795_norm__pre__pure__iff__htt_H)). 87.71/26.55 thf(8581,plain,((! [A:$o,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn),E:nat]: ((time_htt_option_nat @ (times_times_assn @ (pure_assn @ A) @ B) @ C @ (D) @ E) = ((A) => (time_htt_option_nat @ B @ C @ (D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1721])). 87.71/26.55 thf(389,axiom,((! [A:nat]: ((plus_plus_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9009_add__2__eq__Suc_H)). 87.71/26.55 thf(3404,plain,((! [A:nat]: ((plus_plus_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (suc @ (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[389])). 87.71/26.55 thf(498,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_vebt_mint @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_801_vebt__mint_Osimps_I2_J)). 87.71/26.55 thf(3868,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_vebt_mint @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[498])). 87.71/26.55 thf(1518,axiom,((! [A:$o,B:$o]: ((vEBT_T_s_u_c_c2 @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1762_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I1_J)). 87.71/26.55 thf(7828,plain,((! [A:$o,B:$o]: ((vEBT_T_s_u_c_c2 @ (vEBT_Leaf @ A @ B) @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1518])). 87.71/26.55 thf(916,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (((power_power_nat @ B @ A) = (power_power_nat @ C @ A)) = (B = C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7995_power__eq__iff__eq__base)). 87.71/26.55 thf(5503,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (((power_power_nat @ B @ A) = (power_power_nat @ C @ A)) = (B = C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[916])). 87.71/26.55 thf(773,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((A = B) | ~ (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1469_nless__le)). 87.71/26.55 thf(4946,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)],[773])). 87.71/26.55 thf(656,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ (suc @ A)))) = (! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ A)) & (B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_Nat_OAll__less__Suc)). 87.71/26.55 thf(4485,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ (suc @ A)))) = (! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ A)) & (B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[656])). 87.71/26.55 thf(787,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2251_add__mono__thms__linordered__field_I5_J)). 87.71/26.55 thf(5011,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ A @ B) & (ord_less_nat @ C @ D)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[787])). 87.71/26.55 thf(1625,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_old_Onat_Odistinct_I2_J)). 87.71/26.55 thf(8227,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1625])). 87.71/26.55 thf(1024,axiom,((! [A:assn,B:assn,C:assn]: (((entails @ C @ B) => (entails @ (sup_sup_assn @ A @ C) @ B)) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5111_ent__disjE)). 87.71/26.55 thf(5908,plain,((! [A:assn,B:assn,C:assn]: (((entails @ C @ B) => (entails @ (sup_sup_assn @ A @ C) @ B)) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024])). 87.71/26.55 thf(1256,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/sandbox2/benchmark/theBenchmark.p',fact_2870_Nat_Oadd__diff__assoc)). 87.71/26.55 thf(6794,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)],[1256])). 87.71/26.55 thf(1645,axiom,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:assn]: ((hoare_7629718768684598413on_nat @ (times_times_assn @ D @ A) @ B @ (^ [E:option_nat]: (times_times_assn @ D @ (C @ E)))) <= (hoare_7629718768684598413on_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_frame__rule__left)). 87.71/26.55 thf(8300,plain,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:assn]: ((hoare_7629718768684598413on_nat @ (times_times_assn @ D @ A) @ B @ (^ [E:option_nat]: (times_times_assn @ D @ (C @ E)))) | ~ (hoare_7629718768684598413on_nat @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1645])). 87.71/26.55 thf(1547,axiom,((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2471_zero__less__two)). 87.71/26.55 thf(7951,plain,((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1547])). 87.71/26.55 thf(1187,axiom,((! [A:nat,B:nat]: (((A = B) <= (ord_less_eq_nat @ B @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1148_antisym)). 87.71/26.55 thf(6549,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)],[1187])). 87.71/26.55 thf(331,axiom,((! [A:list_nat,B:list_nat,C:nat]: ((nth_nat @ (append_nat @ A @ B) @ (plus_plus_nat @ (size_size_list_nat @ A) @ C)) = (nth_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8270_nth__append__length__plus)). 87.71/26.55 thf(3170,plain,((! [A:list_nat,B:list_nat,C:nat]: ((nth_nat @ (append_nat @ A @ B) @ (plus_plus_nat @ (size_size_list_nat @ A) @ C)) = (nth_nat @ B @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[331])). 87.71/26.55 thf(1504,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((((! [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)))))) <= (! [C:$o,D:$o]: (((((B = (some_nat @ zero_zero_nat)) <= (C)) & ((((~ (D)) => (B = none_nat)) & ((D) => (B = (some_nat @ one_one_nat)))) <= (~ (C)))) => (~ (accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ (vEBT_Leaf @ C @ D)))) <= (A = (vEBT_Leaf @ C @ D))))) <= (accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ A)) <= ((vEBT_vebt_mint @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1894_vebt__mint_Opelims)). 87.71/26.55 thf(7741,plain,((! [A:vEBT_VEBT,B:option_nat]: (((! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: ((A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) => ((B = none_nat) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (~ (accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)) | ~ (B = (some_nat @ C)) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))))) | ~ (! [C:$o,D:$o]: (((((B = (some_nat @ zero_zero_nat)) | ~ (C)) & ((((~ (D)) => (B = none_nat)) & ((D) => (B = (some_nat @ one_one_nat)))) | (C))) => (~ (accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ (vEBT_Leaf @ C @ D)))) | ~ (A = (vEBT_Leaf @ C @ D)))) | ~ (accp_VEBT_VEBT @ (vEBT_vebt_mint_rel) @ A) | ~ ((vEBT_vebt_mint @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1504])). 87.71/26.55 thf(418,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_mult__pos__pos)). 87.71/26.55 thf(3532,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[418])). 87.71/26.55 thf(1669,axiom,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_less__Suc0)). 87.71/26.55 thf(8381,plain,((! [A:nat]: ((ord_less_nat @ A @ (suc @ zero_zero_nat)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1669])). 87.71/26.55 thf(1510,axiom,((~ (ord_less_nat @ one_one_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1078_not__one__less__zero)). 87.71/26.55 thf(7795,plain,((~ (ord_less_nat @ one_one_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1510])). 87.71/26.55 thf(670,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/sandbox2/benchmark/theBenchmark.p',fact_7803_of__nat__zero__less__power__iff)). 87.71/26.55 thf(4526,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)],[670])). 87.71/26.55 thf(674,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2416_less__add__Suc1)). 87.71/26.55 thf(4537,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[674])). 87.71/26.55 thf(1367,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2869_Nat_Oadd__diff__assoc2)). 87.71/26.55 thf(7218,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)],[1367])). 87.71/26.55 thf(105,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/sandbox2/benchmark/theBenchmark.p',fact_9473_div2__even__ext__nat)). 87.71/26.55 thf(2193,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)],[105])). 87.71/26.55 thf(5,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1765_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I4_J)). 87.71/26.55 thf(1786,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])). 87.71/26.55 thf(795,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_not__gr0)). 87.71/26.55 thf(5033,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[795])). 87.71/26.55 thf(111,axiom,((! [A:$o,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn),E:heap_T8145700208782473153_VEBTi]: (((hoare_1429296392585015714_VEBTi @ B @ C @ D) <= (A)) => (((~ (A)) => (hoare_1429296392585015714_VEBTi @ B @ E @ D)) => (hoare_1429296392585015714_VEBTi @ B @ (if_Hea8453224502484754311_VEBTi @ A @ C @ E) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_if__rule)). 87.71/26.55 thf(2220,plain,((! [A:$o,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn),E:heap_T8145700208782473153_VEBTi]: (((hoare_1429296392585015714_VEBTi @ B @ C @ (D)) | ~ (A)) => (((~ (A)) => (hoare_1429296392585015714_VEBTi @ B @ E @ (D))) => (hoare_1429296392585015714_VEBTi @ B @ (if_Hea8453224502484754311_VEBTi @ A @ C @ E) @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[111])). 87.71/26.55 thf(1360,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 @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_less__mono__imp__le__mono)). 87.71/26.55 thf(7191,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 @ D @ E) => (ord_less_nat @ (A @ D) @ (A @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360])). 87.71/26.55 thf(1139,axiom,((! [A:vEBT_VEBT,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_deg__not__0)). 87.71/26.55 thf(6385,plain,((! [A:vEBT_VEBT,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139])). 87.71/26.55 thf(130,axiom,((! [A:list_real,B:list_nat,C:(list_real > (list_nat > $o))]: ((((! [D:real,E:list_real,F:nat,G:list_nat]: (((C @ E @ G) => (C @ (cons_real @ D @ E) @ (cons_nat @ F @ G))) <= ((size_size_list_real @ E) = (size_size_list_nat @ G)))) => (C @ A @ B)) <= (C @ nil_real @ nil_nat)) <= ((size_size_list_real @ A) = (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8532_list__induct2)). 87.71/26.55 thf(2326,plain,((! [A:list_real,B:list_nat,C:(list_real > (list_nat > $o))]: (((! [D:real,E:list_real,F:nat,G:list_nat]: (((C @ E @ G) => (C @ (cons_real @ D @ E) @ (cons_nat @ F @ G))) | ~ ((size_size_list_real @ E) = (size_size_list_nat @ G)))) => (C @ A @ B)) | ~ (C @ nil_real @ nil_nat) | ~ ((size_size_list_real @ A) = (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[130])). 87.71/26.55 thf(816,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_T_p_r_e_d @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = (plus_plus_nat @ one_one_nat @ (if_nat @ B @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2482_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_Osimps_I3_J)). 87.71/26.55 thf(5118,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_T_p_r_e_d @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = (plus_plus_nat @ one_one_nat @ (if_nat @ B @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[816])). 87.71/26.55 thf(877,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_eq_nat @ A @ C) => (B @ C))) => (bit_wf_set_bits_int @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10173_ones)). 87.71/26.55 thf(5363,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((ord_less_eq_nat @ A @ C) => (B @ C))) => (bit_wf_set_bits_int @ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[877])). 87.71/26.55 thf(124,axiom,((! [A:$o,B:assn,C:heap_Time_Heap_o,D:($o > assn),E:heap_Time_Heap_o]: (((hoare_hoare_triple_o @ B @ C @ D) <= (A)) => ((hoare_hoare_triple_o @ B @ (if_Heap_Time_Heap_o @ A @ C @ E) @ D) <= ((~ (A)) => (hoare_hoare_triple_o @ B @ E @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_if__rule)). 87.71/26.55 thf(2293,plain,((! [A:$o,B:assn,C:heap_Time_Heap_o,D:($o > assn),E:heap_Time_Heap_o]: (((hoare_hoare_triple_o @ B @ C @ (D)) | ~ (A)) => ((hoare_hoare_triple_o @ B @ (if_Heap_Time_Heap_o @ A @ C @ E) @ (D)) | ~ ((~ (A)) => (hoare_hoare_triple_o @ B @ E @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[124])). 87.71/26.55 thf(1614,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1823_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I5_J)). 87.71/26.55 thf(8188,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1614])). 87.71/26.55 thf(447,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (minus_minus_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2864_zero__less__diff)). 87.71/26.55 thf(3651,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)],[447])). 87.71/26.55 thf(1009,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (times_times_nat @ B @ (power_power_nat @ A @ C)) @ (power_power_nat @ A @ D)) = (ord_less_nat @ B @ (power_power_nat @ A @ (minus_minus_nat @ D @ C)))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8016_nat__mult__power__less__eq)). 87.71/26.55 thf(5859,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (times_times_nat @ B @ (power_power_nat @ A @ C)) @ (power_power_nat @ A @ D)) = (ord_less_nat @ B @ (power_power_nat @ A @ (minus_minus_nat @ D @ C)))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009])). 87.71/26.55 thf(1498,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (ord_less_eq_nat @ B @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1104_ord__eq__le__trans)). 87.71/26.55 thf(7719,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)],[1498])). 87.71/26.55 thf(224,axiom,((! [A:nat,B:list_int]: ((ord_less_nat @ A @ (size_size_list_int @ B)) => ((cons_int @ (nth_int @ B @ A) @ (drop_int @ (suc @ A) @ B)) = (drop_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8026_Cons__nth__drop__Suc)). 87.71/26.55 thf(2738,plain,((! [A:nat,B:list_int]: ((ord_less_nat @ A @ (size_size_list_int @ B)) => ((cons_int @ (nth_int @ B @ A) @ (drop_int @ (suc @ A) @ B)) = (drop_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[224])). 87.71/26.55 thf(567,axiom,((! [A:assn,B:assn]: ((inf_inf_assn @ A @ (inf_inf_assn @ A @ B)) = (inf_inf_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8935_assn__aci_I4_J)). 87.71/26.55 thf(4149,plain,((! [A:assn,B:assn]: ((inf_inf_assn @ A @ (inf_inf_assn @ A @ B)) = (inf_inf_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[567])). 87.71/26.55 thf(1732,axiom,((! [A:assn,B:nat]: ((times_times_assn @ (power_power_assn @ A @ B) @ A) = (times_times_assn @ A @ (power_power_assn @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7814_power__commutes)). 87.71/26.55 thf(8665,plain,((! [A:assn,B:nat]: ((times_times_assn @ (power_power_assn @ A @ B) @ A) = (times_times_assn @ A @ (power_power_assn @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1732])). 87.71/26.55 thf(32,axiom,((! [A:nat,B:nat,C:list_nat]: ((take_nat @ (suc @ A) @ (cons_nat @ B @ C)) = (cons_nat @ B @ (take_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6287_take__Suc__Cons)). 87.71/26.55 thf(1865,plain,((! [A:nat,B:nat,C:list_nat]: ((take_nat @ (suc @ A) @ (cons_nat @ B @ C)) = (cons_nat @ B @ (take_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[32])). 87.71/26.55 thf(275,axiom,((! [A:(int > (nat > assn)),B:list_nat]: ((vEBT_L77084186935402305nt_nat @ A @ nil_int @ B) = (pure_assn @ (B = nil_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8225_list__assn__aux__simps_I1_J)). 87.71/26.55 thf(2935,plain,((! [A:(int > (nat > assn)),B:list_nat]: ((vEBT_L77084186935402305nt_nat @ (A) @ nil_int @ B) = (pure_assn @ (B = nil_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[275])). 87.71/26.55 thf(1310,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) <= (ord_less_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_mult__less__mono1)). 87.71/26.55 thf(6991,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) | ~ (ord_less_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310])). 87.71/26.55 thf(736,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) = (? [C:nat]: ((B = (suc @ C)) & (ord_less_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Suc__less__eq2)). 87.71/26.55 thf(4822,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)],[736])). 87.71/26.55 thf(1543,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ C @ A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1938_minf_I5_J)). 87.71/26.55 thf(7924,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)],[1543])). 87.71/26.55 thf(229,axiom,((! [A:nat,B:list_o]: (((suc @ A) = (size_size_list_o @ B)) = (? [C:$o,D:list_o]: (((size_size_list_o @ D) = A) & (B = (cons_o @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4668_Suc__length__conv)). 87.71/26.55 thf(2753,plain,((! [A:nat,B:list_o]: (((suc @ A) = (size_size_list_o @ B)) = (? [C:$o,D:list_o]: (((size_size_list_o @ D) = A) & (B = (cons_o @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[229])). 87.71/26.55 thf(483,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ (vEBT_vebt_delete @ A @ C) @ D) = ((C != D) & (vEBT_vebt_member @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2518_dele__member__cont__corr)). 87.71/26.55 thf(3783,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((vEBT_invar_vebt @ A @ B) => ((vEBT_vebt_member @ (vEBT_vebt_delete @ A @ C) @ D) = (~ (C = D) & (vEBT_vebt_member @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[483])). 87.71/26.55 thf(1512,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = A) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8687_nat__mod__eq_H)). 87.71/26.55 thf(7800,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1512])). 87.71/26.55 thf(1213,axiom,((! [A:nat]: ? [B:list_real]: ((size_size_list_real @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2547_Ex__list__of__length)). 87.71/26.55 thf(6638,plain,((! [A:nat]: ? [B:list_real]: ((size_size_list_real @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213])). 87.71/26.55 thf(1486,axiom,((! [A:$o,B:$o]: (((A) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ zero_zero_nat))) & ((~ (A)) => (((~ (B)) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = none_nat)) & ((B) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ one_one_nat)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1451_vebt__mint_Osimps_I1_J)). 87.71/26.55 thf(7671,plain,((! [A:$o,B:$o]: (((A) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ zero_zero_nat))) & ((~ (A)) => (((~ (B)) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = none_nat)) & ((B) => ((vEBT_vebt_mint @ (vEBT_Leaf @ A @ B)) = (some_nat @ one_one_nat)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1486])). 87.71/26.55 thf(1431,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1047_nat__mult__1__right)). 87.71/26.55 thf(7465,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1431])). 87.71/26.55 thf(928,axiom,((! [A:nat,B:nat,C:nat]: (((((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))) <= (ord_less_eq_nat @ A @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3066_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add)). 87.71/26.55 thf(5539,plain,((! [A:nat,B:nat,C:nat]: ((((minus_minus_nat @ B @ A) = C) = (B = (plus_plus_nat @ C @ A))) | ~ (ord_less_eq_nat @ A @ B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[928])). 87.71/26.55 thf(1446,axiom,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2822_diff__0__eq__0)). 87.71/26.55 thf(7536,plain,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1446])). 87.71/26.55 thf(158,axiom,((! [A:nat,B:list_nat]: ((map_nat_nat @ (^ [C:nat]: (A)) @ B) = (replicate_nat @ (size_size_list_nat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3322_map__replicate__const)). 87.71/26.55 thf(2457,plain,((! [A:nat,B:list_nat]: ((map_nat_nat @ (^ [C:nat]: (A)) @ B) = (replicate_nat @ (size_size_list_nat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[158])). 87.71/26.55 thf(746,axiom,((! [A:assn,B:assn]: (entails @ A @ (sup_sup_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5116_ent__disjI1__direct)). 87.71/26.55 thf(4854,plain,((! [A:assn,B:assn]: (entails @ A @ (sup_sup_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[746])). 87.71/26.55 thf(1698,axiom,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) <= (ord_less_nat @ C @ (suc @ A)))) = ((B @ zero_zero_nat) & ! [C:nat]: ((B @ (suc @ C)) <= (ord_less_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_Comparator__Generator_OAll__less__Suc)). 87.71/26.55 thf(8497,plain,((! [A:nat,B:(nat > $o)]: ((! [C:nat]: ((B @ C) | ~ (ord_less_nat @ C @ (suc @ A)))) = ((B @ zero_zero_nat) & ! [C:nat]: ((B @ (suc @ C)) | ~ (ord_less_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1698])). 87.71/26.55 thf(702,axiom,((! [A:nat,B:nat]: ((A != zero_zero_nat) => (? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & ((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C)) & (dvd_dvd_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9468_bezout__add__strong__nat)). 87.71/26.55 thf(4640,plain,((! [A:nat,B:nat]: ((~ (A = zero_zero_nat)) => (? [C:nat,D:nat,E:nat]: ((dvd_dvd_nat @ C @ A) & ((times_times_nat @ A @ D) = (plus_plus_nat @ (times_times_nat @ B @ E) @ C)) & (dvd_dvd_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[702])). 87.71/26.55 thf(978,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/sandbox2/benchmark/theBenchmark.p',fact_7713_power__inject__exp)). 87.71/26.55 thf(5735,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)],[978])). 87.71/26.55 thf(1521,axiom,((! [A:nat]: ~ ((zero_zero_nat != A) & (dvd_dvd_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9452_gcd__nat_Oextremum__strict)). 87.71/26.55 thf(7843,plain,((! [A:nat]: ~ (~ (zero_zero_nat = A) & (dvd_dvd_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1521])). 87.71/26.55 thf(990,axiom,((! [A:nat]: ((A != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_gr__zeroI)). 87.71/26.55 thf(5784,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[990])). 87.71/26.55 thf(163,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = (numeral_numeral_nat @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9399_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J)). 87.71/26.55 thf(2474,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = (numeral_numeral_nat @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[163])). 87.71/26.55 thf(1135,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ (suc @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Suc__less__eq)). 87.71/26.55 thf(6372,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)],[1135])). 87.71/26.55 thf(1671,axiom,((! [A:heap_T2636463487746394924on_nat,B:(option_nat > assn)]: (hoare_7629718768684598413on_nat @ bot_bot_assn @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_972_false__rule)). 87.71/26.55 thf(8387,plain,((! [A:heap_T2636463487746394924on_nat,B:(option_nat > assn)]: (hoare_7629718768684598413on_nat @ bot_bot_assn @ A @ (B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1671])). 87.71/26.55 thf(372,axiom,((numeral_numeral_nat = (^ [A:num]: (suc @ (pred_numeral @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9922_numeral__eq__Suc)). 87.71/26.55 thf(3355,plain,(((numeral_numeral_nat) = (^ [A:num]: (suc @ (pred_numeral @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[372])). 87.71/26.55 thf(1527,axiom,((! [A:(nat > $o),B:nat,C:nat,D:nat]: (((ord_less_nat @ B @ C) => ((ord_less_nat @ D @ C) => ((A @ D) <= (! [E:nat]: (((A @ E) => (A @ (modulo_modulo_nat @ (suc @ E) @ C))) <= (ord_less_nat @ E @ C)))))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8709_mod__induct)). 87.71/26.55 thf(7865,plain,((! [A:(nat > $o),B:nat,C:nat,D:nat]: (((ord_less_nat @ B @ C) => ((ord_less_nat @ D @ C) => ((A @ D) | ~ (! [E:nat]: (((A @ E) => (A @ (modulo_modulo_nat @ (suc @ E) @ C))) | ~ (ord_less_nat @ E @ C)))))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1527])). 87.71/26.55 thf(1667,axiom,(((vEBT_V441764108873111860ildupi @ (suc @ zero_zero_nat)) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_VEBT__internal_OT__vebt__buildupi_Osimps_I2_J)). 87.71/26.55 thf(8376,plain,(((vEBT_V441764108873111860ildupi @ (suc @ zero_zero_nat)) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1667])). 87.71/26.55 thf(639,axiom,((! [A:nat,B:nat,C:nat]: (((((ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = (ord_less_eq_nat @ A @ B)) <= (ord_less_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7780_power__mono__iff)). 87.71/26.55 thf(4433,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)) = (ord_less_eq_nat @ A @ B)) | ~ (ord_less_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ B) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[639])). 87.71/26.55 thf(1420,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3057_ordered__cancel__comm__monoid__diff__class_Odiff__add)). 87.71/26.55 thf(7415,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)],[1420])). 87.71/26.55 thf(1194,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ C @ B)) <= (ord_less_nat @ A @ one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7798_power__decreasing__iff)). 87.71/26.55 thf(6572,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)) = (ord_less_eq_nat @ C @ B)) | ~ (ord_less_nat @ A @ one_one_nat) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194])). 87.71/26.55 thf(491,axiom,((! [A:int,B:list_int]: ((size_size_list_int @ (cons_int @ A @ B)) = (suc @ (size_size_list_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4798_length__Cons)). 87.71/26.55 thf(3815,plain,((! [A:int,B:list_int]: ((size_size_list_int @ (cons_int @ A @ B)) = (suc @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[491])). 87.71/26.55 thf(121,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ B @ C) @ D) = (numeral_numeral_nat @ (bit0 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9395_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_Osimps_I4_J)). 87.71/26.55 thf(2284,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_i_n_s_e_r_t @ (vEBT_Node @ none_P5556105721700978146at_nat @ (suc @ (suc @ A)) @ B @ C) @ D) = (numeral_numeral_nat @ (bit0 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[121])). 87.71/26.55 thf(1126,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ ((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2322_add__leE)). 87.71/26.55 thf(6340,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => (~ (~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126])). 87.71/26.55 thf(888,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) <= ((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2321_less__add__eq__less)). 87.71/26.55 thf(5407,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_nat @ C @ D) | ~ ((plus_plus_nat @ C @ B) = (plus_plus_nat @ A @ D)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[888])). 87.71/26.55 thf(1201,axiom,((! [A:option4927543243414619207at_nat]: ((A != none_P5556105721700978146at_nat) = (? [B:product_prod_nat_nat]: (A = (some_P7363390416028606310at_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_not__None__eq)). 87.71/26.55 thf(6604,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)],[1201])). 87.71/26.55 thf(76,axiom,((! [A:nat,B:nat,C:nat]: ((map_nat_nat @ (^ [D:nat]: (plus_plus_nat @ D @ A)) @ (upt @ B @ C)) = (upt @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8839_map__add__upt_H)). 87.71/26.55 thf(2065,plain,((! [A:nat,B:nat,C:nat]: ((map_nat_nat @ (^ [D:nat]: (plus_plus_nat @ D @ A)) @ (upt @ B @ C)) = (upt @ (plus_plus_nat @ B @ A) @ (plus_plus_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[76])). 87.71/26.55 thf(173,axiom,((((=) @ list_int) = (^ [A:list_int,B:list_int]: (! [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/sandbox2/benchmark/theBenchmark.p',fact_2651_list__eq__iff__nth__eq)). 87.71/26.55 thf(2510,plain,((((=) @ list_int) = (^ [A:list_int,B:list_int]: (! [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)],[173])). 87.71/26.55 thf(1198,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7847_power__mono)). 87.71/26.55 thf(6585,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ zero_zero_nat @ A) => (ord_less_eq_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198])). 87.71/26.55 thf(135,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) & (ord_less_eq_nat @ A @ B)) => ((append_nat @ (upt @ A @ B) @ (upt @ B @ C)) = (upt @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8833_upt__merge)). 87.71/26.55 thf(2346,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) & (ord_less_eq_nat @ A @ B)) => ((append_nat @ (upt @ A @ B) @ (upt @ B @ C)) = (upt @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[135])). 87.71/26.55 thf(456,axiom,((! [A:list_int,B:list_int]: (((size_size_list_int @ A) != (size_size_list_int @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2554_neq__if__length__neq)). 87.71/26.55 thf(3678,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)],[456])). 87.71/26.55 thf(81,axiom,((! [A:vEBT_VEBT]: ((? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B)) <= (~ (vEBT_VEBT_minNull @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2592_not__min__Null__member)). 87.71/26.55 thf(2079,plain,((! [A:vEBT_VEBT]: (? [B:nat]: (vEBT_V8194947554948674370ptions @ A @ B) | (vEBT_VEBT_minNull @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[81])). 87.71/26.55 thf(1055,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: ((C = zero_zero_nat) <= (B = (plus_plus_nat @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2379_canonically__ordered__monoid__add__class_OlessE)). 87.71/26.55 thf(6024,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (! [C:nat]: ((C = zero_zero_nat) | ~ (B = (plus_plus_nat @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055])). 87.71/26.55 thf(218,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((E = (plus_plus_nat @ D @ B)) => (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)))) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9052_nat__add__offset__less)). 87.71/26.55 thf(2721,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D)) => ((E = (plus_plus_nat @ D @ B)) => (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ E)))) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[218])). 87.71/26.55 thf(371,axiom,((! [A:num,B:nat]: ((minus_minus_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (minus_minus_nat @ (pred_numeral @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9919_diff__numeral__Suc)). 87.71/26.55 thf(3352,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)],[371])). 87.71/26.55 thf(1688,axiom,((! [A:nat,B:nat]: ((unique6322359934112328802ux_nat @ (product_Pair_nat_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2536_divides__aux__eq)). 87.71/26.55 thf(8452,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)],[1688])). 87.71/26.55 thf(822,axiom,((! [A:$o]: (((pure_assn @ A) = one_one_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1733_pure__assn__eq__emp__iff)). 87.71/26.55 thf(5143,plain,((! [A:$o]: (((pure_assn @ A) = one_one_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[822])). 87.71/26.55 thf(589,axiom,((! [A:list_real,B:list_real]: (((size_size_list_real @ A) != (size_size_list_real @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2551_neq__if__length__neq)). 87.71/26.55 thf(4228,plain,((! [A:list_real,B:list_real]: ((~ ((size_size_list_real @ A) = (size_size_list_real @ B))) => (~ (A = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[589])). 87.71/26.55 thf(1465,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) = (A = B)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1475_antisym__conv1)). 87.71/26.55 thf(7594,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)],[1465])). 87.71/26.55 thf(1442,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_mult__right__mono)). 87.71/26.55 thf(7514,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1442])). 87.71/26.55 thf(962,axiom,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2415_less__add__Suc2)). 87.71/26.55 thf(5671,plain,((! [A:nat,B:nat]: (ord_less_nat @ A @ (suc @ (plus_plus_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[962])). 87.71/26.55 thf(1204,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/sandbox2/benchmark/theBenchmark.p',fact_10139_nat__mult__min__left)). 87.71/26.55 thf(6613,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)],[1204])). 87.71/26.55 thf(661,axiom,((modulo_modulo_nat = (^ [A:nat,B:nat]: (minus_minus_nat @ A @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8739_modulo__nat__def)). 87.71/26.55 thf(4498,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)],[661])). 87.71/26.55 thf(1292,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ (power_power_nat @ A @ (suc @ B)) @ (power_power_nat @ C @ (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7918_power__le__imp__le__base)). 87.71/26.55 thf(6920,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ A @ 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)],[1292])). 87.71/26.55 thf(1749,axiom,((! [A:nat]: ((binomial @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8869_binomial__1)). 87.71/26.55 thf(8715,plain,((! [A:nat]: ((binomial @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1749])). 87.71/26.55 thf(1091,axiom,((! [A:$o,B:$o]: (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_invar__vebt_Ointros_I1_J)). 87.71/26.55 thf(6179,plain,((! [A:$o,B:$o]: (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091])). 87.71/26.55 thf(1337,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ zero_zero_nat))) => ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ (suc @ D)))) => ((! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))) => ((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E))) => ((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_871_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Ocases)). 87.71/26.55 thf(7077,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$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:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))) => ((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E))) => ((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337])). 87.71/26.55 thf(1772,axiom,(((finite_card_literal @ top_top_set_literal) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10203_card__literal)). 87.71/26.55 thf(8799,plain,(((finite_card_literal @ top_top_set_literal) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1772])). 87.71/26.55 thf(921,axiom,((! [A:nat,B:nat,C:nat]: ((((dvd_dvd_nat @ A @ B) <= (ord_less_eq_nat @ C @ B)) <= (dvd_dvd_nat @ A @ C)) <= (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9459_dvd__diffD)). 87.71/26.55 thf(5520,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ A @ B) | ~ (ord_less_eq_nat @ C @ B) | ~ (dvd_dvd_nat @ A @ C) | ~ (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[921])). 87.71/26.55 thf(300,axiom,((! [A:nat,B:int,C:list_int]: ((drop_int @ (suc @ A) @ (cons_int @ B @ C)) = (drop_int @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7726_drop__Suc__Cons)). 87.71/26.55 thf(3038,plain,((! [A:nat,B:int,C:list_int]: ((drop_int @ (suc @ A) @ (cons_int @ B @ C)) = (drop_int @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[300])). 87.71/26.55 thf(1538,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) <= (ord_less_eq_nat @ B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_mult__nonneg__nonpos)). 87.71/26.55 thf(7907,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_eq_nat @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1538])). 87.71/26.55 thf(1158,axiom,((! [A:nat,B:list_o]: ((foldl_nat_o @ (^ [C:nat,D:$o]: (suc @ C)) @ A @ B) = (plus_plus_nat @ A @ (size_size_list_o @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4747_foldl__length__aux)). 87.71/26.55 thf(6443,plain,((! [A:nat,B:list_o]: ((foldl_nat_o @ (^ [C:nat,D:$o]: (suc @ C)) @ A @ B) = (plus_plus_nat @ A @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158])). 87.71/26.55 thf(1519,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ (vEBT_vebt_delete @ A @ C) @ B) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2517_delete__pres__valid)). 87.71/26.55 thf(7837,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ (vEBT_vebt_delete @ A @ C) @ B) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1519])). 87.71/26.55 thf(1163,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C))) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_mult__le__less__imp__less)). 87.71/26.55 thf(6461,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ A @ B) => (((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C))) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163])). 87.71/26.55 thf(511,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ A @ B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1321_linorder__neq__iff)). 87.71/26.55 thf(3957,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)],[511])). 87.71/26.55 thf(234,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_T_m_i_n_t @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2520_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Osimps_I2_J)). 87.71/26.55 thf(2774,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_T_m_i_n_t @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[234])). 87.71/26.55 thf(1263,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_mult__strict__mono)). 87.71/26.55 thf(6815,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => ((ord_less_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263])). 87.71/26.55 thf(738,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/sandbox2/benchmark/theBenchmark.p',fact_8735_mod__eq__nat2E)). 87.71/26.55 thf(4828,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)],[738])). 87.71/26.55 thf(1628,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_gr0__conv__Suc)). 87.71/26.55 thf(8237,plain,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) = (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1628])). 87.71/26.55 thf(391,axiom,((! [A:nat,B:num]: ((minus_minus_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (minus_minus_nat @ A @ (pred_numeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9918_diff__Suc__numeral)). 87.71/26.55 thf(3419,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)],[391])). 87.71/26.55 thf(1277,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3014_diff__add__inverse)). 87.71/26.55 thf(6866,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277])). 87.71/26.55 thf(1097,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((C != D) & (A != B)) = ((plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) != (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2609_crossproduct__noteq)). 87.71/26.55 thf(6197,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)],[1097])). 87.71/26.55 thf(763,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)) @ D) => ((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))) <= ((A = B) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8993_del__single__cont)). 87.71/26.55 thf(4914,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)) @ D) => ((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))) | ~ ((A = B) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[763])). 87.71/26.55 thf(1004,axiom,((! [A:nat,B:(nat > $o)]: ((ord_less_nat @ zero_zero_nat @ A) => ((B @ one_one_nat) => ((! [C:nat]: (((B @ (suc @ C)) <= (B @ C)) <= (ord_less_nat @ zero_zero_nat @ C))) => (B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1413_nat__induct__non__zero)). 87.71/26.55 thf(5827,plain,((! [A:nat,B:(nat > $o)]: ((ord_less_nat @ zero_zero_nat @ A) => ((B @ one_one_nat) => ((! [C:nat]: ((B @ (suc @ C)) | ~ (B @ C) | ~ (ord_less_nat @ zero_zero_nat @ C))) => (B @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004])). 87.71/26.55 thf(1740,axiom,((! [A:nat,B:nat]: ((ord_min_nat @ (suc @ A) @ (suc @ B)) = (suc @ (ord_min_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10132_min__Suc__Suc)). 87.71/26.55 thf(8688,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)],[1740])). 87.71/26.55 thf(359,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (comm_s4663373288045622133er_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4829_pochhammer__pos)). 87.71/26.55 thf(3270,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)],[359])). 87.71/26.55 thf(118,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ A @ (times_times_int @ B @ C)) = (times_times_int @ B @ (times_times_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_ab__semigroup__mult__class_Omult_Oleft__commute)). 87.71/26.55 thf(2246,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)],[118])). 87.71/26.55 thf(1608,axiom,((! [A:num]: ((size_size_option_num @ (some_num @ A)) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_option_Osize_I4_J)). 87.71/26.55 thf(8171,plain,((! [A:num]: ((size_size_option_num @ (some_num @ A)) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1608])). 87.71/26.55 thf(1691,axiom,((! [A:int]: ((bit_se545348938243370406it_int @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10113_push__bit__int__code_I1_J)). 87.71/26.55 thf(8461,plain,((! [A:int]: ((bit_se545348938243370406it_int @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1691])). 87.71/26.55 thf(912,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_less__nat__zero__code)). 87.71/26.55 thf(5491,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[912])). 87.71/26.55 thf(1388,axiom,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_lambda__zero)). 87.71/26.55 thf(7282,plain,(((^ [A:nat]: (zero_zero_nat)) = (times_times_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388])). 87.71/26.55 thf(1015,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (modulo_modulo_nat @ A @ B)) = (~ (dvd_dvd_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9469_mod__greater__zero__iff__not__dvd)). 87.71/26.55 thf(5880,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)],[1015])). 87.71/26.55 thf(1268,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/sandbox2/benchmark/theBenchmark.p',fact_2_deg__deg__n)). 87.71/26.55 thf(6832,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)],[1268])). 87.71/26.55 thf(801,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ A @ B)) = ((ord_less_eq_nat @ B @ A) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8648_div__greater__zero__iff)). 87.71/26.55 thf(5054,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ A @ B)) = ((ord_less_eq_nat @ B @ A) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[801])). 87.71/26.55 thf(688,axiom,((! [A:assn,B:assn,C:(nat > assn),D:(nat > assn),E:heap_Time_Heap_nat]: ((entails @ A @ B) => (((hoare_3067605981109127869le_nat @ A @ E @ D) <= (hoare_3067605981109127869le_nat @ B @ E @ C)) <= (! [F:nat]: (entails @ (C @ F) @ (D @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4064_cons__rule)). 87.71/26.55 thf(4586,plain,((! [A:assn,B:assn,C:(nat > assn),D:(nat > assn),E:heap_Time_Heap_nat]: ((entails @ A @ B) => ((hoare_3067605981109127869le_nat @ A @ E @ (D)) | ~ (hoare_3067605981109127869le_nat @ B @ E @ (C)) | ~ (! [F:nat]: (entails @ (C @ F) @ (D @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[688])). 87.71/26.55 thf(1635,axiom,((! [A:list_int]: ((foldl_nat_int @ (^ [B:nat,C:int]: (suc @ B)) @ zero_zero_nat @ A) = (size_size_list_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4587_foldl__length)). 87.71/26.55 thf(8269,plain,((! [A:list_int]: ((foldl_nat_int @ (^ [B:nat,C:int]: (suc @ B)) @ zero_zero_nat @ A) = (size_size_list_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1635])). 87.71/26.55 thf(246,axiom,((! [A:nat]: ((dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (suc @ A)) = (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9442_even__Suc)). 87.71/26.55 thf(2839,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)],[246])). 87.71/26.55 thf(584,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2605_add__0__iff)). 87.71/26.55 thf(4213,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[584])). 87.71/26.55 thf(1405,axiom,((! [A:assn,B:assn,C:assn]: ((sup_sup_assn @ (sup_sup_assn @ A @ B) @ C) = (sup_sup_assn @ A @ (sup_sup_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5430_norm__assertion__simps_I15_J)). 87.71/26.55 thf(7360,plain,((! [A:assn,B:assn,C:assn]: ((sup_sup_assn @ (sup_sup_assn @ A @ B) @ C) = (sup_sup_assn @ A @ (sup_sup_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405])). 87.71/26.55 thf(1363,axiom,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_986_mult_Oright__neutral)). 87.71/26.55 thf(7206,plain,((! [A:nat]: ((times_times_nat @ A @ one_one_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363])). 87.71/26.55 thf(340,axiom,((! [A:nat]: ((bit_Sh3965577149348748681tl_nat @ (suc @ zero_zero_nat) @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10182_shiftl__Suc__0)). 87.71/26.55 thf(3197,plain,((! [A:nat]: ((bit_Sh3965577149348748681tl_nat @ (suc @ zero_zero_nat) @ A) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[340])). 87.71/26.55 thf(876,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_member @ (vEBT_Leaf @ A @ B) @ C) = (((C = zero_zero_nat) => (A)) & (((C = one_one_nat) & ((B) <= (C = one_one_nat))) <= (C != zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1415_vebt__member_Osimps_I1_J)). 87.71/26.55 thf(5346,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_member @ (vEBT_Leaf @ A @ B) @ C) = (((C = zero_zero_nat) => (A)) & (((C = one_one_nat) & ((B) | ~ (C = one_one_nat))) | (C = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[876])). 87.71/26.55 thf(10,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ A @ (suc @ (suc @ (suc @ B)))) = (modulo_modulo_nat @ A @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9163_mod__Suc__eq__mod__add3)). 87.71/26.55 thf(1801,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)],[10])). 87.71/26.55 thf(807,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ (power_power_nat @ A @ B) @ one_one_nat) <= (ord_less_eq_nat @ A @ one_one_nat)) <= (ord_less_eq_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7910_power__le__one)). 87.71/26.55 thf(5093,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ B) @ one_one_nat) | ~ (ord_less_eq_nat @ A @ one_one_nat) | ~ (ord_less_eq_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[807])). 87.71/26.55 thf(925,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) <= (ord_less_nat @ B @ zero_zero_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_mult__pos__neg2)). 87.71/26.55 thf(5531,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat) | ~ (ord_less_nat @ B @ zero_zero_nat) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[925])). 87.71/26.55 thf(1700,axiom,((! [A:nat]: (zero_zero_nat != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_Zero__not__Suc)). 87.71/26.55 thf(8502,plain,((! [A:nat]: ~ (zero_zero_nat = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1700])). 87.71/26.55 thf(1476,axiom,((! [A:nat,B:nat]: ((~ (! [C:nat]: (B != (suc @ (plus_plus_nat @ A @ C))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2417_less__natE)). 87.71/26.55 thf(7626,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)],[1476])). 87.71/26.55 thf(575,axiom,((! [A:nat,B:nat,C:list_nat]: ((enumerate_nat @ A @ (cons_nat @ B @ C)) = (cons_P6512896166579812791at_nat @ (product_Pair_nat_nat @ A @ B) @ (enumerate_nat @ (suc @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4607_enumerate__simps_I2_J)). 87.71/26.55 thf(4176,plain,((! [A:nat,B:nat,C:list_nat]: ((enumerate_nat @ A @ (cons_nat @ B @ C)) = (cons_P6512896166579812791at_nat @ (product_Pair_nat_nat @ A @ B) @ (enumerate_nat @ (suc @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[575])). 87.71/26.55 thf(1085,axiom,((! [A:nat,B:(nat > $o),C:nat]: (((B @ C) <= (! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((B @ D) <= (! [E:nat]: ((B @ E) <= (ord_less_nat @ D @ E))))))) <= (! [D:nat]: ((B @ D) <= (ord_less_nat @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1826_nat__descend__induct)). 87.71/26.55 thf(6154,plain,((! [A:nat,B:(nat > $o),C:nat]: ((B @ C) | ~ (! [D:nat]: ((ord_less_eq_nat @ D @ A) => ((B @ D) | ~ (! [E:nat]: ((B @ E) | ~ (ord_less_nat @ D @ E)))))) | ~ (! [D:nat]: ((B @ D) | ~ (ord_less_nat @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085])). 87.71/26.55 thf(1092,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (times_times_nat @ B @ C)) => (ord_less_nat @ (divide_divide_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8643_less__mult__imp__div__less)). 87.71/26.55 thf(6184,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (times_times_nat @ B @ C)) => (ord_less_nat @ (divide_divide_nat @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092])). 87.71/26.55 thf(1715,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_zero__less__Suc)). 87.71/26.55 thf(8561,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1715])). 87.71/26.55 thf(335,axiom,((! [A:list_nat,B:nat]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ B) => ((drop_nat @ B @ A) = nil_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8282_drop__all)). 87.71/26.55 thf(3182,plain,((! [A:list_nat,B:nat]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ B) => ((drop_nat @ B @ A) = nil_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[335])). 87.71/26.55 thf(264,axiom,((! [A:int,B:nat,C:nat]: ((power_power_int @ A @ (plus_plus_nat @ B @ C)) = (times_times_int @ (power_power_int @ A @ B) @ (power_power_int @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7892_power__add)). 87.71/26.55 thf(2896,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)],[264])). 87.71/26.55 thf(1238,axiom,((! [A:$o,B:$o]: ((vEBT_size_VEBT @ (vEBT_Leaf @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3196_VEBT_Osize__gen_I2_J)). 87.71/26.55 thf(6737,plain,((! [A:$o,B:$o]: ((vEBT_size_VEBT @ (vEBT_Leaf @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238])). 87.71/26.55 thf(1041,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ C @ D)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_mult__le__mono)). 87.71/26.55 thf(5972,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ C @ D) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041])). 87.71/26.55 thf(1770,axiom,((! [A:list_nat]: (time_T3621710982123377501ay_nat @ (array_of_list_nat @ A) @ (suc @ (size_size_list_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4744_TBOUND__of__list)). 87.71/26.55 thf(8794,plain,((! [A:list_nat]: (time_T3621710982123377501ay_nat @ (array_of_list_nat @ A) @ (suc @ (size_size_list_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1770])). 87.71/26.55 thf(943,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3020_diff__le__mono)). 87.71/26.55 thf(5616,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[943])). 87.71/26.55 thf(257,axiom,((bit_se727722235901077358nd_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) & ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se727722235901077358nd_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9847_and__nat__rec)). 87.71/26.55 thf(2871,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)],[257])). 87.71/26.55 thf(665,axiom,((! [A:(list_nat > $o),B:list_nat]: ((! [C:list_nat]: ((A @ C) <= (! [D:list_nat]: ((ord_less_nat @ (size_size_list_nat @ D) @ (size_size_list_nat @ C)) => (A @ D))))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2561_length__induct)). 87.71/26.55 thf(4509,plain,((! [A:(list_nat > $o),B:list_nat]: ((! [C:list_nat]: ((A @ C) | ~ (! [D:list_nat]: ((ord_less_nat @ (size_size_list_nat @ D) @ (size_size_list_nat @ C)) => (A @ D))))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[665])). 87.71/26.55 thf(652,axiom,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ A @ B @ C) => (hoare_1429296392585015714_VEBTi @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_is__hoare__triple)). 87.71/26.55 thf(4477,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[652])). 87.71/26.55 thf(63,axiom,((! [A:complex,B:nat]: ((power_power_complex @ A @ (suc @ B)) = (times_times_complex @ (power_power_complex @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7882_power__Suc2)). 87.71/26.55 thf(1969,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)],[63])). 87.71/26.55 thf(851,axiom,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (sup_sup_assn @ A @ B) @ C) = (sup_sup_assn @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5109_star__or__dist1)). 87.71/26.55 thf(5267,plain,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (sup_sup_assn @ A @ B) @ C) = (sup_sup_assn @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[851])). 87.71/26.55 thf(328,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) != (suc @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9027_double__not__eq__Suc__double)). 87.71/26.55 thf(3160,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)],[328])). 87.71/26.55 thf(1254,axiom,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1043_comm__monoid__mult__class_Omult__1)). 87.71/26.55 thf(6789,plain,((! [A:nat]: ((times_times_nat @ one_one_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254])). 87.71/26.55 thf(101,axiom,((! [A:nat,B:list_nat]: (((last_nat @ (drop_nat @ A @ B)) = (last_nat @ B)) <= (ord_less_nat @ A @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7772_last__drop)). 87.71/26.55 thf(2180,plain,((! [A:nat,B:list_nat]: (((last_nat @ (drop_nat @ A @ B)) = (last_nat @ B)) | ~ (ord_less_nat @ A @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[101])). 87.71/26.55 thf(957,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (minus_minus_nat @ B @ C)) = (ord_less_nat @ (plus_plus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3100_less__diff__conv)). 87.71/26.55 thf(5657,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)],[957])). 87.71/26.55 thf(555,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) <= (ord_less_nat @ E @ F))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F)))))) <= (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) <= (ord_less_nat @ E @ F)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1988_pinf_I1_J)). 87.71/26.55 thf(4103,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: (((C @ F) = (D @ F)) | ~ (ord_less_nat @ E @ F))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ E @ F) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F)))))) | ~ (? [E:nat]: ! [F:nat]: (((A @ F) = (B @ F)) | ~ (ord_less_nat @ E @ F)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[555])). 87.71/26.55 thf(1019,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_nat__0__less__mult__iff)). 87.71/26.55 thf(5894,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) = ((ord_less_nat @ zero_zero_nat @ A) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019])). 87.71/26.55 thf(762,axiom,((! [A:nat]: ((binomial @ A @ zero_zero_nat) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8873_binomial__n__0)). 87.71/26.55 thf(4911,plain,((! [A:nat]: ((binomial @ A @ zero_zero_nat) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[762])). 87.71/26.55 thf(1456,axiom,((! [A:nat,B:list_int]: (((suc @ A) = (size_size_list_int @ B)) = (? [C:int,D:list_int]: ((B = (cons_int @ C @ D)) & ((size_size_list_int @ D) = A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4670_Suc__length__conv)). 87.71/26.55 thf(7566,plain,((! [A:nat,B:list_int]: (((suc @ A) = (size_size_list_int @ B)) = (? [C:int,D:list_int]: ((B = (cons_int @ C @ D)) & ((size_size_list_int @ D) = A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1456])). 87.71/26.55 thf(1761,axiom,((! [A:$o,B:assn,C:heap_Time_Heap_o,D:($o > assn)]: (((hoare_hoare_triple_o @ B @ C @ D) <= (A)) => (hoare_hoare_triple_o @ (times_times_assn @ B @ (pure_assn @ A)) @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_norm__pre__pure__rule1)). 87.71/26.55 thf(8750,plain,((! [A:$o,B:assn,C:heap_Time_Heap_o,D:($o > assn)]: (((hoare_hoare_triple_o @ B @ C @ (D)) | ~ (A)) => (hoare_hoare_triple_o @ (times_times_assn @ B @ (pure_assn @ A)) @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1761])). 87.71/26.55 thf(1121,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ A @ (times_times_nat @ B @ C))) @ C) = (modulo_modulo_nat @ (suc @ A) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8697_Suc__mod__mult__self1)). 87.71/26.55 thf(6319,plain,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ A @ (times_times_nat @ B @ C))) @ C) = (modulo_modulo_nat @ (suc @ A) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121])). 87.71/26.55 thf(406,axiom,((! [A:list_o,B:nat]: (((size_size_list_o @ A) = (suc @ B)) = (? [C:$o,D:list_o]: (((size_size_list_o @ D) = B) & (A = (cons_o @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4672_length__Suc__conv)). 87.71/26.55 thf(3483,plain,((! [A:list_o,B:nat]: (((size_size_list_o @ A) = (suc @ B)) = (? [C:$o,D:list_o]: (((size_size_list_o @ D) = B) & (A = (cons_o @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[406])). 87.71/26.55 thf(1060,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1675_order__le__imp__less__or__eq)). 87.71/26.55 thf(6044,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060])). 87.71/26.55 thf(1333,axiom,((zero_zero_nat != one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1033_zero__neq__one)). 87.71/26.55 thf(7066,plain,((~ (zero_zero_nat = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333])). 87.71/26.55 thf(1046,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2992_right__diff__distrib_H)). 87.71/26.55 thf(5987,plain,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046])). 87.71/26.55 thf(919,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) <= (ord_less_nat @ zero_zero_nat @ A)) <= (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_zero__less__mult__pos)). 87.71/26.55 thf(5511,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ B) | ~ (ord_less_nat @ zero_zero_nat @ A) | ~ (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[919])). 87.71/26.55 thf(1050,axiom,((! [A:$o,B:heap_Time_Heap_o,C:($o > assn)]: ((hoare_hoare_triple_o @ (pure_assn @ A) @ B @ C) = ((hoare_hoare_triple_o @ one_one_assn @ B @ C) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1736_norm__pre__pure__iff__sng)). 87.71/26.55 thf(6004,plain,((! [A:$o,B:heap_Time_Heap_o,C:($o > assn)]: ((hoare_hoare_triple_o @ (pure_assn @ A) @ B @ (C)) = ((hoare_hoare_triple_o @ one_one_assn @ B @ (C)) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050])). 87.71/26.55 thf(1756,axiom,((! [A:nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7720_power__Suc0__right)). 87.71/26.55 thf(8735,plain,((! [A:nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1756])). 87.71/26.55 thf(633,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = ((B != A) & (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1090_nle__le)). 87.71/26.55 thf(4401,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)],[633])). 87.71/26.55 thf(638,axiom,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1739_norm__assertion__simps_I2_J)). 87.71/26.55 thf(4430,plain,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[638])). 87.71/26.55 thf(938,axiom,((! [A:nat,B:nat,C:int,D:list_int]: ((((slice_int @ A @ B @ (cons_int @ C @ D)) = (slice_int @ (minus_minus_nat @ A @ one_one_nat) @ (minus_minus_nat @ B @ one_one_nat) @ D)) <= (~ ((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B)))) & (((slice_int @ A @ B @ (cons_int @ C @ D)) = (cons_int @ C @ (slice_int @ A @ (minus_minus_nat @ B @ one_one_nat) @ D))) <= ((ord_less_nat @ zero_zero_nat @ B) & (A = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4783_slice__Cons)). 87.71/26.55 thf(5584,plain,((! [A:nat,B:nat,C:int,D:list_int]: ((((slice_int @ A @ B @ (cons_int @ C @ D)) = (slice_int @ (minus_minus_nat @ A @ one_one_nat) @ (minus_minus_nat @ B @ one_one_nat) @ D)) | ((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B))) & (((slice_int @ A @ B @ (cons_int @ C @ D)) = (cons_int @ C @ (slice_int @ A @ (minus_minus_nat @ B @ one_one_nat) @ D))) | ~ ((ord_less_nat @ zero_zero_nat @ B) & (A = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[938])). 87.71/26.55 thf(1492,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/sandbox2/benchmark/theBenchmark.p',fact_552_nat__mult__le__cancel1)). 87.71/26.55 thf(7699,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)],[1492])). 87.71/26.55 thf(196,axiom,((comm_s4663373288045622133er_nat = (^ [A:nat,B:nat]: (if_nat @ (B = zero_zero_nat) @ one_one_nat @ (set_fo2584398358068434914at_nat @ (^ [C:nat]: (times_times_nat @ (plus_plus_nat @ A @ (semiri1316708129612266289at_nat @ C)))) @ zero_zero_nat @ (minus_minus_nat @ B @ one_one_nat) @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4803_pochhammer__code)). 87.71/26.55 thf(2610,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)],[196])). 87.71/26.55 thf(296,axiom,((! [A:nat,B:list_int,C:nat]: (((nth_int @ (drop_int @ A @ B) @ C) = (nth_int @ B @ (plus_plus_nat @ A @ C))) <= (ord_less_eq_nat @ A @ (size_size_list_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7795_nth__drop)). 87.71/26.55 thf(3027,plain,((! [A:nat,B:list_int,C:nat]: (((nth_int @ (drop_int @ A @ B) @ C) = (nth_int @ B @ (plus_plus_nat @ A @ C))) | ~ (ord_less_eq_nat @ A @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[296])). 87.71/26.55 thf(126,axiom,((! [A:nat,B:nat,C:list_nat,D:list_nat]: ((ord_less_eq_nat @ A @ B) => (((upt @ A @ B) = (append_nat @ C @ D)) = (? [E:nat]: ((ord_less_eq_nat @ A @ E) & ((upt @ A @ E) = C) & ((upt @ E @ B) = D) & (ord_less_eq_nat @ E @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8845_upt__eq__append__conv)). 87.71/26.55 thf(2314,plain,((! [A:nat,B:nat,C:list_nat,D:list_nat]: ((ord_less_eq_nat @ A @ B) => (((upt @ A @ B) = (append_nat @ C @ D)) = (? [E:nat]: ((ord_less_eq_nat @ A @ E) & ((upt @ A @ E) = C) & ((upt @ E @ B) = D) & (ord_less_eq_nat @ E @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[126])). 87.71/26.55 thf(134,axiom,((! [A:nat,B:nat]: ((if_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Nat__Onat_T)). 87.71/26.55 thf(2343,plain,((! [A:nat,B:nat]: ((if_nat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[134])). 87.71/26.55 thf(1603,axiom,((! [A:assn,B:assn,C:(option_nat > assn),D:(option_nat > assn),E:heap_T2636463487746394924on_nat]: (((! [F:option_nat]: (entails @ (C @ F) @ (D @ F))) => ((hoare_7629718768684598413on_nat @ B @ E @ C) => (hoare_7629718768684598413on_nat @ A @ E @ D))) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4061_cons__rule)). 87.71/26.55 thf(8156,plain,((! [A:assn,B:assn,C:(option_nat > assn),D:(option_nat > assn),E:heap_T2636463487746394924on_nat]: (((! [F:option_nat]: (entails @ (C @ F) @ (D @ F))) => ((hoare_7629718768684598413on_nat @ B @ E @ (C)) => (hoare_7629718768684598413on_nat @ A @ E @ (D)))) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1603])). 87.71/26.55 thf(1010,axiom,((! [A:assn,B:assn,C:heap_Time_Heap_o,D:($o > assn)]: (((hoare_hoare_triple_o @ A @ C @ D) <= (hoare_hoare_triple_o @ B @ C @ D)) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4071_cons__pre__rule)). 87.71/26.55 thf(5863,plain,((! [A:assn,B:assn,C:heap_Time_Heap_o,D:($o > assn)]: ((hoare_hoare_triple_o @ A @ C @ (D)) | ~ (hoare_hoare_triple_o @ B @ C @ (D)) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010])). 87.71/26.55 thf(593,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((D != E) & (B = C)) => ((plus_plus_nat @ B @ (times_times_nat @ A @ D)) != (plus_plus_nat @ C @ (times_times_nat @ A @ E)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2586_add__scale__eq__noteq)). 87.71/26.55 thf(4264,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((~ (D = E) & (B = C)) => (~ ((plus_plus_nat @ B @ (times_times_nat @ A @ D)) = (plus_plus_nat @ C @ (times_times_nat @ A @ E))))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[593])). 87.71/26.55 thf(1304,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (suc @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_le__SucI)). 87.71/26.55 thf(6974,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)],[1304])). 87.71/26.55 thf(506,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1239_less__imp__neq)). 87.71/26.55 thf(3932,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[506])). 87.71/26.55 thf(758,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) => ((A = B) <= ((minus_minus_nat @ B @ A) = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3009_diffs0__imp__equal)). 87.71/26.55 thf(4897,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) => ((A = B) | ~ ((minus_minus_nat @ B @ A) = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[758])). 87.71/26.55 thf(645,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/sandbox2/benchmark/theBenchmark.p',fact_8044_power__minus__mult)). 87.71/26.55 thf(4452,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)],[645])). 87.71/26.55 thf(1661,axiom,((! [A:assn,B:$o,C:heap_Time_Heap_o,D:($o > assn)]: ((hoare_hoare_triple_o @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ D) = ((hoare_hoare_triple_o @ A @ C @ D) <= (B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_norm__pre__pure__iff)). 87.71/26.55 thf(8355,plain,((! [A:assn,B:$o,C:heap_Time_Heap_o,D:($o > assn)]: ((hoare_hoare_triple_o @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ (D)) = ((hoare_hoare_triple_o @ A @ C @ (D)) | ~ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1661])). 87.71/26.55 thf(31,axiom,((! [A:nat,B:nat]: ((divide_divide_nat @ A @ (suc @ (suc @ (suc @ B)))) = (divide_divide_nat @ A @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9161_div__Suc__eq__div__add3)). 87.71/26.55 thf(1862,plain,((! [A:nat,B:nat]: ((divide_divide_nat @ A @ (suc @ (suc @ (suc @ B)))) = (divide_divide_nat @ A @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[31])). 87.71/26.55 thf(614,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (time_htt_option_nat @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_vebt_minti @ B) @ (^ [C:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_vebt_mint @ A))))) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1707_vebt__minti__hT)). 87.71/26.55 thf(4332,plain,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (time_htt_option_nat @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_vebt_minti @ B) @ (^ [C:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_vebt_mint @ A))))) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[614])). 87.71/26.55 thf(339,axiom,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ A @ ($true))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2338_VEBT__internal_OminNull_Osimps_I3_J)). 87.71/26.55 thf(3192,plain,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ A @ ($true))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[339])). 87.71/26.55 thf(298,axiom,((((=) @ list_nat) = (^ [A:list_nat,B:list_nat]: (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C))) & ((size_size_list_nat @ A) = (size_size_list_nat @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2650_list__eq__iff__nth__eq)). 87.71/26.55 thf(3034,plain,((((=) @ list_nat) = (^ [A:list_nat,B:list_nat]: (! [C:nat]: ((ord_less_nat @ C @ (size_size_list_nat @ A)) => ((nth_nat @ A @ C) = (nth_nat @ B @ C))) & ((size_size_list_nat @ A) = (size_size_list_nat @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[298])). 87.71/26.55 thf(274,axiom,((! [A:list_int,B:list_real,C:list_o,D:list_real,E:(list_int > (list_real > (list_o > (list_real > $o))))]: ((((size_size_list_real @ B) = (size_size_list_o @ C)) => (((E @ nil_int @ nil_real @ nil_o @ nil_real) => ((! [F:int,G:list_int,H:real,I:list_real,J:$o,K:list_o,L:real,M:list_real]: (((((size_size_list_o @ K) = (size_size_list_real @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_o @ J @ K) @ (cons_real @ L @ M)))) <= ((size_size_list_real @ I) = (size_size_list_o @ K))) <= ((size_size_list_int @ G) = (size_size_list_real @ I)))) => (E @ A @ B @ C @ D))) <= ((size_size_list_o @ C) = (size_size_list_real @ D)))) <= ((size_size_list_int @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8554_list__induct4)). 87.71/26.55 thf(2923,plain,((! [A:list_int,B:list_real,C:list_o,D:list_real,E:(list_int > (list_real > (list_o > (list_real > $o))))]: ((((size_size_list_real @ B) = (size_size_list_o @ C)) => (((E @ nil_int @ nil_real @ nil_o @ nil_real) => ((! [F:int,G:list_int,H:real,I:list_real,J:$o,K:list_o,L:real,M:list_real]: ((((size_size_list_o @ K) = (size_size_list_real @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_o @ J @ K) @ (cons_real @ L @ M)))) | ~ ((size_size_list_real @ I) = (size_size_list_o @ K)) | ~ ((size_size_list_int @ G) = (size_size_list_real @ I)))) => (E @ A @ B @ C @ D))) | ~ ((size_size_list_o @ C) = (size_size_list_real @ D)))) | ~ ((size_size_list_int @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[274])). 87.71/26.55 thf(238,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ C))) & (ord_less_eq_nat @ C @ B)) <= (ord_less_nat @ A @ (divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9067_less__two__pow__divD)). 87.71/26.55 thf(2785,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ C))) & (ord_less_eq_nat @ C @ B)) | ~ (ord_less_nat @ A @ (divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[238])). 87.71/26.55 thf(1506,axiom,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:(nat > assn)]: (((! [E:nat]: (entails @ (C @ E) @ (D @ E))) => (hoare_3067605981109127869le_nat @ A @ B @ D)) <= (hoare_3067605981109127869le_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4068_cons__post__rule)). 87.71/26.55 thf(7778,plain,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:(nat > assn)]: (((! [E:nat]: (entails @ (C @ E) @ (D @ E))) => (hoare_3067605981109127869le_nat @ A @ B @ (D))) | ~ (hoare_3067605981109127869le_nat @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1506])). 87.71/26.55 thf(1154,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (minus_minus_nat @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2910_cancel__ab__semigroup__add__class_Odiff__right__commute)). 87.71/26.55 thf(6429,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)],[1154])). 87.71/26.55 thf(603,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/sandbox2/benchmark/theBenchmark.p',fact_2389_add__mono__thms__linordered__field_I4_J)). 87.71/26.55 thf(4296,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)],[603])). 87.71/26.55 thf(496,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2065_add__cancel__left__left)). 87.71/26.55 thf(3861,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = B) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[496])). 87.71/26.55 thf(1377,axiom,((! [A:nat,B:nat]: ((comm_s4663373288045622133er_nat @ A @ (suc @ B)) = (times_times_nat @ A @ (comm_s4663373288045622133er_nat @ (plus_plus_nat @ A @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4849_pochhammer__rec)). 87.71/26.55 thf(7250,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)],[1377])). 87.71/26.55 thf(1258,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) => (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2275_add__less__imp__less__left)). 87.71/26.55 thf(6802,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)],[1258])). 87.71/26.55 thf(721,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2312_plus__nat_Oadd__0)). 87.71/26.55 thf(4726,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[721])). 87.71/26.55 thf(1159,axiom,((! [A:(nat > (int > assn)),B:nat,C:list_nat,D:int,E:list_int]: ((vEBT_L8298612041380073281at_int @ A @ (cons_nat @ B @ C) @ (cons_int @ D @ E)) = (times_times_assn @ (A @ B @ D) @ (vEBT_L8298612041380073281at_int @ A @ C @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4707_list__assn_Osimps_I2_J)). 87.71/26.55 thf(6446,plain,((! [A:(nat > (int > assn)),B:nat,C:list_nat,D:int,E:list_int]: ((vEBT_L8298612041380073281at_int @ (A) @ (cons_nat @ B @ C) @ (cons_int @ D @ E)) = (times_times_assn @ (A @ B @ D) @ (vEBT_L8298612041380073281at_int @ (A) @ C @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159])). 87.71/26.55 thf(786,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1306_dual__order_Ostrict__implies__not__eq)). 87.71/26.55 thf(5007,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[786])). 87.71/26.55 thf(247,axiom,((bit_se1412395901928357646or_nat = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10049_or__nat__rec)). 87.71/26.55 thf(2842,plain,(((bit_se1412395901928357646or_nat) = (^ [A:nat,B:nat]: (plus_plus_nat @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se1412395901928357646or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[247])). 87.71/26.55 thf(58,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (suc @ (suc @ A))) @ B) = (modulo_modulo_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9173_Suc__mod__eq__add3__mod)). 87.71/26.55 thf(1952,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)],[58])). 87.71/26.55 thf(1454,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((B = C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_mult__cancel__left)). 87.71/26.55 thf(7561,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)],[1454])). 87.71/26.55 thf(270,axiom,((! [A:heap_Time_Heap_nat,B:heap_Time_Heap_nat]: ((if_Hea2662716070787841314ap_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__Nat__Onat_J_T)). 87.71/26.55 thf(2911,plain,((! [A:heap_Time_Heap_nat,B:heap_Time_Heap_nat]: ((if_Hea2662716070787841314ap_nat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[270])). 87.71/26.55 thf(405,axiom,((! [A:list_int]: ((ord_less_nat @ zero_zero_nat @ (size_size_list_int @ A)) = (A != nil_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8253_length__greater__0__conv)). 87.71/26.55 thf(3480,plain,((! [A:list_int]: ((ord_less_nat @ zero_zero_nat @ (size_size_list_int @ A)) = (~ (A = nil_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[405])). 87.71/26.55 thf(739,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: ((((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)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8998_succ__min)). 87.71/26.55 thf(4832,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((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) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[739])). 87.71/26.55 thf(802,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_T_i_n_s_e_r_t2 @ (vEBT_Leaf @ A @ B) @ C) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2731_T_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062s_092_060_094sub_062e_092_060_094sub_062r_092_060_094sub_062t_H_Osimps_I1_J)). 87.71/26.55 thf(5057,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_T_i_n_s_e_r_t2 @ (vEBT_Leaf @ A @ B) @ C) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[802])). 87.71/26.55 thf(1436,axiom,((! [A:$o,B:$o]: ((size_size_VEBT_VEBT @ (vEBT_Leaf @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_VEBT_Osize_I4_J)). 87.71/26.55 thf(7479,plain,((! [A:$o,B:$o]: ((size_size_VEBT_VEBT @ (vEBT_Leaf @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1436])). 87.71/26.55 thf(952,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c2 @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1763_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I3_J)). 87.71/26.55 thf(5641,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c2 @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[952])). 87.71/26.55 thf(316,axiom,((! [A:nat,B:list_nat]: (((cons_nat @ (nth_nat @ B @ A) @ (drop_nat @ (suc @ A) @ B)) = (drop_nat @ A @ B)) <= (ord_less_nat @ A @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8025_Cons__nth__drop__Suc)). 87.71/26.55 thf(3110,plain,((! [A:nat,B:list_nat]: (((cons_nat @ (nth_nat @ B @ A) @ (drop_nat @ (suc @ A) @ B)) = (drop_nat @ A @ B)) | ~ (ord_less_nat @ A @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[316])). 87.71/26.55 thf(975,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/sandbox2/benchmark/theBenchmark.p',fact_3147_nat__diff__add__eq1)). 87.71/26.55 thf(5725,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)],[975])). 87.71/26.55 thf(862,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ zero_zero_nat @ (binomial @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8881_zero__less__binomial)). 87.71/26.55 thf(5299,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)],[862])). 87.71/26.55 thf(108,axiom,((! [A:heap_Time_Heap_nat,B:heap_Time_Heap_nat]: ((if_Hea2662716070787841314ap_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__Nat__Onat_J_T)). 87.71/26.55 thf(2207,plain,((! [A:heap_Time_Heap_nat,B:heap_Time_Heap_nat]: ((if_Hea2662716070787841314ap_nat @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[108])). 87.71/26.55 thf(1056,axiom,((! [A:list_nat,B:list_nat,C:nat]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ (size_size_list_nat @ B)) => (A != (cons_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4677_impossible__Cons)). 87.71/26.55 thf(6029,plain,((! [A:list_nat,B:list_nat,C:nat]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ (size_size_list_nat @ B)) => (~ (A = (cons_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056])). 87.71/26.55 thf(1236,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ (suc @ A) @ B) @ (times_times_nat @ (suc @ A) @ C)) = (ord_less_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_Suc__mult__less__cancel1)). 87.71/26.55 thf(6730,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)],[1236])). 87.71/26.55 thf(980,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3022_le__diff__iff)). 87.71/26.55 thf(5742,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_eq_nat @ B @ C)) | ~ (ord_less_eq_nat @ A @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[980])). 87.71/26.55 thf(1261,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2332_nat__le__iff__add)). 87.71/26.55 thf(6811,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)],[1261])). 87.71/26.55 thf(590,axiom,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_mint @ A) = B) => ((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((C) => (B = (some_nat @ zero_zero_nat))) & ((((B = (some_nat @ one_one_nat)) <= (D)) & ((~ (D)) => (B = none_nat))) <= (~ (C))))))) => (((? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) => (B != none_nat)) => (~ (! [C:nat]: ((? [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))) => (B != (some_nat @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_949_vebt__mint_Oelims)). 87.71/26.55 thf(4232,plain,((! [A:vEBT_VEBT,B:option_nat]: (((vEBT_vebt_mint @ A) = B) => ((! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (((C) => (B = (some_nat @ zero_zero_nat))) & ((((B = (some_nat @ one_one_nat)) | ~ (D)) & ((~ (D)) => (B = none_nat))) | (C)))))) => (((? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) => (~ (B = none_nat))) => (~ (! [C:nat]: ((? [D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))) => (~ (B = (some_nat @ C))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[590])). 87.71/26.55 thf(1324,axiom,((! [A:nat,B:nat,C:list_o]: ((((size_size_list_o @ (slice_o @ A @ B @ C)) = (minus_minus_nat @ B @ A)) <= (ord_less_eq_nat @ B @ (size_size_list_o @ C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3287_slice__len)). 87.71/26.55 thf(7030,plain,((! [A:nat,B:nat,C:list_o]: (((size_size_list_o @ (slice_o @ A @ B @ C)) = (minus_minus_nat @ B @ A)) | ~ (ord_less_eq_nat @ B @ (size_size_list_o @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324])). 87.71/26.55 thf(899,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (plus_plus_nat @ A @ B)) = (plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4550_of__nat__add)). 87.71/26.55 thf(5442,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)],[899])). 87.71/26.55 thf(442,axiom,((! [A:$o,B:$o]: (((A) => ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (some_nat @ zero_zero_nat))) & ((~ (A)) => ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = none_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_823_vebt__pred_Osimps_I2_J)). 87.71/26.55 thf(3627,plain,((! [A:$o,B:$o]: (((A) => ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (some_nat @ zero_zero_nat))) & ((~ (A)) => ((vEBT_vebt_pred @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = none_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[442])). 87.71/26.55 thf(880,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (plus_plus_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2311_add__Suc__shift)). 87.71/26.55 thf(5372,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)],[880])). 87.71/26.55 thf(1160,axiom,((semiri1316708129612266289at_nat = (^ [A:nat]: (semiri8422978514062236437ux_nat @ (^ [B:nat]: (plus_plus_nat @ B @ one_one_nat)) @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4794_of__nat__code)). 87.71/26.55 thf(6449,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)],[1160])). 87.71/26.55 thf(184,axiom,((! [A:list_int,B:list_real,C:list_real,D:list_nat,E:(list_int > (list_real > (list_real > (list_nat > $o))))]: ((((size_size_list_real @ B) = (size_size_list_real @ C)) => (((E @ nil_int @ nil_real @ nil_real @ nil_nat) => ((E @ A @ B @ C @ D) <= (! [F:int,G:list_int,H:real,I:list_real,J:real,K:list_real,L:nat,M:list_nat]: (((size_size_list_int @ G) = (size_size_list_real @ I)) => (((size_size_list_real @ I) = (size_size_list_real @ K)) => (((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_real @ J @ K) @ (cons_nat @ L @ M)) <= (E @ G @ I @ K @ M)) <= ((size_size_list_real @ K) = (size_size_list_nat @ M)))))))) <= ((size_size_list_real @ C) = (size_size_list_nat @ D)))) <= ((size_size_list_int @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8552_list__induct4)). 87.71/26.55 thf(2550,plain,((! [A:list_int,B:list_real,C:list_real,D:list_nat,E:(list_int > (list_real > (list_real > (list_nat > $o))))]: ((((size_size_list_real @ B) = (size_size_list_real @ C)) => (((E @ nil_int @ nil_real @ nil_real @ nil_nat) => ((E @ A @ B @ C @ D) | ~ (! [F:int,G:list_int,H:real,I:list_real,J:real,K:list_real,L:nat,M:list_nat]: (((size_size_list_int @ G) = (size_size_list_real @ I)) => (((size_size_list_real @ I) = (size_size_list_real @ K)) => ((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_real @ J @ K) @ (cons_nat @ L @ M)) | ~ (E @ G @ I @ K @ M) | ~ ((size_size_list_real @ K) = (size_size_list_nat @ M)))))))) | ~ ((size_size_list_real @ C) = (size_size_list_nat @ D)))) | ~ ((size_size_list_int @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[184])). 87.71/26.55 thf(165,axiom,((! [A:real,B:nat]: ((power_power_real @ A @ (suc @ B)) = (times_times_real @ (power_power_real @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7877_power__Suc2)). 87.71/26.55 thf(2481,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)],[165])). 87.71/26.55 thf(837,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t2 @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2626_insert_H__bound__height)). 87.71/26.55 thf(5218,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_T_i_n_s_e_r_t2 @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[837])). 87.71/26.55 thf(1084,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) & (ord_less_eq_nat @ B @ (suc @ A))) = (B = (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_nat__in__between__eq_I1_J)). 87.71/26.55 thf(6151,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) & (ord_less_eq_nat @ B @ (suc @ A))) = (B = (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084])). 87.71/26.55 thf(1580,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/sandbox2/benchmark/theBenchmark.p',fact_10144_min__Suc2)). 87.71/26.55 thf(8084,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)],[1580])). 87.71/26.55 thf(624,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2959_add__implies__diff)). 87.71/26.55 thf(4373,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = C) => (A = (minus_minus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[624])). 87.71/26.55 thf(1252,axiom,((! [A:assn]: (entails @ A @ top_top_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10160_ent__true)). 87.71/26.55 thf(6783,plain,((! [A:assn]: (entails @ A @ top_top_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252])). 87.71/26.55 thf(87,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((some_nat @ C) = (vEBT_vebt_mint @ A)) => (ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8975_misiz)). 87.71/26.55 thf(2139,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((some_nat @ C) = (vEBT_vebt_mint @ A)) => (ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[87])). 87.71/26.55 thf(138,axiom,((! [A:nat,B:list_int,C:int,D:list_int]: (((drop_int @ A @ B) = (cons_int @ C @ D)) => ((drop_int @ (suc @ A) @ B) = D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7834_drop__eq__ConsD)). 87.71/26.55 thf(2369,plain,((! [A:nat,B:list_int,C:int,D:list_int]: (((drop_int @ A @ B) = (cons_int @ C @ D)) => ((drop_int @ (suc @ A) @ B) = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[138])). 87.71/26.55 thf(1483,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_eq_nat @ (plus_plus_nat @ (divide_divide_nat @ A @ C) @ (if_nat @ ((modulo_modulo_nat @ B @ C) = zero_zero_nat) @ one_one_nat @ zero_zero_nat)) @ (divide_divide_nat @ B @ C))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8760_verit__le__mono__div)). 87.71/26.55 thf(7647,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)],[1483])). 87.71/26.55 thf(1399,axiom,((! [A:nat,B:nat]: ((((~ (! [C:nat]: ((A = (suc @ (suc @ C))) => (~ (((B = (suc @ (suc @ (suc @ (plus_plus_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) <= (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) => (B = (suc @ (suc @ (suc @ (plus_plus_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (suc @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (times_times_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))))))))))))))))) <= ((B != (suc @ zero_zero_nat)) <= (A = (suc @ zero_zero_nat)))) <= ((B != (suc @ zero_zero_nat)) <= (A = zero_zero_nat))) <= ((vEBT_V441764108873111860ildupi @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9490_VEBT__internal_OT__vebt__buildupi_Oelims)). 87.71/26.55 thf(7324,plain,((! [A:nat,B:nat]: (~ (! [C:nat]: ((A = (suc @ (suc @ C))) => (~ (((B = (suc @ (suc @ (suc @ (plus_plus_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (times_times_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))))))))))) | ~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) & ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) => (B = (suc @ (suc @ (suc @ (plus_plus_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (suc @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one)))))) @ (plus_plus_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ (bit0 @ one)))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (times_times_nat @ (vEBT_V441764108873111860ildupi @ (suc @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ C @ (numeral_numeral_nat @ (bit0 @ one))))))))))))))))) | ~ (~ (B = (suc @ zero_zero_nat)) | ~ (A = (suc @ zero_zero_nat))) | ~ (~ (B = (suc @ zero_zero_nat)) | ~ (A = zero_zero_nat)) | ~ ((vEBT_V441764108873111860ildupi @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399])). 87.71/26.55 thf(1712,axiom,((! [A:(nat > $o)]: (((? [B:nat]: (~ (A @ B) & (A @ (suc @ B)))) <= (? [B:nat]: (A @ B))) <= (~ (A @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_exists__least__lemma)). 87.71/26.55 thf(8541,plain,((! [A:(nat > $o)]: (? [B:nat]: (~ (A @ B) & (A @ (suc @ B))) | ~ (? [B:nat]: (A @ B)) | (A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1712])). 87.71/26.55 thf(202,axiom,((! [A:nat]: ((binomial @ A @ (numeral_numeral_nat @ (bit0 @ one))) = (divide_divide_nat @ (times_times_nat @ A @ (minus_minus_nat @ A @ one_one_nat)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9070_choose__two)). 87.71/26.55 thf(2633,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)],[202])). 87.71/26.55 thf(1426,axiom,((! [A:nat,B:nat]: ((binomial @ (suc @ A) @ (suc @ B)) = (divide_divide_nat @ (times_times_nat @ (suc @ A) @ (binomial @ A @ B)) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8883_binomial__Suc__Suc__eq__times)). 87.71/26.55 thf(7434,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)],[1426])). 87.71/26.55 thf(1684,axiom,((bot_bot_nat = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1027_bot__nat__def)). 87.71/26.55 thf(8441,plain,((bot_bot_nat = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1684])). 87.71/26.55 thf(606,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) <= (ord_less_nat @ A @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3012_diff__less__mono2)). 87.71/26.55 thf(4304,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A)) | ~ (ord_less_nat @ A @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[606])). 87.71/26.55 thf(334,axiom,((! [A:num]: ((bit0 @ A) != one))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8974_semiring__norm_I85_J)). 87.71/26.55 thf(3178,plain,((! [A:num]: ~ ((bit0 @ A) = one))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[334])). 87.71/26.55 thf(1477,axiom,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => (~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Node @ B @ C @ D @ E) @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_868_VEBT__internal_Ovalid_H_Ocases)). 87.71/26.55 thf(7630,plain,((! [A:produc9072475918466114483BT_nat]: ((! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D))) => (~ (! [B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ B @ C @ D @ E) @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1477])). 87.71/26.55 thf(1642,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ zero_zero_nat) @ C @ D) @ E) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1726_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I6_J)). 87.71/26.55 thf(8291,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ (suc @ zero_zero_nat) @ C @ D) @ E) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1642])). 87.71/26.55 thf(969,axiom,((! [A:$o,B:heap_Time_Heap_nat,C:(nat > assn)]: ((hoare_3067605981109127869le_nat @ (pure_assn @ A) @ B @ C) = ((A) => (hoare_3067605981109127869le_nat @ one_one_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1738_norm__pre__pure__iff__sng)). 87.71/26.55 thf(5693,plain,((! [A:$o,B:heap_Time_Heap_nat,C:(nat > assn)]: ((hoare_3067605981109127869le_nat @ (pure_assn @ A) @ B @ (C)) = ((A) => (hoare_3067605981109127869le_nat @ one_one_assn @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[969])). 87.71/26.55 thf(92,axiom,((! [A:nat,B:num]: (((suc @ A) = (numeral_numeral_nat @ B)) = (A = (pred_numeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9913_Suc__eq__numeral)). 87.71/26.55 thf(2156,plain,((! [A:nat,B:num]: (((suc @ A) = (numeral_numeral_nat @ B)) = (A = (pred_numeral @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[92])). 87.71/26.55 thf(1100,axiom,((! [A:nat]: ((A != zero_zero_nat) => (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_gr0I)). 87.71/26.55 thf(6212,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100])). 87.71/26.55 thf(779,axiom,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (suc @ zero_zero_nat)) => (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9484_even__mod__4__div__2)). 87.71/26.55 thf(4965,plain,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one)))) = (suc @ zero_zero_nat)) => (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (divide_divide_nat @ (minus_minus_nat @ A @ (suc @ zero_zero_nat)) @ (numeral_numeral_nat @ (bit0 @ one))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[779])). 87.71/26.55 thf(286,axiom,((! [A:list_o,B:list_o,C:$o]: ((A != (cons_o @ C @ B)) <= (ord_less_eq_nat @ (size_size_list_o @ A) @ (size_size_list_o @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4676_impossible__Cons)). 87.71/26.55 thf(2984,plain,((! [A:list_o,B:list_o,C:$o]: (~ (A = (cons_o @ C @ B)) | ~ (ord_less_eq_nat @ (size_size_list_o @ A) @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[286])). 87.71/26.55 thf(1253,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((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)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8897_binomial__addition__formula)). 87.71/26.55 thf(6785,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253])). 87.71/26.55 thf(570,axiom,((! [A:option_nat]: ((~ (! [B:nat]: (A != (some_nat @ B)))) <= (A != none_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_option_Oexhaust)). 87.71/26.55 thf(4158,plain,((! [A:option_nat]: (~ (! [B:nat]: ~ (A = (some_nat @ B))) | (A = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[570])). 87.71/26.55 thf(944,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((dvd_dvd_nat @ A @ B) = (dvd_dvd_nat @ A @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9461_less__eq__dvd__minus)). 87.71/26.55 thf(5619,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)],[944])). 87.71/26.55 thf(1354,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (modulo_modulo_nat @ B @ A) @ A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8731_mod__le__divisor)). 87.71/26.55 thf(7172,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (modulo_modulo_nat @ B @ A) @ A) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354])). 87.71/26.55 thf(548,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1578_order__le__less)). 87.71/26.55 thf(4084,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((A = B) | (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[548])). 87.71/26.55 thf(1327,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat) <= (ord_less_eq_nat @ B @ one_one_nat))) <= (ord_less_eq_nat @ A @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1219_mult__le__one)). 87.71/26.55 thf(7049,plain,((! [A:nat,B:nat]: (((ord_less_eq_nat @ zero_zero_nat @ B) => ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ one_one_nat) | ~ (ord_less_eq_nat @ B @ one_one_nat))) | ~ (ord_less_eq_nat @ A @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327])). 87.71/26.55 thf(1000,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2296_distrib__left)). 87.71/26.55 thf(5812,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)],[1000])). 87.71/26.55 thf(905,axiom,((! [A:nat,B:nat]: ((? [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) & ((plus_plus_nat @ A @ C) = B))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2418_less__imp__add__positive)). 87.71/26.55 thf(5463,plain,((! [A:nat,B:nat]: (? [C:nat]: ((ord_less_nat @ zero_zero_nat @ C) & ((plus_plus_nat @ A @ C) = B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[905])). 87.71/26.55 thf(924,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ C @ A) => (ord_less_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1554_dual__order_Ostrict__trans2)). 87.71/26.55 thf(5528,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)],[924])). 87.71/26.55 thf(162,axiom,((! [A:int,B:nat]: ((power_power_int @ A @ (suc @ B)) = (times_times_int @ A @ (power_power_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7874_power__Suc)). 87.71/26.55 thf(2471,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)],[162])). 87.71/26.55 thf(1774,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBTi,C:nat]: (hoare_hoare_triple_o @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_V854960066525838166emberi @ A @ B @ C) @ (^ [D:$o]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (D = (vEBT_vebt_member @ A @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_vebt__memberi_H__rf__abstr)). 87.71/26.55 thf(8804,plain,((! [A:vEBT_VEBT,B:vEBT_VEBTi,C:nat]: (hoare_hoare_triple_o @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_V854960066525838166emberi @ A @ B @ C) @ (^ [D:$o]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (D = (vEBT_vebt_member @ A @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1774])). 87.71/26.55 thf(671,axiom,((! [A:assn]: ((sup_sup_assn @ top_top_assn @ A) = top_top_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10162_norm__assertion__simps_I11_J)). 87.71/26.55 thf(4529,plain,((! [A:assn]: ((sup_sup_assn @ top_top_assn @ A) = top_top_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[671])). 87.71/26.55 thf(517,axiom,((! [A:nat,B:nat,C:nat]: (((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3107_Nat_Odiff__add__assoc2)). 87.71/26.55 thf(3975,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)],[517])). 87.71/26.55 thf(1343,axiom,((! [A:nat]: ((semiri1316708129612266289at_nat @ (suc @ A)) = (plus_plus_nat @ one_one_nat @ (semiri1316708129612266289at_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4595_of__nat__Suc)). 87.71/26.55 thf(7102,plain,((! [A:nat]: ((semiri1316708129612266289at_nat @ (suc @ A)) = (plus_plus_nat @ one_one_nat @ (semiri1316708129612266289at_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343])). 87.71/26.55 thf(1347,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (suc @ (plus_plus_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2414_less__iff__Suc__add)). 87.71/26.55 thf(7122,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)],[1347])). 87.71/26.55 thf(556,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1600_order__less__imp__le)). 87.71/26.55 thf(4113,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[556])). 87.71/26.55 thf(686,axiom,((ord_less_nat = (^ [A:nat,B:nat]: (~ (ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1491_less__le__not__le)). 87.71/26.55 thf(4581,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[686])). 87.71/26.55 thf(1553,axiom,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2075_add__cancel__right__left)). 87.71/26.55 thf(7982,plain,((! [A:nat,B:nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1553])). 87.71/26.55 thf(1280,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ C @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (plus_plus_nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3064_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right)). 87.71/26.55 thf(6875,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)],[1280])). 87.71/26.55 thf(930,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4542_of__nat__less__iff)). 87.71/26.55 thf(5548,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)],[930])). 87.71/26.55 thf(582,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7873_power__Suc)). 87.71/26.55 thf(4207,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)],[582])). 87.71/26.55 thf(967,axiom,((! [A:assn,B:assn]: ((sup_sup_assn @ A @ (sup_sup_assn @ A @ B)) = (sup_sup_assn @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5434_assn__aci_I8_J)). 87.71/26.55 thf(5688,plain,((! [A:assn,B:assn]: ((sup_sup_assn @ A @ (sup_sup_assn @ A @ B)) = (sup_sup_assn @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[967])). 87.71/26.55 thf(1039,axiom,((! [A:$o,B:$o]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1768_VEBT__internal_OT_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_H_Osimps_I2_J)). 87.71/26.55 thf(5959,plain,((! [A:$o,B:$o]: ((vEBT_V1232361888498592333_e_t_e @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039])). 87.71/26.55 thf(761,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/sandbox2/benchmark/theBenchmark.p',fact_2873_diff__Suc__diff__eq1)). 87.71/26.55 thf(4907,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)],[761])). 87.71/26.55 thf(711,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2333_add__mult__distrib)). 87.71/26.55 thf(4690,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)],[711])). 87.71/26.55 thf(271,axiom,((nat_triangle = (^ [A:nat]: (divide_divide_nat @ (times_times_nat @ A @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9063_triangle__def)). 87.71/26.55 thf(2914,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)],[271])). 87.71/26.55 thf(297,axiom,((! [A:nat,B:list_int]: (((drop_int @ A @ B) = nil_int) = (ord_less_eq_nat @ (size_size_list_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8279_drop__eq__Nil)). 87.71/26.55 thf(3031,plain,((! [A:nat,B:list_int]: (((drop_int @ A @ B) = nil_int) = (ord_less_eq_nat @ (size_size_list_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[297])). 87.71/26.55 thf(13,axiom,((! [A:nat,B:list_nat,C:list_nat]: ((take_nat @ A @ (append_nat @ B @ C)) = (append_nat @ (take_nat @ A @ B) @ (take_nat @ (minus_minus_nat @ A @ (size_size_list_nat @ B)) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8292_take__append)). 87.71/26.55 thf(1809,plain,((! [A:nat,B:list_nat,C:list_nat]: ((take_nat @ A @ (append_nat @ B @ C)) = (append_nat @ (take_nat @ A @ B) @ (take_nat @ (minus_minus_nat @ A @ (size_size_list_nat @ B)) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[13])). 87.71/26.55 thf(893,axiom,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat,G:nat]: ((((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ G) = none_nat) <= (ord_less_eq_nat @ B @ G)) <= (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_714_geqmaxNone)). 87.71/26.55 thf(5424,plain,((! [A:nat,B:nat,C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT,F:nat,G:nat]: (((vEBT_vebt_succ @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ G) = none_nat) | ~ (ord_less_eq_nat @ B @ G) | ~ (vEBT_invar_vebt @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ C @ D @ E) @ F)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[893])). 87.71/26.55 thf(631,axiom,((! [A:nat,B:nat,C:list_nat]: (((ord_less_eq_nat @ B @ (size_size_list_nat @ C)) => ((size_size_list_nat @ (slice_nat @ A @ B @ C)) = (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3288_slice__len)). 87.71/26.55 thf(4394,plain,((! [A:nat,B:nat,C:list_nat]: (((ord_less_eq_nat @ B @ (size_size_list_nat @ C)) => ((size_size_list_nat @ (slice_nat @ A @ B @ C)) = (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[631])). 87.71/26.55 thf(641,axiom,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2316_not__add__less1)). 87.71/26.55 thf(4441,plain,((! [A:nat,B:nat]: ~ (ord_less_nat @ (plus_plus_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[641])). 87.71/26.55 thf(564,axiom,((! [A:$o,B:assn]: ((inf_inf_assn @ (pure_assn @ A) @ B) = (times_times_assn @ (inf_inf_assn @ one_one_assn @ B) @ (pure_assn @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8911_and__extract__pure__left__iff)). 87.71/26.55 thf(4136,plain,((! [A:$o,B:assn]: ((inf_inf_assn @ (pure_assn @ A) @ B) = (times_times_assn @ (inf_inf_assn @ one_one_assn @ B) @ (pure_assn @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[564])). 87.71/26.55 thf(35,axiom,((! [A:vEBT_VEBT]: (ord_less_eq_nat @ (vEBT_T_m_a_x_t @ A) @ (numeral_numeral_nat @ (bit1 @ one))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9168_maxt__bound)). 87.71/26.55 thf(1873,plain,((! [A:vEBT_VEBT]: (ord_less_eq_nat @ (vEBT_T_m_a_x_t @ A) @ (numeral_numeral_nat @ (bit1 @ one))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[35])). 87.71/26.55 thf(1018,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_eq_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3148_nat__le__add__iff2)). 87.71/26.55 thf(5890,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_eq_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (ord_less_eq_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018])). 87.71/26.55 thf(529,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_V5719532721284313246member @ (vEBT_Leaf @ A @ B) @ C) = (((C != zero_zero_nat) => (((B) <= (C = one_one_nat)) & (C = one_one_nat))) & ((A) <= (C = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1416_VEBT__internal_Onaive__member_Osimps_I1_J)). 87.71/26.55 thf(4013,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_V5719532721284313246member @ (vEBT_Leaf @ A @ B) @ C) = (((~ (C = zero_zero_nat)) => (((B) | ~ (C = one_one_nat)) & (C = one_one_nat))) & ((A) | ~ (C = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[529])). 87.71/26.55 thf(507,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ top_top_assn)) <= (entails @ A @ (times_times_assn @ B @ top_top_assn))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10157_ent__true__drop_I1_J)). 87.71/26.55 thf(3936,plain,((! [A:assn,B:assn,C:assn]: ((entails @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ top_top_assn)) | ~ (entails @ A @ (times_times_assn @ B @ top_top_assn))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[507])). 87.71/26.55 thf(1184,axiom,((! [A:nat,B:nat]: ((times_times_nat @ A @ (suc @ B)) = (plus_plus_nat @ A @ (times_times_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2156_mult__Suc__right)). 87.71/26.55 thf(6540,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)],[1184])). 87.71/26.55 thf(1534,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2320_trans__less__add2)). 87.71/26.55 thf(7896,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (plus_plus_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1534])). 87.71/26.55 thf(1017,axiom,((! [A:nat,B:int]: (((times_times_int @ (power_power_int @ B @ (minus_minus_nat @ A @ one_one_nat)) @ B) = (power_power_int @ B @ A)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8047_power__minus__mult)). 87.71/26.55 thf(5886,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)],[1017])). 87.71/26.55 thf(1393,axiom,((! [A:list_real]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (size_size_list_real @ A)) = (A != nil_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8327_length__ge__1__conv)). 87.71/26.55 thf(7296,plain,((! [A:list_real]: ((ord_less_eq_nat @ (suc @ zero_zero_nat) @ (size_size_list_real @ A)) = (~ (A = nil_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393])). 87.71/26.55 thf(208,axiom,((! [A:list_real,B:list_real,C:list_real,D:(list_real > (list_real > (list_real > $o)))]: ((((D @ nil_real @ nil_real @ nil_real) => ((D @ A @ B @ C) <= (! [E:real,F:list_real,G:real,H:list_real,I:real,J:list_real]: ((((D @ (cons_real @ E @ F) @ (cons_real @ G @ H) @ (cons_real @ I @ J)) <= (D @ F @ H @ J)) <= ((size_size_list_real @ H) = (size_size_list_real @ J))) <= ((size_size_list_real @ F) = (size_size_list_real @ H)))))) <= ((size_size_list_real @ B) = (size_size_list_real @ C))) <= ((size_size_list_real @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8540_list__induct3)). 87.71/26.55 thf(2665,plain,((! [A:list_real,B:list_real,C:list_real,D:(list_real > (list_real > (list_real > $o)))]: (((D @ nil_real @ nil_real @ nil_real) => ((D @ A @ B @ C) | ~ (! [E:real,F:list_real,G:real,H:list_real,I:real,J:list_real]: ((D @ (cons_real @ E @ F) @ (cons_real @ G @ H) @ (cons_real @ I @ J)) | ~ (D @ F @ H @ J) | ~ ((size_size_list_real @ H) = (size_size_list_real @ J)) | ~ ((size_size_list_real @ F) = (size_size_list_real @ H)))))) | ~ ((size_size_list_real @ B) = (size_size_list_real @ C)) | ~ ((size_size_list_real @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[208])). 87.71/26.55 thf(1484,axiom,((ord_less_nat = (^ [A:nat]: (ord_less_eq_nat @ (plus_plus_nat @ A @ one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2505_discrete)). 87.71/26.55 thf(7650,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)],[1484])). 87.71/26.55 thf(757,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((((((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ C @ E) @ A)) | ((times_times_nat @ C @ D) = (plus_plus_nat @ (times_times_nat @ B @ 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/sandbox2/benchmark/theBenchmark.p',fact_9462_bezout__lemma__nat)). 87.71/26.55 thf(4886,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((((times_times_nat @ B @ D) = (plus_plus_nat @ (times_times_nat @ C @ E) @ A)) | ((times_times_nat @ C @ D) = (plus_plus_nat @ (times_times_nat @ B @ 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)],[757])). 87.71/26.55 thf(1416,axiom,((! [A:nat,B:list_nat]: ((size_size_list_nat @ (cons_nat @ A @ B)) = (suc @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4665_length__nth__simps_I2_J)). 87.71/26.55 thf(7403,plain,((! [A:nat,B:list_nat]: ((size_size_list_nat @ (cons_nat @ A @ B)) = (suc @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1416])). 87.71/26.55 thf(592,axiom,((! [A:nat]: (none_nat != (some_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_option_Odistinct_I1_J)). 87.71/26.55 thf(4260,plain,((! [A:nat]: ~ (none_nat = (some_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[592])). 87.71/26.55 thf(127,axiom,((! [A:list_real]: (((size_size_list_real @ A) = zero_zero_nat) = (A = nil_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8139_length__0__conv)). 87.71/26.55 thf(2318,plain,((! [A:list_real]: (((size_size_list_real @ A) = zero_zero_nat) = (A = nil_real)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[127])). 87.71/26.55 thf(386,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((append_nat @ (upt @ zero_zero_nat @ A) @ (upt @ A @ B)) = (upt @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8848_upt__append)). 87.71/26.55 thf(3395,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((append_nat @ (upt @ zero_zero_nat @ A) @ (upt @ A @ B)) = (upt @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[386])). 87.71/26.55 thf(646,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ A) @ B) => (~ (! [C:nat]: ((ord_less_nat @ A @ C) => (B != (suc @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_Suc__lessE)). 87.71/26.55 thf(4456,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)],[646])). 87.71/26.55 thf(519,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ C) @ (A @ B))) <= (! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_lift__Suc__antimono__le)). 87.71/26.55 thf(3981,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ C) @ (A @ B))) | ~ (! [D:nat]: (ord_less_eq_nat @ (A @ (suc @ D)) @ (A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[519])). 87.71/26.55 thf(1447,axiom,((! [A:nat,B:nat]: (((divide_divide_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8641_Euclidean__Division_Odiv__eq__0__iff)). 87.71/26.55 thf(7539,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)],[1447])). 87.71/26.55 thf(114,axiom,((! [A:vEBT_VEBT,B:nat]: (((vEBT_vebt_maxt @ A) = (some_nat @ B)) => (vEBT_V8194947554948674370ptions @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2593_maxbmo)). 87.71/26.55 thf(2234,plain,((! [A:vEBT_VEBT,B:nat]: (((vEBT_vebt_maxt @ A) = (some_nat @ B)) => (vEBT_V8194947554948674370ptions @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[114])). 87.71/26.55 thf(1095,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2330_trans__le__add1)). 87.71/26.55 thf(6191,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ A @ (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095])). 87.71/26.55 thf(67,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBTi,C:nat]: (time_TBOUND_o @ (vEBT_V854960066525838166emberi @ A @ B @ C) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9002_TBOUND__vebt__memberi)). 87.71/26.55 thf(1990,plain,((! [A:vEBT_VEBT,B:vEBT_VEBTi,C:nat]: (time_TBOUND_o @ (vEBT_V854960066525838166emberi @ A @ B @ C) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit0 @ one))) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[67])). 87.71/26.55 thf(965,axiom,((! [A:list_o,B:list_real,C:($o > (real > assn))]: (((size_size_list_o @ A) != (size_size_list_real @ B)) => ((vEBT_L4725278957065240257o_real @ C @ A @ B) = bot_bot_assn)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3201_list__assn__aux__ineq__len)). 87.71/26.55 thf(5678,plain,((! [A:list_o,B:list_real,C:($o > (real > assn))]: ((~ ((size_size_list_o @ A) = (size_size_list_real @ B))) => ((vEBT_L4725278957065240257o_real @ (C) @ A @ B) = bot_bot_assn)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[965])). 87.71/26.55 thf(684,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4653_less__imp__of__nat__less)). 87.71/26.55 thf(4566,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[684])). 87.71/26.55 thf(748,axiom,((! [A:nat,B:nat,C:list_real]: (((ord_less_eq_nat @ B @ (size_size_list_real @ C)) => ((size_size_list_real @ (slice_real @ A @ B @ C)) = (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3286_slice__len)). 87.71/26.55 thf(4859,plain,((! [A:nat,B:nat,C:list_real]: (((ord_less_eq_nat @ B @ (size_size_list_real @ C)) => ((size_size_list_real @ (slice_real @ A @ B @ C)) = (minus_minus_nat @ B @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[748])). 87.71/26.55 thf(1271,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2105_add__Suc__right)). 87.71/26.55 thf(6843,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ A @ (suc @ B)) = (suc @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271])). 87.71/26.55 thf(1349,axiom,((! [A:$o,B:list_o]: ((size_size_list_o @ (cons_o @ A @ B)) = (plus_plus_nat @ (size_size_list_o @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4751_list_Osize_I4_J)). 87.71/26.55 thf(7137,plain,((! [A:$o,B:list_o]: ((size_size_list_o @ (cons_o @ A @ B)) = (plus_plus_nat @ (size_size_list_o @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349])). 87.71/26.55 thf(998,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1536_dual__order_Oorder__iff__strict)). 87.71/26.55 thf(5807,plain,(((ord_less_eq_nat) = (^ [A:nat,B:nat]: ((ord_less_nat @ A @ B) | (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[998])). 87.71/26.55 thf(364,axiom,((! [A:nat]: ((modulo_modulo_nat @ (suc @ (suc @ A)) @ (numeral_numeral_nat @ (bit0 @ one))) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9012_mod2__Suc__Suc)). 87.71/26.55 thf(3292,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)],[364])). 87.71/26.55 thf(265,axiom,((! [A:nat]: ((~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) => ((suc @ (minus_minus_nat @ A @ (suc @ zero_zero_nat))) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9446_odd__Suc__minus__one)). 87.71/26.55 thf(2899,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)],[265])). 87.71/26.55 thf(1616,axiom,((! [A:nat]: ((A != zero_zero_nat) => (? [B:nat]: (A = (suc @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_not0__implies__Suc)). 87.71/26.55 thf(8194,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) => (? [B:nat]: (A = (suc @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1616])). 87.71/26.55 thf(818,axiom,((! [A:assn,B:assn]: ((entails @ A @ B) => (entails @ A @ (times_times_assn @ B @ top_top_assn))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10158_ent__true__drop_I2_J)). 87.71/26.55 thf(5133,plain,((! [A:assn,B:assn]: ((entails @ A @ B) => (entails @ A @ (times_times_assn @ B @ top_top_assn))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[818])). 87.71/26.55 thf(190,axiom,((! [A:nat]: (((binomial @ A @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = (binomial @ A @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) <= (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9482_central__binomial__odd)). 87.71/26.55 thf(2582,plain,((! [A:nat]: (((binomial @ A @ (suc @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))))) = (binomial @ A @ (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)],[190])). 87.71/26.55 thf(433,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/sandbox2/benchmark/theBenchmark.p',fact_2328_add__le__mono)). 87.71/26.55 thf(3571,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)],[433])). 87.71/26.55 thf(1214,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/sandbox2/benchmark/theBenchmark.p',fact_8664_split__div_H)). 87.71/26.55 thf(6641,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)],[1214])). 87.71/26.55 thf(9,axiom,((! [A:nat,B:num]: ((divide_divide_nat @ (suc @ (suc @ (suc @ A))) @ (numeral_numeral_nat @ B)) = (divide_divide_nat @ (plus_plus_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) @ (numeral_numeral_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9160_Suc__div__eq__add3__div__numeral)). 87.71/26.55 thf(1798,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)],[9])). 87.71/26.55 thf(1227,axiom,((ord_less_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1722_less__numeral__extra_I1_J)). 87.71/26.55 thf(6683,plain,((ord_less_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227])). 87.71/26.55 thf(1330,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2291_comm__semiring__class_Odistrib)). 87.71/26.55 thf(7058,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)],[1330])). 87.71/26.55 thf(1365,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/sandbox2/benchmark/theBenchmark.p',fact_7859_one__le__power)). 87.71/26.55 thf(7211,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)],[1365])). 87.71/26.55 thf(344,axiom,((! [A:nat]: (((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) != (suc @ zero_zero_nat)) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9013_not__mod2__eq__Suc__0__eq__0)). 87.71/26.55 thf(3214,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)],[344])). 87.71/26.55 thf(450,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1924_verit__comp__simplify1_I2_J)). 87.71/26.55 thf(3659,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[450])). 87.71/26.55 thf(176,axiom,((nat_prod_decode_aux = (^ [A:nat,B:nat]: (if_Pro6206227464963214023at_nat @ (ord_less_eq_nat @ B @ A) @ (product_Pair_nat_nat @ B @ (minus_minus_nat @ A @ B)) @ (nat_prod_decode_aux @ (suc @ A) @ (minus_minus_nat @ B @ (suc @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3355_prod__decode__aux_Osimps)). 87.71/26.55 thf(2518,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)],[176])). 87.71/26.55 thf(667,axiom,((! [A:nat]: ((A != bot_bot_nat) = (ord_less_nat @ bot_bot_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1701_bot_Onot__eq__extremum)). 87.71/26.55 thf(4517,plain,((! [A:nat]: ((~ (A = bot_bot_nat)) = (ord_less_nat @ bot_bot_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[667])). 87.71/26.55 thf(142,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((upt @ B @ A) = nil_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8831_upt__conv__Nil)). 87.71/26.55 thf(2386,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((upt @ B @ A) = nil_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[142])). 87.71/26.55 thf(1664,axiom,((! [A:(num > nat)]: ((size_option_num @ A @ none_num) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1730_option_Osize__gen_I1_J)). 87.71/26.55 thf(8364,plain,((! [A:(num > nat)]: ((size_option_num @ (A) @ none_num) = (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1664])). 87.71/26.55 thf(261,axiom,((! [A:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) => (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ A @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9178_small__powers__of__2)). 87.71/26.55 thf(2882,plain,((! [A:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit1 @ one)) @ A) => (ord_less_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)],[261])). 87.71/26.55 thf(1051,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r2 @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1766_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J)). 87.71/26.55 thf(6012,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_m_e_m_b_e_r2 @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051])). 87.71/26.55 thf(535,axiom,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1056_lambda__one)). 87.71/26.55 thf(4045,plain,(((^ [A:nat]: (A)) = (times_times_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[535])). 87.71/26.55 thf(521,axiom,((! [A:nat,B:list_int]: ((ord_less_eq_nat @ (suc @ A) @ (size_size_list_int @ B)) = (? [C:int,D:list_int]: ((ord_less_eq_nat @ A @ (size_size_list_int @ D)) & (B = (cons_int @ C @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4730_Suc__le__length__iff)). 87.71/26.55 thf(3988,plain,((! [A:nat,B:list_int]: ((ord_less_eq_nat @ (suc @ A) @ (size_size_list_int @ B)) = (? [C:int,D:list_int]: ((ord_less_eq_nat @ A @ (size_size_list_int @ D)) & (B = (cons_int @ C @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[521])). 87.71/26.55 thf(187,axiom,((! [A:list_int]: (((size_size_list_int @ A) = zero_zero_nat) = (A = nil_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8142_length__0__conv)). 87.71/26.55 thf(2567,plain,((! [A:list_int]: (((size_size_list_int @ A) = zero_zero_nat) = (A = nil_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[187])). 87.71/26.55 thf(727,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((power_power_nat @ zero_zero_nat @ A) = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7950_zero__power)). 87.71/26.55 thf(4749,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)],[727])). 87.71/26.55 thf(1132,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ B @ C) => ((C = D) => (ord_less_eq_nat @ A @ D))) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_ord__eq__le__eq__trans)). 87.71/26.55 thf(6362,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ B @ C) => ((C = D) => (ord_less_eq_nat @ A @ D))) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132])). 87.71/26.55 thf(1467,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_le__refl)). 87.71/26.55 thf(7600,plain,((! [A:nat]: (ord_less_eq_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1467])). 87.71/26.55 thf(902,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1296_dual__order_Ostrict__trans)). 87.71/26.55 thf(5452,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ A) => (ord_less_nat @ C @ B)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[902])). 87.71/26.55 thf(1723,axiom,((! [A:nat,B:nat]: (((suc @ A) = B) => (A = (minus_minus_nat @ B @ (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3093_Suc__to__right)). 87.71/26.55 thf(8592,plain,((! [A:nat,B:nat]: (((suc @ A) = B) => (A = (minus_minus_nat @ B @ (suc @ zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1723])). 87.71/26.55 thf(380,axiom,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => ((A = B) <= (! [C:nat]: (((nth_nat @ A @ C) = (nth_nat @ B @ C)) <= (ord_less_nat @ C @ (size_size_list_nat @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2662_nth__equalityI)). 87.71/26.55 thf(3376,plain,((! [A:list_nat,B:list_nat]: (((size_size_list_nat @ A) = (size_size_list_nat @ B)) => ((A = B) | ~ (! [C:nat]: (((nth_nat @ A @ C) = (nth_nat @ B @ C)) | ~ (ord_less_nat @ C @ (size_size_list_nat @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[380])). 87.71/26.55 thf(1340,axiom,((! [A:$o,B:$o]: ((vEBT_vebt_delete @ (vEBT_Leaf @ A @ B) @ (suc @ zero_zero_nat)) = (vEBT_Leaf @ A @ ($false))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2534_vebt__delete_Osimps_I2_J)). 87.71/26.55 thf(7087,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)],[1340])). 87.71/26.55 thf(1003,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/sandbox2/benchmark/theBenchmark.p',fact_236_Nat_OlessE)). 87.71/26.55 thf(5822,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)],[1003])). 87.71/26.55 thf(1561,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_mult__right__le__imp__le)). 87.71/26.55 thf(8003,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C)) | ~ (ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1561])). 87.71/26.55 thf(216,axiom,((! [A:int,B:list_int]: ((nth_int @ (cons_int @ A @ B) @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4574_nth__Cons__0)). 87.71/26.55 thf(2715,plain,((! [A:int,B:list_int]: ((nth_int @ (cons_int @ A @ B) @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[216])). 87.71/26.55 thf(1108,axiom,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => ((C @ A) => ((? [D:nat]: ((ord_less_eq_nat @ A @ D) & (ord_less_eq_nat @ D @ B) & ! [E:nat]: (((ord_less_nat @ E @ D) & (ord_less_eq_nat @ A @ E)) => (C @ E)) & ! [E:nat]: ((! [F:nat]: (((ord_less_nat @ F @ E) & (ord_less_eq_nat @ A @ F)) => (C @ F))) => (ord_less_eq_nat @ E @ D)))) <= (~ (C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1902_complete__interval)). 87.71/26.55 thf(6249,plain,((! [A:nat,B:nat,C:(nat > $o)]: ((ord_less_nat @ A @ B) => ((C @ A) => (? [D:nat]: ((ord_less_eq_nat @ A @ D) & (ord_less_eq_nat @ D @ B) & ! [E:nat]: (((ord_less_nat @ E @ D) & (ord_less_eq_nat @ A @ E)) => (C @ E)) & ! [E:nat]: ((! [F:nat]: (((ord_less_nat @ F @ E) & (ord_less_eq_nat @ A @ F)) => (C @ F))) => (ord_less_eq_nat @ E @ D))) | (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108])). 87.71/26.55 thf(1075,axiom,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (vEBT_V441764108873111860ildupi @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_T__vebt__buildupi__gq__0)). 87.71/26.55 thf(6120,plain,((! [A:nat]: (ord_less_nat @ zero_zero_nat @ (vEBT_V441764108873111860ildupi @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075])). 87.71/26.55 thf(443,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_not__less__zero)). 87.71/26.55 thf(3640,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[443])). 87.71/26.55 thf(1434,axiom,((ord_less_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1074_zero__less__one)). 87.71/26.55 thf(7475,plain,((ord_less_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1434])). 87.71/26.55 thf(254,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ C) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ D)) => (ord_less_eq_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (plus_plus_nat @ C @ one_one_nat)) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9077_power__2__mult__step__le)). 87.71/26.55 thf(2863,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ C) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ D)) => (ord_less_eq_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ (plus_plus_nat @ C @ one_one_nat)) @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[254])). 87.71/26.55 thf(1765,axiom,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ (times_times_assn @ A @ C) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_assn__aci_I10_J)). 87.71/26.55 thf(8772,plain,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ (times_times_assn @ A @ C) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1765])). 87.71/26.55 thf(860,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ (times_times_assn @ B @ A) @ C) <= (entails @ (times_times_assn @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4056_fr__rot)). 87.71/26.55 thf(5294,plain,((! [A:assn,B:assn,C:assn]: ((entails @ (times_times_assn @ B @ A) @ C) | ~ (entails @ (times_times_assn @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[860])). 87.71/26.55 thf(1029,axiom,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = one_one_nat) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4554_of__nat__eq__1__iff)). 87.71/26.55 thf(5927,plain,((! [A:nat]: (((semiri1316708129612266289at_nat @ A) = one_one_nat) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029])). 87.71/26.55 thf(1658,axiom,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_zero__reorient)). 87.71/26.55 thf(8345,plain,((! [A:nat]: ((zero_zero_nat = A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1658])). 87.71/26.55 thf(1598,axiom,((times_times_assn = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_assn__times__comm)). 87.71/26.55 thf(8143,plain,(((times_times_assn) = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1598])). 87.71/26.55 thf(1649,axiom,((! [A:$o,B:heap_T2636463487746394924on_nat,C:(option_nat > assn)]: ((hoare_7629718768684598413on_nat @ (pure_assn @ A) @ B @ C) = ((A) => (hoare_7629718768684598413on_nat @ one_one_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1735_norm__pre__pure__iff__sng)). 87.71/26.55 thf(8312,plain,((! [A:$o,B:heap_T2636463487746394924on_nat,C:(option_nat > assn)]: ((hoare_7629718768684598413on_nat @ (pure_assn @ A) @ B @ (C)) = ((A) => (hoare_7629718768684598413on_nat @ one_one_assn @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1649])). 87.71/26.55 thf(770,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B)) @ (power_power_nat @ A @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7971_power__Suc__less)). 87.71/26.55 thf(4937,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ one_one_nat) => (ord_less_nat @ (times_times_nat @ A @ (power_power_nat @ A @ B)) @ (power_power_nat @ A @ B))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[770])). 87.71/26.55 thf(140,axiom,((! [A:(list_nat > $o),B:list_nat]: ((A @ nil_nat) => ((A @ B) <= (! [C:list_nat,D:nat]: ((A @ (append_nat @ C @ (cons_nat @ D @ nil_nat))) <= (! [E:list_nat]: ((A @ E) <= (ord_less_eq_nat @ (size_size_list_nat @ E) @ (size_size_list_nat @ C)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8439_length__compl__rev__induct)). 87.71/26.55 thf(2375,plain,((! [A:(list_nat > $o),B:list_nat]: ((A @ nil_nat) => ((A @ B) | ~ (! [C:list_nat,D:nat]: ((A @ (append_nat @ C @ (cons_nat @ D @ nil_nat))) | ~ (! [E:list_nat]: ((A @ E) | ~ (ord_less_eq_nat @ (size_size_list_nat @ E) @ (size_size_list_nat @ C)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[140])). 87.71/26.55 thf(1283,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2301_distrib__right)). 87.71/26.55 thf(6885,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)],[1283])). 87.71/26.55 thf(74,axiom,(((size_size_list_nat @ nil_nat) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8524_length__nth__simps_I1_J)). 87.71/26.55 thf(2060,plain,(((size_size_list_nat @ nil_nat) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[74])). 87.71/26.55 thf(595,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C) @ B) = (modulo_modulo_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8725_msrevs_I2_J)). 87.71/26.55 thf(4272,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)],[595])). 87.71/26.55 thf(1207,axiom,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((dvd_dvd_nat @ B @ C) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9440_nat__mult__dvd__cancel__disj)). 87.71/26.55 thf(6621,plain,((! [A:nat,B:nat,C:nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((dvd_dvd_nat @ B @ C) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207])). 87.71/26.55 thf(1693,axiom,((! [A:option4927543243414619207at_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_vebt_insert @ (vEBT_Node @ A @ zero_zero_nat @ B @ C) @ D) = (vEBT_Node @ A @ zero_zero_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2581_vebt__insert_Osimps_I2_J)). 87.71/26.55 thf(8466,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)],[1693])). 87.71/26.55 thf(1622,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/sandbox2/benchmark/theBenchmark.p',fact_2525_vebt__delete_Osimps_I6_J)). 87.71/26.55 thf(8218,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)],[1622])). 87.71/26.55 thf(88,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_T_s_u_c_c @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ (bit0 @ (bit1 @ one)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9180_succ__bound__height)). 87.71/26.55 thf(2143,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_T_s_u_c_c @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ (bit0 @ (bit1 @ one)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[88])). 87.71/26.55 thf(765,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (minus_minus_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3016_Nat_Odiff__cancel)). 87.71/26.55 thf(4922,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)],[765])). 87.71/26.55 thf(1133,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) | (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1182_linorder__linear)). 87.71/26.55 thf(6367,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)],[1133])). 87.71/26.55 thf(982,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2315_add__less__mono)). 87.71/26.55 thf(5748,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[982])). 87.71/26.55 thf(55,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10045_or__nat__numerals_I3_J)). 87.71/26.55 thf(1941,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)],[55])). 87.71/26.55 thf(1266,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/sandbox2/benchmark/theBenchmark.p',fact_65_mult__right__cancel)). 87.71/26.55 thf(6826,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)],[1266])). 87.71/26.55 thf(600,axiom,((! [A:nat,B:nat]: ((A != B) = ((ord_less_nat @ B @ A) | (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_nat__neq__iff)). 87.71/26.55 thf(4287,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)],[600])). 87.71/26.55 thf(3,axiom,(((numeral_numeral_nat @ (bit1 @ one)) = (suc @ (suc @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9165_numeral__3__eq__3)). 87.71/26.55 thf(1780,plain,(((numeral_numeral_nat @ (bit1 @ one)) = (suc @ (suc @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])). 87.71/26.55 thf(781,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ A @ (times_times_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_n__less__n__mult__m)). 87.71/26.55 thf(4971,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ (suc @ zero_zero_nat) @ B) => (ord_less_nat @ A @ (times_times_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[781])). 87.71/26.55 thf(1551,axiom,((! [A:option_num,B:(option_num > (option_num > $o)),C:option_num]: ((((B @ A @ C) <= (C = none_num)) => ((B @ A @ C) <= (! [D:num,E:num]: (((B @ A @ C) <= (C = (some_num @ E))) <= (A = (some_num @ D)))))) <= ((B @ A @ C) <= (A = none_num))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_combine__options__cases)). 87.71/26.55 thf(7967,plain,((! [A:option_num,B:(option_num > (option_num > $o)),C:option_num]: ((((B @ A @ C) | ~ (C = none_num)) => ((B @ A @ C) | ~ (! [D:num,E:num]: ((B @ A @ C) | ~ (C = (some_num @ E)) | ~ (A = (some_num @ D)))))) | ~ ((B @ A @ C) | ~ (A = none_num))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1551])). 87.71/26.55 thf(625,axiom,((((=) @ nat) = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ B @ A) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1133_dual__order_Oeq__iff)). 87.71/26.55 thf(4377,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)],[625])). 87.71/26.55 thf(1441,axiom,((! [A:nat,B:nat]: (((A != B) => (ord_less_nat @ B @ A)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1265_linorder__cases)). 87.71/26.55 thf(7511,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)],[1441])). 87.71/26.55 thf(1499,axiom,((! [A:nat,B:list_nat,C:nat,D:nat]: (((cons_nat @ A @ B) = (replicate_nat @ C @ D)) = ((A = D) & (ord_less_nat @ zero_zero_nat @ C) & (B = (replicate_nat @ (minus_minus_nat @ C @ one_one_nat) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4778_Cons__replicate__eq)). 87.71/26.55 thf(7724,plain,((! [A:nat,B:list_nat,C:nat,D:nat]: (((cons_nat @ A @ B) = (replicate_nat @ C @ D)) = ((A = D) & (ord_less_nat @ zero_zero_nat @ C) & (B = (replicate_nat @ (minus_minus_nat @ C @ one_one_nat) @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1499])). 87.71/26.55 thf(250,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => (((vEBT_vebt_member @ A @ D) | (C = D)) <= (vEBT_vebt_member @ (vEBT_vebt_insert @ A @ C) @ D)))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8982_post__member__pre__member)). 87.71/26.55 thf(2850,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((ord_less_nat @ D @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((vEBT_vebt_member @ A @ D) | (C = D) | ~ (vEBT_vebt_member @ (vEBT_vebt_insert @ A @ C) @ D)))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[250])). 87.71/26.55 thf(1462,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_mult__nonneg__nonpos2)). 87.71/26.55 thf(7586,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (times_times_nat @ B @ A) @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1462])). 87.71/26.55 thf(1329,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 @ C @ A) @ (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_ordered__comm__semiring__class_Ocomm__mult__left__mono)). 87.71/26.55 thf(7055,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 @ C @ A) @ (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329])). 87.71/26.55 thf(263,axiom,((! [A:$o,B:assn,C:heap_Time_Heap_nat,D:(nat > assn),E:heap_Time_Heap_nat]: (((hoare_3067605981109127869le_nat @ B @ C @ D) <= (A)) => ((hoare_3067605981109127869le_nat @ B @ (if_Hea2662716070787841314ap_nat @ A @ C @ E) @ D) <= ((~ (A)) => (hoare_3067605981109127869le_nat @ B @ E @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_if__rule)). 87.71/26.55 thf(2888,plain,((! [A:$o,B:assn,C:heap_Time_Heap_nat,D:(nat > assn),E:heap_Time_Heap_nat]: (((hoare_3067605981109127869le_nat @ B @ C @ (D)) | ~ (A)) => ((hoare_3067605981109127869le_nat @ B @ (if_Hea2662716070787841314ap_nat @ A @ C @ E) @ (D)) | ~ ((~ (A)) => (hoare_3067605981109127869le_nat @ B @ E @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[263])). 87.71/26.55 thf(1370,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_less__imp__le__nat)). 87.71/26.55 thf(7228,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370])). 87.71/26.55 thf(1759,axiom,((! [A:assn,B:$o,C:heap_Time_Heap_nat,D:(nat > assn)]: ((hoare_3067605981109127869le_nat @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ D) = ((hoare_3067605981109127869le_nat @ A @ C @ D) <= (B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_norm__pre__pure__iff)). 87.71/26.55 thf(8744,plain,((! [A:assn,B:$o,C:heap_Time_Heap_nat,D:(nat > assn)]: ((hoare_3067605981109127869le_nat @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ (D)) = ((hoare_3067605981109127869le_nat @ A @ C @ (D)) | ~ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1759])). 87.71/26.55 thf(1082,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 @ C @ A) @ (times_times_nat @ C @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_mult__strict__left__mono)). 87.71/26.55 thf(6146,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 @ C @ A) @ (times_times_nat @ C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082])). 87.71/26.55 thf(895,axiom,((! [A:nat,B:nat]: (((binomial @ B @ A) = (binomial @ B @ (minus_minus_nat @ B @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8878_binomial__symmetric)). 87.71/26.55 thf(5431,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)],[895])). 87.71/26.55 thf(492,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (semiri1316708129612266289at_nat @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4661_Abs__fnat__hom__add)). 87.71/26.55 thf(3818,plain,((! [A:nat,B:nat]: ((plus_plus_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B)) = (semiri1316708129612266289at_nat @ (plus_plus_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[492])). 87.71/26.55 thf(1490,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1594_linorder__not__less)). 87.71/26.55 thf(7693,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = (ord_less_eq_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1490])). 87.71/26.55 thf(1058,axiom,((! [A:produc5542196010084753463at_nat]: (((! [B:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),C:product_prod_nat_nat]: (A != (produc2899441246263362727at_nat @ B @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ C) @ none_P5556105721700978146at_nat)))) => (~ (! [B:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),C:product_prod_nat_nat,D:product_prod_nat_nat]: (A != (produc2899441246263362727at_nat @ B @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ C) @ (some_P7363390416028606310at_nat @ D))))))) <= (! [B:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),C:option4927543243414619207at_nat]: (A != (produc2899441246263362727at_nat @ B @ (produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_862_VEBT__internal_Ooption__shift_Ocases)). 87.71/26.55 thf(6037,plain,((! [A:produc5542196010084753463at_nat]: (((! [B:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),C:product_prod_nat_nat]: ~ (A = (produc2899441246263362727at_nat @ (B) @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ C) @ none_P5556105721700978146at_nat)))) => (~ (! [B:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),C:product_prod_nat_nat,D:product_prod_nat_nat]: ~ (A = (produc2899441246263362727at_nat @ (B) @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ C) @ (some_P7363390416028606310at_nat @ D))))))) | ~ (! [B:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),C:option4927543243414619207at_nat]: ~ (A = (produc2899441246263362727at_nat @ (B) @ (produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058])). 87.71/26.55 thf(1344,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/sandbox2/benchmark/theBenchmark.p',fact_2155_add__gr__0)). 87.71/26.55 thf(7105,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)],[1344])). 87.71/26.55 thf(1626,axiom,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:heap_T2636463487746394924on_nat]: (((hoare_7629718768684598413on_nat @ A @ D @ C) <= (refine7594492741263601813on_nat @ D @ B)) <= (hoare_7629718768684598413on_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1888_hoare__triple__refines)). 87.71/26.55 thf(8231,plain,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:heap_T2636463487746394924on_nat]: ((hoare_7629718768684598413on_nat @ A @ D @ (C)) | ~ (refine7594492741263601813on_nat @ D @ B) | ~ (hoare_7629718768684598413on_nat @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1626])). 87.71/26.55 thf(854,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ B @ C) <= (entails @ (sup_sup_assn @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5113_ent__disjI2)). 87.71/26.55 thf(5276,plain,((! [A:assn,B:assn,C:assn]: ((entails @ B @ C) | ~ (entails @ (sup_sup_assn @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[854])). 87.71/26.55 thf(301,axiom,((! [A:list_real,B:list_int,C:(list_real > (list_int > $o))]: ((((C @ A @ B) <= (! [D:real,E:list_real,F:int,G:list_int]: (((size_size_list_real @ E) = (size_size_list_int @ G)) => ((C @ (cons_real @ D @ E) @ (cons_int @ F @ G)) <= (C @ E @ G))))) <= (C @ nil_real @ nil_int)) <= ((size_size_list_real @ A) = (size_size_list_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8533_list__induct2)). 87.71/26.55 thf(3041,plain,((! [A:list_real,B:list_int,C:(list_real > (list_int > $o))]: ((C @ A @ B) | ~ (! [D:real,E:list_real,F:int,G:list_int]: (((size_size_list_real @ E) = (size_size_list_int @ G)) => ((C @ (cons_real @ D @ E) @ (cons_int @ F @ G)) | ~ (C @ E @ G)))) | ~ (C @ nil_real @ nil_int) | ~ ((size_size_list_real @ A) = (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[301])). 87.71/26.55 thf(753,axiom,((! [A:list_real,B:nat]: ((foldr_real_nat @ (^ [C:real]: (suc)) @ A @ B) = (plus_plus_nat @ B @ (size_size_list_real @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2732_foldr__length__aux)). 87.71/26.55 thf(4875,plain,((! [A:list_real,B:nat]: ((foldr_real_nat @ (^ [C:real]: (suc)) @ A @ B) = (plus_plus_nat @ B @ (size_size_list_real @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[753])). 87.71/26.55 thf(1503,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ (modulo_modulo_nat @ B @ A))) => ((ord_less_nat @ D @ A) => ((modulo_modulo_nat @ (plus_plus_nat @ C @ D) @ A) = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8715_word__rot__lem)). 87.71/26.55 thf(7737,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ (modulo_modulo_nat @ B @ A))) => ((ord_less_nat @ D @ A) => ((modulo_modulo_nat @ (plus_plus_nat @ C @ D) @ A) = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1503])). 87.71/26.55 thf(640,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/sandbox2/benchmark/theBenchmark.p',fact_8651_div__less__iff__less__mult)). 87.71/26.55 thf(4437,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)],[640])). 87.71/26.55 thf(1726,axiom,((! [A:list_int]: (time_T8667231999468956601ay_int @ (array_of_list_int @ A) @ (suc @ (size_size_list_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4745_TBOUND__of__list)). 87.71/26.55 thf(8612,plain,((! [A:list_int]: (time_T8667231999468956601ay_int @ (array_of_list_int @ A) @ (suc @ (size_size_list_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1726])). 87.71/26.55 thf(985,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3063_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2)). 87.71/26.55 thf(5767,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ B @ C) @ A) = (plus_plus_nat @ (minus_minus_nat @ B @ A) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[985])). 87.71/26.55 thf(1110,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/sandbox2/benchmark/theBenchmark.p',fact_416_mult__le__mono2)). 87.71/26.55 thf(6280,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)],[1110])). 87.71/26.55 thf(632,axiom,((! [A:nat,B:nat]: ((A = B) | ~ (ord_less_eq_nat @ B @ A) | ~ (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1928_verit__la__disequality)). 87.71/26.55 thf(4398,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)],[632])). 87.71/26.55 thf(1588,axiom,((! [A:list_int]: ((foldr_int_nat @ (^ [B:int]: (suc)) @ A @ zero_zero_nat) = (size_size_list_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2645_foldr__length)). 87.71/26.55 thf(8111,plain,((! [A:list_int]: ((foldr_int_nat @ (^ [B:int]: (suc)) @ A @ zero_zero_nat) = (size_size_list_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1588])). 87.71/26.55 thf(551,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_mult__is__0)). 87.71/26.55 thf(4092,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)],[551])). 87.71/26.55 thf(891,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/sandbox2/benchmark/theBenchmark.p',fact_9458_dvd__minus__self)). 87.71/26.55 thf(5418,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)],[891])). 87.71/26.55 thf(906,axiom,((! [A:(int > (nat > assn)),B:int,C:list_int,D:nat,E:list_nat]: ((vEBT_L77084186935402305nt_nat @ A @ (cons_int @ B @ C) @ (cons_nat @ D @ E)) = (times_times_assn @ (A @ B @ D) @ (vEBT_L77084186935402305nt_nat @ A @ C @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4708_list__assn_Osimps_I2_J)). 87.71/26.55 thf(5467,plain,((! [A:(int > (nat > assn)),B:int,C:list_int,D:nat,E:list_nat]: ((vEBT_L77084186935402305nt_nat @ (A) @ (cons_int @ B @ C) @ (cons_nat @ D @ E)) = (times_times_assn @ (A @ B @ D) @ (vEBT_L77084186935402305nt_nat @ (A) @ C @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[906])). 87.71/26.55 thf(460,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ B @ (minus_minus_nat @ A @ B)) = A) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3069_linordered__semidom__class_Oadd__diff__inverse)). 87.71/26.55 thf(3691,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)],[460])). 87.71/26.55 thf(360,axiom,((! [A:list_real,B:list_o,C:list_int,D:(list_real > (list_o > (list_int > $o)))]: (((size_size_list_real @ A) = (size_size_list_o @ B)) => (((size_size_list_o @ B) = (size_size_list_int @ C)) => ((D @ nil_real @ nil_o @ nil_int) => ((! [E:real,F:list_real,G:$o,H:list_o,I:int,J:list_int]: (((size_size_list_real @ F) = (size_size_list_o @ H)) => (((size_size_list_o @ H) = (size_size_list_int @ J)) => ((D @ (cons_real @ E @ F) @ (cons_o @ G @ H) @ (cons_int @ I @ J)) <= (D @ F @ H @ J))))) => (D @ A @ B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8547_list__induct3)). 87.71/26.55 thf(3273,plain,((! [A:list_real,B:list_o,C:list_int,D:(list_real > (list_o > (list_int > $o)))]: (((size_size_list_real @ A) = (size_size_list_o @ B)) => (((size_size_list_o @ B) = (size_size_list_int @ C)) => ((D @ nil_real @ nil_o @ nil_int) => ((! [E:real,F:list_real,G:$o,H:list_o,I:int,J:list_int]: (((size_size_list_real @ F) = (size_size_list_o @ H)) => (((size_size_list_o @ H) = (size_size_list_int @ J)) => ((D @ (cons_real @ E @ F) @ (cons_o @ G @ H) @ (cons_int @ I @ J)) | ~ (D @ F @ H @ J))))) => (D @ A @ B @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[360])). 87.71/26.55 thf(486,axiom,((! [A:nat,B:nat,C:nat]: (((~ (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ A @ B)) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => (((~ (ord_less_eq_nat @ C @ B)) <= (ord_less_eq_nat @ A @ C)) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => (((~ (ord_less_eq_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C)) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1094_le__cases3)). 87.71/26.55 thf(3791,plain,((! [A:nat,B:nat,C:nat]: ((~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ A @ B)) => (((ord_less_eq_nat @ B @ A) => (~ (ord_less_eq_nat @ A @ C))) => ((~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_eq_nat @ A @ C)) => (((ord_less_eq_nat @ C @ B) => (~ (ord_less_eq_nat @ B @ A))) => ((~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_eq_nat @ B @ C)) => (~ ((ord_less_eq_nat @ C @ A) => (~ (ord_less_eq_nat @ A @ B))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[486])). 87.71/26.55 thf(932,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/sandbox2/benchmark/theBenchmark.p',fact_3142_diff__Suc__less)). 87.71/26.55 thf(5555,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)],[932])). 87.71/26.55 thf(587,axiom,((! [A:option4927543243414619207at_nat]: ((! [B:nat,C:nat]: (A != (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)))) = (A = none_P5556105721700978146at_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_737_not__Some__eq2)). 87.71/26.55 thf(4222,plain,((! [A:option4927543243414619207at_nat]: ((! [B:nat,C:nat]: ~ (A = (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)))) = (A = none_P5556105721700978146at_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[587])). 87.71/26.55 thf(1621,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (hoare_7629718768684598413on_nat @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_vebt_maxti @ B) @ (^ [C:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_vebt_maxt @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_vebt__maxti__h)). 87.71/26.55 thf(8216,plain,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (hoare_7629718768684598413on_nat @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_vebt_maxti @ B) @ (^ [C:option_nat]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_vebt_maxt @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1621])). 87.71/26.55 thf(1178,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1756_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I3_J)). 87.71/26.55 thf(6513,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Leaf @ A @ B) @ (suc @ (suc @ C))) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178])). 87.71/26.55 thf(1113,axiom,((! [A:list_int,B:nat]: (((size_size_list_int @ A) = (suc @ B)) = (? [C:int,D:list_int]: ((A = (cons_int @ C @ D)) & ((size_size_list_int @ D) = B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4674_length__Suc__conv)). 87.71/26.55 thf(6298,plain,((! [A:list_int,B:nat]: (((size_size_list_int @ A) = (suc @ B)) = (? [C:int,D:list_int]: ((A = (cons_int @ C @ D)) & ((size_size_list_int @ D) = B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113])). 87.71/26.55 thf(132,axiom,((! [A:nat,B:list_o]: ((ord_less_eq_nat @ (suc @ A) @ (size_size_list_o @ B)) = (? [C:$o,D:list_o]: ((B = (cons_o @ C @ D)) & (ord_less_eq_nat @ A @ (size_size_list_o @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4728_Suc__le__length__iff)). 87.71/26.55 thf(2337,plain,((! [A:nat,B:list_o]: ((ord_less_eq_nat @ (suc @ A) @ (size_size_list_o @ B)) = (? [C:$o,D:list_o]: ((B = (cons_o @ C @ D)) & (ord_less_eq_nat @ A @ (size_size_list_o @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[132])). 87.71/26.55 thf(1176,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) => (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2279_add__less__imp__less__right)). 87.71/26.55 thf(6508,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)],[1176])). 87.71/26.55 thf(1528,axiom,((! [A:assn]: ((inf_inf_assn @ bot_bot_assn @ A) = bot_bot_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8915_norm__assertion__simps_I9_J)). 87.71/26.55 thf(7879,plain,((! [A:assn]: ((inf_inf_assn @ bot_bot_assn @ A) = bot_bot_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1528])). 87.71/26.55 thf(1077,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((A != B) & (ord_less_eq_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1584_order__less__le)). 87.71/26.55 thf(6125,plain,(((ord_less_nat) = (^ [A:nat,B:nat]: (~ (A = B) & (ord_less_eq_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077])). 87.71/26.55 thf(834,axiom,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2087_add__0)). 87.71/26.55 thf(5203,plain,((! [A:nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[834])). 87.71/26.55 thf(1129,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_mult__zero__left)). 87.71/26.55 thf(6352,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129])). 87.71/26.55 thf(44,axiom,((! [A:(nat > (nat > nat)),B:nat,C:nat,D:nat,E:nat]: ((((E = (set_fo2584398358068434914at_nat @ A @ (plus_plus_nat @ B @ one_one_nat) @ C @ (A @ B @ D))) <= (~ (ord_less_nat @ C @ B))) & ((ord_less_nat @ C @ B) => (E = D))) <= ((set_fo2584398358068434914at_nat @ A @ B @ C @ D) = E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2737_fold__atLeastAtMost__nat_Oelims)). 87.71/26.55 thf(1901,plain,((! [A:(nat > (nat > nat)),B:nat,C:nat,D:nat,E:nat]: ((((E = (set_fo2584398358068434914at_nat @ (A) @ (plus_plus_nat @ B @ one_one_nat) @ C @ (A @ B @ D))) | (ord_less_nat @ C @ B)) & ((ord_less_nat @ C @ B) => (E = D))) | ~ ((set_fo2584398358068434914at_nat @ (A) @ B @ C @ D) = E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[44])). 87.71/26.55 thf(422,axiom,((! [A:assn]: (entails @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4053_ent__refl)). 87.71/26.55 thf(3544,plain,((! [A:assn]: (entails @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[422])). 87.71/26.55 thf(1089,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8638_div__le__dividend)). 87.71/26.55 thf(6174,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (divide_divide_nat @ A @ B) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089])). 87.71/26.55 thf(824,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D) <= (ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B))))) <= (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3049_add__le__add__imp__diff__le)). 87.71/26.55 thf(5152,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B)) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) => ((ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ D) | ~ (ord_less_eq_nat @ C @ (plus_plus_nat @ D @ B))))) | ~ (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[824])). 87.71/26.55 thf(563,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (((modulo_modulo_nat @ C @ B) = A) <= ((modulo_modulo_nat @ C @ B) = (modulo_modulo_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8704_nat__mod__eq)). 87.71/26.55 thf(4132,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (((modulo_modulo_nat @ C @ B) = A) | ~ ((modulo_modulo_nat @ C @ B) = (modulo_modulo_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[563])). 87.71/26.55 thf(1218,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ C) = (ord_less_eq_nat @ B @ (divide_divide_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8660_td__gal)). 87.71/26.55 thf(6653,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ (times_times_nat @ B @ A) @ C) = (ord_less_eq_nat @ B @ (divide_divide_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218])). 87.71/26.55 thf(1600,axiom,((! [A:assn,B:nat]: ((power_power_assn @ A @ (suc @ B)) = (times_times_assn @ A @ (power_power_assn @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7875_power__Suc)). 87.71/26.55 thf(8148,plain,((! [A:assn,B:nat]: ((power_power_assn @ A @ (suc @ B)) = (times_times_assn @ A @ (power_power_assn @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1600])). 87.71/26.55 thf(1402,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1787_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I5_J)). 87.71/26.55 thf(7351,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402])). 87.71/26.55 thf(1156,axiom,((! [A:nat,B:nat]: (((last_nat @ (upt @ A @ B)) = (minus_minus_nat @ B @ one_one_nat)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8834_last__upt)). 87.71/26.55 thf(6436,plain,((! [A:nat,B:nat]: (((last_nat @ (upt @ A @ B)) = (minus_minus_nat @ B @ one_one_nat)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156])). 87.71/26.55 thf(1461,axiom,((! [A:nat,B:nat]: (A = (plus_plus_nat @ (times_times_nat @ (divide_divide_nat @ A @ B) @ B) @ (modulo_modulo_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8738_div__mod__decomp)). 87.71/26.55 thf(7583,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)],[1461])). 87.71/26.55 thf(182,axiom,(((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9010_Suc__1)). 87.71/26.55 thf(2545,plain,(((suc @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[182])). 87.71/26.55 thf(374,axiom,((! [A:nat]: (((A = zero_zero_nat) | (A = (suc @ zero_zero_nat))) <= (ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9033_less__2__cases)). 87.71/26.55 thf(3359,plain,((! [A:nat]: ((A = zero_zero_nat) | (A = (suc @ zero_zero_nat)) | ~ (ord_less_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[374])). 87.71/26.55 thf(724,axiom,(((semiri1316708129612266289at_nat @ one_one_nat) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4562_of__nat__1)). 87.71/26.55 thf(4737,plain,(((semiri1316708129612266289at_nat @ one_one_nat) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[724])). 87.71/26.55 thf(1762,axiom,((! [A:$o,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn),E:nat]: ((time_htt_VEBT_VEBTi @ (times_times_assn @ (pure_assn @ A) @ B) @ C @ D @ E) = ((time_htt_VEBT_VEBTi @ B @ C @ D @ E) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1796_norm__pre__pure__iff__htt_H)). 87.71/26.55 thf(8757,plain,((! [A:$o,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn),E:nat]: ((time_htt_VEBT_VEBTi @ (times_times_assn @ (pure_assn @ A) @ B) @ C @ (D) @ E) = ((time_htt_VEBT_VEBTi @ B @ C @ (D) @ E) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1762])). 87.71/26.55 thf(1311,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_nat @ A @ B) => (((ord_less_nat @ E @ D) => (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ A @ D) @ C) @ (plus_plus_nat @ (times_times_nat @ B @ D) @ E))) <= (ord_less_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2425_mlex__fst__decrI)). 87.71/26.55 thf(6994,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_nat @ A @ B) => (((ord_less_nat @ E @ D) => (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ A @ D) @ C) @ (plus_plus_nat @ (times_times_nat @ B @ D) @ E))) | ~ (ord_less_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311])). 87.71/26.55 thf(951,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2057_add_Oright__neutral)). 87.71/26.55 thf(5638,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[951])). 87.71/26.55 thf(1522,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/sandbox2/benchmark/theBenchmark.p',fact_2361_add__nonpos__nonpos)). 87.71/26.55 thf(7847,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)],[1522])). 87.71/26.55 thf(1316,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1286_order_Ostrict__trans)). 87.71/26.55 thf(7009,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316])). 87.71/26.55 thf(832,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))) <= (ord_less_eq_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8036_power__strict__mono)). 87.71/26.55 thf(5186,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ B) => (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))) | ~ (ord_less_eq_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[832])). 87.71/26.55 thf(161,axiom,((! [A:int,B:int,C:nat]: ((power_power_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ (power_power_int @ A @ C) @ (power_power_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7819_power__mult__distrib)). 87.71/26.55 thf(2468,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)],[161])). 87.71/26.55 thf(315,axiom,((! [A:nat,B:nat,C:nat]: ((((ord_less_nat @ (binomial @ C @ B) @ (binomial @ C @ A)) <= (ord_less_eq_nat @ B @ C)) <= (ord_less_eq_nat @ C @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9058_binomial__strict__antimono)). 87.71/26.56 thf(3107,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (binomial @ C @ B) @ (binomial @ C @ A)) | ~ (ord_less_eq_nat @ B @ C) | ~ (ord_less_eq_nat @ C @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[315])). 87.71/26.56 thf(1654,axiom,((! [A:nat,B:nat]: ((((suc @ (modulo_modulo_nat @ A @ B)) != B) => ((modulo_modulo_nat @ (suc @ A) @ B) = (suc @ (modulo_modulo_nat @ A @ B)))) & (((modulo_modulo_nat @ (suc @ A) @ B) = zero_zero_nat) <= ((suc @ (modulo_modulo_nat @ A @ B)) = B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8708_mod__Suc)). 87.71/26.56 thf(8331,plain,((! [A:nat,B:nat]: (((~ ((suc @ (modulo_modulo_nat @ A @ B)) = B)) => ((modulo_modulo_nat @ (suc @ A) @ B) = (suc @ (modulo_modulo_nat @ A @ B)))) & (((modulo_modulo_nat @ (suc @ A) @ B) = zero_zero_nat) | ~ ((suc @ (modulo_modulo_nat @ A @ B)) = B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1654])). 87.71/26.56 thf(1460,axiom,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2788_zero__diff)). 87.71/26.56 thf(7580,plain,((! [A:nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1460])). 87.71/26.56 thf(59,axiom,((! [A:num]: (one != (bit1 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9130_semiring__norm_I84_J)). 87.71/26.56 thf(1955,plain,((! [A:num]: ~ (one = (bit1 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[59])). 87.71/26.56 thf(189,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_nat @ (minus_minus_nat @ B @ C) @ (minus_minus_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9036_diff__le__diff__pow)). 87.71/26.56 thf(2579,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (ord_less_eq_nat @ (minus_minus_nat @ B @ C) @ (minus_minus_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[189])). 87.71/26.56 thf(1070,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (divide_divide_nat @ B @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8649_div__less__dividend)). 87.71/26.56 thf(6086,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (divide_divide_nat @ B @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070])). 87.71/26.56 thf(1687,axiom,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:assn,E:assn]: ((hoare_7629718768684598413on_nat @ A @ B @ C) => ((hoare_7629718768684598413on_nat @ D @ B @ (^ [F:option_nat]: (times_times_assn @ (C @ F) @ E))) <= (entails @ D @ (times_times_assn @ A @ E)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4074_fi__rule)). 87.71/26.56 thf(8449,plain,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:assn,E:assn]: ((hoare_7629718768684598413on_nat @ A @ B @ (C)) => ((hoare_7629718768684598413on_nat @ D @ B @ (^ [F:option_nat]: (times_times_assn @ (C @ F) @ E))) | ~ (entails @ D @ (times_times_assn @ A @ E)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1687])). 87.71/26.56 thf(1714,axiom,((! [A:$o,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn),E:heap_T2636463487746394924on_nat,F:(option_nat > assn),G:(option_nat > assn)]: ((((hoare_7629718768684598413on_nat @ B @ E @ F) <= (~ (A))) => ((! [H:option_nat]: (entails @ (sup_sup_assn @ (times_times_assn @ (D @ H) @ (pure_assn @ A)) @ (times_times_assn @ (F @ H) @ (pure_assn @ (~ (A))))) @ (G @ H))) => (hoare_7629718768684598413on_nat @ B @ (if_Hea5867803462524415986on_nat @ A @ C @ E) @ G))) <= ((A) => (hoare_7629718768684598413on_nat @ B @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5137_if__rule__split)). 87.71/26.56 thf(8552,plain,((! [A:$o,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn),E:heap_T2636463487746394924on_nat,F:(option_nat > assn),G:(option_nat > assn)]: ((((hoare_7629718768684598413on_nat @ B @ E @ (F)) | (A)) => ((! [H:option_nat]: (entails @ (sup_sup_assn @ (times_times_assn @ (D @ H) @ (pure_assn @ A)) @ (times_times_assn @ (F @ H) @ (pure_assn @ (~ (A))))) @ (G @ H))) => (hoare_7629718768684598413on_nat @ B @ (if_Hea5867803462524415986on_nat @ A @ C @ E) @ (G)))) | ~ ((A) => (hoare_7629718768684598413on_nat @ B @ C @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1714])). 87.71/26.56 thf(1165,axiom,((! [A:(nat > $o),B:nat,C:nat]: (((A @ (minus_minus_nat @ B @ C)) <= (! [D:nat]: ((A @ (suc @ D)) => (A @ D)))) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3008_zero__induct__lemma)). 87.71/26.56 thf(6467,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (minus_minus_nat @ B @ C)) | ~ (! [D:nat]: ((A @ (suc @ D)) => (A @ D))) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165])). 87.71/26.56 thf(1005,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_mult__left__mono)). 87.71/26.56 thf(5841,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005])). 87.71/26.56 thf(209,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8862_fact__ge__self)). 87.71/26.56 thf(2675,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[209])). 87.71/26.56 thf(1692,axiom,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (hoare_hoare_triple_o @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_VEBT_minNulli @ B) @ (^ [C:$o]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_VEBT_minNull @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2109_minNulli__rule)). 87.71/26.56 thf(8464,plain,((! [A:vEBT_VEBT,B:vEBT_VEBTi]: (hoare_hoare_triple_o @ (vEBT_vebt_assn_raw @ A @ B) @ (vEBT_VEBT_minNulli @ B) @ (^ [C:$o]: (times_times_assn @ (vEBT_vebt_assn_raw @ A @ B) @ (pure_assn @ (C = (vEBT_VEBT_minNull @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1692])). 87.71/26.56 thf(1239,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) => (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2194_add__right__imp__eq)). 87.71/26.56 thf(6746,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)],[1239])). 87.71/26.56 thf(1217,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1993_verit__comp__simplify1_I1_J)). 87.71/26.56 thf(6650,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217])). 87.71/26.56 thf(1035,axiom,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_lessI)). 87.71/26.56 thf(5949,plain,((! [A:nat]: (ord_less_nat @ A @ (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035])). 87.71/26.56 thf(1094,axiom,((! [A:(nat > nat),B:nat,C:list_nat]: ((size_list_nat @ A @ (cons_nat @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (A @ B) @ (size_list_nat @ A @ C)) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4764_list_Osize__gen_I2_J)). 87.71/26.56 thf(6188,plain,((! [A:(nat > nat),B:nat,C:list_nat]: ((size_list_nat @ (A) @ (cons_nat @ B @ C)) = (plus_plus_nat @ (plus_plus_nat @ (A @ B) @ (size_list_nat @ (A) @ C)) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094])). 87.71/26.56 thf(146,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_T_m_a_x_t @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2600_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Osimps_I2_J)). 87.71/26.56 thf(2411,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: ((vEBT_T_m_a_x_t @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[146])). 87.71/26.56 thf(1754,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1769_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I4_J)). 87.71/26.56 thf(8729,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1754])). 87.71/26.56 thf(43,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_T_m_e_m_b_e_r @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ (bit1 @ one))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9402_member__bound__height)). 87.71/26.56 thf(1898,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_T_m_e_m_b_e_r @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit1 @ (bit1 @ (bit1 @ one))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[43])). 87.71/26.56 thf(1226,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/sandbox2/benchmark/theBenchmark.p',fact_8997_mi__ma__2__deg)). 87.71/26.56 thf(6679,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)],[1226])). 87.71/26.56 thf(26,axiom,(((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Leaf @ ($false) @ ($false))) = one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1753_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Osimps_I1_J)). 87.71/26.56 thf(1849,plain,(((vEBT_T_m_i_n_N_u_l_l @ (vEBT_Leaf @ ($false) @ ($false))) = one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[26])). 87.71/26.56 thf(1401,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (suc @ (modulo_modulo_nat @ A @ B))) @ B) = (modulo_modulo_nat @ (suc @ (suc @ A)) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8703_mod__Suc__Suc__eq)). 87.71/26.56 thf(7348,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)],[1401])). 87.71/26.56 thf(777,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3176_nat__less__add__iff1)). 87.71/26.56 thf(4959,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((ord_less_nat @ (plus_plus_nat @ (times_times_nat @ B @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ A @ C) @ E)) = (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ D) @ E)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[777])). 87.71/26.56 thf(1211,axiom,((! [A:vEBT_VEBT,B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT]: (ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (vEBT_VEBT_height @ (vEBT_Node @ B @ C @ D @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2028_height__compose__summary)). 87.71/26.56 thf(6633,plain,((! [A:vEBT_VEBT,B:option4927543243414619207at_nat,C:nat,D:list_VEBT_VEBT]: (ord_less_eq_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (vEBT_VEBT_height @ (vEBT_Node @ B @ C @ D @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211])). 87.71/26.56 thf(150,axiom,((! [A:list_o,B:list_nat,C:(list_o > (list_nat > $o))]: (((size_size_list_o @ A) = (size_size_list_nat @ B)) => (((C @ A @ B) <= (! [D:$o,E:list_o,F:nat,G:list_nat]: (((C @ (cons_o @ D @ E) @ (cons_nat @ F @ G)) <= (C @ E @ G)) <= ((size_size_list_o @ E) = (size_size_list_nat @ G))))) <= (C @ nil_o @ nil_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8536_list__induct2)). 87.71/26.56 thf(2426,plain,((! [A:list_o,B:list_nat,C:(list_o > (list_nat > $o))]: (((size_size_list_o @ A) = (size_size_list_nat @ B)) => ((C @ A @ B) | ~ (! [D:$o,E:list_o,F:nat,G:list_nat]: ((C @ (cons_o @ D @ E) @ (cons_nat @ F @ G)) | ~ (C @ E @ G) | ~ ((size_size_list_o @ E) = (size_size_list_nat @ G)))) | ~ (C @ nil_o @ nil_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[150])). 87.71/26.56 thf(288,axiom,((! [A:nat,B:int]: (((replicate_int @ A @ B) = nil_int) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8167_replicate__empty)). 87.71/26.56 thf(2992,plain,((! [A:nat,B:int]: (((replicate_int @ A @ B) = nil_int) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[288])). 87.71/26.56 thf(1542,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ (times_times_nat @ A @ B) @ C)) @ A) = (modulo_modulo_nat @ (suc @ C) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8700_Suc__mod__mult__self4)). 87.71/26.56 thf(7921,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)],[1542])). 87.71/26.56 thf(697,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) <= (A != B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_le__neq__implies__less)). 87.71/26.56 thf(4624,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)],[697])). 87.71/26.56 thf(693,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ one_one_nat @ A) => ((suc @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2874_Suc__diff)). 87.71/26.56 thf(4611,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ one_one_nat @ A) => ((suc @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[693])). 87.71/26.56 thf(1249,axiom,((! [A:nat]: ((A != zero_zero_nat) = ((dvd_dvd_nat @ A @ zero_zero_nat) & (A != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9454_gcd__nat_Onot__eq__extremum)). 87.71/26.56 thf(6775,plain,((! [A:nat]: ((~ (A = zero_zero_nat)) = ((dvd_dvd_nat @ A @ zero_zero_nat) & ~ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249])). 87.71/26.56 thf(942,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/sandbox2/benchmark/theBenchmark.p',fact_7895_nat__power__less__imp__less)). 87.71/26.56 thf(5613,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)],[942])). 87.71/26.56 thf(1134,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((ord_min_nat @ (suc @ A) @ B) = (suc @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10135_min__Suc__gt_I1_J)). 87.71/26.56 thf(6369,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((ord_min_nat @ (suc @ A) @ B) = (suc @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134])). 87.71/26.56 thf(657,axiom,((! [A:assn,B:assn,C:assn]: ((sup_sup_assn @ A @ (sup_sup_assn @ B @ C)) = (sup_sup_assn @ B @ (sup_sup_assn @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5433_assn__aci_I7_J)). 87.71/26.56 thf(4488,plain,((! [A:assn,B:assn,C:assn]: ((sup_sup_assn @ A @ (sup_sup_assn @ B @ C)) = (sup_sup_assn @ B @ (sup_sup_assn @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[657])). 87.71/26.56 thf(1179,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_less__SucI)). 87.71/26.56 thf(6526,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ A @ (suc @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179])). 87.71/26.56 thf(283,axiom,((! [A:nat,B:list_real]: ((ord_less_eq_nat @ (suc @ A) @ (size_size_list_real @ B)) = (? [C:real,D:list_real]: ((B = (cons_real @ C @ D)) & (ord_less_eq_nat @ A @ (size_size_list_real @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4727_Suc__le__length__iff)). 87.71/26.56 thf(2975,plain,((! [A:nat,B:list_real]: ((ord_less_eq_nat @ (suc @ A) @ (size_size_list_real @ B)) = (? [C:real,D:list_real]: ((B = (cons_real @ C @ D)) & (ord_less_eq_nat @ A @ (size_size_list_real @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[283])). 87.71/26.56 thf(1511,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2807_add__diff__cancel__left_H)). 87.71/26.56 thf(7797,plain,((! [A:nat,B:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ A) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1511])). 87.71/26.56 thf(64,axiom,((! [A:nat,B:list_nat,C:nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((size_size_list_nat @ B) = (size_size_list_nat @ (append_nat @ (take_nat @ A @ B) @ (append_nat @ (cons_nat @ C @ nil_nat) @ (drop_nat @ (suc @ A) @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8092_pos__n__replace)). 87.71/26.56 thf(1972,plain,((! [A:nat,B:list_nat,C:nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => ((size_size_list_nat @ B) = (size_size_list_nat @ (append_nat @ (take_nat @ A @ B) @ (append_nat @ (cons_nat @ C @ nil_nat) @ (drop_nat @ (suc @ A) @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[64])). 87.71/26.56 thf(215,axiom,((! [A:num]: (one != (bit0 @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8973_semiring__norm_I83_J)). 87.71/26.56 thf(2711,plain,((! [A:num]: ~ (one = (bit0 @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[215])). 87.71/26.56 thf(999,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2213_verit__sum__simplify)). 87.71/26.56 thf(5809,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[999])). 87.71/26.56 thf(565,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ A @ (times_times_nat @ B @ C)) = (power_power_nat @ (power_power_nat @ A @ B) @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7828_power__mult)). 87.71/26.56 thf(4143,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)],[565])). 87.71/26.56 thf(1613,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ~ (vEBT_vebt_member @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ zero_zero_nat @ B @ C) @ D))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_vebt__member_Osimps_I3_J)). 87.71/26.56 thf(8185,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)],[1613])). 87.71/26.56 thf(1395,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ (inf_inf_assn @ C @ A) @ B) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8912_ent__conjE2)). 87.71/26.56 thf(7303,plain,((! [A:assn,B:assn,C:assn]: ((entails @ (inf_inf_assn @ C @ A) @ B) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395])). 87.71/26.56 thf(253,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ (binomial @ C @ A) @ (binomial @ C @ B)) <= (ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9046_binomial__mono)). 87.71/26.56 thf(2860,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (binomial @ C @ A) @ (binomial @ C @ B)) | ~ (ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[253])). 87.71/26.56 thf(1587,axiom,((! [A:nat]: ((ord_min_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10133_min__0L)). 87.71/26.56 thf(8108,plain,((! [A:nat]: ((ord_min_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1587])). 87.71/26.56 thf(220,axiom,((! [A:nat]: ((bit_se547839408752420682it_nat @ A @ (suc @ zero_zero_nat)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10112_push__bit__of__Suc__0)). 87.71/26.56 thf(2728,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)],[220])). 87.71/26.56 thf(588,axiom,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8871_binomial__eq__0__iff)). 87.71/26.56 thf(4225,plain,((! [A:nat,B:nat]: (((binomial @ A @ B) = zero_zero_nat) = (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[588])). 87.71/26.56 thf(617,axiom,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se547839408752420682it_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ (minus_minus_nat @ C @ A)) & (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10115_bit__push__bit__iff__nat)). 87.71/26.56 thf(4342,plain,((! [A:nat,B:nat,C:nat]: ((bit_se1148574629649215175it_nat @ (bit_se547839408752420682it_nat @ A @ B) @ C) = ((bit_se1148574629649215175it_nat @ B @ (minus_minus_nat @ C @ A)) & (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[617])). 87.71/26.56 thf(1581,axiom,((! [A:assn,B:$o,C:heap_Time_Heap_o,D:($o > assn),E:nat]: ((time_htt_o @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ D @ E) = ((B) => (time_htt_o @ A @ C @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1793_norm__pre__pure__iff__htt)). 87.71/26.56 thf(8087,plain,((! [A:assn,B:$o,C:heap_Time_Heap_o,D:($o > assn),E:nat]: ((time_htt_o @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ (D) @ E) = ((B) => (time_htt_o @ A @ C @ (D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1581])). 87.71/26.56 thf(741,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) <= (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1249_ord__eq__less__trans)). 87.71/26.56 thf(4838,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)) | ~ (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[741])). 87.71/26.56 thf(1131,axiom,((! [A:list_real,B:list_o,C:(real > ($o > assn))]: (((size_size_list_real @ A) != (size_size_list_o @ B)) => ((vEBT_L6234343332106409831real_o @ C @ A @ B) = bot_bot_assn)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3198_list__assn__aux__ineq__len)). 87.71/26.56 thf(6358,plain,((! [A:list_real,B:list_o,C:(real > ($o > assn))]: ((~ ((size_size_list_real @ A) = (size_size_list_o @ B))) => ((vEBT_L6234343332106409831real_o @ (C) @ A @ B) = bot_bot_assn)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131])). 87.71/26.56 thf(1086,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 @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_mult__less__le__imp__less)). 87.71/26.56 thf(6161,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 @ 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)],[1086])). 87.71/26.56 thf(1440,axiom,((! [A:$o,B:$o]: (((~ (A)) => ((vEBT_vebt_succ @ (vEBT_Leaf @ B @ A) @ zero_zero_nat) = none_nat)) & ((A) => ((vEBT_vebt_succ @ (vEBT_Leaf @ B @ A) @ zero_zero_nat) = (some_nat @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1453_vebt__succ_Osimps_I1_J)). 87.71/26.56 thf(7498,plain,((! [A:$o,B:$o]: (((~ (A)) => ((vEBT_vebt_succ @ (vEBT_Leaf @ B @ A) @ zero_zero_nat) = none_nat)) & ((A) => ((vEBT_vebt_succ @ (vEBT_Leaf @ B @ A) @ zero_zero_nat) = (some_nat @ one_one_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1440])). 87.71/26.56 thf(416,axiom,((! [A:$o,B:$o]: ((vEBT_VEBT_height @ (vEBT_Leaf @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1920_VEBT__internal_Oheight_Osimps_I1_J)). 87.71/26.56 thf(3520,plain,((! [A:$o,B:$o]: ((vEBT_VEBT_height @ (vEBT_Leaf @ A @ B)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[416])). 87.71/26.56 thf(1601,axiom,((! [A:array_int,B:list_int]: (hoare_3067605981109127869le_nat @ (snga_assn_int @ A @ B) @ (array_len_int @ A) @ (^ [C:nat]: (times_times_assn @ (snga_assn_int @ A @ B) @ (pure_assn @ (C = (size_size_list_int @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4449_length__rule)). 87.71/26.56 thf(8151,plain,((! [A:array_int,B:list_int]: (hoare_3067605981109127869le_nat @ (snga_assn_int @ A @ B) @ (array_len_int @ A) @ (^ [C:nat]: (times_times_assn @ (snga_assn_int @ A @ B) @ (pure_assn @ (C = (size_size_list_int @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1601])). 87.71/26.56 thf(1181,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_eq_nat @ (suc @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_not__less__eq__eq)). 87.71/26.56 thf(6531,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)],[1181])). 87.71/26.56 thf(293,axiom,((! [A:num,B:nat]: ((ord_less_nat @ (numeral_numeral_nat @ A) @ (suc @ B)) = (ord_less_nat @ (pred_numeral @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9914_less__numeral__Suc)). 87.71/26.56 thf(3007,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)],[293])). 87.71/26.56 thf(1489,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_mult__eq__0__iff)). 87.71/26.56 thf(7690,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)],[1489])). 87.71/26.56 thf(1437,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: (((minus_minus_nat @ (plus_plus_nat @ (times_times_nat @ A @ C) @ D) @ (plus_plus_nat @ (times_times_nat @ B @ C) @ E)) = (minus_minus_nat @ D @ (plus_plus_nat @ (times_times_nat @ (minus_minus_nat @ B @ A) @ C) @ E))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3146_nat__diff__add__eq2)). 87.71/26.56 thf(7488,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)],[1437])). 87.71/26.56 thf(591,axiom,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2786_diff__zero)). 87.71/26.56 thf(4257,plain,((! [A:nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[591])). 87.71/26.56 thf(387,axiom,((! [A:real,B:real,C:real]: ((times_times_real @ A @ (times_times_real @ B @ C)) = (times_times_real @ B @ (times_times_real @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_ab__semigroup__mult__class_Omult_Oleft__commute)). 87.71/26.56 thf(3398,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)],[387])). 87.71/26.56 thf(735,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/sandbox2/benchmark/theBenchmark.p',fact_1618_order__le__less__trans)). 87.71/26.56 thf(4819,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)],[735])). 87.71/26.56 thf(1114,axiom,((! [A:nat,B:nat,C:nat]: ((power_power_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ (power_power_nat @ A @ C) @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7818_power__mult__distrib)). 87.71/26.56 thf(6301,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)],[1114])). 87.71/26.56 thf(1151,axiom,((! [A:vEBT_VEBT]: ((vEBT_invar_vebt @ A @ one_one_nat) = (? [B:$o,C:$o]: (A = (vEBT_Leaf @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_967_deg1Leaf)). 87.71/26.56 thf(6420,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)],[1151])). 87.71/26.56 thf(231,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((A = C) | (A = B)) => (((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F)) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8977_insert__simp__mima)). 87.71/26.56 thf(2760,plain,((! [A:nat,B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (((A = C) | (A = B)) => (((vEBT_vebt_insert @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F) @ A) = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ D @ E @ F)) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[231])). 87.71/26.56 thf(388,axiom,((! [A:nat,B:list_nat]: ((nil_nat = (drop_nat @ A @ B)) = (ord_less_eq_nat @ (size_size_list_nat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8274_drop__eq__Nil2)). 87.71/26.56 thf(3401,plain,((! [A:nat,B:list_nat]: ((nil_nat = (drop_nat @ A @ B)) = (ord_less_eq_nat @ (size_size_list_nat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[388])). 87.71/26.56 thf(1243,axiom,((! [A:nat,B:list_nat]: ((foldl_nat_nat @ (^ [C:nat,D:nat]: (suc @ C)) @ A @ B) = (plus_plus_nat @ A @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4748_foldl__length__aux)). 87.71/26.56 thf(6758,plain,((! [A:nat,B:list_nat]: ((foldl_nat_nat @ (^ [C:nat,D:nat]: (suc @ C)) @ A @ B) = (plus_plus_nat @ A @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243])). 87.71/26.56 thf(1059,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (minus_minus_nat @ A @ B) @ C) = (ord_less_eq_nat @ A @ (plus_plus_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3104_le__diff__conv)). 87.71/26.56 thf(6041,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)],[1059])). 87.71/26.56 thf(1419,axiom,((! [A:assn,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn)]: (((hoare_1429296392585015714_VEBTi @ A @ C @ D) <= (hoare_1429296392585015714_VEBTi @ B @ C @ D)) <= (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4072_cons__pre__rule)). 87.71/26.56 thf(7412,plain,((! [A:assn,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ A @ C @ (D)) | ~ (hoare_1429296392585015714_VEBTi @ B @ C @ (D)) | ~ (entails @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1419])). 87.71/26.56 thf(1269,axiom,((! [A:num,B:nat]: (((modulo_modulo_nat @ (suc @ (times_times_nat @ (numeral_numeral_nat @ A) @ B)) @ (numeral_numeral_nat @ A)) = one_one_nat) <= ((numeral_numeral_nat @ A) != one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8955_Suc__times__numeral__mod__eq)). 87.71/26.56 thf(6835,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)],[1269])). 87.71/26.56 thf(1295,axiom,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_not__gr__zero)). 87.71/26.56 thf(6938,plain,((! [A:nat]: ((~ (ord_less_nat @ zero_zero_nat @ A)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295])). 87.71/26.56 thf(205,axiom,((! [A:list_real,B:list_o,C:(list_real > (list_o > $o))]: (((size_size_list_real @ A) = (size_size_list_o @ B)) => ((C @ nil_real @ nil_o) => ((C @ A @ B) <= (! [D:real,E:list_real,F:$o,G:list_o]: (((size_size_list_real @ E) = (size_size_list_o @ G)) => ((C @ E @ G) => (C @ (cons_real @ D @ E) @ (cons_o @ F @ G)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8531_list__induct2)). 87.71/26.56 thf(2643,plain,((! [A:list_real,B:list_o,C:(list_real > (list_o > $o))]: (((size_size_list_real @ A) = (size_size_list_o @ B)) => ((C @ nil_real @ nil_o) => ((C @ A @ B) | ~ (! [D:real,E:list_real,F:$o,G:list_o]: (((size_size_list_real @ E) = (size_size_list_o @ G)) => ((C @ E @ G) => (C @ (cons_real @ D @ E) @ (cons_o @ F @ G)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[205])). 87.71/26.56 thf(707,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/sandbox2/benchmark/theBenchmark.p',fact_509_mult__left__le__imp__le)). 87.71/26.56 thf(4678,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)],[707])). 87.71/26.56 thf(1777,axiom,((! [A:list_o]: (time_TBOUND_array_o @ (array_of_list_o @ A) @ (suc @ (size_size_list_o @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4743_TBOUND__of__list)). 87.71/26.56 thf(8812,plain,((! [A:list_o]: (time_TBOUND_array_o @ (array_of_list_o @ A) @ (suc @ (size_size_list_o @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1777])). 87.71/26.56 thf(986,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2867_diff__is__0__eq)). 87.71/26.56 thf(5771,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)],[986])). 87.71/26.56 thf(1406,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (~ (! [C:nat]: (B != (plus_plus_nat @ A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2235_less__eqE)). 87.71/26.56 thf(7363,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)],[1406])). 87.71/26.56 thf(1342,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1275_dual__order_Oirrefl)). 87.71/26.56 thf(7099,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342])). 87.71/26.56 thf(678,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/sandbox2/benchmark/theBenchmark.p',fact_2326_add__leD2)). 87.71/26.56 thf(4548,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)],[678])). 87.71/26.56 thf(597,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => (entails @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4057_fr__refl)). 87.71/26.56 thf(4278,plain,((! [A:assn,B:assn,C:assn]: ((entails @ A @ B) => (entails @ (times_times_assn @ A @ C) @ (times_times_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[597])). 87.71/26.56 thf(704,axiom,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1741_assn__one__left)). 87.71/26.56 thf(4651,plain,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[704])). 87.71/26.56 thf(1044,axiom,((! [A:($o > nat)]: ((groups5323242076211637530_o_nat @ A @ bot_bot_set_o) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3789_prod_Oempty_H)). 87.71/26.56 thf(5981,plain,((! [A:($o > nat)]: ((groups5323242076211637530_o_nat @ (A) @ bot_bot_set_o) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044])). 87.71/26.56 thf(200,axiom,((! [A:int,B:int,C:nat]: (((times_times_int @ (power_power_int @ A @ C) @ B) = (times_times_int @ B @ (power_power_int @ A @ C))) <= ((times_times_int @ A @ B) = (times_times_int @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7825_power__commuting__commutes)). 87.71/26.56 thf(2626,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)],[200])). 87.71/26.56 thf(636,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ A @ (plus_plus_nat @ B @ C)) = (plus_plus_nat @ B @ (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2186_ab__semigroup__add__class_Oadd_Oleft__commute)). 87.71/26.56 thf(4424,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)],[636])). 87.71/26.56 thf(399,axiom,((! [A:$o,B:list_o]: ((size_size_list_o @ (cons_o @ A @ B)) = (suc @ (size_size_list_o @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4664_length__nth__simps_I2_J)). 87.71/26.56 thf(3457,plain,((! [A:$o,B:list_o]: ((size_size_list_o @ (cons_o @ A @ B)) = (suc @ (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[399])). 87.71/26.56 thf(1331,axiom,((! [A:assn]: ((sup_sup_assn @ bot_bot_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5123_norm__assertion__simps_I5_J)). 87.71/26.56 thf(7061,plain,((! [A:assn]: ((sup_sup_assn @ bot_bot_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331])). 87.71/26.56 thf(1272,axiom,((ord_less_nat = (^ [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) & ~ (ord_less_eq_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1526_order_Ostrict__iff__not)). 87.71/26.56 thf(6846,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)],[1272])). 87.71/26.56 thf(137,axiom,((! [A:list_o,B:list_o,C:(list_o > (list_o > $o))]: (((size_size_list_o @ A) = (size_size_list_o @ B)) => ((C @ nil_o @ nil_o) => ((C @ A @ B) <= (! [D:$o,E:list_o,F:$o,G:list_o]: (((size_size_list_o @ E) = (size_size_list_o @ G)) => ((C @ (cons_o @ D @ E) @ (cons_o @ F @ G)) <= (C @ E @ G))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8535_list__induct2)). 87.71/26.56 thf(2352,plain,((! [A:list_o,B:list_o,C:(list_o > (list_o > $o))]: (((size_size_list_o @ A) = (size_size_list_o @ B)) => ((C @ nil_o @ nil_o) => ((C @ A @ B) | ~ (! [D:$o,E:list_o,F:$o,G:list_o]: (((size_size_list_o @ E) = (size_size_list_o @ G)) => ((C @ (cons_o @ D @ E) @ (cons_o @ F @ G)) | ~ (C @ E @ G))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[137])). 87.71/26.56 thf(733,axiom,((! [A:$o,B:$o,C:$o,D:$o]: (((vEBT_Leaf @ A @ B) = (vEBT_Leaf @ C @ D)) = ((B = D) & (A = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_VEBT_Oinject_I2_J)). 87.71/26.56 thf(4770,plain,((! [A:$o,B:$o,C:$o,D:$o]: (((vEBT_Leaf @ A @ B) = (vEBT_Leaf @ C @ D)) = ((B = D) & (A = C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[733])). 87.71/26.56 thf(62,axiom,((! [A:real,B:nat]: ((times_times_real @ (power_power_real @ A @ B) @ A) = (times_times_real @ A @ (power_power_real @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7810_power__commutes)). 87.71/26.56 thf(1966,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)],[62])). 87.71/26.56 thf(1147,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (minus_minus_nat @ B @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3096_diff__less)). 87.71/26.56 thf(6408,plain,((! [A:nat,B:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (minus_minus_nat @ B @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147])). 87.71/26.56 thf(1537,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2397_add__le__less__mono)). 87.71/26.56 thf(7904,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1537])). 87.71/26.56 thf(572,axiom,((! [A:nat,B:(nat > $o)]: (((B @ A) <= (! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B @ C))))) => (? [C:nat]: ((B @ C) & (ord_less_eq_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_709_exists__leI)). 87.71/26.56 thf(4165,plain,((! [A:nat,B:(nat > $o)]: (((B @ A) | ~ (! [C:nat]: ((ord_less_nat @ C @ A) => (~ (B @ C))))) => (? [C:nat]: ((B @ C) & (ord_less_eq_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[572])). 87.71/26.56 thf(927,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2095_add__le__cancel__right)). 87.71/26.56 thf(5536,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)],[927])). 87.71/26.56 thf(1303,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ (suc @ B) @ A) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3171_Suc__diff__eq__diff__pred)). 87.71/26.56 thf(6970,plain,((! [A:nat,B:nat]: (((minus_minus_nat @ (suc @ B) @ A) = (minus_minus_nat @ B @ (minus_minus_nat @ A @ one_one_nat))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303])). 87.71/26.56 thf(1396,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: ? [C:nat]: (B = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2240_le__iff__add)). 87.71/26.56 thf(7306,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)],[1396])). 87.71/26.56 thf(281,axiom,((! [A:nat,B:int]: ((replicate_int @ (suc @ A) @ B) = (cons_int @ B @ (replicate_int @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4697_replicate__Suc)). 87.71/26.56 thf(2960,plain,((! [A:nat,B:int]: ((replicate_int @ (suc @ A) @ B) = (cons_int @ B @ (replicate_int @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[281])). 87.71/26.56 thf(988,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) <= ((ord_less_eq_nat @ A @ B) & (C = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2217_add__mono__thms__linordered__semiring_I3_J)). 87.71/26.56 thf(5777,plain,((! [A:nat,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D)) | ~ ((ord_less_eq_nat @ A @ B) & (C = D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[988])). 87.71/26.56 thf(958,axiom,((! [A:(int > (nat > assn)),B:int,C:list_int,D:nat,E:list_nat]: ((vEBT_L77084186935402305nt_nat @ A @ (cons_int @ B @ C) @ (cons_nat @ D @ E)) = (times_times_assn @ (A @ B @ D) @ (vEBT_L77084186935402305nt_nat @ A @ C @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4713_list__assn__simps_I2_J)). 87.71/26.56 thf(5660,plain,((! [A:(int > (nat > assn)),B:int,C:list_int,D:nat,E:list_nat]: ((vEBT_L77084186935402305nt_nat @ (A) @ (cons_int @ B @ C) @ (cons_nat @ D @ E)) = (times_times_assn @ (A @ B @ D) @ (vEBT_L77084186935402305nt_nat @ (A) @ C @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[958])). 87.71/26.56 thf(21,axiom,((! [A:nat,B:list_nat]: (((take_nat @ A @ B) = nil_nat) = ((B = nil_nat) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8161_take__eq__Nil)). 87.71/26.56 thf(1834,plain,((! [A:nat,B:list_nat]: (((take_nat @ A @ B) = nil_nat) = ((B = nil_nat) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[21])). 87.71/26.56 thf(47,axiom,((! [A:num]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9950_xor__nat__numerals_I1_J)). 87.71/26.56 thf(1913,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)],[47])). 87.71/26.56 thf(1141,axiom,(((('?') @ option_num) = (^ [A:(option_num > $o)]: (? [B:num]: (A @ (some_num @ B)) | (A @ none_num))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_split__option__ex)). 87.71/26.56 thf(6390,plain,(((('?') @ option_num) = (^ [A:(option_num > $o)]: (? [B:num]: (A @ (some_num @ B)) | (A @ none_num))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141])). 87.71/26.56 thf(1450,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) <= (ord_less_nat @ A @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_mult__neg__pos)). 87.71/26.56 thf(7547,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)) | ~ (ord_less_nat @ A @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1450])). 87.71/26.56 thf(1463,axiom,((! [A:nat,B:nat,C:nat,D:list_nat]: (((upt @ A @ B) = (cons_nat @ C @ D)) = ((A = C) & ((upt @ (plus_plus_nat @ A @ one_one_nat) @ B) = D) & (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8852_upt__eq__Cons__conv)). 87.71/26.56 thf(7589,plain,((! [A:nat,B:nat,C:nat,D:list_nat]: (((upt @ A @ B) = (cons_nat @ C @ D)) = ((A = C) & ((upt @ (plus_plus_nat @ A @ one_one_nat) @ B) = D) & (ord_less_nat @ A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1463])). 87.71/26.56 thf(918,axiom,((! [A:assn,B:assn]: ((entails @ A @ B) => (entails @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4055_is__entails)). 87.71/26.56 thf(5510,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[918])). 87.71/26.56 thf(1709,axiom,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))) | ((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2412_one__is__add)). 87.71/26.56 thf(8533,plain,((! [A:nat,B:nat]: (((suc @ zero_zero_nat) = (plus_plus_nat @ A @ B)) = (((A = zero_zero_nat) & (B = (suc @ zero_zero_nat))) | ((A = (suc @ zero_zero_nat)) & (B = zero_zero_nat)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1709])). 87.71/26.56 thf(424,axiom,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1066_linordered__nonzero__semiring__class_Ozero__le__one)). 87.71/26.56 thf(3548,plain,((ord_less_eq_nat @ zero_zero_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[424])). 87.71/26.56 thf(682,axiom,((! [A:nat,B:nat]: (((B != zero_zero_nat) => ((times_times_nat @ A @ B) != zero_zero_nat)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_no__zero__divisors)). 87.71/26.56 thf(4559,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)],[682])). 87.71/26.56 thf(1032,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ A @ (plus_plus_nat @ A @ B)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2851_diff__add__zero)). 87.71/26.56 thf(5934,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)],[1032])). 87.71/26.56 thf(892,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_eq_nat @ zero_zero_nat @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2121_le__add__same__cancel1)). 87.71/26.56 thf(5421,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)],[892])). 87.71/26.56 thf(1384,axiom,((! [A:nat,B:nat]: (((ord_less_eq_nat @ A @ B) & (ord_less_nat @ B @ (suc @ A))) = (B = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_nat__in__between__eq_I2_J)). 87.71/26.56 thf(7271,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)],[1384])). 87.71/26.56 thf(578,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_T_m_e_m_b_e_r2 @ (vEBT_Leaf @ A @ B) @ C) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1754_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J)). 87.71/26.56 thf(4185,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_T_m_e_m_b_e_r2 @ (vEBT_Leaf @ A @ B) @ C) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[578])). 87.71/26.56 thf(546,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => ((A = C) <= (ord_less_nat @ zero_zero_nat @ B)))) <= ((power_power_nat @ A @ B) = (power_power_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7999_power__eq__imp__eq__base)). 87.71/26.56 thf(4078,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ C) => ((A = C) | ~ (ord_less_nat @ zero_zero_nat @ B)))) | ~ ((power_power_nat @ A @ B) = (power_power_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[546])). 87.71/26.56 thf(1673,axiom,((! [A:$o,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn),E:heap_T2636463487746394924on_nat]: (((hoare_7629718768684598413on_nat @ B @ C @ D) <= (A)) => ((hoare_7629718768684598413on_nat @ B @ (if_Hea5867803462524415986on_nat @ A @ C @ E) @ D) <= ((~ (A)) => (hoare_7629718768684598413on_nat @ B @ E @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_if__rule)). 87.71/26.56 thf(8392,plain,((! [A:$o,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn),E:heap_T2636463487746394924on_nat]: (((hoare_7629718768684598413on_nat @ B @ C @ (D)) | ~ (A)) => ((hoare_7629718768684598413on_nat @ B @ (if_Hea5867803462524415986on_nat @ A @ C @ E) @ (D)) | ~ ((~ (A)) => (hoare_7629718768684598413on_nat @ B @ E @ (D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1673])). 87.71/26.56 thf(471,axiom,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ 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) => ((A @ F) = (B @ F))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1953_minf_I2_J)). 87.71/26.56 thf(3725,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: (((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ 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) => ((A @ F) = (B @ F))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[471])). 87.71/26.56 thf(1315,axiom,((sup_sup_assn = (^ [A:assn,B:assn]: (sup_sup_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5432_assn__aci_I5_J)). 87.71/26.56 thf(7007,plain,(((sup_sup_assn) = (^ [A:assn,B:assn]: (sup_sup_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315])). 87.71/26.56 thf(1224,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/sandbox2/benchmark/theBenchmark.p',fact_2409_add__mono1)). 87.71/26.56 thf(6674,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)],[1224])). 87.71/26.56 thf(168,axiom,(((numeral_numeral_nat @ (bit0 @ one)) = (suc @ (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9024_numeral__2__eq__2)). 87.71/26.56 thf(2490,plain,(((numeral_numeral_nat @ (bit0 @ one)) = (suc @ (suc @ zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[168])). 87.71/26.56 thf(1639,axiom,((! [A:array_nat,B:list_nat]: (hoare_3067605981109127869le_nat @ (snga_assn_nat @ A @ B) @ (array_len_nat @ A) @ (^ [C:nat]: (times_times_assn @ (snga_assn_nat @ A @ B) @ (pure_assn @ (C = (size_size_list_nat @ B)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4448_length__rule)). 87.71/26.56 thf(8285,plain,((! [A:array_nat,B:list_nat]: (hoare_3067605981109127869le_nat @ (snga_assn_nat @ A @ B) @ (array_len_nat @ A) @ (^ [C:nat]: (times_times_assn @ (snga_assn_nat @ A @ B) @ (pure_assn @ (C = (size_size_list_nat @ B)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1639])). 87.71/26.56 thf(1602,axiom,((! [A:nat]: ((bit_se8570568707652914677it_nat @ A @ (suc @ zero_zero_nat)) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10099_drop__bit__of__Suc__0)). 87.71/26.56 thf(8153,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)],[1602])). 87.71/26.56 thf(273,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/sandbox2/benchmark/theBenchmark.p',fact_2594_dele__bmo__cont__corr)). 87.71/26.56 thf(2919,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)],[273])). 87.71/26.56 thf(1282,axiom,((top_top_assn != bot_bot_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10151_assn__basic__inequalities_I5_J)). 87.71/26.56 thf(6882,plain,((~ (top_top_assn = bot_bot_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282])). 87.71/26.56 thf(573,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/sandbox2/benchmark/theBenchmark.p',fact_8601_nat__mult__div__cancel1)). 87.71/26.56 thf(4170,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)],[573])). 87.71/26.56 thf(1185,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2106_add__is__0)). 87.71/26.56 thf(6543,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((B = zero_zero_nat) & (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185])). 87.71/26.56 thf(648,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_maxt @ A) = (some_nat @ C)) => (vEBT_vebt_member @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_maxt__member)). 87.71/26.56 thf(4463,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (((vEBT_vebt_maxt @ A) = (some_nat @ C)) => (vEBT_vebt_member @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[648])). 87.71/26.56 thf(1585,axiom,((! [A:$o,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn)]: (((A) => (hoare_1429296392585015714_VEBTi @ B @ C @ D)) => (hoare_1429296392585015714_VEBTi @ (times_times_assn @ B @ (pure_assn @ A)) @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_norm__pre__pure__rule1)). 87.71/26.56 thf(8098,plain,((! [A:$o,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn)]: (((A) => (hoare_1429296392585015714_VEBTi @ B @ C @ (D))) => (hoare_1429296392585015714_VEBTi @ (times_times_assn @ B @ (pure_assn @ A)) @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1585])). 87.71/26.56 thf(78,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9045_binomial__maximum_H)). 87.71/26.56 thf(2071,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) @ (binomial @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[78])). 87.71/26.56 thf(505,axiom,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ A @ (sup_sup_assn @ B @ C)) = (sup_sup_assn @ (times_times_assn @ A @ B) @ (times_times_assn @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5110_star__or__dist2)). 87.71/26.56 thf(3929,plain,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ A @ (sup_sup_assn @ B @ C)) = (sup_sup_assn @ (times_times_assn @ A @ B) @ (times_times_assn @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[505])). 87.71/26.56 thf(1430,axiom,((! [A:vEBT_VEBT,B:nat]: (((vEBT_T_m_a_x_t @ A) = B) => ((! [C:$o,D:$o]: ((B != (plus_plus_nat @ one_one_nat @ (if_nat @ D @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))) <= (A = (vEBT_Leaf @ C @ D)))) => (((? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) => (B != one_one_nat)) => (~ ((B != one_one_nat) <= (? [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2589_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Oelims)). 87.71/26.56 thf(7446,plain,((! [A:vEBT_VEBT,B:nat]: (((vEBT_T_m_a_x_t @ A) = B) => ((! [C:$o,D:$o]: (~ (B = (plus_plus_nat @ one_one_nat @ (if_nat @ D @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))) | ~ (A = (vEBT_Leaf @ C @ D)))) => (((? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) => (~ (B = one_one_nat))) => (~ (~ (B = one_one_nat) | ~ (? [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1430])). 87.71/26.56 thf(12,axiom,((! [A:vEBT_VEBT]: (ord_less_eq_nat @ (vEBT_T_m_i_n_N_u_l_l @ A) @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1750_minNull__bound)). 87.71/26.56 thf(1807,plain,((! [A:vEBT_VEBT]: (ord_less_eq_nat @ (vEBT_T_m_i_n_N_u_l_l @ A) @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[12])). 87.71/26.56 thf(1694,axiom,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = ((E = B) | (E = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_824_VEBT__internal_Omembermima_Osimps_I3_J)). 87.71/26.56 thf(8469,plain,((! [A:nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ((vEBT_VEBT_membermima @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ A @ B)) @ zero_zero_nat @ C @ D) @ E) = ((E = B) | (E = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1694])). 87.71/26.56 thf(268,axiom,((vEBT_VEBT_minNull @ (vEBT_Leaf @ ($false) @ ($false)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2336_VEBT__internal_OminNull_Osimps_I1_J)). 87.71/26.56 thf(2907,plain,((vEBT_VEBT_minNull @ (vEBT_Leaf @ ($false) @ ($false)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[268])). 87.71/26.56 thf(69,axiom,(((numeral_numeral_nat @ one) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9074_numeral__1__eq__Suc__0)). 87.71/26.56 thf(1998,plain,(((numeral_numeral_nat @ one) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[69])). 87.71/26.56 thf(1577,axiom,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1812_T_092_060_094sub_062p_092_060_094sub_062r_092_060_094sub_062e_092_060_094sub_062d_H_Osimps_I6_J)). 87.71/26.56 thf(8075,plain,((! [A:product_prod_nat_nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_p_r_e_d2 @ (vEBT_Node @ (some_P7363390416028606310at_nat @ A) @ (suc @ zero_zero_nat) @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1577])). 87.71/26.56 thf(1623,axiom,((! [A:nat]: ((modulo_modulo_nat @ A @ (suc @ zero_zero_nat)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8691_mod__by__Suc__0)). 87.71/26.56 thf(8221,plain,((! [A:nat]: ((modulo_modulo_nat @ A @ (suc @ zero_zero_nat)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1623])). 87.71/26.56 thf(497,axiom,((! [A:nat,B:nat,C:list_int]: ((((size_size_list_int @ (slice_int @ A @ B @ C)) = (minus_minus_nat @ B @ A)) <= (ord_less_eq_nat @ B @ (size_size_list_int @ C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3289_slice__len)). 87.71/26.56 thf(3864,plain,((! [A:nat,B:nat,C:list_int]: (((size_size_list_int @ (slice_int @ A @ B @ C)) = (minus_minus_nat @ B @ A)) | ~ (ord_less_eq_nat @ B @ (size_size_list_int @ C)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[497])). 87.71/26.56 thf(1202,axiom,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7750_power__eq__0__iff)). 87.71/26.56 thf(6607,plain,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202])). 87.71/26.56 thf(86,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_pred @ A @ C) = (some_nat @ D))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8979_helpypredd)). 87.71/26.56 thf(2135,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_pred @ A @ C) = (some_nat @ D)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[86])). 87.71/26.56 thf(550,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_T_p_r_e_d2 @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2491_pred__bound__height_H)). 87.71/26.56 thf(4089,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_T_p_r_e_d2 @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[550])). 87.71/26.56 thf(1617,axiom,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) <= (! [C:nat]: ((A @ (suc @ C)) <= (! [D:nat]: ((ord_less_eq_nat @ D @ C) => (A @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_nat__compl__induct)). 87.71/26.56 thf(8197,plain,((! [A:(nat > $o),B:nat]: ((A @ zero_zero_nat) => ((A @ B) | ~ (! [C:nat]: ((A @ (suc @ C)) | ~ (! [D:nat]: ((ord_less_eq_nat @ D @ C) => (A @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1617])). 87.71/26.56 thf(1520,axiom,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (modulo_modulo_nat @ A @ B)) @ B) = (modulo_modulo_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8702_mod__Suc__eq)). 87.71/26.56 thf(7840,plain,((! [A:nat,B:nat]: ((modulo_modulo_nat @ (suc @ (modulo_modulo_nat @ A @ B)) @ B) = (modulo_modulo_nat @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1520])). 87.71/26.56 thf(840,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3062_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2)). 87.71/26.56 thf(5228,plain,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ C) = (minus_minus_nat @ (plus_plus_nat @ B @ C) @ A)) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[840])). 87.71/26.56 thf(154,axiom,((! [A:nat,B:list_nat,C:nat]: (((nth_nat @ (drop_nat @ A @ B) @ C) = (nth_nat @ B @ (plus_plus_nat @ A @ C))) <= (ord_less_eq_nat @ A @ (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7794_nth__drop)). 87.71/26.56 thf(2443,plain,((! [A:nat,B:list_nat,C:nat]: (((nth_nat @ (drop_nat @ A @ B) @ C) = (nth_nat @ B @ (plus_plus_nat @ A @ C))) | ~ (ord_less_eq_nat @ A @ (size_size_list_nat @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[154])). 87.71/26.56 thf(1325,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_T_s_u_c_c2 @ (vEBT_Leaf @ A @ B) @ (suc @ C)) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1761_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_H_Osimps_I2_J)). 87.71/26.56 thf(7034,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_T_s_u_c_c2 @ (vEBT_Leaf @ A @ B) @ (suc @ C)) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325])). 87.71/26.56 thf(949,axiom,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:assn]: ((hoare_1429296392585015714_VEBTi @ A @ B @ C) => ((hoare_1429296392585015714_VEBTi @ (sup_sup_assn @ A @ D) @ B @ C) <= (hoare_1429296392585015714_VEBTi @ D @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5120_split__rule)). 87.71/26.56 thf(5632,plain,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:assn]: ((hoare_1429296392585015714_VEBTi @ A @ B @ (C)) => ((hoare_1429296392585015714_VEBTi @ (sup_sup_assn @ A @ D) @ B @ (C)) | ~ (hoare_1429296392585015714_VEBTi @ D @ B @ (C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[949])). 87.71/26.56 thf(1122,axiom,((! [A:nat,B:nat]: (((dvd_dvd_nat @ (times_times_nat @ B @ A) @ A) = (B = one_one_nat)) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9475_dvd__mult__cancel2)). 87.71/26.56 thf(6322,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)],[1122])). 87.71/26.56 thf(96,axiom,((! [A:list_int]: ((slice_int @ zero_zero_nat @ (size_size_list_int @ A) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3285_slice__complete)). 87.71/26.56 thf(2167,plain,((! [A:list_int]: ((slice_int @ zero_zero_nat @ (size_size_list_int @ A) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[96])). 87.71/26.56 thf(1241,axiom,((suc = (plus_plus_nat @ one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2419_Suc__eq__plus1__left)). 87.71/26.56 thf(6753,plain,(((suc) = (plus_plus_nat @ one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241])). 87.71/26.56 thf(143,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((bit_se2925701944663578781it_nat @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9890_take__bit__nat__eq__self)). 87.71/26.56 thf(2389,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((bit_se2925701944663578781it_nat @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[143])). 87.71/26.56 thf(1264,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) <= (! [C:nat]: ((A @ C) <= (! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1256_less__induct)). 87.71/26.56 thf(6818,plain,((! [A:(nat > $o),B:nat]: ((A @ B) | ~ (! [C:nat]: ((A @ C) | ~ (! [D:nat]: ((ord_less_nat @ D @ C) => (A @ D)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264])). 87.71/26.56 thf(1170,axiom,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_988_mult_Oright__neutral)). 87.71/26.56 thf(6489,plain,((! [A:assn]: ((times_times_assn @ A @ one_one_assn) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170])). 87.71/26.56 thf(123,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_d_e_l_e_t_e @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit0 @ (bit1 @ (bit1 @ (bit0 @ (bit0 @ (bit0 @ one))))))))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9138_delete__bound__height)). 87.71/26.56 thf(2290,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((ord_less_eq_nat @ (vEBT_T_d_e_l_e_t_e @ A @ C) @ (times_times_nat @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)) @ (numeral_numeral_nat @ (bit0 @ (bit1 @ (bit1 @ (bit0 @ (bit0 @ (bit0 @ one))))))))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[123])). 87.71/26.56 thf(1550,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_mult__le__cancel2)). 87.71/26.56 thf(7964,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) = ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1550])). 87.71/26.56 thf(709,axiom,((! [A:nat,B:nat]: ((A != B) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1396_order__less__imp__not__eq)). 87.71/26.56 thf(4683,plain,((! [A:nat,B:nat]: (~ (A = B) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[709])). 87.71/26.56 thf(382,axiom,((! [A:list_int,B:nat]: ((ord_less_eq_nat @ (size_size_list_int @ A) @ B) => ((drop_int @ B @ A) = nil_int)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8283_drop__all)). 87.71/26.56 thf(3383,plain,((! [A:list_int,B:nat]: ((ord_less_eq_nat @ (size_size_list_int @ A) @ B) => ((drop_int @ B @ A) = nil_int)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[382])). 87.71/26.56 thf(1558,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ B) @ (times_times_nat @ A @ (power_power_nat @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7922_power__less__power__Suc)). 87.71/26.56 thf(7996,plain,((! [A:nat,B:nat]: ((ord_less_nat @ one_one_nat @ A) => (ord_less_nat @ (power_power_nat @ A @ B) @ (times_times_nat @ A @ (power_power_nat @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1558])). 87.71/26.56 thf(1317,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/sandbox2/benchmark/theBenchmark.p',fact_9466_dvd__mult__cancel)). 87.71/26.56 thf(7012,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)],[1317])). 87.71/26.56 thf(561,axiom,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:assn]: ((hoare_hoare_triple_o @ (times_times_assn @ A @ D) @ B @ (^ [E:$o]: (times_times_assn @ (C @ E) @ D))) <= (hoare_hoare_triple_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_frame__rule)). 87.71/26.56 thf(4126,plain,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:assn]: ((hoare_hoare_triple_o @ (times_times_assn @ A @ D) @ B @ (^ [E:$o]: (times_times_assn @ (C @ E) @ D))) | ~ (hoare_hoare_triple_o @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[561])). 87.71/26.56 thf(1353,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/sandbox2/benchmark/theBenchmark.p',fact_2164_group__cancel_Oadd1)). 87.71/26.56 thf(7167,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)],[1353])). 87.71/26.56 thf(534,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ C @ B) <= (ord_less_nat @ C @ A)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1548_dual__order_Ostrict__trans1)). 87.71/26.56 thf(4042,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ C @ B) | ~ (ord_less_nat @ C @ A) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[534])). 87.71/26.56 thf(676,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_V1232361888498592333_e_t_e @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2021_delete__bound__height_H)). 87.71/26.56 thf(4542,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => (ord_less_eq_nat @ (vEBT_V1232361888498592333_e_t_e @ A @ C) @ (plus_plus_nat @ one_one_nat @ (vEBT_VEBT_height @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[676])). 87.71/26.56 thf(245,axiom,((! [A:vEBT_VEBT,B:nat]: (((((~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((B = one_one_nat) => (~ (accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))))) <= (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((~ (accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))) <= (B = one_one_nat)) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E))))) <= (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => ((~ (accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ (vEBT_Leaf @ C @ D))) <= (B = (plus_plus_nat @ one_one_nat @ (if_nat @ D @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))))))) <= (accp_VEBT_VEBT @ vEBT_T_m_a_x_t_rel @ A)) <= ((vEBT_T_m_a_x_t @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2619_T_092_060_094sub_062m_092_060_094sub_062a_092_060_094sub_062x_092_060_094sub_062t_Opelims)). 87.71/26.56 thf(2811,plain,((! [A:vEBT_VEBT,B:nat]: (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((B = one_one_nat) => (~ (accp_VEBT_VEBT @ (vEBT_T_m_a_x_t_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))) | ~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (~ (accp_VEBT_VEBT @ (vEBT_T_m_a_x_t_rel) @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)) | ~ (B = one_one_nat) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) | ~ (! [C:$o,D:$o]: ((A = (vEBT_Leaf @ C @ D)) => (~ (accp_VEBT_VEBT @ (vEBT_T_m_a_x_t_rel) @ (vEBT_Leaf @ C @ D)) | ~ (B = (plus_plus_nat @ one_one_nat @ (if_nat @ D @ one_one_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat))))))) | ~ (accp_VEBT_VEBT @ (vEBT_T_m_a_x_t_rel) @ A) | ~ ((vEBT_T_m_a_x_t @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[245])). 87.71/26.56 thf(718,axiom,((! [A:nat,B:nat,C:list_nat,D:nat,E:list_nat]: (((upt @ A @ B) = (append_nat @ C @ (cons_nat @ D @ E))) = ((ord_less_eq_nat @ A @ D) & (ord_less_nat @ D @ B) & (E = (upt @ (suc @ D) @ B)) & (C = (upt @ A @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8855_upt__eq__lel__conv)). 87.71/26.56 thf(4715,plain,((! [A:nat,B:nat,C:list_nat,D:nat,E:list_nat]: (((upt @ A @ B) = (append_nat @ C @ (cons_nat @ D @ E))) = ((ord_less_eq_nat @ A @ D) & (ord_less_nat @ D @ B) & (E = (upt @ (suc @ D) @ B)) & (C = (upt @ A @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[718])). 87.71/26.56 thf(314,axiom,((! [A:nat,B:nat]: (((replicate_nat @ A @ B) = nil_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8166_replicate__empty)). 87.71/26.56 thf(3104,plain,((! [A:nat,B:nat]: (((replicate_nat @ A @ B) = nil_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[314])). 87.71/26.56 thf(522,axiom,((! [A:assn]: ((sup_sup_assn @ bot_bot_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5049_sup__bot__left)). 87.71/26.56 thf(3991,plain,((! [A:assn]: ((sup_sup_assn @ bot_bot_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[522])). 87.71/26.56 thf(1247,axiom,((bit_wf_set_bits_int = (^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: ((~ (A @ C)) <= (ord_less_eq_nat @ B @ C)) | ! [C:nat]: ((ord_less_eq_nat @ B @ C) => (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10177_wf__set__bits__int__simps)). 87.71/26.56 thf(6770,plain,(((bit_wf_set_bits_int) = (^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: (~ (A @ C) | ~ (ord_less_eq_nat @ B @ C)) | ! [C:nat]: ((ord_less_eq_nat @ B @ C) => (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247])). 87.71/26.56 thf(879,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) & (A = B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2255_add__mono__thms__linordered__field_I2_J)). 87.71/26.56 thf(5368,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ D) & (A = B)) => (ord_less_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[879])). 87.71/26.56 thf(28,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9841_and__nat__numerals_I3_J)). 87.71/26.56 thf(1854,plain,((! [A:num]: ((bit_se727722235901077358nd_nat @ (numeral_numeral_nat @ (bit0 @ A)) @ (suc @ zero_zero_nat)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[28])). 87.71/26.56 thf(1751,axiom,((zero_zero_nat = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9663_zero__natural_Orsp)). 87.71/26.56 thf(8722,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1751])). 87.71/26.56 thf(616,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) <= (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_lift__Suc__mono__less__iff)). 87.71/26.56 thf(4338,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ (A @ B) @ (A @ C)) = (ord_less_nat @ B @ C)) | ~ (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[616])). 87.71/26.56 thf(1289,axiom,((! [A:product_prod_nat_nat]: (none_P5556105721700978146at_nat != (some_P7363390416028606310at_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_option_Odistinct_I1_J)). 87.71/26.56 thf(6910,plain,((! [A:product_prod_nat_nat]: ~ (none_P5556105721700978146at_nat = (some_P7363390416028606310at_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289])). 87.71/26.56 thf(409,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ (divide_divide_nat @ (suc @ A) @ (numeral_numeral_nat @ (bit0 @ one))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9048_Suc__n__div__2__gt__zero)). 87.71/26.56 thf(3501,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)],[409])). 87.71/26.56 thf(17,axiom,((! [A:list_nat,B:nat]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ B) => ((take_nat @ B @ A) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6291_take__all)). 87.71/26.56 thf(1822,plain,((! [A:list_nat,B:nat]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ B) => ((take_nat @ B @ A) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[17])). 87.71/26.56 thf(1410,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1760_T_092_060_094sub_062d_092_060_094sub_062e_092_060_094sub_062l_092_060_094sub_062e_092_060_094sub_062t_092_060_094sub_062e_Osimps_I4_J)). 87.71/26.56 thf(7384,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_d_e_l_e_t_e @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410])). 87.71/26.56 thf(528,axiom,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) <= ((vEBT_vebt_mint @ A) = none_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2044_minminNull)). 87.71/26.56 thf(4010,plain,((! [A:vEBT_VEBT]: ((vEBT_VEBT_minNull @ A) | ~ ((vEBT_vebt_mint @ A) = none_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[528])). 87.71/26.56 thf(414,axiom,((bit_se6528837805403552850or_nat = (^ [A:nat,B:nat]: (if_nat @ (A = zero_zero_nat) @ B @ (if_nat @ (B = zero_zero_nat) @ A @ (plus_plus_nat @ (modulo_modulo_nat @ (plus_plus_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (modulo_modulo_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) @ (numeral_numeral_nat @ (bit0 @ one))) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (bit_se6528837805403552850or_nat @ (divide_divide_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (divide_divide_nat @ B @ (numeral_numeral_nat @ (bit0 @ one))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9991_xor__nat__unfold)). 87.71/26.56 thf(3516,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)],[414])). 87.71/26.56 thf(1768,axiom,((! [A:(nat > $o),B:nat]: (((! [C:nat]: ((A @ (suc @ C)) => (A @ C))) => (A @ zero_zero_nat)) <= (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_zero__induct)). 87.71/26.56 thf(8781,plain,((! [A:(nat > $o),B:nat]: (((! [C:nat]: ((A @ (suc @ C)) => (A @ C))) => (A @ zero_zero_nat)) | ~ (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1768])). 87.71/26.56 thf(845,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2858_le__add__diff__inverse2)). 87.71/26.56 thf(5243,plain,((! [A:nat,B:nat]: (((plus_plus_nat @ (minus_minus_nat @ B @ A) @ A) = B) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[845])). 87.71/26.56 thf(715,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ B @ A)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ B)) <= (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_one__less__mult)). 87.71/26.56 thf(4705,plain,((! [A:nat,B:nat]: ((ord_less_nat @ (suc @ zero_zero_nat) @ (times_times_nat @ B @ A)) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ B) | ~ (ord_less_nat @ (suc @ zero_zero_nat) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[715])). 87.71/26.56 thf(755,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((binomial @ B @ A) = (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8894_binomial__altdef__nat)). 87.71/26.56 thf(4881,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((binomial @ B @ A) = (divide_divide_nat @ (semiri1408675320244567234ct_nat @ B) @ (times_times_nat @ (semiri1408675320244567234ct_nat @ A) @ (semiri1408675320244567234ct_nat @ (minus_minus_nat @ B @ A)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[755])). 87.71/26.56 thf(811,axiom,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:nat]: ((time_htt_o @ A @ B @ C @ D) => (hoare_hoare_triple_o @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1807_htt__htD)). 87.71/26.56 thf(5104,plain,((! [A:assn,B:heap_Time_Heap_o,C:($o > assn),D:nat]: ((time_htt_o @ A @ B @ (C) @ D) => (hoare_hoare_triple_o @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[811])). 87.71/26.56 thf(353,axiom,((! [A:nat,B:list_nat]: (((drop_nat @ A @ B) = nil_nat) = (ord_less_eq_nat @ (size_size_list_nat @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8278_drop__eq__Nil)). 87.71/26.56 thf(3252,plain,((! [A:nat,B:list_nat]: (((drop_nat @ A @ B) = nil_nat) = (ord_less_eq_nat @ (size_size_list_nat @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[353])). 87.71/26.56 thf(1230,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) <= (B = C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1109_ord__le__eq__trans)). 87.71/26.56 thf(6694,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ C) | ~ (B = C) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230])). 87.71/26.56 thf(1728,axiom,((! [A:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),B:option4927543243414619207at_nat,C:option4927543243414619207at_nat,D:option4927543243414619207at_nat]: ((((((D = none_P5556105721700978146at_nat) => (~ (accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ (produc2899441246263362727at_nat @ A @ (produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ C))))) <= (B = none_P5556105721700978146at_nat)) => ((! [E:product_prod_nat_nat]: (((C = none_P5556105721700978146at_nat) => ((D = none_P5556105721700978146at_nat) => (~ (accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ (produc2899441246263362727at_nat @ A @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ E) @ none_P5556105721700978146at_nat)))))) <= (B = (some_P7363390416028606310at_nat @ E)))) => (~ (! [E:product_prod_nat_nat]: ((! [F:product_prod_nat_nat]: (((~ (accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ (produc2899441246263362727at_nat @ A @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ E) @ (some_P7363390416028606310at_nat @ F))))) <= (D = (some_P7363390416028606310at_nat @ (A @ E @ F)))) <= (C = (some_P7363390416028606310at_nat @ F)))) <= (B = (some_P7363390416028606310at_nat @ E))))))) <= (accp_P3267385326087170368at_nat @ vEBT_V7235779383477046023at_nat @ (produc2899441246263362727at_nat @ A @ (produc488173922507101015at_nat @ B @ C)))) <= ((vEBT_V1502963449132264192at_nat @ A @ B @ C) = D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2500_VEBT__internal_Ooption__shift_Opelims)). 87.71/26.56 thf(8617,plain,((! [A:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),B:option4927543243414619207at_nat,C:option4927543243414619207at_nat,D:option4927543243414619207at_nat]: (((((D = none_P5556105721700978146at_nat) => (~ (accp_P3267385326087170368at_nat @ (vEBT_V7235779383477046023at_nat) @ (produc2899441246263362727at_nat @ (A) @ (produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ C))))) | ~ (B = none_P5556105721700978146at_nat)) => ((! [E:product_prod_nat_nat]: (((C = none_P5556105721700978146at_nat) => ((D = none_P5556105721700978146at_nat) => (~ (accp_P3267385326087170368at_nat @ (vEBT_V7235779383477046023at_nat) @ (produc2899441246263362727at_nat @ (A) @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ E) @ none_P5556105721700978146at_nat)))))) | ~ (B = (some_P7363390416028606310at_nat @ E)))) => (~ (! [E:product_prod_nat_nat]: (! [F:product_prod_nat_nat]: (~ (accp_P3267385326087170368at_nat @ (vEBT_V7235779383477046023at_nat) @ (produc2899441246263362727at_nat @ (A) @ (produc488173922507101015at_nat @ (some_P7363390416028606310at_nat @ E) @ (some_P7363390416028606310at_nat @ F)))) | ~ (D = (some_P7363390416028606310at_nat @ (A @ E @ F))) | ~ (C = (some_P7363390416028606310at_nat @ F))) | ~ (B = (some_P7363390416028606310at_nat @ E))))))) | ~ (accp_P3267385326087170368at_nat @ (vEBT_V7235779383477046023at_nat) @ (produc2899441246263362727at_nat @ (A) @ (produc488173922507101015at_nat @ B @ C))) | ~ ((vEBT_V1502963449132264192at_nat @ (A) @ B @ C) = D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1728])). 87.71/26.56 thf(179,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/sandbox2/benchmark/theBenchmark.p',fact_8842_map__add__upt)). 87.71/26.56 thf(2526,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)],[179])). 87.71/26.56 thf(482,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]: (((B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)) => (A @ D)) <= (ord_less_nat @ E @ C)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8657_split__div)). 87.71/26.56 thf(3780,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ (divide_divide_nat @ B @ C)) = (((C = zero_zero_nat) => (A @ zero_zero_nat)) & ((~ (C = zero_zero_nat)) => (! [D:nat,E:nat]: (((B = (plus_plus_nat @ (times_times_nat @ C @ D) @ E)) => (A @ D)) | ~ (ord_less_nat @ E @ C)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[482])). 87.71/26.56 thf(759,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) => (~ (dvd_dvd_nat @ B @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9457_nat__dvd__not__less)). 87.71/26.56 thf(4900,plain,((! [A:nat,B:nat]: (((ord_less_nat @ A @ B) => (~ (dvd_dvd_nat @ B @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[759])). 87.71/26.56 thf(1629,axiom,((! [A:$o,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn)]: (((hoare_7629718768684598413on_nat @ B @ C @ D) <= (A)) => (hoare_7629718768684598413on_nat @ (times_times_assn @ B @ (pure_assn @ A)) @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_norm__pre__pure__rule1)). 87.71/26.56 thf(8240,plain,((! [A:$o,B:assn,C:heap_T2636463487746394924on_nat,D:(option_nat > assn)]: (((hoare_7629718768684598413on_nat @ B @ C @ (D)) | ~ (A)) => (hoare_7629718768684598413on_nat @ (times_times_assn @ B @ (pure_assn @ A)) @ C @ (D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1629])). 87.71/26.56 thf(1701,axiom,((type_l4264026598287037464l_num0 = (^ [A:itself_Numeral_num0]: (zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10131_len__num0)). 87.71/26.56 thf(8506,plain,(((type_l4264026598287037464l_num0) = (^ [A:itself_Numeral_num0]: (zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1701])). 87.71/26.56 thf(370,axiom,((! [A:vEBT_VEBT,B:nat]: (((vEBT_T_m_i_n_t @ A) = B) => (((! [C:$o,D:$o]: (((B = (plus_plus_nat @ one_one_nat @ (if_nat @ C @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))) => (~ (accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ (vEBT_Leaf @ C @ D)))) <= (A = (vEBT_Leaf @ C @ D)))) => ((~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (((~ (accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))) <= (B = one_one_nat)) <= (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G))))) <= (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((B = one_one_nat) => (~ (accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) <= (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))) <= (accp_VEBT_VEBT @ vEBT_T_m_i_n_t_rel @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2523_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062t_Opelims)). 87.71/26.56 thf(3324,plain,((! [A:vEBT_VEBT,B:nat]: (((vEBT_T_m_i_n_t @ A) = B) => (((! [C:$o,D:$o]: (((B = (plus_plus_nat @ one_one_nat @ (if_nat @ C @ zero_zero_nat @ (plus_plus_nat @ one_one_nat @ one_one_nat)))) => (~ (accp_VEBT_VEBT @ (vEBT_T_m_i_n_t_rel) @ (vEBT_Leaf @ C @ D)))) | ~ (A = (vEBT_Leaf @ C @ D)))) => (~ (! [C:nat,D:nat,E:nat,F:list_VEBT_VEBT,G:vEBT_VEBT]: (~ (accp_VEBT_VEBT @ (vEBT_T_m_i_n_t_rel) @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)) | ~ (B = one_one_nat) | ~ (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ C @ D)) @ E @ F @ G)))) | ~ (! [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (((B = one_one_nat) => (~ (accp_VEBT_VEBT @ (vEBT_T_m_i_n_t_rel) @ (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) | ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))))) | ~ (accp_VEBT_VEBT @ (vEBT_T_m_i_n_t_rel) @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[370])). 87.71/26.56 thf(1382,axiom,((! [A:assn]: ((inf_inf_assn @ A @ bot_bot_assn) = bot_bot_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8916_norm__assertion__simps_I10_J)). 87.71/26.56 thf(7266,plain,((! [A:assn]: ((inf_inf_assn @ A @ bot_bot_assn) = bot_bot_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382])). 87.71/26.56 thf(610,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) <= (ord_less_nat @ (suc @ A) @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_Suc__less__SucD)). 87.71/26.56 thf(4321,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)],[610])). 87.71/26.56 thf(989,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ A) => (A = (suc @ (minus_minus_nat @ A @ one_one_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3172_Suc__pred_H)). 87.71/26.56 thf(5781,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)],[989])). 87.71/26.56 thf(358,axiom,((! [A:assn,B:assn]: ((if_assn @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Assertions__Oassn_T)). 87.71/26.56 thf(3267,plain,((! [A:assn,B:assn]: ((if_assn @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[358])). 87.71/26.56 thf(1680,axiom,((! [A:nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9438_dvd__1__left)). 87.71/26.56 thf(8420,plain,((! [A:nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1680])). 87.71/26.56 thf(1415,axiom,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((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))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3151_nat__eq__add__iff1)). 87.71/26.56 thf(7399,plain,((! [A:nat,B:nat,C:nat,D:nat,E:nat]: ((ord_less_eq_nat @ A @ B) => (((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))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1415])). 87.71/26.56 thf(417,axiom,((! [A:nat]: ((bit_se1412395901928357646or_nat @ A @ (suc @ zero_zero_nat)) = (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10048_or__Suc__0__eq)). 87.71/26.56 thf(3529,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)],[417])). 87.71/26.56 thf(634,axiom,((! [A:nat,B:list_nat,C:array_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => (hoare_3067605981109127869le_nat @ (snga_assn_nat @ C @ B) @ (array_nth_nat @ C @ A) @ (^ [D:nat]: (times_times_assn @ (snga_assn_nat @ C @ B) @ (pure_assn @ (D = (nth_nat @ B @ A))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4431_nth__rule)). 87.71/26.56 thf(4404,plain,((! [A:nat,B:list_nat,C:array_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => (hoare_3067605981109127869le_nat @ (snga_assn_nat @ C @ B) @ (array_nth_nat @ C @ A) @ (^ [D:nat]: (times_times_assn @ (snga_assn_nat @ C @ B) @ (pure_assn @ (D = (nth_nat @ B @ A))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[634])). 87.71/26.56 thf(979,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ (power_power_nat @ (semiri1316708129612266289at_nat @ B) @ C)) = (ord_less_nat @ A @ (power_power_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7761_of__nat__power__less__of__nat__cancel__iff)). 87.71/26.56 thf(5739,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)],[979])). 87.71/26.56 thf(445,axiom,((! [A:nat]: ~ (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4640_of__nat__less__0__iff)). 87.71/26.56 thf(3645,plain,((! [A:nat]: ~ (ord_less_nat @ (semiri1316708129612266289at_nat @ A) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[445])). 87.71/26.56 thf(1417,axiom,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((A = B) | (ord_less_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1291_not__less__iff__gr__or__eq)). 87.71/26.56 thf(7406,plain,((! [A:nat,B:nat]: ((~ (ord_less_nat @ A @ B)) = ((A = B) | (ord_less_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1417])). 87.71/26.56 thf(236,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => (((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)))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8980_valid__insert__both__member__options__pres)). 87.71/26.56 thf(2779,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: (((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => ((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)))) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[236])). 87.71/26.56 thf(1747,axiom,((times_times_assn = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_ab__semigroup__mult__class_Omult_Ocommute)). 87.71/26.56 thf(8710,plain,(((times_times_assn) = (^ [A:assn,B:assn]: (times_times_assn @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1747])). 87.71/26.56 thf(155,axiom,((! [A:nat,B:nat,C:list_int,D:nat]: (((ord_less_eq_nat @ B @ (size_size_list_int @ C)) => ((ord_less_nat @ D @ (minus_minus_nat @ B @ A)) => ((nth_int @ (slice_int @ A @ B @ C) @ D) = (nth_int @ C @ (plus_plus_nat @ A @ D))))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3233_slice__nth)). 87.71/26.56 thf(2447,plain,((! [A:nat,B:nat,C:list_int,D:nat]: (((ord_less_eq_nat @ B @ (size_size_list_int @ C)) => ((ord_less_nat @ D @ (minus_minus_nat @ B @ A)) => ((nth_int @ (slice_int @ A @ B @ C) @ D) = (nth_int @ C @ (plus_plus_nat @ A @ D))))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[155])). 87.71/26.56 thf(278,axiom,((! [A:list_real,B:list_real,C:list_int,D:(list_real > (list_real > (list_int > $o)))]: (((size_size_list_real @ A) = (size_size_list_real @ B)) => ((((! [E:real,F:list_real,G:real,H:list_real,I:int,J:list_int]: ((((size_size_list_real @ H) = (size_size_list_int @ J)) => ((D @ (cons_real @ E @ F) @ (cons_real @ G @ H) @ (cons_int @ I @ J)) <= (D @ F @ H @ J))) <= ((size_size_list_real @ F) = (size_size_list_real @ H)))) => (D @ A @ B @ C)) <= (D @ nil_real @ nil_real @ nil_int)) <= ((size_size_list_real @ B) = (size_size_list_int @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8543_list__induct3)). 87.71/26.56 thf(2944,plain,((! [A:list_real,B:list_real,C:list_int,D:(list_real > (list_real > (list_int > $o)))]: (((size_size_list_real @ A) = (size_size_list_real @ B)) => (((! [E:real,F:list_real,G:real,H:list_real,I:int,J:list_int]: ((((size_size_list_real @ H) = (size_size_list_int @ J)) => ((D @ (cons_real @ E @ F) @ (cons_real @ G @ H) @ (cons_int @ I @ J)) | ~ (D @ F @ H @ J))) | ~ ((size_size_list_real @ F) = (size_size_list_real @ H)))) => (D @ A @ B @ C)) | ~ (D @ nil_real @ nil_real @ nil_int) | ~ ((size_size_list_real @ B) = (size_size_list_int @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[278])). 87.71/26.56 thf(577,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2341_add__decreasing)). 87.71/26.56 thf(4182,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ C) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[577])). 87.71/26.56 thf(1427,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/sandbox2/benchmark/theBenchmark.p',fact_10138_min__numeral__Suc)). 87.71/26.56 thf(7437,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)],[1427])). 87.71/26.56 thf(864,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) <= (ord_less_eq_nat @ C @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3102_diff__less__mono)). 87.71/26.56 thf(5304,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (minus_minus_nat @ A @ C) @ (minus_minus_nat @ B @ C)) | ~ (ord_less_eq_nat @ C @ A) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[864])). 87.71/26.56 thf(82,axiom,((! [A:vEBT_VEBT,B:$o]: (((((B) <= (? [C:$o]: (A = (vEBT_Leaf @ ($true) @ C)))) => (((? [C:$o]: (A = (vEBT_Leaf @ C @ ($true)))) => (B)) => (((~ (B)) <= (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ ((B) <= (? [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F)))))))) <= ((A = (vEBT_Leaf @ ($false) @ ($false))) => (~ (B)))) <= ((vEBT_VEBT_minNull @ A) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2481_VEBT__internal_OminNull_Oelims_I1_J)). 87.71/26.56 thf(2081,plain,((! [A:vEBT_VEBT,B:$o]: ((((B) | ~ (? [C:$o]: (A = (vEBT_Leaf @ ($true) @ C)))) => (((? [C:$o]: (A = (vEBT_Leaf @ C @ ($true)))) => (B)) => ((~ (B) | ~ (? [C:nat,D:list_VEBT_VEBT,E:vEBT_VEBT]: (A = (vEBT_Node @ none_P5556105721700978146at_nat @ C @ D @ E)))) => (~ ((B) | ~ (? [C:product_prod_nat_nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT]: (A = (vEBT_Node @ (some_P7363390416028606310at_nat @ C) @ D @ E @ F)))))))) | ~ ((A = (vEBT_Leaf @ ($false) @ ($false))) => (~ (B))) | ~ ((vEBT_VEBT_minNull @ A) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[82])). 87.71/26.56 thf(1632,axiom,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ A @ (times_times_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_star__assoc)). 87.71/26.56 thf(8253,plain,((! [A:assn,B:assn,C:assn]: ((times_times_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ A @ (times_times_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1632])). 87.71/26.56 thf(1379,axiom,((! [A:nat,B:nat]: ((plus_plus_nat @ (suc @ A) @ B) = (suc @ (plus_plus_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2310_add__Suc)). 87.71/26.56 thf(7256,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)],[1379])). 87.71/26.56 thf(461,axiom,((! [A:product_prod_nat_nat]: ~ (! [B:nat,C:nat]: (A != (product_Pair_nat_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_799_prod__decode__aux_Ocases)). 87.71/26.56 thf(3694,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)],[461])). 87.71/26.56 thf(690,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/sandbox2/benchmark/theBenchmark.p',fact_8847_map__decr__upt)). 87.71/26.56 thf(4602,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)],[690])). 87.71/26.56 thf(1636,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/sandbox2/benchmark/theBenchmark.p',fact_316_Ex__less__Suc2)). 87.71/26.56 thf(8272,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)],[1636])). 87.71/26.56 thf(602,axiom,((! [A:nat]: ((zero_zero_nat = (semiri1316708129612266289at_nat @ A)) = (zero_zero_nat = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4533_of__nat__0__eq__iff)). 87.71/26.56 thf(4293,plain,((! [A:nat]: ((zero_zero_nat = (semiri1316708129612266289at_nat @ A)) = (zero_zero_nat = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[602])). 87.71/26.56 thf(730,axiom,((! [A:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),B:product_prod_nat_nat]: ((vEBT_V1502963449132264192at_nat @ A @ (some_P7363390416028606310at_nat @ B) @ none_P5556105721700978146at_nat) = none_P5556105721700978146at_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_716_VEBT__internal_Ooption__shift_Osimps_I2_J)). 87.71/26.56 thf(4759,plain,((! [A:(product_prod_nat_nat > (product_prod_nat_nat > product_prod_nat_nat)),B:product_prod_nat_nat]: ((vEBT_V1502963449132264192at_nat @ (A) @ (some_P7363390416028606310at_nat @ B) @ none_P5556105721700978146at_nat) = none_P5556105721700978146at_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[730])). 87.71/26.56 thf(1053,axiom,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ (power_power_nat @ A @ B))) <= (ord_less_eq_nat @ one_one_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8007_self__le__power)). 87.71/26.56 thf(6018,plain,((! [A:nat,B:nat]: (((ord_less_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ A @ (power_power_nat @ A @ B))) | ~ (ord_less_eq_nat @ one_one_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053])). 87.71/26.56 thf(629,axiom,((! [A:option4927543243414619207at_nat]: ((~ (! [B:product_prod_nat_nat]: (A != (some_P7363390416028606310at_nat @ B)))) <= (A != none_P5556105721700978146at_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_option_Oexhaust)). 87.71/26.56 thf(4387,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)],[629])). 87.71/26.56 thf(653,axiom,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1780_le__numeral__extra_I4_J)). 87.71/26.56 thf(4478,plain,((ord_less_eq_nat @ one_one_nat @ one_one_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[653])). 87.71/26.56 thf(1351,axiom,((! [A:nat,B:nat,C:nat]: (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = ((A = zero_zero_nat) | (B = C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_mult__cancel1)). 87.71/26.56 thf(7157,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)],[1351])). 87.71/26.56 thf(94,axiom,((bit_se547839408752420682it_nat = (^ [A:nat,B:nat]: (times_times_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10116_push__bit__nat__def)). 87.71/26.56 thf(2162,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)],[94])). 87.71/26.56 thf(936,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/sandbox2/benchmark/theBenchmark.p',fact_2345_add__increasing)). 87.71/26.56 thf(5568,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)],[936])). 87.71/26.56 thf(1067,axiom,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = zero_zero_nat) => (? [C:nat]: (A = (times_times_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8721_mod__eq__0D)). 87.71/26.56 thf(6062,plain,((! [A:nat,B:nat]: (((modulo_modulo_nat @ A @ B) = zero_zero_nat) => (? [C:nat]: (A = (times_times_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067])). 87.71/26.56 thf(1531,axiom,((! [A:assn,B:assn,C:(vEBT_VEBTi > assn),D:(vEBT_VEBTi > assn),E:heap_T8145700208782473153_VEBTi]: ((entails @ A @ B) => ((! [F:vEBT_VEBTi]: (entails @ (C @ F) @ (D @ F))) => ((hoare_1429296392585015714_VEBTi @ A @ E @ D) <= (hoare_1429296392585015714_VEBTi @ B @ E @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4063_cons__rule)). 87.71/26.56 thf(7887,plain,((! [A:assn,B:assn,C:(vEBT_VEBTi > assn),D:(vEBT_VEBTi > assn),E:heap_T8145700208782473153_VEBTi]: ((entails @ A @ B) => ((! [F:vEBT_VEBTi]: (entails @ (C @ F) @ (D @ F))) => ((hoare_1429296392585015714_VEBTi @ A @ E @ (D)) | ~ (hoare_1429296392585015714_VEBTi @ B @ E @ (C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1531])). 87.71/26.56 thf(211,axiom,((! [A:list_int,B:list_real,C:list_o,D:list_int,E:(list_int > (list_real > (list_o > (list_int > $o))))]: (((((size_size_list_o @ C) = (size_size_list_int @ D)) => (((E @ A @ B @ C @ D) <= (! [F:int,G:list_int,H:real,I:list_real,J:$o,K:list_o,L:int,M:list_int]: (((((E @ G @ I @ K @ M) => (E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_o @ J @ K) @ (cons_int @ L @ M))) <= ((size_size_list_o @ K) = (size_size_list_int @ M))) <= ((size_size_list_real @ I) = (size_size_list_o @ K))) <= ((size_size_list_int @ G) = (size_size_list_real @ I))))) <= (E @ nil_int @ nil_real @ nil_o @ nil_int))) <= ((size_size_list_real @ B) = (size_size_list_o @ C))) <= ((size_size_list_int @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8557_list__induct4)). 87.71/26.56 thf(2680,plain,((! [A:list_int,B:list_real,C:list_o,D:list_int,E:(list_int > (list_real > (list_o > (list_int > $o))))]: ((((size_size_list_o @ C) = (size_size_list_int @ D)) => ((E @ A @ B @ C @ D) | ~ (! [F:int,G:list_int,H:real,I:list_real,J:$o,K:list_o,L:int,M:list_int]: (((E @ G @ I @ K @ M) => (E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_o @ J @ K) @ (cons_int @ L @ M))) | ~ ((size_size_list_o @ K) = (size_size_list_int @ M)) | ~ ((size_size_list_real @ I) = (size_size_list_o @ K)) | ~ ((size_size_list_int @ G) = (size_size_list_real @ I)))) | ~ (E @ nil_int @ nil_real @ nil_o @ nil_int))) | ~ ((size_size_list_real @ B) = (size_size_list_o @ C)) | ~ ((size_size_list_int @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[211])). 87.71/26.56 thf(102,axiom,((! [A:nat]: ((bit_se6528837805403552850or_nat @ A @ (suc @ zero_zero_nat)) = (minus_minus_nat @ (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9996_xor__Suc__0__eq)). 87.71/26.56 thf(2183,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)],[102])). 87.71/26.56 thf(266,axiom,((! [A:nat]: (ord_less_eq_nat @ (suc @ zero_zero_nat) @ (semiri1408675320244567234ct_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8864_fact__ge__Suc__0__nat)). 87.71/26.56 thf(2902,plain,((! [A:nat]: (ord_less_eq_nat @ (suc @ zero_zero_nat) @ (semiri1408675320244567234ct_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[266])). 87.71/26.56 thf(1444,axiom,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option_nat > $o)),C:option_nat]: (((B @ A @ C) <= (A = none_P5556105721700978146at_nat)) => (((C = none_nat) => (B @ A @ C)) => ((B @ A @ C) <= (! [D:product_prod_nat_nat,E:nat]: (((C = (some_nat @ E)) => (B @ A @ C)) <= (A = (some_P7363390416028606310at_nat @ D))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_combine__options__cases)). 87.71/26.56 thf(7520,plain,((! [A:option4927543243414619207at_nat,B:(option4927543243414619207at_nat > (option_nat > $o)),C:option_nat]: (((B @ A @ C) | ~ (A = none_P5556105721700978146at_nat)) => (((C = none_nat) => (B @ A @ C)) => ((B @ A @ C) | ~ (! [D:product_prod_nat_nat,E:nat]: (((C = (some_nat @ E)) => (B @ A @ C)) | ~ (A = (some_P7363390416028606310at_nat @ D))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1444])). 87.71/26.56 thf(751,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2862_le__add__diff__inverse)). 87.71/26.56 thf(4869,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((plus_plus_nat @ A @ (minus_minus_nat @ B @ A)) = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[751])). 87.71/26.56 thf(199,axiom,((! [A:list_nat,B:nat,C:list_nat]: ((nth_nat @ (append_nat @ A @ (cons_nat @ B @ C)) @ (size_size_list_nat @ A)) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8264_nth__append__length)). 87.71/26.56 thf(2623,plain,((! [A:list_nat,B:nat,C:list_nat]: ((nth_nat @ (append_nat @ A @ (cons_nat @ B @ C)) @ (size_size_list_nat @ A)) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[199])). 87.71/26.56 thf(1705,axiom,((! [A:(product_prod_nat_nat > nat)]: ((size_o8335143837870341156at_nat @ A @ none_P5556105721700978146at_nat) = (suc @ zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1729_option_Osize__gen_I1_J)). 87.71/26.56 thf(8520,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)],[1705])). 87.71/26.56 thf(426,axiom,((! [A:nat,B:nat,C:nat]: ((((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_mult__left__cancel)). 87.71/26.56 thf(3552,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)],[426])). 87.71/26.56 thf(1173,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => (((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_eq_nat @ zero_zero_nat @ B))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_mult__mono)). 87.71/26.56 thf(6499,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_eq_nat @ C @ D) => ((ord_less_eq_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D)) | ~ (ord_less_eq_nat @ zero_zero_nat @ C) | ~ (ord_less_eq_nat @ zero_zero_nat @ B))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173])). 87.71/26.56 thf(858,axiom,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((((ord_less_eq_nat @ D @ C) <= (vEBT_vebt_member @ A @ D)) <= ((vEBT_vebt_maxt @ A) = (some_nat @ C))) <= (vEBT_invar_vebt @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_maxt__corr__help)). 87.71/26.56 thf(5287,plain,((! [A:vEBT_VEBT,B:nat,C:nat,D:nat]: ((ord_less_eq_nat @ D @ C) | ~ (vEBT_vebt_member @ A @ D) | ~ ((vEBT_vebt_maxt @ A) = (some_nat @ C)) | ~ (vEBT_invar_vebt @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[858])). 87.71/26.56 thf(148,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (binomial @ A @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9047_binomial__le__pow2)). 87.71/26.56 thf(2421,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)],[148])). 87.71/26.56 thf(45,axiom,((! [A:num]: ((bit_se1412395901928357646or_nat @ (numeral_numeral_nat @ (bit1 @ A)) @ (suc @ zero_zero_nat)) = (numeral_numeral_nat @ (bit1 @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10043_or__nat__numerals_I4_J)). 87.71/26.56 thf(1908,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)],[45])). 87.71/26.56 thf(122,axiom,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => (vEBT_V8194947554948674370ptions @ (vEBT_vebt_insert @ A @ C) @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8981_valid__insert__both__member__options__add)). 87.71/26.56 thf(2287,plain,((! [A:vEBT_VEBT,B:nat,C:nat]: ((vEBT_invar_vebt @ A @ B) => ((ord_less_nat @ C @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) => (vEBT_V8194947554948674370ptions @ (vEBT_vebt_insert @ A @ C) @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[122])). 87.71/26.56 thf(1123,axiom,((! [A:(nat > $o),B:nat]: ((! [C:nat]: ((? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D))) <= (~ (A @ C)))) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_infinite__descent)). 87.71/26.56 thf(6326,plain,((! [A:(nat > $o),B:nat]: ((! [C:nat]: (? [D:nat]: ((ord_less_nat @ D @ C) & ~ (A @ D)) | (A @ C))) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123])). 87.71/26.56 thf(1605,axiom,((! [A:assn,B:$o,C:heap_T2636463487746394924on_nat,D:(option_nat > assn),E:nat]: ((time_htt_option_nat @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ D @ E) = ((time_htt_option_nat @ A @ C @ D @ E) <= (B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1791_norm__pre__pure__iff__htt)). 87.71/26.56 thf(8162,plain,((! [A:assn,B:$o,C:heap_T2636463487746394924on_nat,D:(option_nat > assn),E:nat]: ((time_htt_option_nat @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ (D) @ E) = ((time_htt_option_nat @ A @ C @ (D) @ E) | ~ (B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1605])). 87.71/26.56 thf(192,axiom,((! [A:nat,B:nat,C:list_nat]: ((drop_nat @ (suc @ A) @ (cons_nat @ B @ C)) = (drop_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7725_drop__Suc__Cons)). 87.71/26.56 thf(2587,plain,((! [A:nat,B:nat,C:list_nat]: ((drop_nat @ (suc @ A) @ (cons_nat @ B @ C)) = (drop_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[192])). 87.71/26.56 thf(1294,axiom,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_succ @ (vEBT_Leaf @ A @ B) @ (suc @ C)) = none_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_vebt__succ_Osimps_I2_J)). 87.71/26.56 thf(6925,plain,((! [A:$o,B:$o,C:nat]: ((vEBT_vebt_succ @ (vEBT_Leaf @ A @ B) @ (suc @ C)) = none_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294])). 87.71/26.56 thf(357,axiom,((! [A:(int > (nat > assn)),B:list_int]: ((vEBT_L77084186935402305nt_nat @ A @ B @ nil_nat) = (pure_assn @ (B = nil_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8219_list__assn__aux__simps_I2_J)). 87.71/26.56 thf(3264,plain,((! [A:(int > (nat > assn)),B:list_int]: ((vEBT_L77084186935402305nt_nat @ (A) @ B @ nil_nat) = (pure_assn @ (B = nil_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[357])). 87.71/26.56 thf(742,axiom,((! [A:nat,B:nat]: ((A != B) => ((ord_less_eq_nat @ A @ B) => (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1612_order__neq__le__trans)). 87.71/26.56 thf(4843,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)],[742])). 87.71/26.56 thf(922,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((plus_plus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ D)) = (plus_plus_nat @ (times_times_nat @ A @ D) @ (times_times_nat @ C @ B))) = ((A = C) | (B = D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2614_crossproduct__eq)). 87.71/26.56 thf(5522,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)],[922])). 87.71/26.56 thf(232,axiom,((! [A:list_nat]: ((slice_nat @ zero_zero_nat @ (size_size_list_nat @ A) @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3284_slice__complete)). 87.71/26.56 thf(2768,plain,((! [A:list_nat]: ((slice_nat @ zero_zero_nat @ (size_size_list_nat @ A) @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[232])). 87.71/26.56 thf(1666,axiom,((! [A:$o,B:assn,C:heap_Time_Heap_nat,D:(nat > assn),E:nat]: ((time_htt_nat @ (times_times_assn @ (pure_assn @ A) @ B) @ C @ D @ E) = ((time_htt_nat @ B @ C @ D @ E) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1798_norm__pre__pure__iff__htt_H)). 87.71/26.56 thf(8368,plain,((! [A:$o,B:assn,C:heap_Time_Heap_nat,D:(nat > assn),E:nat]: ((time_htt_nat @ (times_times_assn @ (pure_assn @ A) @ B) @ C @ (D) @ E) = ((time_htt_nat @ B @ C @ (D) @ E) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1666])). 87.71/26.56 thf(110,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B) => (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9032_power2__nat__le__imp__le)). 87.71/26.56 thf(2218,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ B) => (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[110])). 87.71/26.56 thf(1656,axiom,(((comp_nat_nat_nat @ suc @ suc) = (comp_nat_nat_nat @ suc @ suc))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10181_card_Ocomp__fun__commute__on)). 87.71/26.56 thf(8341,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1656])). 87.71/26.56 thf(1007,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((C != A) <= (ord_less_nat @ C @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1943_minf_I4_J)). 87.71/26.56 thf(5852,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: (~ (C = A) | ~ (ord_less_nat @ C @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007])). 87.71/26.56 thf(533,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ (times_times_nat @ A @ B) @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_mult__nonpos__nonneg)). 87.71/26.56 thf(4039,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)],[533])). 87.71/26.56 thf(1338,axiom,((! [A:nat]: ((A = zero_zero_nat) <= (dvd_dvd_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9455_gcd__nat_Oextremum__uniqueI)). 87.71/26.56 thf(7081,plain,((! [A:nat]: ((A = zero_zero_nat) | ~ (dvd_dvd_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338])). 87.71/26.56 thf(1448,axiom,((! [A:assn,B:assn,C:assn]: ((entails @ (sup_sup_assn @ A @ B) @ C) => (entails @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5112_ent__disjI1)). 87.71/26.56 thf(7542,plain,((! [A:assn,B:assn,C:assn]: ((entails @ (sup_sup_assn @ A @ B) @ C) => (entails @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1448])). 87.71/26.56 thf(1064,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (binomial @ B @ A) @ (power_power_nat @ B @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8880_binomial__le__pow)). 87.71/26.56 thf(6055,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (binomial @ B @ A) @ (power_power_nat @ B @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064])). 87.71/26.56 thf(1575,axiom,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:nat]: ((time_htt_option_nat @ A @ B @ C @ D) => (hoare_7629718768684598413on_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1806_htt__htD)). 87.71/26.56 thf(8070,plain,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:nat]: ((time_htt_option_nat @ A @ B @ (C) @ D) => (hoare_7629718768684598413on_nat @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1575])). 87.71/26.56 thf(464,axiom,((! [A:nat,B:nat,C:nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ C @ B)) = (A = C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2051_add__right__cancel)). 87.71/26.56 thf(3705,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)],[464])). 87.71/26.56 thf(650,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((hd_nat @ (upt @ A @ B)) = A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8901_hd__upt)). 87.71/26.56 thf(4472,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => ((hd_nat @ (upt @ A @ B)) = A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[650])). 87.71/26.56 thf(1319,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1821_T_092_060_094sub_062s_092_060_094sub_062u_092_060_094sub_062c_092_060_094sub_062c_Osimps_I3_J)). 87.71/26.56 thf(7016,plain,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT,D:nat]: ((vEBT_T_s_u_c_c @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C) @ D) = one_one_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319])). 87.71/26.56 thf(710,axiom,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:assn]: ((hoare_1429296392585015714_VEBTi @ A @ B @ C) => (hoare_1429296392585015714_VEBTi @ (times_times_assn @ D @ A) @ B @ (^ [E:vEBT_VEBTi]: (times_times_assn @ D @ (C @ E))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_frame__rule__left)). 87.71/26.56 thf(4687,plain,((! [A:assn,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn),D:assn]: ((hoare_1429296392585015714_VEBTi @ A @ B @ (C)) => (hoare_1429296392585015714_VEBTi @ (times_times_assn @ D @ A) @ B @ (^ [E:vEBT_VEBTi]: (times_times_assn @ D @ (C @ E))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[710])). 87.71/26.56 thf(141,axiom,((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9025_pos2)). 87.71/26.56 thf(2385,plain,((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[141])). 87.71/26.56 thf(940,axiom,((! [A:nat,B:nat]: (((~ (ord_less_nat @ B @ A)) = (B = A)) <= (~ (ord_less_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1260_antisym__conv3)). 87.71/26.56 thf(5606,plain,((! [A:nat,B:nat]: (((~ (ord_less_nat @ B @ A)) = (B = A)) | (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[940])). 87.71/26.56 thf(1478,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2204_add_Ocomm__neutral)). 87.71/26.56 thf(7634,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1478])). 87.71/26.56 thf(1312,axiom,((! [A:nat,B:nat,C:$o]: (((ord_less_nat @ B @ A) => (C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1386_order__less__imp__triv)). 87.71/26.56 thf(6997,plain,((! [A:nat,B:nat,C:$o]: (((ord_less_nat @ B @ A) => (C)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312])). 87.71/26.56 thf(348,axiom,(((size_size_list_real @ nil_real) = zero_zero_nat)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8522_length__nth__simps_I1_J)). 87.71/26.56 thf(3232,plain,(((size_size_list_real @ nil_real) = zero_zero_nat)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[348])). 87.71/26.56 thf(524,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (divide_divide_nat @ C @ B) @ (divide_divide_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8647_div__le__mono2)). 87.71/26.56 thf(3997,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (divide_divide_nat @ C @ B) @ (divide_divide_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[524])). 87.71/26.56 thf(1157,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ B @ A) @ C) @ A) = (plus_plus_nat @ (divide_divide_nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8618_msrevs_I1_J)). 87.71/26.56 thf(6439,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((divide_divide_nat @ (plus_plus_nat @ (times_times_nat @ B @ A) @ C) @ A) = (plus_plus_nat @ (divide_divide_nat @ C @ A) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157])). 87.71/26.56 thf(1265,axiom,((! [A:list_o,B:list_nat,C:($o > (nat > assn))]: (((size_size_list_o @ A) != (size_size_list_nat @ B)) => ((vEBT_L4785011123346445925_o_nat @ C @ A @ B) = bot_bot_assn)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3203_list__assn__aux__ineq__len)). 87.71/26.56 thf(6822,plain,((! [A:list_o,B:list_nat,C:($o > (nat > assn))]: ((~ ((size_size_list_o @ A) = (size_size_list_nat @ B))) => ((vEBT_L4785011123346445925_o_nat @ (C) @ A @ B) = bot_bot_assn)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265])). 87.71/26.56 thf(994,axiom,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1963_pinf_I7_J)). 87.71/26.56 thf(5796,plain,((! [A:nat]: ? [B:nat]: ! [C:nat]: ((ord_less_nat @ B @ C) => (ord_less_nat @ A @ C)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[994])). 87.71/26.56 thf(1037,axiom,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_valid__tree__deg__neq__0)). 87.71/26.56 thf(5954,plain,((! [A:vEBT_VEBT]: ~ (vEBT_invar_vebt @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037])). 87.71/26.56 thf(1380,axiom,((! [A:nat,B:nat]: ((minus_minus_nat @ (suc @ A) @ (suc @ B)) = (minus_minus_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2820_diff__Suc__Suc)). 87.71/26.56 thf(7259,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)],[1380])). 87.71/26.56 thf(841,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1496_not__le__imp__less)). 87.71/26.56 thf(5232,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) => (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[841])). 87.71/26.56 thf(1062,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_le__imp__less__Suc)). 87.71/26.56 thf(6050,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)],[1062])). 87.71/26.56 thf(313,axiom,((! [A:vEBT_VEBT]: ((A != (vEBT_Leaf @ ($false) @ ($false))) => (((! [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:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: (A != (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))))) <= (! [B:$o]: (A != (vEBT_Leaf @ ($true) @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_847_T_092_060_094sub_062m_092_060_094sub_062i_092_060_094sub_062n_092_060_094sub_062N_092_060_094sub_062u_092_060_094sub_062l_092_060_094sub_062l_Ocases)). 87.71/26.56 thf(3100,plain,((! [A:vEBT_VEBT]: ((~ (A = (vEBT_Leaf @ ($false) @ ($false)))) => (((! [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:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ~ (A = (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D))))) | ~ (! [B:$o]: ~ (A = (vEBT_Leaf @ ($true) @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[313])). 87.71/26.56 thf(379,axiom,((! [A:nat,B:num]: ((ord_less_nat @ (suc @ A) @ (numeral_numeral_nat @ B)) = (ord_less_nat @ A @ (pred_numeral @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9915_less__Suc__numeral)). 87.71/26.56 thf(3373,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)],[379])). 87.71/26.56 thf(400,axiom,((! [A:nat]: ((bit_se6528837805403552850or_nat @ (suc @ zero_zero_nat) @ A) = (minus_minus_nat @ (plus_plus_nat @ A @ (zero_n2687167440665602831ol_nat @ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))) @ (zero_n2687167440665602831ol_nat @ (~ (dvd_dvd_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9997_Suc__0__xor__eq)). 87.71/26.56 thf(3464,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)],[400])). 87.71/26.56 thf(1753,axiom,((! [A:assn,B:$o,C:heap_Time_Heap_nat,D:(nat > assn),E:nat]: ((time_htt_nat @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ D @ E) = ((B) => (time_htt_nat @ A @ C @ D @ E))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1794_norm__pre__pure__iff__htt)). 87.71/26.56 thf(8726,plain,((! [A:assn,B:$o,C:heap_Time_Heap_nat,D:(nat > assn),E:nat]: ((time_htt_nat @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ (D) @ E) = ((B) => (time_htt_nat @ A @ C @ (D) @ E))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1753])). 87.71/26.56 thf(669,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/sandbox2/benchmark/theBenchmark.p',fact_10140_nat__mult__min__right)). 87.71/26.56 thf(4523,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)],[669])). 87.71/26.56 thf(223,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) <= (ord_less_eq_nat @ C @ B)) <= (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9069_nat__less__power__trans)). 87.71/26.56 thf(2736,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C) @ A) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B)) | ~ (ord_less_eq_nat @ C @ B) | ~ (ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[223])). 87.71/26.56 thf(71,axiom,((! [A:heap_T8145700208782473153_VEBTi,B:heap_T8145700208782473153_VEBTi]: ((if_Hea8453224502484754311_VEBTi @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Heap____Time____Monad__OHeap_It__VEBT____BuildupMemImp__OVEBTi_J_T)). 87.71/26.56 thf(2008,plain,((! [A:heap_T8145700208782473153_VEBTi,B:heap_T8145700208782473153_VEBTi]: ((if_Hea8453224502484754311_VEBTi @ ($false) @ A @ B) = B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[71])). 87.71/26.56 thf(66,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => ((? [C:nat]: ((ord_less_nat @ (power_power_nat @ A @ C) @ B) & (ord_less_eq_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat))))) <= (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9066_ex__power__ivl2)). 87.71/26.56 thf(1986,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) => (? [C:nat]: ((ord_less_nat @ (power_power_nat @ A @ C) @ B) & (ord_less_eq_nat @ B @ (power_power_nat @ A @ (plus_plus_nat @ C @ one_one_nat)))) | ~ (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[66])). 87.71/26.56 thf(1223,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/sandbox2/benchmark/theBenchmark.p',fact_8011_one__less__power)). 87.71/26.56 thf(6671,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)],[1223])). 87.71/26.56 thf(324,axiom,((! [A:(nat > nat),B:nat]: ((groups7488368174851004413at_nat @ A @ B @ nil_nat) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8194_horner__sum__simps_I1_J)). 87.71/26.56 thf(3132,plain,((! [A:(nat > nat),B:nat]: ((groups7488368174851004413at_nat @ (A) @ B @ nil_nat) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[324])). 87.71/26.56 thf(1719,axiom,((! [A:nat]: ((semiri1316708129612266289at_nat @ (suc @ A)) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4645_semiring__char__0__class_Oof__nat__neq__0)). 87.71/26.56 thf(8574,plain,((! [A:nat]: ~ ((semiri1316708129612266289at_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1719])). 87.71/26.56 thf(658,axiom,((ord_less_eq_nat = (^ [A:nat,B:nat]: (vEBT_VEBT_lesseq @ (some_nat @ A) @ (some_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_lesseq__shift)). 87.71/26.56 thf(4491,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)],[658])). 87.71/26.56 thf(1648,axiom,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:assn]: (((hoare_7629718768684598413on_nat @ D @ B @ C) => (hoare_7629718768684598413on_nat @ (sup_sup_assn @ A @ D) @ B @ C)) <= (hoare_7629718768684598413on_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5118_split__rule)). 87.71/26.56 thf(8309,plain,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:assn]: (((hoare_7629718768684598413on_nat @ D @ B @ (C)) => (hoare_7629718768684598413on_nat @ (sup_sup_assn @ A @ D) @ B @ (C))) | ~ (hoare_7629718768684598413on_nat @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1648])). 87.71/26.56 thf(1722,axiom,((! [A:nat]: ((? [B:nat]: (A = (suc @ B))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_gr0__implies__Suc)). 87.71/26.56 thf(8589,plain,((! [A:nat]: (? [B:nat]: (A = (suc @ B)) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1722])). 87.71/26.56 thf(1549,axiom,((! [A:nat,B:nat,C:nat,D:list_nat]: (((~ ((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B))) => ((slice_nat @ A @ B @ (cons_nat @ C @ D)) = (slice_nat @ (minus_minus_nat @ A @ one_one_nat) @ (minus_minus_nat @ B @ one_one_nat) @ D))) & (((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B)) => ((slice_nat @ A @ B @ (cons_nat @ C @ D)) = (cons_nat @ C @ (slice_nat @ A @ (minus_minus_nat @ B @ one_one_nat) @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4782_slice__Cons)). 87.71/26.56 thf(7955,plain,((! [A:nat,B:nat,C:nat,D:list_nat]: (((~ ((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B))) => ((slice_nat @ A @ B @ (cons_nat @ C @ D)) = (slice_nat @ (minus_minus_nat @ A @ one_one_nat) @ (minus_minus_nat @ B @ one_one_nat) @ D))) & (((A = zero_zero_nat) & (ord_less_nat @ zero_zero_nat @ B)) => ((slice_nat @ A @ B @ (cons_nat @ C @ D)) = (cons_nat @ C @ (slice_nat @ A @ (minus_minus_nat @ B @ one_one_nat) @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1549])). 87.71/26.56 thf(1773,axiom,((! [A:nat,B:nat]: ((tl_nat @ (upt @ A @ B)) = (upt @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8860_tl__upt)). 87.71/26.56 thf(8801,plain,((! [A:nat,B:nat]: ((tl_nat @ (upt @ A @ B)) = (upt @ (suc @ A) @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1773])). 87.71/26.56 thf(329,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (power_power_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) @ (power_power_nat @ B @ (numeral_numeral_nat @ (bit0 @ one)))) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9031_power2__nat__le__eq__le)). 87.71/26.56 thf(3164,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)],[329])). 87.71/26.56 thf(566,axiom,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1045_comm__monoid__mult__class_Omult__1)). 87.71/26.56 thf(4146,plain,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[566])). 87.71/26.56 thf(228,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9883_take__bit__nat__less__eq__self)). 87.71/26.56 thf(2751,plain,((! [A:nat,B:nat]: (ord_less_eq_nat @ (bit_se2925701944663578781it_nat @ A @ B) @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[228])). 87.71/26.56 thf(1209,axiom,((! [A:nat,B:nat,C:nat,D:nat]: ((plus_plus_nat @ (times_times_nat @ A @ B) @ (plus_plus_nat @ (times_times_nat @ C @ B) @ D)) = (plus_plus_nat @ (times_times_nat @ (plus_plus_nat @ A @ C) @ B) @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2335_left__add__mult__distrib)). 87.71/26.56 thf(6627,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)],[1209])). 87.71/26.56 thf(1674,axiom,((! [A:nat]: ((bit_Sh2154871086232339855tr_nat @ (suc @ zero_zero_nat) @ A) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10183_shiftr__Suc__0)). 87.71/26.56 thf(8400,plain,((! [A:nat]: ((bit_Sh2154871086232339855tr_nat @ (suc @ zero_zero_nat) @ A) = (zero_n2687167440665602831ol_nat @ (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1674])). 87.71/26.56 thf(1453,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/sandbox2/benchmark/theBenchmark.p',fact_8663_le__div__geq)). 87.71/26.56 thf(7557,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)],[1453])). 87.71/26.56 thf(637,axiom,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2107_Nat_Oadd__0__right)). 87.71/26.56 thf(4427,plain,((! [A:nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[637])). 87.71/26.56 thf(780,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_less__Suc__eq__le)). 87.71/26.56 thf(4968,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)],[780])). 87.71/26.56 thf(1215,axiom,((bit_wf_set_bits_int = (^ [A:(nat > $o)]: (? [B:nat]: ! [C:nat]: ((A @ C) <= (ord_less_eq_nat @ B @ C)) | ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ B @ C) => (~ (A @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10175_wf__set__bits__int_Osimps)). 87.71/26.56 thf(6644,plain,(((bit_wf_set_bits_int) = (^ [A:(nat > $o)]: (? [B:nat]: ! [C:nat]: ((A @ C) | ~ (ord_less_eq_nat @ B @ C)) | ? [B:nat]: ! [C:nat]: ((ord_less_eq_nat @ B @ C) => (~ (A @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215])). 87.71/26.56 thf(6,axiom,((! [A:nat,B:list_nat]: ((nil_nat = (take_nat @ A @ B)) = ((A = zero_zero_nat) | (B = nil_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8164_take__eq__Nil2)). 87.71/26.56 thf(1789,plain,((! [A:nat,B:list_nat]: ((nil_nat = (take_nat @ A @ B)) = ((A = zero_zero_nat) | (B = nil_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])). 87.71/26.56 thf(796,axiom,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1776_less__numeral__extra_I3_J)). 87.71/26.56 thf(5036,plain,((~ (ord_less_nat @ zero_zero_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[796])). 87.71/26.56 thf(241,axiom,((! [A:list_nat,B:list_nat,C:list_nat,D:list_nat]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ (size_size_list_nat @ B)) => (((append_nat @ B @ C) = (append_nat @ A @ D)) => (? [E:list_nat]: (D = (append_nat @ E @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8510_list__rest__coinc)). 87.71/26.56 thf(2795,plain,((! [A:list_nat,B:list_nat,C:list_nat,D:list_nat]: ((ord_less_eq_nat @ (size_size_list_nat @ A) @ (size_size_list_nat @ B)) => (((append_nat @ B @ C) = (append_nat @ A @ D)) => (? [E:list_nat]: (D = (append_nat @ E @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[241])). 87.71/26.56 thf(1144,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) <= (ord_less_eq_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2353_add__increasing2)). 87.71/26.56 thf(6398,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ (plus_plus_nat @ C @ A)) | ~ (ord_less_eq_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144])). 87.71/26.56 thf(133,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((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)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9054_power__minus__is__div)). 87.71/26.56 thf(2340,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((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)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[133])). 87.71/26.56 thf(609,axiom,((! [A:nat,B:nat]: (((minus_minus_nat @ A @ B) = zero_zero_nat) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2866_diff__is__0__eq_H)). 87.71/26.56 thf(4318,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)],[609])). 87.71/26.56 thf(368,axiom,((! [A:list_int,B:list_real,C:list_o,D:list_nat,E:(list_int > (list_real > (list_o > (list_nat > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => (((size_size_list_real @ B) = (size_size_list_o @ C)) => (((size_size_list_o @ C) = (size_size_list_nat @ D)) => (((E @ A @ B @ C @ D) <= (! [F:int,G:list_int,H:real,I:list_real,J:$o,K:list_o,L:nat,M:list_nat]: ((((size_size_list_real @ I) = (size_size_list_o @ K)) => (((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_o @ J @ K) @ (cons_nat @ L @ M)) <= (E @ G @ I @ K @ M)) <= ((size_size_list_o @ K) = (size_size_list_nat @ M)))) <= ((size_size_list_int @ G) = (size_size_list_real @ I))))) <= (E @ nil_int @ nil_real @ nil_o @ nil_nat))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8556_list__induct4)). 87.71/26.56 thf(3309,plain,((! [A:list_int,B:list_real,C:list_o,D:list_nat,E:(list_int > (list_real > (list_o > (list_nat > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => (((size_size_list_real @ B) = (size_size_list_o @ C)) => (((size_size_list_o @ C) = (size_size_list_nat @ D)) => ((E @ A @ B @ C @ D) | ~ (! [F:int,G:list_int,H:real,I:list_real,J:$o,K:list_o,L:nat,M:list_nat]: ((((size_size_list_real @ I) = (size_size_list_o @ K)) => ((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_o @ J @ K) @ (cons_nat @ L @ M)) | ~ (E @ G @ I @ K @ M) | ~ ((size_size_list_o @ K) = (size_size_list_nat @ M)))) | ~ ((size_size_list_int @ G) = (size_size_list_real @ I)))) | ~ (E @ nil_int @ nil_real @ nil_o @ nil_nat))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[368])). 87.71/26.56 thf(203,axiom,((! [A:int,B:int,C:int]: ((times_times_int @ (times_times_int @ A @ B) @ C) = (times_times_int @ A @ (times_times_int @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_mult_Oassoc)). 87.71/26.56 thf(2636,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)],[203])). 87.71/26.56 thf(295,axiom,((! [A:list_int,B:list_real,C:list_real,D:list_o,E:(list_int > (list_real > (list_real > (list_o > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => (((size_size_list_real @ B) = (size_size_list_real @ C)) => ((((! [F:int,G:list_int,H:real,I:list_real,J:real,K:list_real,L:$o,M:list_o]: (((size_size_list_int @ G) = (size_size_list_real @ I)) => (((size_size_list_real @ I) = (size_size_list_real @ K)) => (((size_size_list_real @ K) = (size_size_list_o @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_real @ J @ K) @ (cons_o @ L @ M))))))) => (E @ A @ B @ C @ D)) <= (E @ nil_int @ nil_real @ nil_real @ nil_o)) <= ((size_size_list_real @ C) = (size_size_list_o @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8551_list__induct4)). 87.71/26.56 thf(3015,plain,((! [A:list_int,B:list_real,C:list_real,D:list_o,E:(list_int > (list_real > (list_real > (list_o > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => (((size_size_list_real @ B) = (size_size_list_real @ C)) => (((! [F:int,G:list_int,H:real,I:list_real,J:real,K:list_real,L:$o,M:list_o]: (((size_size_list_int @ G) = (size_size_list_real @ I)) => (((size_size_list_real @ I) = (size_size_list_real @ K)) => (((size_size_list_real @ K) = (size_size_list_o @ M)) => ((E @ G @ I @ K @ M) => (E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_real @ J @ K) @ (cons_o @ L @ M))))))) => (E @ A @ B @ C @ D)) | ~ (E @ nil_int @ nil_real @ nil_real @ nil_o) | ~ ((size_size_list_real @ C) = (size_size_list_o @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[295])). 87.71/26.56 thf(1148,axiom,((! [A:nat,B:nat]: (ord_less_eq_nat @ (times_times_nat @ A @ (divide_divide_nat @ B @ A)) @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8644_times__div__less__eq__dividend)). 87.71/26.56 thf(6411,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)],[1148])). 87.71/26.56 thf(1500,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (suc @ A) @ B) = (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_Suc__le__eq)). 87.71/26.56 thf(7727,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)],[1500])). 87.71/26.56 thf(1358,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3023_eq__diff__iff)). 87.71/26.56 thf(7184,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_eq_nat @ A @ C) => (((minus_minus_nat @ B @ A) = (minus_minus_nat @ C @ A)) = (B = C))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358])). 87.71/26.56 thf(1618,axiom,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((vEBT_size_VEBT @ (vEBT_Node @ A @ B @ C @ D)) = (plus_plus_nat @ (plus_plus_nat @ (size_list_VEBT_VEBT @ vEBT_size_VEBT @ C) @ (vEBT_size_VEBT @ D)) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2746_VEBT_Osize__gen_I1_J)). 87.71/26.56 thf(8207,plain,((! [A:option4927543243414619207at_nat,B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT]: ((vEBT_size_VEBT @ (vEBT_Node @ A @ B @ C @ D)) = (plus_plus_nat @ (plus_plus_nat @ (size_list_VEBT_VEBT @ (vEBT_size_VEBT) @ C) @ (vEBT_size_VEBT @ D)) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1618])). 87.71/26.56 thf(131,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (binomial @ C @ A) @ (binomial @ C @ B)) <= (ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9057_binomial__strict__mono)). 87.71/26.56 thf(2334,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (binomial @ C @ A) @ (binomial @ C @ B)) | ~ (ord_less_eq_nat @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ C) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[131])). 87.71/26.56 thf(729,axiom,((! [A:nat,B:nat,C:nat]: ((((minus_minus_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (minus_minus_nat @ B @ C)) <= (ord_less_eq_nat @ A @ C)) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3021_Nat_Odiff__diff__eq)). 87.71/26.56 thf(4755,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)],[729])). 87.71/26.56 thf(887,axiom,((! [A:assn,B:assn]: ((bot_bot_assn = (sup_sup_assn @ A @ B)) = ((B = bot_bot_assn) & (A = bot_bot_assn))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5059_bot__eq__sup__iff)). 87.71/26.56 thf(5404,plain,((! [A:assn,B:assn]: ((bot_bot_assn = (sup_sup_assn @ A @ B)) = ((B = bot_bot_assn) & (A = bot_bot_assn))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[887])). 87.71/26.56 thf(103,axiom,((! [A:nat,B:list_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => (B != nil_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8528_len__greater__imp__nonempty)). 87.71/26.56 thf(2186,plain,((! [A:nat,B:list_nat]: ((ord_less_nat @ A @ (size_size_list_nat @ B)) => (~ (B = nil_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[103])). 87.71/26.56 thf(598,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1356_order__less__irrefl)). 87.71/26.56 thf(4281,plain,((! [A:nat]: ~ (ord_less_nat @ A @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[598])). 87.71/26.56 thf(1047,axiom,((! [A:$o,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn),E:heap_T8145700208782473153_VEBTi,F:(vEBT_VEBTi > assn),G:(vEBT_VEBTi > assn)]: (((hoare_1429296392585015714_VEBTi @ B @ C @ D) <= (A)) => (((~ (A)) => (hoare_1429296392585015714_VEBTi @ B @ E @ F)) => ((hoare_1429296392585015714_VEBTi @ B @ (if_Hea8453224502484754311_VEBTi @ A @ C @ E) @ G) <= (! [H:vEBT_VEBTi]: (entails @ (sup_sup_assn @ (times_times_assn @ (D @ H) @ (pure_assn @ A)) @ (times_times_assn @ (F @ H) @ (pure_assn @ (~ (A))))) @ (G @ H)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5139_if__rule__split)). 87.71/26.56 thf(5990,plain,((! [A:$o,B:assn,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn),E:heap_T8145700208782473153_VEBTi,F:(vEBT_VEBTi > assn),G:(vEBT_VEBTi > assn)]: (((hoare_1429296392585015714_VEBTi @ B @ C @ (D)) | ~ (A)) => (((~ (A)) => (hoare_1429296392585015714_VEBTi @ B @ E @ (F))) => ((hoare_1429296392585015714_VEBTi @ B @ (if_Hea8453224502484754311_VEBTi @ A @ C @ E) @ (G)) | ~ (! [H:vEBT_VEBTi]: (entails @ (sup_sup_assn @ (times_times_assn @ (D @ H) @ (pure_assn @ A)) @ (times_times_assn @ (F @ H) @ (pure_assn @ (~ (A))))) @ (G @ H)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047])). 87.71/26.56 thf(583,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (power_power_nat @ A @ B) @ A) = (times_times_nat @ A @ (power_power_nat @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7812_power__commutes)). 87.71/26.56 thf(4210,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)],[583])). 87.71/26.56 thf(699,axiom,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: ((~ (A @ C)) <= (ord_less_nat @ C @ B)) & (A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1277_exists__least__iff)). 87.71/26.56 thf(4631,plain,(((('?') @ nat) = (^ [A:(nat > $o)]: ? [B:nat]: (! [C:nat]: (~ (A @ C) | ~ (ord_less_nat @ C @ B)) & (A @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[699])). 87.71/26.56 thf(1703,axiom,((! [A:real]: ((power_power_real @ A @ (suc @ zero_zero_nat)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7721_power__Suc0__right)). 87.71/26.56 thf(8510,plain,((! [A:real]: ((power_power_real @ A @ (suc @ zero_zero_nat)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1703])). 87.71/26.56 thf(1746,axiom,((! [A:nat]: ((suc @ A) != zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_Suc__neq__Zero)). 87.71/26.56 thf(8706,plain,((! [A:nat]: ~ ((suc @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1746])). 87.71/26.56 thf(411,axiom,((! [A:(nat > (int > assn)),B:list_int]: ((vEBT_L8298612041380073281at_int @ A @ nil_nat @ B) = (pure_assn @ (B = nil_int))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8224_list__assn__aux__simps_I1_J)). 87.71/26.56 thf(3506,plain,((! [A:(nat > (int > assn)),B:list_int]: ((vEBT_L8298612041380073281at_int @ (A) @ nil_nat @ B) = (pure_assn @ (B = nil_int))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[411])). 87.71/26.56 thf(830,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) != zero_zero_nat) => ((A != zero_zero_nat) & (B != zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_mult__not__zero)). 87.71/26.56 thf(5176,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)],[830])). 87.71/26.56 thf(454,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_mult__right__less__imp__less)). 87.71/26.56 thf(3673,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ C @ B)) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[454])). 87.71/26.56 thf(1117,axiom,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:assn]: (((hoare_3067605981109127869le_nat @ D @ B @ C) => (hoare_3067605981109127869le_nat @ (sup_sup_assn @ A @ D) @ B @ C)) <= (hoare_3067605981109127869le_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5121_split__rule)). 87.71/26.56 thf(6309,plain,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn),D:assn]: (((hoare_3067605981109127869le_nat @ D @ B @ (C)) => (hoare_3067605981109127869le_nat @ (sup_sup_assn @ A @ D) @ B @ (C))) | ~ (hoare_3067605981109127869le_nat @ A @ B @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117])). 87.71/26.56 thf(813,axiom,((! [A:nat,B:nat]: (((~ (ord_less_eq_nat @ A @ B)) => (A = (suc @ B))) <= (ord_less_eq_nat @ A @ (suc @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_le__SucE)). 87.71/26.56 thf(5110,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)],[813])). 87.71/26.56 thf(487,axiom,((! [A:int,B:list_int]: ((size_size_list_int @ (cons_int @ A @ B)) = (suc @ (size_size_list_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4666_length__nth__simps_I2_J)). 87.71/26.56 thf(3805,plain,((! [A:int,B:list_int]: ((size_size_list_int @ (cons_int @ A @ B)) = (suc @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[487])). 87.71/26.56 thf(898,axiom,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1070_not__one__le__zero)). 87.71/26.56 thf(5440,plain,((~ (ord_less_eq_nat @ one_one_nat @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[898])). 87.71/26.56 thf(206,axiom,((! [A:nat,B:list_int]: ((B != nil_int) <= (ord_less_nat @ A @ (size_size_list_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8529_len__greater__imp__nonempty)). 87.71/26.56 thf(2651,plain,((! [A:nat,B:list_int]: (~ (B = nil_int) | ~ (ord_less_nat @ A @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[206])). 87.71/26.56 thf(1183,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/sandbox2/benchmark/theBenchmark.p',fact_7926_power__gt1__lemma)). 87.71/26.56 thf(6537,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)],[1183])). 87.71/26.56 thf(1487,axiom,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1589_linorder__not__le)). 87.71/26.56 thf(7684,plain,((! [A:nat,B:nat]: ((~ (ord_less_eq_nat @ A @ B)) = (ord_less_nat @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1487])). 87.71/26.56 thf(1735,axiom,(((times_times_assn @ top_top_assn @ top_top_assn) = top_top_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10149_merge__true__star)). 87.71/26.56 thf(8675,plain,(((times_times_assn @ top_top_assn @ top_top_assn) = top_top_assn)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1735])). 87.71/26.56 thf(1620,axiom,((! [A:nat,B:nat]: (((power_power_nat @ A @ B) = (suc @ zero_zero_nat)) = ((B = zero_zero_nat) | (A = (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7708_nat__power__eq__Suc__0__iff)). 87.71/26.56 thf(8213,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)],[1620])). 87.71/26.56 thf(961,axiom,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1012_one__reorient)). 87.71/26.56 thf(5668,plain,((! [A:nat]: ((one_one_nat = A) = (A = one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[961])). 87.71/26.56 thf(558,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ A @ C) <= (ord_less_eq_nat @ zero_zero_nat @ C)) <= (ord_less_nat @ (power_power_nat @ A @ B) @ (power_power_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7906_power__less__imp__less__base)). 87.71/26.56 thf(4118,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)],[558])). 87.71/26.56 thf(1473,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ (modulo_modulo_nat @ B @ A) @ A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8711_mod__less__divisor)). 87.71/26.56 thf(7617,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)],[1473])). 87.71/26.56 thf(618,axiom,((! [A:list_int,B:nat]: ((foldr_int_nat @ (^ [C:int]: (suc)) @ A @ B) = (plus_plus_nat @ B @ (size_size_list_int @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2735_foldr__length__aux)). 87.71/26.56 thf(4345,plain,((! [A:list_int,B:nat]: ((foldr_int_nat @ (^ [C:int]: (suc)) @ A @ B) = (plus_plus_nat @ B @ (size_size_list_int @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[618])). 87.71/26.56 thf(1394,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/sandbox2/benchmark/theBenchmark.p',fact_8633_div__mult__self__is__m)). 87.71/26.56 thf(7299,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)],[1394])). 87.71/26.56 thf(1697,axiom,((! [A:nat]: (A != (suc @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_n__not__Suc__n)). 87.71/26.56 thf(8493,plain,((! [A:nat]: ~ (A = (suc @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1697])). 87.71/26.56 thf(1366,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((minus_minus_nat @ (plus_plus_nat @ C @ B) @ A) = (plus_plus_nat @ C @ (minus_minus_nat @ B @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3061_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc)). 87.71/26.56 thf(7214,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)],[1366])). 87.71/26.56 thf(915,axiom,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_bot__nat__0_Oextremum__strict)). 87.71/26.56 thf(5500,plain,((! [A:nat]: ~ (ord_less_nat @ A @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[915])). 87.71/26.56 thf(85,axiom,((! [A:list_nat,B:list_real,C:(list_nat > (list_real > $o))]: (((C @ nil_nat @ nil_real) => ((! [D:nat,E:list_nat,F:real,G:list_real]: (((size_size_list_nat @ E) = (size_size_list_real @ G)) => ((C @ E @ G) => (C @ (cons_nat @ D @ E) @ (cons_real @ F @ G))))) => (C @ A @ B))) <= ((size_size_list_nat @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8538_list__induct2)). 87.71/26.56 thf(2127,plain,((! [A:list_nat,B:list_real,C:(list_nat > (list_real > $o))]: (((C @ nil_nat @ nil_real) => ((! [D:nat,E:list_nat,F:real,G:list_real]: (((size_size_list_nat @ E) = (size_size_list_real @ G)) => ((C @ E @ G) => (C @ (cons_nat @ D @ E) @ (cons_real @ F @ G))))) => (C @ A @ B))) | ~ ((size_size_list_nat @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[85])). 87.71/26.56 thf(93,axiom,((! [A:nat,B:nat]: ((nil_nat = (replicate_nat @ A @ B)) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8170_empty__replicate)). 87.71/26.56 thf(2159,plain,((! [A:nat,B:nat]: ((nil_nat = (replicate_nat @ A @ B)) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[93])). 87.71/26.56 thf(1079,axiom,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_mult__0)). 87.71/26.56 thf(6136,plain,((! [A:nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079])). 87.71/26.56 thf(375,axiom,((! [A:int]: ((^ [B:int]: (times_times_int @ B @ A)) = (times_times_int @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5688_mult__commute__abs)). 87.71/26.56 thf(3362,plain,((! [A:int]: ((^ [B:int]: (times_times_int @ B @ A)) = (times_times_int @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[375])). 87.71/26.56 thf(221,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ C))) => ((ord_less_nat @ A @ (divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) <= (ord_less_eq_nat @ C @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9068_less__two__pow__divI)). 87.71/26.56 thf(2731,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ A @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ B @ C))) => ((ord_less_nat @ A @ (divide_divide_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C))) | ~ (ord_less_eq_nat @ C @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[221])). 87.71/26.56 thf(322,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) => (ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ C @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9053_nat__power__less__diff)). 87.71/26.56 thf(3128,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A) @ B) @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ C)) => (ord_less_nat @ B @ (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (minus_minus_nat @ C @ A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[322])). 87.71/26.56 thf(562,axiom,((! [A:nat,B:nat,C:nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2172_add_Oassoc)). 87.71/26.56 thf(4129,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)],[562])). 87.71/26.56 thf(1240,axiom,((! [A:(num > nat),B:num]: ((size_option_num @ A @ (some_num @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2489_option_Osize__gen_I2_J)). 87.71/26.56 thf(6750,plain,((! [A:(num > nat),B:num]: ((size_option_num @ (A) @ (some_num @ B)) = (plus_plus_nat @ (A @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240])). 87.71/26.56 thf(1555,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ A @ (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2823_diff__diff__left)). 87.71/26.56 thf(7987,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)],[1555])). 87.71/26.56 thf(1073,axiom,((! [A:list_int,B:heap_e7401611519738050253t_unit]: ((time_time_array_int @ (array_of_list_int @ A) @ B) = (plus_plus_nat @ (size_size_list_int @ A) @ one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4786_time__array__of__list)). 87.71/26.56 thf(6099,plain,((! [A:list_int,B:heap_e7401611519738050253t_unit]: ((time_time_array_int @ (array_of_list_int @ A) @ B) = (plus_plus_nat @ (size_size_list_int @ A) @ one_one_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073])). 87.71/26.56 thf(1653,axiom,((! [A:assn]: ((^ [B:assn]: (times_times_assn @ B @ A)) = (times_times_assn @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5689_mult__commute__abs)). 87.71/26.56 thf(8328,plain,((! [A:assn]: ((^ [B:assn]: (times_times_assn @ B @ A)) = (times_times_assn @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1653])). 87.71/26.56 thf(303,axiom,((! [A:nat]: (ord_less_eq_nat @ A @ (bit_se2002935070580805687sk_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9865_less__eq__mask)). 87.71/26.56 thf(3057,plain,((! [A:nat]: (ord_less_eq_nat @ A @ (bit_se2002935070580805687sk_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[303])). 87.71/26.56 thf(243,axiom,((! [A:real,B:list_real]: ((size_size_list_real @ (cons_real @ A @ B)) = (suc @ (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4663_length__nth__simps_I2_J)). 87.71/26.56 thf(2803,plain,((! [A:real,B:list_real]: ((size_size_list_real @ (cons_real @ A @ B)) = (suc @ (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[243])). 87.71/26.56 thf(1260,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (B != A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__not__refl2)). 87.71/26.56 thf(6807,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ B) => (~ (B = A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260])). 87.71/26.56 thf(249,axiom,((! [A:nat,B:nat]: ((size_size_list_nat @ (replicate_nat @ A @ B)) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3261_length__replicate)). 87.71/26.56 thf(2847,plain,((! [A:nat,B:nat]: ((size_size_list_nat @ (replicate_nat @ A @ B)) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[249])). 87.71/26.56 thf(627,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/sandbox2/benchmark/theBenchmark.p',fact_9456_dvd__pos__nat)). 87.71/26.56 thf(4382,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)],[627])). 87.71/26.56 thf(437,axiom,((! [A:list_o,B:list_o]: (((size_size_list_o @ A) != (size_size_list_o @ B)) => (A != B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2552_neq__if__length__neq)). 87.71/26.56 thf(3605,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)],[437])). 87.71/26.56 thf(65,axiom,((! [A:list_real,B:list_o,C:list_real,D:(list_real > (list_o > (list_real > $o)))]: ((((D @ nil_real @ nil_o @ nil_real) => ((D @ A @ B @ C) <= (! [E:real,F:list_real,G:$o,H:list_o,I:real,J:list_real]: ((((D @ (cons_real @ E @ F) @ (cons_o @ G @ H) @ (cons_real @ I @ J)) <= (D @ F @ H @ J)) <= ((size_size_list_o @ H) = (size_size_list_real @ J))) <= ((size_size_list_real @ F) = (size_size_list_o @ H)))))) <= ((size_size_list_o @ B) = (size_size_list_real @ C))) <= ((size_size_list_real @ A) = (size_size_list_o @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8544_list__induct3)). 87.71/26.56 thf(1976,plain,((! [A:list_real,B:list_o,C:list_real,D:(list_real > (list_o > (list_real > $o)))]: (((D @ nil_real @ nil_o @ nil_real) => ((D @ A @ B @ C) | ~ (! [E:real,F:list_real,G:$o,H:list_o,I:real,J:list_real]: ((D @ (cons_real @ E @ F) @ (cons_o @ G @ H) @ (cons_real @ I @ J)) | ~ (D @ F @ H @ J) | ~ ((size_size_list_o @ H) = (size_size_list_real @ J)) | ~ ((size_size_list_real @ F) = (size_size_list_o @ H)))))) | ~ ((size_size_list_o @ B) = (size_size_list_real @ C)) | ~ ((size_size_list_real @ A) = (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[65])). 87.71/26.56 thf(1583,axiom,(((size_size_option_nat @ none_nat) = (suc @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_option_Osize_I3_J)). 87.71/26.56 thf(8093,plain,(((size_size_option_nat @ none_nat) = (suc @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1583])). 87.71/26.56 thf(1042,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (semiri1316708129612266289at_nat @ A) @ B) = (times_times_nat @ B @ (semiri1316708129612266289at_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4630_mult__of__nat__commute)). 87.71/26.56 thf(5975,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)],[1042])). 87.71/26.56 thf(664,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ A @ C)) = (ord_less_eq_nat @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2091_add__le__cancel__left)). 87.71/26.56 thf(4506,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)],[664])). 87.71/26.56 thf(1335,axiom,((! [A:nat,B:nat]: (((times_times_nat @ A @ B) = one_one_nat) = ((B = one_one_nat) & (A = one_one_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_990_nat__mult__eq__1__iff)). 87.71/26.56 thf(7071,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)],[1335])). 87.71/26.56 thf(542,axiom,((! [A:nat,B:nat,C:nat]: ((modulo_modulo_nat @ (suc @ (plus_plus_nat @ A @ (times_times_nat @ B @ C))) @ B) = (modulo_modulo_nat @ (suc @ A) @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8698_Suc__mod__mult__self2)). 87.71/26.56 thf(4066,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)],[542])). 87.71/26.56 thf(856,axiom,((! [A:nat,B:nat,C:nat]: ((B = C) <= ((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2190_add__left__imp__eq)). 87.71/26.56 thf(5280,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)],[856])). 87.71/26.56 thf(408,axiom,((! [A:list_int,B:list_real,C:list_nat,D:list_o,E:(list_int > (list_real > (list_nat > (list_o > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => (((size_size_list_real @ B) = (size_size_list_nat @ C)) => ((((! [F:int,G:list_int,H:real,I:list_real,J:nat,K:list_nat,L:$o,M:list_o]: (((size_size_list_int @ G) = (size_size_list_real @ I)) => (((size_size_list_real @ I) = (size_size_list_nat @ K)) => (((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_nat @ J @ K) @ (cons_o @ L @ M)) <= (E @ G @ I @ K @ M)) <= ((size_size_list_nat @ K) = (size_size_list_o @ M)))))) => (E @ A @ B @ C @ D)) <= (E @ nil_int @ nil_real @ nil_nat @ nil_o)) <= ((size_size_list_nat @ C) = (size_size_list_o @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8559_list__induct4)). 87.71/26.56 thf(3489,plain,((! [A:list_int,B:list_real,C:list_nat,D:list_o,E:(list_int > (list_real > (list_nat > (list_o > $o))))]: (((size_size_list_int @ A) = (size_size_list_real @ B)) => (((size_size_list_real @ B) = (size_size_list_nat @ C)) => (((! [F:int,G:list_int,H:real,I:list_real,J:nat,K:list_nat,L:$o,M:list_o]: (((size_size_list_int @ G) = (size_size_list_real @ I)) => (((size_size_list_real @ I) = (size_size_list_nat @ K)) => ((E @ (cons_int @ F @ G) @ (cons_real @ H @ I) @ (cons_nat @ J @ K) @ (cons_o @ L @ M)) | ~ (E @ G @ I @ K @ M) | ~ ((size_size_list_nat @ K) = (size_size_list_o @ M)))))) => (E @ A @ B @ C @ D)) | ~ (E @ nil_int @ nil_real @ nil_nat @ nil_o) | ~ ((size_size_list_nat @ C) = (size_size_list_o @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[408])). 87.71/26.56 thf(1411,axiom,((! [A:nat,B:nat]: ((power_power_nat @ A @ (suc @ B)) = (times_times_nat @ (power_power_nat @ A @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7879_power__Suc2)). 87.71/26.56 thf(7387,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)],[1411])). 87.71/26.56 thf(172,axiom,((! [A:nat]: ((ord_less_nat @ zero_zero_nat @ (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))) = ((modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one))) = one_one_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9017_mod2__gr__0)). 87.71/26.56 thf(2507,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)],[172])). 87.71/26.56 thf(1408,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ B @ (suc @ A)) = (B = A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_le__less__Suc__eq)). 87.71/26.56 thf(7370,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)],[1408])). 87.71/26.56 thf(385,axiom,((! [A:list_real]: ((ord_less_nat @ zero_zero_nat @ (size_size_list_real @ A)) = (A != nil_real)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8250_length__greater__0__conv)). 87.71/26.56 thf(3392,plain,((! [A:list_real]: ((ord_less_nat @ zero_zero_nat @ (size_size_list_real @ A)) = (~ (A = nil_real))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[385])). 87.71/26.56 thf(1322,axiom,((! [A:(nat > $o),B:nat]: ((ord_less_nat @ B @ zero_zero_nat) => (A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_forall__finite_I1_J)). 87.71/26.56 thf(7025,plain,((! [A:(nat > $o),B:nat]: ((ord_less_nat @ B @ zero_zero_nat) => (A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322])). 87.71/26.56 thf(1128,axiom,((! [A:list_nat,B:list_nat]: ((A != B) <= ((size_size_list_nat @ A) != (size_size_list_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_size__neq__size__imp__neq)). 87.71/26.56 thf(6348,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)],[1128])). 87.71/26.56 thf(987,axiom,((bot_bot_assn != one_one_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1734_assn__basic__inequalities_I3_J)). 87.71/26.56 thf(5774,plain,((~ (bot_bot_assn = one_one_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[987])). 87.71/26.56 thf(420,axiom,((! [A:nat,B:list_nat]: ((times_times_nat @ A @ (foldl_nat_nat @ times_times_nat @ one_one_nat @ B)) = (foldl_nat_nat @ times_times_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4702_foldl__absorb1)). 87.71/26.56 thf(3538,plain,((! [A:nat,B:list_nat]: ((times_times_nat @ A @ (foldl_nat_nat @ (times_times_nat) @ one_one_nat @ B)) = (foldl_nat_nat @ (times_times_nat) @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[420])). 87.71/26.56 thf(508,axiom,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se545348938243370406it_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ B @ (minus_minus_nat @ C @ A)) & (ord_less_eq_nat @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10114_bit__push__bit__iff__int)). 87.71/26.56 thf(3939,plain,((! [A:nat,B:int,C:nat]: ((bit_se1146084159140164899it_int @ (bit_se545348938243370406it_int @ A @ B) @ C) = ((bit_se1146084159140164899it_int @ B @ (minus_minus_nat @ C @ A)) & (ord_less_eq_nat @ A @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[508])). 87.71/26.56 thf(181,axiom,((! [A:nat,B:nat,C:(int > $o),D:int]: ((ord_less_nat @ A @ B) => ((C @ (nth_int @ (replicate_int @ B @ D) @ A)) <= (C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3237_intind)). 87.71/26.56 thf(2539,plain,((! [A:nat,B:nat,C:(int > $o),D:int]: ((ord_less_nat @ A @ B) => ((C @ (nth_int @ (replicate_int @ B @ D) @ A)) | ~ (C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[181])). 87.71/26.56 thf(1737,axiom,((! [A:array_VEBT_VEBTi,B:list_VEBT_VEBTi]: (hoare_3904069481286416050_VEBTi @ (snga_assn_VEBT_VEBTi @ A @ B) @ (array_8141364883501958055_VEBTi @ A) @ (^ [C:list_VEBT_VEBTi]: (times_times_assn @ (snga_assn_VEBT_VEBTi @ A @ B) @ (pure_assn @ (C = B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4432_freeze__rule)). 87.71/26.56 thf(8680,plain,((! [A:array_VEBT_VEBTi,B:list_VEBT_VEBTi]: (hoare_3904069481286416050_VEBTi @ (snga_assn_VEBT_VEBTi @ A @ B) @ (array_8141364883501958055_VEBTi @ A) @ (^ [C:list_VEBT_VEBTi]: (times_times_assn @ (snga_assn_VEBT_VEBTi @ A @ B) @ (pure_assn @ (C = B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1737])). 87.71/26.56 thf(308,axiom,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ ($true) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2337_VEBT__internal_OminNull_Osimps_I2_J)). 87.71/26.56 thf(3076,plain,((! [A:$o]: ~ (vEBT_VEBT_minNull @ (vEBT_Leaf @ ($true) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[308])). 87.71/26.56 thf(317,axiom,(((pure_assn @ ($true)) = one_one_assn)),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1732_pure__true)). 87.71/26.56 thf(3113,plain,(((pure_assn @ ($true)) = one_one_assn)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[317])). 87.71/26.56 thf(1250,axiom,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_le__zero__eq)). 87.71/26.56 thf(6778,plain,((! [A:nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250])). 87.71/26.56 thf(166,axiom,((! [A:list_o]: ((ord_less_nat @ zero_zero_nat @ (size_size_list_o @ A)) = (A != nil_o)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8251_length__greater__0__conv)). 87.71/26.56 thf(2484,plain,((! [A:list_o]: ((ord_less_nat @ zero_zero_nat @ (size_size_list_o @ A)) = (~ (A = nil_o))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[166])). 87.71/26.56 thf(1718,axiom,((! [A:nat]: ((~ (! [B:nat]: (A != (suc @ B)))) <= (A != zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_old_Onat_Oexhaust)). 87.71/26.56 thf(8570,plain,((! [A:nat]: (~ (! [B:nat]: ~ (A = (suc @ B))) | (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1718])). 87.71/26.56 thf(908,axiom,((! [A:assn,B:assn]: ((bot_bot_assn = (sup_sup_assn @ A @ B)) = ((B = bot_bot_assn) & (A = bot_bot_assn))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5079_sup__bot_Oneutr__eq__iff)). 87.71/26.56 thf(5473,plain,((! [A:assn,B:assn]: ((bot_bot_assn = (sup_sup_assn @ A @ B)) = ((B = bot_bot_assn) & (A = bot_bot_assn))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[908])). 87.71/26.56 thf(139,axiom,((! [A:nat,B:list_int]: ((size_size_list_int @ (drop_int @ A @ B)) = (minus_minus_nat @ (size_size_list_int @ B) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7730_length__drop)). 87.71/26.56 thf(2372,plain,((! [A:nat,B:list_int]: ((size_size_list_int @ (drop_int @ A @ B)) = (minus_minus_nat @ (size_size_list_int @ B) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[139])). 87.71/26.56 thf(260,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/sandbox2/benchmark/theBenchmark.p',fact_8863_fact__less__mono__nat)). 87.71/26.56 thf(2879,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)],[260])). 87.71/26.56 thf(1452,axiom,((! [A:nat,B:nat,C:nat]: (((suc @ A) = (plus_plus_nat @ B @ (suc @ C))) <= (A = (plus_plus_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2309_nat__arith_Osuc1)). 87.71/26.56 thf(7553,plain,((! [A:nat,B:nat,C:nat]: (((suc @ A) = (plus_plus_nat @ B @ (suc @ C))) | ~ (A = (plus_plus_nat @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1452])). 87.71/26.56 thf(1407,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/sandbox2/benchmark/theBenchmark.p',fact_8888_binomial__fact__lemma)). 87.71/26.56 thf(7367,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)],[1407])). 87.71/26.56 thf(1564,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3017_diff__le__mono2)). 87.71/26.56 thf(8023,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (minus_minus_nat @ C @ B) @ (minus_minus_nat @ C @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1564])). 87.71/26.56 thf(774,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/sandbox2/benchmark/theBenchmark.p',fact_561_mint__corr__help)). 87.71/26.56 thf(4949,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)],[774])). 87.71/26.56 thf(255,axiom,((times_times_real = (^ [A:real,B:real]: (times_times_real @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_ab__semigroup__mult__class_Omult_Ocommute)). 87.71/26.56 thf(2866,plain,(((times_times_real) = (^ [A:real,B:real]: (times_times_real @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[255])). 87.71/26.56 thf(1611,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/sandbox2/benchmark/theBenchmark.p',fact_10143_min__Suc1)). 87.71/26.56 thf(8179,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)],[1611])). 87.71/26.56 thf(1533,axiom,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C))) <= (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_lift__Suc__mono__less)). 87.71/26.56 thf(7893,plain,((! [A:(nat > nat),B:nat,C:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (A @ B) @ (A @ C))) | ~ (! [D:nat]: (ord_less_nat @ (A @ D) @ (A @ (suc @ D))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1533])). 87.71/26.56 thf(1423,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/sandbox2/benchmark/theBenchmark.p',fact_8049_power__minus__mult)). 87.71/26.56 thf(7424,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)],[1423])). 87.71/26.56 thf(574,axiom,((! [A:nat,B:list_VEBT_VEBT,C:vEBT_VEBT]: (vEBT_VEBT_minNull @ (vEBT_Node @ none_P5556105721700978146at_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2429_VEBT__internal_OminNull_Osimps_I4_J)). 87.71/26.56 thf(4174,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)],[574])). 87.71/26.56 thf(1281,axiom,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:nat,E:assn,F:(option_nat > assn),G:nat]: ((((! [H:option_nat]: (entails @ (C @ H) @ (F @ H))) => ((ord_less_eq_nat @ D @ G) => (time_htt_option_nat @ E @ B @ F @ G))) <= (entails @ E @ A)) <= (time_htt_option_nat @ A @ B @ C @ D)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4078_htt__cons__rule)). 87.71/26.56 thf(6879,plain,((! [A:assn,B:heap_T2636463487746394924on_nat,C:(option_nat > assn),D:nat,E:assn,F:(option_nat > assn),G:nat]: (((! [H:option_nat]: (entails @ (C @ H) @ (F @ H))) => ((ord_less_eq_nat @ D @ G) => (time_htt_option_nat @ E @ B @ (F) @ G))) | ~ (entails @ E @ A) | ~ (time_htt_option_nat @ A @ B @ (C) @ D)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281])). 87.71/26.56 thf(476,axiom,((! [A:nat,B:nat,C:nat]: ((minus_minus_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (minus_minus_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2803_add__diff__cancel__right)). 87.71/26.56 thf(3753,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)],[476])). 87.71/26.56 thf(512,axiom,((! [A:nat]: (((suc @ (minus_minus_nat @ A @ one_one_nat)) = A) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2885_Suc__diff__1)). 87.71/26.56 thf(3960,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)],[512])). 87.71/26.56 thf(1739,axiom,((! [A:(int > option4927543243414619207at_nat),B:int,C:list_int,D:product_prod_nat_nat,E:list_P6011104703257516679at_nat]: ((map_up4628693354496902621at_nat @ A @ (cons_int @ B @ C) @ (cons_P6512896166579812791at_nat @ D @ E)) = (map_up4628693354496902621at_nat @ (fun_up1740315431458976348at_nat @ A @ B @ (some_P7363390416028606310at_nat @ D)) @ C @ E)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6339_map__upds__Cons)). 87.71/26.56 thf(8685,plain,((! [A:(int > option4927543243414619207at_nat),B:int,C:list_int,D:product_prod_nat_nat,E:list_P6011104703257516679at_nat]: ((map_up4628693354496902621at_nat @ A @ (cons_int @ B @ C) @ (cons_P6512896166579812791at_nat @ D @ E)) = (map_up4628693354496902621at_nat @ (fun_up1740315431458976348at_nat @ A @ B @ (some_P7363390416028606310at_nat @ D)) @ C @ E)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1739])). 87.71/26.56 thf(1361,axiom,((! [A:$o,B:$o]: ~ (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Leaf__0__not)). 87.71/26.56 thf(7195,plain,((! [A:$o,B:$o]: ~ (vEBT_invar_vebt @ (vEBT_Leaf @ A @ B) @ zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361])). 87.71/26.56 thf(804,axiom,((! [A:nat]: (ord_less_eq_nat @ bot_bot_nat @ A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1681_bot_Oextremum)). 87.71/26.56 thf(5073,plain,((! [A:nat]: (ord_less_eq_nat @ bot_bot_nat @ A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[804])). 87.71/26.56 thf(668,axiom,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_lift__Suc__mono__le)). 87.71/26.56 thf(4520,plain,((! [A:(nat > nat),B:nat,C:nat]: ((! [D:nat]: (ord_less_eq_nat @ (A @ D) @ (A @ (suc @ D)))) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ (A @ B) @ (A @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[668])). 87.71/26.56 thf(128,axiom,((! [A:heap_T2636463487746394924on_nat,B:heap_T2636463487746394924on_nat]: ((if_Hea5867803462524415986on_nat @ ($true) @ A @ B) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Heap____Time____Monad__OHeap_It__Option__Ooption_It__Nat__Onat_J_J_T)). 87.71/26.56 thf(2321,plain,((! [A:heap_T2636463487746394924on_nat,B:heap_T2636463487746394924on_nat]: ((if_Hea5867803462524415986on_nat @ ($true) @ A @ B) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[128])). 87.71/26.56 thf(56,axiom,((! [A:nat,B:list_int]: (((last_int @ (drop_int @ A @ B)) = (last_int @ B)) <= (ord_less_nat @ A @ (size_size_list_int @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7773_last__drop)). 87.71/26.56 thf(1944,plain,((! [A:nat,B:list_int]: (((last_int @ (drop_int @ A @ B)) = (last_int @ B)) | ~ (ord_less_nat @ A @ (size_size_list_int @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[56])). 87.71/26.56 thf(698,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_nat @ B @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3103_less__diff__iff)). 87.71/26.56 thf(4627,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ A @ C) => ((ord_less_nat @ (minus_minus_nat @ B @ A) @ (minus_minus_nat @ C @ A)) = (ord_less_nat @ B @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[698])). 87.71/26.56 thf(61,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (vEBT_V441764108873111860ildupi @ B) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ (bit0 @ one)))) @ A)) <= (A = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9126_T__vebt__buildupi__univ)). 87.71/26.56 thf(1962,plain,((! [A:nat,B:nat]: ((ord_less_eq_nat @ (vEBT_V441764108873111860ildupi @ B) @ (times_times_nat @ (numeral_numeral_nat @ (bit0 @ (bit1 @ (bit0 @ one)))) @ A)) | ~ (A = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[61])). 87.71/26.56 thf(1357,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/sandbox2/benchmark/theBenchmark.p',fact_373_one__le__mult__iff)). 87.71/26.56 thf(7181,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)],[1357])). 87.71/26.56 thf(865,axiom,((! [A:nat,B:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ (binomial @ A @ B)) = (times_times_nat @ A @ (binomial @ (minus_minus_nat @ A @ one_one_nat) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8885_binomial__absorb__comp)). 87.71/26.56 thf(5307,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)],[865])). 87.71/26.56 thf(913,axiom,((! [A:array_VEBT_VEBTi,B:list_VEBT_VEBTi,C:list_VEBT_VEBTi]: ((times_times_assn @ (snga_assn_VEBT_VEBTi @ A @ B) @ (snga_assn_VEBT_VEBTi @ A @ C)) = bot_bot_assn))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4247_snga__same__false)). 87.71/26.56 thf(5494,plain,((! [A:array_VEBT_VEBTi,B:list_VEBT_VEBTi,C:list_VEBT_VEBTi]: ((times_times_assn @ (snga_assn_VEBT_VEBTi @ A @ B) @ (snga_assn_VEBT_VEBTi @ A @ C)) = bot_bot_assn))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[913])). 87.71/26.56 thf(1237,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ (minus_minus_nat @ B @ A)) = (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3105_Nat_Ole__diff__conv2)). 87.71/26.56 thf(6733,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)],[1237])). 87.71/26.56 thf(1516,axiom,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ zero_zero_nat)) => (? [C:nat]: (! [D:nat]: ((ord_less_nat @ D @ C) => (~ (A @ D))) & (A @ C) & (ord_less_eq_nat @ C @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_ex__least__nat__le)). 87.71/26.56 thf(7812,plain,((! [A:(nat > $o),B:nat]: ((A @ B) => ((~ (A @ zero_zero_nat)) => (? [C:nat]: (! [D:nat]: ((ord_less_nat @ D @ C) => (~ (A @ D))) & (A @ C) & (ord_less_eq_nat @ C @ B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1516])). 87.71/26.56 thf(831,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_mult__strict__right__mono)). 87.71/26.56 thf(5183,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[831])). 87.71/26.56 thf(290,axiom,((! [A:list_nat]: (((size_size_list_nat @ A) = zero_zero_nat) = (A = nil_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8141_length__0__conv)). 87.71/26.56 thf(2998,plain,((! [A:list_nat]: (((size_size_list_nat @ A) = zero_zero_nat) = (A = nil_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[290])). 87.71/26.56 thf(1758,axiom,((! [A:assn,B:assn,C:nat]: ((power_power_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ (power_power_assn @ A @ C) @ (power_power_assn @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7820_power__mult__distrib)). 87.71/26.56 thf(8741,plain,((! [A:assn,B:assn,C:nat]: ((power_power_assn @ (times_times_assn @ A @ B) @ C) = (times_times_assn @ (power_power_assn @ A @ C) @ (power_power_assn @ B @ C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1758])). 87.71/26.56 thf(1389,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ B @ C) & (ord_less_nat @ zero_zero_nat @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_nat__mult__less__cancel__disj)). 87.71/26.56 thf(7284,plain,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = ((ord_less_nat @ B @ C) & (ord_less_nat @ zero_zero_nat @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389])). 87.71/26.56 thf(1468,axiom,((! [A:nat,B:nat,C:nat]: ((times_times_nat @ (minus_minus_nat @ A @ B) @ C) = (minus_minus_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3025_diff__mult__distrib)). 87.71/26.56 thf(7602,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)],[1468])). 87.71/26.56 thf(1563,axiom,((! [A:$o,B:$o,C:nat]: (((A) => ((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ one_one_nat))) & ((~ (A)) => (((~ (B)) => ((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = none_nat)) & (((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ zero_zero_nat)) <= (B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1702_vebt__pred_Osimps_I3_J)). 87.71/26.56 thf(8006,plain,((! [A:$o,B:$o,C:nat]: (((A) => ((vEBT_vebt_pred @ (vEBT_Leaf @ B @ A) @ (suc @ (suc @ C))) = (some_nat @ one_one_nat))) & ((~ (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)],[1563])). 87.71/26.56 thf(1274,axiom,((! [A:nat]: ((modulo_modulo_nat @ (suc @ zero_zero_nat) @ A) = (zero_n2687167440665602831ol_nat @ (A != (suc @ zero_zero_nat)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9804_Suc__0__mod__eq)). 87.71/26.56 thf(6857,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)],[1274])). 87.71/26.56 thf(728,axiom,((! [A:nat,B:nat]: ((ord_less_eq_nat @ A @ B) => ((semiri1316708129612266289at_nat @ (minus_minus_nat @ B @ A)) = (minus_minus_nat @ (semiri1316708129612266289at_nat @ B) @ (semiri1316708129612266289at_nat @ A)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4726_of__nat__diff)). 87.71/26.56 thf(4752,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)],[728])). 87.71/26.56 thf(1246,axiom,((! [A:int,B:list_int]: ((size_size_list_int @ (cons_int @ A @ B)) = (plus_plus_nat @ (size_size_list_int @ B) @ (suc @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4753_list_Osize_I4_J)). 87.71/26.56 thf(6767,plain,((! [A:int,B:list_int]: ((size_size_list_int @ (cons_int @ A @ B)) = (plus_plus_nat @ (size_size_list_int @ B) @ (suc @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246])). 87.71/26.56 thf(900,axiom,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ C @ (modulo_modulo_nat @ D @ A)) @ B) @ (times_times_nat @ C @ A))) <= (ord_less_nat @ zero_zero_nat @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8740_mod__lemma)). 87.71/26.56 thf(5445,plain,((! [A:nat,B:nat,C:nat,D:nat]: (((ord_less_nat @ B @ C) => (ord_less_nat @ (plus_plus_nat @ (times_times_nat @ C @ (modulo_modulo_nat @ D @ A)) @ B) @ (times_times_nat @ C @ A))) | ~ (ord_less_nat @ zero_zero_nat @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[900])). 87.71/26.56 thf(1345,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) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1958_minf_I1_J)). 87.71/26.56 thf(7108,plain,((! [A:(nat > $o),B:(nat > $o),C:(nat > $o),D:(nat > $o)]: ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((A @ F) = (B @ F)))) => ((? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => ((C @ F) = (D @ F)))) => (? [E:nat]: ! [F:nat]: ((ord_less_nat @ F @ E) => (((C @ F) & (A @ F)) = ((D @ F) & (B @ F))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345])). 87.71/26.56 thf(1572,axiom,((! [A:$o,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ (pure_assn @ A) @ B @ C) <= ((hoare_1429296392585015714_VEBTi @ one_one_assn @ B @ C) <= (A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1744_norm__pre__pure__rule2)). 87.71/26.56 thf(8055,plain,((! [A:$o,B:heap_T8145700208782473153_VEBTi,C:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ (pure_assn @ A) @ B @ (C)) | ~ ((hoare_1429296392585015714_VEBTi @ one_one_assn @ B @ (C)) | ~ (A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1572])). 87.71/26.56 thf(1244,axiom,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1740_norm__assertion__simps_I1_J)). 87.71/26.56 thf(6761,plain,((! [A:assn]: ((times_times_assn @ one_one_assn @ A) = A))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244])). 87.71/26.56 thf(1594,axiom,((! [A:nat]: ((binomial @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8870_binomial__0__Suc)). 87.71/26.56 thf(8130,plain,((! [A:nat]: ((binomial @ zero_zero_nat @ (suc @ A)) = zero_zero_nat))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1594])). 87.71/26.56 thf(393,axiom,((! [A:product_prod_nat_nat,B:product_prod_nat_nat]: ((if_Pro6206227464963214023at_nat @ ($false) @ A @ B) = B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T)). 87.71/26.56 thf(3432,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)],[393])). 87.71/26.56 thf(198,axiom,((! [A:list_nat,B:list_o,C:(list_nat > (list_o > $o))]: (((C @ nil_nat @ nil_o) => ((! [D:nat,E:list_nat,F:$o,G:list_o]: (((C @ E @ G) => (C @ (cons_nat @ D @ E) @ (cons_o @ F @ G))) <= ((size_size_list_nat @ E) = (size_size_list_o @ G)))) => (C @ A @ B))) <= ((size_size_list_nat @ A) = (size_size_list_o @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8539_list__induct2)). 87.71/26.56 thf(2615,plain,((! [A:list_nat,B:list_o,C:(list_nat > (list_o > $o))]: (((C @ nil_nat @ nil_o) => ((! [D:nat,E:list_nat,F:$o,G:list_o]: (((C @ E @ G) => (C @ (cons_nat @ D @ E) @ (cons_o @ F @ G))) | ~ ((size_size_list_nat @ E) = (size_size_list_o @ G)))) => (C @ A @ B))) | ~ ((size_size_list_nat @ A) = (size_size_list_o @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[198])). 87.71/26.56 thf(1724,axiom,((! [A:assn,B:$o,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ D) = ((B) => (hoare_1429296392585015714_VEBTi @ A @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_norm__pre__pure__iff)). 87.71/26.56 thf(8596,plain,((! [A:assn,B:$o,C:heap_T8145700208782473153_VEBTi,D:(vEBT_VEBTi > assn)]: ((hoare_1429296392585015714_VEBTi @ (times_times_assn @ A @ (pure_assn @ B)) @ C @ (D)) = ((B) => (hoare_1429296392585015714_VEBTi @ A @ C @ (D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1724])). 87.71/26.56 thf(1385,axiom,((! [A:nat,B:nat,C:nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ (plus_plus_nat @ C @ B)) = (ord_less_nat @ A @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2103_add__less__cancel__right)). 87.71/26.56 thf(7274,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)],[1385])). 87.71/26.56 thf(783,axiom,((! [A:nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9453_gcd__nat_Oextremum__unique)). 87.71/26.56 thf(4977,plain,((! [A:nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[783])). 87.71/26.56 thf(539,axiom,((! [A:nat,B:nat]: (((plus_plus_nat @ A @ B) = zero_zero_nat) = ((A = zero_zero_nat) & (B = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2082_add__eq__0__iff__both__eq__0)). 87.71/26.56 thf(4056,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)],[539])). 87.71/26.56 thf(1229,axiom,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => ((? [D:nat]: (! [E:nat]: ((ord_less_eq_nat @ E @ D) <= (A @ E)) & (A @ D))) <= (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_Nat_Oex__has__greatest__nat)). 87.71/26.56 thf(6686,plain,((! [A:(nat > $o),B:nat,C:nat]: ((A @ B) => (? [D:nat]: (! [E:nat]: ((ord_less_eq_nat @ E @ D) | ~ (A @ E)) & (A @ D)) | ~ (! [D:nat]: ((A @ D) => (ord_less_eq_nat @ D @ C))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229])). 87.71/26.56 thf(1146,axiom,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (minus_minus_nat @ B @ A) @ C) = (ord_less_nat @ B @ (plus_plus_nat @ C @ A))) <= (ord_less_eq_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3145_less__diff__conv2)). 87.71/26.56 thf(6404,plain,((! [A:nat,B:nat,C:nat]: (((ord_less_nat @ (minus_minus_nat @ B @ A) @ C) = (ord_less_nat @ B @ (plus_plus_nat @ C @ A))) | ~ (ord_less_eq_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146])). 87.71/26.56 thf(749,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) <= (ord_less_eq_nat @ B @ zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2464_add__neg__nonpos)). 87.71/26.56 thf(4863,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat) | ~ (ord_less_eq_nat @ B @ zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[749])). 87.71/26.56 thf(97,axiom,((! [A:nat]: ((suc @ (bit_se2002935070580805687sk_nat @ A)) = (power_power_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9867_Suc__mask__eq__exp)). 87.71/26.56 thf(2170,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)],[97])). 87.71/26.56 thf(1270,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:$o,D:nat]: (A != (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_873_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases)). 87.71/26.56 thf(6839,plain,((! [A:produc9072475918466114483BT_nat]: (((! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ (suc @ zero_zero_nat) @ C @ D) @ E))) => (~ (! [B:nat,C:nat,D:nat,E:list_VEBT_VEBT,F:vEBT_VEBT,G:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ (product_Pair_nat_nat @ B @ C)) @ (suc @ (suc @ D)) @ E @ F) @ G))))) | ~ (! [B:product_prod_nat_nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ (some_P7363390416028606310at_nat @ B) @ zero_zero_nat @ C @ D) @ E))) | ~ (! [B:nat,C:list_VEBT_VEBT,D:vEBT_VEBT,E:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Node @ none_P5556105721700978146at_nat @ B @ C @ D) @ E))) | ~ (! [B:$o,C:$o,D:nat]: ~ (A = (produc738532404422230701BT_nat @ (vEBT_Leaf @ B @ C) @ D)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270])). 87.71/26.56 thf(977,axiom,((! [A:nat,B:nat]: (((some_nat @ A) = (some_nat @ B)) = (A = B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_option_Oinject)). 87.71/26.56 thf(5732,plain,((! [A:nat,B:nat]: (((some_nat @ A) = (some_nat @ B)) = (A = B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[977])). 87.71/26.56 thf(341,axiom,((! [A:list_real,B:list_real,C:list_nat,D:(list_real > (list_real > (list_nat > $o)))]: ((((size_size_list_real @ B) = (size_size_list_nat @ C)) => ((D @ nil_real @ nil_real @ nil_nat) => ((! [E:real,F:list_real,G:real,H:list_real,I:nat,J:list_nat]: (((size_size_list_real @ F) = (size_size_list_real @ H)) => (((D @ (cons_real @ E @ F) @ (cons_real @ G @ H) @ (cons_nat @ I @ J)) <= (D @ F @ H @ J)) <= ((size_size_list_real @ H) = (size_size_list_nat @ J))))) => (D @ A @ B @ C)))) <= ((size_size_list_real @ A) = (size_size_list_real @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8542_list__induct3)). 87.71/26.56 thf(3200,plain,((! [A:list_real,B:list_real,C:list_nat,D:(list_real > (list_real > (list_nat > $o)))]: ((((size_size_list_real @ B) = (size_size_list_nat @ C)) => ((D @ nil_real @ nil_real @ nil_nat) => ((! [E:real,F:list_real,G:real,H:list_real,I:nat,J:list_nat]: (((size_size_list_real @ F) = (size_size_list_real @ H)) => ((D @ (cons_real @ E @ F) @ (cons_real @ G @ H) @ (cons_nat @ I @ J)) | ~ (D @ F @ H @ J) | ~ ((size_size_list_real @ H) = (size_size_list_nat @ J))))) => (D @ A @ B @ C)))) | ~ ((size_size_list_real @ A) = (size_size_list_real @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[341])). 87.71/26.56 thf(1221,axiom,((! [A:assn,B:heap_Time_Heap_nat,C:(nat > assn)]: ((hoare_3067605981109127869le_nat @ A @ B @ C) => (hoare_3067605981109127869le_nat @ A @ B @ C)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_is__hoare__triple)). 87.71/26.56 thf(6668,plain,(($true)),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221])). 87.71/26.56 thf(14,axiom,((! [A:nat]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ A) = (modulo_modulo_nat @ A @ (numeral_numeral_nat @ (bit0 @ one)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9845_Suc__0__and__eq)). 87.71/26.56 thf(1812,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)],[14])). 87.71/26.56 thf(771,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 @ E) @ C) @ (plus_plus_nat @ (times_times_nat @ B @ E) @ D)) <= (ord_less_eq_nat @ C @ D))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2427_mlex__leI)). 87.71/26.56 thf(4940,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 @ E) @ C) @ (plus_plus_nat @ (times_times_nat @ B @ E) @ D)) | ~ (ord_less_eq_nat @ C @ D))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[771])). 87.71/26.56 thf(1025,axiom,((! [A:$o,B:assn]: ((entails @ (pure_assn @ A) @ B) = ((A) => (entails @ one_one_assn @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4051_ent__pure__pre__iff__sng)). 87.71/26.56 thf(5911,plain,((! [A:$o,B:assn]: ((entails @ (pure_assn @ A) @ B) = ((A) => (entails @ one_one_assn @ B))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025])). 87.71/26.56 thf(604,axiom,((! [A:nat,B:nat]: ((semiri1316708129612266289at_nat @ (times_times_nat @ A @ B)) = (times_times_nat @ (semiri1316708129612266289at_nat @ A) @ (semiri1316708129612266289at_nat @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4583_of__nat__mult)). 87.71/26.56 thf(4298,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)],[604])). 87.71/26.56 thf(207,axiom,((! [A:list_real,B:list_o,C:list_o,D:(list_real > (list_o > (list_o > $o)))]: (((size_size_list_real @ A) = (size_size_list_o @ B)) => (((D @ nil_real @ nil_o @ nil_o) => ((! [E:real,F:list_real,G:$o,H:list_o,I:$o,J:list_o]: ((((D @ F @ H @ J) => (D @ (cons_real @ E @ F) @ (cons_o @ G @ H) @ (cons_o @ I @ J))) <= ((size_size_list_o @ H) = (size_size_list_o @ J))) <= ((size_size_list_real @ F) = (size_size_list_o @ H)))) => (D @ A @ B @ C))) <= ((size_size_list_o @ B) = (size_size_list_o @ C)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8545_list__induct3)). 87.71/26.56 thf(2655,plain,((! [A:list_real,B:list_o,C:list_o,D:(list_real > (list_o > (list_o > $o)))]: (((size_size_list_real @ A) = (size_size_list_o @ B)) => (((D @ nil_real @ nil_o @ nil_o) => ((! [E:real,F:list_real,G:$o,H:list_o,I:$o,J:list_o]: (((D @ F @ H @ J) => (D @ (cons_real @ E @ F) @ (cons_o @ G @ H) @ (cons_o @ I @ J))) | ~ ((size_size_list_o @ H) = (size_size_list_o @ J)) | ~ ((size_size_list_real @ F) = (size_size_list_o @ H)))) => (D @ A @ B @ C))) | ~ ((size_size_list_o @ B) = (size_size_list_o @ C)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[207])). 87.71/26.56 thf(526,axiom,((! [A:nat,B:nat]: (((suc @ (minus_minus_nat @ B @ (suc @ A))) = (minus_minus_nat @ B @ A)) <= (ord_less_nat @ A @ B)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3094_Suc__diff__Suc)). 87.71/26.56 thf(4002,plain,((! [A:nat,B:nat]: (((suc @ (minus_minus_nat @ B @ (suc @ A))) = (minus_minus_nat @ B @ A)) | ~ (ord_less_nat @ A @ B)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[526])). 87.71/26.56 thf(34,axiom,((! [A:num]: ((bit_se727722235901077358nd_nat @ (suc @ zero_zero_nat) @ (numeral_numeral_nat @ (bit0 @ A))) = zero_zero_nat))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9840_and__nat__numerals_I1_J)). 87.71/26.56 thf(1870,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)],[34])). 87.71/26.56 thf(1659,axiom,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (? [C:nat]: ((A = (suc @ C)) & (ord_less_nat @ C @ B)) | (A = zero_zero_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_less__Suc__eq__0__disj)). 87.71/26.56 thf(8348,plain,((! [A:nat,B:nat]: ((ord_less_nat @ A @ (suc @ B)) = (? [C:nat]: ((A = (suc @ C)) & (ord_less_nat @ C @ B)) | (A = zero_zero_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[1659])). 87.71/26.56 thf(233,axiom,((! [A:nat,B:nat]: ((replicate_nat @ (suc @ A) @ B) = (append_nat @ (replicate_nat @ A @ B) @ (cons_nat @ B @ nil_nat))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8441_replicate__Suc__conv__snoc)). 87.71/26.56 thf(2771,plain,((! [A:nat,B:nat]: ((replicate_nat @ (suc @ A) @ B) = (append_nat @ (replicate_nat @ A @ B) @ (cons_nat @ B @ nil_nat))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[233])). 87.71/26.56 thf(8848,plain,(($false)),inference(e,[status(thm)],[4447,3944,5593,6712,3969,5999,6986,5131,8536,2199,8062,2630,3873,4201,7373,6387,5116,6979,2612,2744,6669,6355,7890,4005,7569,8288,5260,8663,6976,3661,4062,3666,4729,3167,8114,2876,5320,6283,4290,8338,3698,3979,5390,6285,2463,1840,4852,5654,5676,6317,7990,3566,5028,6566,6954,7396,4931,8417,2512,4075,3813,6219,2590,7253,5224,4326,8045,6480,4532,6057,3185,8005,6576,3072,2210,5141,6944,7517,4500,8723,7409,5718,2231,3858,5644,2908,2062,3549,3509,6619,6813,4391,8682,4697,8118,5625,5878,6798,2014,5793,5173,4711,6830,6426,7850,7781,5691,4614,2854,8563,4479,6194,3217,6278,7573,6127,3175,6089,5316,4856,6078,5163,7188,3562,3717,4762,8303,7793,8320,8182,4633,6764,8765,6505,6401,5565,3049,4739,7431,3004,6246,3367,3648,3942,3135,4097,4884,3365,6665,8747,7096,2434,6416,8342,5701,3616,1919,8210,7716,2844,6804,3577,6894,7980,2146,4980,4047,6570,6914,8325,4496,8578,4618,8472,5301,4198,2173,6102,3878,3688,7390,7605,3370,7944,5252,7064,3994,7637,1782,8539,3249,4371,6872,3513,7734,8133,5476,5921,7240,1935,8256,5903,8165,7856,4030,4963,6483,7178,4467,8224,7592,7993,5024,4637,4539,7790,7620,5284,7652,3776,5160,5461,6892,2603,2916,7277,8500,4348,7279,7914,4866,6552,1792,7262,4563,6034,7825,7696,4956,7418,5883,3574,8806,3061,6423,2708,3821,4654,1860,4334,3125,5150,6676,6315,4275,3749,2562,1992,7000,4568,4766,6208,3855,8121,8278,6502,4179,6579,5480,3470,3657,5746,2989,8483,4514,3788,1922,7862,1892,5256,2857,5866,8389,6455,6905,7124,7209,7803,6149,4928,5397,5622,6781,8367,7047,4368,8384,2520,8703,3708,2301,1815,4460,8037,1875,8738,5020,3602,6382,3258,5663,6227,2451,6534,3357,5135,4115,2777,8411,2178,5682,5787,5957,4205,2237,7492,7144,4329,3966,2324,8029,4583,4903,5084,7564,4072,7290,7175,5013,1911,3295,2782,7247,6657,3670,4733,5333,5856,3473,3702,7775,8791,5558,5946,3438,7926,4050,4815,6176,8065,1828,3621,6964,5804,5156,8526,3569,6559,4556,2073,4162,7899,6562,5448,6755,5169,5489,3226,8443,6616,7354,3389,7707,1843,6591,4718,8438,2437,1928,6451,8001,4033,3739,5096,2190,5375,5384,5101,7004,3685,8306,5648,1886,8406,6947,3808,2523,3036,4364,6221,5296,3157,7645,5343,5246,4307,5897,6772,4825,6863,8691,3756,6021,2799,2639,4379,3559,3211,2392,8033,2718,6860,4475,2884,7882,7230,3229,7533,7022,8078,5017,6588,7269,7642,6307,6200,8523,3435,7952,4700,2954,7321,8508,2011,3450,3503,5875,4216,4323,8655,3303,4589,4407,5751,6015,7393,3720,5411,3984,7550,6047,6684,2164,5438,6139,5968,7885,5070,5291,7019,5562,7357,8250,4100,2496,4059,1868,8668,7999,2000,6464,4925,6092,8712,3735,2409,6635,2249,7710,7428,3778,8513,5206,7730,3261,6343,2601,8778,6122,5630,3711,2733,8168,7703,3972,4878,6528,4989,5044,5455,5815,5366,3069,8550,7084,5470,7640,4449,8081,4493,5754,4284,2150,6496,5507,2414,4836,4661,6232,7244,3682,5924,3286,6582,1883,2958,2873,6432,4849,4155,3556,6556,4385,4553,6143,5341,7713,6060,3926,2112,8136,7308,7237,6646,1837,5937,8672,4608,7576,8026,8700,4053,2477,3090,8651,6848,2565,8145,7902,5534,2068,1819,5551,3546,5038,4746,3535,5113,6392,2547,3763,2492,7853,2741,5729,8287,2228,4680,8403,5330,8358,8073,6888,6709,7608,6413,5270,7917,5798,2692,3237,6215,6728,8297,5313,7346,5189,8694,3467,8530,8446,5714,5609,2115,7421,5221,2515,1851,5098,8677,3122,5238,6335,5673,4974,1804,6375,7623,6477,8414,5635,3381,8041,4693,5428,8768,3518,3963,1878,3386,2726,5919,5978,6941,4095,3119,3746,6624,8567,7204,7222,7468,7809,3440,4219,5497,3001,5951,4301,5031,5107,4721,2868,6304,4648,2349,6395,7806,7293,6065,2460,8176,8105,5075,6967,5818,3922,3407,5705,5651,3210,5791,3714,4315,3010,2455,4545,5337,2196,2240,8053,6164,8275,6630,1937,5932,3723,3643,4444,5905,1889,2978,4621,5387,8159,3541,2243,7069,7495,4934,8191,8425,4152,6186,3083,4361,1825,2504,8599,5273,4846,8458,7948,3486,3654,7544,8351,3787,2487,7014,3059,6331,2153,1831,5234,5900,8294,4482,1932,7597,8732,1947,4120,7027,7614,3115,3760,8455,8775,8090,5801,4953,5026,4069,4086,6224,6988,2756,5310,8614,4081,3173,5415,5434,6378,2440,1895,7074,3147,3454,6171,3476,8127,4535,8174,8796,1857,2788,5544,3563,8247,1779,3624,7052,6486,8361,8422,7687,5571,3306,1846,2076,2748,2963,3321,5209,5930,3190,7476,6982,6610,8378,4036,3422,5513,2995,5249,6869,6950,5872,3675,2423,2529,7444,8234,4550,6922,5722,1959,2585,6699,5278,7225,6792,5048,3888,4503,7910,5400,5241,7160,7985,5666,5327,8322,4919,3130,2677,2176,4708,4872,2904,8095,5138,2253,3871,2570,2941,6001,3289,6546,5525,8718,4269,7118,6492,6052,7287,3255,6312,2981,4122,8124,8697,7472,2695,6705,4943,7611,4000,3187,1916,8259,3234,6916,2938,6510,3811,2791,3240,3609,7233,5844,8814,3086,8139,7440,3081,3283,5627,8809,4605,5050,2806,5984,6898,1795,8581,3404,3868,7828,5503,4946,4485,5011,8227,5908,6794,8300,7951,6549,3170,7741,3532,8381,7795,4526,4537,7218,2193,1786,5033,2220,7191,6385,2326,5118,5363,2293,8188,3651,5859,7719,2738,4149,8665,1865,2935,6991,4822,7924,2753,3783,7800,6638,7671,7465,5539,7536,2457,4854,8497,4640,5735,7843,5784,2474,6372,8387,3355,7865,8376,4433,7415,6572,3815,2284,6340,5407,6604,2065,2510,6585,2346,3678,2079,6024,2721,3352,8452,5143,4228,7594,7514,5671,6613,4498,6920,8715,6179,7077,8799,5520,3038,7907,6443,7837,6461,3957,2774,6815,4828,8237,3419,6866,6197,4914,5827,8688,3270,2246,8171,8461,5491,7282,5880,6832,5054,4586,8269,2839,4213,7360,7206,3197,5346,1801,5093,5531,8502,7626,4176,6154,6184,8561,3182,2896,6737,5972,8794,5616,2871,4509,4477,1969,5267,3160,6789,2180,5657,4103,5894,4911,7566,8750,6319,3483,6044,7066,5987,5511,6004,8735,4401,4430,5584,7699,2610,3027,2314,2343,8156,5863,4264,6974,3932,4897,4452,8355,1862,4332,3192,3034,2923,2785,7778,6429,4296,3861,7250,6802,4726,6446,5007,2842,1952,7561,2911,3480,4832,5057,7479,5641,3110,5725,5299,2207,6029,6730,5742,6811,4232,7030,5442,3627,5372,6449,2550,2481,5218,6151,8084,4373,6783,2139,2369,7647,7324,8541,2633,7434,8441,4304,3178,7630,8291,5693,2156,6212,4965,2984,6785,4158,5619,7172,4084,7049,5812,5463,5528,2471,8804,4529,3975,7102,7122,4113,4581,7982,6875,5548,4207,5688,5959,4907,4690,2914,3031,1809,5424,4394,4441,4136,1873,5890,4013,3936,6540,7896,5886,7296,2665,7650,4886,7403,4260,2318,3395,4456,3981,7539,2234,6191,1990,5678,4566,4859,6843,7137,5807,3292,2899,8194,5133,2582,3571,6641,1798,6683,7058,7211,3214,3659,2518,4517,2386,8364,2882,6012,4045,3988,2567,4749,6362,7600,5452,8592,3376,7087,5822,8003,2715,6249,6120,3640,7475,2863,8772,5294,5927,8345,8143,8312,4937,2375,6885,2060,4272,6621,8466,8218,2143,4922,6367,5748,1941,6826,4287,1780,4971,7967,4377,7511,7724,2850,7586,7055,2888,7228,8744,6146,5431,3818,7693,6037,7105,8231,5276,3041,4875,7737,4437,8612,5767,6280,4398,8111,4092,5418,5467,3691,3273,3791,5555,4222,8216,6513,6298,2337,6508,7879,6125,5203,6352,1901,3544,6174,5152,4132,6653,8148,7351,6436,7583,2545,3359,4737,8757,6994,5638,7847,7009,5186,2468,3107,8331,7580,1955,2579,6086,8449,8552,6467,5841,2675,8464,6746,6650,5949,6188,2411,8729,1898,6679,1849,7348,4959,6633,2426,2992,7921,4624,4611,6775,5613,6369,4488,6526,2975,7797,1972,2711,5809,4143,8185,7303,2860,8108,2728,4225,4342,8087,4838,6358,6161,7498,3520,8151,6531,3007,7690,7488,4257,3398,4819,6301,6420,2760,3401,6758,6041,7412,6835,6938,2643,4678,8812,5771,7363,7099,4548,4278,4651,5981,2626,4424,3457,7061,6846,2352,4770,1966,6408,7904,4165,5536,6970,7306,2960,5777,5660,1834,1913,6390,7547,7589,5510,8533,3548,4559,5934,5421,7271,4185,4078,8392,3725,7007,6674,2490,8285,8153,2919,6882,4170,6543,4463,8098,2071,3929,7446,1807,8469,2907,1998,8075,8221,3864,6607,2135,4089,8197,7840,5228,2443,7034,5632,6322,2167,6753,2389,6818,6489,2290,7964,4683,3383,7996,7012,4126,7167,4042,4542,2811,4715,3104,3991,6770,5368,1854,8722,4338,6910,3501,1822,7384,4010,3516,8781,5243,4705,4881,5104,3252,6694,8617,2526,3780,4900,8240,8506,3324,7266,4321,5781,3267,8420,7399,3529,4404,5739,3645,7406,2779,8710,2447,2944,4182,7437,5304,2081,8253,7256,3694,4602,8272,4293,4759,6018,4387,4478,7157,2162,5568,6062,7887,2680,2183,2902,7520,4869,2623,8520,3552,6499,5287,2421,1908,2287,6326,8162,2587,6925,3264,4843,5522,2768,8368,2218,8341,5852,4039,7081,7542,6055,8070,3705,4472,7016,4687,2385,5606,7634,6997,3232,3997,6439,6822,5796,5954,7259,5232,6050,3100,3373,3464,8726,4523,2736,2008,1986,6671,3132,8574,4491,8309,8589,7955,8801,3164,4146,2751,6627,8400,7557,4427,4968,6644,1789,5036,2795,6398,2340,4318,3309,2636,3015,6411,7727,7184,8207,2334,4755,5404,2186,4281,5990,4210,4631,8510,8706,3506,5176,3673,6309,5110,3805,5440,2651,6537,7684,8675,8213,5668,4118,7617,4345,7299,8493,7214,5500,2127,2159,6136,3362,2731,3128,4129,6750,7987,6099,8328,3057,2803,6807,2847,4382,3605,1976,8093,5975,4506,7071,4066,5280,3489,7387,2507,7370,3392,7025,6348,5774,3538,3939,2539,8680,3076,3113,6778,2484,8570,5473,2372,2879,7553,7367,8023,4949,2866,8179,7893,7424,4174,6879,3753,3960,8685,7195,5073,4520,2321,1944,4627,1962,7181,5307,5494,6733,7812,5183,2998,8741,7284,7602,8006,6857,4752,6767,5445,7108,8055,6761,8130,3432,2615,8596,7274,4977,4056,6686,6404,4863,2170,6839,5732,3200,6668,1812,4940,5911,4298,2655,4002,1870,8348,2771])). 87.71/26.56 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 87.71/26.56 % [INFO] Killing All external provers ... 87.84/26.66 EOF